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The anisotropic diffusion equation is imperative in understanding cosmic ray diffusion across the Galaxy, the heliosphere, and its interplay with the ambient magnetic field. This diffusion term contributes to the highly stiff nature of the…
A ubiquitous observation in cell biology is that diffusion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This…
Langevin simulations provide an effective way to study collective effects of Brownian particles immersed in a two-dimensional periodic potential. In this paper, we concentrate essentially on the behaviour of the tracer (DTr) and bulk (DB)…
We study the problem of homogenization for inertial particles moving in a periodic velocity field, and subject to molecular diffusion. We show that, under appropriate assumptions on the velocity field, the large scale, long time behavior of…
We introduce MRF-DiPh, a novel physics informed denoising diffusion approach for multiparametric tissue mapping from highly accelerated, transient-state quantitative MRI acquisitions like Magnetic Resonance Fingerprinting (MRF). Our method…
Statistics of closed paths in two-dimensional (2D) systems, which just determines the interference quantum correction to conductivity and anomalous magnetoconductance, has been studied by computer simulation of a particle motion over the…
We develop a new Monte Carlo method that solves hyperbolic transport equations with stiff terms, characterized by a (small) scaling parameter. In particular, we focus on systems which lead to a reduced problem of parabolic type in the limit…
Quantum transport in inhomogeneous magnetic fields is investigated numerically in two-dimensional systems using the equation of motion method. In particular, the diffusion of electrons in random magnetic fields in the presence of additional…
High diffusion-sensitizing magnetic field gradients have been more and more often applied nowadays to achieve a better characterization of the microstructure. As the resulting spin-echo signal significantly deviates from the conventional…
Restrictions to molecular motion by barriers (membranes) are ubiquitous in biological tissues, porous media and composite materials. A major challenge is to characterize the microstructure of a material or an organism nondestructively using…
Partial wave theory of a three dmensional scattering problem for an arbitray short range potential and a nonlocal Aharonov-Bohm magnetic flux is established. The scattering process of a ``hard shere'' like potential and the magnetic flux is…
We generalize Einstein's probabilistic method for the Brownian motion to study compressible fluids in porous media. The multi-dimensional case is considered with general probability distribution functions. By relating the expected…
Statistics of closed paths in two-dimensional systems, which just determines the interference quantum correction to conductivity and anomalous magnetoconductance, has been studied by computer simulation of a particle motion over the plane…
We study the phase transition dynamics of a fluid system in which the particles diffuse anisotropically in space. The motivation to study such a situation is provided by systems of interacting magnetic colloidal particles subject to the…
When magnetohydrodynamic turbulence evolves in the presence of a large-scale mean magnetic field, an anisotropy develops relative to that preferred direction. The well-known tendency is to develop stronger gradients perpendicular to the…
Diffusion of self-propelled particles in the presence of randomly distributed obstacles in three dimensions is studied using molecular dynamics simulations. It is found that depending on the magnitude of the propelling force and the…
The Maxwell equations for an homogeneous medium in which electric currents are composed of Ohmic, diffusive and impressed currents are written in the static approximation in which displacements currents are neglected. Closed exact…
The dynamics of polymer-nanoparticle (NP) mixtures, which involves multiple scales and system-specific variables, has posed a long-standing challenge on its theoretical description. In this paper, we construct a microscopic theory for…
Astrophysical plasmas are subject to a tight connection between magnetic fields and the diffusion of particles, which leads to an anisotropic transport of energy. Under the fluid assumption, this effect can be reduced to an…
The transport of energetic charged particles (e.g., cosmic rays) in turbulent magnetic fields is usually characterized in terms of the diffusion parallel and perpendicular to a large-scale (or mean) magnetic field. The nonlinear guiding…