Dissertations / Theses: 'Statistical mechanics in chemistry'

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Matek, Christian C. A. "Statistical mechanics of nucleic acids under mechanical stress." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:ce44cf50-2001-4f54-8e57-d1757f709fd6.

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In this thesis, the response of DNA and RNA to linear and torsional mechanical stress is studied using coarse-grained models. Inspired by single-molecule assays developed over the last two decades, the end-to-end extension, buckling and torque response behaviour of the stressed molecules is probed under conditions similar to experimentally used setups. Direct comparison with experimental data yields excellent agreement for many conditions. Results from coarse-grained simulations are also compared to the predictions of continuum models of linear polymer elasticity. A state diagram for supercoiled DNA as a function of twist and tension is determined. A novel confomational state of mechanically stressed DNA is proposed, consisting of a plectonemic structure with a denaturation bubble localized in its end-loop. The interconversion between this novel state and other, known structural motifs of supercoiled DNA is studied in detail. In particular, the influence of sequence properties on the novel state is investigated. Several possible implications for supercoiled DNA structures in vivo are discussed. Furthermore, the dynamical consequences of coupled denaturation and writhing are studied, and used to explain observations from recent single molecule experiments of DNA strand dynamics. Finally, the denaturation behaviour, topology and dynamics of short DNA minicircles is studies using coarse-grained simulations. Long-range interactions in the denaturation behaviour of the system are observed. These are induced by the topology of the system, and are consistent with results from recent molecular imaging studies. The results from coarse-grained simulations are related to modelling of the same system in all-atom simulations and a local denaturation model of DNA, yielding insight into the applicability of these different modelling approaches to study different processes in nucleic acids.

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Farhat, Hikmat. "Studies in computational methods for statistical mechanics of fluids." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape10/PQDD_0026/NQ50157.pdf.

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Rah, Kyun-Il. "Statistical mechanics and the viscosity of simple and molecular liquids." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0029/NQ64653.pdf.

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Hu, Zhonghan. "Transport properties, optical response and slow dynamics of ionic liquids." Diss., University of Iowa, 2007. http://ir.uiowa.edu/etd/160.

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Apte, Pankaj A. "Phase equilibria and nucleation in condensed phases a statistical mechanical study /." Columbus, Ohio : Ohio State University, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1135876018.

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Swaminathan, Narasimhan. "Stress-defect transport interactions in ionic solids." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/28273.

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Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2009.
Committee Chair: Qu, Jianmin; Committee Member: Kohl,Paul A.; Committee Member: Liu, Meilin; Committee Member: McDowell, David L.; Committee Member: Zhu, Ting.

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Ochs, Leonard Ryder. "A statistical mechanical non-lattice coordination theory to describe the solution thermodynamics of polymer mixtures." Diss., The University of Arizona, 1993. http://hdl.handle.net/10150/186340.

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A theoretical model has been developed to advance the study of the thermodynamics of highly concentrated binary polymer solutions. This statistical mechanical theory was developed to allow the modeling of the molar Gibbs and Helmholtz free energies of mixing as well as the standard derived functions, such as the solvent and solute activities, and the molar enthalpies and entropies of mixing. Three major results have been generated from this work: (1) The polymer/solvent interactions can be partitioned into a coordination term, which leads to a configurational entropy, and an interaction energy of mixing term, which leads to the standard enthalpy of mixing; (2) The temperature dependence of the enthalpy of mixing yields an interaction energy of mixing which incorporates an additional entropy of mixing which is present for all types of systems, even athermal mixtures; and (3) The theory enables the use of experimentally obtained enthalpies of mixing to be used directly in the prediction of solvent activities, and experimentally determined solvent activities to be used as a predictor of the enthalpies of mixing without differentiating the experimental data. The theory was tested on fifteen binary systems. These systems had a range of physical property characteristics, from mixtures which can be considered almost ideal, to highly non-ideal athermal polymer solutions, to aqueous polymer solutions. The studied systems were; benzene/cyclopentane, benzene/cyclohexane, benzene/biphenyl, benzene/diphenylmethane, benzene/1,2-diphenylethane, cyclohexane/bicyclohexyl, n-hexane/n-hexadecane, toluene/polystyrene, chloroform/polystyrene, methylethylketone/polystyrene, cyclohexane/polystyrene, benzene/polypropylene glycol, benzene/polyethylene glycol, water/glucose, and water/polyethylene glycol. Parameters for each of these systems and components are tabulated. The experimental solvent activity data are graphed with the regression lines, and the experimental enthalpy of mixing data are graphed with the curves predicted from the solvent activity parameters. The average relative error of fit for the regression of the solvent activity data up to a polymer volume fraction of about 0.85 is less than ±0.0035, while for the entire solvent activity data set it is ±0.025. The average relative error of fit for the molar enthalpy of mixing predictions (excluding the water/PEG data) is less than ±0.005.

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Pham, Tony. "Theoretical Investigations of Gas Sorption and Separation in Metal-Organic Materials." Scholar Commons, 2015. http://scholarcommons.usf.edu/etd/5759.

