Random walk on the boundary methods for computing reaction rate and capacitance
نویسندگان
چکیده
In this article we describe Monte Carlo methods for computing two intimately related quantities, the capacitance of a conducting body the diffusion-limited reaction rate. Both quantities can be represented as integral functionals of the solution to an integral equation on the surface of an object. The Monte Carlo methods we describe are derived by using “random walk on the boundary” Markov chains to form appropriate statistics.
منابع مشابه
The Random Walk on the Boundary Method for Calculating Capacitance
Here we consider the problem of the computing the capacitance of a conducting body. The capacitance can be represented as an integral functional of the stationary distribution of particular “random walk on the boundary” Markov chain. The computational algorithm derived from this is used to compute the capacitance of the unit cube with relative error 4× 10−7, the most accurate estimate known.
متن کاملCoprocessing Architecture in System-on- programmable-chip for Monte Carlo Simulation
Monte Carlo simulation is mainly done in computer clusters, supercomputers or computers coupled with hardware accelerators. These processing methods are sufficiently fast; however, this speed comes at the expense of physical area and power consumption. The current study aims to use System-OnProgrammable-Chip (SOPC) to accomplish the same task but using a smaller physical area. The SOPC approach...
متن کاملMonte Carlo Methods for Calculating Some Physical Properties of Large Molecules
In this paper we describe Monte Carlo methods for solving some boundary-value problems for elliptic partial differential equations arising in the computation of physical properties of large molecules. The constructed algorithms are based on walk on spheres, Green’s function first passage, walk in subdomains techniques, and finite-difference approximations of the boundary condition. The methods ...
متن کاملA Fuzzy Random Walk Technique to Forecasting Volatility of Iran Stock Exchange Index
Study of volatility has been considered by the academics and decision makers dur-ing two last decades. First since the volatility has been a risk criterion it has been used by many decision makers and activists in capital market. Over the years it has been of more importance because of the effect of volatility on economy and capital markets stability for stocks, bonds, and foreign exchange mark...
متن کاملA survey on random walk-based stochastic modeling in eukaryotic cell migration with emphasis on its application in cancer
Impairments in cell migration processes may cause various diseases, among which cancer cell metastasis, tumor angiogenesis, and the disability of immune cells to infiltrate into tumors are prominent ones. Mathematical modeling has been widely used to analyze the cell migration process. Cell migration is a complicated process and requires statistical methods such as random walk for proper analys...
متن کامل