Dissertations / Theses on the topic 'Fluctuation theorem'
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1
Carberry, David Michael, and dave_carberry@yahoo com au. "Optical Tweezers: Experimental Demonstrations of the Fluctuation Theorem." The Australian National University. Research School of Chemistry, 2006. http://thesis.anu.edu.au./public/adt-ANU20060410.122727.
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In the late 19th and early 20th centuries famous scientists like Boltzmann, Loschmidt, Maxwell and Einstein tried, unsuccessfully, to find the link between the time-reversible equations of motion of individual molecules and irreversible thermodynamics. The solution to this puzzle was found in 1993, and the link is now known as the Fluctuation Theorem (FT). In the decade that followed theory and computer simulation tested the FT and, in 2002, an experiment indirectly demonstrated the FT.¶
This thesis describes original experiments that demonstrate the FT directly using Optical Tweezers. A related expression, known as the Kawasaki Identity, is also experimentally demonstrated. These experimental results provide a rigorous demonstration that irreversible dynamics can be obtained from a system with time-reversible dynamics.
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Carberry, David Michael. "Optical tweezers : experimental demonstrations of the fluctuation theorem /." View thesis entry in Australian Digital Theses Program, 2005. http://thesis.anu.edu.au/public/adt-ANU20060410.122727/index.html.
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Bulnes, Cuetara Gregory. "Fluctuation theorem for quantum electron transport in mesoscopic circuits." Doctoral thesis, Universite Libre de Bruxelles, 2013. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209435.
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Dans cette thèse nous étudions les propriétés statistique des courants dans des systèmes à l'échelle mésoscopique. Nous utilisons le formalisme de la statistique de comptage afin de caractériser les fluctuations de courant importantes à cette échelle. Celle-ci est obtenue en partant du Hamiltonien microscopique décrivant la dynamique des électrons sur le circuit considéré dans le régime quantique.Nous considérons deux modèles particuliers de circuits à deux canaux, chacun comportant deux électrodes. Le premier modèle étudié est constitué de deux plots quantiques en couplage capacitif, et chacun échangeant des électrons avec deux électrodes. Le deuxième modèle est quant à lui constitué d'un double plot quantique connecté à deux électrodes et modulant le courant dans un point quantique formé lui-même par la jonction de deux électrodes. Pour ces deux modèles, chaque canal est soumis à une différence de potentiel, ou force thermodynamique, générant des courants stationnaires fluctuants.
La statistique des courants pour ces deux modèles est obtenue en utilisant une équation maîtresse pour les probabilités d'occupation dans les plots quantiques et le nombre d'électrons transférés entre ceux-ci et les électrodes. Nous vérifions que la distribution de probabilité jointes des courants dans chaque canal ainsi obtenue vérifie un théorème de fluctuation dans la limite des temps long faisant intervenir les forces thermodynamique des deux canaux.
La question de l'émergence d'un théorème de fluctuation effectif pour la distribution de probabilité marginale du courant dans un des deux canaux est également investiguée. Nous montrons que dans la limite ou le rapport des courants est grande, un tel théorème de fluctuation effectif est satisfait individuellement pour le canal de plus faible courant comme observé expérimentalement. Ce théorème fait intervenir une affinité effective dépendante des forces thermodynamiques des deux canaux et des spécificités du modèle considéré. Son étude détaillée est faite pour les deux modèles mentionnés.
Par ailleurs, nous posons également la question de l'existence d'un théorème de fluctuation pour des temps de mesure finis. Nous montrons qu'en présence d'un théorème de fluctuation dans la limite de temps longs, un critère peut être énoncé sur la condition initiale des plots quantiques menant à un théorème de fluctuations à temps fini. Ce critère est également étendu au cas des théorèmes de fluctuations effectifs.
Finalement, nous faisons une étude thermodynamique du modèle composé d'un double plot quantique en présence de différences de potentiel électrique et de température entre les électrodes du circuit.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
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Siemer, Bernd, Viktor Holubec, Petr Chvosta, and Philipp Maass. "Fluctuation dissipation theorem and Onsager coefficients in driven diffusion systems." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-198659.
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Siemer, Bernd, Viktor Holubec, Petr Chvosta, and Philipp Maass. "Fluctuation dissipation theorem and Onsager coefficients in driven diffusion systems." Diffusion fundamentals 24 (2015) 47, S. 1, 2015. https://ul.qucosa.de/id/qucosa%3A14567.
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Gundermann, Julia. "The Crooks Fluctuation Theorem Derived for Two-Dimensional Fluid Flow and its Potential to Improve Predictions." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-156748.
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The weather dynamics are significantly determined by the motion of the atmosphere and the ocean. This motion is often turbulent, characterized by fluctuations of the flow velocity over wide spatial and temporal scales. This fact, besides limited observability and inaccurate models, impedes the predictability of quantities such as the velocity of winds, which are relevant for the everyday life. One is always interested in improving such predictions - by employing better models or obtaining more information about the system.
The Crooks fluctuation theorem is a relation from nonequilibrium thermodynamics, which has its typical applications in nanoscale systems. It quantifies the distribution of imposed work in a process, where the system is pushed out of thermal equilibrium. This distribution is broadened due to the fluctuations of the microscopic degrees of freedom in the system.
The fluctuations of the velocity field in turbulent flow suggest the derivation of an analogy of Crooks' theorem for this macroscopic system. The knowledge about the validity of such a relation is additional information, which one in reverse could use to improve predictions about the system. In this thesis both issues are addressed: the derivation of the theorem, and the improvement of predictions.
We illustrate the application of Crooks' theorem to hydrodynamic flow within a model of a two-dimensional inviscid and incompressible fluid field, when pushed out of dynamical equilibrium. The flow on a rectangular domain is approximated by the two-dimensional vorticity equation with spectral truncation. In this setting, the equilibrium statistics of the flow can be described through a canonical ensemble with two conserved quantities, kinetic energy and enstrophy. To perturb the system out of equilibrium, we change the shape of the domain according to a protocol, which changes the kinetic energy but leaves the enstrophy constant. This is interpreted as doing work to the system. Evolving along a forward and its corresponding backward process, we find that the distributions of the work performed in these processes satisfy the Crooks relation with parameters derived from the canonical ensembles.
We address the issue of prediction in this thesis in a concrete setting: There are examples where the distributions of a variable in the forward and the backward process collapse into one, hence Crooks' theorem relates the distribution of one variable with itself. For a finite data set drawn from such a distribution, we are interested in an estimate of this variable to exceed a certain threshold. We demonstrate that, using the knowledge about Crooks' relation, forecast schemes can be proposed which improve compared to a pure frequency estimate on the data set. The findings are illustrated in three examples, studies of parameters such as exceedance threshold and data set size are presented.
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Gundermann, Julia. "The Crooks Fluctuation Theorem Derived for Two-Dimensional Fluid Flow and its Potential to Improve Predictions." Doctoral thesis, Technische Universität Dresden, 2014. https://tud.qucosa.de/id/qucosa%3A28433.
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The weather dynamics are significantly determined by the motion of the atmosphere and the ocean. This motion is often turbulent, characterized by fluctuations of the flow velocity over wide spatial and temporal scales. This fact, besides limited observability and inaccurate models, impedes the predictability of quantities such as the velocity of winds, which are relevant for the everyday life. One is always interested in improving such predictions - by employing better models or obtaining more information about the system.
The Crooks fluctuation theorem is a relation from nonequilibrium thermodynamics, which has its typical applications in nanoscale systems. It quantifies the distribution of imposed work in a process, where the system is pushed out of thermal equilibrium. This distribution is broadened due to the fluctuations of the microscopic degrees of freedom in the system.
The fluctuations of the velocity field in turbulent flow suggest the derivation of an analogy of Crooks' theorem for this macroscopic system. The knowledge about the validity of such a relation is additional information, which one in reverse could use to improve predictions about the system. In this thesis both issues are addressed: the derivation of the theorem, and the improvement of predictions.
We illustrate the application of Crooks' theorem to hydrodynamic flow within a model of a two-dimensional inviscid and incompressible fluid field, when pushed out of dynamical equilibrium. The flow on a rectangular domain is approximated by the two-dimensional vorticity equation with spectral truncation. In this setting, the equilibrium statistics of the flow can be described through a canonical ensemble with two conserved quantities, kinetic energy and enstrophy. To perturb the system out of equilibrium, we change the shape of the domain according to a protocol, which changes the kinetic energy but leaves the enstrophy constant. This is interpreted as doing work to the system. Evolving along a forward and its corresponding backward process, we find that the distributions of the work performed in these processes satisfy the Crooks relation with parameters derived from the canonical ensembles.
We address the issue of prediction in this thesis in a concrete setting: There are examples where the distributions of a variable in the forward and the backward process collapse into one, hence Crooks' theorem relates the distribution of one variable with itself. For a finite data set drawn from such a distribution, we are interested in an estimate of this variable to exceed a certain threshold. We demonstrate that, using the knowledge about Crooks' relation, forecast schemes can be proposed which improve compared to a pure frequency estimate on the data set. The findings are illustrated in three examples, studies of parameters such as exceedance threshold and data set size are presented.
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Wong, Chun-Shang. "Statistical physics principles tested using dusty plasma and aerosol experiments." Diss., University of Iowa, 2018. https://ir.uiowa.edu/etd/6523.
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Statistical physics has been the foundation for much of our understanding about plasma physics. Often, plasma physics phenomena are explained using statistical physics principles and theories. Here, I reverse this paradigm to instead use plasma experiments to test statistical physics principles.
In this thesis, I test statistical physics principles with an experimental dusty plasma, which is a four-component mixture of micron-sized ``dust'' particles, electrons, ions, and neutral gas molecules. When immersed in the plasma, the dust particles acquire large negative charges, since they accumulate more electrons than ions. Due to their large electric charges, the dust particles have interparticle potential energies that greatly exceed their kinetic energies, so that the collection of dust particles is considered to be a strongly coupled plasma. Like other strongly coupled plasma, the collection of dust particles can exhibit solid-like or liquid-like behavior.
A key advantage offered by dusty plasma experiments is the ability to track the motion of individual dust particles. Dust particles are sufficiently large to allow for direct imaging using a video camera, so that time series data can be obtained for particle positions and velocities. These particle-level data provide a richer description of the dynamics and structure than can be obtained for most other strongly coupled plasmas, simple liquids, or solid materials. In particular, the particle-level data of positions and velocities are often required inputs for testing statistical physics theories or principles.
The dusty plasma data I analyze are from the experiment of Haralson~\textit{et al.} [1,2], where dust particles were electrically levitated in a single horizontal layer within a vacuum chamber. The collection of dust particles initially settled into a crystalline lattice with solid-like behavior. To reach a liquid-like state, or to drive a shear flow, dust particles were manipulated using the radiation pressure force of lasers.
In this thesis, I test three different statistical physics principles using an experimental dusty plasma.
First, I test the fluctuation theorem, which was first was presented in 1993 by Evans, Cohen, and Morriss [3]. The fluctuation theorem, which is one of the most important recent developments in statistical physics, quantifies the probability that the entropy production rate will temporarily fluctuate to negative values in ``violations'' of the second law of thermodynamics. The original formulation of the fluctuation theorem described the entropy production due to viscous heating in a shear flow; this version of the fluctuation theorem had never been experimentally demonstrated in a liquid of any kind. In Chapter 2, I provide the first such demonstration by showing that the entropy production rate in a liquid-like dusty plasma shear flow satisfies the fluctuation theorem. This result also serves as the first demonstration that a strongly coupled plasma obeys the fluctuation theorem.
