Dissertations / Theses on the topic 'Nonequilibrium statistical mechanics'
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Baras, Florence. "Topics in nonequilibrium statistical mechanics of reactive systems." Doctoral thesis, Universite Libre de Bruxelles, 2000. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211748.
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Polettini, Matteo <1982>. "Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2012. http://amsdottorato.unibo.it/4305/1/polettini_matteo_tesi.pdf.
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Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.
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Polettini, Matteo <1982>. "Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2012. http://amsdottorato.unibo.it/4305/.
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Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.
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Dymov, Andrey. "Nonequilibrium statistical mechanics of a crystal interacting with medium." Thesis, Cergy-Pontoise, 2015. http://www.theses.fr/2015CERG0771/document.
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Dans cette thèse nous étudions des systèmes hamiltoniens de particules en interaction, où chaque particule est faiblement couplée avec son propre thermostat de type Langevin de température positive arbitraire. Les modèles peuvent être vu comme des cristaux plongés dans un milieu continue et interagissants faiblement avec ce dernier.Nous nous intéressons au transport d'énergie dans les systèmes quand les couplages des particules avec leurs thermostats tendent vers zéro simultanément avec les couplages entre eux.Nous examinons deux situations opposées, quand la mesure de Lebesgue des resonances du système de particules découplées est nulle et quand elle est pleine. Dans le premier cas, en utilisant la méthode de moyennisation stochastique, nous démontrons que dans la limite ci-dessus le comportement de l'énergie locale des particules sur des intervalles de temps longs, et dans le régime stationnaire est donné par une équation autonome stochastique, laquelle predit uniquement le transport d'énergie non hamiltonien.Dans le second cas, en utilisant la méthode de moyennisation resonante stochastique, nous prouvons que la dynamique limite de l'énergie locale est contrôlée par une équation efficace stochastique. La dernière prevoit le transport d'energie hamiltonien entre les particules. Cependant, elle n'est pas autonome pour l'énergie locale. En utilisant cette asymptotique, nous montrons que dans la limite ci-dessus le flux d'énergie hamiltonien du système satisfait des relations qui ressemblent à la loi de Fourier et à la formule de Green-Kubo (cependant, elles ne le sont pas).La plupart des résultats et convergences que nous obtenons dans la thèse sont uniformes par rapport au nombre de particules dans les systèmes, qui rend nos résultats pertinents du point de vue de la physique statistiqueIn the present thesis we study Hamiltonian systems of particles with weak nearest-neighbour interaction, where each particle is weakly coupled with its own stochastic Langevin-type thermostat of arbitrary positive temperature.The models can be seen as crystals plugged in some medium and weakly interacting with it.We are interested in the energy transport through the systems when the couplings of the particles with the thermostats go to zero simultaneously with their couplings with each other.We investigate two opposite situations, when resonances of the system of uncoupled particles have Lebesgue measure zero and when they are of full Lebesgue measure.In the first case, using the method of stochastic averaging, we prove that under the limit above behaviour of the local energy of particles on long time intervals and in a stationary regime is given by an autonomous stochastic equation, which does not provide any Hamiltonian energy transport.For the second situation, using the method of resonant stochastic averaging, we show that the limiting dynamics of the local energy is governed by a stochastic effective equation. The latter provides Hamiltonian energy transport between the particles, however, is not an autonomous equation for the local energy. Using this asymptotics, we prove that under the limit above the Hamiltonian energy flow in the system satisfies some relations which resemble the Fourier law and the Green-Kubo formula (however, which are not).Most of results and convergences obtained in the thesis are uniform with respect to the number of particles in the systems, what makes our results relevant from the point of view of statistical physics
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Abu-Samreh, Mohammad Mahmud. "Thermalization theory in heavy ion collisions by nonequilibrium statistical mechanics." Diss., The University of Arizona, 1991. http://hdl.handle.net/10150/185391.
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This dissertation presents a semiclassical microscopic approach based on the Uehling-Uhlenbeck equation for studying the equilibration processes due to nucleon-nucleon collisions during the collision of two heavy ions in the low and intermediate energy domain (5-100 MeV/nucleon). The state formed in the early stages of a heavy-ion collision can be characterized by a highly excited non-equilibrium system of nucleons. Equilibration processes then take place resulting in a system for which a temperature can be defined at least locally. The single-nucleon distribution function for the nucleons during the early stage of the ion-ion collision is represented in momentum-space either by two Fermi-spheres separated by the relative momentum of the impacting ions or by a deformed Fermi-sphere. The equilibration (thermalization) of this initial distribution in momentum-space is studied by calculating the collision term as a function of time. The relaxation-times are investigated through a microscopic model that incorporates the UU collision term with the relaxation-time approximation. Relaxation-times for the equilibration are obtained as a function of density and temperature. The temperature dependence is strong at low temperatures and this is a consequence of the Fermi statistics. The mode dependence of the relaxation-times is also calculated by expanding the angular dependence of the distribution in spherical harmonics. The RTA is also tested against thermalization of the Fermi-sphere systems and is found to be reasonable. Transport coefficients for viscosity, thermal conductivity and diffusion are also calculated as well as their temperature and density dependencies. Their relation to relaxation-times are derived. The mean free path of nucleons in hot nuclear matter is also studied in the same frame of work. The numerical calculations of the collision term are an important part of this investigation. They involve five-dimensional integrations carried out using Gaussian and Simpson's numerical methods.
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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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Angel, Andrew George. "Nonequilibrium statistical mechanics of the zero-range process and application to networks." Thesis, University of Edinburgh, 2005. http://hdl.handle.net/1842/11870.
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In this thesis a simple, stochastic, interacting particle system – the zero-range process (ZRP) – is studied with various analytical and numerical methods. in particular, the application of the ZRP and some of its generalisations to complex networks is focused upon. The ZRP is a hopping particle model where particles hop between sites of a lattice under certain rules that depend only on the properties of the site from which the particles hop – hence the name zero-range. Through its simplicity the steady state of the ZRP can be solved, even for nonequilibrium dynamics, and yet despite its simplicity it can exhibit interesting phenomena such as condensation transitions, where a finite fraction of the total particles in the system will condense onto a single site of the lattice. Firstly, interesting finite-size effects surrounding the condensation transition in a one-dimensional, driven version of the ZRP are studied. These take the form of discrepancies in the current-density diagram between finite and infinite systems, with the finite behaviour resembling that seen in real traffic data. Following this, direct applications of the ZRP to complex networks, and interesting phenomena arising from the specifics of the applications, are studied. The ZRP is applied as a model of networks and is found capable of reproducing power-law degree distributions, as observed in many real networks, at the critical point of the condensation transition. The degree is the number of connections a component of the network has. This model is then generalised to include creation and annihilation of particles or links, and this is found to exhibit critical behaviour – namely power-law particle and degree distributions – in a region of the parameter space, rather than at a critical point. The full phase diagram of this system is investigated, revealing low density and high density phases as well as subdivisions of the critical phase.