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Metal--organic frameworks (MOFs) are porous crystalline materials that are synthesized from rigid organic ligands and metal-containing clusters. They are highly tunable as a number of different structures can be made by simply changing the organic ligand and/or metal ion. MOFs are a promising class of materials for many energy-related applications, including H2 storage and CO2 capture and sequestration. Computational studies can provide insights into MOFs and the mechanism of gas sorption and separation. Theoretical studies on existing MOFs are performed to determine what structural characteristics leads to favorable gas sorption mechanisms. The results from these studies can provide insights into designing new MOFs that are tailored for specific applications. In this work, grand canonical Monte Carlo (GCMC) simulations were performed in various MOFs to understand the gas sorption mechanisms and identify the favorable sorption sites in the respective materials. Experimental observables such as sorption isotherms and associated isosteric heat of adsorption, Qst, values can be generated using this method. Outstanding agreement with experimental measurements engenders confidence in a variety of molecular level predictions. Explicit many-body polarization effects were shown to be important for the modeling of gas sorption in highly charged/polar MOFs that contain open-metal sites. Indeed, this was demonstrated through a series of simulation studies in various MOFs with rht topology that contain such sites. Specifically, the inclusion of many-body polarization interactions was essential to reproduce the experimentally observed sorption isotherms and Qst values and capture the binding of sorbate molecules onto the open-metal sites in these MOFs. This work also presents computational studies on a family of pillared square grid that are water-stable and display high CO2 sorption and selectivity. These MOFs are deemed promising for industrial applications and CO2 separations. Simulations in these materials revealed favorable interactions between the CO2 molecules and the SiF62- pillars. Further, the compound with the smallest pore size exhibits the highest selectivity for CO2 as demonstrated through both experimental and theoretical studies. Many other MOFs with intriguing sorption properties are investigated in this work and their sorption mechanisms have been discerned through molecular simulation.

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Llano, Jorge. "Modern Computational Physical Chemistry : An Introduction to Biomolecular Radiation Damage and Phototoxicity." Doctoral thesis, Uppsala University, Department of Cell and Molecular Biology, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4224.

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The realm of molecular physical chemistry ranges from the structure of matter and the fundamental atomic and molecular interactions to the macroscopic properties and processes arising from the average microscopic behaviour.

Herein, the conventional electrodic problem is recast into the simpler molecular problem of finding the electrochemical, real chemical, and chemical potentials of the species involved in redox half-reactions. This molecular approach is followed to define the three types of absolute chemical potentials of species in solution and to estimate their standard values. This is achieved by applying the scaling laws of statistical mechanics to the collective behaviour of atoms and molecules, whose motion, interactions, and properties are described by first principles quantum chemistry. For atomic and molecular species, calculation of these quantities is within the computational implementations of wave function, density functional, and self-consistent reaction field theories. Since electrons and nuclei are the elementary particles in the realm of chemistry, an internally consistent set of absolute standard values within chemical accuracy is supplied for all three chemical potentials of electrons and protons in aqueous solution. As a result, problems in referencing chemical data are circumvented, and a uniform thermochemical treatment of electron, proton, and proton-coupled electron transfer reactions in solution is enabled.

The formalism is applied to the primary and secondary radiation damage to DNA bases, e.g., absorption of UV light to yield electronically excited states, formation of radical ions, and transformation of nucleobases into mutagenic lesions as OH radical adducts and 8-oxoguanine. Based on serine phosphate as a model compound, some insight into the direct DNA strand break mechanism is given.

Psoralens, also called furocoumarins, are a family of sensitizers exhibiting cytostatic and photodynamic actions, and hence, they are used in photochemotherapy. Molecular design of more efficient photosensitizers can contribute to enhance the photophysical and photochemical properties of psoralens and to reduce the phototoxic reactions. The mechanisms of photosensitization of furocoumarins connected to their dark toxicity are examined quantum chemically.

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Siretskiy, Alexey. "Monte Carlo Simulations of the Equilibrium Properties of Semi-stiff Polymer Chains : Efficient Sampling from Compact to Extended Structures." Doctoral thesis, Uppsala universitet, Fysikalisk kemi, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-151618.

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Polymers is a class of molecules which can have many different structures due to a large number of degrees of freedom. Many biopolymers, e.g. DNA, but also synthetic macromolecules have special structural features due to their backbone stiffness. Since such structural properties are important for e.g. the biological function, a lot of effort has been put into the investigation of the configurational properties of semi-stiff molecules. A theoretical treatment of these systems is often accompanied by computer simulations. The main idea is to compare theoretically derived models with experimental results for real polymers. Using Monte Carlo simulations, I have investigated how this computational technique can build a bridge between theoretical models and experimentally observed phenomena. The effort was mainly directed to develop sampling techniques, for efficiently exploring the configurational space of semi-stiff chains in a wide range of structures. The work was concentrated on compact conformations, since they, as is well known from previous studies, are difficult to sample using conventional methods. In my studies I have shown that the simple and, at a first glance, time consuming method of bead-by-bead regrow as a way of changing the configuration of a semi-stiff chain gave very promising and encouraging results when combined with modern simulation techniques, like Entropic Sampling with the Wang-Landau algorithm. The resulting simulation package was also suitable for parallelization which resulted in a further speed-up of the calculations. In addition to the more elaborate sampling methods, I also investigated external conditions to induce compaction of a semi-stiff polymer. In the case of a polyampholyte the condensing agent could be a multivalent salt, creating effective attraction between the loops of the chain, while for neutral polymers, an external field and the geometry of the confining volume can induce a compaction.

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Knight, Christopher J. "Hydrogen bond topology order/disorder transitions in ice and the behavior of defects in a disordered ice lattice /." Columbus, Ohio : Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1236788109.