Second, I measure the Einstein frequency $\Omega_E$, which describes the stochastic process of collisions in a strongly coupled plasma, and I compare my measurement to predictions made in the literature that used simulation data. Often, for weakly coupled plasma, a collision frequency is obtained to provide a measure of the strength of particle-particle interactions. However, for strongly coupled plasma (and likewise for liquids and solids), a collision frequency is not well defined since collisions are multibody and occur continuously. Another quantity is needed to describe the strength of particle-particle interactions. I propose that the Einstein frequency $\Omega_E$, a concept more commonly used in solid physics, is better suited for describing particle-particle interactions in a strongly coupled plasma. In Chapter 3, I present and use a new method to obtain the Einstein frequency of a 2D dusty plasma in both a liquid-like state and a crystalline state. My measurement of the Einstein frequency, which serves as a proxy for a collision frequency, is consistent with simulation predictions in the literature.
Third, I present particle-coordination survival functions, which provide a richer description of microscopic dynamics in a liquid than the commonly used relaxation time. Relaxation times have been used, for example the Maxwell relaxation time, to describe the characteristic time scale for the crossover between elastic and viscous behavior in viscoelastic liquids. However, relaxation times are single-value measures that cannot fully describe the complexity of a liquid. In Chapter 4, using a survival function that retains temporal information about the local structural in a liquid, I discover that the microscopic arrangements in a liquid-like 2D dusty plasma have multiple time scales. Unexpectedly, non-defects have two time scales, while defects have one. My survival functions are time-series graphs of the probability that a particle's number of nearest neighbors, i.e., its coordination, remains the same. The two time scales for non-defects are revealed by an elbow in their survival-function curve.
As a spinoff with a considerable amount of importance, I performed the simplest fluctuation theorem experiment to date, using an aerosol. An aerosol is simply a particle that is immersed in air. In Chapter 5, I show that the fluctuation theorem is applicable for an aerosol particle undergoing free-fall in air due to gravity. While the particle typically fell downwards, it is observed to occasionally fall upwards, against the force of gravity. For such upward displacements, the work done on the particle is negative, which is a temporary violation of the second law. I find that the probability of these temporarily violations obeys the work fluctuation theorem. This result also allowed an application: a novel diagnostic method to measure the mass of aerosol particles.
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Graf, Daniel [Verfasser], and Christian [Akademischer Betreuer] Ochsenfeld. "Development of efficient electronic-structure methods based on the adiabatic-connection fluctuation-dissipation theorem and Møller–Plesset perturbation theory / Daniel Graf ; Betreuer: Christian Ochsenfeld." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2021. http://d-nb.info/123217629X/34.
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Watanabe, Kota. "Non-adiabatic effects in quantum geometric pumping." Kyoto University, 2017. http://hdl.handle.net/2433/225998.
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Clark, Matthew Taylor. "The driven and stochastic dynamics of micro and nanoscale cantilevers in viscous fluid and near a solid boundary." Diss., Virginia Tech, 2008. http://hdl.handle.net/10919/29411.
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Micro and nanoscale systems are rapidly evolving to improve the resolution of experimental measurements. Experiments involving such small scale devices are difficult and expensive, and the available analytical theory to describe their dynamics is idealized. The dynamics of microscopic cantilevers in fluid are complicated and include significant contributions from many sources in an actual experiment. Some examples are: complex cantilever geometries, near-wall effects, thermal and external actuation techniques, and a variety of measurement techniques. Numerical simulations are a powerful approach to describe the dynamics of micro and nanoscale systems for the precise conditions of experiment. This thesis provides a numerical approach capable of addressing these inherent challenges and quantifies the dynamics of microscopic cantilevers in fluid for experimentally relevant conditions.
A thermodynamic approach based upon the fluctuation-dissipation theorem allows for the calculation of stochastic dynamics from deterministic dynamics. Using numerical simulations, the thermal motion can be described for the precise conditions of experiment. It is found that the measured dynamics of cantilevers differs depending on the quantity being measured. In particular, the dynamics of displacement and angle of the cantilever tip distribute energy differently to the higher flexural modes. The externally driven dynamics of microscale cantilevers in fluid are also considered. The driven dynamics are calculated using numerical simulations of the cantilever response to a force impulse. It is found that the driven dynamics depend upon the type of actuation in addition to the quantity measured. A comparison of the driven dynamics to the corresponding stochastic dynamics yields insight into the nature of the Brownian force acting on the cantilever.
Another experimentally relevant condition is the use of cantilevers with V-shaped planforms in fluid. The resulting flow field is three-dimensional and complex in contrast to what is found for a long and slender rectangular cantilever. Despite the flow complexity, the stochastic and driven dynamics of the fundamental mode can be predicted using a two-dimensional model with an appropriately chosen length scale. An experimentally motivated magnetomotive actuation technique is investigated. Results show that this approach generates power spectra nearly equivalent to the noise spectra. Furthermore, the case of a V-shaped cantilever in fluid and oscillating in proximity of a solid boundary is investigated. In the presence of a solid surface the fluid damping and added mass of fluid on the cantilever are larger than for a cantilever far from boundaries. This results in a lower frequency and quality factor for the fundamental resonance. This can impede experimental efforts because broad peaks lack distinct features that can be used to identify experimental signals.
An option to overcome the large viscous damping is to take advantage of higher modes of cantilever oscillation. The higher frequency oscillations of the higher modes generate a smaller viscous boundary layer and have a reduced added mass. As a result, the quality factor increases with increasing mode number. The frequency dependence of the fluid dynamics around a fluctuating microscale cantilever is also studied. The mass of fluid entrained by the cantilever and the viscous damping quantify the interaction of a cantilever with the surrounding fluid and are computed. Analytical expressions for these parameters are derived for moderate mode number. The techniques and findings of this thesis have broad applicability to a wide range of micro and nanotechnologies that rely upon understanding the dynamics of small scale structures in fluid.Ph. D.
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Brossault, Marc-Antoine. "Suivi temporel de la dynamique des structures : apports du théorème fluctuation-dissipation et de la dynamique lente pour l'évaluation de l'intégrité des structures de génie civil." Thesis, Université Grenoble Alpes (ComUE), 2017. http://www.theses.fr/2017GREAU031/document.
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Soumise à une sollicitation sismique importante, une structure de génie civil peut être endommagée. Cela se traduit par l'apparition de fissures et donc une réduction de ses propriétés élastiques de la structure. Cependant, dans le cas d'un événement sismique d'amplitude inférieure, la variation observée est seulement transitoire. Elle consiste en une perturbation brutale de la fréquence et de l'amortissement suivie d'un recouvrement lent vers leurs valeurs initiales. Ce phénomène non linéaire de relaxation est appelé Dynamique Lente. Il s'explique par la fermeture progressive des fissures initialement présentes dans la structure et qui ont été ouvertes par la sollicitation. Nous avons observé en laboratoire que l'analyse de la Dynamique Lente dans une poutre avant et après son endommagement permet de détecter cette augmentation de la densité de fissures. La sensibilité différentielle des modes à une dégradation locale indique, de plus, une piste pour le développement d'une méthode de localisation de l'endommagement. L'étude de la Dynamique Lente que nous avons menée dans deux structures de génie civil a montré que nous pouvions également y détecter l'apparition de l'endommagement. Le suivi de l'amortissement de manière continue a mis en évidence une relation linéaire entre l'amortissement et l'intensité des vibrations ambiantes à la fois dans les poutres et les structures de génie civil. Nous expliquons celle-ci via l'application du théorème Fluctuation-Dissipation à ces systèmes. Les résultats en laboratoire et la proximité de l'expression de la relation avec les équations utilisées dans le cas de la Dynamique Lente suggère une dépendance de ce phénomène vis à vis de la densité des hétérogénéités dans le matériau composant la structure. De plus amples recherches sont cependant nécessaires afin d'expliquer complètement nos observations et ainsi pouvoir les utiliser dans le cadre de la surveillance des structures uniquement à partir de données de très faible amplitudeDuring strong seismic loadings, a structure may be damaged. This results in the appearing of cracks and then a reduction of the elastic properties of the structure. The degradation remains only transitory in the case of smaller seismic events. It consists in a sharp disruption of both the frequency and damping followed by their slow recovery to their initial values. This non linear phenomenon is called Slow Dynamics. It is explained by the gradual closing of the cracks which were initially present in the material and which were opened during the loading. We observed in the laboratory that the analysis of the Slow Dynamics in a beam before and after it is damaged allows to detect the increase of the crack density. The different sensitivties of the modes regarding a local damaging indicates a track to develop a method to locate the damages. The study of the Slow Dynamics in civil engineering structures demonstrated the possibility to detect the damaging also in this kind of system. The continuous monitoring of the damping highlighted a linear relationship between damping and the intensity of the ambiante vibration in the case of both the beams and real case structures. We explain this relation by applying the Fluctuation-Dissipation to these systems. Laboratory results and the proximity of the expression of the linear relationship wit hthe equations used in the theory of the Slow Dynamics suggest a dependency of this phenonmenon on the density of heterogeneities in the structure. Further research is however required in order to fully explain our observations and thus, to use them to monitor the state of health of structures
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Gomez-Solano, Juan Rubén. "Nonequilibrium fluctuations of a Brownian particle." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2011. http://tel.archives-ouvertes.fr/tel-00680302.
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This thesis describes an experimental study on fluctuations of a Brownian particle immersed in a fluid, confined by optical tweezers and subject to two different kinds of non-equilibrium conditions. We aim to gain a rather general understanding of the relation between spontaneous fluctuations, linear response and total entropy production for processes away from thermal equilibrium. The first part addresses the motion of a colloidal particle driven into a periodic non-equilibrium steady state by a nonconservative force and its response to an external perturbation. The dynamics of the system is analyzed in the context of several generalized fluctuation-dissipation relations derived from different theoretical approaches. We show that, when taking into account the role of currents due to the broken detailed balance, the theoretical relations are verified by the experimental data. The second part deals with fluctuations and response of a Brownian particle in two different aging baths relaxing towards thermal equilibrium: a Laponite colloidal glass and an aqueous gelatin solution. The experimental results show that heat fluxes from the particle to the bath during the relaxation process play the same role of steady state currents as a non-equilibrium correction of the fluctuation-dissipation theorem. Then, the present thesis provides evidence that the total entropy production constitutes a unifying concept which links the statistical properties of fluctuations and the linear response function for non-equilibrium systems either in stationary or non stationary states.
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Pedurand, Richard. "Instrumentation for Thermal Noise Spectroscopy." Thesis, Lyon, 2019. http://www.theses.fr/2019LYSE1356.
