Alexander L. Kholmetskii, Oleg V. Missevitch, Tolga Yarman
We analyse the physical meaning of the Aharonov–Bohm (AB) phase based on its representation through electromagnetic (EM) potentials as a sum of four components, which, in addition to the known electric and magnetic phase components, contains two more terms recently disclosed by our team in the analysis of quantum phase effects for dipoles and charges, and which we named the complementary electric AB phase and the complementary magnetic AB phase. Using the complete expression for the AB phase, we reveal that the phase component, explicitly depending on time, is determined by the interactional electric energy, while the phase component, explicitly depending on the velocity of charge, is determined by the interactional EM momentum for an isolated system ‘source of EM field and charge’. These findings shed new light on the origin of the AB phase and, in particular, allow us to generalize the de Broglie relationship and the Heisenberg uncertainty relations for a charged particle in an EM field.
除了已知的电相分量和磁相分量之外，我们还分析了阿哈诺夫-玻姆（AB）相的物理意义，并将其通过电磁（EM）势表示为四个分量之和，其中还包含我们团队最近在分析偶极子和电荷的量子相位效应时发现的另外两个项，我们将其命名为互补电AB相和互补磁AB相。利用 AB 相的完整表达式，我们发现，对于一个孤立的系统 "电磁场和电荷源 "来说，明确取决于时间的相分量是由相互作用电能决定的，而明确取决于电荷速度的相分量是由相互作用电磁动量决定的。这些发现为我们揭示 AB 相的起源提供了新的思路，特别是使我们能够概括电磁场中带电粒子的德布罗格利关系和海森堡不确定性关系。
{"title":"Role of electromagnetic energy and momentum in the Aharonov–Bohm effect","authors":"Alexander L. Kholmetskii, Oleg V. Missevitch, Tolga Yarman","doi":"10.1098/rspa.2023.0286","DOIUrl":"https://doi.org/10.1098/rspa.2023.0286","url":null,"abstract":"We analyse the physical meaning of the Aharonov–Bohm (AB) phase based on its representation through electromagnetic (EM) potentials as a sum of four components, which, in addition to the known electric and magnetic phase components, contains two more terms recently disclosed by our team in the analysis of quantum phase effects for dipoles and charges, and which we named the complementary electric AB phase and the complementary magnetic AB phase. Using the complete expression for the AB phase, we reveal that the phase component, explicitly depending on time, is determined by the interactional electric energy, while the phase component, explicitly depending on the velocity of charge, is determined by the interactional EM momentum for an isolated system ‘source of EM field and charge’. These findings shed new light on the origin of the AB phase and, in particular, allow us to generalize the de Broglie relationship and the Heisenberg uncertainty relations for a charged particle in an EM field.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we present a new model for heat transfer in compressible fluid flows. The model is derived from Hamilton’s principle of stationary action in Eulerian coordinates, in a setting where the entropy conservation is recovered as an Euler–Lagrange equation. A sufficient criterion for the hyperbolicity of the model is formulated. The governing equations are asymptotically consistent with the Euler equations for compressible heat conducting fluids, provided the addition of suitable relaxation terms. A study of the Rankine–Hugoniot conditions and Clausius–Duhem inequality is performed for a specific choice of the equation of state. In particular, this reveals that contact discontinuities cannot exist while expansion waves and compression fans are possible solutions to the governing equations. Evidence of these properties is provided on a set of numerical test cases.
{"title":"An Eulerian hyperbolic model for heat transfer derived via Hamilton’s principle: analytical and numerical study","authors":"Firas Dhaouadi, Sergey Gavrilyuk","doi":"10.1098/rspa.2023.0440","DOIUrl":"https://doi.org/10.1098/rspa.2023.0440","url":null,"abstract":"In this paper, we present a new model for heat transfer in compressible fluid flows. The model is derived from Hamilton’s principle of stationary action in Eulerian coordinates, in a setting where the entropy conservation is recovered as an Euler–Lagrange equation. A sufficient criterion for the hyperbolicity of the model is formulated. The governing equations are asymptotically consistent with the Euler equations for compressible heat conducting fluids, provided the addition of suitable relaxation terms. A study of the Rankine–Hugoniot conditions and Clausius–Duhem inequality is performed for a specific choice of the equation of state. In particular, this reveals that contact discontinuities cannot exist while expansion waves and compression fans are possible solutions to the governing equations. Evidence of these properties is provided on a set of numerical test cases.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bifurcations organize the dynamics of many natural and engineered systems. They induce qualitative and quantitative changes to a system’s dynamics, which can have catastrophic consequences if ignored during design. In this paper, we propose a general computational method to control the local bifurcations of dynamical systems by optimizing design parameters. We define an objective functional that enforces the appearance of local bifurcation points at targeted locations or even encourages their disappearance. The methodology is an efficient alternative to bifurcation tracking techniques capable of handling many design parameters ( >102 ). The method is demonstrated on a Duffing oscillator featuring a hardening cubic nonlinearity and an autonomous van der Pol-Duffing oscillator coupled to a nonlinear tuned vibration absorber. The finite-element model of a clamped-free Euler–Bernoulli beam, coupled with a reduced-order modelling technique, is also used to show the extension to the shape optimization of more complicated structures. Results demonstrate that several local bifurcations of various types can be handled simultaneously by the bifurcation control framework, with both parameter and state target values.