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Cui, Wenping. "Statistical Mechanics of Microbiomes:." Thesis, Boston College, 2021. http://hdl.handle.net/2345/bc-ir:109135.

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Thesis advisor: Pankaj Mehta
Thesis advisor: Ziqiang Wang
Nature has revealed an astounding degree of phylogenetic and physiological diversity in natural environments -- especially in the microbial world. Microbial communities are incredibly diverse, ranging from 500-1000 species in human guts to over 1000 species in marine ecosystems. Historically, theoretical ecologists have devoted considerable effort to analyzing ecosystems consisting of a few species. However, analytical approaches and theoretical insights derived from small ecosystems consisting of a few species may not scale up to diverse ecosystems. Understanding such large complex ecosystems poses fundamental challenges to current theories and analytical approaches for modeling and understanding the microbial world. One promising approach for tackling this challenge that I develop in my thesis is to adapt and expand ideas from statistical mechanics to theoretical ecology. Statistical mechanics has helped us to understand how collective behaviors emerge from the interaction of many individual components. In this thesis, I present a unified theoretical framework for understanding complex ecosystems based on statistical mechanics, random matrix theories, and convex optimization. My thesis work has three key aspects: modeling, simulations, and theories. Modeling: Classical ecological models often focus on predator-prey relationships. However, this is not the norm in the microbial world. Unlike most macroscopic organisms, microbes relie on consuming and producing small organic molecules for energy and reproduction. In this thesis, we develop a new Microbial Consumer Resource Model that takes into account these types of metabolic cross-feeding interactions. We demonstrate that this model can qualitatively reproduce and explain statistical patterns observed in large survey data, including Earth Microbiome Project and the Human Microbiome Project. Simulations: Computational simulations are essential in theoretical ecology. Complex ecological models often involve ordinary differential equations (ODE) containing hundreds to thousands of interacting variables. Typical ODE solvers are based on numerical integration methods, which are both time and resource intensive. To overcome this bottleneck, we derived a surprising duality between constrained convex optimization and generalized consumer-resource models describing ecological dynamics. This allows us to develop a fast algorithm to solve the steady-state of complex ecological models. This improves computational performance by between 2-3 orders of magnitude compared to direct numerical integration of the corresponding ODEs. Theories:Few theoretical approaches allow for the analytic study of communities containing a large number of species. Recently, there has been considerable interest in the idea that ecosystems can be thought of as a type of disordered systems. This mapping suggests that understanding community coexistence patterns is actually a problem in "spin-glass'' physics. This has motivated physicists to use insights from spin glass theory to uncover the universal features of complex ecosystems. In this thesis, I use and extend the cavity method, originally developed in spin glass theories, to answer fundamental ecological questions regarding the stability, diversity, and robustness of ecosystems. I use the cavity method to derive new species backing bounds and uncover novel phase transitions to typicality
Thesis (PhD) — Boston College, 2021
Submitted to: Boston College. Graduate School of Arts and Sciences
Discipline: Physics

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Grigo, Alexander. "Billiards and statistical mechanics." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29610.

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Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2009.
Committee Chair: Bunimovich, Leonid; Committee Member: Bonetto, Federico; Committee Member: Chow, Shui-Nee; Committee Member: Cvitanovic, Predrag; Committee Member: Weiss, Howard. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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Gaspard, Pierre. "Chaos, scattering and statistical mechanics." Doctoral thesis, Universite Libre de Bruxelles, 1996. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/212440.

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Oakeshott, Robert Bernard Simon. "The statistical mechanics of powders." Thesis, University of Cambridge, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.359838.

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Gillin, Peter. "Statistical mechanics of multispin glasses." Thesis, University of Oxford, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.393228.

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Rau, Albrecht. "Statistical mechanics of neural networks." Thesis, University of Oxford, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.306030.

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Corbett, D. "Statistical mechanics of photo-elastomers." Thesis, University of Cambridge, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.597994.

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Liquid Crystalline Elastomers (LCE) are unusual materials. As suggested by their name they inhabit the grey area between liquids and solids. They have many remarkable properties. This dissertation is concerned with the equilibrium statistical mechanics of dye doped LCE films. We propose a free energy to describe the destabilising effects of illumination on the underlying nematic order and combine this with the phantom chain model for the elastic free energy of elastomeric films in order to calculate the equilibrium mechanical response. We consider thin polydomain films, and describe the effects of illuminating them with both polarised and unpolarised light. In both cases we predict that the mechanical response is a non-monotonic function of the incident intensity, which should allow a rich set of deformation modes when thicker samples are illuminated. The underlying mechanisms leading to the mechanical response are the optically induced reorientation of the nematic ordering direction and the associated changes in the order parameters. We investigate these changes in some detail and in chapter 4 we predict the results of Nuclear Magnetic Resonance (NMR) experiments designed to detect them. In chapter 5 we consider the stress generated by films which are rigidly clamped, in this case mechanical relaxation is not possible. Director reorientation and order parameter reduction are still important in determining the stress response. We predict that the stress is a non-monotonic function of the incident intensity, in much the same way as the mechanical response. In the same chapter we also consider the mechanical response of a doped cholesteric film when illuminated with unpolarised light. We predict that the deformation in this case can be extremely large.

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Whyte, William John. "Statistical mechanics of neural networks." Thesis, University of Oxford, 1995. http://ora.ox.ac.uk/objects/uuid:e17f9b27-58ac-41ad-8722-cfab75139d9a.

