Related papers: Universal wavenumber selection laws in apical grow…
We consider the distribution of the major index on standard tableaux of arbitrary straight shape and certain skew shapes. We use cumulants to classify all possible limit laws for any sequence of such shapes in terms of a simple auxiliary…
In this letter, we study some evolution networks that grow with linear preferential attachment. Based upon some recent results on the quotient Gamma function, we give a rigorous proof of the asymptotic Mandelbrot law for the degree…
Granular mixtures frequently segregate by grain size along the axis of partially-filled, horizontal, rotating tubes. When segregation approaches saturation at the surface, a well-defined pattern of bands with wavelength $\lambda$ emerges.…
We consider pattern formation in periodically forced binary systems. In particular we focus on systems in which the two species are differentially forced, one being accelerated with respect to the other. Using a continuum model consisting…
Scaling limits of critical percolation models show major differences between low and high dimensional models. The article discusses the formulation of the continuum limit for the former case. A mathematical framework is proposed for the…
Diffusion processes are central to human interactions. One common prediction of the current modeling frameworks is that initial spreading dynamics follow exponential growth. Here, we find that, ranging from mobile handsets to automobiles,…
It is shown that an alternative approach for the characterization of growing branched patterns consists of the statistical analysis of frozen structures, which cannot be modified by further growth, that arise due to competitive processes…
We analyze numerically three different models exhibiting an absorbing phase transition. We focus on the finite-size scaling as well as the dynamical scaling behavior. An accurate determination of several critical exponents allows to…
We apply scaling and the theory of the fundamental limits of the second-order molecular susceptibility to identify material classes with ultralarge nonlinear-optical response. Size effects are removed by normalizing all nonlinearities to…
Under the condition of nonuniformly bounded growth, %nonuniform exponential dichotomy spectrum for nonautonomous linear system is proposed the relationship of the nonuniform exponential dichotomy spectrum and the other two classical…
We introduce a model in which cells belonging to two species proliferate with volume exclusion on an expanding surface. If the surface expands uniformly, we show that the domains formed by the two species present a critical behavior. We…
In this paper we study pattern formation arising in a system of a single reaction-diffusion equation coupled with subsystem of ordinary differential equations, describing spatially-distributed growth of clonal populations of precancerous…
This paper is a short review of the connection between certain types of growth processes and the integrable systems theory, written from the viewpoint of the latter. Starting from the dispersionless Lax equations for the 2D Toda hierarchy,…
We develop a velocity-dependent one-scale model for the evolution of domain wall networks in flat expanding or collapsing homogeneous and isotropic universes with an arbitrary number of spatial dimensions, finding the corresponding scaling…
We consider a (1+1)-dimensional ballistic deposition process with next-nearest neighbor interaction, which belongs to the KPZ universality class, and introduce for this discrete model a variational formulation similar to that for the…
We consider Galton--Watson trees conditioned on both the total number of vertices $n$ and the number of leaves $k$. The focus is on the case in which both $k$ and $n$ grow to infinity and $k = \alpha n + O(1)$, with $\alpha \in (0, 1)$.…
Recently a Hamiltonian formulation for the evolution of the universe dominated by multiple oscillatory scalar fields was developed by the present author and was applied to the investigation of the evolution of cosmological perturbations on…
We propose a stochastic model of a fragmentation process, developed by taking into account fragment lifetime as a function of their size based on the Gibrat process. If lifetime is determined by a power function of fragment size, numerical…
We prove Freidlin-Wentzell type large deviation principles for various rescaled models in populations dynamics that have immigration and possibly harvesting: birth-death processes, Galton-Watson trees, epidemic SI models, and prey-predator…
We determine the characteristic length scale, $L(t)$, in phase ordering kinetics for both scalar and vector fields, with either short- or long-range interactions, and with or without conservation laws. We obtain $L(t)$ consistently by…