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Ha, Meesoon. "Scaling and phase transitions in one-dimensional nonequilibrium driven systems /." Thesis, Connect to this title online; UW restricted, 2003. http://hdl.handle.net/1773/9758.
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He, Dahai. "Thermal rectification in one-dimensional nonlinear systems." HKBU Institutional Repository, 2008. http://repository.hkbu.edu.hk/etd_ra/865.
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Chin, Chen-Shan. "Stochastic fluctuations far from equilibrium : statistical mechanics of surface growth /." Thesis, Connect to this title online; UW restricted, 2002. http://hdl.handle.net/1773/9759.
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Guttal, Vishwesha. "Applications of nonequilibrium statistical physics to ecological systems." Columbus, Ohio : Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1209696541.
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Yamaga, Kazuki. "Conduction and diffusion of Fermi particles on lattices -from the standpoint of nonequilibrium statistical mechanics-." Doctoral thesis, Kyoto University, 2021. http://hdl.handle.net/2433/263654.
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Wustmann, Waltraut. "Statistical mechanics of time-periodic quantum systems." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-38126.
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The asymptotic state of a quantum system, which is in contact with a heat bath, is strongly disturbed by a time-periodic driving in comparison to a time-independent system. In this thesis an extensive picture of the asymptotic state of time-periodic quantum systems is drawn by relating it to the structure of the corresponding classical phase space. To this end the occupation probabilities of the Floquet states are analyzed with respect to their semiclassical property of being either regular or chaotic. The regular Floquet states are occupied with exponential weights e^{-betaeff Ereg} similar to the canonical weights e^{-beta E} of time-independent systems. The regular energies Ereg are defined by the quantization of the time-periodic system, whose classical properties also determine the effective temperature 1/betaeff. In contrast, the chaotic Floquet states acquire almost equal probabilities, irrespective of their time-averaged energy. Beyond these semiclassical properties the existence of avoided crossings in the spectrum is an intrinsic quantum property of time-periodic systems. Avoided crossings can strongly influence the entire occupation distribution. As an impressive application a novel switching mechanism is proposed in a periodically driven double well potential coupled to a heat bath. By a weak variation of the driving amplitude its asymptotic state is switched from the ground state in one well to a state with higher average energy in the other wellDer asymptotische Zustand eines Quantensystems, das in Kontakt mit einem Wärmebad steht, wird durch einen zeitlich periodischen Antrieb gegenüber einem zeitunabhängigen System nachhaltig verändert. In dieser Arbeit wird ein umfassendes Bild über den asymptotischen Zustand zeitlich periodischer Quantensysteme entworfen, indem es diesen zur Struktur des zugehörigen klassischen Phasenraums in Beziehung setzt. Dazu werden die Besetzungswahrscheinlichkeiten der Floquet-Zustände hinsichtlich ihrer semiklassischen Eigenschaft analysiert, nach welcher sie entweder regulär oder chaotisch sind. Die regulären Floquet-Zustände sind mit exponentiellen Gewichten e^{-betaeff Ereg} ähnlich der kanonischen Verteilung e^{-beta E} zeitunabhängiger Systeme besetzt. Dabei sind die reguläre Energien Ereg durch die Quantisierung des Systems vorgegeben, dessen klassische Eigenschaften auch die effektive Temperatur 1/betaeff bestimmen. Die chaotischen Zustände dagegen haben fast einheitliche Besetzungswahrscheinlichkeiten, welche unabhängig von ihrer mittleren Energie sind. Über diese semiklassischen Eigenschaften hinaus ist das Auftreten von vermiedenen Kreuzungen im Spektrum eine intrinsisch quantenmechanische Eigenschaft zeitlich periodischer Systeme. Diese können die gesamte Besetzungsverteilung nachhaltig beeinflussen und finden eine eindrucksvolle Anwendung in Form eines neuartigen Schaltmechanismus in einem harmonisch modulierten Doppelmuldenpotential in Kontakt mit einem Wärmebad. Der asymptotische Zustand kann unter geringer Variation der Antriebsamplitude vom Grundzustand der einen Mulde in einen Zustand höherer mittlerer Energie in der anderen Mulde geschaltet werden
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Acconcia, Thiago Vaz 1991. "Caminhos ótimos degenerados em sistemas termicamente isolados." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/276953.
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Orientadores: Marcus Vinícius Segantini Bonança, Maurice de KoningDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin
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Resumo: A termodinâmica é uma teoria do calor e trabalho, a qual descreve perfeitamente os processos quase-estáticos somente. Entretanto, além dos estados de equilíbrio, nós encontramos uma ampla classe de processos operando em tempo finito. Uma meta onipresente na termodinâmica é a otimização dos processes a tempo finito através da minimização do trabalho dissipado ou trabalho em excesso. Para o oscilador harmônico paramétrico, nós derivamos uma família altamente degenerada de protocolos ótimos a tempo finito, ao longo dos quais o trabalho em excesso produzido se anula exatamente. Para isso, o sistema de interesse se mantém termicamente isolado durante todo o processo de atuação do protocolo de switching. Esses protocolos ótimos são obtidos através da teoria de resposta linear para sistemas inicialmente preparados segundo uma distribuição canônica. Para sistemas com um grau de liberdade, mostramos evidências de que esses caminhos ótimos podem também levar à conservação do invariante adiabático correspondente. Além dos resultados analíticos para os osciladores harmônicos clássico e quântico, nós apresentamos resultados numéricos para alguns exemplos anarmônicos. Finalmente, nós reformulamos os resultados anteriores quantificando-os em termos do comprimento termodinâmico para a versão quântica do sistema oscilador harmônico
Abstract: Thermodynamics is a theory of heat and work, which describes perfectly only the quasistatic processes. However, if we shift our view away from the equilibrium states, we find a wide class of processes operating in finite-time. An ubiquitous goal in thermodynamics is to optimize the finite time processes by minimizing the dissipated or excess work. For the parametric harmonic oscillator, we derive a family of degenerated finite-time optimal protocols for which the excess work during a non-equilibrium process vanishes exactly. For this, the system of interest is kept thermally isolated during the switching of a control parameter. These optimal paths are obtained within linear response for systems initially prepared in a canonical distribution. For systems with one degree of freedom, we claim that these optimal paths may also lead to the conservation of the corresponding adiabatic invariant. Besides the analytical results for both classical and quantum harmonic oscillator, we present numerical results for certain anharmonic examples. Finally, we discuss the reformulation of the latter results terms of the thermodynamic length for the quantum version of the harmonic oscillator system
Mestrado
Física
Mestre em Física
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Haga, Taiki. "Renormalization Group Analysis of Nonequilibrium Phase Transitions in Driven Disordered Systems." Kyoto University, 2018. http://hdl.handle.net/2433/232230.