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We investigate five different problems in the field of the statistical mechanics of neural networks. The first three problems involve attractor neural networks that optimise particular cost functions for storage of static memories as attractors of the neural dynamics. We study the effects of replica symmetry breaking (RSB) and attempt to find algorithms that will produce the optimal network if error-free storage is impossible. For the Gardner-Derrida network we show that full RSB is necessary for an exact solution everywhere above saturation. We also show that, no matter what the cost function that is optimised, if the distribution of stabilities has a gap then the Parisi replica ansatz that has been made is unstable. For the noise-optimal network we find a continuous transition to replica symmetry breaking at the AT line, in line with previous studies of RSB for different networks. The change to RSBl improves the agreement between "experimental" and theoretical calculations of the local stability distribution ρ(λ) significantly. The effect on observables is smaller. We show that if the network is presented with a training set which has been generated from a set of prototypes by some noisy rule, but neither the noise level nor the prototypes are known, then the perceptron algorithm is the best initial choice to produce a network that will generalise well. If additional information is available more sophisticated algorithms will be faster and give a smaller generalisation error. The remaining problems deal with attractor neural networks with separable interaction matrices which can be used (under parallel dynamics) to store sequences of patterns without the need for time delays. We look at the effects of correlations on a singlesequence network, and numerically investigate the storage capacity of a network storing an extensive number of patterns in such sequences. When correlations are implemented along with a term in the interaction matrix designed to suppress some of the effects of those correlations, the competition between the two produces a rich range of behaviour. Contrary to expectations, increasing the correlations and the operating temperature proves capable of improving the sequenceprocessing behaviour of the network. Finally, we demonstrate that a network storing a large number of sequences of patterns using a Hebb-like rule can store approximately twice as many patterns as the network trained with the Hebb rule to store individual patterns.

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McCabe, Clare. "Statistical mechanics of chain molecules." Thesis, University of Sheffield, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.287724.

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Wang, Xin-Jiu. "Statistical mechanics of nematic polymers." Thesis, Open University, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.293371.

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In this work I model the liquid crystal polymers as worms and explore the Spheroidal approach to examine their statistical mechanics. Several models are presented in this work to describe main chain-, side chain-polymers, polymer networks and gels in their nematic state. In the case of main chain nematic polymers, the worm flexibility, favouring disorder, and the nematic potential, tending to align segments to be parallel to each other, compete to determine the properties of polymers. I predict the temperature dependence of order parameter and phase transition behaviour for different lengths of the polymers, and the dimensions as well. Subsequently, I examine the critical features of the nematic polymer when an electrical field is applied. Side chain polymers with semi-flexible backbone and stiff nematogenic pendants form interesting nematic phases, largely as a consequence of competition between backbone entropy and pendant order. I classify them into three categories: NI, NII, and NIII phase, according to volume fractions, temperature, nematic coupling constants, and stiffness. In these phases the backbone and pendants have orders different in magnitude and/or in sign in order to achieve a stable state. Phase diagrams are given. In addition, I predict unusual properties such as anomalous temperature variation of optical anisotropy and molecular conformational changes. Crosslinks confine polymer chains in a network so that their strands have a shape different from their natural ones. Such constraints shift phase transition temperature. The other effect is that crosslinks give the system rubber elasticity. Combining rubber elasticity with liquid crystal features, networks exhibit unusual phenomena, such as discontinuous stress-strain relations, spontaneous shape changes, non-linear stress-optical laws and deviations from classical behaviour of conventional elastomers. It is proposed that residual nematic interaction is responsible for deviations found in classical elastomers. The nematic networks swollen by isotropic solvent form nematic gels. At low temperatures a nematic gel coexists with excess solvent, at high temperatures the coexisting gel is isotropic. In addition, coexistence is predicted between nematic and isotropic gels. There is an associated triple point. There are possible elastic problems associated with different phases coexisting in one gel sample. Main chain nematic polymers have been modelled either as homogeneous worms, or as jointed rods by others. In reality the polymers are composed of the mesogens linked by semi-flexible spacers. One must expect that the spacers have an order differing from the mesogens. The consecutive mesogens are not decoupled and the spacers are able to talk to each other via the mesogens in between. The model presented takes account of molecular parameters, such as length of the mesogen and spacer, and their interactions. The nematic order of the two components, the nematic-isotropic transition, and dimensions of the polymers are addressed. Finally, I examine both worm and jointed rod models, to see when each is applicable. Accordingly an elastically jointed rod model is presented. Hairpins, found naturally in the worm problem, also exist for jointed systems but their scaling is quite different. Comparisons of these results with experiments are accordingly made and are found to be satisfactory.

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Morgado, Welles A. M. (Welles Antonio Martinez). "Statistical mechanics of granular systems." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/42631.

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Grinev, Dmitri. "Statistical mechanics of granular materials." Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621514.

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Venegas-Ortiz, Juan. "Statistical mechanics of gene competition." Thesis, University of Edinburgh, 2013. http://hdl.handle.net/1842/9372.

