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Statistical mechanics of non-Markovian exclusion processesConcannon, Robert James January 2014 (has links)
The Totally Asymmetric Simple Exclusion Process (TASEP) is often considered one of the fundamental models of non-equilibrium statistical mechanics, due to its well understood steady state and the fact that it can exhibit condensation, phase separation and phase transitions in one spatial dimension. As a minimal model of traffic flow it has enjoyed many applications, including the transcription of proteins by ribosomal motors moving along an mRNA track, the transport of cargo between cells and more human-scale traffic flow problems such as the dynamics of bus routes. It consists of a one-dimensional lattice of sites filled with a number of particles constrained to move in a particular direction, which move to adjacent sites probabilistically and interact by mutual exclusion. The study of non-Markovian interacting particle systems is in its infancy, due in part to a lack of a framework for addressing them analytically. In this thesis we extend the TASEP to allow the rate of transition between sites to depend on how long the particle in question has been stationary by using non-Poissonian waiting time distributions. We discover that if the waiting time distribution has infinite variance, a dynamic condensation effect occurs whereby every particle on the system comes to rest in a single traffic jam. As the lattice size increases, so do the characteristic condensate lifetimes and the probability that a condensate will interact with the preceding one by forming out of its remnants. This implies that the thermodynamic limit depends on the dynamics of such spatially complete condensates. As the characteristic condensate lifetimes increase, the standard continuous time Monte Carlo simulation method results in an increasingly large fraction of failed moves. This is computationally costly and led to a limit on the sizes of lattice we could simulate. We integrate out the failed moves to create a rejection-free algorithm which allows us to see the interacting condensates more clearly. We find that if condensates do not fully dissolve, the condensate lifetime ages and saturates to a particular value. An unforeseen consequence of this new technique, is that it also allowed us to gain a mathematical understanding of the ageing of condensates, and its dependence on system size. Using this we can see that the fraction of time spent in the spatially complete condensate tends to one in the thermodynamic limit. A random walker in a random force field has to escape potential wells of random depth, which gives rise to a power law waiting time distribution. We use the non-Markovian TASEP to investigate this model with a number of interacting particles. We find that if the potential well is re-sampled after every failed move, then this system is equivalent to the non-Markovian TASEP. If the potential well is only re-sampled after a successful move, then we restore particle-hole symmetry, allow condensates to completely dissolve, and the thermodynamic limit spends a finite fraction of time in the spatially complete state. We then generalised the non-Markovian TASEP to allow for particles to move in both directions. We find that the full condensation effect remains robust except for the case of perfect symmetry.
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Modeling and analysis of continuous opinion dynamics using statistical mechanical methodsWong, Ching-yat, 黃靜逸 January 2015 (has links)
In the past two decades, the advance in computational power and the availability of social interaction data have opened the way for applying statistical physics such as Monte-Carlo simulations, mean-field approximations, and theories of non-linear dynamics and network topology to explain and predict social dynamics. Opinion dynamics is an important topic in the study of social dynamics. In particular, Social Judgment Theory (SJT) is a well-established theory which explains how an individual's opinion changes upon encountering a new idea. SJT is not limited to predicting individual behavior. It also provides a framework for us to exploit statistical mechanical methods to simulate the collective opinion dynamics. Therefore, we proposed a SJT-based model to study opinion dynamics by using both agent-based and density-based approaches. Our model can be regarded as an extension of the famous Deffuant model. Unlike the Deffuant model, our model exhibits opinion polarization, which is a crucial topic in the real world. Through in-depth investigation, we found that the boomerang effect suggested in SJT could be an origin of opinion polarization. In this thesis, I presented and compared the results obtained from agent-based and density-based approaches. I also applied mean-field analysis to explain the interesting observations in phase diagrams and collective opinion dynamics. Lastly, by further adapting our model to heterogeneous agents, I discovered that advocating open-mindedness to a small fraction of agents could reduce the total number of final opinion clusters and the degree of opinion polarization. Our findings might help us to search for feasible solutions towards the problem of opinion polarization. / published_or_final_version / Physics / Master / Master of Philosophy
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Computer simulation of liquid crystalsBates, Martin Alexander January 1996 (has links)
No description available.
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The Statistical Fingerprints of Quantum GravityAnsari, Mohammad Hossein 12 September 2008 (has links)
In this thesis some equilibrium and non-equilibrium statistical
methods are implied on two different versions of non-perturbative
quantum gravity.
Firstly, we report a novel statistical mechanics in which a class of evolutionary maps
act on trivalent spin network in randomly chosen initial states
and give rise to Self-organized Criticality. The result of continuously applying these maps indicate an expansion in the space-time area associated.
Secondly, a previously unknown statistical mechanics in quantum gravity is introduced in the framework of two dimensional Causal Dynamical Triangulations. This provides us a useful and new tools to understand this quantum gravity in terms of effective spins. This study reveals a correspondence between the statistics of Anti-ferromagnetic
systems and Causal Dynamical quantum gravity. More importantly, it provides a basis for studying anti-ferromagnetic systems in a background independent way.