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Myers, Owen Dale. "Spatiotemporally Periodic Driven System with Long-Range Interactions." ScholarWorks @ UVM, 2015. http://scholarworks.uvm.edu/graddis/524.
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It is well known that some driven systems undergo transitions when a system parameter is changed adiabatically around a critical value. This transition can be the result of a fundamental change in the structure of the phase space, called a bifurcation. Most of these transitions are well classified in the theory of bifurcations. Among the driven systems, spatiotemporally periodic (STP) potentials are noteworthy due to the intimate coupling between their time and spatial components. A paradigmatic example of such a system is the Kapitza pendulum, which is a pendulum with an oscillating suspension point. The Kapitza pendulum has the strange property that it will stand stably in the inverted position for certain driving frequencies and amplitudes. A particularly interesting and useful STP system is an array of parallel electrodes driven with an AC electrical potential such that adjacent electrodes are 180 degrees out of phase. Such an electrode array embedded in a surface is called an Electric Curtain (EC). As we will show, by using two ECs and a quadrupole trap it is posible to produce an electric potential simular in form to that of the Kapitza pendulum.
Here I will present the results of four related pieces of work, each focused on understanding the behaviors STP systems, long-range interacting particles, and long-range interacting particles in STP systems. I will begin with a discussion on the experimental results of the EC as applied to the cleaning of solar panels in extraterrestrial environments, and as a way to produce a novel one-dimensional multiparticle STP potential. Then I will present a numerical investigation and dynamical systems analysis of the dynamics that may be possible in an EC. Moving to a simpler model in order to explore the rudimentary physics of coulomb interactions in a STP potential, I will show that the tools of statistical mechanics may be important to the study of such systems to understand transitions that fall outside of bifurcation theory. Though the Coulomb and, similarly, gravitational interactions of particles are prevalent in nature, these long-range interactions are not well understood from a statistical mechanics perspective because they are not extensive or additive. Finally, I will present a simple model for understanding long-range interacting pendula, finding interesting non-equilibrium behavior of the pendula angles. Namely, that a quasistationary clustered state can exist when the angles are initially ordered by their index.
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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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Kyriakopoulos, Nikos. "Flocking in active matter systems : structure and response to perturbations." Thesis, University of Aberdeen, 2016. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=231666.
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Flocking, the collective motion of systems consisting of many agents, is a ubiquitous phenomenon in nature, observed both in biological and artificial systems. The understanding of such systems is important from both a theoretical point of view, as it extends the field of statistical physics to non-equilibrium systems, and from a practical point of view, due to the emergence of applications that are based on the modelling. In the present thesis I numerically investigated several aspects of flocking dynamics, simulating systems consisting of up to millions of particles. One first problem I worked on regarded the flocks response to external perturbations, something that had received little attention so far. The result was a scaling relation, connecting the asymptotic response of a flock to the strength of the external fleld affecting it. Additionally, my preliminary results point towards a generalised fluctuation-dissipation relation for the short-time response, with two different effective temperatures depending on the direction at which the perturbing field is applied. Another aspect I studied was the stability and dynamical properties of non-confined active systems (finite flocks in open space). The results showed that these flocks are stable only when an attracting 'social force' keeps the agents from drifting away from each other. The velocity fluctuations correlations were found to be different than the asymptotic limit predictions of hydrodynamic theories for infinite flocks. Finally, I studied the clustering dynamics of flocking systems. The conclusion was that the non-equilibrium clustering in the ordered phase is regulated by an anisotropic percolation transition, while it does not drive the order-disorder transition, contrary to earlier conjectures. I believe the results of this work answer some important questions in the field of ordered active matter, while at the same time opening new and intriguing ones, that will hopefully be tackled in the near future.
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Vachier, Jeremy [Verfasser], Marco Giacomo [Akademischer Betreuer] Mazza, Marco Giacomo [Gutachter] Mazza, and Jörg [Gutachter] Enderlein. "Nonequilibrium Statistical Mechanics : Collective behavior of active particles / Jeremy Vachier ; Gutachter: Marco Giacomo Mazza, Jörg Enderlein ; Betreuer: Marco Giacomo Mazza." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2020. http://d-nb.info/1207543047/34.
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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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Hirata, Flávia Mayumi Ruziska. "Dinâmica estocástica de populações biológicas." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-19092017-145805/.
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Nesta tese investigamos modelos irreversíveis dentro do contexto da mecânica estatística de não-equilíbrio motivados por alguns problemas de dinâmicas de populações biológicas. Procuramos identificar a existência de transições de fase e as classes de universalidade às quais os modelos pertencem. Além disso, buscamos modelos que capturem as principais características dos sistemas biológicos que procuramos descrever. Encontramos a solução analítica exata para o modelo suscetível-infectado-recuperado (SIR) em uma rede unidimensional. Investigamos o modelo suscetível-infectado-recuperado com infecção recorrente. Mostramos que o modelo pertence à classe de universalidade da percolação isotrópica, salvo pelos parâmetros em que se torna o processo de contato. Obtivemos também a linha de transição entre as fases em que há e não há propagação da epidemia, através de aproximações de campo médio e por simulações de Monte Carlo do modelo na rede quadrada. Investigamos uma dinâmica para duas espécies biológicas e dois nichos ecológicos; para tanto introduzimos um modelo estocástico irreversível de quatro estados. Concluímos que o modelo oferece uma descrição para as oscilações temporais das populações das espécies e para a alternância de dominância entre estas. Para chegar a esta conclusão, utilizamos simulações de Monte Carlo do modelo na rede quadrada, aproximações de campo médio e a abordagem da equação mestra de nascimento e morte, a qual, para grandes populações, pode ser aproximada por uma equação de Fokker-Planck que é associada a um conjunto de equações de Langevin. Por fim, usando simulações de Monte Carlo, analisamos a dinâmica de duas espécies biológicas e dois nichos ecológicos incluindo difusão. Novamente verificamos que o modelo gera cenários com oscilações temporais das populações das espécies e alternância de dominância entre estas. Ademais, concluímos que modelo pertence à classe de universalidade da percolação direcionada e obtivemos o diagrama de fase.In this thesis we investigate irreversible models within the context of nonequilibrium statistical mechanics motivated by some problems of biological population dynamics. We look for dentifying the existence of phase transition and the universality classes to which the models belong. In addition to that, we look for models that capture the main characteristics of the biological systems which we are interested in describing. We found the exact analytic solution of the susceptible-infected-recovered (SIR) model on one-dimensional lattice. We investigated the susceptible-infected-recovered model with recurrent infection. We showed that the model belongs to the isotropic percolation universality class, except for the parameters that make the model become a contact process. We obtained the transition line between the phases in which there is propagation of the epidemic and in which there is not, by means of mean-field approximations and Monte Carlo simulations on a square lattice. Furthermore, we investigated a dynamic for two biological species and ecological niches; for this purpose we introduced an irreversible stochastic model with four states. We conclude that the modoffers a description of time oscillations of the species populations and of the alternating dominance between them. To achieve this conclusion we used Monte Carlo simulations of this model on a square lattice, mean-field approximation, and the birth and death master equation approach, which for large populations can be approximated by a Fokker-Planck equation that is associated to a set of Langevin equations. Finally, using Monte Carlo simulations, we analyzed a dynamic for two biological species and ecological niches including diffusion. Again, we verified that the model generates scenarios with time oscillations of the species populations and with alternating dominance between them. Also, we conclude that the model belongs to the directed percolation universality class and we found the phase diagram.
