Generalized Ising measures for one-dimensional lattice gases and their applications
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da USP |
Texto Completo: | https://doi.org/10.11606/T.45.2022.tde-24052023-114357 |
Resumo: | The processes studied are Interacting Particle Systems in which particles move on sites of a lattice with periodic boundary conditions. The particle interaction rule is the exclusion rule. Among the two classes of processes studied here, the first class is a generalization of the Exclusion Process. The generalization amounts to an extension of the dependence upon neighboring particles of a particle transition rate. In the other class of the processes studied, we substituted particles with rods that occupy several contiguous sites, defined that each rod may be in one of two possible states, and defined the rules for state switch. The transition rules for rod motion are similar to the rules for particles in our generalizations of the Exclusion Process. For each process constructed, we studied the conditions that ensure that its time-invariant distribution is an Ising type measure. The results relate the rates of motion and their ranges to the range and the interactions expressed in the potential function of Ising measure. We also studied the behavior of the process when they evolve in their respective invariant states. The study revealed novel phenomena in the behavior of particle flux as a function of particle density. One of the phenomena is non-monotonicity which has not been observed in the Classical Exclusion Process. For the interacting rod system, we revealed and explained the effect of cooperative pushing that had been observed previously in the RNA transcription process executed by RNA polymerase enzymes. Our results apply to understanding this biological process and to the traffic of cars that are traditionally modeled by the Exclusion Process. |
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info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesis Generalized Ising measures for one-dimensional lattice gases and their applications Medidas de Gibbs generalizadas para os gases em redes unidimensionais e suas aplicações 2022-05-09Vladimir BelitskyGunter Markus SchutzAnatoli IambartsevJosé Ricardo Gonçalves de MendonçaManuel Alejandro Gonzalez NavarretePaulo Afonso Faria da VeigaNgo Phuoc Nguyen NgocUniversidade de São PauloEstatísticaUSPBR Alongamento de transcrição de RNA Canonical ensemble Conjunto canônico Conjunto grand canônico Cooperatividade Cooperativity Exclusion process Gibbs measure Grand-canonical ensemble Ising measure Kramers-Wannier matrices Markov models Matrizes de Kramers-Wannier Medida de Gibbs Medida de Ising Modelos de Markov Processo de exclusão RNA polimerase RNA polymerase Transcription elongation The processes studied are Interacting Particle Systems in which particles move on sites of a lattice with periodic boundary conditions. The particle interaction rule is the exclusion rule. Among the two classes of processes studied here, the first class is a generalization of the Exclusion Process. The generalization amounts to an extension of the dependence upon neighboring particles of a particle transition rate. In the other class of the processes studied, we substituted particles with rods that occupy several contiguous sites, defined that each rod may be in one of two possible states, and defined the rules for state switch. The transition rules for rod motion are similar to the rules for particles in our generalizations of the Exclusion Process. For each process constructed, we studied the conditions that ensure that its time-invariant distribution is an Ising type measure. The results relate the rates of motion and their ranges to the range and the interactions expressed in the potential function of Ising measure. We also studied the behavior of the process when they evolve in their respective invariant states. The study revealed novel phenomena in the behavior of particle flux as a function of particle density. One of the phenomena is non-monotonicity which has not been observed in the Classical Exclusion Process. For the interacting rod system, we revealed and explained the effect of cooperative pushing that had been observed previously in the RNA transcription process executed by RNA polymerase enzymes. Our results apply to understanding this biological process and to the traffic of cars that are traditionally modeled by the Exclusion Process. Os processes estudados na tese são sistemas de partículas que se movimentam pelos sítios de uma rede unidimensional com a condição periódica de fronteira. As partículas interagem pela lei de exclusão. Os processos estudados, nos quais cada partícula pode ocupar um só sítio da rede, são generalizações do Processo de Exclusão; a essência da generalização é a extensão do alcance de dependência de parâmetros de movimentos de partícula da posição e da presença de outras partículas. No outro tipo dos processos estudados substituímos partículas por bastões que ocupam mais que um sítio e defi nimos que cada bastão pode estar num de dois possíveis estados. As regras de interação entre os bostões são parecidas com as regras aplicadas na generalização do processo de Exclusão. Para cada processo construído estudamos as condições necessárias e sufi cientes para que a distribuição invariante de processo esteja do tipo da medida de Ising. Os resultados mostram as relações entre os parâmetros de interação entre partículas (ou bastões) e a forma da função-potencial nas correspondentes medidas de Ising. Na tese, analisamos também o comportamento dos processos construídos quando