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The eco-evolutionary dynamics of strategic species 战略物种的生态进化动态
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-04-01 DOI: 10.1098/rspa.2024.0127
Sourav Roy, Subrata Ghosh, Arindam Saha, Prakash Chandra Mali, M. Perc, Dibakar Ghosh
Much research has in recent years been devoted to better our understanding of the intricate relationships between ecology and the evolutionary success of species. These explorations have often focused on understanding the complex interplay among ecological factors and evolutionary rhythms of the species in various environments. Central to these studies is the concept of the survival of the fittest, proposed by Charles Darwin, where evolutionary circumstances, often portrayed as social dilemmas, favour the welfare of self-interested over others. To further advance this line of research, we here develop a theoretical framework that features three interconnected traits in an evolutionary setting, namely: prey, predator and parasite, each adopting distinct strategies akin to a social dilemma and resembling a Rock-Paper-Scissors scenario. These traits, which we term strategic species, adhere to the eco-evolutionary game dynamics. We further extend our analysis by conducting a sensitivity assessment of the system’s payoff parameters using the Sobol indices.
近年来,许多研究都致力于更好地理解生态学与物种进化成功之间错综复杂的关系。这些探索通常侧重于了解生态因素与物种在不同环境中的进化节奏之间复杂的相互作用。这些研究的核心是查尔斯-达尔文(Charles Darwin)提出的 "适者生存"(survival of the fittest)概念,即进化环境(通常被描述为社会困境)有利于自身利益而非他人利益。为了进一步推进这一研究方向,我们在此建立了一个理论框架,其特点是在进化环境中三个相互关联的特征,即:猎物、捕食者和寄生虫,它们各自采取不同的策略,类似于社会困境,也类似于 "石头-剪子-布 "的情景。我们将这些特征称为战略物种,它们遵循生态进化博弈动力学。我们利用索博尔指数对系统的报酬参数进行了敏感性评估,从而进一步扩展了我们的分析。
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引用次数: 0
Two-dimensional nonlocal Eshelby’s inclusion theory: eigenstress-driven formulation and applications 二维非局部埃舍尔比包容理论:特征应力驱动公式及应用
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-04-01 DOI: 10.1098/rspa.2023.0842
Wei Ding, F. Semperlotti
The classical Eshelby’s theory, developed based on local linear elasticity, cannot be applied to inclusion problems that involve nonlocal (long range) elastic effects often observed in micromechanical systems. In this study, we introduce the extension of Eshelby’s inclusion theory to nonlocal elasticity. Starting from Eringen’s integral formulation of nonlocal elasticity, an eigenstress-driven nonlocal Eshelby’s inclusion theory is presented. The eigenstress-driven approach is shown to be a valid mathematical extension of the classical eigenstrain-driven approach in the context of nonlocal inclusion problems. Two individual numerical approaches are developed and applied to simulate inclusion problems and numerically extract the corresponding nonlocal Eshelby tensor. The numerical results obtained from both approaches confirm the validity of the derived nonlocal Eshelby tensor and its ability to capture the non-uniform eigenstress distribution within an elliptic inclusion. These results also help reveal the fundamental difference between the mechanical behaviour of the classical local and the nonlocal inclusion problems. The eigenstress-driven nonlocal inclusion theory could provide the necessary theoretical foundation for the development of homogenization methods of nonlocal heterogeneous media.
经典的 Eshelby 理论是基于局部线性弹性发展而来的,无法应用于微观机械系统中经常出现的涉及非局部(长程)弹性效应的包含问题。在本研究中,我们介绍了埃舍尔比包含理论在非局部弹性方面的扩展。从 Eringen 的非局部弹性积分公式出发,介绍了特征应力驱动的非局部 Eshelby 包容理论。在非局部包含问题的背景下,特征应力驱动方法被证明是经典特征应变驱动方法的有效数学扩展。我们开发并应用了两种单独的数值方法来模拟包容问题,并从数值上提取相应的非局部 Eshelby 张量。两种方法得出的数值结果都证实了推导出的非局部 Eshelby 张量的有效性及其捕捉椭圆包体内部非均匀特征应力分布的能力。这些结果还有助于揭示经典局部和非局部包含体问题的力学行为之间的根本区别。特征应力驱动的非局部包含理论可为非局部异质介质均质化方法的发展提供必要的理论基础。
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引用次数: 0
Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from polydisperse spheroidal particles, II: characterization 多分散球形颗粒扩散控制溶解的准稳态建模和表征,II:表征
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-03-27 DOI: 10.1098/rspa.2023.0768
Yanxing Wang, Hui Wan, Cody Barka, Tie Wei, Fangjun Shu

