We study two-dimensional Rayleigh–Bénard convection with Navier-slip, fixed temperature boundary conditions and establish bounds on the Nusselt number. As the slip-length varies with Rayleigh number Ra, this estimate interpolates between the Whitehead–Doering bound by Ra512 for free-slip conditions (Whitehead & Doering. 2011 Ultimate state of two-dimensional Rayleigh–Bénard convection between free-slip fixed-temperature boundaries. Phys. Rev. Lett. 106, 244501) and the classical Doering–Constantin Ra12 bound (Doering & Constantin. 1996 Variational bounds on energy dissipation in incompressible flows. III. Convection. Phys. Rev. E 53, 5957–5981). This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 1)’.
本文研究了具有navier滑移、固定温度边界条件的二维rayleigh - bassanard对流，并建立了Nusselt数的边界。由于滑移长度随瑞利数Ra的变化而变化，该估计在自由滑移条件下由Ra512的Whitehead - Doering边界之间进行插值(Whitehead & Doering. 2011自由滑移固定温度边界之间二维Rayleigh - b nard对流的最终状态)。理论物理。经典的Doering - Constantin Ra12界(Doering & Constantin. 1996)和不可压缩流能量耗散的变分界。3对流。理论物理。Rev. E 53,5957 - 5981)。本文是主题问题“物理流体动力学中的数学问题(第一部分)”的一部分。
{"title":"Bounds on heat flux for Rayleigh–Bénard convection between Navier-slip fixed-temperature boundaries","authors":"Theodore D. Drivas, H. Nguyen, Camilla Nobili","doi":"10.1098/rsta.2021.0025","DOIUrl":"https://doi.org/10.1098/rsta.2021.0025","url":null,"abstract":"We study two-dimensional Rayleigh–Bénard convection with Navier-slip, fixed temperature boundary conditions and establish bounds on the Nusselt number. As the slip-length varies with Rayleigh number Ra, this estimate interpolates between the Whitehead–Doering bound by Ra512 for free-slip conditions (Whitehead & Doering. 2011 Ultimate state of two-dimensional Rayleigh–Bénard convection between free-slip fixed-temperature boundaries. Phys. Rev. Lett. 106, 244501) and the classical Doering–Constantin Ra12 bound (Doering & Constantin. 1996 Variational bounds on energy dissipation in incompressible flows. III. Convection. Phys. Rev. E 53, 5957–5981). This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 1)’.","PeriodicalId":20020,"journal":{"name":"Philosophical Transactions of the Royal Society A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90664836","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}
Víctor Buendía, Pablo Villegas, R. Burioni, M. A. Muñoz
Many of the amazing functional capabilities of the brain are collective properties stemming from the interactions of large sets of individual neurons. In particular, the most salient collective phenomena in brain activity are oscillations, which require the synchronous activation of many neurons. Here, we analyse parsimonious dynamical models of neural synchronization running on top of synthetic networks that capture essential aspects of the actual brain anatomical connectivity such as a hierarchical-modular and core-periphery structure. These models reveal the emergence of complex collective states with intermediate and flexible levels of synchronization, halfway in the synchronous–asynchronous spectrum. These states are best described as broad Griffiths-like phases, i.e. an extension of standard critical points that emerge in structurally heterogeneous systems. We analyse different routes (bifurcations) to synchronization and stress the relevance of ‘hybrid-type transitions’ to generate rich dynamical patterns. Overall, our results illustrate the complex interplay between structure and dynamics, underlining key aspects leading to rich collective states needed to sustain brain functionality. This article is part of the theme issue ‘Emergent phenomena in complex physical and socio-technical systems: from cells to societies’.
