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Statistical Physics (statistical + physics)

Distribution by Scientific Domains

Mathematics and Statistics	50%

Selected Abstracts

Reconstructing Macroeconomics: A Perspective from Statistical Physics and Combinational Stochastic Processes.

ECONOMICA, Issue 301 2009
By MASANAO AOKI, HIROSHI YOSHIKAWA
No abstract is available for this article. [source]

BML revisited: Statistical physics, computer simulation, and probability,

COMPLEXITY, Issue 2 2006
Raissa M. D'Souza
Abstract Statistical physics, computer simulation, and discrete mathematics are intimately related through the study of shared lattice models. These models lie at the foundation of all three fields, are studied extensively, and can be highly influential. Yet new computational and mathematical tools may challenge even well-established beliefs. Consider the BML model, which is a paradigm for modeling self-organized patterns of traffic flow and first-order jamming transitions. Recent findings, on the existence of intermediate states, bring into question the standard understanding of the jamming transition. We review the results and show that the onset of full-jamming can be considerably delayed based on the geometry of the system. We also introduce an asynchronous version of BML, which lacks the self-organizing properties of BML, has none of the puzzling intermediate states, but has a sharp, discontinuous, transition to full jamming. We believe this asynchronous version will be more amenable to rigorous mathematical analysis than standard BML. We discuss additional models, such as bootstrap percolation, the honey-comb dimer model and the rotor-router, all of which exemplify the interplay between the three fields, while also providing cautionary tales. Finally, we synthesize implications for how results from one field may relate to the other, and also implications specific to computer implementations. © 2006 Wiley Periodicals, Inc. Complexity, 12, 30,39, 2006 [source]

The maximum entropy formalism and the idiosyncratic theory of biodiversity

ECOLOGY LETTERS, Issue 11 2007
Salvador Pueyo
Abstract Why does the neutral theory, which is based on unrealistic assumptions, predict diversity patterns so accurately? Answering questions like this requires a radical change in the way we tackle them. The large number of degrees of freedom of ecosystems pose a fundamental obstacle to mechanistic modelling. However, there are tools of statistical physics, such as the maximum entropy formalism (MaxEnt), that allow transcending particular models to simultaneously work with immense families of models with different rules and parameters, sharing only well-established features. We applied MaxEnt allowing species to be ecologically idiosyncratic, instead of constraining them to be equivalent as the neutral theory does. The answer we found is that neutral models are just a subset of the majority of plausible models that lead to the same patterns. Small variations in these patterns naturally lead to the main classical species abundance distributions, which are thus unified in a single framework. [source]

Counterintuitive influence of microscopic chirality on helical order in polymers

JOURNAL OF PHYSICAL ORGANIC CHEMISTRY, Issue 9 2004
Kap Soo Cheon
Abstract Studies of copolymers of chiral and achiral units forming a helical array correlate to statistical physical predictions of the influence of the chiral units on the helical sense taken by the array. In the absence of conflict among the chiral units for helical sense control, the sergeants and soldiers experiment, a larger chiral bias leads to increased control. However, when conflict exists among the chiral units for helical sense control, the majority rule experiment, a larger chiral bias leads to decreased control of the helical sense and therefore a smaller optical activity. Changing the achiral units in the majority rule experiment can change the nature of the statistical physics between statistical and thermal randomness. In general, the experiments quantitatively demonstrate that the effect of chirality is not an intrinsic property of the chiral moiety but rather depends on the molecular environment. Copyright © 2004 John Wiley & Sons, Ltd. [source]