{"title":"Multi-parametric optimization for controlling bifurcation structures","authors":"A. Mélot, E. Denimal, L. Renson","doi":"10.1098/rspa.2023.0505","DOIUrl":"https://doi.org/10.1098/rspa.2023.0505","url":null,"abstract":"Bifurcations organize the dynamics of many natural and engineered systems. They induce qualitative and quantitative changes to a system’s dynamics, which can have catastrophic consequences if ignored during design. In this paper, we propose a general computational method to control the local bifurcations of dynamical systems by optimizing design parameters. We define an objective functional that enforces the appearance of local bifurcation points at targeted locations or even encourages their disappearance. The methodology is an efficient alternative to bifurcation tracking techniques capable of handling many design parameters ( <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>></mml:mo> </mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>2</mml:mn> </mml:msup> </mml:math> </jats:inline-formula> ). The method is demonstrated on a Duffing oscillator featuring a hardening cubic nonlinearity and an autonomous van der Pol-Duffing oscillator coupled to a nonlinear tuned vibration absorber. The finite-element model of a clamped-free Euler–Bernoulli beam, coupled with a reduced-order modelling technique, is also used to show the extension to the shape optimization of more complicated structures. Results demonstrate that several local bifurcations of various types can be handled simultaneously by the bifurcation control framework, with both parameter and state target values.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Paolo Conti, Mengwu Guo, Andrea Manzoni, Attilio Frangi, Steven L. Brunton, J. Nathan Kutz
High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated. Multi-fidelity surrogate modelling aims to leverage less accurate, lower-fidelity models that are computationally inexpensive in order to enhance predictive accuracy when high-fidelity data are scarce. However, low-fidelity models, while often displaying the qualitative solution behaviour, fail to accurately capture fine spatio-temporal and dynamic features of high-fidelity models. To address this shortcoming, we present a data-driven strategy that combines dimensionality reduction with multi-fidelity neural network surrogates. The key idea is to generate a spatial basis by applying proper orthogonal decomposition (POD) to high-fidelity solution snapshots, and approximate the dynamics of the reduced states—time-parameter-dependent expansion coefficients of the POD basis—using a multi-fidelity long short-term memory network. By mapping low-fidelity reduced states to their high-fidelity counterpart, the proposed reduced-order surrogate model enables the efficient recovery of full solution fields over time and parameter variations in a non-intrusive manner. The generality of this method is demonstrated by a collection of PDE problems where the low-fidelity model can be defined by coarser meshes and/or time stepping, as well as by misspecified physical features.