{"title":"The broad edge of synchronization: Griffiths effects and collective phenomena in brain networks","authors":"Víctor Buendía, Pablo Villegas, R. Burioni, M. A. Muñoz","doi":"10.1098/rsta.2020.0424","DOIUrl":"https://doi.org/10.1098/rsta.2020.0424","url":null,"abstract":"Many of the amazing functional capabilities of the brain are collective properties stemming from the interactions of large sets of individual neurons. In particular, the most salient collective phenomena in brain activity are oscillations, which require the synchronous activation of many neurons. Here, we analyse parsimonious dynamical models of neural synchronization running on top of synthetic networks that capture essential aspects of the actual brain anatomical connectivity such as a hierarchical-modular and core-periphery structure. These models reveal the emergence of complex collective states with intermediate and flexible levels of synchronization, halfway in the synchronous–asynchronous spectrum. These states are best described as broad Griffiths-like phases, i.e. an extension of standard critical points that emerge in structurally heterogeneous systems. We analyse different routes (bifurcations) to synchronization and stress the relevance of ‘hybrid-type transitions’ to generate rich dynamical patterns. Overall, our results illustrate the complex interplay between structure and dynamics, underlining key aspects leading to rich collective states needed to sustain brain functionality. This article is part of the theme issue ‘Emergent phenomena in complex physical and socio-technical systems: from cells to societies’.","PeriodicalId":20020,"journal":{"name":"Philosophical Transactions of the Royal Society A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74266841","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}
The information content of symbolic sequences (such as nucleic or amino acid sequences, but also neuronal firings or strings of letters) can be calculated from an ensemble of such sequences, but because information cannot be assigned to single sequences, we cannot correlate information to other observables attached to the sequence. Here we show that an information score obtained from multivariate (multiple-variable) correlations within sequences of a ‘training’ ensemble can be used to predict observables of out-of-sample sequences with an accuracy that scales with the complexity of correlations, showing that functional information emerges from a hierarchy of multi-variable correlations. This article is part of the theme issue ‘Emergent phenomena in complex physical and socio-technical systems: from cells to societies’.
{"title":"Emergence of functional information from multivariate correlations","authors":"C. Adami, Nitash C G","doi":"10.1098/rsta.2021.0250","DOIUrl":"https://doi.org/10.1098/rsta.2021.0250","url":null,"abstract":"The information content of symbolic sequences (such as nucleic or amino acid sequences, but also neuronal firings or strings of letters) can be calculated from an ensemble of such sequences, but because information cannot be assigned to single sequences, we cannot correlate information to other observables attached to the sequence. Here we show that an information score obtained from multivariate (multiple-variable) correlations within sequences of a ‘training’ ensemble can be used to predict observables of out-of-sample sequences with an accuracy that scales with the complexity of correlations, showing that functional information emerges from a hierarchy of multi-variable correlations. This article is part of the theme issue ‘Emergent phenomena in complex physical and socio-technical systems: from cells to societies’.","PeriodicalId":20020,"journal":{"name":"Philosophical Transactions of the Royal Society A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84302837","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}
In this work, we study a model of opinion dynamics considering activation/deactivation of agents. In other words, individuals are not static and can become inactive and drop out from the discussion. A probability w governs the deactivation dynamics, whereas social interactions are ruled by kinetic exchanges, considering competitive positive/negative interactions. Inactive agents can become active due to interactions with active agents. Our analytical and numerical results show the existence of two distinct non-equilibrium phase transitions, with the occurrence of three phases, namely ordered (ferromagnetic-like), disordered (paramagnetic-like) and absorbing phases. The absorbing phase represents a collective state where all agents are inactive, i.e. they do not participate in the dynamics, inducing a frozen state. We determine the critical value wc above which the system is in the absorbing phase independently of the other parameters. We also verify a distinct critical behaviour for the transitions among different phases. This article is part of the theme issue ‘Kinetic exchange models of societies and economies’.
