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

Lukas Frannek, Tomohisa Hayakawa, Ahmet Cetinkaya

Research output: Contribution to journalConference articlepeer-review

3 Citations (Scopus)


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 languageEnglish
Article number6425832
Pages (from-to)5548-5553
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Publication statusPublished - 2012
Externally publishedYes
Event51st IEEE Conference on Decision and Control, CDC 2012 - Maui, HI, United States
Duration: 2012 Dec 102012 Dec 13

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization


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