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Santos, Carlos Eduardo Fiore dos. "\"Sistemas fora do equilíbrio termodinâmico: Um estudo em diferentes abordagens\"." Universidade de São Paulo, 2006. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-11042007-140207/.
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Nesta tese de doutorado apresentamos um estudo sobre o comportamento de diversos sistemas irrevers?veis, caracterizados pela existencia de estados absorventes, atraves de abordagens distintas. Utilizamos aproximacoes de campo medio dinamico, simulacoes numericas usuais, mudanca de ensemble e expanso em serie. Alem disso, mostramos numa parte deste trabalho que a abordagem proposta para o estudo de sistemas irrevers?veis no ensemble em que o numero de part?culas e constante tambem pode ser estendida para sistemas em equil´?brio termodinamico, descrito pela distribuicao de probabilidades de Gibbs. Finalmente mostramos problemas em aberto para trabalhos futuros.In this PHD thesis, we have presented a study about several nonequilibrium systems with absorbing states by means of different approaches, such as mean-field analysis, usual numerical simulations, analysis in another ensemble and perturbative series expansions. In a specific part of this thesis, we have shown that the approach proposed here for describing nonequilibrium systems in the constant particle number ensemble can also be used to caracterize equilibrium systems, described by Gibbs probability distribution. Finally, we have shown open problems for future researchs.
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Badreddine, Jawad. "Modélisation du grenaillage ultrason pour des pièces à géométrie complexe." Thesis, Troyes, 2014. http://www.theses.fr/2014TROY0015/document.
Full textAbstract:
Le grenaillage ultrason est un procédé mécanique de traitement de surfaces. Il consiste à projeter des billes à la surface de pièces métalliques, à l’aide d’un système acoustique vibrant ultrasonore. Lors du traitement, les billes sont contenues dans une enceinte spécialement conçue pour la pièce à traiter, et adoptent un comportement similaire à celui d’un gaz granulaire vibré. Le grenaillage ultrason sert à introduire des contraintes résiduelles de compression dans le matériau traité. Ces contraintes de compression sont bénéfiques pour la tenue en fatigue de la pièce et sa résistance à la corrosion sous contraintes.L’objectif des présents travaux de thèse consiste à modéliser la dynamique des billes pendant le traitement, et pour des pièces et géométries complexes. En effet, depuis son industrialisation, la mise au point du procédé se fait de manière empirique qui, avec la complexification des pièces mécaniques traitées pousse cette approche à ses limites. La mise au point peut donc s’avérer coûteuse en temps et aboutir à une solution partiellement optimisée. Ainsi, le modèle développé donne accès à une compréhension détaillée du grenaillage ultrason dans des conditions de traitement industrielles. Il constitue pour la première fois un outil d’aide à la conception des enceintes de traitement, offrant la possibilité d’une meilleure maitrise et optimisation du traitement, tout en réduisant les coûts de mise au point. La seconde contribution est de fournir aux modèles de prédiction des contraintes des données fiables et réalistesUltrasonic shot peening is a mechanical surface treatment process. It consists on projecting spherical shot onto a metallic surface, using an ultrasonic accoustic system. During the treatement, the shot are contained in a chamber, specially designed for the peened part, and behave similarely to a vibrated granular gas. Ultrasonic shot peening is used to introduce compressive residual stresses in the peened material. These compressive stresses help increasing the fatigue life span of the part and its resistance to stress corrosion cracking.The objectif of the present work consists on modeling the shot dynamics of the shot during the traitement, and for complex parts and geometries. Since its industrialization, the choice of the process parameters is done experimentally with trial and error. And with the ever increasing complexity of the peened parts, this approach is reaching its limits; thus becoming sometimes time consuming and providing partially optimized solutions.Therfore, the developped model gives access to a detailed understanding of ultrasonic shot peening in industrial treatment conditions. It represents for the first time a support tool for the design of peening chambers. This offers the possibility of a better control and optimization of the process, while reducing development costs. The second contribution lies in the model capacity to provide reliable and realistic input data to residual stresses prediction models
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"Statistical mechanics of strongly driven Ising systems." 2001. http://docserver.bis.uni-oldenburg.de/publikationen/dissertation/2001/hausta01/hausta01.html.
Full text
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Standish, Russell Kim. "On various questions in nonequilibrium statistical mechanics relating to swarms and fluid flow." Phd thesis, 1990. http://hdl.handle.net/1885/138858.
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Petersen, Charlotte Frances. "An Investigation Into the Significance of Dissipation in Statistical Mechanics." Phd thesis, 2016. http://hdl.handle.net/1885/110514.
Full textAbstract:
The dissipation function is a key quantity in nonequilibrium
statistical mechanics. It was originally derived for use in the
Evans-Searles Fluctuation Theorem, which quantitatively describes
thermal fluctuations in nonequilibrium systems. It is now the
subject of a number of other exact results, including the
Dissipation Theorem, describing the evolution of a system in
time, and the Relaxation Theorem, proving the ubiquitous
phenomena of relaxation to equilibrium. The aim of this work is
to study the significance of the dissipation function, and
examine a number of exact results for which it is the argument.
First, we investigate a simple system relaxing towards
equilibrium, and use this as a medium to investigate the role of
the dissipation function in relaxation. The initial system has a
non-uniform density distribution. We demonstrate some of the
existing significant exact results in nonequilibrium statistical
mechanics. By modifying the initial conditions of our system we
are able to observe both monotonic and non-monotonic relaxation
towards equilibrium.
A direct result of the Evans-Searles Fluctuation Theorem is the
Nonequilibrium Partition Identity (NPI), an ensemble average
involving the dissipation function. While the derivation is
straightforward, calculation of this quantity is anything but.
