Philosophical Transactions of the Royal Society A最新文献_第7页

A critical appraisal of the singularity theorems 奇点定理的批判性评价

Philosophical Transactions of the Royal Society A Pub Date : 2021-08-16 DOI: 10.1098/rsta.2021.0174

J. Senovilla

引用次数: 7

Opinion polarization in social networks 社交网络中的意见两极分化

Philosophical Transactions of the Royal Society A Pub Date : 2021-08-05 DOI: 10.1098/rsta.2021.0158

N. Loy, Matteo Raviola, A. Tosin

{"title":"Opinion polarization in social networks","authors":"N. Loy, Matteo Raviola, A. Tosin","doi":"10.1098/rsta.2021.0158","DOIUrl":"https://doi.org/10.1098/rsta.2021.0158","url":null,"abstract":"In this paper, we propose a Boltzmann-type kinetic description of opinion formation on social networks, which takes into account a general connectivity distribution of the individuals. We consider opinion exchange processes inspired by the Sznajd model and related simplifications but we do not assume that individuals interact on a regular lattice. Instead, we describe the structure of the social network statistically, assuming that the number of contacts of a given individual determines the probability that their opinion reaches and influences the opinion of another individual. From the kinetic description of the system, we study the evolution of the mean opinion, whence we find precise analytical conditions under which a polarization switch of the opinions, i.e. a change of sign between the initial and the asymptotic mean opinions, occurs. In particular, we show that a non-zero correlation between the initial opinions and the connectivity of the individuals is necessary to observe polarization switch. Finally, we validate our analytical results through Monte Carlo simulations of the stochastic opinion exchange processes on the social network. 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":"2021-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88195085","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: 7

Stability of asymptotic behaviour within polarized T2-symmetric vacuum solutions with cosmological constant 具有宇宙学常数的偏振t2对称真空解的渐近行为稳定性

Philosophical Transactions of the Royal Society A Pub Date : 2021-08-05 DOI: 10.1098/rsta.2021.0173

E. Ames, F. Beyer, J. Isenberg, T. Oliynyk

{"title":"Stability of asymptotic behaviour within polarized T2-symmetric vacuum solutions with cosmological constant","authors":"E. Ames, F. Beyer, J. Isenberg, T. Oliynyk","doi":"10.1098/rsta.2021.0173","DOIUrl":"https://doi.org/10.1098/rsta.2021.0173","url":null,"abstract":"We prove the nonlinear stability of the asymptotic behaviour of perturbations of subfamilies of Kasner solutions in the contracting time direction within the class of polarized T2-symmetric solutions of the vacuum Einstein equations with arbitrary cosmological constant Λ. This stability result generalizes the results proven in Ames E et al. (2022 Stability of AVTD Behavior within the Polarized T2-symmetric vacuum spacetimes. Ann. Henri Poincaré. (doi:10.1007/s00023-021-01142-0)), which focus on the Λ=0 case, and as in that article, the proof relies on an areal time foliation and Fuchsian techniques. Even for Λ=0, the results established here apply to a wider class of perturbations of Kasner solutions within the family of polarized T2-symmetric vacuum solutions than those considered in Ames E et al. (2022 Stability of AVTD Behavior within the Polarized T2-symmetric vacuum spacetimes. Ann. Henri Poincaré. (doi:10.1007/s00023-021-01142-0)) and Fournodavlos G et al. (2020 Stable Big Bang formation for Einstein’s equations: the complete sub-critical regime. Preprint. (http://arxiv.org/abs/2012.05888)). Our results establish that the areal time coordinate takes all values in (0,T0] for some T0>0, for certain families of polarized T2-symmetric solutions with cosmological constant. 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":"2021-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78748824","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: 1

Geometrical origins of the universe dark sector: string-inspired torsion and anomalies as seeds for inflation and dark matter 宇宙暗区的几何起源:弦激发的扭曲和异常是暴胀和暗物质的种子

Philosophical Transactions of the Royal Society A Pub Date : 2021-08-04 DOI: 10.1098/rsta.2021.0188

N. Mavromatos

{"title":"Geometrical origins of the universe dark sector: string-inspired torsion and anomalies as seeds for inflation and dark matter","authors":"N. Mavromatos","doi":"10.1098/rsta.2021.0188","DOIUrl":"https://doi.org/10.1098/rsta.2021.0188","url":null,"abstract":"In a modest attempt to present potentially new paradigms in cosmology, including its inflationary epoch, and initiate discussions, I review in this article some novel, string-inspired cosmological models, which entail a purely geometrical origin of the dark sector of the Universe but also of its observed matter-antimatter asymmetry. The models contain gravitational (string-model independent, Kalb–Ramond (KR)) axion fields coupled to primordial gravitational anomalies via CP-violating interactions. The anomaly terms are four-space–time-dimensional remnants of the Green–Schwarz counterterms appearing in the definition of the field strength of the spin-one antisymmetric tensor field of the (bosonic) massless gravitational string multiplet, which also plays the role of a totally antisymmetric component of torsion. I show how in such cosmologies the presence of primordial gravitational waves can lead to anomaly condensates and dynamical inflation of a ‘running-vacuum-model’ type, without external inflatons, but also to leptogenesis in the radiation era due to anomaly induced Lorentz and CPT violating KR axion backgrounds. I also discuss how the torsion-related KR-axion could acquire a mass during the QCD epoch, thus playing the role of (a component of) dark matter. Phenomenological considerations of the inflationary and post-inflationary (in particular, modern) eras of the model are briefly discussed, including its potential for alleviating the observed tensions in the cosmological data of the current epoch. 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":"2021-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82726529","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: 13

