Numerical simulations for stochastic lattice equations.
Numerical simulations of fractionated electrograms and pathological cardiac action potential.
Numerical solution of a stochastic model of a ball-type vibration absorber
The mathematical model of a ball-type vibration absorber represents a non-linear differential system which includes non-holonomic constraints. When a random ambient excitation is taken into account, the system has to be treated as a stochastic deferential equation. Depending on the level of simplification, an analytical solution is not practicable and numerical solution procedures have to be applied. The contribution presents a simple stochastic analysis of a particular resonance effect which can...
Numerical solutions for a model of tissue invasion and migration of tumour cells.
Numerical studies of parameter estimation techniques for nonlinear evolution equations
We briefly discuss an abstract approximation framework and a convergence theory of parameter estimation for a general class of nonautonomous nonlinear evolution equations. A detailed discussion of the above theory has been given earlier by the authors in another paper. The application of this theory together with numerical results indicating the feasibility of this general least squares approach are presented in the context of quasilinear reaction diffusion equations.
Numerical study of the 6-vertex model with domain wall boundary conditions
A Markov process converging to a random state of the 6-vertex model is constructed. It is used to show that a droplet of c-vertices is created in the antiferromagnetic phase and that the shape of this droplet has four cusps.
Numerical study of the stopping of aura during migraine
This work is devoted to the study of migraine with aura in the human brain. Following [6], we class migraine as a propagation of a wave of depolarization through the cells. The mathematical model used, based on a reaction-diffusion equation, is briefly presented. The equation is considered in a duct containing a bend, in order to model one of the numerous circumvolutions of the brain. For a wide set of parameters, one can establish the existence...
Numerical study of the systematic error in Monte Carlo schemes for semiconductors
The paper studies the convergence behavior of Monte Carlo schemes for semiconductors. A detailed analysis of the systematic error with respect to numerical parameters is performed. Different sources of systematic error are pointed out and illustrated in a spatially one-dimensional test case. The error with respect to the number of simulation particles occurs during the calculation of the internal electric field. The time step error, which is related to the splitting of transport and electric field...