The statistics of the average are difficult to work with because
its value is extremely dependent on rare events. It is often
observed to converge with high accuracy to a value less than
expected. We investigate the mechanism for this asymmetric bias
and provide alternatives to calculating the full ensemble average
that display better statistics. While the NPI is derived exactly
for transient systems it is expected that it will hold in steady
state systems as well. We show that this is not true, regardless
of the statistics of the calculation.
A new exact result involving the dissipation function, the
Instantaneous Fluctuation Theorem, is derived and demonstrated
computationally. This new theorem has the same form as previous
fluctuation theorems, but provides information about the
instantaneous value of phase functions, rather than path
integrals. We extend this work by deriving an approximate form of
the theorem for steady state systems, and examine the validity of
the assumptions used.
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Kumar, K. Vijay. "Nonequilibrium Fluctuations In Sedimenting And Self-Propelled Systems." Thesis, 2010. https://etd.iisc.ac.in/handle/2005/2037.
Full textAbstract:
Equilibrium statistical mechanics has a remarkable property: the steady state probability distribution can be calculated by a procedure independent of the detailed dynamics of the system under consideration. The partition function contains the complete thermodynamics of the system. The calculation of the partition function itself might be a daunting task and one might need to resort to approximate methods in practice. But there is no problem in principle on how to do the statistical mechanics of a system that is at thermal equilibrium.
Nonequilibrium statistical mechanics is a completely different story. There is no general formalism, even in principle, the application of which is guaranteed to yield the probability distribution, even for stationary states, without explicit consideration of the dynamics of the system. Instead, there are several methods of wide applicability drawn from experience which work for particular classes of systems. Frequently, one writes down phenomenological equations of motion based on general principles of conservation and symmetry and attempts to extract the dynamical response and correlations.
The motivation for studying nonequilibrium systems is the very simple fact that they are ubiquitous in nature and exhibit very rich, diverse and often counter-intuitive phenomenon. We ourselves are an example of a very complex nonequilibrium system.
This thesis examines three problems which illustrate the generic features of a typical driven system maintained out of thermal equilibrium.
The first chapter provides a very brief discussion of nonequilibrium systems. We outline the tools that are commonly employed in the theoretical description of driven systems, and discuss the response of physical systems to applied perturbations.
Chapter two considers a very simple model for a single self-propelled particle with an internal asymmetry, and nonequilibrium energy input in the form of Gaussianwhite noise. Our model connects three key nonequilibrium quantities – drift velocity, mean internal force and position-velocity correlations. We examine this model in detail and solve it using perturbative, numerical and exact methods.
We begin chapter three with a brief introduction to the sedimentation of particle-fluid suspensions. Some peculiarities of low Reynolds number hydrodynamics are discussed with particular emphasis on the sedimentation of colloidal particles in a viscous fluid. We then introduce the problem of velocity fluctuations in steady sedi-mentation. The relevance of the current study to an earlier model and improvements made in the present work are then discussed. A physical understanding of our model and the conclusions that result from its analysis are an attempt to resolve the old problem of divergent velocity fluctuations in steadily sedimentating suspensions.
The fourth chapter is a study to probe the nature of the fluctuations in a driven suspension of point-particles. Fluctuation relations that characterise large-deviations are a current topic of intense study. We show in this chapter that the random dynamics of suspended particles in a driven suspension occasionally move against the driving force, and that the probability of such rare events obeys a steady state fluctuation relation.
In the final chapter, we summarise the models studied and point out the common features that they display. We conclude by pointing out some ways in which the problems discussed in this thesis can be extended upon in the future.
28
Kumar, K. Vijay. "Nonequilibrium Fluctuations In Sedimenting And Self-Propelled Systems." Thesis, 2010. http://etd.iisc.ernet.in/handle/2005/2037.
Full textAbstract:
Equilibrium statistical mechanics has a remarkable property: the steady state probability distribution can be calculated by a procedure independent of the detailed dynamics of the system under consideration. The partition function contains the complete thermodynamics of the system. The calculation of the partition function itself might be a daunting task and one might need to resort to approximate methods in practice. But there is no problem in principle on how to do the statistical mechanics of a system that is at thermal equilibrium.
Nonequilibrium statistical mechanics is a completely different story. There is no general formalism, even in principle, the application of which is guaranteed to yield the probability distribution, even for stationary states, without explicit consideration of the dynamics of the system. Instead, there are several methods of wide applicability drawn from experience which work for particular classes of systems. Frequently, one writes down phenomenological equations of motion based on general principles of conservation and symmetry and attempts to extract the dynamical response and correlations.
The motivation for studying nonequilibrium systems is the very simple fact that they are ubiquitous in nature and exhibit very rich, diverse and often counter-intuitive phenomenon. We ourselves are an example of a very complex nonequilibrium system.
This thesis examines three problems which illustrate the generic features of a typical driven system maintained out of thermal equilibrium.
The first chapter provides a very brief discussion of nonequilibrium systems. We outline the tools that are commonly employed in the theoretical description of driven systems, and discuss the response of physical systems to applied perturbations.
Chapter two considers a very simple model for a single self-propelled particle with an internal asymmetry, and nonequilibrium energy input in the form of Gaussianwhite noise. Our model connects three key nonequilibrium quantities – drift velocity, mean internal force and position-velocity correlations. We examine this model in detail and solve it using perturbative, numerical and exact methods.
We begin chapter three with a brief introduction to the sedimentation of particle-fluid suspensions. Some peculiarities of low Reynolds number hydrodynamics are discussed with particular emphasis on the sedimentation of colloidal particles in a viscous fluid. We then introduce the problem of velocity fluctuations in steady sedi-mentation. The relevance of the current study to an earlier model and improvements made in the present work are then discussed. A physical understanding of our model and the conclusions that result from its analysis are an attempt to resolve the old problem of divergent velocity fluctuations in steadily sedimentating suspensions.
The fourth chapter is a study to probe the nature of the fluctuations in a driven suspension of point-particles. Fluctuation relations that characterise large-deviations are a current topic of intense study. We show in this chapter that the random dynamics of suspended particles in a driven suspension occasionally move against the driving force, and that the probability of such rare events obeys a steady state fluctuation relation.
In the final chapter, we summarise the models studied and point out the common features that they display. We conclude by pointing out some ways in which the problems discussed in this thesis can be extended upon in the future.
29
Hansen, David Peter. "Nonequilibrium molecular dynamics simulations on distributed memory machines." Phd thesis, 1994. http://hdl.handle.net/1885/138526.
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Mittag, Emil Joshua. "Applications of the fluctuation theorem." Phd thesis, 2002. http://hdl.handle.net/1885/146086.
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Giovannelli, Edoardo. "Sampling methods and free energy estimators for computer simulations: development and applications." Doctoral thesis, 2018. http://hdl.handle.net/2158/1124398.
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Carberry, David. "Optical Tweezers: Experimental Demonstrations of the Fluctuation Theorem." Phd thesis, 2005. http://hdl.handle.net/1885/46235.
