Related papers: A coupled map lattice model for spontaneous pore f…
We introduce a class of ${\mathbb{Z}}_N$ graded discrete Lax pairs, with $N\times N$ matrices, linear in the spectral parameter. We give a classification scheme for such Lax pairs and the associated discrete integrable systems. We present…
Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an…
Topological matter is a popular topic in both condensed matter and cold atom research. In the past decades, a variety of models have been identified with fascinating topological features. Some, but not all, of the models can be found in…
In this paper we propose a novel coupled poroelasticity-diffusion model for the formation of extracellular oedema and infectious myocarditis valid in large deformations, manifested as an interaction between interstitial flow and the…
This paper studies pattern formations in coupled elliptic PDE systems governed by transparent boundary conditions. Such systems unify diverse areas, including inverse boundary problems (via a single passive/active boundary measurement),…
Based on the Lippmann-Schwinger equation approach, a generalized L\"uscher's formula in 1+1 dimensions for two particles scattering in both the elastic and coupled-channel cases in moving frames is derived. A 2D coupled-channel scattering…
Laser metal additive manufacturing technology is capable of producing components with complex geometries and compositions that cannot be realized by conventional manufacturing methods. However, a large number of pores generated during the…
We introduce a new coupled map lattice model in which the weak interaction takes place via rare "collisions". By "collision" we mean a strong (possibly discontinuous) change in the system. For such models we prove uniqueness of the SRB…
We review the construction of exactly solvable lattice models whose continuum limits are $N=2$ supersymmetric models. Both critical and off-critical models are discussed. The approach we take is to first find lattice models with natural…
We study travelling waves on a two--dimensional lattice with linear and nonlinear coupling between nearest particles and a periodic nonlinear substrate potential. Such a discrete system can model molecules adsorbed on a substrate crystal…
In this article, a compliance minimisation scheme for designing spatially varying orthotropic porous structures is proposed. With the utilisation of conformal mapping, the porous structures here can be generated by two controlling field…
We prove finite-time singularity formation for Lipschitz continuous solutions of the inviscid porous medium equation which vanish on the boundary of the domain. As the density vanishes on the boundary of the domain, the full regularizing…
Biot's consolidation model is a classical model for the evolution of deformable porous media saturated by a fluid and has various interdisciplinary applications. While numerical solution methods to solve poroelasticity by typical schemes…
We develop a unified approach for construction of symplectic forms for 1D integrable equations with the periodic and rapidly decaying initial data. As an example we consider the cubic nonlinear Schr\"{o}dinger equation.
An atomistic model of near-crack-tip plasticity on a square lattice under anti-plane shear kinematics is formulated and studied. The model is based upon a new geometric and functional framework of a lattice manifold complex, which ensures…
The existence of photonic stop bands in the self-assembled arrangement of pores in porous anodic alumina structures is investigated by means of rigorous 2D finite- difference time-domain calculations. Self-assembled porous anodic alumina…
We present integrable lattice equations on a two dimensional square lattice with coupled vertex and bond variables. In some of the models the vertex dynamics is independent of the evolution of the bond variables, and one can write the…
We propose a novel meshless method to compute harmonic maps and conformal maps for surfaces embedded in the Euclidean 3-space, using point cloud data only. Given a surface, or a point cloud approximation, we simply use the standard cubic…
We have performed a numerical solution for band structure of an Abrikosov vortex lattice in type-II superconductors forming a periodic array in two dimensions for applications of incorporating the photonic crystals concept into…
A simple, discrete, parametric model is proposed to describe conditional (correlated) deposition of particles on a surface and formation of a connecting (percolating) cluster. The surface changes spontaneously its properties (phase…