A quasi-steady-state model for accurately predicting the detailed diffusion-dominated dissolution process of polydisperse spheroidal (prolate, oblate and spherical) particle systems was presented in Part I of this study. In the present paper, the dissolution characteristics of typical polydisperse spheroidal particle systems have been extensively investigated. The effects of the distributions of particle size and shape have been studied by examining the detailed dissolution processes, such as the size reduction rates of individual particles, the increase in bulk concentration and the dissolution time of the polydisperse systems. Some important factors controlling the dissolution process, including initial particle concentration, smallest and largest particle sizes, and the smallest and largest Taylor shape parameters, have been identified.

本研究的第一部分提出了一个准稳态模型,用于准确预测多分散球形(扁球形、扁球形和球形)颗粒体系以扩散为主的详细溶解过程。本文广泛研究了典型多分散球形颗粒体系的溶解特性。通过研究详细的溶解过程,如单个颗粒的尺寸减小率、体积浓度的增加以及多分散体系的溶解时间,对颗粒尺寸和形状分布的影响进行了研究。确定了一些控制溶解过程的重要因素,包括初始颗粒浓度、最小和最大颗粒尺寸以及最小和最大泰勒形状参数。
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引用次数: 0
Structural identifiability analysis of linear reaction–advection–diffusion processes in mathematical biology 数学生物学中线性反应-平流-扩散过程的结构可识别性分析
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-03-27 DOI: 10.1098/rspa.2023.0911
Alexander P. Browning, Maria Taşcă, Carles Falcó, Ruth E. Baker

Effective application of mathematical models to interpret biological data and make accurate predictions often requires that model parameters are identifiable. Approaches to assess the so-called structural identifiability of models are well established for ordinary differential equation models, yet there are no commonly adopted approaches that can be applied to assess the structural identifiability of the partial differential equation (PDE) models that are requisite to capture spatial features inherent to many phenomena. The differential algebra approach to structural identifiability has recently been demonstrated to be applicable to several specific PDE models. In this brief article, we present general methodology for performing structural identifiability analysis on partially observed reaction–advection–diffusion PDE models that are linear in the unobserved quantities. We show that the differential algebra approach can always, in theory, be applied to such models. Moreover, despite the perceived complexity introduced by the addition of advection and diffusion terms, consideration of spatial analogues of non-spatial models cannot exacerbate structural identifiability. We conclude by discussing future possibilities and the computational cost of performing structural identifiability analysis on more general PDE models.

要有效地应用数学模型来解释生物数据并做出准确的预测,通常需要模型参数是可识别的。评估模型的所谓结构可识别性的方法已在常微分方程模型中得到广泛应用,但对于偏微分方程(PDE)模型的结构可识别性却没有普遍采用的方法,而偏微分方程模型是捕捉许多现象固有的空间特征所必需的。结构可识别性的微分代数方法最近被证明适用于几个特定的偏微分方程模型。在这篇短文中,我们介绍了对部分观测到的反应-平流-扩散 PDE 模型进行结构可识别性分析的一般方法,这些模型在未观测量中是线性的。我们表明,微分代数方法在理论上总是可以应用于这类模型。此外,尽管增加平流和扩散项会带来复杂性,但考虑非空间模型的空间类比并不会加剧结构可识别性。最后,我们讨论了对更一般的 PDE 模型进行结构可识别性分析的未来可能性和计算成本。
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引用次数: 0
A mathematical model of thermoplastic elastomers for analysing the topology of microstructures and mechanical properties during elongation 用于分析伸长过程中微结构拓扑和机械性能的热塑性弹性体数学模型
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-03-27 DOI: 10.1098/rspa.2023.0389
Hiroki Kodama, Hiroshi Morita, Motoko Kotani

