Topological structure preserving numerical simulations of dynamical models

Topological structure preserving numerical simulations of dynamical models

This paper brings together two methods producing numerical solutions with a statement of their quality — the nonstandard finite difference method and the method of validated computing. It deals with the construction and the analysis of reliable numerical discretizations of dynamical systems by employing these two techniques. An epidemiological model is used as a model example for their combined...

Topological simulations of dynamical features in coarsening soap froth.

Simulations performed using the recently introduced topological model B with deterministic T2 processes do not agree with some very recent results concerning the evolution of a single perturbed cluster. We analyze the source of the discrepancy and introduce a new topological model that is in very good agreement with experiments and simulations available up to now.

Numerical Simulations of Cooling and Topological Excitations of Quantum Gases

This thesis describes the numerical investigation of the production of ultra-cold particle ensembles and the manipulation of Bose-Einstein condensate (BEC) clouds. Ultra-cold particle ensembles are commonly obtained by several cooling steps, the last and most effective of which is the evaporation of particles from a trap. A simulation program has been developed for the simulation of the evapora...

00 4 Dynamical Models and Numerical Simulations of Incomplete Violent Relaxation

N-body simulations of collisionless collapse have offered important clues to the construction of realistic stellar dynamical models of elliptical galaxies. Such simulations confirm and quantify the qualitative expectation that rapid collapse of a self-gravitating collisionless system, initially cool and significantly far from equilibrium, leads to incomplete relaxation. In this paper we revisit...

Numerical Simulations of the Dynamical Behavior of the SK Model