Understanding the impact of human behaviour is crucial for successful mitigation of climate change across the globe. To shed light onto this issue, here we couple the forest dieback model with human behaviours. Using evolutionary game theory, we build a time-delay system where forest growth is impacted by both temperature and human mitigation choices, the latter being informed by temperature forecasts. Simulations of the coupled system over 200 years show us the varying outcomes: forest dies out and no one is a mitigator, forest dies out and everyone is a mitigator, or the forest survives and everyone is a mitigator. There exist rare cases where no one is a mitigator and yet the forest survives, but with a low coverage. We also find occasional oscillations where the proportion of mitigators vary between 0 and 1. Our results are based on simple models but have profound insights into determinants of behaviour changes desired in social-climate dynamics.
{"title":"Determinants of successful mitigation in coupled social-climate dynamics","authors":"Longmei Shu, Feng Fu","doi":"10.1098/rspa.2023.0679","DOIUrl":"https://doi.org/10.1098/rspa.2023.0679","url":null,"abstract":"Understanding the impact of human behaviour is crucial for successful mitigation of climate change across the globe. To shed light onto this issue, here we couple the forest dieback model with human behaviours. Using evolutionary game theory, we build a time-delay system where forest growth is impacted by both temperature and human mitigation choices, the latter being informed by temperature forecasts. Simulations of the coupled system over 200 years show us the varying outcomes: forest dies out and no one is a mitigator, forest dies out and everyone is a mitigator, or the forest survives and everyone is a mitigator. There exist rare cases where no one is a mitigator and yet the forest survives, but with a low coverage. We also find occasional oscillations where the proportion of mitigators vary between 0 and 1. Our results are based on simple models but have profound insights into determinants of behaviour changes desired in social-climate dynamics.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"54 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139340278","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 complete set of bounds for the technical constants of an elastic layer, plate or laminate is given. The bounds are valid in general, also for completely anisotropic bodies. They are obtained transforming the polar bounds previously found. These bounds complete the knowledge of classical elasticity at least in the two-dimensional case and are useful in several situations, e.g. for determining the correct feasibility domain in design problems or as necessary conditions for accepting the results of laboratory tests on anisotropic layers.
{"title":"Bounds of the technical constants for two-dimensional anisotropic elasticity","authors":"P. Vannucci","doi":"10.1098/rspa.2023.0662","DOIUrl":"https://doi.org/10.1098/rspa.2023.0662","url":null,"abstract":"The complete set of bounds for the technical constants of an elastic layer, plate or laminate is given. The bounds are valid in general, also for completely anisotropic bodies. They are obtained transforming the polar bounds previously found. These bounds complete the knowledge of classical elasticity at least in the two-dimensional case and are useful in several situations, e.g. for determining the correct feasibility domain in design problems or as necessary conditions for accepting the results of laboratory tests on anisotropic layers.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"150 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139341621","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 study, a new set of fifth-order Stokes wave solutions, incorporating the effects of a linear shear current, is derived by using the perturbation method originally proposed for pure waves that was recently published. The present solutions are checked against the existing experimental data, the third-order stream function solutions, as well as the numerical results. The comparisons demonstrate that the present solutions are more accurate in describing the velocity distributions during wave propagation, especially in strong following currents and negative vorticity conditions. Subsequently, the present solutions are used to investigate the fluid particle trajectories for different wave–current interaction conditions. The results indicate that the background vorticity can alter the patterns of fluid particle trajectories and the direction of Stokes drifts.
