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The Phases of a Discrete Flow of Particles on Graphs

Ekström, Henrik LU orcid (2020) In Markov Processes and Related Fields 26(2). p.343-364
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.
Abstract (Swedish)
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.

Vi detaljstuderar ett linjärt flöde av partiklar på en graf med en nod och k+1 oändliga kanter. Detta har ett rikt... (More)
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.

Vi detaljstuderar ett linjärt flöde av partiklar på en graf med en nod och k+1 oändliga kanter. Detta har ett rikt beteende med många olika utfall beroende på systemets parametrar. Den abrupta förändringen av systemets beteende när parametrarna ändras kontinuerligt visar på flertalet fasövergångar. Vi diskuterar den fysikaliska tolkningen av den studerade modellen och ser att den överensstämmer med Ohms och Kirchhoffs elektricitetslagar. Studien banar väg för utforskandet av diskreta flöden på mer komplicerade grafer. (Less)
Please use this url to cite or link to this publication:
author
organization
alternative title
Faserna hos ett diskret flöde av partiklar på grafer
publishing date
type
Contribution to journal
publication status
published
subject
keywords
dynamics classification, state space partitioning, limit sets, repulsion modelling, dynamics classification, state space partitioning, limit sets, repulsion modeling
in
Markov Processes and Related Fields
volume
26
issue
2
pages
22 pages
publisher
Polymat Ltd
external identifiers
  • scopus:85147742562
ISSN
1024-2953
language
English
LU publication?
yes
additional info
Special issue: Structure of Mathematical Physics (SMPh-2)
id
82bd9a07-1456-4e9a-8ca6-3cf504be0fb4
alternative location
https://dlib.eastview.com/browse/doc/58666123
date added to LUP
2021-04-20 13:09:41
date last changed
2023-09-11 04:29:24
@article{82bd9a07-1456-4e9a-8ca6-3cf504be0fb4,
  abstract     = {{We study in detail the linear flow of particles on a graph with one<br/>vertex and k+1 infinite edges. This has a rich environment with many different<br/>emergent behaviours depending on the system parameters. The abrupt change<br/>in the behaviour of the system along a continuous change of the parameters<br/>manifests multiple phase transitions.<br/>We discuss the physical interpretation of the considered simple model of<br/>particle flows and find that it adheres to the fundamental laws of electricity<br/>discovered by Ohm and Kirchhoff.<br/>This study paves the way for further analysis of discrete flows on more<br/>complicated graphs.}},
  author       = {{Ekström, Henrik}},
  issn         = {{1024-2953}},
  keywords     = {{dynamics classification; state space partitioning; limit sets; repulsion modelling; dynamics classification; state space partitioning; limit sets; repulsion modeling}},
  language     = {{eng}},
  month        = {{04}},
  number       = {{2}},
  pages        = {{343--364}},
  publisher    = {{Polymat Ltd}},
  series       = {{Markov Processes and Related Fields}},
  title        = {{The Phases of a Discrete Flow of Particles on Graphs}},
  url          = {{https://dlib.eastview.com/browse/doc/58666123}},
  volume       = {{26}},
  year         = {{2020}},
}