Thirdly, two novel properties of area operator in
Loop Quantum Gravity are reported: 1) the generic degeneracy
and 2) the ladder symmetry. These were not known previously for years. The first one indicates that
corresponding to any eigenvalue of area operator in loop quantum gravity there exists a finite number of
degenerate eigenstates. This degeneracy is shown to be one way for the explanation of black hole entropy in a microscopic way. More importantly, we reproduce Bekenstein-Hawking entropy of black hole by comparing the minimal energy of a decaying frequency from a loop quantum black hole and the extracted energy from a perturbed black hole in the highly damping mode. This consistency reveals a treasure model for describing a black hole in loop quantum gravity that does nor suffer from the restrictions of an isolated horizon. The second property indicates there exists a ladder symmetry unexpectedly
in the complete spectrum of area eigenvalues. This symmetry suggests the eigenvalues of area could be classified into different evenly
spaced subsets, each called a `generation.' All generations are evenly
spaced; but the gap between the levels in any every generation is
unique. One application of the two new properties of area operator
have been considered here for introducing a generalized picture of
horizon whose area cells are not restricted to the subset considered
in quantum isolated horizon theory. Instead, the area cells accepts
values from the complete spectrum. Such horizon in the presence of
all elements of diffeomorphism group contains a number of degrees
of freedom independently from the bulk freedom whose logarithm
scales with the horizon area. Note that this is not the case in quantum isolated horizon when the complete elements of diffeomorphism
applies.
Finally, we use a simple statistical method in which no pre-assumption is made for the essence of the energy quanta radiated
from the hole. We derive the effects of the black hole horizon fluctuations and reveal a new phenomenon called "quantum amplification
effects" affecting black hole radiation. This effect causes unexpectedly a few un-blended radiance modes manifested in spectrum as
discrete brightest lines. The frequency of these modes scales with
the mass of black hole. This modification to Hawking's radiation
indicates a window at which loop quantum gravity can be observationally tested at least for primordial black holes.
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The Statistical Fingerprints of Quantum GravityAnsari, Mohammad Hossein 12 September 2008 (has links)
In this thesis some equilibrium and non-equilibrium statistical
methods are implied on two different versions of non-perturbative
quantum gravity.
Firstly, we report a novel statistical mechanics in which a class of evolutionary maps
act on trivalent spin network in randomly chosen initial states
and give rise to Self-organized Criticality. The result of continuously applying these maps indicate an expansion in the space-time area associated.
Secondly, a previously unknown statistical mechanics in quantum gravity is introduced in the framework of two dimensional Causal Dynamical Triangulations. This provides us a useful and new tools to understand this quantum gravity in terms of effective spins. This study reveals a correspondence between the statistics of Anti-ferromagnetic
systems and Causal Dynamical quantum gravity. More importantly, it provides a basis for studying anti-ferromagnetic systems in a background independent way.
Thirdly, two novel properties of area operator in
Loop Quantum Gravity are reported: 1) the generic degeneracy
and 2) the ladder symmetry. These were not known previously for years. The first one indicates that
corresponding to any eigenvalue of area operator in loop quantum gravity there exists a finite number of
degenerate eigenstates. This degeneracy is shown to be one way for the explanation of black hole entropy in a microscopic way. More importantly, we reproduce Bekenstein-Hawking entropy of black hole by comparing the minimal energy of a decaying frequency from a loop quantum black hole and the extracted energy from a perturbed black hole in the highly damping mode. This consistency reveals a treasure model for describing a black hole in loop quantum gravity that does nor suffer from the restrictions of an isolated horizon. The second property indicates there exists a ladder symmetry unexpectedly
in the complete spectrum of area eigenvalues. This symmetry suggests the eigenvalues of area could be classified into different evenly
spaced subsets, each called a `generation.' All generations are evenly
spaced; but the gap between the levels in any every generation is
unique. One application of the two new properties of area operator
have been considered here for introducing a generalized picture of
horizon whose area cells are not restricted to the subset considered
in quantum isolated horizon theory. Instead, the area cells accepts
values from the complete spectrum. Such horizon in the presence of
all elements of diffeomorphism group contains a number of degrees
of freedom independently from the bulk freedom whose logarithm
scales with the horizon area. Note that this is not the case in quantum isolated horizon when the complete elements of diffeomorphism
applies.
Finally, we use a simple statistical method in which no pre-assumption is made for the essence of the energy quanta radiated
from the hole. We derive the effects of the black hole horizon fluctuations and reveal a new phenomenon called "quantum amplification
effects" affecting black hole radiation. This effect causes unexpectedly a few un-blended radiance modes manifested in spectrum as
discrete brightest lines. The frequency of these modes scales with
the mass of black hole. This modification to Hawking's radiation
indicates a window at which loop quantum gravity can be observationally tested at least for primordial black holes.
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Statistics of turbulence in a rapidly rotating systemJung, Sunghwan 28 August 2008 (has links)
Not available / text
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Maxwell [is to] Boltzmann [as time tends to infinity]Davis, Joel 08 1900 (has links)
No description available.
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Numerical experiments and theoretical analysis on the sources of irreversibility in mechanical systemsStoddard, Spotswood D. 05 1900 (has links)
No description available.
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Fundamental concepts concerning the derivation of kinetic equations for mixturesThibault, Paul. January 1978 (has links)
No description available.
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Modeling of contaminant dispersion by statistical mechanicsChing, Wing-han, Michael. January 2009 (has links)
Thesis (Ph. D.)--University of Hong Kong, 2009. / Includes bibliographical references (p. 187-204). Also available in print.
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