In this study, a mathematical model based on graph theory is developed to analyse the deformed structures and mechanical properties of thermoplastic elastomers (TPEs) using ABA-type triblock copolymers. TPEs exhibit a network structure formed by bridge chains; deformation of this network structure causes stress. During the deformation of TPEs, domain breakage and coalescence occur, accompanied by topological changes in the chains, such as conformational transitions between the bridge and loop chains. By employing the mathematical concepts of harmonic realization of graphs in the physical space and the tension tensor to quantify the stress in the bridge-chain network structure, an effective method for analysing topologicalchanges in microstructures caused by elongation is proposed. As an application of this method, optimal geometric structures of block copolymers with desired functionalities can be determined.

本研究基于图论建立了一个数学模型,用于分析使用 ABA 型三嵌段共聚物的热塑性弹性体(TPE)的变形结构和机械性能。TPE 具有由桥链形成的网络结构,这种网络结构的变形会产生应力。在 TPE 的变形过程中,会发生畴断裂和凝聚,同时伴随着链的拓扑变化,如桥链和环链之间的构象转变。通过采用物理空间中图形的谐波实现和张力张量的数学概念来量化桥链网络结构中的应力,提出了一种分析拉伸引起的微结构拓扑变化的有效方法。应用这种方法,可以确定具有所需功能的嵌段共聚物的最佳几何结构。
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引用次数: 0
The Robin boundary condition for modelling heat transfer 模拟传热的罗宾边界条件
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-03-27 DOI: 10.1098/rspa.2023.0850
Eduard Marušić-Paloka, Igor Pažanin

The heat exchange between a rigid body and a fluid is usually modelled by the Robin boundary condition saying that the heat flux through the interface is proportional to the difference between their temperatures. Such interface law describes only the unilateral heat exchange. The goal of this paper is to compare the Robin boundary condition starting with the transmission condition (the temperature and the flux continuity) using rigorous mathematical analysis. Our main results are the following. We first show that a generalized version of the Robin boundary condition can be justified. Second, we prove that replacing the generalized by the standard Robin condition can be justified for high convection velocity if the conductivity of the surrounding liquid is much lower than that of the body. On the other hand, if the fluid conducts much better than the body, then the effective boundary condition is shown not to be the Robin one, but it involves second-order derivatives. We strongly believe that those findings bring new insights to the physics of the heat exchange processes and, thus, could prove useful in engineering practice.

刚体和流体之间的热交换通常采用罗宾边界条件建模,即通过界面的热通量与两者的温差成正比。这种界面定律只描述单侧热交换。本文的目的是通过严格的数学分析,对罗宾边界条件和传输条件(温度和流量连续性)进行比较。我们的主要结果如下。首先,我们证明了罗宾边界条件的广义版本是合理的。其次,我们证明,如果周围液体的电导率远低于本体的电导率,那么在高对流速度下,用标准罗宾条件取代广义罗宾条件是合理的。另一方面,如果液体的传导性比主体好得多,那么有效边界条件就不是罗宾条件,而是涉及二阶导数。我们坚信,这些发现为热交换过程的物理学带来了新的见解,因此在工程实践中可能会很有用。
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引用次数: 0
Periodic finite-band solutions to the focusing nonlinear Schrödinger equation by the Fokas method: inverse and direct problems 用福卡斯方法求聚焦非线性薛定谔方程的周期有限带解:逆问题和直接问题
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-03-27 DOI: 10.1098/rspa.2023.0828
Dmitry Shepelsky, Iryna Karpenko, Stepan Bogdanov, Jaroslaw E. Prilepsky