Full textAbstract:
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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Mishra, Shradha. "Dynamics, Order And Fluctuations In Active Nematics : Numerical And Theoretical Studies." Thesis, 2008. https://etd.iisc.ac.in/handle/2005/832.
Full textAbstract:
In this thesis we studied theoretically and numerically dynamics, order and fluctuations in two dimensional active matter with specific reference to the nematic phase in collections of self-driven particles.The aim is to study the ways in which a nonequilibrium steady state with nematic order differs from a thermal equilibrium system of the same spatial symmetry. The models we study are closely related to “flocking”[1], as well as to equations written down to describe the interaction of molecular motors and filaments in a living cell[2,3] and granular nematics [4]. We look at (i) orientational and density fluctuations in the ordered phase, (ii) the way in which density fluctuations evolve in a nematic background, and finally (iii) the coarsening of nematic order and the density field starting from a statistically homogeneous and isotropic initial state. Our work establishes several striking differences between active nematics and their thermal equilibrium counterparts.
We studied two-dimensional nonequilibrium active nematics. Two-dimensional nonequilibrium nematic steady states, as found in agitated granular-rod monolayers or films of orientable amoeboid cells, were predicted [5] to have giant number fluctuations, with the standard deviation proportional to the mean. We studied this problem more closely, asking in particular whether the active nematic steady state is intrinsically phase-separated. Our work has close analogy to the work of Das and Barma[6] on particles sliding downhill on fluctuating surfaces, so we looked at a model in which particles were advected passively by the broken-symmetry modes of a nematic, via a rule proposed in [5]. We found that an initially homogeneous distribution of particles on a well-ordered nematic background clumped spontaneously, with domains growing as t1/2, and an apparently finite phase-separation order parameter in the limit of large system size. The density correlation function shows a cusp, indicating that Porod’s Law does not hold here and that the phase-separation is fluctuation-dominated[7].
Dynamics of active particles can be implemented either through microscopic rules as in[8,9]or in a long-wavelength phenomenological approach as in[5]It is important to understand how the two methods are related. The purely phenomenological approach introduces the simplest possible (and generally additive)noise consistent with conservation laws and symmetries. Deriving the long-wavelength equation by explicit coarse-graining of the microscopic rule will in general give additive and multiplicative noise terms, as seen in e.g., in [10]. We carry out such a derivation and obtain coupled fluctuating hydrodynamic equations for the orientational order parameter (polar as well as apolar) and density fields. The nonequilibrium “curvature-induced” current term postulated on symmetry grounds in[5]emerges naturally from this approach. In addition, we find a multiplicative contribution to the noise whose presence should be of importance during coarsening[11].
We studied nonequilibrium phenomena in detail by solving stochastic partial differential equations for apolar objects as obtained from microscopic rules in[8]. As a result of “curvature-induced” currents, the growth of nematic order from an initially isotropic, homogeneous state is shown to be accompanied by a remarkable clumping of the number density around topological defects. The consequent coarsening of both density and nematic order are characterised by cusps in the short-distance behaviour of the correlation functions, a breakdown of Porod’s Law. We identify the origins of this breakdown; in particular, the nature of the noise terms in the equations of motion is shown to play a key role[12].
Lastly we studied an active nematic steady-state, in two space dimensions, keeping track of only the orientational order parameter, and not the density. We apply the Dynamic Renormalization Group to the equations of motion of the order parameter. Our aim is to check whether certain characteristic nonlinearities entering these equations lead to singular renormalizations of the director stiffness coefficients, which would stabilize true long-range order in a two-dimensional active nematic, unlike in its thermal equilibrium counterpart. The nonlinearities are related to those in[13]but free of a constraint that applies at thermal equilibrium. We explore, in particular, the intriguing but ultimately deceptive similarity between a limiting case of our model and the fluctuating Burgers/KPZequation. By contrast with that case, we find that the nonlinearities are marginally irrelevant. This implies in particular that 2-dactive nematics too have only quasi-long-range order[14].
34
Mishra, Shradha. "Dynamics, Order And Fluctuations In Active Nematics : Numerical And Theoretical Studies." Thesis, 2008. http://hdl.handle.net/2005/832.
Full textAbstract:
In this thesis we studied theoretically and numerically dynamics, order and fluctuations in two dimensional active matter with specific reference to the nematic phase in collections of self-driven particles.The aim is to study the ways in which a nonequilibrium steady state with nematic order differs from a thermal equilibrium system of the same spatial symmetry. The models we study are closely related to “flocking”[1], as well as to equations written down to describe the interaction of molecular motors and filaments in a living cell[2,3] and granular nematics [4]. We look at (i) orientational and density fluctuations in the ordered phase, (ii) the way in which density fluctuations evolve in a nematic background, and finally (iii) the coarsening of nematic order and the density field starting from a statistically homogeneous and isotropic initial state. Our work establishes several striking differences between active nematics and their thermal equilibrium counterparts.
We studied two-dimensional nonequilibrium active nematics. Two-dimensional nonequilibrium nematic steady states, as found in agitated granular-rod monolayers or films of orientable amoeboid cells, were predicted [5] to have giant number fluctuations, with the standard deviation proportional to the mean. We studied this problem more closely, asking in particular whether the active nematic steady state is intrinsically phase-separated. Our work has close analogy to the work of Das and Barma[6] on particles sliding downhill on fluctuating surfaces, so we looked at a model in which particles were advected passively by the broken-symmetry modes of a nematic, via a rule proposed in [5]. We found that an initially homogeneous distribution of particles on a well-ordered nematic background clumped spontaneously, with domains growing as t1/2, and an apparently finite phase-separation order parameter in the limit of large system size. The density correlation function shows a cusp, indicating that Porod’s Law does not hold here and that the phase-separation is fluctuation-dominated[7].
Dynamics of active particles can be implemented either through microscopic rules as in[8,9]or in a long-wavelength phenomenological approach as in[5]It is important to understand how the two methods are related. The purely phenomenological approach introduces the simplest possible (and generally additive)noise consistent with conservation laws and symmetries. Deriving the long-wavelength equation by explicit coarse-graining of the microscopic rule will in general give additive and multiplicative noise terms, as seen in e.g., in [10]. We carry out such a derivation and obtain coupled fluctuating hydrodynamic equations for the orientational order parameter (polar as well as apolar) and density fields. The nonequilibrium “curvature-induced” current term postulated on symmetry grounds in[5]emerges naturally from this approach. In addition, we find a multiplicative contribution to the noise whose presence should be of importance during coarsening[11].