{"title":"The theory of fifth-order Stokes waves in a linear shear current","authors":"Haiqi Fang, Philip L.-F. Liu, Lian Tang, P. Lin","doi":"10.1098/rspa.2023.0565","DOIUrl":"https://doi.org/10.1098/rspa.2023.0565","url":null,"abstract":"In this study, a new set of fifth-order Stokes wave solutions, incorporating the effects of a linear shear current, is derived by using the perturbation method originally proposed for pure waves that was recently published. The present solutions are checked against the existing experimental data, the third-order stream function solutions, as well as the numerical results. The comparisons demonstrate that the present solutions are more accurate in describing the velocity distributions during wave propagation, especially in strong following currents and negative vorticity conditions. Subsequently, the present solutions are used to investigate the fluid particle trajectories for different wave–current interaction conditions. The results indicate that the background vorticity can alter the patterns of fluid particle trajectories and the direction of Stokes drifts.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139351545","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, the paraxial approximation of the free Dirac equation is examined. The results are first obtained by constructing superpositions of exact solutions with suitable profiles, which are borrowed from paraxial optics. In this manner, the paraxial Dirac beams are obtained in four cases: as Gaussian, Bessel-Gaussian, modified Bessel-Gaussian and elegant Laguerre-Gaussian beams. In the second part of the work, the paraxial Dirac equation is derived, and then its solutions in the aforementioned cases are directly obtained. All the resulting wave functions conform to those derived formerly by virtue of superpositions, except for terms that are negligible upon the assumption that the paraxial functions along the propagation axis vary only slightly over a distance equal to the de Broglie wavelength, which is the standard paraxial requirement.
{"title":"Paraxial Dirac equation","authors":"Tomasz Rado.zycki","doi":"10.1098/rspa.2023.0493","DOIUrl":"https://doi.org/10.1098/rspa.2023.0493","url":null,"abstract":"In this work, the paraxial approximation of the free Dirac equation is examined. The results are first obtained by constructing superpositions of exact solutions with suitable profiles, which are borrowed from paraxial optics. In this manner, the paraxial Dirac beams are obtained in four cases: as Gaussian, Bessel-Gaussian, modified Bessel-Gaussian and elegant Laguerre-Gaussian beams. In the second part of the work, the paraxial Dirac equation is derived, and then its solutions in the aforementioned cases are directly obtained. All the resulting wave functions conform to those derived formerly by virtue of superpositions, except for terms that are negligible upon the assumption that the paraxial functions along the propagation axis vary only slightly over a distance equal to the de Broglie wavelength, which is the standard paraxial requirement.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139361927","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}
A process of growth and division of cells is modelled by an initial boundary value problem that involves a first-order linear functional partial differential equation, the so-called sell growth equation. The analytical solution to this problem was given in the paper Zaidi et al. (Zaidi et al. 2015 Solutions to an advanced functional partial differential equation of the pantograph type (Proc. R. Soc. A 471, 20140947 (doi:10.1098/rspa.2014.0947)). In this note, we simplify the arguments given in the paper mentioned above by using the theory of operator semigroups. This theory enables us to prove the existence and uniqueness of the solution and to express this solution in terms of Dyson–Phillips series. The asymptotics of the solution is also discussed from the point of view of the theory of operator semigroups.
细胞的生长和分裂过程由初始边界值问题模拟，该问题涉及一阶线性函数偏微分方程，即所谓的卖出生长方程。Zaidi 等人的论文（Zaidi et al. 2015 Solutions to an advanced functional partial differential equation of the pantograph type (Proc. R. Soc. A 471, 20140947)给出了这一问题的解析解。R. Soc. A 471, 20140947 (doi:10.1098/rspa.2014.0947) ）。在本说明中，我们利用算子半群理论简化了上述论文中给出的论证。这一理论使我们能够证明解的存在性和唯一性，并用戴森-菲利普斯数列来表达这一解。我们还从算子半群理论的角度讨论了解的渐近性。
{"title":"Some remarks on the solution of the cell growth equation","authors":"A. Mirotin","doi":"10.1098/rspa.2023.0534","DOIUrl":"https://doi.org/10.1098/rspa.2023.0534","url":null,"abstract":"A process of growth and division of cells is modelled by an initial boundary value problem that involves a first-order linear functional partial differential equation, the so-called sell growth equation. The analytical solution to this problem was given in the paper Zaidi et al. (Zaidi et al. 2015 Solutions to an advanced functional partial differential equation of the pantograph type (Proc. R. Soc. A 471, 20140947 (doi:10.1098/rspa.2014.0947)). In this note, we simplify the arguments given in the paper mentioned above by using the theory of operator semigroups. This theory enables us to prove the existence and uniqueness of the solution and to express this solution in terms of Dyson–Phillips series. The asymptotics of the solution is also discussed from the point of view of the theory of operator semigroups.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139362444","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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