On the noise correlation matrix for multiple radio frequency coils

MAGNETIC RESONANCE IN MEDICINE, Issue 2 2007
Ryan Brown
Abstract Noise correlation between multiple receiver coils is discussed using principles of statistical physics. Using the general fluctuation-dissipation theorem we derive the prototypic correlation formula originally determined by Redpath (Magn Res Med 1992;24:85,89), which states that correlation of current spectral noise depends on the real part of the inverse impedance matrix at a given frequency. A distinct correlation formula is also derived using the canonical partition function, which states that correlation of total current noise over the entire frequency spectrum depends on the inverse inductance matrix. The Kramers-Kronig relation is used to equate the inverse inductance matrix to the spectral integral of the inverse impedance matrix, implying that the total noise is equal to the summation of the spectral noise over the entire frequency spectrum. Previous conflicting arguments on noise correlation may be reconciled by differentiating between spectral and total noise correlation. These theoretical derivations are verified experimentally using two-coil arrays. Magn Reson Med 58:218,224, 2007. © 2007 Wiley-Liss, Inc. [source]

Sampling independent sets in the discrete torus,

RANDOM STRUCTURES AND ALGORITHMS, Issue 3 2008
David GalvinArticle first published online: 27 MAY 200
Abstract The even discrete torus is the graph TL,d on vertex set {0,,,L , 1}d (with L even) in which two vertices are adjacent if they differ on exactly one coordinate and differ by 1(modL) on that coordinate. The hard-core measure with activity , on TL,d is the probability distribution ,, on the independent sets (sets of vertices spanning no edges) of TL,d in which an independent set I is chosen with probability proportional to ,|I|. This distribution occurs naturally in problems from statistical physics and the study of communication networks. We study Glauber dynamics, a single-site update Markov chain on the set of independent sets of TL,d whose stationary distribution is ,,. We show that for , = ,(d,1/4 log 3/4d) and d sufficiently large the convergence to stationarity is (essentially) exponentially slow in Ld,1. This improves a result of Borgs, Chayes, Frieze, Kim, Tetali, Vigoda, and Vu (Proceedings of the IEEE FOCS (1999), 218,229) 5 who had shown slow mixing of Glauber dynamics for , growing exponentially with d. Our proof, which extends to ,-local chains (chains which alter the state of at most a proportion , of the vertices in each step) for suitable ,, closely follows the conductance argument of Borgs et al., 5 adding to it some combinatorial enumeration methods that are modifications of those used by Galvin and Kahn (Combinatorics, Probability and Computing 13 (2004), 137,164) 12 to show that the hard-core model with parameter , on the integer lattice ,d exhibits phase coexistence for , = ,(d,1/4 log 3/4d). The discrete even torus is a bipartite graph, with partition classes , (consisting of those vertices the sum of whose coordinates is even) and . Our result can be expressed combinatorially as the statement that for each sufficiently large ,, there is a ,(,) > 0 such that if I is an independent set chosen according to ,,, then the probability that ,I ,,|,|I ,, is at most ,(,)Ld is exponentially small in Ld,1. In particular, we obtain the combinatorial result that for all , > 0 the probability that a uniformly chosen independent set from TL,d satisfies ,I ,,|,|I ,,, (.25 - ,)Ld is exponentially small in Ld,1. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008 [source]

The ,(2) limit in the random assignment problem

RANDOM STRUCTURES AND ALGORITHMS, Issue 4 2001
David J. Aldous
Abstract The random assignment (or bipartite matching) problem asks about An=min,,,c(i,,,(i)), where (c(i,,j)) is a n×n matrix with i.i.d. entries, say with exponential(1) distribution, and the minimum is over permutations ,. Mézard and Parisi (1987) used the replica method from statistical physics to argue nonrigorously that EAn,,(2)=,2/6. Aldous (1992) identified the limit in terms of a matching problem on a limit infinite tree. Here we construct the optimal matching on the infinite tree. This yields a rigorous proof of the ,(2) limit and of the conjectured limit distribution of edge-costs and their rank-orders in the optimal matching. It also yields the asymptotic essential uniqueness property: every almost-optimal matching coincides with the optimal matching except on a small proportion of edges. ©2001 John Wiley & Sons, Inc. Random Struct. Alg., 18: 381,418, 2001 [source]