{"title":"Multi-fidelity reduced-order surrogate modelling","authors":"Paolo Conti, Mengwu Guo, Andrea Manzoni, Attilio Frangi, Steven L. Brunton, J. Nathan Kutz","doi":"10.1098/rspa.2023.0655","DOIUrl":"https://doi.org/10.1098/rspa.2023.0655","url":null,"abstract":"High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated. Multi-fidelity surrogate modelling aims to leverage less accurate, lower-fidelity models that are computationally inexpensive in order to enhance predictive accuracy when high-fidelity data are scarce. However, low-fidelity models, while often displaying the qualitative solution behaviour, fail to accurately capture fine spatio-temporal and dynamic features of high-fidelity models. To address this shortcoming, we present a data-driven strategy that combines dimensionality reduction with multi-fidelity neural network surrogates. The key idea is to generate a spatial basis by applying proper orthogonal decomposition (POD) to high-fidelity solution snapshots, and approximate the dynamics of the reduced states—time-parameter-dependent expansion coefficients of the POD basis—using a multi-fidelity <jats:italic>long short-term memory</jats:italic> network. By mapping low-fidelity reduced states to their high-fidelity counterpart, the proposed reduced-order surrogate model enables the efficient recovery of full solution fields over time and parameter variations in a non-intrusive manner. The generality of this method is demonstrated by a collection of PDE problems where the low-fidelity model can be defined by coarser meshes and/or time stepping, as well as by misspecified physical features.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yang Ye, Zhidong Cao, Daniel Dajun Zeng, Qingpeng Zhang
Since the start of the COVID-19 pandemic, many firms have been shifting their supply chains away from countries with stringent control measures to mitigate supply-chain disruption. Nowadays, the global economy has reopened from the COVID-19 pandemic at various paces in different countries. Understanding how the global supply network evolves during and after the pandemic is necessary for determining the timing and speed of reopening. By harnessing the real-world and real-time global human movement and the latest macroeconomic data, we propose an evolutionary economic-epidemiological model to explore the evolutionary dynamics of the global supply network under various global reopening scenarios. We find that, for highly restrictive countries, the delay in reopening has limited public health benefits in the long run but leads to significant supply-chain loss. A longer duration of stringent control measures substantially hurts the profitability of firms in highly restrictive countries, leading to slower supply-chain recovery in 5 years. This research presents the first data-driven evidence of supply chain loss due to the timing and speed of reopening and sheds light on the post-pandemic supply-chain reformation and recovery. Insights learned from COVID-19 will also be a valuable policymaking reference for combating future infectious disease epidemics and geopolitical changes.
{"title":"Supply chain loss from easing COVID-19 restrictions: an evolutionary economic-epidemiological modelling study","authors":"Yang Ye, Zhidong Cao, Daniel Dajun Zeng, Qingpeng Zhang","doi":"10.1098/rspa.2023.0803","DOIUrl":"https://doi.org/10.1098/rspa.2023.0803","url":null,"abstract":"Since the start of the COVID-19 pandemic, many firms have been shifting their supply chains away from countries with stringent control measures to mitigate supply-chain disruption. Nowadays, the global economy has reopened from the COVID-19 pandemic at various paces in different countries. Understanding how the global supply network evolves during and after the pandemic is necessary for determining the timing and speed of reopening. By harnessing the real-world and real-time global human movement and the latest macroeconomic data, we propose an evolutionary economic-epidemiological model to explore the evolutionary dynamics of the global supply network under various global reopening scenarios. We find that, for highly restrictive countries, the delay in reopening has limited public health benefits in the long run but leads to significant supply-chain loss. A longer duration of stringent control measures substantially hurts the profitability of firms in highly restrictive countries, leading to slower supply-chain recovery in 5 years. This research presents the first data-driven evidence of supply chain loss due to the timing and speed of reopening and sheds light on the post-pandemic supply-chain reformation and recovery. Insights learned from COVID-19 will also be a valuable policymaking reference for combating future infectious disease epidemics and geopolitical changes.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139823483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Complex dynamical systems are subject to perturbations across space and time, which can induce a critical transition or tipping in the state of the system. External perturbations are often correlated in time and can interplay with the underlying nonlinearity of the spatial system, affecting the occurrence of critical transitions. Theoretical analysis of the spatial system perturbed by the Ornstein–Uhlenbeck (OU) correlated noise poses challenges beyond the white noise assumptions and is yet to be done. Here, we resort to the mean-field approximation of a spatially extended system perturbed with OU noise and obtain the stationary probability density function deriving the Fokker–Planck equation for the same. This allows us to determine the role of diffusion and noise on the resilience of the spatial system. While the theoretical analysis guides us on the landscape of tipping thresholds of the system, critical transitions customary to a variety of systems, require a priori prediction. Here, we propose a probabilistic information-based indicator—spatial mutual information—that can successfully forecast tippings, complementing the previously developed spatial indicators. Further, validating its reliability on empirical data, we show that spatial mutual information serves as a robust indicator capturing information characteristic to an imminent tipping reaching peaks in its vicinity.