{"title":"Double transition in kinetic exchange opinion models with activation dynamics","authors":"Marcelo A. Pires, N. Crokidakis","doi":"10.1098/rsta.2021.0164","DOIUrl":"https://doi.org/10.1098/rsta.2021.0164","url":null,"abstract":"In this work, we study a model of opinion dynamics considering activation/deactivation of agents. In other words, individuals are not static and can become inactive and drop out from the discussion. A probability w governs the deactivation dynamics, whereas social interactions are ruled by kinetic exchanges, considering competitive positive/negative interactions. Inactive agents can become active due to interactions with active agents. Our analytical and numerical results show the existence of two distinct non-equilibrium phase transitions, with the occurrence of three phases, namely ordered (ferromagnetic-like), disordered (paramagnetic-like) and absorbing phases. The absorbing phase represents a collective state where all agents are inactive, i.e. they do not participate in the dynamics, inducing a frozen state. We determine the critical value wc above which the system is in the absorbing phase independently of the other parameters. We also verify a distinct critical behaviour for the transitions among different phases. This article is part of the theme issue ‘Kinetic exchange models of societies and economies’.","PeriodicalId":20020,"journal":{"name":"Philosophical Transactions of the Royal Society A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85719155","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 investigate the large-scale circulation (LSC) in a turbulent Rayleigh-Bénard convection flow in a cubic closed convection cell by means of direct numerical simulations at a Rayleigh number Ra = 106. The numerical studies are conducted for single flow trajectories up to 105 convective free-fall times to obtain a sufficient sampling of the four discrete LSC states, which can be summarized to one macrostate, and the two crossover configurations which are taken by the flow in between for short periods. We find that large-scale dynamics depends strongly on the Prandtl number Pr of the fluid which has values of 0.1, 0.7, and 10. Alternatively, we run an ensemble of 3600 short-term direct numerical simulations to study the transition probabilities between the discrete LSC states. This second approach is also used to probe the Markov property of the dynamics. Our ensemble analysis gave strong indication of Markovianity of the transition process from one LSC state to another, even though the data are still accompanied by considerable noise. It is based on the eigenvalue spectrum of the transition probability matrix, further on the distribution of persistence times and the joint distribution of two successive microstate persistence times. This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 1)’.
{"title":"Large-scale flow in a cubic Rayleigh–Bénard cell: long-term turbulence statistics and Markovianity of macrostate transitions","authors":"P. Maity, P. Koltai, J. Schumacher","doi":"10.1098/rsta.2021.0042","DOIUrl":"https://doi.org/10.1098/rsta.2021.0042","url":null,"abstract":"We investigate the large-scale circulation (LSC) in a turbulent Rayleigh-Bénard convection flow in a cubic closed convection cell by means of direct numerical simulations at a Rayleigh number Ra = 106. The numerical studies are conducted for single flow trajectories up to 105 convective free-fall times to obtain a sufficient sampling of the four discrete LSC states, which can be summarized to one macrostate, and the two crossover configurations which are taken by the flow in between for short periods. We find that large-scale dynamics depends strongly on the Prandtl number Pr of the fluid which has values of 0.1, 0.7, and 10. Alternatively, we run an ensemble of 3600 short-term direct numerical simulations to study the transition probabilities between the discrete LSC states. This second approach is also used to probe the Markov property of the dynamics. Our ensemble analysis gave strong indication of Markovianity of the transition process from one LSC state to another, even though the data are still accompanied by considerable noise. It is based on the eigenvalue spectrum of the transition probability matrix, further on the distribution of persistence times and the joint distribution of two successive microstate persistence times. This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 1)’.","PeriodicalId":20020,"journal":{"name":"Philosophical Transactions of the Royal Society A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76191374","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}
Viktor Stojkoski, Petar Jolakoski, Arnab K. Pal, Trifce Sandev, L. Kocarev, R. Metzler
We explore the role of non-ergodicity in the relationship between income inequality, the extent of concentration in the income distribution, and income mobility, the feasibility of an individual to change their position in the income rankings. For this purpose, we use the properties of an established model for income growth that includes ‘resetting’ as a stabilizing force to ensure stationary dynamics. We find that the dynamics of inequality is regime-dependent: it may range from a strictly non-ergodic state where this phenomenon has an increasing trend, up to a stable regime where inequality is steady and the system efficiently mimics ergodicity. Mobility measures, conversely, are always stable over time, but suggest that economies become less mobile in non-ergodic regimes. By fitting the model to empirical data for the income share of the top earners in the USA, we provide evidence that the income dynamics in this country is consistently in a regime in which non-ergodicity characterizes inequality and immobility. Our results can serve as a simple rationale for the observed real-world income dynamics and as such aid in addressing non-ergodicity in various empirical settings across the globe. This article is part of the theme issue ‘Kinetic exchange models of societies and economies’.
