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Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
Superdiffusive transport with dynamical exponent $z=3/2$ has been firmly established at finite temperature for a class of integrable systems with a non-abelian global symmetry $G$. On the inclusion of integrability-breaking perturbations,…
We prove dispersive estimates for the wave equation in the exterior of a torus. Because no separation of variables into a basis of eigenfunctions and eigenvalues exists for the time harmonic problem, we introduce a related approximate…
In this paper we consider a representative a priori unstable Hamiltonian system with 2+1/2 degrees of freedom, to which we apply the geometric mechanism for diffusion introduced in the paper Delshams et al., Mem. Amer. Math. Soc. 2006, and…
We study the angular diffusion in a classical $d-$dimensional inertial XY model with interactions decaying with the distance between spins as $r^{-\alpha}$, wiht $\alpha\geqslant 0$. After a very short-time ballistic regime, with…
We investigate the role of the form of the spatial diffusion coefficient in shock acceleration of fast particles. Referring to non-classical diffusion and using the results of numerical (hybrid) simulations tailored for the downstream shock…
The famous Fisher-KPP reaction-diffusion model combines linear diffusion with the typical KPP reaction term, and appears in a number of relevant applications in biology and chemistry. It is remarkable as a mathematical model since it…
We develop a non-perturbative theory to study large-scale quantum dynamics of Dirac particles in disordered scalar potentials (the so-called "topological metal"). For general disorder strength and carrier doping, we find that at large…
In this paper we investigate the variable coefficient two-sided fractional diffusion, advection, reaction equations on a bounded interval. It is known that the fractional diffusion operator may lose coercivity due to the variable…
A wave front of Fisher and Kolmogorov, Petrovskii, and Piskunov type involving two species A and B with different diffusion coefficients $D_A$ and $D_B$ is studied using a master equation approach in dilute and concentrated solutions.…
A superconductive model characterized by a third order parabolic operator L" is analysed. When the viscous terms, represented by higher - order deriva- tives, tend to zero, a hyperbolic operator L0 appears. Furthermore, if P" is the…
In this work an activator-depleted reaction-diffusion system is investigated on polar coordinates with the aim of exploring the relationship and the corresponding influence of domain size on the types of possible diffusion-driven…
Conventional transport theory focuses on either the diffusive or ballistic regimes and neglects the crossover region between the two. In the presence of spin-orbit coupling, the transport equations are known only in the diffusive regime,…
A constructive approach to theory of diffusion processes is proposed, which is based on application of both the symmetry analysis and method of modelling functions. An algorithm for construction of the modelling functions is suggested. This…
Magnetic element tracking is often used to study the transport and diffusion of the magnetic field on the solar photosphere. From the analysis of the displacement spectrum of these tracers, it has been recently agreed that a regime of…
In this paper the experimental results of the recent dynamic aperture at top energy for the CERN Large Hadron Collider are analysed by means of a diffusion model whose novelty consists of deriving the functional form of the diffusion…
We study a turbulence closure model in which the fractional Laplacian $(-\Delta)^\alpha$ of the velocity field represents the turbulence diffusivity. We investigate the energy spectrum of the model by applying Pao's energy transfer theory.…
The analysis of the Rayleigh-B\'enard instability due to the mass diffusion in a fluid-saturated horizontal porous layer is reconsidered. The standard diffusion theory based on the variance of the molecular position growing linearly in time…
By means of analytical calculations and numerical simulations we study the diffusion properties in quasi-two-dimensional structures with two exciton subsystems with an exchange between them. The experimental realisation is possible in…
This paper is concerned with quasilinear parabolic reaction-diffusion-advection systems on extended domains. Frameworks for well-posedness in Hilbert spaces and spaces of continuous functions are presented, based on known results using…