复杂的动力系统会受到跨时空的扰动，从而诱发系统状态的临界转换或倾覆。外部扰动通常在时间上具有相关性，会与空间系统的基本非线性相互作用，影响临界转换的发生。对受到奥恩斯坦-乌伦贝克（OU）相关噪声扰动的空间系统进行理论分析，是超越白噪声假设的挑战，目前尚未完成。在此，我们采用平均场近似方法来处理受 OU 噪声扰动的空间扩展系统，并通过福克-普朗克方程求得静态概率密度函数。这样，我们就能确定扩散和噪声对空间系统复原力的作用。虽然理论分析可以指导我们确定系统的临界阈值，但各种系统的临界转换需要先验预测。在此，我们提出了一种基于概率信息的指标--空间互信息，它可以成功预测临界点，是对之前开发的空间指标的补充。此外，通过经验数据验证其可靠性，我们表明空间互信息是一种稳健的指标，能捕捉即将发生的临界点达到其附近峰值的特征信息。
{"title":"Critical transitions in spatial systems induced by Ornstein–Uhlenbeck noise: spatial mutual information as a precursor","authors":"S. Deb, P. Dutta","doi":"10.1098/rspa.2023.0594","DOIUrl":"https://doi.org/10.1098/rspa.2023.0594","url":null,"abstract":"\u0000 Complex dynamical systems are subject to perturbations across space and time, which can induce a critical transition or tipping in the state of the system. External perturbations are often correlated in time and can interplay with the underlying nonlinearity of the spatial system, affecting the occurrence of critical transitions. Theoretical analysis of the spatial system perturbed by the Ornstein–Uhlenbeck (OU) correlated noise poses challenges beyond the white noise assumptions and is yet to be done. Here, we resort to the mean-field approximation of a spatially extended system perturbed with OU noise and obtain the stationary probability density function deriving the Fokker–Planck equation for the same. This allows us to determine the role of diffusion and noise on the resilience of the spatial system. While the theoretical analysis guides us on the landscape of tipping thresholds of the system, critical transitions customary to a variety of systems, require\u0000 a priori\u0000 prediction. Here, we propose a probabilistic information-based indicator—spatial mutual information—that can successfully forecast tippings, complementing the previously developed spatial indicators. Further, validating its reliability on empirical data, we show that spatial mutual information serves as a robust indicator capturing information characteristic to an imminent tipping reaching peaks in its vicinity.\u0000","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139825347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Filipe A. dos Santos, A. Favata, Andrea Micheletti, Roberto Paroni, M. Picchi Scardaoni
The control of the shape of complex metasurfaces is a challenging task often addressed in the literature. This work presents a class of tessellated plates able to deform into surfaces of preprogrammed shape upon activation by any flexural load and that can be controlled by a single actuator. Quadric metasurfaces are obtained from infinitesimal origami maps of monohedral hexagonal tessellations of the plane, that is pavings in which all tiles are congruent to each other. Monohedral tessellated portions can be joined together to obtain more complex shapes, which can be locally synclastic or anticlastic and can have a certain roughness. We broaden previous work by providing a complete characterization of all the three known types of monohedral tessellations composed by irregular hexagons. The proposed two-dimensional structures may have applications in prosthetics, tissue engineering, wearable devices, energy harvesting devices, tunable focus mirrors and adaptive facades. The study is divided in two parts. In Part I, after introducing the discrete kinematics of tessellated plates, it is proved analytically that essentially each type of monohedral hexagonal tessellation possesses only one deformation mode. Afterwards, several numerical examples are provided to demonstrate the variety of achievable surface shapes. In Part II, first the metasurfaces corresponding to assigned tile geometries are given a continuum description, which establishes that the continuous interpolant is always a quadric. Then, experimental results on fabrication, assembly and surface accuracy are reported.
