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Stochastic Modelling of Reaction–Diffusion Processes最新文献

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Stochastic Modelling of Reaction–Diffusion Processes Pub Date : 2019-11-30 DOI: 10.1017/9781108628389.013
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引用次数: 0
Deterministic versus Stochastic Modelling 确定性与随机模型
Stochastic Modelling of Reaction–Diffusion Processes Pub Date : 2019-11-30 DOI: 10.1017/9781108628389.003
{"title":"Deterministic versus Stochastic Modelling","authors":"","doi":"10.1017/9781108628389.003","DOIUrl":"https://doi.org/10.1017/9781108628389.003","url":null,"abstract":"","PeriodicalId":318545,"journal":{"name":"Stochastic Modelling of Reaction–Diffusion Processes","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132678240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Efficient Stochastic Modelling of Chemical Reactions 化学反应的高效随机模型
Stochastic Modelling of Reaction–Diffusion Processes Pub Date : 2019-11-30 DOI: 10.1017/9781108628389.006
{"title":"Efficient Stochastic Modelling of Chemical Reactions","authors":"","doi":"10.1017/9781108628389.006","DOIUrl":"https://doi.org/10.1017/9781108628389.006","url":null,"abstract":"","PeriodicalId":318545,"journal":{"name":"Stochastic Modelling of Reaction–Diffusion Processes","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116213083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stochastic Differential Equations 随机微分方程
Stochastic Modelling of Reaction–Diffusion Processes Pub Date : 2019-11-30 DOI: 10.1017/9781108628389.004
G. Leobacher
{"title":"Stochastic Differential Equations","authors":"G. Leobacher","doi":"10.1017/9781108628389.004","DOIUrl":"https://doi.org/10.1017/9781108628389.004","url":null,"abstract":"In the second part we show how the classical result can be used also for SDEs with drift that may be discontinuous and diffusion that may be degenerate. In that context I will present a concept of (multidimensional) piecewise Lipschitz drift where the set of discontinuities is a sufficiently smooth hypersurface in the multi-dimensional euclidean space. We discuss geometric properties of the set of discontinuities that are needed to transfer the convergence result from the Lipschitz case to the piecewise Lipschitz case.","PeriodicalId":318545,"journal":{"name":"Stochastic Modelling of Reaction–Diffusion Processes","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132402016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Appendix 附录
Stochastic Modelling of Reaction–Diffusion Processes Pub Date : 2019-11-30 DOI: 10.1017/9781108628389.011
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引用次数: 0
Microscopic Models of Brownian Motion 布朗运动的微观模型
Stochastic Modelling of Reaction–Diffusion Processes Pub Date : 2019-11-30 DOI: 10.1017/9781108628389.009
{"title":"Microscopic Models of Brownian Motion","authors":"","doi":"10.1017/9781108628389.009","DOIUrl":"https://doi.org/10.1017/9781108628389.009","url":null,"abstract":"","PeriodicalId":318545,"journal":{"name":"Stochastic Modelling of Reaction–Diffusion Processes","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124968441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multiscale and Multi-Resolution Methods 多尺度和多分辨率方法
Stochastic Modelling of Reaction–Diffusion Processes Pub Date : 1900-01-01 DOI: 10.1017/9781108628389.010
R. Erban, S. Chapman
{"title":"Multiscale and Multi-Resolution Methods","authors":"R. Erban, S. Chapman","doi":"10.1017/9781108628389.010","DOIUrl":"https://doi.org/10.1017/9781108628389.010","url":null,"abstract":"This chapter discusses multi-resolution simulation methods for modelling reaction–diffusion processes. They use a detailed modelling approach only in certain parts of the computational domain, whilst in the remainder of the domain a coarser, less detailed, method is used. Two examples of multi-resolution methods are presented. The first example couples the Brownian dynamics with the corresponding compartment-based description. The second example couples molecular dynamics together with its coarser Langevin description. The chapter concludes with an overview of related multi-resolution approaches in the literature.","PeriodicalId":318545,"journal":{"name":"Stochastic Modelling of Reaction–Diffusion Processes","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123434996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stochastic Reaction–Diffusion Models 随机反应扩散模型
Stochastic Modelling of Reaction–Diffusion Processes Pub Date : 1900-01-01 DOI: 10.1017/9781108628389.007
R. Erban, S. Chapman
{"title":"Stochastic Reaction–Diffusion Models","authors":"R. Erban, S. Chapman","doi":"10.1017/9781108628389.007","DOIUrl":"https://doi.org/10.1017/9781108628389.007","url":null,"abstract":"This chapter discusses stochastic approaches for modelling chemical reactions (introduced in Chapter 1) and molecular diffusion at the same time. The presented stochastic reaction–diffusion processes add chemical reactions to the two position-jump models of molecular diffusion that are introduced in Chapter 4: the compartment-based approach (described by the reaction–diffusion master equation) and the SDE-based approach, which gives the Brownian dynamics. Basic principles of each approach are explained using an example that includes only zeroth- and first-order chemical reactions. This is followed by discussion of more complicated systems when some chemical species are subject to higher-order chemical reactions. The reaction radius, reaction probability and the choice of the compartment size are studied in detail. The chapter concludes with the discussion of applications to pattern formation in biology, including stochastic French flag model and stochastic Turing patterns.","PeriodicalId":318545,"journal":{"name":"Stochastic Modelling of Reaction–Diffusion Processes","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133282062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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