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La résolution des interféromètres gravitationnels est limitée par le mouvement Brownien - ou bruit thermique - de leurs miroirs dans la partie centrale de leur bande de détection, entre 10Hz et 1kHz. La répartition en fréquence de ce bruit thermique est dictée par les mécanismes de dissipation d'énergie mécanique à l'origine de cette vibration aléatoire, en accord avec le théorème fluctuation-dissipation. Cette dissipation provient principalement des revêtements optiques déposés sur les miroirs pour leur donner leur réflectivité. Dans le but de réduire le bruit thermique, une nouvelle génération de détecteurs d'ondes gravitationnelles employant des miroirs refroidis à température cryogénique a été proposée. Le développement de nouveaux matériaux optiques en couche mince à faible dissipation mécanique, opérant à la fois à température ambiante et température cryogénique, demande donc de nouveaux outils expérimentaux. L'objet principal de cette thèse est la construction d'un nouvel instrument, le CryoQPDI, qui consiste en l'association d'un interféromètre haute résolution et d'un cryostat basé sur un refroidisseur pulse tube. Il est capable de mesurer directement le mouvement Brownien d'un microlevier entre 300 K et 7 K. En combinant des mesures effectuées sur un microlevier avant et après le dépôt d'une couche mince, il est possible de caractériser la dissipation mécanique interne de cette couche mince. Cet instrument participera ainsi à l'optimisation des revêtements optiques des futurs interféromètres gravitationnels, dans le but de minimiser les nuisances dues au bruit thermiqueThe resolution limit of gravitational wave interferometers is set by their mirrors' Brownian motion – or thermal noise - in the central part of their detection band, from 10Hz to 1kHz. This thermal noise frequency distribution is given by the mechanical energy dissipation mechanisms it originates from, in agreement with the fluctuation-dissipation theorem. This dissipation mainly derives from the optical coatings deposited on the mirrors to give them their reflectivity. To reduce this thermal noise, a new generation of gravitational wave detectors employing mirrors cooled to cryogenic temperature has been suggested. The development of new optical thin-film materials with low mechanical dissipation, operating at both room and cryogenic temperatures, therefore requires new experimental tools. The main object of this thesis is the construction of a new instrument, the CryoQPDI, which is an association between a high-resolution interferometer and a cryostat based on a pulse tube cooler. It can directly measure the Brownian motion of a microcantilever between 300 K and 7 K. By combining measurements made on a microcantilever before and after the deposition of a thin film, it is possible to characterize the internal mechanical dissipation of this thin film. This instrument will eventually contribute to the optimisation of optical coatings of future gravitational wave detectors, aiming at minimizing the limitations due to thermal noise
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LEGGIO, Bruno. "Quantum fluctuations and correlations in equilibrium and nonequilibrium thermodynamics." Doctoral thesis, Università degli Studi di Palermo, 2014. http://hdl.handle.net/10447/90914.
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Itami, Masato. "Non-equilibrium Statistical Theory for Singular Fluid Stresses." 京都大学 (Kyoto University), 2016. http://hdl.handle.net/2433/215285.
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Robbins, Brian Alan. "The Correlated Dynamics of Micron-Scale Cantilevers in a Viscous Fluid." Diss., Virginia Tech, 2014. http://hdl.handle.net/10919/51090.
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A number of microcantilever systems of fundamental importance are explored using theoretical and numerical methods to quantify and provide physical insights into the dynamics of experimentally accessible systems that include a variety of configurations and viscous fluids. It is first shown that the correlated dynamics of both a laterally and vertically offset cantilever pair can be accurately predicted by numerical simulations. This is verified by comparing the correlated dynamics yielded by numerical simulations with experimental measurement. It is also demonstrated that in order to obtain these accurate predictions, geometric details of the cantilever must be included in the numerical simulation to directly reflect the experimental cantilever. A microrheology technique that utilizes the fluctuation-dissipation theorem is proposed. It is shown that by including the frequency dependence of the fluid damping, improvements in accuracy of the predictions of the rheological properties of the surrounding fluid are observed over current techniques. The amplitude spectrum of a 2-D cantilever in a power-law fluid is studied. The resulting amplitude spectrum yielded a curve similar to an overdamped system. It is observed that the amplitude and noise spectrum yield the same qualitative response for a 2-D cantilever in a shear thinning, power-law fluid. The correlated dynamics of a tethered vertically offset cantilever pair is investigated. It is shown that for a range of stiffness ratios, which is the ratio of the spring constant of the tethering relative to the cantilever spring constant, the change in the correlated dynamics of a Hookean spring tethered cantilever pair can be seen in the presence of fluid coupling. The dynamics of a spring-mass tethered, vertically offset cantilever pair is qualitatively studied by simplifying the model to an array of springs and masses. The resulting study found that the correlated dynamics of the displacement of mass of the tethered object yielded newly observed features and characteristics. It is shown that the curve shape of the cross-correlation of the displacement of the mass of the tethered object is similar to that of the auto-correlation of the displacement of the mass representing a step forced cantilever. The cross-correlation of the displacement of the mass of the tethered object, however, is found to be significantly more dependent on the stiffness ratio than the auto-correlation of the displacement of the mass representing a cantilever for t > 0. At t = 0, it is observed that the mass of the tethered object yields the same finite value for the cross-correlation for all studied values of the stiffness ratio. This characteristic is a result of the symmetry of the studied spring-mass system.Ph. D.
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Gundermann, Julia [Verfasser], Holger [Akademischer Betreuer] Kantz, and Günter [Akademischer Betreuer] Radons. "The Crooks Fluctuation Theorem Derived for Two-Dimensional Fluid Flow and its Potential to Improve Predictions / Julia Gundermann. Gutachter: Holger Kantz ; Günter Radons. Betreuer: Holger Kantz." Dresden : Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2015. http://d-nb.info/1069091766/34.
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Beuerle, Matthias [Verfasser], and Christian [Akademischer Betreuer] Ochsenfeld. "Development of low-scaling methods to calculate ground state energies and analytical gradients based on the adiabatic-connection fluctuation-dissipation theorem / Matthias Beuerle ; Betreuer: Christian Ochsenfeld." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2019. http://d-nb.info/1190563657/34.
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Gundermann, Julia [Verfasser], Holger Akademischer Betreuer] Kantz, and Günter [Akademischer Betreuer] [Radons. "The Crooks Fluctuation Theorem Derived for Two-Dimensional Fluid Flow and its Potential to Improve Predictions / Julia Gundermann. Gutachter: Holger Kantz ; Günter Radons. Betreuer: Holger Kantz." Dresden : Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-156748.
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Caussarieu, Aude. "Propriétés dynamiques de la transition de Fréedericksz et vieillissement au point critique." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2012. http://tel.archives-ouvertes.fr/tel-00790177.
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Le vieillissement physique est un sujet très actif en physique statistique car il ouvre la perspective d'une généralisation de la physique statistique à l'équilibre à des cas faiblement hors équilibre. Dans ce contexte où d'importants travaux ont été réalisés sur les polymères et les verres de spin, des travaux théoriques ont montré l'intérêt que pouvait apporter l'étude de système subissant une transition de phase du second ordre, les ingrédients théoriques étant plus simples. Nous avons donc étudié dans le détail la transition de Fréedericksz dans un cristal liquide qui est décrite par une transition du second ordre afin d'utiliser ensuite ce système pour faire une étude expérimentale du vieillissement au point critique. Nous avons alors montré que les équations usuellement utilisées (développement de l'énergie libre à la Landau) pour décrire la dynamique de cette transition ont un domaine de validité extrêmement mince qui n'est pas accessible expérimentalement. Il faut donc tenir compte des termes non linéaires de l'énergie libre pour décrire la dynamique du système, même dans le cadre de la réponse linéaire. Nous avons montré dans ce cadre le très bon accord entre la simulation numérique sans paramètre ajustable et les résultats expérimentaux. Nous avons ensuite étudié le comportement des fluctuations au voisinage du seuil de la transition et montré que lorsque la normalisation tenait bien compte du fait que la mesure est celle d'une variable quadratique, alors les fluctuations étaient d'amplitude maximale au seuil de la transition de Fréedericksz, comme on l'attend d'une transition du second ordre. L'étude de ces fluctuations permet alors de mesurer précisément la valeur du champ critique, ce qui est une mesure totalement nouvelle. Nous avons ensuite réalisé une étude de la dynamique des fluctuations du système lors de la réponse à une marche du paramètre de contrôle de la transition de Fréedericksz, et en particulier lors de trempes au point critique. Nous avons alors retrouvé les résultats prédits sur les systèmes de verres de spin, et nous montrons le lien entre la violation du théorème de fluctuation dissipation et l'évolution de la variance. Enfin nous avons monté un dispositif permettant de faire l'étude spatio-temporelle du système, nous avons montré que les 2 dispositifs mis en œuvre étaient limités par leur sensibilité dépendant de la valeur moyenne du paramètre d'ordre et nous proposons donc un autre système de mesure que nous n'avons pas eu le temps d'implémenter.
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Boedecker, Geesche. "Resonance Fluorescence in a Photonic Crystal." Phd thesis, Universität Potsdam, 2013. http://opus.kobv.de/ubp/volltexte/2014/6959/.
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The problem under consideration in the thesis is a two level atom in a photonic crystal and a pumping laser. The photonic crystal provides an environment for the atom, that modifies the decay of the exited state, especially if the atom frequency is close to the band gap. The population inversion is investigated als well as the emission spectrum.
The dynamics is analysed in the context of open quantum systems. Due to the multiple reflections in the photonic crystal, the system has a finite memory that inhibits the Markovian approximation. In the Heisenberg picture the equations of motion for the system variables form a infinite hierarchy of integro-differential equations. To get a closed system, approximations like a weak coupling approximation are needed.
The thesis starts with a simple photonic crystal that is amenable to analytic calculations: a one-dimensional photonic crystal, that consists of alternating layers. The Bloch modes inside and the vacuum modes outside a finite crystal are linked with a transformation matrix that is interpreted as a transfer matrix. Formulas for the band structure, the reflection from a semi-infinite crystal, and the local density of states in absorbing crystals are found; defect modes and negative refraction are discussed.
The quantum optics section of the work starts with the discussion of three problems, that are related to the full resonance fluorescence problem: a pure dephasing model, the driven atom and resonance fluorescence in free space.
In the lowest order of the system-environment coupling, the one-time expectation values for the full problem are calculated analytically and the stationary states are discussed for certain cases.
For the calculation of the two time correlation functions and spectra, the additional problem of correlations between the two times appears. In the Markovian case, the quantum regression theorem is valid. In the general case, the fluctuation dissipation theorem can be used instead. The two-time correlation functions are calculated by the two different methods. Within the chosen approximations, both methods deliver the same result. Several plots show the dependence of the spectrum on the parameters. Some examples for squeezing spectra are shown with different approximations.