We consider the Riemann–Hilbert (RH) approach to the construction of periodic finite-band solutions to the focusing nonlinear Schrödinger (NLS) equation. An RH problem for the solution of the finite-band problem has been recently derived via the Fokas method (Deconinck et al. 2021 Lett. Math. Phys. 111, 1–18. (doi:10.1007/s11005-021-01356-7); Fokas & Lenells. 2021 Proc. R. Soc. A 477, 20200605. (doi:10.1007/s11005-021-01356-7)) Building on this method, a finite-band solution to the NLS equation can be given in terms of the solution of an associated RH problem, the jump conditions for which are characterized by specifying the endpoints of the arcs defining the contour of the RH problem and the constants (so-called phases) involved in the jump matrices. In our work, we solve the problem of retrieving the phases given the solution of the NLS equation evaluated at a fixed time. Our findings are corroborated by numerical examples of phases computation, demonstrating the viability of the method proposed.

我们考虑用黎曼-希尔伯特(RH)方法来构建聚焦非线性薛定谔方程(NLS)的周期性有限带解。最近通过 Fokas 方法推导出了有限带问题求解的 RH 问题(Deconinck et al.Math.111, 1-18.(doi:10.1007/s11005-021-01356-7); Fokas & Lenells.2021 Proc.R. Soc. A 477, 20200605.(doi:10.1007/s11005-021-01356-7))在此方法的基础上,NLS 方程的有限带解法可以通过相关 RH 问题的解来给出,其跃迁条件可以通过指定定义 RH 问题轮廓的弧的端点和跃迁矩阵中涉及的常数(即所谓的相位)来描述。在我们的研究中,我们解决了根据固定时间评估的 NLS 方程解找回相位的问题。我们的研究结果得到了相位计算实例的证实,证明了所提方法的可行性。
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引用次数: 0
Variational implicit solvation with Legendre-transformed Poisson–Boltzmann electrostatics 用 Legendre 变换的泊松-玻尔兹曼静电进行变量隐式求解
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-03-27 DOI: 10.1098/rspa.2023.0731
Zunding Huang, Bo Li

The variational implicit-solvent model (VISM) is an efficient approach to biomolecular interactions, where electrostatic interactions are crucial. The total VISM free energy of a dielectric boundary (i.e. solute–solvent interface) consists of the interfacial energy, solute–solvent interaction energy and dielectric electrostatic energy. The last part is the maximum value of the classical and concave Poisson–Boltzmann (PB) energy functional of electrostatic potentials, with the maximizer being the equilibrium electrostatic potential governed by the PB equation. For the consistency of energy minimization and computational stability, here we propose alternatively to minimize the convex Legendre-transformed Poisson–Boltzmann (LTPB) electrostatic energy functional of all dielectric displacements constrained by Gauss’ Law in the solute region. Both integrable and discrete solute charge densities are treated, and the duality of the LTPB and PB functionals is established. A penalty method is designed for the constrained minimization of the LTPB functional. In application to biomolecular interactions, we minimize the total VISM free energy iteratively, while in each step of such iteration, minimize the LTPB energy. Convergence of such a min–min algorithm is shown. Our numerical results on the solvation of a single ion indicate that the LTPB performs better than the PB formulation, providing possibilities for efficient biomolecular simulations.

