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We derive diffusive macroscopic equations for the particle and energy density of a system whose time evolution is described by a kinetic equation for the one particle position and velocity function f(r,v,t) that consists of a part that…
The propagation of high-energy cosmic rays through giant molecular clouds constitutes a fundamental process in astronomy and astrophysics. The diffusion of cosmic-rays through these magnetically turbulent environments is often studied…
Multidimensional affine diffusions have been studied in detail for the case of a canonical state space. We present results for general state spaces and provide a complete characterization of all possible affine diffusions with polyhedral…
The effective diffusion of Brownian particles in periodic potential has been a central topic in nonequilibrium statistical physcis. A classical result is the Lifson formula which provides the effective diffusion constant in periodic…
We develop a theoretical framework for the diffusion of a single unconstrained species of atoms on a crystal lattice that provides a generalization of the classical theories of atomic diffusion and diffusion-induced phase separation to…
As the deep learning revolution marches on, masked modeling has emerged as a distinctive approach that involves predicting parts of the original data that are proportionally masked during training, and has demonstrated exceptional…
Reaction-diffusion systems have been proposed as a model for pattern formation and morphogenesis. The Fickian diffusion typically employed in these constructions model the Brownian motion of particles. The biological and chemical elements…
Molecular communication emerges as a promising communication paradigm for nanotechnology. However, solid mathematical foundations for information-theoretic analysis of molecular communication have not yet been built. In particular, no one…
We consider a charged quantum particle in a random magnetic field with Gaussian, delta-correlated statistics. We show that although the single particle properties are peculiar, two particle quantities such as the diffusion constant can be…
We consider the linear dissipative Boltzmann equation describing inelastic interactions of particles with a fixed background. For the simplified model of Maxwell molecules first, we give a complete spectral analysis, and deduce from it the…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
We show how the scattering-into-cones and flux-across-surfaces theorems in Quantum Mechanics have very intuitive pathwise probabilistic versions based on some results by Carlen about large time behaviour of paths of Nelson diffusions. The…
In this article, we review the principles of macroscopic quantum electrodynamics and discuss a variety of applications of this theory to medium-assisted atom-field coupling and dispersion forces. The theory generalises the standard mode…
A general information-theoretic framework for deriving physical laws is presented and a principle of informational physics is enunciated within its context. Existing approaches intended to derive physical laws from information-theoretic…
We sketch a derivation of abstract scattering theory from the microscopic first principles defined by Bohmian mechanics. We emphasize the importance of the flux-across-surfaces theorem for the derivation, and of randomness in the impact…
Diffusion magnetic resonance imaging is a noninvasive imaging technique that can indirectly infer the microstructure of tissues and provide metrics which are subject to normal variability across subjects. Potentially abnormal values or…
A popular numerical method to model the dynamics of a 'full spectrum' of cosmic rays (CRs), also applicable to radiation/neutrino hydrodynamics (RHD), is to discretize the spectrum at each location/cell as a piecewise power law in 'bins' of…
I explain the concept that light quarks diffuse in the QCD vacuum following the spontaneous breakdown of chiral symmetry. I exploit the striking analogy to disordered electrons in metals, identifying, among others, the universal regime…
Denoising diffusion models, a class of generative models, have garnered immense interest lately in various deep-learning problems. A diffusion probabilistic model defines a forward diffusion stage where the input data is gradually perturbed…
We study the interface dynamics of a binary particle mixture in a rotating cylinder numerically. By considering only the particle motion in axial direction, it is shown that the initial dynamics can be well described by a one-dimensional…