A projection operator method is used to establish two kinds of Markovian expansion with and without time convolution. The lowest order is identical with the lowest order of system environment coupling, but higher orders give different results.Die Arbeit befasst sich mit der Emission eines 2-Niveau-Atoms in einem photonischen Kristall mit einem treibenden Laser. Der photonische Kristall stellt für das Atom eine Umgebung dar, die seinen Zerfall verändert, insbesondere wenn die Übergangsfrequenz des Atoms nahe an der Bandkante ist. Es werden sowohl die Besetzungen als auch das Emissionsspektrum untersucht. Die Dynamik wird im Kontext offener Quantensysteme analysiert. Durch die vielfachen Reflexionen im photonischen Kristall hat das System ein endliches Gedächtnis, das die Markov-Näherung verhindert. Im Heisenberg-Bild stellen die Bewegungsgleichungen für die Systemvariablen eineunendliche Hierachie von Integro-Differentialgleichungen dar. Um ein geschlossenes System zu erhalten, sind Näherungen wie eine schwache Kopplung nötig. Zunächst wird ein einfacher photonischer Kristall betrachtet.: Der eindimensionale photonische Kristall, der aus wechselnden Lagen besteht. Die Blochmoden innerhalb und die Vakuummoden außerhalb des endlichen photonischen Kristalls sind durch eine Transformationsmatrix, die als Transfermatrix interpretiert werden kann, miteinander verbunden. Einfache Formeln für die Bandstruktur, Reflexion eines halb-unendlichen Kristalls, die lokale Zustandsdichte im absorbierenden Kristall werden gefunden; außerdem werden Defektmoden und negative Brechung diskutiert. Im quantenoptischen Teil der Arbeit werden zu Anfang drei Probleme diskutiert, die im Zusammenhang zum Problem der Resonanzfluoreszenz stehen und die analytisch berechnet werden können: Ein Dephasierungsmodell, das getriebenen Atom und Resonanzfluoreszenz im freien Raum. In der niedrigsten Ordnung der System-Bad-Kopplung werden die Erwartungswerte analytisch berechnet und die stationären Zustände werden für bestimmte Fälle diskutiert. Bei der Berechnung der Zweizeitkorrelationsfunktion und der Spektren taucht das zusätzliche Problem der Korrelationen zwischen den beiden Zeiten auf. Im Markov-Fall gilt das Quantenregressionstheorem. Im allgemeinen Fall kann stattdessen das Fluktuations-Dissipations-Theorem benutzt werden. Die Korrelationsfunktionen werden mit zwei verschiedenen Methoden berechnet. Innerhalb der gewählten Näherungen liefern beide Methoden dasselbe Resultat. Einige Plots zeigen die Abhängigkeit des Spektrums von den verschiedenen Parametern. Mehrere Beispiele für Squeezing-Spektren werden mit den verschiedenen Näherungen gezeigt. Eine Projektions-Operator-Methode wird benutzt, um zwei Arten einer Markov-Entwicklung zu implementieren, mit und ohne Faltungsintegral. Die niedrigste Ordnung ist identisch mit der niedrigsten Ordnung der System-Bad-Kopplung, wohingegen höhere Ordnungen andere Resultate ergeben.
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Bérut, Antoine. "Fluctuations and Interactions of Brownian particles in multiple Optical Traps." Thesis, Lyon, École normale supérieure, 2015. http://www.theses.fr/2015ENSL1003/document.
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Nous avons étudié expérimentalement les fluctuations de micro-particules browniennes piégées à l'aide de pinces optiques dans un réseau de puits de potentiels voisins. Nous donnons un descriptif général du montage expérimental, puis détaillons quatre utilisations différentes du système. Nous avons d'abord utilisé une unique particule dans un double puits de potentiel pour modéliser un système mémoire à deux niveaux, avec lequel nous avons vérifié le principe de Landauer sur le coût minimal en énergie pour l'effacement d'un bit d'information. Nous avons également appliqué une version détaillée d'un théorème de fluctuation à la procédure d'effacement de l'information pour retrouver la limite énergétique attendue. Nous avons ensuite étudié l'interaction hydrodynamique entre deux particules dont l'une est soumise à une température effective. Nous avons montré qu'il n'y a pas de fluctuations anormales lors de la transition sol-gel de la gélatine, contrairement à ce qui avait été observé précédemment, et que ce système ne pouvait donc pas être utilisé pour étudier des températures effectives. En revanche, nous avons montré que l'ajout d'un forçage aléatoire bien choisi sur la position d'un piège créait une température effective. Nous avons montré que le forçage d'une des particules résultait en une corrélation instantanée entre les mouvements des deux particules, et s'accompagnait d'un échange de chaleur de la particule virtuellement chaude à la particule froide en équilibre avec le bain thermique. Nous avons obtenu un bon accord entre les données expérimentales et les prédictions d'un modèle de couplage hydrodynamique. Enfin, nous décrivons l'utilisation de canaux micro-fluidiques pour réaliser un écoulement cisaillé à l'échelle micrométrique, et nous discutons de la possibilité d'interpréter un cisaillement en terme de température effective en testant une relation de fluctuation-dissipationWe experimentally study the fluctuations of Brownian micro-particles trapped with optical tweezers arranged in various spatial configurations. We give a general description of the set-up and detail four different experiments we conducted. We first use a single particle in a double-well potential to model a two-state memory system. We verify the Landauer principle on the minimal energetic cost to erase one bit of information, and we use a detailed version of a fluctuation theorem to retrieve the expected energetic bound. We then use two particles in two different traps to study the hydrodynamic interactions between two systems kept at different effective temperatures. Contrary to what was previously observed, we show that the sol-gel transition of gelatine does not provide any anomalous fluctuations for the trapped particle when the sample is quenched below gelification temperature. However, we show that an effective temperature is created when a well chosen random noise is added on one trap position. We demonstrate that the random forcing on one particle induces an instantaneous correlation between the two particles motions, and an energy exchange from the virtually hot particle to the cold one, which is in equilibrium with the thermal bath. We show a good agreement between the experimental data and the predictions from an hydrodynamic coupling model. Finally, we describe the use of micro-fluidic channels to create a shear flow at the micron size, and we discuss the possibility to interpret the force due to the shear-flow in terms of an effective temperature by testing a fluctuation-dissipation relation
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Ghosh, Santunu. "Study on the origin of 1/f in bulk acoustic wave resonators." Thesis, Besançon, 2014. http://www.theses.fr/2014BESA2046/document.
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Depuis quelques décennies, la technologie de contrôle de la fréquence a été au coeur de l'électronique des tempsmodernes grâce à son vaste domaine d'applications dans les systèmes de communication, les ordinateurs, les systèmesde navigation ou de défense militaire. Les dispositifs temps-fréquence fournissent des stabilités de fréquence et despuretés spectrales élevées dans le domaine de la stabilité court-terme. L'amélioration de la performance de cesdispositifs reste un grand défi pour les chercheurs. La réduction du bruit afin d'augmenter cette stabilité court-terme etd'éviter les commutations non souhaitées entre les canaux est donc très souhaitable. Il est communément admis que lalimitation fondamentale à cette stabilité court-terme est due au bruit flicker de fréquence des résonateurs. Dans cemanuscrit, un premier chapitre rappelle quelques faits de base sur l’acoustique, la cristallographie et les définitions dudomaine temps-fréquence nécessaires à l’étude des résonateurs et oscillateurs ultra-stables. Le deuxième chapitre estconsacré à un résumé de la littérature sur le bruit de fréquence en 1/f. Ensuite, le troisième chapitre concerne nos étudessur le modèle quantique de bruit en 1/f du Pr. Handel, qui, bien que critiqué par beaucoup, est encore le seul qui fournitune estimation de l'amplitude de plancher de bruit en 1/f et qui n'est pas infirmé par les données expérimentales. Dans lequatrième chapitre, une autre approche, basée sur le théorème de fluctuation-dissipation, est utilisée afin de mettre descontraintes numériques sur un modèle de bruit en 1/f causé par une dissipation interne (ou de structure) proportionnelleà l'amplitude, et non à la vitesse. Le dernier chapitre est consacré aux résultats expérimentaux. Le design et lesparamètres du résonateur ultra-stable utilisé lors de cette étude sont décrits. Les mesures de bruit de phase sur plusieurslots de résonateurs sont données. Les mesures des paramètres de résonateur ont été effectuées à basse température afinde les corréler avec les résultats de bruit. Afin d'évaluer rapidement la qualité des différents résonateurs, une autreapproche dans le domaine temporel a été testée. Elle utilise des oscillations pseudo-périodiques transitoires mettant lesoscilloscopes numériques actuellement disponibles à leurs limites de capacité. Enfin, les conclusions et perspectivessont présentéesSince a few decades, frequency control technology has been at the heart of modern day electronics due to its huge areaof applications in communication systems, computers, navigation systems or military defense. Frequency controldevices provide high frequency stabilities and spectral purities in the short term domain. However, improvement of theperformance of these devices, in terms of frequency stability, remains a big challenge for researchers. Reducing noise inorder to increase the short term stability and avoid unwanted switching between channels is thus very desirable. It iscommonly admitted that the fundamental limitation to this short-term stability is due to flicker frequency noise in theresonators. In this manuscript, a first chapter recalls some basic facts about acoustic, crystallography and definitions oftime and frequency domain needed to explore ultra-stable resonators and oscillators. The second chapter is devoted to asummary of the literature on flicker frequency noise. Then, the third chapter concerns our studies on Handel’s quantum1/f noise model, which although criticized by many, is still the only one that provides an estimation of the flooramplitude of 1/f noise that is not invalidated by experimental data. In the fourth chapter, another approach, based on thefluctuation-dissipation theorem, is used in order to put numerical constraints on a model of 1/f noise caused by aninternal (or structural) dissipation proportional to the amplitude and not to the speed. The last chapter is devoted toexperimental results. An ultra-stable resonator used during this study is described. Phase noise measurements on severalbatches of resonators are given. Measurements of resonator parameters have been done at low temperature in order tocorrelate them with noise results. Another approach with a procedure that use transient pseudo periodic oscillations andput to their limits the capacities of presently available digital oscilloscopes, is presented, in order to assess rapidly thequality of various resonators. Finally, conclusions and perspectives are given
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Zeileis, Achim. "A unified approach to structural change tests based on F statistics, OLS residuals, and ML scores." Institut für Statistik und Mathematik, WU Vienna University of Economics and Business, 2005. http://epub.wu.ac.at/714/1/document.pdf.
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Three classes of structural change tests (or tests for parameter instability) which have been receiving much attention in both the statistics and econometrics communities but have been developed in rather loosely connected lines of research are unified by embedding them into the framework of generalized M-fluctuation tests (Zeileis and Hornik, 2003). These classes are tests based on F statistics (supF, aveF, expF tests), on OLS residuals (OLS-based CUSUM and MOSUM tests) and on maximum likelihood scores (including the Nyblom-Hansen test). We show that (represantives from) these classes are special cases of the generalized M-fluctuation tests, based on the same functional central limit theorem, but employing different functionals for capturing excessive fluctuations. After embedding these tests into the same framework and thus understanding the relationship between these procedures for testing in historical samples, it is shown how the tests can also be extended to a monitoring situation. This is achieved by establishing a general M-fluctuation monitoring procedure and then applying the different functionals corresponding to monitoring with F statistics, OLS residuals and ML scores. In particular, an extension of the supF test to a monitoring scenario is suggested and illustrated on a real-world data set.Series: Research Report Series / Department of Statistics and Mathematics
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Zimmermann, Robert. "How large spheres spin and move in turbulent flows." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2012. http://tel.archives-ouvertes.fr/tel-00737746.
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Le but de ce travail de thèse est l'étude de la dynamique de sphères de grande taille dans un écoulement fortement turbulent. Pour ce faire, nous avons développé une nouvelle technique optique permettant de suivre la dynamique à 6 dimensions - position et orientation absolues - de plusieurs particules dans un écoulement complexe. Bien que la taille des particules soit comparable à l'échelle intégrale de l'écoulement, nous trouvons que sa dynamique de rotation et de translation est intermittente. De plus, nous observons que la translation et la rotation sont reliées par la force de Magnus. La répartition statistique de l'accélération n'est pas gaussienne et l'échange d'énergie avec le fluide est gouverné par la théorie mathématique des grandes déviations. Nous trouvons que le diamètre influence fortement la manière dont la particule explore l'écoulement. Nous avons ensuite appliqué le suivi de position et d'orientation à une particule instrumentée. Ce système mesure en permanence l'accélération lagrangienne qu'il subit via un accéléromètre embarqué et émet l'information à travers une électronique radio fréquence. L'orientation absolue est nécessaire pour exprimer les signaux de l'accéléromètre et ceux du suivi optique dans un repère commun; cela nous permet de comparer rigoureusement les mesures issues de ces deux techniques indépendantes. À partir de ces résultats nous avons développé des méthodes pour inférer des propriétés de l'écoulement à partir des signaux d'accélération de la particule instrumentée.
