Related papers: Growth Equation with Conservation Law
We study the dynamics of a growing crystalline facet where the growth mechanism is controlled by the geometry of the local curvature. A continuum model, in (2+1) dimensions, is developed in analogy with the Kardar-Parisi-Zhang (KPZ) model…
This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…
We succeed in writing 2-dimensional conformally invariant non-linear elliptic PDE (harmonic map equation, prescribed mean curvature equations...etc) in divergence form. This divergence free quantities generalize to target manifolds without…
This paper presents an overview of the derivation and significance of recently derived conservation laws for the matrix moments of Hermitean random matrices with dominant exponential weights that may be either even or odd. This is based on…
We carry out an analysis of the existence of solutions for a class of nonlinear partial differential equations of parabolic type. The equation is associated to a nonlocal initial condition, written in general form which includes, as…
Conservation laws of the nonlinear Schr\"{o}dinger equation are studied in the presence of higher-order nonlinear optical effects including the third-order dispersion and the self-steepening. In a context of group theory, we derive a…
A crystal surface which is miscut with respect to a high symmetry plane exhibits steps with a characteristic distance. It is argued that the continuum description of growth on such a surface, when desorption can be neglected, is given by…
In the past many papers have appeared which simulated surface growth with different growth models. The results showed that, if models differed only slightly in their `growth' rules, the resulting surfaces may belong to different…
Well known biological approximations are universal, i.e. invariant to transformations from one species to another. With no other experimental data, such invariance yields exact conservation (with respect to biological diversity and…
The Kardar-Parisi-Zhang (KPZ) equation defines the main universality class for nonlinear growth and roughening of surfaces. But under certain conditions, a conserved KPZ equation (cKPZ) is thought to set the universality class instead. This…
We have developed a continuum model that explains the complex surface shapes observed in epitaxial regrowth on micron scale gratings. This model describes the dependence of the surface morphology on film thickness and growth temperature in…
In all dimensions, infinite-range Kawasaki spin exchange in a quenched Ising model leads to an asymptotic length-scale $L \sim (\rho t)^{1/2} \sim t^{1/3}$ at $T=0$ because the kinetic coefficient is renormalized by the broken-bond density,…
Here we show a hidden regularity result for nonlinear wave equations with an integral term of convolution type and Dirichlet boundary conditions. Under general assumptions on the nonlinear term and on the integral kernel we are able to…
A scale--dependent effective action for gravity is introduced and an exact nonperturbative evolution equation is derived which governs its renormalization group flow. It is invariant under general coordinate transformations and satisfies…
We consider normalizing sequences that can give rise to nondegenerate limittheorems for Birkhoff sums under the iteration of a conservative map. Mostclassical limit theorems involve normalizing sequences that are polynomial,possibly with an…
Growth-fragmentation processes describe systems of particles in which each particle may grow larger or smaller, and divide into smaller ones as time proceeds. Unlike previous studies, which have focused mainly on the self-similar case, we…
In this paper we study the generalized variable-coefficient Gardner equations of the form $u_t + A(t)u^n\,u_x+ C(t)\,u^{2n}u_x + B(t)\,u_{xxx} + Q(t)\,u =0$. This class broadens out many other equations previously considered: Johnpillai and…
The celebrated L\'evy--Khintchine theorem is a fundamental limiting law that describes the growth rate of the denominators of the convergents in the continued fraction expansion of a Lebesgue-typical real number. In a recent breakthrough,…
The existence of conservation laws is one of the most important requirement of physical theories. Some of them, like energy conservation, knows no experimental exception. However, the generalization of these conservation laws to curved…
This article is devoted to the study of existence of a mass conserving global solution for the collision-induced nonlinear fragmentation model which arises in particulate processes, with the singular type of collision kernel. The above…