International Journal of Statistical Mechanics
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Fractional Diffusion Equations for Lattice and Continuum: GrünwaldLetnikov Differences and Derivatives Approach
Mon, 08 Dec 2014 13:16:25 +0000
http://www.hindawi.com/journals/ijsm/2014/873529/
Fractional diffusion equations for threedimensional lattice models based on fractionalorder differences of the GrünwaldLetnikov type are suggested. These lattice fractional diffusion equations contain difference operators that describe longrange jumps from one lattice site to another. In continuum limit, the suggested lattice diffusion equations with noninteger order differences give the diffusion equations with the GrünwaldLetnikov fractional derivatives for continuum. We propose a consistent derivation of the fractional diffusion equation with the fractional derivatives of GrünwaldLetnikov type. The suggested lattice diffusion equations can be considered as a new microstructural basis of spacefractional diffusion in nonlocal media.
Vasily E. Tarasov
Copyright © 2014 Vasily E. Tarasov. All rights reserved.

A Fractional Entropy in Fractal Phase Space: Properties and Characterization
Wed, 24 Sep 2014 00:00:00 +0000
http://www.hindawi.com/journals/ijsm/2014/460364/
A twoparameter generalization of BoltzmannGibbsShannon entropy based on natural logarithm is introduced. The generalization of the ShannonKhinchin axioms corresponding to the twoparameter entropy is proposed and verified. We present the relative entropy, JensenShannon divergence measure and check their properties. The Fisher information measure, the relative Fisher information, and the JensenFisher information corresponding to this entropy are also derived. Also the Lesche stability and the thermodynamic stability conditions are verified. We propose a generalization of a complexity measure and apply it to a twolevel system and a system obeying exponential distribution. Using different distance measures we define the statistical complexity and analyze it for twolevel and fivelevel system.
Chandrashekar Radhakrishnan, Ravikumar Chinnarasu, and Segar Jambulingam
Copyright © 2014 Chandrashekar Radhakrishnan et al. All rights reserved.

The Statistical Mechanics of Random Set Packing and a Generalization of the KarpSipser Algorithm
Mon, 10 Mar 2014 09:07:19 +0000
http://www.hindawi.com/journals/ijsm/2014/136829/
We analyse the asymptotic behaviour of random instances of the maximum set packing (MSP) optimization problem, also known as maximum matching or maximum strong independent set on hypergraphs. We give an analytic prediction of the MSPs size using the 1RSB cavity method from statistical mechanics of disordered systems. We also propose a heuristic algorithm, a generalization of the celebrated KarpSipser one, which allows us to rigorously prove that the replica symmetric cavity method prediction is exact for certain problem ensembles and breaks down when a core survives the leaf removal process. The phenomena threshold discovered by Karp and Sipser, marking the onset of core emergence and of replica symmetry breaking, is elegantly generalized to for one of the ensembles considered, where is the size of the sets.
C. Lucibello and F. RicciTersenghi
Copyright © 2014 C. Lucibello and F. RicciTersenghi. All rights reserved.

An Independence Test Based on Symbolic Time Series
Mon, 24 Feb 2014 07:49:50 +0000
http://www.hindawi.com/journals/ijsm/2014/809383/
An independence test based on symbolic time series analysis (STSA) is developed. Considering an independent symbolic time series there is a statistic asymptotically distributed as a CHI2 with degrees of freedom. Size and power experiments for small samples were conducted applying Monte Carlo simulations and comparing the results with BDS and runs test. The introduced test shows a good performance detecting independence in nonlinear and chaotic systems.
Wiston Adrián Risso
Copyright © 2014 Wiston Adrián Risso. All rights reserved.

Exact Solution to the Extended Zwanzig Model for QuasiSigmoidal Chemically Induced Denaturation Profiles: Specific Heat and Configurational Entropy
Thu, 23 Jan 2014 07:10:18 +0000
http://www.hindawi.com/journals/ijsm/2014/439891/
Temperature and chemically induced denaturation comprise two of the most characteristic mechanisms to achieve the passage from the native state to any of the unstructured states in the denatured ensemble in proteins and peptides. In this work we present a full analytical solution for the configurational partition function of a homopolymer chain polyX in the extended Zwanzig model (EZM) for a quasisigmoidal denaturation profile. This solution is built up from an EZM exact solution in the case where the fraction of native contacts follows exact linear dependence on denaturant’s concentration ; thus an analytical solution for in the case of an exact linear denaturation profile is also provided. A recently established connection between the number of potential nonnative conformations per residue and temperatureindependent helical propensity complements the model in order to identify specific proteinogenic polyX chains, where X represents any of the twenty naturally occurring aminoacid residues. From , equilibrium thermodynamic potentials like entropy and average internal energy and thermodynamic susceptibilities like specific heat are calculated for polyvaline (polyV) and polyalanine (polyA) chains. The influence of the rate at which native contacts denature as function of on thermodynamic stability is also discussed.
G. E. AguilarPineda and L. OlivaresQuiroz
Copyright © 2014 G. E. AguilarPineda and L. OlivaresQuiroz. All rights reserved.