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Statistical mechanics has been applied to a wide range of systems in physics, biology, medicine and even anthropology. This theory has been recently used to model the complex biochemical processes of gene expression and regulation. In particular, genetic networks offer a large number of interesting phenomena, such as multistability and oscillatory behaviour, that can be modelled with statistical mechanics tools. In the first part of this thesis we introduce gene regulation, genetic switches, and the colonization of a spatially structured media. We also introduce statistical mechanics and some of its useful tools, such as the master equation and mean- field theories. We present simple examples that are both pedagogical and also set the basis for the study of more complicated scenarios. In the second part we consider the exclusive genetic switch, a fundamental example of genetic networks. In this system, two proteins compete to regulate each other's dynamics. We characterize the switch by solving the stationary state in different limits of the protein binding and unbinding rates. We perform a study of the bistability of the system by examining its probability distribution, and by applying information theory techniques. We then present several versions of a mean field theory that offers further information about the switch. Finally, we compute the stationary probability distribution with an exact perturbative approach in the unbinding parameter, obtaining a valid result for a wide range of parameters values. The techniques used for this calculation are successfully applied to other switches. The topic studied in the third part of the thesis is the propagation of a trait inside an expanding population. This trait may represent resistance to an antibiotic or being infected with a certain virus. Although our model accounts for different examples in the genetic context, it is also very useful for the general study of a trait propagating in a population. We compute the speed of expansion and the stationary population densities for the invasion of an established and an expanding population, finding non-trivial criteria for speed selection and interesting speed transitions. The obtained formulae for the different wave speeds show excellent agreement with the results provided by simulations. Moreover, we are able to obtain the value of the speeds through a detailed analysis of the populations, and establish the requirements for our equations to present speed transitions. We finally apply our model to the propagation in a position-dependent fitness landscape. In this situation, the growth rate or the maximum concentration depends on the position. The amplitudes and speeds of the waves are again successfully predicted in every case.

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Rominger, Andrew Rominger. "The Statistical Mechanics of Biodiversity." Thesis, University of California, Berkeley, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10150924.

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Since at least the time of Darwin biologists have searched for a simple set of universal governing mechanisms that dictate the dynamics of biodiversity. While much progress has been made in understanding system-specific processes and in documenting the context-dependent roles of such mechanisms as competition and facilitation, we still lack a universal governing rule set. The goal of understanding and predicting biodiversity dynamics comes at a critical moment when human systems are disrupting those very dynamics. In this thesis I approach this long-standing problem with the hypothesis that general patterns in biodiversity emerge from a combination of the statistical mechanics of large systems and the unique non-equilibrium dynamics imparted to biological systems by their evolutionary history. Statistical mechanics provides the key analytical approaches to abstracting the complex details of biodiversity into general macroscopic predictions that I show receive support from empirical data. However, key deviations from the simplest statistical mechanics of biodiversity reveal the key role of biological evolution in driving systems away from the idealized steady state predicted by statistical mechanics.

In Chapter 1 I expand a branch of non-equilibrial statistical mechanics, known as super statistics, to explain previously unaccounted for wild fluctuations in the richness of taxa through the Phanerozoic marine invertebrate fossil record and show how this non-equilibrium is driven by clades' punctuated exploration of their adaptive landscapes. This theory provides a novel explanation for deep time diversity dynamics invoking emergence of lineage-level traits as the drivers of complexity via the same mechanisms by which complexity emerges in large physical and social systems. In the context of fossil diversity I show how this complexity arises naturally from the uniquely biological mechanisms of punctuated adaptive radiation followed by long durations of niche conservatism, and thus identify these mechanisms as sufficient and necessary to produce observed patterns in the fossil record. I test this theory using two seminal fossil datasets.

In Chapter 2 I use the chronosequence afforded by the Hawaiian Islands to capture evolutionary snapshots of arthropod communities at different ages and stages of assembly to understand how the history underlying an assemblage determine its contemporary biodiversity patterns. I apply static ecological theory of trophic networks based on statistical mechanics to these rapidly evolving ecosystems to highlight what about the evolutionary process drives communities away from statistical idealizations. This study indicates that rapid assembly from immigration and speciation in young ecosystems and extinction in old ecosystems could drive observed patterns.

In Chapter 3 I highlight and explain the computational requirements to testing one statistical theory of biodiversity—the Maximum Entropy Theory of Ecology—with real data and make those test available in a stream-lined framework via the R package meteR that I authored.

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Andrade, João Pedro Jericó de. "Statistical Mechanics of Economic Systems." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-03012017-104524/.