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Ploetz, Elizabeth Anne. "Fluctuation solution theory." Diss., Kansas State University, 2014. http://hdl.handle.net/2097/18390.
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Doctor of PhilosophyDepartment of Chemistry
Paul E. Smith
The Kirkwood-Buff (KB) theory of solutions, published in 1951, established a route from integrals over radial (pair) distribution functions (RDFs) in the grand canonical ensemble to a set of thermodynamic quantities in an equivalent closed ensemble. These “KB integrals” (KBIs) can also be expressed in terms of the particle-particle (i.e., concentration or density) fluctuations within grand canonical ensemble regions. Contributions by Ben-Naim in 1977 provided the means to obtain the KBIs if one already knew the set of thermodynamic quantities for the mixture of interest; that is, he provided the inversion procedure. Thus, KB theory provides a two-way bridge between local (microscopic) and global (bulk/thermodynamic) properties. Due to its lack of approximations, its wide ranging applicability, and the absence of a competitive theory for rigorously understanding liquid mixtures, it has been used to understand solution microheterogeneity, solute solubility, cosolvent effects on biomolecules, preferential solvation, etc. Here, after using KB theory to test the accuracy of pair potentials, we present and illustrate two extensions of the theory, resulting in a general Fluctuation Solution Theory (FST). First, we generalize KB theory to include two-way relationships between the grand canonical ensemble’s particle-energy and energy-energy fluctuations and additional thermodynamic quantities. This extension allows for non-isothermal conditions to be considered, unlike traditional KB theory. We illustrate these new relationships using analyses of experimental data and molecular dynamics (MD) simulations for pure liquids and binary mixtures. Furthermore, we use it to obtain conformation-specific infinitely dilute partial molar volumes and compressibilities for proteins (other properties will follow) from MD simulations and compare the method to a non-FST method for obtaining the same properties. The second extension of KB theory involves moving beyond doublet particle fluctuations to additionally consider triplet and quadruplet particle fluctuations, which are related to derivatives of the thermodynamic properties involved in regular KB theory. We present these higher order fluctuations obtained from experiment and simulation for pure liquids and binary mixtures. Using the newfound experimental third and fourth cumulants of the distribution of particles in solution, which can be extracted from bulk thermodynamic data using this extension, we also probe particle distributions’ non-Gaussian nature.
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Mahajan, Salil. "CCM3 as applied to an idealized all land zonally symmetric planet, Terra Blanda 3." Texas A&M University, 2004. http://hdl.handle.net/1969.1/1422.
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Community Climate Model 3 (CCM3) is run on an idealized all land zonally
symmetric planet (Terra Blanda) with no seasonality, no snow and fixed soil moisture
to obtain a stationary time series effectively much longer than conventional runs with
geography and seasons. The surface temperature field generated is studied to analyze
the spatial and temporal spectra, estimate the length scale and time scale of the
model, and test the linearity of response to periodic and steady heat source forcings.
The length scale of the model is found to be in the range of 1000-2000 km and the time
scale is estimated to be 24 days for the global average surface temperature field. The
response of the global average temperature is found to be fairly linear to periodic and
the steady heat source forcings. The results obtained are compared with the results
of a similar study that used CCM0. Fluctuation Dissipation theorem is also tested
for applicability on CCM3. The response of the surface temperature field to a step
function forcing is demonstrated to be very similar to the decay of naturally occurring
anomalies, and the auto-correlation function. Return period of surface temperature
anomalies is also studied. It is observed that the length of the data obtained from
CCM3, though sufficient for analysis of first and second moments, is significantly
deficient for return period analysis. An AR1 process is simulated to model the global
averaged surface temperature of Terra Blanda 3 to assess the sampling error associated
with short runs.
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Friedrich, Benjamin M. "Nonlinear dynamics and fluctuations in biological systems." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2018. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-234307.
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The present habilitation thesis in theoretical biological physics addresses two central dynamical processes in cells and organisms: (i) active motility and motility control and (ii) self-organized pattern formation. The unifying theme is the nonlinear dynamics of biological function and its robustness in the presence of strong fluctuations, structural variations, and external perturbations. We theoretically investigate motility control at the cellular scale, using cilia and flagella as ideal model system. Cilia and flagella are highly conserved slender cell appendages that exhibit spontaneous bending waves. This flagellar beat represents a prime example of a chemo-mechanical oscillator, which is driven by the collective dynamics of molecular motors inside the flagellar axoneme. We study the nonlinear dynamics of flagellar swimming, steering, and synchronization, which encompasses shape control of the flagellar beat by chemical signals and mechanical forces. Mechanical forces can synchronize collections of flagella to beat at a common frequency, despite active motor noise that tends to randomize flagellar synchrony. In Chapter 2, we present a new physical mechanism for flagellar synchronization by mechanical self-stabilization that applies to free-swimming flagellated cells. This new mechanism is independent of direct hydrodynamic interactions between flagella. Comparison with experimental data provided by experimental collaboration partners in the laboratory of J. Howard (Yale, New Haven) confirmed our new mechanism in the model organism of the unicellular green alga Chlamydomonas. Further, we characterize the beating flagellum as a noisy oscillator. Using a minimal model of collective motor dynamics, we argue that measured non-equilibrium fluctuations of the flagellar beat result from stochastic motor dynamics at the molecular scale. Noise and mechanical coupling are antagonists for flagellar synchronization. In addition to the control of the flagellar beat by mechanical forces, we study the control of the flagellar beat by chemical signals in the context of sperm chemotaxis. We characterize a fundamental paradigm for navigation in external concentration gradients that relies on active swimming along helical paths. In this helical chemotaxis, the direction of a spatial concentration gradient becomes encoded in the phase of an oscillatory chemical signal. Helical chemotaxis represents a distinct gradient-sensing strategy, which is different from bacterial chemotaxis. Helical chemotaxis is employed, for example, by sperm cells from marine invertebrates with external fertilization. We present a theory of sensorimotor control, which combines hydrodynamic simulations of chiral flagellar swimming with a dynamic regulation of flagellar beat shape in response to chemical signals perceived by the cell. Our theory is compared to three-dimensional tracking experiments of sperm chemotaxis performed by the laboratory of U. B. Kaupp (CAESAR, Bonn). In addition to motility control, we investigate in Chapter 3 self-organized pattern formation in two selected biological systems at the cell and organism scale, respectively. On the cellular scale, we present a minimal physical mechanism for the spontaneous self-assembly of periodic cytoskeletal patterns, as observed in myofibrils in striated muscle cells. This minimal mechanism relies on the interplay of a passive coarsening process of crosslinked actin clusters and active cytoskeletal forces. This mechanism of cytoskeletal pattern formation exemplifies how local interactions can generate large-scale spatial order in active systems. On the organism scale, we present an extension of Turing’s framework for self-organized pattern formation that is capable of a proportionate scaling of steady-state patterns with system size. This new mechanism does not require any pre-pattering clues and can restore proportional patterns in regeneration scenarios. We analytically derive the hierarchy of steady-state patterns and analyze their stability and basins of attraction. We demonstrate that this scaling mechanism is structurally robust. Applications to the growth and regeneration dynamics in flatworms are discussed (experiments by J. Rink, MPI CBG, Dresden)Das Thema der vorliegenden Habilitationsschrift in Theoretischer Biologischer Physik ist die nichtlineare Dynamik funktionaler biologischer Systeme und deren Robustheit gegenüber Fluktuationen und äußeren Störungen. Wir entwickeln hierzu theoretische Beschreibungen für zwei grundlegende biologische Prozesse: (i) die zell-autonome Kontrolle aktiver Bewegung, sowie (ii) selbstorganisierte Musterbildung in Zellen und Organismen. In Kapitel 2, untersuchen wir Bewegungskontrolle auf zellulärer Ebene am Modelsystem von Zilien und Geißeln. Spontane Biegewellen dieser dünnen Zellfortsätze ermöglichen es eukaryotischen Zellen, in einer Flüssigkeit zu schwimmen. Wir beschreiben einen neuen physikalischen Mechanismus für die Synchronisation zweier schlagender Geißeln, unabhängig von direkten hydrodynamischen Wechselwirkungen. Der Vergleich mit experimentellen Daten, zur Verfügung gestellt von unseren experimentellen Kooperationspartnern im Labor von J. Howard (Yale, New Haven), bestätigt diesen neuen Mechanismus im Modellorganismus der einzelligen Grünalge Chlamydomonas. Der Gegenspieler dieser Synchronisation durch mechanische Kopplung sind Fluktuationen. Wir bestimmen erstmals Nichtgleichgewichts-Fluktuationen des Geißel-Schlags direkt, wofür wir eine neue Analyse-Methode der Grenzzykel-Rekonstruktion entwickeln. Die von uns gemessenen Fluktuationen entstehen mutmaßlich durch die stochastische Dynamik molekularen Motoren im Innern der Geißeln, welche auch den Geißelschlag antreiben. Um die statistische Physik dieser Nichtgleichgewichts-Fluktuationen zu verstehen, entwickeln wir eine analytische Theorie der Fluktuationen in einem minimalen Modell kollektiver Motor-Dynamik. Zusätzlich zur Regulation des Geißelschlags durch mechanische Kräfte untersuchen wir dessen Regulation durch chemische Signale am Modell der Chemotaxis von Spermien-Zellen. Dabei charakterisieren wir einen grundlegenden Mechanismus für die Navigation in externen Konzentrationsgradienten. Dieser Mechanismus beruht auf dem aktiven Schwimmen entlang von Spiralbahnen, wodurch ein räumlicher Konzentrationsgradient in der Phase eines oszillierenden chemischen Signals kodiert wird. Dieser Chemotaxis-Mechanismus unterscheidet sich grundlegend vom bekannten Chemotaxis-Mechanismus von Bakterien. Wir entwickeln eine Theorie der senso-motorischen Steuerung des Geißelschlags während der Spermien-Chemotaxis. Vorhersagen dieser Theorie werden durch Experimente der Gruppe von U.B. Kaupp (CAESAR, Bonn) quantitativ bestätigt. In Kapitel 3, untersuchen wir selbstorganisierte Strukturbildung in zwei ausgewählten biologischen Systemen. Auf zellulärer Ebene schlagen wir einen einfachen physikalischen Mechanismus vor für die spontane Selbstorganisation von periodischen Zellskelett-Strukturen, wie sie sich z.B. in den Myofibrillen gestreifter Muskelzellen finden. Dieser Mechanismus zeigt exemplarisch auf, wie allein durch lokale Wechselwirkungen räumliche Ordnung auf größeren Längenskalen in einem Nichtgleichgewichtssystem entstehen kann. Auf der Ebene des Organismus stellen wir eine Erweiterung der Turingschen Theorie für selbstorganisierte Musterbildung vor. Wir beschreiben eine neue Klasse von Musterbildungssystemen, welche selbst-organisierte Muster erzeugt, die mit der Systemgröße skalieren. Dieser neue Mechanismus erfordert weder eine vorgegebene Kompartimentalisierung des Systems noch spezielle Randbedingungen. Insbesondere kann dieser Mechanismus proportionale Muster wiederherstellen, wenn Teile des Systems amputiert werden. Wir bestimmen analytisch die Hierarchie aller stationären Muster und analysieren deren Stabilität und Einzugsgebiete. Damit können wir zeigen, dass dieser Skalierungs-Mechanismus strukturell robust ist bezüglich Variationen von Parametern und sogar funktionalen Beziehungen zwischen dynamischen Variablen. Zusammen mit Kollaborationspartnern im Labor von J. Rink (MPI CBG, Dresden) diskutieren wir Anwendungen auf das Wachstum von Plattwürmern und deren Regeneration in Amputations-Experimenten
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Urbani, Pierfrancesco. "Theory of fluctuations in disordered systems." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112019.
