Related papers: Asymptotic shape in a continuum growth model
An effect generated by the nonexponential behavior of the survival amplitude of an unstable state at the long time region is considered. It is known that this amplitude tends to zero as $t$ goes to the infinity more slowly than any…
Let a random geometric graph be defined in the supercritical regime for the existence of a unique infinite connected component in Euclidean space. Consider the first-passage percolation model with independent and identically distributed…
A new type of asymptotic behavior in a game dynamics system is discovered. The system exhibits behavior which combines chaotic motion and attraction to heteroclinic cycles; the trajectory visits several unstable stationary states repeatedly…
In this paper, we study the asymptotic behavior of the volume of spheres in metric measure spaces. We first introduce a general setting adapted to the study of asymptotic isoperimetry in a general class of metric measure spaces. We then…
A steady-state convection-diffusion problem with a small diffusion of order $\mathcal{O}(\varepsilon)$ is considered in a thin three-dimensional graph-like junction consisting of thin cylinders connected through a domain (node) of diameter…
Let $N(t)$ be the collection of particles alive at time $t$ in a branching Brownian motion in $\mathbb{R}^d$, and for $u\in N(t)$, let $\mathbf{X}_u(t)$ be the position of particle $u$ at time $t$. For $\theta\in \mathbb{R}^d$, we define…
A large class of evolutionary processes can be modeled by a rule which involves self-replication of some physical quantity with a non local rescaling. I show that a class of such models are exactly solvable -- in the discrete as well as…
We investigate how thin structures change their shape in response to non-mechanical stimuli that can be interpreted as variations in the structure's natural curvature. Starting from the theory of non-Euclidean plates and shells, we derive…
Consider the following class of conformable time-fractional stochastic equation $$T_{\alpha,t}^a u(x,t)=\lambda\sigma(u(x,t))\dot{W}_t,\,\,\,\,x\in\mathbb{R},\,t\in[a,\infty), \,\,0<\alpha<1,$$ with a non-random initial condition…
We study a "burst" event, i. e. the evolution of an initial condition having support only in a finite interval of k-space, in the continuum shell model due to Parisi. We show that the continuum equation without forcing or dissipation can be…
The asymptotic shape theorem for the contact process in random environment gives the existence of a norm $\mu$ on $\Rd$ such that the hitting time $t(x)$ is asymptotically equivalent to $\mu(x)$ when the contact process survives. We provide…
In this text, we prove the existence of an asymptotic growth rate of the number of dominating sets (and variants) on finite rectangular grids, when the dimensions of the grid grow to infinity. Moreover, we provide, for each of the variants,…
The rotor-router model is a deterministic analogue of random walk invented by Jim Propp. It can be used to define a deterministic aggregation model analogous to internal diffusion limited aggregation. We prove an isoperimetric inequality…
Spherically symmetric expansionfree distributions are systematically studied. The whole set of field equations and junction conditions are presented for a general distribution of dissipative anisotropic fluid (principal stresses unequal),…
We study the first and second orders of the asymptotic expansion, as the dimension goes to infinity, of the moments of the Hilbert-Schmidt norm of a uniformly distributed matrix in the p-Schatten unit ball. We consider the case of matrices…
We study a shape evolution framework in which the deformation of shapes from time t to t + dt is governed by a regularized anisotropic elasticity model. More precisely, we assume that at each time shapes are infinitesimally deformed from a…
We consider a model of Branching Brownian Motion in which the usual spatially-homogeneous and catalytic branching at a single point are simultaneously present. We establish the almost sure growth rates of population in certain…
In physics, I noticed subjects not explained by formulas were often not studied, like how uncontrolled growth systems changed form. Weather, businesses, societies, environments, communities, cultures, groups, relationships, lives, and…
A point source on a plane constantly emits particles which rapidly diffuse and then stick to a growing cluster. The growth probability of a cluster is presented as a sum over all possible scenarios leading to the same final shape. The…
We establish higher-order nonasymptotic expansions for a difference between probability distributions of sums of i.i.d. random vectors in a Euclidean space. The derived bounds are uniform over two classes of sets: the set of all Euclidean…