相关论文: Exact Solution for a 1-dimensional model for Repta…

The duality between a class of the Davey-Stewartson type coupled systems and a class of two-dimensional Toda type lattices is discussed. A new coupled system related to the recently found lattice is presented. A method for eliminating…

We study an exact rotating and expanding solution of the fluid dynamical model of heavy ion reactions, that take into account the rate of slowing down of the rotation due to the longitudinal and transverse expansion of the system. The…

Inspired by recent experiments on DNA replication, we apply a one-dimensional nucleation-and-growth model to DNA-replication kinetics, focusing on how to extract the time-dependent nucleation rate I(t) and growth speed v from data. We…

Polymer melts with chains undergoing reversible crosslinking have distinctively favorable dynamic properties, e.g., self healing and reprocessability. In these situations there are two relevant elementary time scales: the segmental and the…

This article presents a review of some old and new results on the long time behavior of reflected diffusions. First, we present a summary of prior results on construction, ergodicity and geometric ergodicity of reflected diffusions in the…

This paper is concerned with the inverse scattering problem involving the time-domain elastic wave equations in a bounded $d$-dimensional domain. First, an explicit reconstruction formula for the density is established by means of the…

Sequencing by synthesis is the underlying technology for many next-generation DNA sequencing platforms. We developed a new model, the fixed flow cycle model, to derive the distributions of sequence length for a given number of flow cycles…

We present a set of uniform polynomial equations that provides multidimensional on-lattice higher-order models of the lattice Boltzmann theory, while keeping compact the number of discrete velocities. As examples, we explicitly derive two-…

It is well known that rather general mutation-recombination models can be solved algorithmically (though not in closed form) by means of Haldane linearization. The price to be paid is that one has to work with a multiple tensor product of…

We introduce the new, exactly solvable model of the two-dimensional Dirac fermion in presence of an asymmetric, P\"oschl-Teller-like vector potential. Utilizing the translation invariance of the system, the effective one-dimensional…

An interacting spin-fermion model is exactly solved on an open chain. In a certain representation, it is the nearest-neighbor Hubbard model in the limit of infinite $U$ (local interaction). Exact solution of its complete energy…

As a prelude to what might be expected as forthcoming breakthroughs in finding new approaches toward solving three-dimensional lattice models in the twenty-first century, we review the exact solutions of two lattice models in three…

We introduce a new approach to connectivity-dependent properties of diluted systems, which is based on the transfer-matrix formulation of the percolation problem. It simultaneously incorporates the connective properties reflected in…

A new kinetic model is proposed where the equilibrium distribution with bounded support has a range of velocities about two average velocities in 1D. In 2D, the equilibrium distribution function has a range of velocities about four average…

Exactly solvable models provide an opportunity to study different aspects of reduced quantum dynamics in detail. We consider the reduced dynamics of a single spin in finite XX and XY spin 1/2 chains. First we introduce a general expression…

Exact results on particle-densities as well as correlators in two models of immobile particles, containing either a single species or else two distinct species, are derived. The models evolve following a descent dynamics through…

We study reversible deterministic dynamics of classical charged particles on a lattice with hard-core interaction. It is rigorously shown that the system exhibits three types of transport phenomena, ranging from ballistic, through diffusive…

This paper derives recursion equations for a robust smoothing problem for a class of nonlinear systems with uncertainties in modeling and exogenous noise sources. The systems considered operate in discrete-time and the uncertainties are…

We construct a dynamical system for a reaction diffusion system due to Murray, which relies on the use of the Thomas system nonlinearities and describes the formation of animal coat patterns. First, we prove existence and uniqueness of…

We study the dynamics of solutions of infinitely thin needles up to densities deep in the semidilute regime by Brownian dynamics simulations. For high densities, these solutions become strongly entangled and the motion of a needle is…