Related papers: The character and the wave front set correspondenc…
In the paper, we experimentally study the inverse problem with the resonant scattering determinant. We analyze the structure of characteristics of perturbed linear waves. Assuming there is the common part of potential perturbation…
A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…
This paper is concerned with the existence and qualitative properties of pulsating fronts for spatially periodic reaction-diffusion equations with bistable nonlinearities. We focus especially on the influence of the spatial period and,…
A narrow energy band of the electronic spectrum in some direction in low-dimensional crystals may lead to a negative differential conductance and N-shaped I-V curve that results in an instability of the uniform stationary state. A…
We relate the notions of spectral gap for unitary representations and subfactors with definability of certain important sets in the corresponding structures. We give several applications of this relationship.
The propagation of unstable interfaces is at the origin of remarkable patterns that are observed in various areas of science as chemical reactions, phase transitions, growth of bacterial colonies. Since a scalar equation generates usually…
In a dissipative Fermi-Pasta-Ulam-Tsingou chain particles interact with their nearest neighbors through anharmonic potentials and linear dissipative forces. We prove the existence of front solutions connecting two different uniformly…
In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the context of observability inequalities for the linear wave…
This paper explores the classification of parameter spaces for reaction-diffusion systems of two chemical species on stationary domains. The dynamics of the system are explored both in the absence and presence of diffusion. The parameter…
The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial Laplacian with a temporal memory term through a time…
The descent set D(w) of a permutation w of 1,2,...,n is a standard and well-studied statistic. We introduce a new statistic, the connectivity set C(w), and show that it is a kind of dual object to D(w). The duality is stated in terms of the…
In this paper, we characterize the wave front sets of solutions to fractional Schr\"{o}dinger equations \(i\partial_{t}u =(-\Delta)^{\theta/2}u + V(x)u\) with $0<\theta <2$ via the wave packet transform (short-time Fourier transform). We…
We consider the dynamics of diffusing particles in one space dimension with annihilation on collision and nucleation (creation of particles) with constant probability per unit time and length. The cases of nucleation of single particles and…
This paper is devoted to reaction-diffusion equations with bistable nonlinearities depending periodically on time. These equations admit two linearly stable states. However, the reaction terms may not be bistable at every time. These may…
We study 2D fronts propagating up a co-moving reaction rate gradient in finite number reaction-diffusion systems. We show that in a 2D rectangular channel, planar solutions to the deterministic mean-field equation are stable with respect to…
The matrix-vector wave equation is a compact first-order differential equation. It was originally used for the analysis of elastodynamic plane waves in laterally invariant media. It has been extended by various authors for laterally varying…
This paper establishes the spectral stability of monotone traveling front solutions for reaction-diffusion equations where the reaction function is of Nagumo (or bistable) type and with diffusivities which are density dependent and…
We present results of a linear stability analysis of relativistic detonation fronts, which have been considered as representing phase interfaces in cosmological first order phase transitions. After discussing general stability conditions…
Several important mechanisms that explain the coherent pulsar radio emission rely on streaming (or beam) instabilities of the relativistic pair plasma in a pulsar magnetosphere. However, it is still not clear whether a streaming instability…
This paper gives a complete classification of the unitary irreducible spherical representations of split real and p-adic groups. The results were obtained around 2000, the changes to the new version are expository.