First Passage Monte-Carlo Simulation for Charge Distribution and Capacitance
Aditya Kumar Singh1, Apurva Anand2, Anindya Sundar Das3
1Aditya Kumar Singh, Department of ECE, ICFAI University, Jharkhand, Ranchi. India.
2Apurva Anand, Department of ECE, BIT Mesra, Ranchi, Jharkhand, India.
3Anindya Sundar Das, Department of Physics, Sidho-Kanho-Birsha University, Purulia, West Bengal, India.
Manuscript received on April 17, 2015. | Revised Manuscript received on April 26, 2015. | Manuscript published on March 05, 2015. | PP: 109-112 | Volume-5, Issue-2, May 2015. | Retrieval Number: C2295074314/2015©BEIESP
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©The Authors. Published By: Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/
Abstract: A novel scheme has been studied and demonstrated for Monte Carlo simulations of diffusion-reaction processes. The new algorithm skips the traditional small diffusion hops and propagates the diffusing particles over long distances through a sequence of super-hops, one particle at a time. By partitioning the simulation space into non- overlapping protecting domains each containing only one or two particles, the algorithm factorizes the N-body problem of collisions among multiple Brownian particles into a set of much simpler single-body and two-body problems. Efficient propagation of particles inside their protective do- mains is enabled through the use of time-dependent Green’s functions (propagators) obtained as solutions for the first-passage statistics of random walks. The resulting Monte Carlo algorithm is event-driven and asynchronous; each Brownian particle propagates inside its own protective domain and on its own time clock. The algorithm reproduces the statistics of the underlying Monte-Carlo model exactly. The new algorithm is efficient at low particle densities, where other existing algorithms slow down severely. Thus we have analyzed the application of this algorithm in the charge distribution and the capacitance detection.
Keywords: Monte Carlo Simulation, Charge distribution, capacitance, Markov chain.