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Dans cette thèse nous avons étudié de nombreux aspects de la théorie des systèmes désordonnés. En particulier, nous avons étudié les systèmes vitreux. La description détaillée des systèmes désordonnés et vitreux est un problème ouvert en physique de la matière condensée. Dans le cadre de la théorie de champ moyen pour les verres structuraux nous avons étudié la théorie des fluctuations proche de la transition vitreuse dynamique. L’étude des fluctuations peut etre fait avec le formalisme statique de la théorie de répliques. Nous avons fait cela en introduisant une théorie des champs pour la transition vitreuse à partir du potentiel microscopique entre les particules. Nous avons étudié dans ce cadre les fluctuations au niveau gaussien et nous avons évalués les exposants critiques dans ces approximations. Nous avons aussi étudié la région de validité de la prédiction gaussienne avec l’introduction d’un critère de Ginzburg pour la transition vitreuse. Les résultats que nous avons obtenues ne sont valides que dans la région β. Pour obtenir des resultats dans la région α nous avons étudié la pseudodynamique de Boltzmann que a été introduit par Franz and Parisi. Nous sommes parti des équations de Ornstein-Zernike et nous avons obtenu un ensemble d’équations dynamiques. En utilisant l’approximation Hypernetted Chain nous avons obtenu un ensemble complet d’équations qui sont très similaires aux équations de la théorie de mode-coupling. La troisième partie de la thèse porte sur l’étude des états amorphes des sphères dures en hautes dimensions. Pour obtenir les exposants dynamique dans ce cas, nous avons étudié la stabilité du diagramme de phase 1RSB (one-step-replica-symmetry-breaking). Nous avons découvert que ce diagramme de phase possède une région où la solution 1RSB est instable. La région où la solution 1RSB est instable est connectée avec la description théorique de la physique de jamming des sphères dures et nous avons montré que l’instabilité 1RSB est responsable d’une transition de phase en haute densité. Cette transition s’appelle la transition de Gardner. Nous avons cherché une solution 2RSB et nous avons vu qu’il existait un point en densité après lequel on peut avoir une solution 2RSB (et aussi fullRSB). Nous avons étudié le diagramme de phase 2RSB dans la limite de jamming où la pression devient infini. Après la solution 2RSB nous avons cherché à décrire la solution fullRSB. Nous avons écrit les équations fullRSB et nous avons découvert qu’elles sont identiques aux equations que l’on a dans le cas de un modèle de verres de spins qui s’appelle modèle de Sherrington et Kirkpatrick. Nous avons aussi étudié la solution numerique des équations fullRSB dans la limite de jamming. Cette solution montre beaucoup des choses intéressantes. La plus importante est le comportement du mean square displacement dans la limite de jamming. Si l’on regard les résultats numériques et éxperimentaux, il semble que le plateau de le mean square displacement s’approche a zero comme la pression à un exposant proche de −3/2. Nous avons vu que la solution numérique des équations fullRSB est en mesure de reproduire ce comportement. La quatrième partie de la thése a porté sur la dynamique de mode-coupling dans le régime où la transition vitreuse devient continueIn this thesis we have studied many aspects of the physics of disordered and glassy systems. The first part of the work is about the theory of dynamical fluctuations in the beta regime. When a system undergoes a dynamical arrest, it can be studied by introducing an appropriate dynamical correlation function that plays the role of the order parameter of the transition. To understand the collective effects underlying the glass transition we have studied the fluctuations of the order parameter on a time scale where the system is relaxed in a typical metastable glassy state. To do this we have seen that coming from the glass phase the system develops critical fluctuations with a diverging correlation length at the mean field level. We have thus derived an effective field theory by focusing only on them. This field theory can be used firstly to derive the mode-coupling exponent parameter that controls the relaxation of the dynamical correlation function when the system relaxes in a metastable glassy state. Moreover we can give a Ginzburg Criterion that can be used to determine the region of validity of the Gaussian approximation. These considerations are valid in the beta regime. To clarify what happens in the alpha regime we have studied a quasi-equilibrium construction, called Boltzmann-Pseudodynamics, recently introduced in order to describe with static techniques the long time regime of glassy dynamics. We have extended this formalism to structural glasses by producing a new set of dynamical equations. We have done this in the simplest approximation scheme that is called Hypernetted Chain. Two results have been obtained : firstly, we have computed the mode-coupling exponent parameter and we have shown that it coincides with the one obtained with the formalism of the first part of the thesis ; secondly we have studied the aging regime and we have derived that the condition that determines the fluctuation-dissipation ratio is a marginal stability one. In the third part of the thesis we have studied the theory of amorphous states of hard spheres in high dimensions. Hard spheres provide simple models of glasses and they are extensively studied for the jamming transition. In our framework jammed states can be thought as infinite pressure limit of metastable glassy states. During the last years it has been derived a mean field theory of hard spheres based on the 1RSB assumption on the structure of the free energy landscape. However it has been realized that this construction is inconsistent for what concerns the property of the packings at jamming. In the present work we have firstly investigated the possibility of an instability of the 1RSB solution and we have actually found that the 1RSB solution is unstable in the jamming part of the phase diagram. At the same time we have been able to compute the mode-coupling exponent parameter for this system. In order to go beyond the 1RSB solution we have first tried a 2RSB ansatz and then a fullRSB solution. We have derived a set of variational equations that are very close to the ones that have been derived in the Sherrington-Kirkpatrick model. We have solved numerically the equations and we have shown that the fullRSB solution seems to predict that the plateau value of the mean square displacement scale as the pressure to a power close to 3/2 as it seems to be predicted by scaling arguments and in contrast with the 1RSB predictions that show a scaling with the inverse of the pressure. The last chapter of the thesis is on the mode-coupling theory when the glass transition is becoming continuous. We have been able to show that in such a situation a detailed characterization of the solution of the equations can be obtained in the long time regime
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Marchal, Philippe. "Theorie des fluctuations, probabilites sur les arbres." Paris 6, 1999. http://www.theses.fr/1999PA066323.
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Nous donnons une demonstration d'une formule de wiener-hopf due a alili-doney au moyen d'une transformation trajectorielle. Nous etudions le probleme de double sortie pour les marches aleatoires continues a gauche par une methode combinatoire. Cette methode s'applique aux marches aleatoires sur un cercle, deja etudiees par pitman. Nous caracterisons le comportement presque sur du temps passe positif pour une marche aleatoire ou un processus de levy sous la condition de spitzer. Nous etudions la loi du temps passe positif pour un processus de levy en ses temps de retour en o. Nous donnons une inegalite optimale pour le theoreme de lyons. Nous construisons une classe de processus auto-similaires sur la frontiere d'un arbre regulier et etudions les points lents et points multiples de ces processus.
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Rousakis, Michail. "Essays on economic fluctuations." Thesis, University of Warwick, 2012. http://wrap.warwick.ac.uk/55269/.
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This thesis consists of two essays on economic fluctuations. The first essay (Chapter 2) explores the role of expectations in economic fluctuations. It does so within a cashless, monetary, and competitive economy featuring producers and consumers/workers with asymmetric information. Only workers observe current productivity and hence they perfectly anticipate prices, whereas all agents observe a noisy signal about long-run productivity. Information asymmetries imply that monetary policy and consumers' expectations have real effects. Non-fundamental, purely expectational shocks are conventionally thought of as demand shocks. While this remains a possibility, expectational shocks can also have the characteristics of supply shocks: if positive, they increase output and employment, and lower in flation. Whether expectational shocks manifest themselves as demand or supply shocks depends on the monetary policy pursued. Forward-looking policies generate multiple equilibria in which the role of consumers' expectations is arbitrary. Optimal policies restore the complete information equilibrium. They do so by manipulating prices so that producers correctly anticipate their revenue despite their uncertainty about current productivity. I design targets for forward-looking interest-rate rules which restore the complete information equilibrium for any policy parameters. In flation stabilization per se is typically suboptimal as it can at best eliminate uncertainty arising through prices. This offers a motivation for the Dual Mandate of central banks. The second essay (Chapter 3) shows that implementation cycles, introduced in Shleifer (1986) , are possible in the presence of capital and the absence of borrowing constraints. In a two-sector economy, patents on cost-saving ideas which take the form of investment-specific technological change arrive exogenously at a sequential, perfectly smooth rate: in odd-numbered periods, they reach a firm producing capital of type 1 and, in the even-numbered ones, a firm producing capital of type 2 . Firms can make profits out of these once. While the immediate appropriation (henceforth, "implementation") of patents is always a possibility, for accordingly formed expectations, firms can alternatively implement their patents simultaneously. This is because investment-specific technological change naturally introduces a one-period discrepancy between the time firms implement their patents and the time they receive revenue out of them. The implementation of a patent implies a sharp fall in investment which, in turn, causes a boom in current consumption. As a result, the consumption boom takes place before the wealth boom. This not only eliminates the need to smooth consumption away from the wealth boom to the period before it as conjectured, but, further, it implies that the interest rate paid when revenue is realized -and wealth expands- falls. Consequently, present discounted profits rise and implementation cycles can become a possibility. In a policy extension, I show that prolonging patent rights to two periods rules out "implementation cycles" and may lead to a welfare improvement.
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Mennuni, Alessandro. "Aggregate and disaggregated fluctuations." Thesis, University of Southampton, 2011. https://eprints.soton.ac.uk/192743/.
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In the usual version of the neoclassical growth model used to identify neutral (N-Shock) and investment shocks (I-Shock), a linear transformation frontier between consumption and investment goods is assumed. This paper extends the original framework, allowing for curvature in the transformation frontier, and studies how this affects the relative price of investment goods and hence the identification of investment shocks. A concave frontier allows a substantial improvement in the prediction of the saving rate. Furthermore, a concave frontier induces short-run aggregate effects of relative demand shifts, thereby fostering the propagation of the shocks under consideration, which overall account for 86% of the aggregate fluctuations. When I identify shocks with curvature, the N-shock appears to be stationary while the I-shock is a unit root. This leads the N-shock to play a major role: 91% of the fluctuations explained are due to the N- shock
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Haselwandter, Christoph Andreas. "Multiscale theory of fluctuating interfaces." Thesis, Imperial College London, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.444163.
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Garrity, Patrick Louis. "Nanoscale Thermal Fluctuation Spectroscopy." ScholarWorks@UNO, 2009. http://scholarworks.uno.edu/td/912.