eles evoluem de acordo com suas distribuições invariantes. Os resultados de análise revelam diversos fenómenos novos que ocorrem no fluxo de partículas e de bostões. Observamos e explicamos o comportamento não monótono de fluxo em relação da densidade de partículas que estaria ausente caso as partículas se movimentassem no Processo clássico de Exclusão. Também, observamos e explicamos o efeito de cooperação de bastões que aumenta a velocidade de cada bastão (\"empurrão coletivo\"). Os resultados aplicam-se aos estudos do processo de transcrição de RNA produzido por RNA polimerase a partir da informação contida em DNA, e também aos estudos de trânsito de veículos. https://doi.org/10.11606/T.45.2022.tde-24052023-114357info:eu-repo/semantics/openAccessengreponame:Biblioteca Digital de Teses e Dissertações da USPinstname:Universidade de São Paulo (USP)instacron:USP2023-12-21T20:03:19Zoai:teses.usp.br:tde-24052023-114357Biblioteca Digital de Teses e Dissertaçõeshttp://www.teses.usp.br/PUBhttp://www.teses.usp.br/cgi-bin/mtd2br.plvirginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.bropendoar:27212023-12-22T13:14:29.664192Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP)false |
dc.title.en.fl_str_mv |
Generalized Ising measures for one-dimensional lattice gases and their applications |
dc.title.alternative.pt.fl_str_mv |
Medidas de Gibbs generalizadas para os gases em redes unidimensionais e suas aplicações |
title |
Generalized Ising measures for one-dimensional lattice gases and their applications |
spellingShingle |
Generalized Ising measures for one-dimensional lattice gases and their applications Ngo Phuoc Nguyen Ngoc |
title_short |
Generalized Ising measures for one-dimensional lattice gases and their applications |
title_full |
Generalized Ising measures for one-dimensional lattice gases and their applications |
title_fullStr |
Generalized Ising measures for one-dimensional lattice gases and their applications |
title_full_unstemmed |
Generalized Ising measures for one-dimensional lattice gases and their applications |
title_sort |
Generalized Ising measures for one-dimensional lattice gases and their applications |
author |
Ngo Phuoc Nguyen Ngoc |
author_facet |
Ngo Phuoc Nguyen Ngoc |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Vladimir Belitsky |
dc.contributor.advisor-co1.fl_str_mv |
Gunter Markus Schutz |
dc.contributor.referee1.fl_str_mv |
Anatoli Iambartsev |
dc.contributor.referee2.fl_str_mv |
José Ricardo Gonçalves de Mendonça |
dc.contributor.referee3.fl_str_mv |
Manuel Alejandro Gonzalez Navarrete |
dc.contributor.referee4.fl_str_mv |
Paulo Afonso Faria da Veiga |
dc.contributor.author.fl_str_mv |
Ngo Phuoc Nguyen Ngoc |
contributor_str_mv |
Vladimir Belitsky Gunter Markus Schutz Anatoli Iambartsev José Ricardo Gonçalves de Mendonça Manuel Alejandro Gonzalez Navarrete Paulo Afonso Faria da Veiga |
description |
The processes studied are Interacting Particle Systems in which particles move on sites of a lattice with periodic boundary conditions. The particle interaction rule is the exclusion rule. Among the two classes of processes studied here, the first class is a generalization of the Exclusion Process. The generalization amounts to an extension of the dependence upon neighboring particles of a particle transition rate. In the other class of the processes studied, we substituted particles with rods that occupy several contiguous sites, defined that each rod may be in one of two possible states, and defined the rules for state switch. The transition rules for rod motion are similar to the rules for particles in our generalizations of the Exclusion Process. For each process constructed, we studied the conditions that ensure that its time-invariant distribution is an Ising type measure. The results relate the rates of motion and their ranges to the range and the interactions expressed in the potential function of Ising measure. We also studied the behavior of the process when they evolve in their respective invariant states. The study revealed novel phenomena in the behavior of particle flux as a function of particle density. One of the phenomena is non-monotonicity which has not been observed in the Classical Exclusion Process. For the interacting rod system, we revealed and explained the effect of cooperative pushing that had been observed previously in the RNA transcription process executed by RNA polymerase enzymes. Our results apply to understanding this biological process and to the traffic of cars that are traditionally modeled by the Exclusion Process. |
publishDate |
2022 |
dc.date.issued.fl_str_mv |
2022-05-09 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://doi.org/10.11606/T.45.2022.tde-24052023-114357 |
url |
https://doi.org/10.11606/T.45.2022.tde-24052023-114357 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade de São Paulo |
dc.publisher.program.fl_str_mv |
Estatística |
dc.publisher.initials.fl_str_mv |
USP |
dc.publisher.country.fl_str_mv |
BR |
publisher.none.fl_str_mv |
Universidade de São Paulo |
dc.source.none.fl_str_mv |
reponame:Biblioteca Digital de Teses e Dissertações da USP instname:Universidade de São Paulo (USP) instacron:USP |
instname_str |
Universidade de São Paulo (USP) |
instacron_str |
USP |
institution |
USP |
reponame_str |
Biblioteca Digital de Teses e Dissertações da USP |
collection |
Biblioteca Digital de Teses e Dissertações da USP |
repository.name.fl_str_mv |
Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP) |
repository.mail.fl_str_mv |
virginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.br |
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1794503018828267520 |