The Phases of a Discrete Flow of Particles on Graphs

Henrik Ekström

The Phases of a Discrete Flow of Particles on Graphs

Henrik Ekström

Mathematical Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

We study in detail the linear ﬂow of particles on a graph with one
vertex and k+1 inﬁnite edges. This has a rich environment with many diﬀerent
emergent behaviours depending on the system parameters. The abrupt change
in the behaviour of the system along a continuous change of the parameters
manifests multiple phase transitions.
We discuss the physical interpretation of the considered simple model of
particle ﬂows and ﬁnd that it adheres to the fundamental laws of electricity
discovered by Ohm and Kirchhoﬀ.
This study paves the way for further analysis of discrete ﬂows on more
complicated graphs.

Translated title of the contribution	Faserna hos ett diskret flöde av partiklar på grafer
Original language	English
Pages (from-to)	343-364
Number of pages	22
Journal	Markov Processes and Related Fields
Volume	26
Issue number	2
Publication status	Published - 2020 Apr 16

Bibliographical note

Special issue: Structure of Mathematical Physics (SMPh-2)

Subject classification (UKÄ)

Discrete Mathematics

Free keywords

dynamics classification
state space partitioning
limit sets
repulsion modeling

Access to Document

https://dlib.eastview.com/browse/doc/58666123

1 Doctoral Thesis (compilation)

Modelling and analysis of multi-scale networks
Ekström, H., 2024, Lunds universitet, Media-Tryck . 114 p.
Research output: Thesis › Doctoral Thesis (compilation)

Open Access
File

Cite this

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N2 - We study in detail the linear ﬂow of particles on a graph with onevertex and k+1 inﬁnite edges. This has a rich environment with many diﬀerentemergent behaviours depending on the system parameters. The abrupt changein the behaviour of the system along a continuous change of the parametersmanifests multiple phase transitions.We discuss the physical interpretation of the considered simple model ofparticle ﬂows and ﬁnd that it adheres to the fundamental laws of electricitydiscovered by Ohm and Kirchhoﬀ.This study paves the way for further analysis of discrete ﬂows on morecomplicated graphs.

AB - We study in detail the linear ﬂow of particles on a graph with onevertex and k+1 inﬁnite edges. This has a rich environment with many diﬀerentemergent behaviours depending on the system parameters. The abrupt changein the behaviour of the system along a continuous change of the parametersmanifests multiple phase transitions.We discuss the physical interpretation of the considered simple model ofparticle ﬂows and ﬁnd that it adheres to the fundamental laws of electricitydiscovered by Ohm and Kirchhoﬀ.This study paves the way for further analysis of discrete ﬂows on morecomplicated graphs.

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KW - state space partitioning

KW - limit sets

KW - repulsion modelling

KW - dynamics classification

KW - state space partitioning

KW - limit sets

KW - repulsion modeling

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EP - 364

JO - Markov Processes and Related Fields

JF - Markov Processes and Related Fields

IS - 2

ER -

The Phases of a Discrete Flow of Particles on Graphs

Abstract

Bibliographical note

Subject classification (UKÄ)

Free keywords

Access to Document

Fingerprint

Research output

Modelling and analysis of multi-scale networks

Cite this