{"title":"Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part I","authors":"Filipe A. dos Santos, A. Favata, Andrea Micheletti, Roberto Paroni, M. Picchi Scardaoni","doi":"10.1098/rspa.2023.0430","DOIUrl":"https://doi.org/10.1098/rspa.2023.0430","url":null,"abstract":"The control of the shape of complex metasurfaces is a challenging task often addressed in the literature. This work presents a class of tessellated plates able to deform into surfaces of preprogrammed shape upon activation by any flexural load and that can be controlled by a single actuator. Quadric metasurfaces are obtained from infinitesimal origami maps of monohedral hexagonal tessellations of the plane, that is pavings in which all tiles are congruent to each other. Monohedral tessellated portions can be joined together to obtain more complex shapes, which can be locally synclastic or anticlastic and can have a certain roughness. We broaden previous work by providing a complete characterization of all the three known types of monohedral tessellations composed by irregular hexagons. The proposed two-dimensional structures may have applications in prosthetics, tissue engineering, wearable devices, energy harvesting devices, tunable focus mirrors and adaptive facades. The study is divided in two parts. In Part I, after introducing the discrete kinematics of tessellated plates, it is proved analytically that essentially each type of monohedral hexagonal tessellation possesses only one deformation mode. Afterwards, several numerical examples are provided to demonstrate the variety of achievable surface shapes. In Part II, first the metasurfaces corresponding to assigned tile geometries are given a continuum description, which establishes that the continuous interpolant is always a quadric. Then, experimental results on fabrication, assembly and surface accuracy are reported.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139818683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Complex dynamical systems are subject to perturbations across space and time, which can induce a critical transition or tipping in the state of the system. External perturbations are often correlated in time and can interplay with the underlying nonlinearity of the spatial system, affecting the occurrence of critical transitions. Theoretical analysis of the spatial system perturbed by the Ornstein–Uhlenbeck (OU) correlated noise poses challenges beyond the white noise assumptions and is yet to be done. Here, we resort to the mean-field approximation of a spatially extended system perturbed with OU noise and obtain the stationary probability density function deriving the Fokker–Planck equation for the same. This allows us to determine the role of diffusion and noise on the resilience of the spatial system. While the theoretical analysis guides us on the landscape of tipping thresholds of the system, critical transitions customary to a variety of systems, require a priori prediction. Here, we propose a probabilistic information-based indicator—spatial mutual information—that can successfully forecast tippings, complementing the previously developed spatial indicators. Further, validating its reliability on empirical data, we show that spatial mutual information serves as a robust indicator capturing information characteristic to an imminent tipping reaching peaks in its vicinity.
复杂的动力系统会受到跨时空的扰动，从而诱发系统状态的临界转换或倾覆。外部扰动通常在时间上具有相关性，会与空间系统的基本非线性相互作用，影响临界转换的发生。对受到奥恩斯坦-乌伦贝克（OU）相关噪声扰动的空间系统进行理论分析，是超越白噪声假设的挑战，目前尚未完成。在此，我们采用平均场近似方法来处理受 OU 噪声扰动的空间扩展系统，并通过福克-普朗克方程求得静态概率密度函数。这样，我们就能确定扩散和噪声对空间系统复原力的作用。虽然理论分析可以指导我们确定系统的临界阈值，但各种系统的临界转换需要先验预测。在此，我们提出了一种基于概率信息的指标--空间互信息，它可以成功预测临界点，是对之前开发的空间指标的补充。此外，通过经验数据验证其可靠性，我们表明空间互信息是一种稳健的指标，能捕捉即将发生的临界点达到其附近峰值的特征信息。
{"title":"Critical transitions in spatial systems induced by Ornstein–Uhlenbeck noise: spatial mutual information as a precursor","authors":"S. Deb, P. Dutta","doi":"10.1098/rspa.2023.0594","DOIUrl":"https://doi.org/10.1098/rspa.2023.0594","url":null,"abstract":"\u0000 Complex dynamical systems are subject to perturbations across space and time, which can induce a critical transition or tipping in the state of the system. External perturbations are often correlated in time and can interplay with the underlying nonlinearity of the spatial system, affecting the occurrence of critical transitions. Theoretical analysis of the spatial system perturbed by the Ornstein–Uhlenbeck (OU) correlated noise poses challenges beyond the white noise assumptions and is yet to be done. Here, we resort to the mean-field approximation of a spatially extended system perturbed with OU noise and obtain the stationary probability density function deriving the Fokker–Planck equation for the same. This allows us to determine the role of diffusion and noise on the resilience of the spatial system. While the theoretical analysis guides us on the landscape of tipping thresholds of the system, critical transitions customary to a variety of systems, require\u0000 a priori\u0000 prediction. Here, we propose a probabilistic information-based indicator—spatial mutual information—that can successfully forecast tippings, complementing the previously developed spatial indicators. Further, validating its reliability on empirical data, we show that spatial mutual information serves as a robust indicator capturing information characteristic to an imminent tipping reaching peaks in its vicinity.\u0000","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139885008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Founded on a novel analytical formulation that led to a rigorous yet compact path-integral representation of the time-domain elastodynamic half-space Green's function, a unified analysis of the possible occurrence of different singular wavefront behaviour in the response under arbitrary impulsive internal or surface point loads at arbitrary source-receiver locations is presented. With the decomposition of the general solution into distinct initiating and reflected wave group integrals that share a common factored format and simple contour definitions, the mathematical framework is shown to allow a straightforward identification of the specific conditions and the particular wave groups that are responsible for the singular wavefront phenomena without resorting to advanced analytic function theories or asymptotic methods. Analytic characterizations of the nature, strength and direction of all intrinsic singular wavefront behaviours of the three-dimensional Green's function in three canonical cases of source-receiver configurations are given in a dual integral-closed form format to facilitate their theoretical understanding as well as computational applications. Graphical illustrations of their variation with the source-receiver configuration and the medium's Poisson's ratio together with relevant comparison and clarifications of some classical treatments are included.
