Heat diffusion modelling with random walks on triangular lattices

Lukas Frannek; Tomohisa Hayakawa; Ahmet Cetinkaya

doi:10.1109/acc.2013.6579986

Heat diffusion modelling with random walks on triangular lattices

Lukas Frannek, Tomohisa Hayakawa, Ahmet Cetinkaya

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

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.

Original language	English
Title of host publication	2013 American Control Conference, ACC 2013
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1118-1123
Number of pages	6
ISBN (Print)	9781479901777
DOIs	https://doi.org/10.1109/acc.2013.6579986
Publication status	Published - 2013
Externally published	Yes
Event	2013 1st American Control Conference, ACC 2013 - Washington, DC, United States Duration: 2013 Jun 17 → 2013 Jun 19

Publication series

Name	Proceedings of the American Control Conference
ISSN (Print)	0743-1619

Conference

Conference	2013 1st American Control Conference, ACC 2013
Country/Territory	United States
City	Washington, DC
Period	13/6/17 → 13/6/19

ASJC Scopus subject areas

Electrical and Electronic Engineering

Access to Document

10.1109/acc.2013.6579986

Cite this

Heat diffusion modelling with random walks on triangular lattices. / Frannek, Lukas; Hayakawa, Tomohisa; Cetinkaya, Ahmet.
2013 American Control Conference, ACC 2013. Institute of Electrical and Electronics Engineers Inc., 2013. p. 1118-1123 6579986 (Proceedings of the American Control Conference).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Frannek, L, Hayakawa, T & Cetinkaya, A 2013, Heat diffusion modelling with random walks on triangular lattices. in 2013 American Control Conference, ACC 2013., 6579986, Proceedings of the American Control Conference, Institute of Electrical and Electronics Engineers Inc., pp. 1118-1123, 2013 1st American Control Conference, ACC 2013, Washington, DC, United States, 13/6/17. https://doi.org/10.1109/acc.2013.6579986

@inproceedings{0d9ba4087f314b2882cea15d6d1f6566,

title = "Heat diffusion modelling with random walks on triangular lattices",

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.",

author = "Lukas Frannek and Tomohisa Hayakawa and Ahmet Cetinkaya",

year = "2013",

doi = "10.1109/acc.2013.6579986",

language = "English",

isbn = "9781479901777",

series = "Proceedings of the American Control Conference",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "1118--1123",

booktitle = "2013 American Control Conference, ACC 2013",

note = "2013 1st American Control Conference, ACC 2013 ; Conference date: 17-06-2013 Through 19-06-2013",

}

TY - GEN

T1 - Heat diffusion modelling with random walks on triangular lattices

AU - Frannek, Lukas

AU - Hayakawa, Tomohisa

AU - Cetinkaya, Ahmet

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84883528418&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883528418&partnerID=8YFLogxK

U2 - 10.1109/acc.2013.6579986

DO - 10.1109/acc.2013.6579986

M3 - Conference contribution

AN - SCOPUS:84883528418

SN - 9781479901777

T3 - Proceedings of the American Control Conference

SP - 1118

EP - 1123

BT - 2013 American Control Conference, ACC 2013

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2013 1st American Control Conference, ACC 2013

Y2 - 17 June 2013 through 19 June 2013

ER -

Heat diffusion modelling with random walks on triangular lattices

Abstract

Publication series

Conference

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this