Related papers: Radiative transfer with long-range interactions: r…
Using random walk simulations we explore diffusive transport through monodisperse sphere packings over a range of packing fractions, $\phi$, in the vicinity of the jamming transition at $\phi_{c}$. Various diffusion properties are computed…
We investigate the propagation of infinitesimal harmonic mechanical waves emitted from a boundary with variable velocity and arriving at a stationary observer. In the classical Doppler effect, $X_\mathrm{s}(t) = vt$ is the location of the…
A common wisdom posits that transports of conserved quantities across clean nonintegrable quantum systems at high temperatures are diffusive when probed from the emergent hydrodynamic regime. We show that this empirical paradigm may alter…
The transport of charged particles in the heliosphere and the interstellar medium is governed by the interaction of particles and magnetic irregularities. For the transport of protons a rather simple model using a linear Alfv\'en wave…
The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear…
We introduce a non-exponential radiative framework that takes into account the local spatial correlation of scattering particles in a medium. Most previous works in graphics have ignored this, assuming uncorrelated media with a uniform,…
We present a general method to calculate radiative transfer including scattering in the continuum as well as in lines in spherically symmetric systems that are influenced by the effects of general relativity (GR). We utilize a comoving…
Mathematical network models are extremely useful to capture complex propagation processes between different regions (nodes), for example the spread of an infectious agent between different countries, or the transport and replication of…
We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two…
We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we…
Since the dawn of the space age, observations of energetic particles in planetary radiation belts have been interpreted within a diffusive transport framework, even though the processes that populate and deplete these belts produce highly…
We consider the boundary value problem of the stationary transport equation in the slab domain of general dimensions. In this paper, we discuss the relation between discontinuity of the incoming boundary data and that of the solution to the…
We solved the radiative transfer and statistical equilibrium equations in a two-dimensional cross-section of a cylindrical structure oriented horizontally and lying above the solar surface. The cylinder is filled with a mixture of hydrogen…
Multiple scattering of light by resonant vapor is characterized by L\'evy-type superdiffusion with a single-step size distribution $p(x)\propto 1/x^{1+\alpha}$. We investigate L\'evy flight of light in a hot rubidium vapor…
Modelling diffusion processes in heterogeneous media requires addressing inherent discontinuities across interfaces, where specific conditions are to be met. These challenges fall under the purview of Mathematical Analysis as…
A stationary distribution function that describes the entire processes of propagation of relativistic particles, including the transition between the ballistic and diffusion regimes, is obtained. The spacial component of the constructed…
We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly…
We study the long-range spatial correlations in the nonequilibrium steady state of a randomly driven granular fluid with the emphasis on obtaining the explicit form of the static structure factors. The presence of immobile particles…
We address the issue of the proximity of interacting diffusion models on large graphs with a uniform degree property and a corresponding mean field model, i.e. a model on the complete graph with a suitably renormalized interaction…
We present a short overview of the recent results in the theory of diffusion and wave equations with generalised derivative operators. We give generic examples of such generalised diffusion and wave equations, which include time-fractional,…