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In this thesis, we explore the potential of employing Statistical Mechanics techniques to study economic systems, showing how such an approach could greatly contribute by allowing the study of very complex systems, exhibiting rich behavior such as phase transitions, criticality and glassy phases, which are not found in the usual economic models. We exemplify this potential via three specific problems: (i) a Statistical Mechanics framework for dealing with irrational consumers, in which the rationality is set by a parameter akin to a temperature which controls deviations from the maximum of his utility function. We show that an irrational consumer increases the economic activity while decreasing his own utility; (ii) an analysis using Information Theory of real world Input-Output matrices, showing that the aggregation methods used to build them most likely underestimated the dependency of the production chain on a few crucial sectors, having important consequences for the analysis of these data; (iii) a zero intelligence model in which agents with a power law distributed initial wealth randomly trade goods of different prices. We show that this initial inequality generates a higher inequality in free cash, reducing the overall liquidity in the economy and slowing down the number of trades. We discuss the insights obtained with these three problems, along with their relevance for the larger picture in Economics.
Nesta tese, exploramos o potencial de ser usar técnicas de Mecânica Estatística para o estudo de sistemas econômicos, mostrando como tal abordagem pode contribuir significativamente ao permitir o estudo de sistemas complexos que exibem comportamentos ricos como transições de fase, criticalidade e fases vítreas, não encontradas normalmente em modelos econômicos tradicionais. Exemplificamos este potencial através de três problemas específicos: (i) um framework de Mecânica Estatística para lidar com consumidores irracionais, no qual a racionalidade é controlada pela temperatura do sistema, que define o tamanho dos desvios do estado de máxima utilidade. Mostramos que um consumidor irracional aumenta a atividade econômica ao mesmo tempo que diminui seu próprio bem estar; (ii) uma anáise usando Teoria da Informação de matrizes Input-Output de economias reais, mostrando que os métodos de agregação utilizados para construí-las provavelmente subestima a dependência das cadeias de produção em certos setores cruciais, com consequências importantes para a analíse destes dados; (iii) um modelo em que agentes com uma riqueza inicial distributida como lei de potências trocam aleatoriamente objetos com preços distintos. Mostramos que esta desigualdade inicial gera uma desigualdade ainda maior em dinheiro livre, reduzindo a liquidez total na economia e diminuindo a quantidade de trocas. Discutimos as consequências dos resultados destes três problemas, bem como sua relevância na perspectiva geral em Economia.

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Nasiev, Diar. "Statistical mechanics of distribution networks." Thesis, Aston University, 2009. http://publications.aston.ac.uk/15362/.

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We present a stability analysis against cascading failures. We propose a spin [binary] model, based on concepts of statistical mechanics. We test macroscopic properties of distribution networks with respect to various topological structures and distributions of microparameters. The equilibrium properties of the systems are obtained in a statistical mechanics framework by application of the replica method. We demonstrate the validity of our approach by comparing it with Monte Carlo simulations. We analyse the network properties in terms of phase diagrams and found both qualitative and quantitative dependence of the network properties on the network structure and macroparameters. The structure of the phase diagrams points at the existence of phase transition and the presence of stable and metastable states in the system. We also present an analysis of robustness against overloading in the distribution networks.

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28

Robles, Alexandro Heiblum. "Statistical mechanics of animal territoriality." Thesis, University of Bristol, 2016. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.707747.

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29

Wahba, Karim A. "Statistical mechanics of membrane proteins." Diss., Restricted to subscribing institutions, 2009. http://proquest.umi.com/pqdweb?did=1905048771&sid=1&Fmt=2&clientId=1564&RQT=309&VName=PQD.

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30

Camilli, Francesco. "Statistical mechanics perspectives on Boltzmann machines." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/19302/.

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La tesi contiene un approccio rigoroso alla meccanica statistica dei sistemi disordinati con particolare attenzione a modelli di campo medio. Il punto di partenza è un’introduzione al modello Curie-Weiss in cui si presentano sia risultati classici sia una nuova proprietà di stabilità per cambio di normalizzazione. Il modello è stato risolto per interazioni ferromagnetiche ed antiferromagnetiche. Una volta introdotti gli strumenti fondamentali, si passa al modello di Sherringtone Kirkpatrick, in cui le interazioni sono estratte da una gaussiana standard ed indipendenti. Si provano l’esistenza del limite termodinamico e la correttezza del replica symmetry breaking ansatz di Parisi per l’energia libera. Il lower bound per quest'ultima è rigorosamente provato tramite lo schema di Aizenmann, Sims e Starr. Nei due capitoli successivi, sono stati studiati modelli multi-specie. Nel caso non disordinato, il modello multi-layer viene risolto. A seguire, un’analisi di modelli in cui la matrice di interazioni tra le specie è definita (negativa o positiva). Per sistemi multi-specie disordinati invece è stato analizzato solo il caso ellittico, con matrice delle covarianze delle interazioni definita positiva. Un caso iperbolico, la Deep Boltzmann Machine (DBM), è infine discusso. Proprio a causa dell'iperbolicità di questo modello si ha soltanto un upper bound, costruito con combinazioni delle energie libere di SK, che è più grande dell’energia libera. Delle prospettive interessanti emergono dallo studio della regione di annealing e di replica symmetry, due particolari regimi associati a fasi di alte temperature. Si può provare che, a campo esterno nullo, la stabilità della soluzione replica symmetric è implicata dalle stesse condizioni che assicurano l’annealing. Per finire, si mostra che, trovando degli opportuni fattori di forma, ovvero i rapporti tra le taglie dei layers della DBM, la regione di annealing di questo modello può essere compressa.

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31

Ha, Eugene. "Quantum statistical mechanics of Shimura varieties." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980749964.

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32

Mondani, Hernan. "Statistical Mechanics of Organizational Growth Processes." Thesis, KTH, Fysik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-98070.

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33

Malevanets, Anatoly. "Statistical mechanics of hydrodynamic lattice gases." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ27690.pdf.

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34

Ostojic, Srdjan. "Statistical mechanics of static granular matter." [S.l. : Amsterdam : s.n.] ; Universiteit van Amsterdam [Host], 2006. http://dare.uva.nl/document/30843.

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35

Chan, Yao-ban. "Selected problems in lattice statistical mechanics /." Connect to thesis, 2005. http://eprints.unimelb.edu.au/archive/00001449.

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36

Evans, Allan Kenneth. "Foundations of non-equilibrium statistical mechanics." Thesis, University of Cambridge, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.389831.