We studied nonequilibrium phenomena in detail by solving stochastic partial differential equations for apolar objects as obtained from microscopic rules in[8]. As a result of “curvature-induced” currents, the growth of nematic order from an initially isotropic, homogeneous state is shown to be accompanied by a remarkable clumping of the number density around topological defects. The consequent coarsening of both density and nematic order are characterised by cusps in the short-distance behaviour of the correlation functions, a breakdown of Porod’s Law. We identify the origins of this breakdown; in particular, the nature of the noise terms in the equations of motion is shown to play a key role[12].
Lastly we studied an active nematic steady-state, in two space dimensions, keeping track of only the orientational order parameter, and not the density. We apply the Dynamic Renormalization Group to the equations of motion of the order parameter. Our aim is to check whether certain characteristic nonlinearities entering these equations lead to singular renormalizations of the director stiffness coefficients, which would stabilize true long-range order in a two-dimensional active nematic, unlike in its thermal equilibrium counterpart. The nonlinearities are related to those in[13]but free of a constraint that applies at thermal equilibrium. We explore, in particular, the intriguing but ultimately deceptive similarity between a limiting case of our model and the fluctuating Burgers/KPZequation. By contrast with that case, we find that the nonlinearities are marginally irrelevant. This implies in particular that 2-dactive nematics too have only quasi-long-range order[14].
35
Falasco, Gianmaria. "Four out-of-equilibrium lectures." Doctoral thesis, 2017. https://ul.qucosa.de/id/qucosa%3A15937.
Full text
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Narayan, Vijay. "Phase Behaviour & Dynamics Of An Agitated Monolayer Of Granular Rods." Thesis, 2008. https://etd.iisc.ac.in/handle/2005/898.
Full textAbstract:
In this thesis we have explored the no equilibrium phase behavior and dynamics of an agitated monolayer of macroscopic rod-like particles. The main objective of this thesis was to highlight the ways in which even the simplest nonequilibrium 2Dliquid-crystallinen system differs qualitatively from its thermal equilibrium counter part.
One major finding of ours is the extreme sensitivity to shape in these nonequilibrium systems. In chapter 3 we saw that tapering the ends of the particles induced a change from 2–fold ordering to 4–fold ordering. As far as we know, this is the first experimental observation of ‘tetratic’ correlations in equilibrium or nonequilibrium settings. This shape dependence is also pronounced in the single particle dynamics where, in chapter 5, we saw that similar-shaped objects behave differently even if they have dissimilar aspect ratios.
Another important finding of ours is that the density fluctuations in the nonequilibrium nematic are not merely larger than, but qualitatively different from, those seen in their equilibrium counterparts: the fluctuations of the population, in a region containing on average N particles, grow much faster than √N . Then on equilibrium nature of the systems we study is clearly visible even at the single-particle level where we observe violations of equipartition in all the particles we study.
The anomalous fluctuations we observe can be under stood in the light of theories of flocking. We have motivated why our system can be thought of as a granular flock and in chapter 4 presented various quantitative observations that justify this claim: we see giant fluctuations that decay only logarithmically in time as predicted by a theory of active nematics. This supports the idea that granular systems can provide a faithful imitation of the collective dynamics of living flocks, thus offering an attractive and easily control able system on which to test the predictions of flocking theories. A part from being a table-top experiment, , our system has the two substantial advantages over living systems that there are no products of metabolism which need removing and that the population remains constant. Our work highlights the fact that the fascinating phenomena of flocking ,coherent motion and large-scale in homogeneity seen in living matter can be obtained in a system in which particles do not communicate except by contact, have no sensing mechanisms and are not influenced by the spatially-varying pressures and incentives of a biological environment.
Directions to go from here are aplenty. There is a lot that needs to be done towards understanding the origins of the anomalous fluctuations: do they arise due to the coupling of mass currents to gradients in the nematic director field or is there some other mechanism at play? Though the observed motion of disclinations suggests the former, a thorough hand systematic study of defect behavior is lacking. How defects interact and whether there is any analogy to thermal-equilibrium defect-behavior is completely unexplored, theoretically and experimentally. Indeed, this would be of interest purely as a problem in nonequilibrium statistical mechanics independent of whether or not the system is described by theories of active nematics.
A part from settling the important, fundamental issues regarding the giant fluctuations, one can explore the entire spectrum of rod-like particles and study its dynamics and phase behaviour. What happens to collections of javelins that are agitated in 2D geometries?
Do they form steadily-moving flocks? What about the short cylinders? We have seen that in the dilute limit they behave in a polar fashion but at high area fractions they form a polar, 4–fold correlated states. At Intermediate densities will they form a polar phase? Why is it that the long cylinders do not show any polar dynamics? What factors govern whether a particle is polar or not? Can one engineer particles to efficiently translate random impulses in to directed motion?
Thus, even the single particle dynamics offers many avenues for experimental exploration. However, there is also scope for theoretical work in this direction. A sound theoretical understanding of the individual particle’s behaviour will then pave the way for a microscopic theory for the collective granular-rod state.. This can then be compared to the active and flocking literature which his, largely, of a phenomenological nature as of now.
In conclusion, we would like to say that our experiments have revealed many important and fascinating nonequilibrium phenomena. Our experiments demonstrate situations where ‘effective equilibrium’ approaches are in adequate. Such descriptions can accommodate neither the slow, giant, collective fluctuations we observe nor the non-equipartition at the single-particle level. Finally, as is often the case, our studies have thrown open many more questions than they have answered. We hope our experiments stimulate further studies and we believe that we are witnessing the birth of a new subfield at the crossroads of granular physics and the physics of flocks.
37
Narayan, Vijay. "Phase Behaviour & Dynamics Of An Agitated Monolayer Of Granular Rods." Thesis, 2008. http://hdl.handle.net/2005/898.
Full textAbstract:
In this thesis we have explored the no equilibrium phase behavior and dynamics of an agitated monolayer of macroscopic rod-like particles. The main objective of this thesis was to highlight the ways in which even the simplest nonequilibrium 2Dliquid-crystallinen system differs qualitatively from its thermal equilibrium counter part.
One major finding of ours is the extreme sensitivity to shape in these nonequilibrium systems. In chapter 3 we saw that tapering the ends of the particles induced a change from 2–fold ordering to 4–fold ordering. As far as we know, this is the first experimental observation of ‘tetratic’ correlations in equilibrium or nonequilibrium settings. This shape dependence is also pronounced in the single particle dynamics where, in chapter 5, we saw that similar-shaped objects behave differently even if they have dissimilar aspect ratios.
Another important finding of ours is that the density fluctuations in the nonequilibrium nematic are not merely larger than, but qualitatively different from, those seen in their equilibrium counterparts: the fluctuations of the population, in a region containing on average N particles, grow much faster than √N . Then on equilibrium nature of the systems we study is clearly visible even at the single-particle level where we observe violations of equipartition in all the particles we study.
