Asymptotic Shape in a Continuum Growth Model
نویسنده
چکیده
A continuum growth model is introduced. The state at time t, St, is a subset of R and consists of a connected union of randomly sized Euclidean balls, which emerge from outbursts at their center points. An outburst occurs somewhere in St after an exponentially distributed time with expected value |St| −1 and the location of the outburst is uniformly distributed over St. The main result is that if the distribution of the radii of the outburst balls has bounded support, then St grows linearly and St/t has a non-random shape as t → ∞. Due to rotation invariance the asymptotic shape must be a Euclidean ball.
منابع مشابه
Design and Analysis of a Novel Tendon-less Backbone Robot
A new type of backbone robot is presented in this paper. The core idea is to use a cross shape mechanism with the principle of functioning of the scissors linkages, known as a pantograph. Although this continuum arm acts quite similar to tendon-driven robot, this manipulator does not include any tendon in its structure. This design does not suffer from the weaknesses of the continuum design suc...
متن کاملSecond order sensitivity analysis for shape optimization of continuum structures
This study focuses on the optimization of the plane structure. Sequential quadratic programming (SQP) will be utilized, which is one of the most efficient methods for solving nonlinearly constrained optimization problems. A new formulation for the second order sensitivity analysis of the two-dimensional finite element will be developed. All the second order required derivatives will be calculat...
متن کاملOn Some Growth Models with a Small Parameter
We consider the behavior of the asymptotic speed of growth and the asymptotic shape in some growth models, when a certain parameter becomes small. The basic example treated is the variant of Richardson's growth model on Z d in which each site which is not yet occupied becomes occupied at rate 1 if it has at least two occupied neighbors, at rate " 1 if it has exactly 1 occupied neighbor and, of ...
متن کاملExperimental Identification and Hybrid PID-Fuzzy Position Control of Continuum Robotic Arms
Continuum robotic arms that are inspired from nature, have many advantages compared to traditional robots, which motivate researchers in this field. Dynamic modeling and controlling these robots are challenging subjects due to complicated nonlinearities and considerable uncertainties existing in these structures. In this paper, first a dynamic three-dimensional model of the continuum robotic ar...
متن کاملInelastic Continuum Modeling of Carbon Nanotube,s Behavior Using Finite Element Method
This paper describes a continuum model for analyzing the inelastic behavior of a single walled carbon nanotube (SWCNT) in different loading conditions. Because of limitations in using molecular dynamics (and other atomic methods) to model the failure load of the SWCNT, continuum mechanics methods are considered in this paper. Based on some experimental and theoretical results, an elasto-plastic...
متن کامل