Pub Date : 2020-02-21DOI: 10.1007/978-3-642-27737-5-676-1
H. Fuks
{"title":"Orbits of Bernoulli Measures in Cellular Automata","authors":"H. Fuks","doi":"10.1007/978-3-642-27737-5-676-1","DOIUrl":"https://doi.org/10.1007/978-3-642-27737-5-676-1","url":null,"abstract":"","PeriodicalId":436460,"journal":{"name":"arXiv: Cellular Automata and Lattice Gases","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125401289","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}
V. Vangelista, Karl Amjad-Ali, Minhyeok Kwon, P. H. Acioli
Spiral waves are self-repeating waves that can form in excitable media, propagating outward from their center in a spiral pattern. Spiral waves have been observed in different natural phenomena and have been linked to medical conditions such as epilepsy and atrial fibrillation. We used a simple cellular automaton model to study propagation in excitable media, with a particular focus in understanding spiral wave behavior. The main ingredients of this cellular automaton model are an excitation condition and characteristic excitation and refractory periods. The literature shows that fixed excitation and refractory periods together with specific initial conditions generate stationary and stable spiral waves. In the present work we allowed the activation and refractory periods to fluctuate uniformly over a range of values. Under these conditions formed spiral waves might drift, the wave front might break, and in some extreme cases it might lead to a complete breakdown of the spiral pattern.
{"title":"Effects of randomization of characteristic times on spiral wave generation in a simple cellular automaton model of excitable media","authors":"V. Vangelista, Karl Amjad-Ali, Minhyeok Kwon, P. H. Acioli","doi":"10.1063/5.0008717","DOIUrl":"https://doi.org/10.1063/5.0008717","url":null,"abstract":"Spiral waves are self-repeating waves that can form in excitable media, propagating outward from their center in a spiral pattern. Spiral waves have been observed in different natural phenomena and have been linked to medical conditions such as epilepsy and atrial fibrillation. We used a simple cellular automaton model to study propagation in excitable media, with a particular focus in understanding spiral wave behavior. The main ingredients of this cellular automaton model are an excitation condition and characteristic excitation and refractory periods. The literature shows that fixed excitation and refractory periods together with specific initial conditions generate stationary and stable spiral waves. In the present work we allowed the activation and refractory periods to fluctuate uniformly over a range of values. Under these conditions formed spiral waves might drift, the wave front might break, and in some extreme cases it might lead to a complete breakdown of the spiral pattern.","PeriodicalId":436460,"journal":{"name":"arXiv: Cellular Automata and Lattice Gases","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126618171","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}
Pub Date : 2018-02-06DOI: 10.1007/978-3-662-55663-4_12
G. Mart'inez, A. Adamatzky, Bo Chen, F. Chen, J. C. Mora
{"title":"Simple Networks on Complex Cellular Automata: From de Bruijn Diagrams to Jump-Graphs","authors":"G. Mart'inez, A. Adamatzky, Bo Chen, F. Chen, J. C. Mora","doi":"10.1007/978-3-662-55663-4_12","DOIUrl":"https://doi.org/10.1007/978-3-662-55663-4_12","url":null,"abstract":"","PeriodicalId":436460,"journal":{"name":"arXiv: Cellular Automata and Lattice Gases","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127406448","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}
Pub Date : 2017-04-03DOI: 10.5506/aphyspolbsupp.9.49
H. Fuk's, Joel Midgley-Volpato
In a recent paper [arXiv:1506.06649 [nlin.CG]], we presented an example of a 3-state cellular automaton which exhibits behaviour analogous to degenerate hyperbolicity often observed in finite-dimensional dynamical systems. We also calculated densities of 0, 1 and 2 after n iterations of this rule, using finite state machines to conjecture patterns present in preimage sets. Here, we re-derive the same formulae in a rigorous way, without resorting to any semi-empirical methods. This is done by analysing the behaviour of continuous clusters of symbols and by considering their interactions.
