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

The results of investigations of main characteristics of a one-dimensional percolation theory (percolation threshold, critical exponents of correlation radius and specific heat, and free energy) are presented for the problem of bonds and…

Selection systems and the corresponding replicator equations model the evolution of replicators with a high level of abstraction. In this paper we apply novel methods of analysis of selection systems to the replicator equations. To be…

We study the problem of a random walk on a lattice in which bonds connecting nearest neighbor sites open and close randomly in time, a situation often encountered in fluctuating media. We present a simple renormalization group technique to…

We study the evolution of one-dimensional relativistic jets, using the exact solution of the Riemann problem for relativistic flows. For this purpose, we solve equations for the ideal special relativistic fluid composed of dissimilar…

We extend our approach for the exact solution of the Riemann problem in relativistic hydrodynamics to the case in which the fluid velocity has components tangential to the initial discontinuity. As in one-dimensional flows, we here show…

A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent…

An $(a,b)$-difference necklace of length $n$ is a circular arrangement of the integers $0, 1, 2, \ldots , n-1$ such that any two neighbours have absolute difference $a$ or $b$. We prove that, subject to certain conditions on $a$ and $b$,…

Solutions of Rough Differential Equations (RDE) may be defined as paths whose increments are close to an approximation of the associated flow. They are constructed through a discrete scheme using a non-linear sewing lemma. In this article,…

A generalisation of reaction diffusion systems and their travelling solutions to cases when the productive part of the reaction happens only on a surface in space or on a line on plane but the degradation and the diffusion happen in bulk…

We present a procedure in which known solutions to reflection equations for interaction-round-a-face lattice models are used to construct new solutions. The procedure is particularly well-suited to models which have a known fusion hierarchy…

We solve a class of attractor neural network models with a mixture of 1D nearest-neighbour and infinite-range interactions, which are of a Hebbian-type form. Our solution is based on a combination of mean-field methods, transfer matrices…

We have generalised the exact solution of the Riemann problem in special relativistic hydrodynamics for arbitrary tangential flow velocities. The solution is obtained by solving the jump conditions across shocks plus an ordinary…

A new method is introduced allowing to solve exactly the reactions A+A->inert and A+A->A on the 1D lattice with synchronous diffusional dynamics (simultaneous hopping of all particles). Exact connections are found relating densities and…

We survey recent results on reaction-diffusion equations with discontinuous hysteretic nonlinearities. We connect these equations with free boundary problems and introduce a related notion of spatial transversality for initial data and…

We revisit the velocity-dependent one-scale model for topological defect evolution, and present a new alternative formulation in terms of a physical (rather than invariant) characteristic length scale. While the two approaches are…

Residual distributions (RD) schemes are a class of of high-resolution finite volume methods for unstructured grids. A key feature of these schemes is that they make use of genuinely multidimensional (approximate) Riemann solvers as opposed…

We derive the fully time-dependent solution to a run-and-tumble model for a particle which has tumbling restricted to the boundaries of a one-dimensional interval. This is achieved through a field-theoretic perturbative framework by…

Graphene and other recently developed 2D materials exhibit exceptionally strong in-plane stiffness. Relaxation of few-layer structures, either free-standing or on slightly mismatched substrates occurs mostly through out-of-plane bending and…

We consider general approach to exactly solvable 2D dilaton cosmology with one-loop backreaction from conformal fields taken into account. It includes as particular cases previous models discussed in literature. We list different types of…

We derive the long-time dynamics of a tracer immersed in a one-dimensional active bath. In contrast to previous studies, we find that the damping and noise correlations possess long-time tails with exponents that depend on the tracer…