Boundary effects in the TASEP model

Asymmetrinen ekskluusioprosessi on keskeinen malli poissa tasapainosta tapahtuville siirtoprosesseille. Vertaan tässä tutkielmassa normaalia TASEP- mallia (totally asymmetric exclusion process) kahteen uuteen malliin, joissa on erilaiset reunaehdot systeemin etureunassa. Yhdessä mallissa hiukkaset s...

Full description

Bibliographic Details
Main Author: Elo, Eino
Other Authors: Matemaattis-luonnontieteellinen tiedekunta, Faculty of Sciences, Fysiikan laitos, Department of Physics, Jyväskylän yliopisto, University of Jyväskylä
Format: Master's thesis
Language:eng
Published: 2018
Subjects:
Online Access: https://jyx.jyu.fi/handle/123456789/59586
_version_ 1826225747766804480
author Elo, Eino
author2 Matemaattis-luonnontieteellinen tiedekunta Faculty of Sciences Fysiikan laitos Department of Physics Jyväskylän yliopisto University of Jyväskylä
author_facet Elo, Eino Matemaattis-luonnontieteellinen tiedekunta Faculty of Sciences Fysiikan laitos Department of Physics Jyväskylän yliopisto University of Jyväskylä Elo, Eino Matemaattis-luonnontieteellinen tiedekunta Faculty of Sciences Fysiikan laitos Department of Physics Jyväskylän yliopisto University of Jyväskylä
author_sort Elo, Eino
datasource_str_mv jyx
description Asymmetrinen ekskluusioprosessi on keskeinen malli poissa tasapainosta tapahtuville siirtoprosesseille. Vertaan tässä tutkielmassa normaalia TASEP- mallia (totally asymmetric exclusion process) kahteen uuteen malliin, joissa on erilaiset reunaehdot systeemin etureunassa. Yhdessä mallissa hiukkaset saapuvat systeemiin pareittain. Toisessa mallissa hiukkasten systeemiintulotaajuus riippuu siitä, onko toisessa hilapaikassa hiukkanen vai ei. Näiden mallien tarkoituksena on reunailmiöiden tutkiminen. Käyttämäni menetelmät ovat matriisiyrite, keskimääräisen kentän approksimaatio, kineettinen jatkuvan ajan Monte Carlo -simulaatio ja master-yhtälöiden symbolinen ja numeerinen ratkaiseminen. Saavutetuista tuloksista mielenkiintoisin on se, että mallien tiheysprofiilit ja tiheyden todennäköisyystiheydet saadaan hyvänä approksimaationa vastaamaan tavallista TASEPia, jossa hiukkasilla on tietty keskimääräisen kentän approksimaation ennustama sisääntulotaajuus. Matalan tiheyden faasissa sekä matalan ja korkean tiheyden faasien koeksistenssiviivalla tämä tosin ei toimi kovin hyvin. The asymmetric exclusion process is the quintessential model of non- equilibrium transport phenomena. In this graduate thesis I compare TASEP (totally asymmetric exclusion process) to two new models that have a different behavior at the right edge of the system. In one model particles enter the system two at a time filling the two leftmost lattice sites. In the other one particles enter the system with different rates depending on whether the second lattice site is occupied or not. The aim in creating these models is to study boundary effects. Techniques I use to this end are the matrix ansatz method, mean field theory, domain-wall theory, continuous time kinetic Monte Carlo simulations and solving the Master equations exactly for small systems symbolically and numerically. The most interesting result is that the density profiles and the probability density profiles of the average densities have a close correspondence with those of normal TASEP that has a certain entry frequency anticipated by mean field theory. For small density phase this works less well.
first_indexed 2019-08-19T08:21:16Z
format Pro gradu
free_online_boolean 1
fullrecord [{"key": "dc.contributor.advisor", "value": "Merikoski, Juha", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Elo, Eino", "language": "", "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2018-09-20T05:51:18Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2018-09-20T05:51:18Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2018", "language": "", "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/59586", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Asymmetrinen ekskluusioprosessi on keskeinen malli poissa tasapainosta\ntapahtuville siirtoprosesseille. Vertaan t\u00e4ss\u00e4 tutkielmassa normaalia TASEP-\nmallia (totally asymmetric exclusion process) kahteen uuteen malliin, joissa on\nerilaiset reunaehdot systeemin etureunassa. Yhdess\u00e4 mallissa hiukkaset saapuvat systeemiin pareittain. Toisessa mallissa hiukkasten systeemiintulotaajuus\nriippuu siit\u00e4, onko toisessa hilapaikassa hiukkanen vai ei.\nN\u00e4iden mallien tarkoituksena on reunailmi\u00f6iden tutkiminen. K\u00e4ytt\u00e4m\u00e4ni\nmenetelm\u00e4t ovat matriisiyrite, keskim\u00e4\u00e4r\u00e4isen kent\u00e4n approksimaatio, kineettinen jatkuvan ajan Monte Carlo -simulaatio ja master-yht\u00e4l\u00f6iden symbolinen\nja numeerinen ratkaiseminen.