From extensive numerical simulations, we find that periodic polygonal billiard channels with angles which are irrational multiples of pi generically exhibit normal diffusion (linear growth of the mean squared displacement) when they have a finite horizon, i.e., when no particle can travel arbitrarily far without colliding. For the infinite horizon case we present numerical tests showing that th...

We measure all nonzero elements of the three-dimensional diffusion tensor D for clusters of colloidal spheres to a precision of 1% or better using digital holographic microscopy. We study both dimers and triangular trimers of spheres, for which no analytical calculations of the diffusion tensor exist. We observe anisotropic rotational and translational diffusion arising from the asymmetries of ...

Mathematical restoration models, in particular, total variationbased models can easily lose fine structures during image denoising. In order to overcome the drawback, this article introduces two strategies: the nonconvex (NC) diffusion and the texture-free residual (TFR) parameterization. A non-standard numerical procedure is suggested and its stability is analyzed to effectively solve the NC d...

In this paper we construct numerical schemes to approximate linear transport equations with slab geometry by one-dimensional diffusion equations. We treat both the case of pure diffusive scaling and the case where kinetic and diffusive scalings coexist. The diffusion equations and their data are derived from asymptotic and layer analysis which allows general scattering kernels and general data....

Direct numerical simulation of turbulent flow behind a cylinder, wake flow, using the random vortex method for an incompressible fluid in two dimensions is presented. In the random vortex method, the primary variable is vorticity of the flow field. After generation on the cylinder wall, it is followed in two fractional time step in a Lagrangian system of coordinates, namely convection and diffu...

In this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm Ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. We applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. The main properties of deterministic difference schemes,...

Abstract. In this work, which is the continuation of [9], we propose numerical schemes for linear kinetic equation which are able to deal with the fractional diffusion limit. When the collision frequency degenerates for small velocities it is known that for an appropriate time scale, the small mean free path limit leads to an anomalous diffusion equation. From a numerical point of view, this de...

The parabolic partial differential equation arises in many application of technologies. In this paper, we propose an approximate method for solution of the heat and advection-diffusion equations using Laguerre-Gaussians radial basis functions (LG-RBFs). The results of numerical experiments are compared with the other radial basis functions and the results of other schemes to confirm the validit...

Citation: Ginsburger K, Poupon F, Beaujoin J, Estournet D, Matuschke F, Mangin J-F, Axer M and Poupon C (2018) Improving the Realism of White Matter Numerical Phantoms: A Step toward a Better Understanding of the Influence of Structural Disorders in Diffusion MRI. Front. Phys. 6:12. doi: 10.3389/fphy.2018.00012 Improving the Realism of White Matter Numerical Phantoms: A Step toward a Better Und...