All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 3

Displaying 41 – 45 of 45

Showing per page

Time splitting for wave equations in random media

Guillaume Bal, Lenya Ryzhik (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Numerical simulation of high frequency waves in highly heterogeneous media is a challenging problem. Resolving the fine structure of the wave field typically requires extremely small time steps and spatial meshes. We show that capturing macroscopic quantities of the wave field, such as the wave energy density, is achievable with much coarser discretizations. We obtain such a result using a time splitting algorithm that solves separately and successively propagation and scattering in the...

Towards effective dynamics in complex systems by Markov kernel approximation

Christof Schütte, Tobias Jahnke (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

Many complex systems occurring in various application share the property that the underlying Markov process remains in certain regions of the state space for long times, and that transitions between such metastable sets occur only rarely. Often the dynamics within each metastable set is of minor importance, but the transitions between these sets are crucial for the behavior and the understanding of the system. Since simulations of the original process are usually prohibitively expensive, the effective...

Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck equation

François Bolley, Arnaud Guillin, Florent Malrieu (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a Vlasov-Fokker-Planck equation governing the evolution of the density of interacting and diffusive matter in the space of positions and velocities. We use a probabilistic interpretation to obtain convergence towards equilibrium in Wasserstein distance with an explicit exponential rate. We also prove a propagation of chaos property for an associated particle system, and give rates on the approximation of the solution by the particle system. Finally, a transportation inequality...

Tumour angiogenesis model with variable vessels' effectiveness

Jan Poleszczuk, Iwona Skrzypczak (2011)

Applicationes Mathematicae

We propose a model of vascular tumour growth, which generalises the well recognised model formulated by Hahnfeldt et al. in 1999. Our model is based on the same idea that the carrying capacity for any solid tumour depends on its vessel density but it also incorporates vasculature quality which may be lost during angiogenesis as recognised by Jain in 2005. In the model we assume that the loss of vessel quality affects the diffusion coefficient inside the tumour. We analyse basic mathematical properties...

Currently displaying 41 – 45 of 45

Previous Page 3