Title :
Heat diffusion modelling with random walks on triangular lattices
Author :
Frannek, Lukas ; Hayakawa, Takeshi ; Cetinkaya, Ahmet
Author_Institution :
Tokyo Inst. of Technol., Tokyo, Japan
Abstract :
In order to approximate heat diffusion in two dimensions, we view diffusion processes as the random motion of particles and model the behavior of each particle with a continuous-time Markov chain. The infinitesimal generator of each Markov chain is characterized by the distances between lattice points imposed on a given two-dimensional surface. We derive requirements for the mean and the covariance matrix of a Markov chain and present simulations to demonstrate how a large number of Markov chains behave in the proposed framework on an exemplary lattice.
Keywords :
Markov processes; covariance matrices; diffusion; lattice theory; random processes; continuous-time Markov chain; covariance matrix; diffusion processes; exemplary lattice framework; heat diffusion modelling; infinitesimal generator; lattice point distances; mean matrix; particle behavior model; random particle motion; random walks; triangular lattices; two dimension heat diffusion approximation; two-dimensional surface; Equations; Generators; Heating; Indexes; Lattices; Markov processes; Mathematical model;
Conference_Titel :
American Control Conference (ACC), 2013
Conference_Location :
Washington, DC
Print_ISBN :
978-1-4799-0177-7
DOI :
10.1109/ACC.2013.6579986
