Exponential convergence to equilibrium for a class of random-walk models

We prove exponential convergence to equilibrium (L ² geometric ergodicity) for a random walk with inward drift on a sub-Cayley rooted tree. This randomwalk model generalizes a Monte Carlo algorithm for the self-avoiding walk proposed by Berretti and Sokal. If the number of vertices of levelN in the tree grows asC _N ~ ^N N ^–1 , we prove that the autocorrelation time satisfies N² N¹⁺     

一类燃烧模型的同伦分析解法

研究了一类非线性燃烧模型.利用同伦分析方法,得到了该模型的近似解. 关键词： 非线性方程 燃烧模型 同伦分析法 近似解     

一类复杂流行病学模型的混沌研究

研究了一类周期变化的非线性复杂发病率的广义流行病学模型(SIR(susceptible, infected, recovered)模型). 通过一系列坐标变换将原模型转化为Hamilton系统,运用Melnikov方法证明了该系统存在混沌运动,给出了发生同宿分岔的条件,并用数值模拟验证了上述结果. 关键词： SIR(susceptible infected recovered)模型 混沌运动 Melnikov方法 同宿分岔     

On a class of equilibrium states under the Kubo-Martin-Schwinger condition

We study equilibrium states of a quantum Bose gas using Kubo-Martin-Schwinger boundary conditions, for a special class of time evolutions, namely the quasi-free evolutions. Under suitable restrictions, in particular positivity of the elementary excitation spectrum, we are able to describe the states fulfilling the Kubo-Martin-Schwinger conditions. In contrast to the Fermi case the solution is, in general, not unique; this is related to a possible Bose condensation.Attaché de Recherche, C.N.R.S.This work is a part of a «Thèse de Doctorat d'Etat» presented to the «Faculté des Sciences de Marseille», under the number A.O. 3680.     

Absence of mass gap for a class of stochastic contour models

We study a class of Markovian stochastic processes in which the state space is a space of lattice contours and the elementary motions are local deformations. We show, under suitable hypotheses on the jump rates, that the infinitesimal generator has zero mass gap. This result covers (among others) the BFACF dynamics for fixed-endpoint self-avoiding walks and the Sterling-Greensite dynamics for fixed-boundary self-avoiding surfaces. Our models also mimic the Glauber dynamics for the low-temperature Ising model. The proofs are based on two new general principles: the minimum hitting-time argument and the mean (or mean-exponential) hitting-time argument.     

Exact eigenstates for a class of models describing two-mode multiphoton processes

We present an efficient approach to studying the spectra and eigenstates for nonlinear models describing multiphoton processes. We obtain the exact explicit analytical expressions of all the energy spectra and eigenstates in terms of a parameter for a class of models describing two-mode multiphoton processes. The parameter is shown to be determined by the roots of a simple polynomial.     

A globally accurate theory for a class of binary mixture models

The self-consistent Ornstein-Zernike approximation results for the 3D Ising model are used to obtain phase diagrams for binary mixtures described by decorated models, yielding the plait point, binodals, and closed-loop coexistence curves for the models proposed by Widom, Clark, Neece, and Wheeler. The results are in good agreement with series expansions and experiments.     

Parametrizing coarse grained models for molecular systems at equilibrium

Hierarchical coarse graining of atomistic molecular systems at equilibrium has been an intensive research topic over the last few decades. In this work we (a) review theoretical and numerical aspects of different parametrization methods (structural-based, force matching and relative entropy) to derive the effective interaction potential between coarse-grained particles. All methods approximate the many body potential of mean force; resulting, however, in different optimization problems. (b) We also use a reformulation of the force matching method by introducing a generalized force matching condition for the local mean force in the sense that allows the approximation of the potential of mean force under both linear and non-linear coarse graining mappings (E. Kalligiannaki, et al., J. Chem. Phys. 2015). We apply and compare these methods to: (a) a benchmark system of two isolated methane molecules; (b) methane liquid; (c) water; and (d) an alkane fluid. Differences between the effective interactions, derived from the various methods, are found that depend on the actual system under study. The results further reveal the relation of the various methods and the sensitivities that may arise in the implementation of numerical methods used in each case.     