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The utilization of thermal fluctuations or Johnson/Nyquist noise as a spectroscopic method to determine transport properties in conductors or semiconductors is developed in this paper. The autocorrelation function is obtained from power spectral density measurements thus enabling electronic transport property calculation through the Green-Kubo formalism. This experimental approach is distinct from traditional numerical methods such as molecular dynamics simulations, which have been used to extract the autocorrelation function and directly related physics only. This work reports multi-transport property measurements consisting of the electronic relaxation time, resistivity, mobility, diffusion coefficient, electronic contribution to thermal conductivity and Lorenz number from experimental data. Double validation of the experiment was accomplished through the use of a standard reference material and a standard measurement method, i.e. four-probe collinear resistivity technique. The advantages to this new experimental technique include the elimination of any required thermal or potential gradients, multi-transport property measurements within one experiment, very low error and the ability to apply controlled boundary conditions while gathering data. This research has experimentally assessed the gas pressure and flow effects of helium and argon on 30 nm Au and Cu thin films. The results show a reduction in Au and Cu electronic thermal conductivity and electrical resistivity when subjected to helium and argon pressure and flow. The perturbed electronic transport coefficients, attributed to increased electron scattering at the surface, were so dominant that further data was collected through straight-forward resistance measurements. The resistance data confirmed the thermal noise measurements thus lending considerable evidence to the presence of thin film surface scattering due to elastic and inelastic gas particle scattering effects with the electron ensemble.
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Hägg, Jonas. "Gaussian fluctuations in some determinantal processes." Doctoral thesis, KTH, Matematik (Inst.), 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4343.
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This thesis consists of two parts, Papers A and B, in which some stochastic processes, originating from random matrix theory (RMT), are studied. In the first paper we study the fluctuations of the kth largest eigenvalue, xk, of the Gaussian unitary ensemble (GUE). That is, let N be the dimension of the matrix and k depend on N in such a way that k and N-k both tend to infinity as N - ∞. The main result is that xk, when appropriately rescaled, converges in distribution to a Gaussian random variable as N → ∞. Furthermore, if k1 < ...< km are such that k1, ki+1 - ki and N - km, i =1, ... ,m - 1, tend to infinity as N → ∞ it is shown that (xk1 , ... , xkm) is multivariate Gaussian in the rescaled N → ∞ limit. In the second paper we study the Airy process, A(t), and prove that it fluctuates like a Brownian motion on a local scale. We also prove that the Discrete polynuclear growth process (PNG) fluctuates like a Brownian motion in a scaling limit smaller than the one where one gets the Airy process.QC 20100716
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LEMARCHAND, FRAIKIN ANNE. "Fluctuations dans les systemes macroscopiques : theorie et experience." Paris 6, 1990. http://www.theses.fr/1990PA066508.
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Ce travail regroupe trois themes illustrant les effets des fluctuations sur le comportement des sytemes macroscopiques. Les deux premiers themes, de nature theorique, abordent l'analyse stochastique de systemes reaction-diffusion au voisinage de bifurcations complexes. La premiere etape consiste en une approche de la surface de probabilite stationnaire par un developpement local autour d'un point fixe de son cologarithme, le potentiel stochastique u. On montre ici, qu'en general, u n'est pas analytique. La deuxieme etape consiste a se placer directement sur un attracteur de dimension un caracterise par une variable phase et a entreprendre l'etude stochastique de l'equation de diffusion de la phase en ajoutant un bruit a l'equation de kuramoto-sivashinsky. Le troisieme theme, de nature experimentale, illustre l'effet des fluctuations sur la distribution des temps d'auto-inflammation d'un melange pentane-air au voisinage d'une transition. La distribution obtenue est large et asymetrique en accord avec les previsions theoriques de baras, nicolis et peeters
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Kennedy, Thomas Albert Brian. "Theory of fluctuations and collisions in quantum optics." Thesis, Queen's University Belfast, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.254184.
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Porter, Andrew Robert. "Quantum fluctuations and excitations within electronic-structure theory." Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621983.
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Alemany, i. Arias Anna. "Dynamic force spectroscopy and folding kinetics in molecular systems." Doctoral thesis, Universitat de Barcelona, 2014. http://hdl.handle.net/10803/284197.
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Codification of genetic information; regulation of gene expression; transport of nutrients inside cells; immune protection against infectious agents; transduction of external signals... These are some of the crucial processes that take place in living organisms at the molecular level. A deep understanding of how these phenomena occur is vital to get a precise knowledge of the laws governing the microscopic world and understand, prevent and even find cures for many illnesses with an origin in the molecular scale.
Single-molecule experiments emerge as a powerful and versatile tool to investigate molecular processes at the level of individual molecules and trajectories with unprecedented spatial and temporal resolution. A paradigmatic experimental technique is given by “optical tweezers” (OT), which consist of a laser beam that captures micron-sized plastic beads using light momentum conservation. This instrument makes it possible to manipulate with nanometric precision a biomolecule and exert forces on it in the range of [0-100] pN.
The diversity of systems being studied using optical tweezers increases every day. In this thesis, OT are used to unravel the mechanisms of unfolding and folding of several small nucleic acid hairpins and a protein when a force is applied to their ends. Moreover, single antigen-antibody bonds are investigated by qualitatively measuring the correlation between bond affinity and bond elasticity. All single-molecule experiments have in common the relevant role played by thermal fluctuations. These are crucial at the microscopic scale and contain overriding thermodynamic and kinetic information of molecular systems.
The study of the characteristic forces at which molecular cooperative transitions occur, such as molecular unfolding or bond dissociation, is known as dynamic force spectroscopy (DFS). In this thesis DFS combined with Markov models are widely used to characterize the unfolding/folding reaction pathway, the transition states present in the molecular free-energy landscape, and the elastic, kinetic and thermodynamic properties of a protein, the antigen-antibody bond and nucleic acid hairpins under different conditions. A general result is that non-equilibrium DFS methods provide an excellent platform to extract thermodynamic properties of molecular states that can only be observed under dynamical conditions (that is, they are never observed in equilibrium at reasonable time scales), such as intermediate or bound configurations.
An alternative method to extract thermodynamic properties of molecular systems is the use of fluctuation relations (FR). These are mathematical identities that relate non-equilibrium work measurements to free-energy differences. When an irreversible transformation is mechanically induced in an otherwise full-equilibrated molecular system, a work is performed between an initial and a final state that differs in each independent repetition of the experiment. FR relate a collection of these work measurements to the difference in free energy between the initial and the final states, independently of the molecular reaction pathway. If the system is initially found at a partially equilibrated state, an extended version of FR can be used to measure its free energy of formation. This grants access to the thermodynamic properties of misfolded and intermediate states that are rarely sampled in full equilibrium. Additionally, the extended FR allow us to reconstruct the free-energy branches of molecular states observed during non-equilibrium experiments from irreversible work measurements. Hence, relative stabilities between molecular native, unfolded, misfolded an intermediate states can be compared at different stages of the irreversible experiment.
Results in this thesis pave the way to characterize the thermodynamics and kinetics of complex molecular process that occur under partial equilibrium conditions (as is the case in living organisms), using both DFS and FR. Examples are found in many kinetic states related to intermolecular binding or in transient non-equilibrium states occurring in polymerization reactions (e.g. translocating). Hence the influence of the findings and methods developed in this thesis remains to be seen.La codificació de la informació genètica, la regulació de l'expressió dels gens, el transport de nutrients dins la cèl·lula, la protecció immunològica contra agents infecciosos... Aquests són alguns dels processos moleculars que s'esdevenen en organismes vius i són crucials per la seva supervivència. Entendre el funcionament d'aquests fenòmens és vital per conèixer les lleis que governen l'escala microscòpica i per entendre, preveure, o fins i tot trobar cures de malalties amb origen molecular, com el Parkinson, l'Alzheimer, o alguns càncers. Els experiments amb una única molècula són una eina molt poderosa i versàtil que permet investigar molts processos moleculars a escala de molècula i trajectòria individual, amb una resolució espaio-temporal sense precedents. Una eina paradigmàtica per dur a terme aquest tipus d'estudis són les “pinces òptiques”, consistents en un feix de llum coherent focalitzat capaç d'atrapar partícules de plàstic microscòpiques utilitzant la conservació del moment. Aquest instrument permet manipular una única biomolècula amb precisió nanomètrica, i exercir-hi forces en el rang entre 0 i 100 pN. La diversitat de sistemes estudiats amb les pinces òptiques augmenta cada dia. En aquesta tesi, s'utilitzen per desxifrar els mecanismes del plegament i desplegament d'àcids nucleics i d'una proteïna quan s'hi aplica una força. A més, les propietats d'un únic enllaç entre un antigen i un anticòs s'investiguen de manera qualitativa, mesurant la correlació entre l'afinitat i l'elasticitat de la unió. Els resultats d'aquesta tesi obren la porta a la caracterització termodinàmica i cinètica de processos moleculars complexos que s'esdevenen en condicions d'equilibri parcial (com ocorre en organismes vius) utilitzant l'espectroscòpia dinàmica de forces (és a dir, l'estudi de les forces característiques per induir transicions moleculars) i els teoremes de fluctuació (que proporcionen estimacions de l'energia lliure mitjançant mesures irreversibles). Alguns exemples poden trobar-se en els estats cinètics i metaestables relacionats amb el plegament mecànic -com els estats intermedis i mal plegats-, en la interacció intermolecular, o en estats metaestables que es donen en reaccions de polimerització -com la translocació dels motors moleculars.
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Acharya, Arjun R. "Free energy differences : representations, estimators, and sampling strategies." Thesis, University of Edinburgh, 2004. http://hdl.handle.net/1842/602.
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In this thesis we examine methodologies for determining free energy differences (FEDs) of phases via Monte Carlo simulation. We identify and address three generic issues that arise in FED calculations; the choice of representation, the choice of estimator, and the choice of sampling strategy. In addition we discuss how the classical framework may be extended to take into account quantum effects. Key words: Phase Mapping, Phase Switch, Lattice Switch, Simulated Tempering, Multi-stage, Weighted Histogram Analysis Method, Fast Growth, Jarzynski method, Umbrella, Multicanonical, Path Integral Monte Carlo, Path Sampling, Multihamiltonian, fluctuation theorem.
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BENHASSINE, BAHA. "Theorie semi-classique des fluctuations dans la matiere nucleaire." Nantes, 1994. http://www.theses.fr/1994NANT2030.
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L'etude des collisions entre ions lourds aux energies intermediaires peut etre traitee dans le cadre d'une approche semi-classique basee sur l'equation de vlasov-uehling-uhlenbeck (vuu). Une telle approche reduit le probleme a n-corps a sa representation en terme de distribution a un corps et constitue la base de plusieurs modeles de simulations numeriques pour la description de la dynamique des observables collectives. On se propose d'etendre, par le biais de considerations statistiques, cette description aux dispersions autour des valeurs moyennes. Dans le cadre d'une approximation lineaire on deduit une equation de transport stochastique dans l'espace de phase: une equation de fokker-planck. La reduction aux premiers moments de cette derniere permet de deduire l'equation d'evolution de la trajectoire moyenne (vuu) ainsi que celle des correlations. Par projection, il sera possible de deduire les coefficients de transports gouvernant la dynamique des moyennes et des dispersions des variables collectives. D'autre part, en utilisant une technique de projection sur les constantes du mouvement, introduite par van kampen, on deduira les solutions stationnaires pour la matrice de covariance dans l'espace de phase. On en deduira des expressions analytiques pour les fluctuations a l'equilibre sur les observables a un corps dans les cas d'un systeme homogene et d'un systeme a symetrie spherique. Les predictions ainsi faites seront confrontees aux resultats de deux types de simulations numeriques dans le cadre d'une approximation de temps de relaxation. Dans la premiere, basee sur un modele a particules, les coefficients de transports pour les variables collectives seront directement extraits de la simulation permettant ainsi de separer les fluctuations physiques du bruit numerique. La seconde, etant de type eulerien, permet une comparaison au niveau microscopique
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Avanzini, Francesco. "Quantum molecular trajectory and stochastic theories of quantum fluctuations." Doctoral thesis, Università degli studi di Padova, 2017. http://hdl.handle.net/11577/3424724.