The anomalous fluctuations we observe can be under stood in the light of theories of flocking. We have motivated why our system can be thought of as a granular flock and in chapter 4 presented various quantitative observations that justify this claim: we see giant fluctuations that decay only logarithmically in time as predicted by a theory of active nematics. This supports the idea that granular systems can provide a faithful imitation of the collective dynamics of living flocks, thus offering an attractive and easily control able system on which to test the predictions of flocking theories. A part from being a table-top experiment, , our system has the two substantial advantages over living systems that there are no products of metabolism which need removing and that the population remains constant. Our work highlights the fact that the fascinating phenomena of flocking ,coherent motion and large-scale in homogeneity seen in living matter can be obtained in a system in which particles do not communicate except by contact, have no sensing mechanisms and are not influenced by the spatially-varying pressures and incentives of a biological environment.
Directions to go from here are aplenty. There is a lot that needs to be done towards understanding the origins of the anomalous fluctuations: do they arise due to the coupling of mass currents to gradients in the nematic director field or is there some other mechanism at play? Though the observed motion of disclinations suggests the former, a thorough hand systematic study of defect behavior is lacking. How defects interact and whether there is any analogy to thermal-equilibrium defect-behavior is completely unexplored, theoretically and experimentally. Indeed, this would be of interest purely as a problem in nonequilibrium statistical mechanics independent of whether or not the system is described by theories of active nematics.
A part from settling the important, fundamental issues regarding the giant fluctuations, one can explore the entire spectrum of rod-like particles and study its dynamics and phase behaviour. What happens to collections of javelins that are agitated in 2D geometries?
Do they form steadily-moving flocks? What about the short cylinders? We have seen that in the dilute limit they behave in a polar fashion but at high area fractions they form a polar, 4–fold correlated states. At Intermediate densities will they form a polar phase? Why is it that the long cylinders do not show any polar dynamics? What factors govern whether a particle is polar or not? Can one engineer particles to efficiently translate random impulses in to directed motion?
Thus, even the single particle dynamics offers many avenues for experimental exploration. However, there is also scope for theoretical work in this direction. A sound theoretical understanding of the individual particle’s behaviour will then pave the way for a microscopic theory for the collective granular-rod state.. This can then be compared to the active and flocking literature which his, largely, of a phenomenological nature as of now.
In conclusion, we would like to say that our experiments have revealed many important and fascinating nonequilibrium phenomena. Our experiments demonstrate situations where ‘effective equilibrium’ approaches are in adequate. Such descriptions can accommodate neither the slow, giant, collective fluctuations we observe nor the non-equipartition at the single-particle level. Finally, as is often the case, our studies have thrown open many more questions than they have answered. We hope our experiments stimulate further studies and we believe that we are witnessing the birth of a new subfield at the crossroads of granular physics and the physics of flocks.
38
Soni, Harsh. "Flocks, Flow and Fluctuations in Inanimate Matter : Simulations and Theory." Thesis, 2015. https://etd.iisc.ac.in/handle/2005/4229.
Full textAbstract:
In this thesis we study a novel soft-matter system that imitates motility. Our system consists of a few asymmetrically tapered brass rods and aluminium beads which are confined between two vertically shaking plates. The rods are motile due to interplay of their the fore-aft asymmetric shape, vibrational energy input, and the mechanics of contact with the bounding surfaces. Experiments done by our col-
laborators revealed that the system undergoes a phase transition from a disordered state to an ordered coherently moving flock above a critical bead concentration. We have used time-driven numerical simulations and analytical theory to understand
the physics underlying the phenomenon.
39
Zangara, Pablo René. "El eco de Loschmidt en sistemas de espines: decoherencia, equilibración, localización y mecanismos emergentes de irreversibilidad." Doctoral thesis, 2015. http://hdl.handle.net/11086/2765.
Full textAbstract:
Tesis (Doctor en Física)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2016.Los fenómenos irreversibles son omnipresentes en la naturaleza. En el mundo microscópico, por ejemplo, un exceso de polarización magnética difunde en un sistema de espines interactuantes hasta desparramarse completamente. En esta Tesis estudiamos la dinámica de tal proceso para sistemas abiertos y cerrados. El primer caso corresponde al fenómeno de decoherencia inducida por un ambiente externo, mientras que el segundo engloba dos fenómenos opuestos que pueden ocurrir en sistemas cerrados: la equilibración de observables y la localización de muchos cuerpos. Utilizamos como testigo dinámico al eco de Loschmidt, una magnitud que se define a partir de una reversión temporal imperfecta y que puede evaluarse experimentalmente en resonancia magnética nuclear. Estudiando tal eco y sus escalas de tiempo características, identificamos los mecanismos emergentes que rigen la irreversibilidad en el límite termodinámico.
Irreversible phenomena are ubiquitous in Nature. In the microscopic world, for example, an excess of magnetic polarization diffuses in a system of interacting spins until it spreads all over. In this Thesis we study the dynamics of such a process for open and closed systems. The first case corresponds to the phenomenon of decoherence induced by an external environment, while the second comprises two opposite phenomena that can occur in closed systems: the equilibration of observables and the many-body localization. We use a spin autocorrelation function, the Loschmidt echo, as our main dynamical witness. This magnitude is defined by means of an imperfect time reversal procedure and it can be experimentally evaluated in nuclear magnetic resonance. Studying the Loschmidt echo and its characteristic time scales, leads us to identify the emergent mechanisms governing the irreversibility in the thermodynamic limit.
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Steinigeweg, Robin. "Application of Projection Operator Techniques to Transport Investigations in Closed Quantum Systems." Doctoral thesis, 2008. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2008082910.
Full textAbstract:
The work at hand presents a novel approach to transport in closed quantum systems. To this end a method is introduced which is essentially based on projection operator techniques, in particular on the time-convolutionless (TCL) technique. The projection onto local densities of quantities such as energy, magnetization, particles, etc. yields the reduced dynamics of the respective quantities in terms of a systematic perturbation expansion. Especially, the lowest order contribution of this expansion is used as a strategy for the analysis of transport in "modular" quantum systems. The term modular basically corresponds to (quasi-) one-dimensional structures consisting of identical or at least similar many-level subunits. Modular quantum systems are demonstrated to represent many physical situations and several examples are given. In the context of these quantum systems lowest order TCL is shown as an efficient tool which also allows to investigate the dependence of transport on the considered length scale. In addition an estimation for the validity range of lowest order TCL is derived. As a first application a "design" model is considered for which a complete characterization of all available transport types as well as the transitions to each other is possible. For this model the relationship to quantum chaos and the validity of the Kubo formula is further discussed. As an example for a "real" system the Anderson model is finally analyzed. The results are partially verified by the numerical solution of the full time-dependent Schroedinger equation which is obtained by exact diagonalization or approximative integrators.