Statistical Mechanics

Thermodynamic Calculations for Molecules with Asymmetric Internal Rotors - Application to 1,3-Butadiene

by Bryan Wong

Journal of Computational Chemistry, 28, 759 (2007)

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Thermodynamic Calculations for Molecules with Asymmetric Internal Rotors. II. Application to the 1,2-Dihaloethanes

by Bryan Wong

Journal of Computational Chemistry, 29, 481 (2008)

Effects of Large-Amplitude Torsions on Partition Functions: Beyond the Conventional Separability Assumption

by Bryan Wong

Molecular Physics, 103, 1027 (2005)

Temperature and Molecular Size Dependence of the High-Pressure Limit

by Bryan Wong

Journal of Physical Chemistry A, 107, 6206 (2003)

Analytic influence functionals for numerical Feynman integrals in most open quantum systems

by Nike Dattani

Oscillatory settling in wormlike-micelle solutions: bursts and a long time scale

by Nitin Kumar

Nitin Kumar, Sayantan Majumdar, Aditya Sood, Rama Govindarajan, Sriram Ramaswamy and A.K. Sood

Soft Matter, 2012, 8, 4310-4313
DOI: 10.1039/C2SM25077B

Preprint available here:
http://arxiv.org/pdf/1203.2130.pdf

We study the dynamics of a spherical steel ball falling freely through a solution of entangled wormlike-micelles. If... more We study the dynamics of a spherical steel ball falling freely through a solution of entangled wormlike-micelles. If the sphere diameter is larger than a threshold value, the settling velocity shows repeated short oscillatory bursts separated by long periods of relative quiescence. We propose a model incorporating the interplay of settling-induced flow, viscoelastic stress and, as in M. E. Cates, D. A. Head and A. Ajdari, Phys. Rev. E, 2002, 66, 025202(R) and A. Aradian and M. E. Cates, Phys. Rev. E, 2006, 73, 041508, a slow structural variable for which our experiments offer independent evidence.

Statistical Market Equilibrium Revisited

by Frank Witte

This is a preliminary version of a working paper that I hope to have completed by the end of March. YES a spelling check is still needed and YES a check on many of the equations is also still needed.

WORK IN PROGRESS:

I analyze Foley's Statistical Market Equilibrium theory in some detail and a number of... more WORK IN PROGRESS:

I analyze Foley's Statistical Market Equilibrium theory in some detail and a number of problems in the interpretation are highlighted. Most significant of these are the initial-state dependence of the equilibrium state, the fact that equilibrium allocations fluctuate and thus market-clearing occurs on average only and that a manifest connection to Walrassian equilibria is obscured.

A "kinetic" derivation of the statistical market ensemble allows for a more dynamical understanding of how statistical equilibrium can arise as a result of "collission-like, market-value and/or utillity preserving interactions between agents. The outcome of these interactions, that drive equilibration, can be formulated in terms of individualised marginal values of commodities and the individual risk-adversity of the agents.

The initial-state dependence can be shown to be largely removable upon this re-interpretation and minor modification of the formalism. The new formalism can accomodate exact market-clearing by a Legendre transformation to a different ensemble which endogenizes the prices and leads to endogeneous price fluctuations. It is also illustrated that a statistical market where the weight depends on the constrained-utillity of the total commodity bundle, rather than the total value of the bundle, has the Walrassian equilibrium as its expectation values in the limit of vanishing negative temperatures and the Foley model as its positive high-temperature limit. Studying fluctuations reveals clearly that statistical market equilibrium is reached by agents that are in interaction with a commodity-bath of secondary agents that do not explicitly appear in Foley's theory. The role of the initial iso-utillity manifold on which the agents are positioned is clarified.

Finally an attempt is made to study the "thermodynamics" of statistical equilibrium markets. It is shown how in this context the "economic temperature" has a natural interpretation as the average market-value per agent. An economic entropy can be defined which allows the definition of "isentropic" quasi-static market processes that are shown to generate supply and demand curves for the different types of agents. An equation of state is derived for a simple example of a market and used to show how simple market processes, such as the effects of price-changes and total commodity-bundle changes, can be analysed. As a last issue it is shown how, in principle, such models can also accomodate the statistical mechanics of agents "aggregating" into larger agents of a different type.

