Simulation of stochastic reaction-diffusion processes on unstructured meshes

Stochastic chemical systems with diffusion are modeled with a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic level, the master equation for a well stirred chemical system is combined with Brownian motion in space to obtain the reaction-diffusion master equation. The space is covered by an unstructured mesh and the diffusion coefficients on the mesoscale are obtained from a finite element discretization of the Laplace operator on the macroscale. The resulting method is a flexible hybrid algorithm in that the diffusion can be handled either on the meso- or on the macroscale level. The accuracy and the efficiency of the method are illustrated in three numerical examples inspired by molecular biology

Site fidelity and range size of wintering Barnacle Geese Branta leucopsis

Barnacle Geese restrict their movements to relatively few key sites and exhibit considerable variation in ranging behaviour. To examine individual and seasonal variation in site fidelity, habitat use, range size and foraging strategies of Barnacle Geese Branta leucopsis, the movements of 18 male Barnacle Geese tagged in two discrete areas were tracked for 3–6 months from late autumn until departure on the spring migration. Tagged geese concentrated their feeding in a relatively small proportion of apparently suitable habitat. Geese moved increasingly further afield in midwinter, and there was a clear predeparture shift to the largest area of relatively undisturbed, and possibly more nitrogen-rich, saltmarsh on the Solway. Birds from one of the two capture sites tended to be more sedentary and have smaller home ranges

Mechanical Systems of Rigid Bodies Subject to Unilateral Constraints

International audienceThe properties of mechanical systems of rigid bodies subject to unilateral constraints are investigated. In particular, properties of interest for the digital simulation of the motion of such systems are studied. The constraints give rise to discontinuities in the solution. Under general assumptions on the system a unique solution is constructed using the linear complementarity theory of mathematical programming. A numerical method for solution of these problems and generalizations of the constraints studied in this paper are briefly discussed

Stability and non-normality of the k - ε equations

AbstractThe analytical and numerical solutions of the equations of the k-ε turbulence model are analyzed. Under certain conditions on the boundary values and the interior values of k and ε the analytical and numerical solutions are bounded. If the steady state solution is obtained numerically by a Runge-Kutta time-stepping method, then severe constraints on the time-step and the non-normality of the jacobian matrix make the convergence very slow. The simplifications and conclusions are supported by data from a numerical solution of flow over a flat plate