{"title":"An example of a deterministic cellular automaton exhibiting linear-exponential convergence to the steady state","authors":"H. Fuk's, Joel Midgley-Volpato","doi":"10.5506/aphyspolbsupp.9.49","DOIUrl":"https://doi.org/10.5506/aphyspolbsupp.9.49","url":null,"abstract":"In a recent paper [arXiv:1506.06649 [nlin.CG]], we presented an example of a 3-state cellular automaton which exhibits behaviour analogous to degenerate hyperbolicity often observed in finite-dimensional dynamical systems. We also calculated densities of 0, 1 and 2 after n iterations of this rule, using finite state machines to conjecture patterns present in preimage sets. Here, we re-derive the same formulae in a rigorous way, without resorting to any semi-empirical methods. This is done by analysing the behaviour of continuous clusters of symbols and by considering their interactions.","PeriodicalId":436460,"journal":{"name":"arXiv: Cellular Automata and Lattice Gases","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124148879","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}
Pub Date : 2016-08-29DOI: 10.1142/S0129183116501473
Zhu Su, Weibing Deng, Jihui Han, Wei Li, Xu Cai
The Nagel-Schreckenberg model with overtaking strategy (NSOS) is proposed, and numerical simulations are performed for both closed and open boundary conditions. The fundamental diagram, space-time diagram, and spatial-temporal distribution of speed are investigated. In order to identify the synchronized flow state, both the correlation functions (autocorrelation and cross-correlation) and the one-minute average flow rate vs. density diagram are studied. All the results verify that synchronized flow does occur in our model.
{"title":"Occurrence of synchronized flow due to overtaking strategy in the Nagel-Schreckenberg model","authors":"Zhu Su, Weibing Deng, Jihui Han, Wei Li, Xu Cai","doi":"10.1142/S0129183116501473","DOIUrl":"https://doi.org/10.1142/S0129183116501473","url":null,"abstract":"The Nagel-Schreckenberg model with overtaking strategy (NSOS) is proposed, and numerical simulations are performed for both closed and open boundary conditions. The fundamental diagram, space-time diagram, and spatial-temporal distribution of speed are investigated. In order to identify the synchronized flow state, both the correlation functions (autocorrelation and cross-correlation) and the one-minute average flow rate vs. density diagram are studied. All the results verify that synchronized flow does occur in our model.","PeriodicalId":436460,"journal":{"name":"arXiv: Cellular Automata and Lattice Gases","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128278991","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}
Pub Date : 2015-12-07DOI: 10.1007/978-3-319-33482-0_51
A. Schadschneider, J. Schmidt, V. Popkov
{"title":"When Is a Bottleneck a Bottleneck","authors":"A. Schadschneider, J. Schmidt, V. Popkov","doi":"10.1007/978-3-319-33482-0_51","DOIUrl":"https://doi.org/10.1007/978-3-319-33482-0_51","url":null,"abstract":"","PeriodicalId":436460,"journal":{"name":"arXiv: Cellular Automata and Lattice Gases","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127235823","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}
Pub Date : 2015-06-22DOI: 10.1007/978-3-319-65558-1_10
H. Fuks
{"title":"An Example of Computation of the Density of Ones in Probabilistic Cellular Automata by Direct Recursion","authors":"H. Fuks","doi":"10.1007/978-3-319-65558-1_10","DOIUrl":"https://doi.org/10.1007/978-3-319-65558-1_10","url":null,"abstract":"","PeriodicalId":436460,"journal":{"name":"arXiv: Cellular Automata and Lattice Gases","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127930073","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}
Pub Date : 2010-03-09DOI: 10.1201/9781420035063.ch18
Y. Young, Xin-She Yang
State-of-the-art review of cellular automata, cellular automata for partial differential equations, differential equations for cellular automata and pattern formation in biology and engineering.
元胞自动机、元胞自动机的偏微分方程、元胞自动机的微分方程和生物与工程中的模式形成的最新进展。
{"title":"Cellular Automata, PDEs, and Pattern Formation","authors":"Y. Young, Xin-She Yang","doi":"10.1201/9781420035063.ch18","DOIUrl":"https://doi.org/10.1201/9781420035063.ch18","url":null,"abstract":"State-of-the-art review of cellular automata, cellular automata for partial differential equations, differential equations for cellular automata and pattern formation in biology and engineering.","PeriodicalId":436460,"journal":{"name":"arXiv: Cellular Automata and Lattice Gases","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124215861","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}
We derive the Euler equations as the hydrodynamic limit of a stochastic model of a hard-sphere gas on a lattice. We show that the system does not produce entropy.
我们导出了晶格上硬球气体随机模型的欧拉方程作为水动力极限。我们证明了系统不产生熵。
{"title":"No production of entropy in the Euler fluid","authors":"R. Streater","doi":"10.4064/BC66-0-21","DOIUrl":"https://doi.org/10.4064/BC66-0-21","url":null,"abstract":"We derive the Euler equations as the hydrodynamic limit of a stochastic model of a hard-sphere gas on a lattice. We show that the system does not produce entropy.","PeriodicalId":436460,"journal":{"name":"arXiv: Cellular Automata and Lattice Gases","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114992810","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}
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