Bumps on the Road to Here (from Eternity)

by Eric Winsberg

In his recent book, _From Eternity to Here_, and in other more technical papers, Sean Carroll (partly in collaboration... more In his recent book, _From Eternity to Here_, and in other more technical papers, Sean Carroll (partly in collaboration with Jennifer Chen) has put forward an intriguing new way to think about the origin of the Universe. His approach, in a nutshell, is to raise certain worries about a standard Boltzmannian picture of statistical mechanics, and to present certain commitments that he thinks we ought to hold—commitments that the standard picture doesn’t share. He then proposes a cosmological model—one that purports to give us insight into what sort of process brought about the “initial state” of the universe—that can uniquely accommodate those commitments. The conclusion of Carroll’s argument is that statistical mechanical reasoning provides grounds for provisionally accepting that cosmological model. My goal in this paper is to reconstruct and critically assess this proposal. I argue that “statistical cosmology” requires a careful balance of philosophical intuitions and commitments against technical, scientific considerations; how much stock we ought to place in these intuitions and commitments should depend on where they lead us—those that lead us astray scientifically might well be in need of philosophical re examination.

The inefficiency of re-weighted sampling and the curse of system size in high order path integration

by Michele Ceriotti

Published on Proc. R. Soc. A 8 January 2012 vol. 468 no. 2137 2-17

Computing averages over a target probability density by statistical re-weighting of a set of samples with a different... more Computing averages over a target probability density by statistical re-weighting of a set of samples with a different distribution is a strategy which is commonly adopted in fields as diverse as atomistic simulation and finance. Here we present a very general analysis of the accuracy and efficiency of this approach, highlighting some of its weaknesses. We then give an example of how our results can be used, specifically to assess the feasibility of high-order path integral methods. We demonstrate that the most promising of these techniques -- which is based on re-weighted sampling -- is bound to fail as the size of the system is increased, because of the exponential growth of the statistical uncertainty in the re-weighted average.

Learning with a network of competing synapses

by Ajaz Bhat

Predatory trading and risk minimisation: how to (b)eat the competition

by Anita Mehta

Arithmetic of Potts Model Hypersurfaces

by Jessica Su

We consider Potts model hypersurfaces defined by the multivariate Tutte polynomial of graphs (Potts model partition... more We consider Potts model hypersurfaces defined by the multivariate Tutte polynomial of graphs (Potts model partition function). We focus on the behavior of the number of points over finite fields for these hypersurfaces, in comparison with the graph hypersurfaces of perturbative quantum field theory defined by the Kirchhoff graph polynomial. We give a very simple example of the failure of the "fibration condition" in the dependence of the Grothendieck class on the number of spin states and of the polynomial countability condition for these Potts model hypersurfaces. We then show that a period computation, formally similar to the parametric Feynman integrals of quantum field theory, arises by considering certain thermodynamic averages. One can show that these evaluate to combinations of multiple zeta values for Potts models on polygon polymer chains, while silicate tetrahedral chains provide a candidate for a possible occurrence of non-mixed Tate periods.

Random imperfection fields to model the size effect in laboratory wood specimens

by Sara Casciati

Casciati S. and Domaneschi M. (2007). “Random imperfection fields to model the size effect in laboratory wood specimens”. Structural Safety, 29(4), 308-321. ISSN: 0167-4730.

DATA E LUOGO DI PUBBLICAZIONE: October 2007; Elsevier Science Bv, 1000 AE Amsterdam, Netherlands.

ABSTRACT. The composite nature of a wood continuum prevents one from extrapolating the results of laboratory tests on... more ABSTRACT. The composite nature of a wood continuum prevents one from extrapolating the results of laboratory tests on standard wood specimens to structural elements of significant size. Therefore, these elements are usually tested under standardized loading conditions in order to detect a sort of average material behaviour.
In this paper, the initial step consists, instead, of testing the material specimens. The extension of the results to structural elements is then pursued by introducing a random field, or, in a discretized model, a random array of imperfections.
The calibration of the suitable spatial distribution of the imperfections is then investigated by a mixed experimental–numerical approach, for a reference beam. The analyses on the relative finite elements model are iterated to match the response of the full scale laboratory tests.