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Bohm theory is a formulation of Quantum Mechanics that characterises the state of a quantum system according to both the wave function, as in the conventional formulation, and the coordinates (positions) of all the particles that evolve in time drawing quantum continuous trajectories. Furthermore, a statistical ensemble of all the possible trajectories, raising from the impossibility to know the initial position of all the particles, establishes the exact correspondence with the traditional Quantum Mechanics. From a computational point of view, Bohm theory has found many applications in Chemical Physics especially to develop new methodologies for solving the Schrödinger equation and to address semi-classical approximations of Quantum Mechanics.
From a theoretical point of view, the most appealing feature of Bohm theory is its capability to supply a conceptual map between the quantum formalism and our representation of what a chemical system is. Chemical systems are composed of molecules, but the same idea of molecule requires a specific arrangement in the space of particles, i.e., the nuclei of the atoms. The statistical description of conventional Quantum Mechanics on the basis of wave function alone is insufficient to establish a clear correspondence with such a picture of molecules. Indeed, chemists employ usually Classical Mechanics in order to overcome this drawback of the standard quantum theory. On the other hand, if the particles position is included in the quantum formalism, as Bohm theory does, the map can be defined in a self-consistent way. In other words, Bohm theory appears to be the suitable quantum framework to represent molecules and their motion.
The chemical representation of molecular systems finds a natural correspondence with a single Bohm trajectory, since it is always implicitly assumed that molecular components have specific spatial position independently of our knowledge about it. Consequently, we develop a quantum method whose fundamental assumption is that a single Bohm trajectory, i.e., a quantum molecular trajectory, describes the molecular systems and the molecular motion correctly.
First of all, we examine the correspondence between a single Bohm trajectory and the conventional Quantum Mechanics, without using the ensemble of trajectories. We verify that such a correspondence exists through numerical simulations and we prove formally that the statistical properties of a single Bohm trajectory explain the probabilistic description of Quantum Mechanics. Once the consistency of this original approach has been established, we investigate the predicted properties. For instance, we take into account the constants of motion (such as the energy) corresponding to the time evolution of the coordinates and the behaviour of simple chemical systems, e.g., the vibrational motion of single molecules interacting with a resonant field. In this way, unexpected features of the molecular motion are found.
Secondly, we tackle the challenge of describing many components systems (like the chemical systems in ordinary conditions). As a matter of fact, the computation of the Bohm trajectory and of the wave function is extremely demanding. However, the statistical properties of the Bohm trajectory allow the derivation of stochastic theories for examining the dynamics of open quantum systems, i.e., few molecules (or few degrees of freedom) interacting with their environment (the other molecules). One of the developed stochastic methods correlates the dynamics of the reduced density matrix, for the degrees of freedom of interest, to the evolution of the corresponding Bohm coordinates. In other words, the Bohm equation, determining the set of all the particles velocities according to the full wave function, is replaced with a stochastic one that approximates the velocity of a subset of coordinates according to the reduced density matrix. In such a way, the quantum fluctuations induced by the environment are taken into account.
The advantage of this method concerns its capability of describing quantum systems, including open quantum systems, in terms of a quantum trajectory. This could allow the understanding of the molecular motion during a spectroscopical experiment. The possibility of investigating reactive systems, such as conformational changes, is particularly interesting. As a matter of fact, chemical reactions can be completely characterised only through the particles motion and we define the suit- able quantum methodology providing a self-consistent description of the molecular motion.La teoria di Bohm è una formulazione della Meccanica Quantistica che caratterizza lo stato di un sistema quantistico attraverso sia la funzione d’onda, come la teoria standard, sia le coordinate (le posizioni) di tutte le particelle che evolvono nel tempo secondo traiettorie quantistiche continue. Inoltre, un ensemble statistico di tutte le possibile traiettorie, che deriva dall’impossibilità di conoscere la posizione iniziale di tutte le particelle, stabilisce l’esatta corrispondenza con la Meccanica Quantistica tradizionale. Da un punto di vista computazionale, la teoria di Bohm è stata impiegata in Chimica Fisica principalmente per sviluppare nuove strategie risolutive dell’equazione di Schrödinger o nuove approssimazioni semi-classiche della Meccanica Quantistica. Da un punto di vista teorico, la caratteristica più attraente della teoria di Bohm è quella di essere il contesto naturale per definire un mappa concettuale tra il formalismo quantistico e la nostra rappresentazione dei sistemi chimici. I sistemi chimici sono composti di molecole, ma l’idea stessa di molecola è associata ad una specifica posizione spaziale delle particelle, i.e., i nuclei degli atomi. La descrizione statistica della Meccanica Quantistica convenzionale, sulla base della sola funzione d’onda, è insufficiente per definire una chiara corrispondenza con questa immagine delle molecole. Infatti, i chimici fanno spesso affidamento alla Meccanica Classica per aggirare questa difficoltà della teoria quantistica standard. Tuttavia, se la posizione delle particelle è inclusa nel formalismo quantistico, così come fa la teoria di Bohm, la corrispondenza può essere definita in modo autoconsistente. In altre parole, la teoria di Bohm sembra essere il contesto formale idoneo per rappresentare quantisticamente le molecole e il loro moto. Comunque, la raffigurazione chimica dei sistemi molecolari corrisponde ad una singola traiettoria di Bohm dato che si assume implicitamente che i componenti delle molecole abbiano una specifica posizione spaziale indipendentemente dal fatto che essa sia nota o meno. Di conseguenza, si è sviluppata una metodologia quantistica che si basa sull’assunzione che una singola traiettoria di Bohm, cioè una traiettoria molecolare quantistica, descrive correttamente i sistemi molecolari e il moto molecolare. In primo luogo, viene esaminata la corrispondenza tra una singola traiettoria di Bohm e la Meccanica Quantistica convenzionale dato che si rinuncia all’ensemble di traiettorie. Si verifica che tale corrispondenza esiste attraverso un esperimento numerico e si dimostra formalmente che le proprietà statistiche di una singola traiettoria spiegano la descrizione probabilistica della Meccanica Quantistica. Una volta che la coerenza di questa metodologia è stata verificata, vengono esaminate accuratamente le sue previsioni. Per esempio, si prendono in considerazione le costanti del moto (come l’energia) associate all’evoluzione temporale delle particelle e il comportamento di semplici sistemi chimici, e.g., il moto vibrazionale di singole molecole che interagiscono con un campo esterno risonante. In questo modo, proprietà inaspettate del moto molecolare emergono naturalmente. In secondo luogo, si considera la sfida di descrivere sistemi a molti componenti (quali sono i sistemi chimici in condizioni ordinarie). È ben noto che il calcolo della traiettoria di Bohm e della funzione d’onda è molto costoso computazionalmente. Comunque, le proprietà statistiche della traiettoria di Bohm permettono di derivare teorie stocastiche per esaminare la dinamica di sistemi quantistici aperti, come qualche molecola (o qualche grado di libertà) interagente con l’ambiente (le altre molecole). Uno dei metodi stocastici sviluppati correla la dinamica della matrice densità ridotta, per i gradi di libertà di interesse, all’evoluzione delle corrispondenti coordinate di Bohm. In altre parole, l’equazione di Bohm, che determina la velocità delle particelle attraverso la funzione d’onda, è sostituita da un’equazione stocastica che approssima la velocità di un sott’insieme di coordinate attraverso la matrice densità ridotta. In questo modo, le fluttuazioni quantistiche indotte dall’ambiente sono prese in considerazione. Il vantaggio del metodo riguarda la sua capacità di descrivere i sistemi quantistici, compresi quelli aperti, in termini di una traiettoria quantistica. Questo potrebbe permettere la comprensione del moto molecolare durante un esperimento spettroscopico. Di particolare interesse è la possibilità di esaminare sistemi reattivi, come quelli in cui avvengono cambi conformazionali. Come è ben noto, le reazioni chimiche possono essere totalmente caratterizzate solo attraverso il moto delle particelle e in questa tesi viene definita esattamente una metodologia quantistica che fornisce una descrizione autoconsistente del moto molecolare.
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Burren, Daniel. "Essays on economic fluctuations." Berlin dissertation.de, 2009. http://d-nb.info/994502990/04.
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Bridgman, Helen Amanda. "Classical and quantum fluctuations in superstring cosmology." Thesis, University of Portsmouth, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.247490.
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Westerhoff, Frank. "Chartists, fundamentalists, and exchange rate fluctuations /." Aachen : Shaker, 2002. http://www.gbv.de/dms/zbw/355764563.pdf.
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Chotibut, Thiparat. "Statistical Fluctuations in Evolutionary and Population Dynamics." Thesis, Harvard University, 2016. http://nrs.harvard.edu/urn-3:HUL.InstRepos:33493257.
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In this thesis, we study collective phenomena that arise from microscopic fluctuations at the individual level of two different living populations. First, we study evolutionary dynamics of two-species competitions in a well-mixed environment subject to population size fluctuations. We demonstrate a mechanism for neutral evolution such that population size fluctuations favor a fixation of one species over the other. An effective evolutionary dynamics for fluctuation-induced selection is derived. We then investigate strong mutualism, in a limit where a varying population size can strongly influence the evolutionary dynamics. We determine fixation probabilities as well as mean fixation times taking into account the population size degree of freedom. The results elucidate the interplay between population size fluctuations and evolutionary dynamics in well-mixed systems. Second, we investigate single species marine population subject to a constant flow field and quenched random spatially fluctuating growth rates. We show that the non-equilibrium steady-state population density of a generalized Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation develops a flow-driven striation pattern. The striations are highly asymmetric with a longitudinal correlation length that diverges linearly with the flow speed and a transverse correlation length that approaches a finite velocity-independent value. The findings suggest that, although the growth disorder can be spatially uncorrelated, correlated population structures with striations emerge naturally at sufficiently strong advection.Physics
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Karahasanovic, Una. "Fluctuation-driven phase reconstruction at itinerant ferromagnetic quantum critical points." Thesis, University of St Andrews, 2012. http://hdl.handle.net/10023/3188.
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The formation of new phases close to itinerant electron quantum critical points has been observed experimentally in many compounds. We present a unified analytical model that explains the emergence of new types of phases around itinerant ferromagnetic quantum critical points. The central idea of our analysis is that certain deformations of the Fermi surface enhance the phase-space available for low-energy quantum fluctuations and so self-consistently lower the free energy. Using this quantum order-by-disorder mechanism, we find instabilities towards the formation of a spiral ferromagnet and spin-nematic phase close to an itinerant ferromagnetic quantum critical point. Further, we employ the quantum order-by-disorder mechanism to describe the partially ordered phase of MnSi. Using the simplest model of a Stoner-like helimagnetic transition, we show that quantum fluctuations naturally lead to the formation of an unusual phase near to the putative quantum critical point that shares many of the observed features of the partially ordered phase in MnSi. In particular, we predict an angular dependence of neutron scattering that is in good agreement with neutron-scattering data.
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Elston, Timothy G. "The effects on intrinsic fluctuations of chaotic dynamics." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/29440.
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Hahn, Aljoscha M. [Verfasser], and Andreas [Akademischer Betreuer] Engel. "On free energy calculations using fluctuation theorems of work / Aljoscha M. Hahn. Betreuer: Andreas Engel." Oldenburg : IBIT - Universitätsbibliothek, 2011. http://d-nb.info/1016981139/34.
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