{"title":"Income inequality and mobility in geometric Brownian motion with stochastic resetting: theoretical results and empirical evidence of non-ergodicity","authors":"Viktor Stojkoski, Petar Jolakoski, Arnab K. Pal, Trifce Sandev, L. Kocarev, R. Metzler","doi":"10.1098/rsta.2021.0157","DOIUrl":"https://doi.org/10.1098/rsta.2021.0157","url":null,"abstract":"We explore the role of non-ergodicity in the relationship between income inequality, the extent of concentration in the income distribution, and income mobility, the feasibility of an individual to change their position in the income rankings. For this purpose, we use the properties of an established model for income growth that includes ‘resetting’ as a stabilizing force to ensure stationary dynamics. We find that the dynamics of inequality is regime-dependent: it may range from a strictly non-ergodic state where this phenomenon has an increasing trend, up to a stable regime where inequality is steady and the system efficiently mimics ergodicity. Mobility measures, conversely, are always stable over time, but suggest that economies become less mobile in non-ergodic regimes. By fitting the model to empirical data for the income share of the top earners in the USA, we provide evidence that the income dynamics in this country is consistently in a regime in which non-ergodicity characterizes inequality and immobility. Our results can serve as a simple rationale for the observed real-world income dynamics and as such aid in addressing non-ergodicity in various empirical settings across the globe. This article is part of the theme issue ‘Kinetic exchange models of societies and economies’.","PeriodicalId":20020,"journal":{"name":"Philosophical Transactions of the Royal Society A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88280842","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}
Transitional localized turbulence in shear flows is known to either decay to an absorbing laminar state or to proliferate via splitting. The average passage times from one state to the other depend super-exponentially on the Reynolds number and lead to a crossing Reynolds number above which proliferation is more likely than decay. In this paper, we apply a rare-event algorithm, Adaptative Multilevel Splitting, to the deterministic Navier–Stokes equations to study transition paths and estimate large passage times in channel flow more efficiently than direct simulations. We establish a connection with extreme value distributions and show that transition between states is mediated by a regime that is self-similar with the Reynolds number. The super-exponential variation of the passage times is linked to the Reynolds number dependence of the parameters of the extreme value distribution. Finally, motivated by instantons from Large Deviation theory, we show that decay or splitting events approach a most-probable pathway. This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 2)’.
{"title":"Extreme events in transitional turbulence","authors":"Sébastien Gomé, L. Tuckerman, D. Barkley","doi":"10.1098/rsta.2021.0036","DOIUrl":"https://doi.org/10.1098/rsta.2021.0036","url":null,"abstract":"Transitional localized turbulence in shear flows is known to either decay to an absorbing laminar state or to proliferate via splitting. The average passage times from one state to the other depend super-exponentially on the Reynolds number and lead to a crossing Reynolds number above which proliferation is more likely than decay. In this paper, we apply a rare-event algorithm, Adaptative Multilevel Splitting, to the deterministic Navier–Stokes equations to study transition paths and estimate large passage times in channel flow more efficiently than direct simulations. We establish a connection with extreme value distributions and show that transition between states is mediated by a regime that is self-similar with the Reynolds number. The super-exponential variation of the passage times is linked to the Reynolds number dependence of the parameters of the extreme value distribution. Finally, motivated by instantons from Large Deviation theory, we show that decay or splitting events approach a most-probable pathway. This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 2)’.","PeriodicalId":20020,"journal":{"name":"Philosophical Transactions of the Royal Society A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89538351","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}
Sanjukta Paul, Sudip Mukherjee, Biji Joseph, A. Ghosh, B. Chakrabarti
We report the numerical results for the steady-state income or wealth distribution P(m) and the resulting inequality measures (Gini g and Kolkata k indices) in the kinetic exchange models of market dynamics. We study the variations of P(m) and of the indices g and k with the saving propensity λ of the agents, with two different kinds of trade (kinetic exchange) dynamics. In the first case, the exchange occurs between randomly chosen pairs of agents and in the next, one of the agents in the chosen pair is the poorest of all and the other agent is randomly picked up from the rest of the population (where, in the steady state, a self-organized poverty level or SOPL appears). These studies have also been made for two different kinds of saving behaviours. One, where each agent has the same value of λ (constant over time) and the other where λ for each agent can take two values (0 and 1), changing randomly over a fraction of time ρ(<1) of choosing λ=1. We find that the inequality decreases with increasing savings (λ); inequality indices (g and k) decrease and SOPL increases with increasing λ, indicating possible applications in economic policy making. This article is part of the theme issue ‘Kinetic exchange models of societies and economies’.