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37

Graham, I. "Statistical mechanics of protein interaction networks." Thesis, University of Cambridge, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.599596.

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The chemotaxis signalling network of Escherichia coli is a paradigm for signal transduction and sensation in biology. A chemical signal, perceived by receptor proteins, is relayed to the bacterial motor through the network. The network components are localized in a large structure that is anchored to the polar membrane. Most of the components have been characterized, and many network interactions and rate constants have been measured. The network consists of a small number of interacting proteins, yet exhibits many fascinating features. There is a remarkable sensitivity to small changes in the chemical composition of the cell environment. The network adapts to an unchanging environment: Following a change in chemical concentration, the network slowly resets itself to the pre-stimulus state. Chemotaxis is robust – cells can respond to stimuli even when chemotaxis proteins are under-expressed or mutated. This thesis is concerned with the study of these network properties. The first issue addressed is the sensitivity of the chemotaxis response. One way to model sensitivity is to allow the conformation of each chemotaxis receptor to be coupled to the conformations of its neighbours. This simple model exhibits large amplification of changes in the concentration of one chemical species. The general problem of maintaining a sensitive response in a stochastic environment comprised of different chemicals is addressed. The results are applied to the chemotaxis network, and its sensitivity, as chemical species and background concentrations change, is analyzed. Different adaptation mechanisms are introduced, and their ability to maintain a sensitive response to different chemicals and different background concentrations is discussed. The second issue considered is the mechanism by which the chemotaxis network localizes at the cell pole.

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38

Barford, William. "The statistical mechanics of adsorbed polymers." Thesis, University of Cambridge, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.328503.

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39

Baldock, Robert John Nicholas. "Classical statistical mechanics with nested sampling." Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.709164.

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40

Pryce, Jonathan Michael. "The statistical mechanics of image restoration." Thesis, University of Edinburgh, 1993. http://hdl.handle.net/1842/12805.

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Image restoration is concerned with the recovery of an 'improved' image from a corrupted picture, utilizing a prior model of the source and noise processes. We present a Bayesian derivation of the posterior probability distribution, which describes the relative probabilities that a certain image was the original source, given the corrupted picture. The ensemble of such restored images is modelled as a Markov random field (Ising spin system). Using a prior on the density of edges in the source, we obtain the cost function of Geman and Geman via information theoretic arguments. Using a combination of Monte Carlo simulation, the mean field approximation, and series expansion methods, we investigate the performance of the restoration scheme as a function of the parameters we have identified in the posterior distribution. We find phase transitions separating regions in which the posterior distribution is data-like, from regions in which it is prior-like, and we can explain these sudden changes of behaviour in terms of the relative free energies of metastable states. We construct a measure of the quality of the posterior distribution and use this to explore the way in which the appropriateness of the choice of prior affects the performance of the restoration. The data-like and prior-like characteristics of the posterior distribution indicate the regions of parameter space where the restoration scheme is effective and ineffective respectively. We examine the question of how best to use the posterior distribution to prescribe a single 'optimal' restored image. We make a detailed comparison of two different estimators to determine which better characterizes the posterior distribution. We propose that the TPM estimate, based on the mean of the posterior, is a more sensible choice than the MAP estimate (the mode of the posterior), both in principle and in practice, and we provide several practical and theoretical arguments in support.

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41

Cates, Michael Elmhirst. "The statistical mechanics of complex polymers." Thesis, University of Cambridge, 1985. https://www.repository.cam.ac.uk/handle/1810/283815.

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42

Chana, Kamaljeet S. "Statistical mechanics of itinerant-electron magnets." Thesis, Loughborough University, 1993. https://dspace.lboro.ac.uk/2134/33080.

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The transition metal iron is the archetypal magnetic material. However some aspects of its magnetic behaviour are still not fully understood. The conceptual difficulty is that, while unpaired electrons responsible for magnetism in an insulator are localised on the atomic sites, in a metal they have extended states. In iron these itinerant 3-D electrons may conspire to form well-defined local magnetic moments. In this limit one can treat metals such as iron in a similar fashion to insulators in the framework of the Heisenberg model. The local moments align at low temperatures giving rise to ferromagnetic behaviour and above the Curie temperature, Tc, misalign to destroy long range order. The correlation between the directions of the neighbouring moments in the paramagnetic phase remains a subject of controversy. Neutron scattering data would indicate that the magnetic moments are more correlated than would be expected in an insulator. This is generally referred to as magnetic short range order.

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43

Welsh, Thomas. "Statistical mechanics of boundary driven systems." Thesis, University of Leeds, 2012. http://etheses.whiterose.ac.uk/2873/.

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Statistical mechanics is concerned with finding the macroscopic behaviour of a physical system given its microscopic characteristics. At equilibrium there is a general framework given in terms of the various statistical ensembles that describes how to calculate the macroscopic quantity that is desired. Out of equilibrium there is no such framework, leading to the treatment of microscopic models on an individual basis and the investigation of arbitrarily defined models. However, there exists a recent theory of boundary driven steady states and an associated nonequilibrium counterpart to detailed balance due to Evans. In this thesis I first review this theory of boundary driven steady states and the associated nonequilibrium counterpart to detailed balance due to Evans, before applying the theory to some toy models of driven athermal systems. These initial attempts do not reproduce the qualitative behaviour of granular systems such as jamming but are a valuable and novel starting point for a more thorough investigation of this technique. I then move on to the general theory of boundary driven systems and formulate a nonequilibrium free energy principle. The physical content of this is illustrated through a simple diffusion model. I then provide a reformulation of the principle which is more suitable for calculation and demonstrate its validity in a more complex model. Finally I investigate a particular example of a boundary driven system, a toy model of a complex fluid called the rotor model. I first use simulation to investigate the model and its phase behaviour, before using an analytical approach to do the same. This approach takes the form of a nonequilibrium real space renormalisation group calculation, and qualitatively reproduces some of the features seen in the simulations.

