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A definition for elliptical tempered stable distribution, based on the characteristic function, have been explained which involve a unique spectral measure. This definition provides a framework for creating a connection between infinite…
Dispersion curves to a oscillatory reaction-diffusion system with the self-consistent flow have obtained by means of numerical calculations. The flow modulates the shape of dispersion curves and characteristics of traveling waves. The point…
Atomic diffusion is usually understood as a succession of random, independent displacements of an adatom over the surface's potential energy landscape. Nevertheless, an analysis of Molecular Dynamics simulations of self-diffusion on Cu(111)…
We derive some regularity estimates of the solution to a time fractional diffusion equation, that are useful for numerical analysis, and partially unravel the singularity structure of the solution with respect to the time variable.
We study the stability of reaction-diffusion equations in presence of noise. The relationship of stability of solutions between the stochastic ordinary different equations and the corresponding stochastic reaction-diffusion equation is…
In a companion paper, we established nonlinear stability with detailed diffusive rates of decay of spectrally stable periodic traveling-wave solutions of reaction diffusion systems under small perturbations consisting of a nonlocalized…
We consider in this contribution a simplified idealized one-dimensional model in a nuclear core reactor coupling the diffusion equation on the neutron flux withthe enthalpy equation for the water which collects the heat produced by this…
In this paper, we give a review of fractal calculus which is an expansion of standard calculus. Fractal calculus is applied for functions which are not differentiable or integrable on totally disconnected fractal sets such as middle-$\mu$…
Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic…
The buoyancy-induced parallel flow in a vertical cylindrical porous layer is analysed. A radial thermal gradient caused by a uniformly distributed heat source is assumed to induce the buoyant flow. The layer boundaries are modelled as…
The generalized Taylor's Formula is used to derive a fractional radial-cylindrical diffusivity model via a fractional conservation of mass in radial geometry in a petroleum reservoir. The result is a space-fractional generalization of the…
In this work we define the plasma dispersion function for a suprathermal plasma described with a regularized kappa distribution. As is known from Maxwellian as well as (standard) kappa plasmas, the respective Fried-Conte and the modified…
Thermally bistable fluid tends to self-organize into clouds of hot and cold material, which are internally uniform and separated by thin conduction fronts. The evolution of these clouds has been studied for isobaric systems, but when…
The classical problem of thermal explosion is modified so that the chemically active gas is not at rest but is flowing in a long cylindrical pipe. Up to a certain section the heat-conducting walls of the pipe are held at low temperature so…
GTPase molecules are important regulators in cells that continuously run through an activation/deactivation and membrane-attachment/membrane-detachment cycle. Activated GTPase is able to localize in parts of the membranes and to induce cell…
We study the planar front solution for a class of reaction diffusion equations in multidimensional space in the case when the essential spectrum of the linearization in the direction of the front touches the imaginary axis. At the linear…
We investigate the stability and nonlinear local dynamics of spectrally stable wave trains in reaction-diffusion systems. For each $N\in\mathbb{N}$, such $T$-periodic traveling waves are easily seen to be nonlinearly asymptotically stable…
The dynamics of a mathematical model of the Calvin cycle, which is part of photosynthesis, is analysed. Since diffusion of ATP is included in the model a system of reaction-diffusion equations is obtained. It is proved that for a suitable…
Fluid discontinuities, such as shock fronts and vortex sheets, can reflect waves and become unstable to corrugation. Analytical calculations of these phenomena are tractable in the simplest cases only, while their numerical simulations are…
We study a numerical method for convection diffusion equations, in the regime of small viscosity. It can be described as an exponentially fitted conforming Petrov-Galerkin method. We identify norms for which we have both continuity and an…