{"title":"Kinetic exchange income distribution models with saving propensities: inequality indices and self-organized poverty level","authors":"Sanjukta Paul, Sudip Mukherjee, Biji Joseph, A. Ghosh, B. Chakrabarti","doi":"10.1098/rsta.2021.0163","DOIUrl":"https://doi.org/10.1098/rsta.2021.0163","url":null,"abstract":"We report the numerical results for the steady-state income or wealth distribution P(m) and the resulting inequality measures (Gini g and Kolkata k indices) in the kinetic exchange models of market dynamics. We study the variations of P(m) and of the indices g and k with the saving propensity λ of the agents, with two different kinds of trade (kinetic exchange) dynamics. In the first case, the exchange occurs between randomly chosen pairs of agents and in the next, one of the agents in the chosen pair is the poorest of all and the other agent is randomly picked up from the rest of the population (where, in the steady state, a self-organized poverty level or SOPL appears). These studies have also been made for two different kinds of saving behaviours. One, where each agent has the same value of λ (constant over time) and the other where λ for each agent can take two values (0 and 1), changing randomly over a fraction of time ρ(<1) of choosing λ=1. We find that the inequality decreases with increasing savings (λ); inequality indices (g and k) decrease and SOPL increases with increasing λ, indicating possible applications in economic policy making. This article is part of the theme issue ‘Kinetic exchange models of societies and economies’.","PeriodicalId":20020,"journal":{"name":"Philosophical Transactions of the Royal Society A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78558147","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}
Two recent articles (Moncrief V. 2015 In General relativity and gravitation-A centennial perspective (eds A Asthekar, B Berger, J Isenberg, M MacCallum), pp. 480–498. Cambridge, UK: Cambridge University Press; Moncrief V, Mondal P. 2019 Pure Appl. Math. Q. 15, 921–965. (doi:10.4310/PAMQ.2019.v15.n3.a7)) suggested an interesting dynamical mechanism within the framework of the vacuum Einstein flow (or Einstein-Λ flow if a positive cosmological constant Λ is included) which suggests that many closed (compact without boundary) manifolds that do not support homogeneous and isotropic metrics at all will nevertheless evolve to be asymptotically compatible with the observed approximate homogeneity and isotropy of the physical universe. These studies however did not include matter sources. Therefore, the aim of the present study is to include suitable matter sources and investigate whether one is able to draw a similar conclusion. This article is part of the theme issue ‘The future of mathematical cosmology, Volume 1’.