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44

Mariani, Riccardo. "Irreversible parallel dynamics in statistical mechanics." Thesis, Aix-Marseille, 2018. http://www.theses.fr/2018AIXM0744/document.

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Nous présentons des approches théoriques et numériques pour deux dynamiques irréversibles et parallèles sur des modèles de mécanique statistique. Dans le premier chapitre, nous présentons les résultats théoriques sur un système de particules induite par une chaîne de Markov irréversible, à savoir le TASEP. Permettant des multiples retournements de spin \`à chaque itération, nous définissons un modèle avec une dynamique parallèle appartenant à la famille des PCA et nous dérivons sa mesure stationnaire. Dans ce cadre, nous traitons {\it le problème du blocage}, {\it i.e.} comprendre les effets d’une perturbation localisée dans le taux de transition des particules sur des systèmes irréversibles: le problème du blocage. Dans le deuxième chapitre, nous présentons une version unidimensionnelle du modèle d'Ising avec potentiel de Kac. Nous définissons une PCA avec une interaction asymétrique et nous trouvons sa mesure stationnaire avec condition aux limites périodique.Ensuite, nous prouvons la convergence, dans la limite thermodynamique, de cette mesure stationnaire vers la mesure de Gibbs pour toutes les températures supérieures à la température critique via les estimations de F\"ollmer et le théorème d'unicité de Dobrushin. Dans la seconde partie de la thèse, nous étudions ces deux dynamiques à travers des expériences numériques. Dans le cas du TASEP en exploitant des processeurs graphiques (GPU) et CUDA pour identifier une estimation raisonnable du {temps de m\'elange} et renforcer la conjecture qu’à la fois dans la version, la règle de mise à jour série ou parallèle, le courant peut ne pas être analytique dans l’intensité du blocage autour de la valeur $ \varepsilon = 0 $
In this thesis we present theoretical and numerical approaches for two irreversible and parallel dynamics on one-dimensional statistical mechanics models. In the first chapter we present theoretical results on a particles system driven by an irreversible Markov chain namely the totally asymmetric simple exclusion process (TASEP). Allowing multiples spin-flips in each time-step we define a model with a parallel dynamics that belongs to the family of the probabilistic cellular automata (PCA) and we derive its stationary measure. In this framework we deal with {\it the blockage problem}, {\it i.e.} to understand the effects of a localized perturbation in the transition rates of the particles on irreversible systems: the blockage problem. In the second chapter we present a one-dimensional version of the Ising model with Kac potential. Again we define a PCA dynamics with asymmetric interaction between particles and we find its stationary measure for periodic boundary condition. Then we prove the convergence, in the thermodynamic limit, of such stationary measure to the Gibbs measure for all temperatures above the critical one via F\"ollmer estimates and dobrushin's uniqueness theorem. In the second part of the thesis, we investigate these two dynamics through numerical experiments.In the case of the TASEP we exploit general purpose graphical processors unit (GPGPU) writing a parallel code in CUDA to identify a reasonable {\it mixing time} and reinforce the conjecture that in both version, serial or parallel update rule, the current may be non-analytic in the blockage intensity around the value $\varepsilon = 0$

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45

Hausmann, Johannes. "Statistical mechanics of strongly driven Ising systems." [S.l.] : [s.n.], 2001. http://deposit.ddb.de/cgi-bin/dokserv?idn=963559311.

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46

Siebert, Julien. "Statistical mechanics of the self-gravitating gases." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2005. http://tel.archives-ouvertes.fr/hal-00009142.

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The self-gravitating systems are formed by particles interacting through gravity. They describe structure formation in the universe. As a consequence of the long range interaction of gravity, they are inhomogeneous even at thermal equilibrium. We study the self-gravitating systems with several kinds of particles and the self-gravitating systems in the presence of the cosmological constant $ Lambda$. We formulate the statistical mechanics and the mean field approach describing the gaseous phase. We explicitely compute the density of particles and thermodynamic quantities. The presence of $ Lambda$ extends the domain of stability of the gaseous phase. Monte Carlo simulations show that the mean field describes the gaseous phase with an excellent accuracy. Scalling law of the self-gravitating systems with several kinds of particles is found. At the critical point the fractal dimension is independant of their composition and is $1.6...$~.

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47

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 well
Der 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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48

Moghaddam, Maria Sabaye. "Statistical mechanics of the adsorption of copolymers." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ63603.pdf.

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49

Nielsen, Steven Ole. "Mixed quantum-classical dynamics and statistical mechanics." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ63602.pdf.

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50

Röhl, Torsten [Verfasser]. "Statistical mechanics of evolutionary dynamics / Torsten Röhl." Kiel : Universitätsbibliothek Kiel, 2009. http://d-nb.info/1019813091/34.

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Dissertations / Theses on the topic 'Statistical mechanics in chemistry'

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