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This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis is based on variational techniques and in…
In cond-mat/0103603 Diffusion algebras have been introduced in the context of one-dimensional stochastic processes with exclusion in statistical mechanics. While this reference is focused on the needs of the physicist reader and thus states…
Recent experimental and theoretical developments in the understanding of high energy diffraction, presented in the working group on diffraction at DIS98 in Brussels, are summarised. A template, giving the definition of the most commonly…
Galactic diffuse continuum gamma-ray emission is intricately related to cosmic-ray physics and radio astronomy. We describe recent results from an approach which endeavours to take advantage of this. Information from cosmic-ray composition…
The theory of diffusive particle acceleration explains the spectral properties of the cosmic rays below energies of approx. 10^6 GeV as produced at strong shocks in supernova remnants (SNR's). To supply the observed flux of cosmic rays, a…
A system of diffusion-reaction equations coupled with a dissolution-precipitation model is discussed. We start by introducing a microscale model together with its homogenized version. In the present paper, we first derive the corrector…
The movement of a particle described by Brownian motion is quantified by a single parameter, $D$, the diffusion constant. The estimation of $D$ from a discrete sequence of noisy observations is a fundamental problem in biological single…
In this paper, we study a parabolic reaction diffusion system with constraints that model biofilm growth. Within a unified framework encompassing multiple numerical schemes, we derive the first general convergence rates for approximating…
Diffuse $\gamma$-ray emission is the most prominent observable signature of celestial cosmic-ray interactions at high energies. While already being investigated at GeV energies over several decades, assessments of diffuse $\gamma$-ray…
Diffusion in coulomb crystals can be important for the structure of neutron star crusts. We determine diffusion constants $D$ from molecular dynamics simulations. We find that $D$ for coulomb crystals with relatively soft-core $1/r$…
Diffusive shock acceleration is considered as the main mechanism for particle energization in supernova remnants, as well as in other classes of sources. The existence of some remnants that show a bilateral morphology in the X-rays and…
The self-diffusion coefficient of crystalline solids as a function of density and temperature may derive from thermodynamics concepts and an earlier elastic thermodynamic point defect model [P. Varotsos and K. Alexopoulos, Phys. Rev. B 15,…
The paper entitled "Well posedness of general cross-diffusion systems", by C. Choquet, C. Rosier, L. Rosier, J. Diff. Eq. 2021, is devoted to the mathematical analysis of the Cauchy problem for general cross-diffusion systems without any…
We propose an alternative method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized…
We consider the emission of high energy to very high energy $\gamma$-rays in radio-quiet active galactic nuclei (AGN) or the central regions of radio-loud AGN. We use our results to estimate the $\gamma$-ray flux from the central regions of…
The positron excess measured by PAMELA and AMS can only be explained if there is one or several sources injecting them. Moreover, at the highest energies, it requires the presence of nearby ($\sim$hundreds of parsecs) and middle age…
We describe the motion of a tracer in an environment given by a kinetically constrained spin model (KCSM) at equilibrium. We check convergence of its trajectory properly rescaled to a Brownian motion and positivity of the diffusion…
The scaling form of the whole distribution P(D) of the random diffusion coefficient D(x) in a model of classically diffusing particles is investigated. The renormalization group approach above the lower critical dimension d=0 is applied to…
Diffusion models may be viewed as hierarchical variational autoencoders (VAEs) with two improvements: parameter sharing for the conditional distributions in the generative process and efficient computation of the loss as independent terms…
Deepgenerative models havebecomeapromisingapproach for human motion prediction due to their ability to capture multimodal distributions and represent diverse human be haviors. However, generating predictions that are both di verse and…