One-dimensional heat diffusion modelling and random walks on non-uniform grids

Lukas Frannek; Tomohisa Hayakawa; Ahmet Cetinkaya

doi:10.1109/CDC.2012.6425832

One-dimensional heat diffusion modelling and random walks on non-uniform grids

Lukas Frannek, Tomohisa Hayakawa, Ahmet Cetinkaya

Research output: Contribution to journal › Conference article › peer-review

3 Citations (Scopus)

Abstract

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.

Original language	English
Article number	6425832
Pages (from-to)	5548-5553
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
DOIs	https://doi.org/10.1109/CDC.2012.6425832
Publication status	Published - 2012
Externally published	Yes
Event	51st IEEE Conference on Decision and Control, CDC 2012 - Maui, HI, United States Duration: 2012 Dec 10 → 2012 Dec 13

ASJC Scopus subject areas

Control and Systems Engineering
Modelling and Simulation
Control and Optimization

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10.1109/CDC.2012.6425832

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abstract = "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.",

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AU - Hayakawa, Tomohisa

AU - Cetinkaya, Ahmet

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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.

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ER -

One-dimensional heat diffusion modelling and random walks on non-uniform grids

Abstract

ASJC Scopus subject areas

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