{"title":"Unified wavefront singularity characterization of three-dimensional elastodynamic time-domain half-space Green's function under impulsive boundary and internal loads","authors":"Ronald Y. S. Pak, X. Bai","doi":"10.1098/rspa.2023.0515","DOIUrl":"https://doi.org/10.1098/rspa.2023.0515","url":null,"abstract":"Founded on a novel analytical formulation that led to a rigorous yet compact path-integral representation of the time-domain elastodynamic half-space Green's function, a unified analysis of the possible occurrence of different singular wavefront behaviour in the response under arbitrary impulsive internal or surface point loads at arbitrary source-receiver locations is presented. With the decomposition of the general solution into distinct initiating and reflected wave group integrals that share a common factored format and simple contour definitions, the mathematical framework is shown to allow a straightforward identification of the specific conditions and the particular wave groups that are responsible for the singular wavefront phenomena without resorting to advanced analytic function theories or asymptotic methods. Analytic characterizations of the nature, strength and direction of all intrinsic singular wavefront behaviours of the three-dimensional Green's function in three canonical cases of source-receiver configurations are given in a dual integral-closed form format to facilitate their theoretical understanding as well as computational applications. Graphical illustrations of their variation with the source-receiver configuration and the medium's Poisson's ratio together with relevant comparison and clarifications of some classical treatments are included.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140466138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yang Ye, Zhidong Cao, Daniel Dajun Zeng, Qingpeng Zhang
Since the start of the COVID-19 pandemic, many firms have been shifting their supply chains away from countries with stringent control measures to mitigate supply-chain disruption. Nowadays, the global economy has reopened from the COVID-19 pandemic at various paces in different countries. Understanding how the global supply network evolves during and after the pandemic is necessary for determining the timing and speed of reopening. By harnessing the real-world and real-time global human movement and the latest macroeconomic data, we propose an evolutionary economic-epidemiological model to explore the evolutionary dynamics of the global supply network under various global reopening scenarios. We find that, for highly restrictive countries, the delay in reopening has limited public health benefits in the long run but leads to significant supply-chain loss. A longer duration of stringent control measures substantially hurts the profitability of firms in highly restrictive countries, leading to slower supply-chain recovery in 5 years. This research presents the first data-driven evidence of supply chain loss due to the timing and speed of reopening and sheds light on the post-pandemic supply-chain reformation and recovery. Insights learned from COVID-19 will also be a valuable policymaking reference for combating future infectious disease epidemics and geopolitical changes.
{"title":"Supply chain loss from easing COVID-19 restrictions: an evolutionary economic-epidemiological modelling study","authors":"Yang Ye, Zhidong Cao, Daniel Dajun Zeng, Qingpeng Zhang","doi":"10.1098/rspa.2023.0803","DOIUrl":"https://doi.org/10.1098/rspa.2023.0803","url":null,"abstract":"Since the start of the COVID-19 pandemic, many firms have been shifting their supply chains away from countries with stringent control measures to mitigate supply-chain disruption. Nowadays, the global economy has reopened from the COVID-19 pandemic at various paces in different countries. Understanding how the global supply network evolves during and after the pandemic is necessary for determining the timing and speed of reopening. By harnessing the real-world and real-time global human movement and the latest macroeconomic data, we propose an evolutionary economic-epidemiological model to explore the evolutionary dynamics of the global supply network under various global reopening scenarios. We find that, for highly restrictive countries, the delay in reopening has limited public health benefits in the long run but leads to significant supply-chain loss. A longer duration of stringent control measures substantially hurts the profitability of firms in highly restrictive countries, leading to slower supply-chain recovery in 5 years. This research presents the first data-driven evidence of supply chain loss due to the timing and speed of reopening and sheds light on the post-pandemic supply-chain reformation and recovery. Insights learned from COVID-19 will also be a valuable policymaking reference for combating future infectious disease epidemics and geopolitical changes.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139883447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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