Dynamics of a lattice gas model

Lotka–Volterra equations (LVEs) for mutualisms predict that when mutualistic effects between species are strong, population sizes of the species increase infinitely, which is the so-called divergence problem. Although many models have been established to avoid the problem, most of them are rather complicated. This paper considers a mutualism model of two species, which is derived from reactions on lattice and has a form similar to that of LVEs. Population sizes in the model will not increase infinitely since there is interspecific competition for sites on the lattice. Global dynamics of the model demonstrate essential features of mutualisms and basic mechanisms by which the mutualisms can lead to persistence/extinction of mutualists. Our analysis not only confirms typical dynamics obtained by numerical simulations in a previous work, but also exhibits a new one. Saddle-node bifurcation, transcritical bifurcation and pitchfork bifurcation in the system are demonstrated, while a relationship between saddle-node bifurcation and pitchfork bifurcation in the model is displayed. Numerical simulations validate and extend our conclusions.     

Traveling wavefronts of a delayed lattice reaction-diffusion model

We investigate a system of delayed lattice differential system which is a model of pioneer-climax species distributed on one dimensional discrete space. We show that there exists a constant $c^*>0$, such that the model has traveling wave solutions connecting a boundary equilibrium to a co-existence equilibrium for $c\geq c^*$. We also argue that $c^*$ is the minimal wave speed and the delay is harmless. The Schauder's fixed point theorem combining with upper-lower solution technique is used for showing the existence of wave solution.     

Infinite paths in a Lorentz lattice gas model

We consider infinite paths in an illumination problem on the lattice ℤ², where at each vertex, there is either a two-sided mirror (with probability p≥ 0) or no mirror (with probability 1 −p). The mirrors are independently oriented NE-SW or NW-SE with equal probability. We consider beams of light which are shone from the origin and deflected by the mirrors. The beam of light is either periodic or unbounded. The novel feature of this analysis is that we concentrate on the measure on the space of paths. In particular, under the assumption that the set of unbounded paths has positive measure, we are able to establish a useful ergodic property of the measure. We use this to prove results about the number and geometry of infinite light beams. Extensions to higher dimensions are considered. Received: 14 November 1996 / Revised version: 1 September 1998     

An effective model of a porous-fluid medium

For a medium containing alternating porous Biot layers and fluid layers, an effective model is established by the method of matrix averaging. An investigation of equations of this effective model shows that the wave field consists of a leading front and two triangular fronts. The velocities of these fronts along the axes are determined. If the thicknesses of the fluid layers are very small, then the second triangular front is converted into a back concave front, and a slow wave arises. This slow wave is of interest for seismology. Bibliography: 11 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 354, 2008, pp. 190–211.     

On the hydrodynamic limit of a Ginzburg-Landau lattice model

Summary A lattice system of interacting diffusion processes is investigated. The evolution is attractive and time reversible, the spin satisfies a conservation law. It is shown that the rescaled spin field converges in probability to the corresponding solution to a nonlinear diffusion equation.Supported in part by the Hungarian National Foundation for Scientific Research, grant No. 819/1, and by the Mathematical Department of Rutgers University, N.S.F. grant DMR 8612369     

Generalized coherent states and nonlinear dynamics of a lattice quasispin model

The nonlinear lattice equation of the ϕ⁶ theory is studied by using the technique of generalized coherent states associated to a SU(2) Lie group. We analyze the discrete nonlinear equation with weak interaction between sites. The existence of saddles and centers is shown. The qualitative parametric domains which contain kinks, bubbles and plane waves were obtained. The specific implications of saddles and centers to the parametric first- and second-order phase transitions are identified and analyzed.     

Accelerating the coarse time-stepper for a lattice Boltzmann model

The equation-free framework for multiscale computing is built around the central idea of a coarse time-stepper, which is an approximate time integrator for the macroscopic variables when only a microscopic simulator is available. In a previous paper, we studied the accuracy and stability of the coarse time-stepper when the microscopic simulator is a lattice Boltzmann model for one-dimensional diffusion. In this paper, we rely on these results to show how the coarse time-stepper can be accelerated using the recently proposed teleprojective method or the multistep state extrapolation method. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Binary operations and lattice structure for a model of matching with contracts

We consider a restricted model of many-to-one matching with contracts and we order the set of stable allocations according both to the unanimous-for-doctors partial ordering and Blair’s partial ordering for hospitals. We define two binary operations to calculate the least upper bound and greatest lower bound for each pair of elements of this set in a simple way. By using these operations, we show that the set of stable allocations has dual lattice structures, thus reflecting an expected counterposition of interests between both sides of the market.     

Modeling the effective permeability of microcracked materials using continuum and lattice micromechanics

Using the framework of the mean-field homogenization method, we propose a continuum and a lattice version of the cascade micromechanics model for the estimation of the effective permeability of microcracked materials. Estimates for the critical microcrack density below which the REV becomes effectively impermeable are derived for both the continuum and the lattice idealizations. A validation example that compares model predictions with direct numerical simulations for the effective permeability as a function of the microcrack volume fraction is provided. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Liouville's equation and the lattice sinh-Gordon model

The equivalence of the Liouville lattice model and the massless version of the sinh-Gordon lattice model is established. Thus Liouville's equation is included in the class of systems to which the quantum method of the inverse problem is applicable. A Hamiltonian of the quantum lattice model is constructed.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 161, pp. 24–44, 1987.     

The lattice of recursively enumerable substructures of an effective closure system

Necessary and sufficient conditions are found to prove that there exists an isomorphism preserving r.e. degrees and mapping the lattice of r.e. sets onto the lattice of superstructures of a recursive substructure of an effective closure system. Every recursive Boolean algebra is shown to contain a recursive subalgebra and a special sequence over it, satisfying a certain condition. This allows us to obtain the results proving the existence of r-maximal subalgebras.Translated fromAlgebra i Logika, Vol. 34, No. 4, pp. 472–484, July-August, 1995.Supported by the Competitive Center for Basic Science Research of the Committee of Higher Schools of Learning, grant No. 93-1-88-12.     

Multidimensional Lee-Carter model with switching mortality processes

This paper proposes a multidimensional Lee-Carter model, in which the time dependent components are ruled by switching regime processes. The main feature of this model is its ability to replicate the changes of regimes observed in the mortality evolution. Changes of measure, preserving the dynamics of the mortality process under a pricing measure, are also studied. After a review of the calibration method, a 2D, 2-regimes model is fitted to the male and female French population, for the period 1946-2007. Our analysis reveals that one regime corresponds to longevity conditions observed during the decade following the second world war, while the second regime is related to longevity improvements observed during the last 30 years. To conclude, we analyze, in a numerical application, the influence of changes of measure affecting transition probabilities, on prices of life and death insurances.     

Essential spectrum of a model operator associated with a three-particle system on a lattice

We consider a model operator H associated with the system of three particles interacting via nonlocal pair potentials on a ν-dimensional lattice. We identify channel operators and use their spectra to describe the position and structure of the essential spectrum of H. We obtain an analogue of the Faddeev equation for the eigenfunctions of H.