\nSaavutetuista tuloksista mielenkiintoisin on se, ett\u00e4 mallien tiheysprofiilit\nja tiheyden todenn\u00e4k\u00f6isyystiheydet saadaan hyv\u00e4n\u00e4 approksimaationa vastaamaan tavallista TASEPia, jossa hiukkasilla on tietty keskim\u00e4\u00e4r\u00e4isen kent\u00e4n\napproksimaation ennustama sis\u00e4\u00e4ntulotaajuus. Matalan tiheyden faasissa sek\u00e4\nmatalan ja korkean tiheyden faasien koeksistenssiviivalla t\u00e4m\u00e4 tosin ei toimi\nkovin hyvin.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.abstract", "value": "The asymmetric exclusion process is the quintessential model of non-\nequilibrium transport phenomena. In this graduate thesis I compare TASEP\n(totally asymmetric exclusion process) to two new models that have a different\nbehavior at the right edge of the system. In one model particles enter the\nsystem two at a time filling the two leftmost lattice sites. In the other one\nparticles enter the system with different rates depending on whether the second\nlattice site is occupied or not.\nThe aim in creating these models is to study boundary effects. Techniques\nI use to this end are the matrix ansatz method, mean field theory, domain-wall\ntheory, continuous time kinetic Monte Carlo simulations and solving the Master\nequations exactly for small systems symbolically and numerically.\nThe most interesting result is that the density profiles and the probability\ndensity profiles of the average densities have a close correspondence with those\nof normal TASEP that has a certain entry frequency anticipated by mean field\ntheory. For small density phase this works less well.", "language": "en", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2018-09-20T05:51:18Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2018-09-20T05:51:18Z (GMT). No. of bitstreams: 0\n Previous issue date: 2018", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "39", "language": "", "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.format.mimetype", "value": "application/pdf", "language": null, "element": "format", "qualifier": "mimetype", "schema": "dc"}, {"key": "dc.language.iso", "value": "eng", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.title", "value": "Boundary effects in the TASEP model", "language": "", "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-201809204181", "language": "", "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Fysiikan laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Physics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Fysiikka", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Physics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "yvv.contractresearch.funding", "value": "0", "language": "", "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": null, "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4021", "language": "", "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matemaattiset mallit", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "mathematical models", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.format.content", "value": "fulltext", "language": null, "element": "format", "qualifier": "content", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}, {"key": "dc.type.okm", "value": "G2", "language": null, "element": "type", "qualifier": "okm", "schema": "dc"}]
id jyx.123456789_59586
language eng
last_indexed 2025-02-18T10:54:36Z
main_date 2018-01-01T00:00:00Z
main_date_str 2018
online_boolean 1
online_urls_str_mv {"url":"https:\/\/jyx.jyu.fi\/bitstreams\/372ea927-bc7b-487f-807c-e8d481899502\/download","text":"URN:NBN:fi:jyu-201809204181.pdf","source":"jyx","mediaType":"application\/pdf"}
publishDate 2018
record_format qdc
source_str_mv jyx
spellingShingle Elo, Eino Boundary effects in the TASEP model Fysiikka Physics 4021 matemaattiset mallit mathematical models
title Boundary effects in the TASEP model
title_full Boundary effects in the TASEP model
title_fullStr Boundary effects in the TASEP model Boundary effects in the TASEP model
title_full_unstemmed Boundary effects in the TASEP model Boundary effects in the TASEP model
title_short Boundary effects in the TASEP model
title_sort boundary effects in the tasep model
title_txtP Boundary effects in the TASEP model
topic Fysiikka Physics 4021 matemaattiset mallit mathematical models
topic_facet 4021 Fysiikka Physics matemaattiset mallit mathematical models
url https://jyx.jyu.fi/handle/123456789/59586 http://www.urn.fi/URN:NBN:fi:jyu-201809204181
work_keys_str_mv AT eloeino boundaryeffectsinthetasepmodel