KEYWORDS: Biaxial tests; Finite element model; Imperfections; Laboratory tests; Random field; Wood specimens

Cohesive Crack Propagation in a Random Elastic Medium

by Sara Casciati

Bruggi M., Casciati S., and Faravelli L. (2008). “Cohesive crack propagation in a random elastic medium”. Probabilistic Engineering Mechanics, 23(1), 23-35. ISSN: 0266-8920.

DATA E LUOGO DI PUBBLICAZIONE: January 2008; Elsevier Sci Ltd, Kidlington, Oxford OX5 1GB, Oxon, England.

ABSTRACT. The issue of generating non-Gaussian, multivariate and correlated random fields, while preserving the... more ABSTRACT. The issue of generating non-Gaussian, multivariate and correlated random fields, while preserving the internal auto-correlation structure of each single-parameter field, is discussed with reference to the problem of cohesive crack propagation. Three different fields are introduced to model the spatial variability of the Young modulus, the tensile strength of the material, and the fracture energy, respectively. Within a finite-element context, the crack-propagation phenomenon is analyzed by coupling a Monte Carlo simulation scheme with an iterative solution algorithm based on a truly-mixed variational formulation which is derived from the Hellinger–Reissner principle. The selected approach presents the advantage of exploiting the finite-element technology without the need to introduce additional modes to model the displacement discontinuity along the crack boundaries. Furthermore, the accuracy of the stress estimate pursued by the truly-mixed approach is highly desirable, the direction of crack propagation being determined on the basis of the principal stress criterion. The numerical example of a plain concrete beam with initial crack under a three-point bending test is considered. The statistics of the response is analyzed in terms of peak load and load–mid deflection curves, in order to investigate the effects of the uncertainties on both the carrying capacity and the post-peak behaviour. A sensitivity analysis is preliminarily performed and its results emphasize the negative effects of not accounting for the auto-correlation structure of each random field. A probabilistic method is then applied to enforce the auto-correlation without significantly altering the target marginal distributions. The novelty of the proposed approach with respect to other methods found in the literature consists of not requiring the a priori knowledge of the global correlation structure of the multivariate random field.

KEYWORDS: Multivariate non-Gaussian random fields; Auto-correlation; Cohesive crack propagation; Truly-mixed finite element method; Monte Carlo simulations

A Bound on Equipartition of Energy v2

by Nicolo' Masi

The statistical mechanics of community assembly and species distributions

by Gordon Fox

Kelly, C. K., S. J. Blundell, M. G. Bowler, G. A. Fox, P. A. Harvey, M. R. Lomas, and I. F. Woodward. 2011. The statistical mechanics of community assembly and species distribution. New Phytologist 191:815-827. doi:10.1111/j.1469-8137.2011.03721.x

Theoretically, communities at or near their equilibrium species number resist entry of new species. Such ‘biotic... more Theoretically, communities at or near their equilibrium species number resist entry of new species. Such ‘biotic resistance’ recently has been questioned because of successful entry of alien species into diverse natural communities.
•
Data on 10 409 naturalizations of 5350 plant species over 16 sites dispersed globally show exponential distributions both for species over sites and for sites over number of species shared. These exponentials signal a statistical mechanics of species distribution, assuming two conditions. First, species and sites are equivalent, either identical (‘neutral’) or so complex that the chance a species is in the right place at the right time is vanishingly small (‘idiosyncratic’); the range of species and sites in our data disallows a neutral explanation. Secondly, the total number of naturalizations is fixed in any era by a ‘regulator’.
•
Previous correlation of species naturalization rates with net primary productivity over time suggests that the regulator is related to productivity.
•
We conclude that biotic resistance is a moving ceiling, with resistance controlled by productivity. The general observation that the majority of species occur naturally at only a few sites, and only a few species occur at many sites, now has a quantitative (exponential) character, offering the study of species’ distributions a previously unavailable rigor.