On the dynamics of point vortices for the two-dimensional Euler equation with Lp vorticity 带Lp涡度的二维欧拉方程的点涡动力学

Philosophical Transactions of the Royal Society A Pub Date : 2021-07-27 DOI: 10.1098/rsta.2021.0046

S. Ceci, Christian Seis

引用次数: 3

Optimal control of epidemic spreading in the presence of social heterogeneity 社会异质性条件下疫情传播的最优控制

Philosophical Transactions of the Royal Society A Pub Date : 2021-07-26 DOI: 10.1098/rsta.2021.0160

G. Dimarco, G. Toscani, M. Zanella

{"title":"Optimal control of epidemic spreading in the presence of social heterogeneity","authors":"G. Dimarco, G. Toscani, M. Zanella","doi":"10.1098/rsta.2021.0160","DOIUrl":"https://doi.org/10.1098/rsta.2021.0160","url":null,"abstract":"The spread of COVID-19 has been thwarted in most countries through non-pharmaceutical interventions. In particular, the most effective measures in this direction have been the stay-at-home and closure strategies of businesses and schools. However, population-wide lockdowns are far from being optimal, carrying heavy economic consequences. Therefore, there is nowadays a strong interest in designing more efficient restrictions. In this work, starting from a recent kinetic-type model which takes into account the heterogeneity described by the social contact of individuals, we analyse the effects of introducing an optimal control strategy into the system, to limit selectively the mean number of contacts and reduce consequently the number of infected cases. Thanks to a data-driven approach, we show that this new mathematical model permits us to assess the effects of the social limitations. Finally, using the model introduced here and starting from the available data, we show the effectiveness of the proposed selective measures to dampen the epidemic trends. 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":"2021-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78822117","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: 19

The background method: theory and computations 背景方法:理论与计算相结合

Philosophical Transactions of the Royal Society A Pub Date : 2021-07-23 DOI: 10.1098/rsta.2021.0038

Giovanni Fantuzzi, A. Arslan, A. Wynn

引用次数: 14

On a kinetic opinion formation model for pre-election polling 选前民意调查的动态民意形成模型

Philosophical Transactions of the Royal Society A Pub Date : 2021-07-13 DOI: 10.1098/rsta.2021.0154

Bertram Düring, Oliver Wright

引用次数: 6

On the Prandtl–Kolmogorov 1-equation model of turbulence 湍流的Prandtl-Kolmogorov 1-方程模型

Philosophical Transactions of the Royal Society A Pub Date : 2021-06-18 DOI: 10.1098/rsta.2021.0054

Kiera Kean, W. Layton, M. Schneier

{"title":"On the Prandtl–Kolmogorov 1-equation model of turbulence","authors":"Kiera Kean, W. Layton, M. Schneier","doi":"10.1098/rsta.2021.0054","DOIUrl":"https://doi.org/10.1098/rsta.2021.0054","url":null,"abstract":"We prove an estimate of total (viscous plus modelled turbulent) energy dissipation in general eddy viscosity models for shear flows. The ratio of the near wall average viscosity to the effective global viscosity is the key parameter in the estimate. This result is then applied to the 1-equation, URANS model of turbulence for which this ratio depends on the specification of the turbulence length scale. The model, which was derived by Prandtl in 1945, is a component of a 2-equation model derived by Kolmogorov in 1942 and is the core of many unsteady, Reynolds averaged models for prediction of turbulent flows. Let τ denote a selected time scale. Away from walls, interpreting an early suggestion of Prandtl, we set l=2k1/2τ.In the near-wall region analysis suggests replacing the traditional l=0.41d (d= wall normal distance) with l=0.41dd/L giving l=min{2k 1/2τ, 0.41ddL}.This specification of l results in a simpler model with correct near wall asymptotics. Its energy dissipation rate scales no larger than the physically correct O(U3/L), balancing energy input with energy dissipation. 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":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83865993","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: 3

An econometric model for intraday electricity trading 日内电力交易的计量经济模型

Philosophical Transactions of the Royal Society A Pub Date : 2021-06-07 DOI: 10.2139/ssrn.3489214

Marcel Kremer, Ruediger Kiesel, Florentina Paraschiv

引用次数: 22