Stochastic Regularization and Eigenvalue Concentration Bounds for Singular Ensembles of Random Operators
Wed, 27 Nov 2013 08:42:11 +0000
http://www.hindawi.com/journals/ijsm/2013/931063/
We propose a simple approach allowing reducing the eigenvalue
concentration analysis of a class of random operator ensembles with singular
probability distribution to the analysis of an auxiliary ensemble with bounded probability density. Our results apply to the Wegner and
Minamitype estimates for single and multiparticle operators.
Victor Chulaevsky
Copyright © 2013 Victor Chulaevsky. All rights reserved.

Solution and Analysis of a OneDimensional FirstPassage Problem with a Nonzero Halting Probability
Sun, 27 Oct 2013 13:19:34 +0000
http://www.hindawi.com/journals/ijsm/2013/831390/
This paper treats a kind of a onedimensional firstpassage problem, which seeks the probability that a random walker first hits the origin at a specified time. In addition to a usual random walk which hops either rightwards or leftwards, the present paper introduces the “halt” that the walker does not hop with a nonzero probability. The solution to the problem is expressed using a Gauss hypergeometric function. The moment generating function of the hitting time is also calculated, and a calculation technique of the moments is developed. The author derives the longtime behavior of the hittingtime distribution, which exhibits powerlaw behavior if the walker hops to the right and left with equal probability.
Ken Yamamoto
Copyright © 2013 Ken Yamamoto. All rights reserved.

Thermalization of Lévy Flights: PathWise Picture in 2D
Thu, 03 Oct 2013 15:22:33 +0000
http://www.hindawi.com/journals/ijsm/2013/738345/
We analyze twodimensional (2D) random systems driven by a symmetric Lévy stable noise which in the presence of confining potentials may asymptotically set down at Boltzmanntype thermal equilibria. In view of the EliazarKlafter nogo statement, such dynamical behavior is plainly incompatible with the standard Langevin modeling of Lévy flights. No explicit pathwise description has been so far devised for the thermally equilibrating random motion we address, and its formulation is the principal goal of the present work. To this end we prescribe a priori the target pdf ρ∗ in the Boltzmann form ~exp[] and next select the Lévy noise (e.g., its Lévy measure) of interest. To reconstruct random paths of the underlying stochastic process we resort to numerical methods. We create a suitably modified version of the time honored Gillespie algorithm, originally invented
in the chemical kinetics context. A statistical analysis of generated sample trajectories allows us to infer a surrogate pdf dynamics which sets down at a predefined target, in consistency with the associated kinetic (master) equation.
Mariusz Żaba and Piotr Garbaczewski
Copyright © 2013 Mariusz Żaba and Piotr Garbaczewski. All rights reserved.

Spectral Functions and Properties of Nuclear Matter
Mon, 15 Jul 2013 12:28:04 +0000
http://www.hindawi.com/journals/ijsm/2013/317491/
The Green’s function method in the KadanoffBaym version provides a basic theory for nuclear dynamics which is applicable also to nonzero temperature and to nonequilibrium systems. At the same time, it maintains the basic manybody techniques of the Brueckner theory that makes reasonable a comparison of the numerical results of the two methods for equilibrium systems. The correct approximation to the spectral function which takes into account the widths of energy levels is offered and discussed, and the comparison of the values of binding energy in the two methods is produced.
V. A. Danilenko, K. A. Gridnev, and A. S. Kondratyev
Copyright © 2013 V. A. Danilenko et al. All rights reserved.

An Especial Fractional Oscillator
Sun, 23 Jun 2013 13:56:12 +0000
http://www.hindawi.com/journals/ijsm/2013/175273/
We propose a peculiar fractional oscillator. By assuming that the motion takes
place in a complex media where the level of fractionality is low, we find that the time
rate of change of the energy of this system has an oscillatory behavior.
A. Tofighi
Copyright © 2013 A. Tofighi. All rights reserved.