TY - JOUR
T1 - One-dimensional heat diffusion modelling and random walks on non-uniform grids
AU - Frannek, Lukas
AU - Hayakawa, Tomohisa
AU - Cetinkaya, Ahmet
PY - 2012
Y1 - 2012
N2 - A probabilistic model for the diffusion of heat on one-dimensional spaces is developed. Specifically, grid points are arbitrarily placed on the real line and the heat particles are assumed to jump between these grid points in continuous time. This random walk by the heat particles is represented by a continuous-time Markov chain and state-transition intensities depends on the underlying, possibly non-uniform, spacing of the grid points to characterize the Markov chain. Several numerical examples are demonstrated to show the efficacy of the proposed framework for exemplary non-uniform grids.
AB - A probabilistic model for the diffusion of heat on one-dimensional spaces is developed. Specifically, grid points are arbitrarily placed on the real line and the heat particles are assumed to jump between these grid points in continuous time. This random walk by the heat particles is represented by a continuous-time Markov chain and state-transition intensities depends on the underlying, possibly non-uniform, spacing of the grid points to characterize the Markov chain. Several numerical examples are demonstrated to show the efficacy of the proposed framework for exemplary non-uniform grids.
UR - http://www.scopus.com/inward/record.url?scp=84874242079&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84874242079&partnerID=8YFLogxK
U2 - 10.1109/CDC.2012.6425832
DO - 10.1109/CDC.2012.6425832
M3 - Conference article
AN - SCOPUS:84874242079
SN - 0743-1546
SP - 5548
EP - 5553
JO - Proceedings of the IEEE Conference on Decision and Control
JF - Proceedings of the IEEE Conference on Decision and Control
M1 - 6425832
T2 - 51st IEEE Conference on Decision and Control, CDC 2012
Y2 - 10 December 2012 through 13 December 2012
ER -