最近的两篇文章(Moncrief V. 2015广义相对论和引力——百年视角)，第480-498页。英国剑桥:剑桥大学出版社;Moncrief V, Mondal P. 2019纯苹果。数学。问题15,921-965。(doi:10.4310/ pamq.com .2019.v15.n3.a7))在真空爱因斯坦流(或爱因斯坦-Λ流，如果包括一个正的宇宙常数Λ)的框架内提出了一个有趣的动力机制，这表明许多完全不支持齐次和各向同性指标的封闭(紧致无界)流形将进化为与观测到的物理宇宙的近似均匀性和各向同性渐近兼容。然而，这些研究没有包括物质来源。因此，本研究的目的是纳入合适的物质来源，并调查是否能够得出类似的结论。本文是主题问题“数学宇宙学的未来，第一卷”的一部分。
{"title":"Einstein flow with matter sources: stability and convergence","authors":"V. Moncrief, P. Mondal","doi":"10.1098/rsta.2021.0190","DOIUrl":"https://doi.org/10.1098/rsta.2021.0190","url":null,"abstract":"Two recent articles (Moncrief V. 2015 In General relativity and gravitation-A centennial perspective (eds A Asthekar, B Berger, J Isenberg, M MacCallum), pp. 480–498. Cambridge, UK: Cambridge University Press; Moncrief V, Mondal P. 2019 Pure Appl. Math. Q. 15, 921–965. (doi:10.4310/PAMQ.2019.v15.n3.a7)) suggested an interesting dynamical mechanism within the framework of the vacuum Einstein flow (or Einstein-Λ flow if a positive cosmological constant Λ is included) which suggests that many closed (compact without boundary) manifolds that do not support homogeneous and isotropic metrics at all will nevertheless evolve to be asymptotically compatible with the observed approximate homogeneity and isotropy of the physical universe. These studies however did not include matter sources. Therefore, the aim of the present study is to include suitable matter sources and investigate whether one is able to draw a similar conclusion. This article is part of the theme issue ‘The future of mathematical cosmology, Volume 1’.","PeriodicalId":20020,"journal":{"name":"Philosophical Transactions of the Royal Society A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91129149","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}
In this short review, we present some recently obtained traversable wormhole models in the framework of general relativity (GR) in four and six dimensions that somehow widen our common ideas on wormhole existence and properties. These are, first, rotating cylindrical wormholes, asymptotically flat in the radial direction and existing without exotic matter. The topological censorship theorems are not violated due to lack of asymptotic flatness in all spatial directions. Second, these are cosmological wormholes constructed on the basis of the Lemaître–Tolman–Bondi solution. They connect two copies of a closed Friedmann world filled with dust, or two otherwise distant parts of the same Friedmann world. Third, these are wormholes obtained in six-dimensional GR, whose one entrance is located in ‘our’ asymptotically flat world with very small extra dimensions while the other ‘end’ belongs to a universe with large extra dimensions and therefore different physical properties. The possible observable features of such wormholes are briefly discussed. This article is part of the theme issue ‘The future of mathematical cosmology, Volume 1’.
{"title":"Some unusual wormholes in general relativity","authors":"K. Bronnikov","doi":"10.1098/rsta.2021.0176","DOIUrl":"https://doi.org/10.1098/rsta.2021.0176","url":null,"abstract":"In this short review, we present some recently obtained traversable wormhole models in the framework of general relativity (GR) in four and six dimensions that somehow widen our common ideas on wormhole existence and properties. These are, first, rotating cylindrical wormholes, asymptotically flat in the radial direction and existing without exotic matter. The topological censorship theorems are not violated due to lack of asymptotic flatness in all spatial directions. Second, these are cosmological wormholes constructed on the basis of the Lemaître–Tolman–Bondi solution. They connect two copies of a closed Friedmann world filled with dust, or two otherwise distant parts of the same Friedmann world. Third, these are wormholes obtained in six-dimensional GR, whose one entrance is located in ‘our’ asymptotically flat world with very small extra dimensions while the other ‘end’ belongs to a universe with large extra dimensions and therefore different physical properties. The possible observable features of such wormholes are briefly discussed. This article is part of the theme issue ‘The future of mathematical cosmology, Volume 1’.","PeriodicalId":20020,"journal":{"name":"Philosophical Transactions of the Royal Society A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78703381","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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