Search results for "Statistical physics"
showing 10 items of 1402 documents
Finite-size scaling in Ising-like systems with quenched random fields: Evidence of hyperscaling violation
2010
In systems belonging to the universality class of the random field Ising model, the standard hyperscaling relation between critical exponents does not hold, but is replaced by a modified hyperscaling relation. As a result, standard formulations of finite size scaling near critical points break down. In this work, the consequences of modified hyperscaling are analyzed in detail. The most striking outcome is that the free energy cost \Delta F of interface formation at the critical point is no longer a universal constant, but instead increases as a power law with system size, \Delta F proportional to $L^\theta$, with $\theta$ the violation of hyperscaling critical exponent, and L the linear ex…
Growth, percolation, and correlations in disordered fiber networks
1997
This paper studies growth, percolation, and correlations in disordered fiber networks. We start by introducing a 2D continuum deposition model with effective fiber-fiber interactions represented by a parameter $p$ which controls the degree of clustering. For $p=1$, the deposited network is uniformly random, while for $p=0$ only a single connected cluster can grow. For $p=0$, we first derive the growth law for the average size of the cluster as well as a formula for its mass density profile. For $p>0$, we carry out extensive simulations on fibers, and also needles and disks to study the dependence of the percolation threshold on $p$. We also derive a mean-field theory for the threshold ne…
A Hebbian approach to complex-network generation
2011
Through a redefinition of patterns in an Hopfield-like model, we introduce and develop an approach to model discrete systems made up of many, interacting components with inner degrees of freedom. Our approach clarifies the intrinsic connection between the kind of interactions among components and the emergent topology describing the system itself; also, it allows to effectively address the statistical mechanics on the resulting networks. Indeed, a wide class of analytically treatable, weighted random graphs with a tunable level of correlation can be recovered and controlled. We especially focus on the case of imitative couplings among components endowed with similar patterns (i.e. attribute…
Non-Periodic Systems with Continuous Diffraction Measures
2015
The present state of mathematical diffraction theory for systems with continuous spectral components is reviewed and extended. We begin with a discussion of various characteristic examples with singular or absolutely continuous diffraction, and then continue with a more general exposition of a systematic approach via stationary stochastic point processes. Here, the intensity measure of the Palm measure takes the role of the autocorrelation measure in the traditional approach. We furthermore introduce a ‘Palm-type’ measure for general complex-valued random measures that are stationary and ergodic, and relate its intensity measure to the autocorrelation measure.
Analysis of random walks on a hexagonal lattice
2019
We consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice. We determine the probability generating functions, the transition probabilities and the relevant moments. The convergence of the stochastic process to a 2-dimensional Brownian motion is also discussed. Furthermore, we obtain some results on its asymptotic behavior making use of large deviation theory. Finally, we investigate the first-passage-time problem of the random walk through a vertical straight-line. Under suitable symmetry assumptions we are able to determine the first-passage-time probabilities in a closed form, which deserve interest in applied fields.
Contextuality Analysis of the Double Slit Experiment (With a Glimpse Into Three Slits)
2018
The Contextuality-by-Default theory is illustrated on contextuality analysis of the idealized double-slit experiment. The experiment is described by a system of contextually labeled binary random variables each of which answers the question: has the particle hit the detector, having passed through a given slit (left or right) in a given state (open or closed)? This system of random variables is a cyclic system of rank 4, formally the same as the system describing the EPR/Bell paradigm with signaling. Unlike the latter, however, the system describing the double-slit experiment is always noncontextual, i.e., the context-dependence in it is entirely explainable in terms of direct influences of…
A Lotka-type model for oscillations in surface reactions
1997
In this paper we introduce a reaction model on a lattice which leads to oscillations. The model consists of two monomolecular and one bimolecular reaction step and is related to the Lotka model. Despite the simple evolution rules, the model shows a complex behaviour (i.e. the appearance of oscillations). This offers us the opportunity to test different types of stochastic approximations and compare them with the results of a Monte Carlo simulation. The simulation is performed on a large lattice (L = 1024) in order to take long-range correlations into account. Comparing the results of this simulation with the stochastic approaches shows that only advanced numerical approximations are able to…
Survival probability approach to the relaxation of a macroscopic system in the defect-diffusion framework
2004
Monte-Carlo Methods
2003
The article conbtains sections titled: 1 Introduction and Overview 2 Random-Number Generation 2.1 General Introduction 2.2 Properties That a Random-Number Generator (RNG) Should Have 2.3 Comments about a Few Frequently Used Generators 3 Simple Sampling of Probability Distributions Using Random Numbers 3.1 Numerical Estimation of Known Probability Distributions 3.2 “Importance Sampling” versus “Simple Sampling” 3.3 Monte-Carlo as a Method of Integration 3.4 Infinite Integration Space 3.5 Random Selection of Lattice Sites 3.6 The Self-Avoiding Walk Problem 3.7 Simple Sampling versus Biased Sampling: the Example of SAWs Continued 4 Survey of Applications to Simulation of Transport Processes 4.…
Thermodynamics of a small system in a μT reservoir
2011
Abstract Due to advances in experimental techniques operating at the nanoscale, it is possible to compute properties from density fluctuations by studying ‘snapshots’ of particle configurations. Thermodynamics on a small scale is different from thermodynamics in bulk systems. We show how the molar enthalpy h and the inverse thermodynamic correction factor Γ - 1 depend on system size and how these properties can be computed from fluctuations at the nanoscale. We find a 1/ L finite size effect for all thermodynamic quantities for a small system in contact with a reservoir, where L is the length of the system in a single dimension.