Relativistic models of a class of compact objects

A class of general relativistic solutions in isotropic spherical polar coordinates which describe compact stars in hydrostatic equilibrium are discussed. The stellar models obtained here are characterized by four parameters, namely, ??, k, A and R of geometrical significance related to the inhomogeneity of the matter content of the star. The stellar models obtained using the solutions are physically viable for a wide range of values of the parameters. The physical features of the compact objects taken up here are studied numerically for a number of admissible values of the parameters. Observational stellar mass data are used to construct suitable models of the compact stars.     

On a class of equilibrium states under the Kubo-Martin-Schwinger boundary condition

Using the Kubo-Martin-Schwinger boundary condition for equilibrium states of quantum statistical mechanics of fermion gas, we prove that forT;0 a one-particle evolution (corresponding essentially to bilinear hamiltonians) generally defines a unique equilibrium state, which is quasi-free. Conversely any quasi-free state is the equilibrium state for a single one-particle evolution if it has no Fock part in its product decomposition. Limiting cases whereT 0 andT are studied. In the case whereT 0 one shows that the state generally converges to a Fock state linked to the evolution.Attaché de Recherche au C.N.R.S.This work is a part of a Thèse de Doctorat d'Etat presented to the Faculté des Sciences de Marseille, April 23, 1969, under the number A.O. 3073.     

Higher symmetries in a class of cosmological models

A particular class of solutions of Einstein's field equations, in which the source is a perfect fluid and the geometry admits a two-parameter Abelian isometry group with spacelike orbits, is examined for the possible admission of higher symmetries. It is shown that in certain cases the geometry is spatially homogeneous, being either of the orthogonal Bianchi type I or of the tilted Bianchi-Behr type VIU_h withh = –4, and that no other cases of higher symmetry (in the sense of isometry groups) are possible. The global behaviour of the Bianchi-Behr type VIU_h, models is studied, and conformal diagrams are given. This investigation is extended to the case when additional homothetic vectors are admitted, and a parallel study of the global behaviour, complete with conformal diagrams, is provided. A brief argument also shows that, within the class considered, whenever the fluid flow-lines possess identical thermal histories, the geometry is necessarily spatially homogeneous.     

Discrete isotropies in a class of cosmological models

It is shown that a certain class of cosmological models admits discrete isotropies. These models are solutions of Einsteins field equations, characterised by: (1) the matter is described as a perfect fluid, and (2) there exists a group of motions simply transitive on three-surfaces orthogonal to the fluid flow vector.     

The canonical equilibrium of constrained molecular models

In order to increase the efficiency of the computer simulation of biological molecules, it is very common to impose holonomic constraints on the fastest degrees of freedom; normally bond lengths, but also possibly bond angles. Since the maximum time step required for the stability of the dynamics is proportional to the shortest period associated with the motions of the system, constraining the fastest vibrations allows to increase it and, assuming that the added numerical cost is not too high, also increase the overall efficiency of the simulation. However, as any other element that affects the physical model, the imposition of constraints must be assessed from the point of view of accuracy: both the dynamics and the equilibrium statistical mechanics are model-dependent, and they will be changed if constraints are used. In this review, we investigate the accuracy of constrained models at the level of the equilibrium statistical mechanics distributions produced by the different dynamics. We carefully derive the canonical equilibrium distributions of both the constrained and unconstrained dynamics, comparing the two of them by means of a “stiff” approximation to the latter. We do so both in the case of flexible and hard constraints, i.e., when the value of the constrained coordinates depends on the conformation and when it is a constant number. We obtain the different correcting terms associated with the kinetic energy mass-metric tensor determinants, but also with the details of the potential energy in the vicinity of the constrained subspace (encoded in its first and second derivatives). This allows us to directly compare, at the conformational level, how the imposition of constraints changes the thermal equilibrium of molecular systems with respect to the unconstrained case. We also provide an extensive review of the relevant literature, and we show that all models previously reported can be considered special cases of the most general treatments presented in this work. Finally, we numerically analyze a simple methanol molecule in order to illustrate the theoretical concepts in a practical case.     

Integral representation for non-maxwell models and the approach to equilibrium

An integral representation is proved for the nonequilibrium distribution function of molecules interaction through potentials which are repulsive near r = 0 and diverge less rapidly than r^?4 as r→ 0. The asymptotic approach to the absolute-equilibrium distribution is studied for general initial states.