On the thermodynamics of phase transitions in metal hydrides

by Andrea Di Vita

Centr. Eur. J. Phys. 10, 1, 86-95 (2012) DOI 10.2478/s11534-011-0094-4

Metal hydrides are solutions of hydrogen in a metal, where phase transitions may occur
depending on temperature,... more Metal hydrides are solutions of hydrogen in a metal, where phase transitions may occur
depending on temperature, pressure etc. We apply Le Chatelier’s principle of thermodynamics to a
particular phase transition in TiHx, which can approximately be described as a second-order phase
transition. We show that the fluctuations of the order parameter correspond to fluctuations both of the
density of H+ ions and of the distance between adjacent H+ ions. Moreover, as the system approaches the
transition and the correlation radius increases we show –with the help of statistical mechanics– that the
statistical weight of modes involving a large number of H+ ions (‘collective modes’) increases sharply, in
spite of the fact that the Boltzmann factor of each collective mode is exponentially small. As a result, it
turns out that the interaction of the H+ ions with collective modes makes a tiny suprathermal fraction of the
H+ population to appear. Our results hold for similar transitions in metal deuterides too. A violation of a –
insofar undisputed– upper bound on hydrogen loading follows.

Dynamics of movie competition and popularity spreading in recommender systems

by Giulio Cimini

Achieving fast convergence of ab initio free energy perturbation calculations with the adaptive force matching method

by Camilo Calderon

manuscript accepted.

This paper studies the possibility of improving the convergence of ab initio free energy perturbation (FEP)... more This paper studies the possibility of improving the convergence of ab initio free energy perturbation (FEP) calculations by developing a customized force field with the adaptive force matching (AFM) method. The ab initio FEP method relies on a molecular mechanics (MM) potential to sample the configuration space. If the Boltzmann weight of the MM sampling is close to that of the ab initio method, the efficiency of the ab initio FEP will be optimal. The difference in the Boltzmann weights can be quantified by the relative energy difference distribution (REDD). The force field developed through AFM significantly improves the REDD when compared with standard MM models, thus improving the convergence of the ab initio FEP calculation. The static dielectric constant εs of ice-Ih was studied with PW-91 through ab initio FEP. With a customized force field developed through AFM, we were able to converge εs to 43 ± 7 with 3600 configurations. A similar ab initio FEP calculation with the TIP4P model would require 220 times more configurations to achieve the same accuracy. It is established that PW-91 underestimates ice-Ih εs by about 50% when compared with the
experimental value, indicating a deficiency of the PW-91 functional.

Entropy of Hidden Markov Models

by Sandra (A.C.C.) van Wijk

Master Thesis under supervision of dr. E.A. Verbitskiy, dr. R. Rietman, prof.dr. R.W. van der Hofstad and prof.dr.ir. S.C. Borst.
For slides of presentation, see http://tue.academia.edu/SandraVanWijk/Talks/18035/Entropy_of_Hidden_Markov_Models and http://tue.academia.edu/SandraVanWijk/Talks/25083/Entropy_of_Hidden_Markov_Models.
For my research and contact details, visit http://tue.academia.edu/SandraVanWijk/About.

In this thesis we investigate the entropy of hidden Markov models. A hidden Markov model is a stochastic process... more In this thesis we investigate the entropy of hidden Markov models. A hidden Markov model is a stochastic process {Yn}_{n>=0}, which can be seen as a noisy observation of a Markov chain. The entropy is a measure for the randomness of the process. It is known that the conditional probability P[Y_0 = y_0 | Y_1 = y_1, . . . Y_n = y_n] converges at an exponential rate. The literature on this is reviewed and different upper bounds for the convergence rate are compared. Next we give series expansions for this conditional probability in the special case of the so-called binary symmetric model. We consider expansions in different variables. A remarkable result for these expansions is that the coefficients in the beginning of the expansion will not change anymore as n becomes larger. Finally we describe a method to obtain a series expansion for the entropy making use of a recurrence relation for the given conditional probability.