Related papers: Evolution with size in a locally periodic system: …
We study the nonlinear wave equation with a sign-changing potential in any space dimension. If the potential is small and rapidly decaying, then the existence of small-amplitude solutions is driven by the nonlinear term. If the potential…
We analyse the evolution of cosmological perturbations which leads to the formation of large isolated voids in the Universe. We assume that initial perturbations are spherical and all components of the Universe (radiation, matter and dark…
We study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…
A novel local evolution equation for one-dimensional interfaces is derived in the context of erosion by ion beam sputtering. We present numerical simulations of this equation which show interrupted coarsening in which an ordered cell…
The Loschmidt echo measures the sensitivity to perturbations of quantum evolutions. We study its short time decay in classically chaotic systems. Using perturbation theory and throwing out all correlation imposed by the initial state and…
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment…
We have simulated the evolution of age structured populations whose individuals represented by their diploid genomes were distributed on a square lattice. The environmental conditions on the whole territory changed simultaneously in the…
We study how environmental stochasticity influences the long-term population size in certain one- and two-species models. The difficulty is that even when one can prove that there is persistence, it is usually impossible to say anything…
We study the statistics of the fluorescence decay rates for single quantum emitters embedded in a scattering medium undergoing a phase transition. Under certain circumstances, the structural properties of the scattering medium explore a…
Loschmidt echo (LE) is a measure of reversibility and sensitivity to perturbations of quantum evolutions. For weak perturbations its decay rate is given by the width of the local density of states (LDOS). When the perturbation is strong…
We study the linear wave equation on a class of spatially homogeneous and isotropic Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetimes in the decelerated regime with spatial topology $\mathbb{R}^3$. Employing twisted $t$-weighted…
We study the finite-size scaling behaviour at the critical point, resulting from the addition of a homogeneous size-dependent perturbation, decaying as an inverse power of the system size. The scaling theory is first formulated in a general…
Regardless of a system's complexity or scale, its growth can be considered to be a spontaneous thermodynamic response to a local convergence of down-gradient material flows. Here it is shown how growth can be constrained to a few distinct…
Let P be a long range metric perturbation of the Euclidean Laplacian on R^d, d>1. We prove local energy decay for the solutions of the wave, Klein-Gordon and Schroedinger equations associated to P. The problem is decomposed in a low and…
The measured distribution of the single-channel delay time of localized microwave radiation and its correlation with intensity differ sharply from the behavior of diffusive waves. The delay time is found to increase with intensity, while…
We study the numerical error in solitary wave solutions of nonlinear dispersive wave equations. A number of existing results for discretizations of solitary wave solutions of particular equations indicate that the error grows quadratically…
The distribution of the deformations of elementary cells is studied in an abstract lattice constructed from the existence of the empty set. One combination rule determining oriented sequences with continuity of set-distance function in such…
This paper presents the Landau damping effects on the microwave instability of a coasting long bunch in an isochronous ring due to finite energy spread and emittance. Our two-dimensional (2D) dispersion relation gives more accurate…
Hyperuniform many particle systems in d-dimensional space, which includes crystals, quasicrystals, and some exotic disordered systems, are characterized by an anomalous suppression of density fluctuations at large length scales such that…
We study localized traveling waves and chaotic states in strongly nonlinear one-dimensional Hamiltonian lattices. We show that the solitary waves are super-exponentially localized, and present an accurate numerical method allowing to find…