变分隐含溶剂模型(VISM)是一种高效的生物分子相互作用方法,其中静电相互作用至关重要。介质边界(即溶质-溶剂界面)的总 VISM 自由能由界面能、溶质-溶剂相互作用能和介质静电能组成。最后一部分是静电势的经典凹面泊松-波尔兹曼(PB)能量函数的最大值,最大值是受 PB 方程支配的平衡静电势。为了保证能量最小化的一致性和计算的稳定性,我们在此提出另一种方法,即最小化溶质区域内受高斯定律约束的所有介电位移的凸勒根变换泊松-玻尔兹曼(LTPB)静电能量函数。对可积分和离散的溶质电荷密度都进行了处理,并建立了 LTPB 和 PB 函数的对偶性。为 LTPB 函数的约束最小化设计了一种惩罚方法。在应用于生物分子相互作用时,我们以迭代方式最小化总 VISM 自由能,同时在迭代的每一步中最小化 LTPB 能量。结果表明了这种最小化算法的收敛性。我们对单个离子溶解的数值结果表明,LTPB 的性能优于 PB 公式,为高效生物分子模拟提供了可能。
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引用次数: 0
Data-driven discovery of invariant measures 数据驱动的不变量测量发现
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-03-27 DOI: 10.1098/rspa.2023.0627
Jason J. Bramburger, Giovanni Fantuzzi

Invariant measures encode the long-time behaviour of a dynamical system. In this work, we propose an optimization-based method to discover invariant measures directly from data gathered from a system. Our method does not require an explicit model for the dynamics and allows one to target specific invariant measures, such as physical and ergodic measures. Moreover, it applies to both deterministic and stochastic dynamics in either continuous or discrete time. We provide convergence results and illustrate the performance of our method on data from the logistic map and a stochastic double-well system, for which invariant measures can be found by other means. We then use our method to approximate the physical measure of the chaotic attractor of the Rössler system, and we extract unstable periodic orbits embedded in this attractor by identifying discrete-time periodic points of a suitably defined Poincaré map. This final example is truly data-driven and shows that our method can significantly outperform previous approaches based on model identification.

不变度量编码了动态系统的长期行为。在这项工作中,我们提出了一种基于优化的方法,直接从系统收集的数据中发现不变度量。我们的方法不需要明确的动力学模型,而且可以针对特定的不变度量,如物理和遍历度量。此外,它还适用于连续或离散时间的确定性和随机动力学。我们提供了收敛结果,并说明了我们的方法在逻辑图和随机双井系统数据上的性能,这些数据可以通过其他方法找到不变度量。然后,我们使用我们的方法来近似测量罗斯勒系统混乱吸引子的物理量,并通过识别适当定义的波恩卡莱图的离散时间周期点来提取嵌入该吸引子的不稳定周期轨道。最后这个例子是真正由数据驱动的,表明我们的方法大大优于以往基于模型识别的方法。
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引用次数: 0
Scattering of surface waves by inhomogeneities in crystalline structures 晶体结构中的不均匀性对表面波的散射
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-03-20 DOI: 10.1098/rspa.2023.0683
Basant Lal Sharma

In current scientific and technological scenarios, studies of transmittance of surface waves across structured interfaces have gained some wind amidst applications to metasurfaces, electronic edge-waves, crystal grain boundaries, etc. The results presented in the present article shed a light on the influence of material inhomogeneities on propagation of surface waves. Within the framework of classical mechanics, an analogue of the Gurtin–Murdoch model is employed where elastic properties on surface are assumed to be distinct from bulk. Restricting to scalar waves on prototype square lattice half-plane, particles on considered structured surface have piecewise-constant mass and surface force-constants across an interfacial point. Particles in bulk lattice interact with nearest neighbours in a way that involves unequal force-constants parallel to surface versus normal to it. A surface wave band exists for such lattice structure wherein the waveform decays exponentially inside the half-plane. A formula for surface wave transmittance is given based on an exact solution on half-plane, and, thus, previous work (Sharma & Eremeyev 2019 Int. J. Eng. Sci. 143, 33–38 (doi:10.1016/j.ijengsci.2019.06.007)) is extended. An explicit expression for fraction of energy influx leaked via bulk waves is a highlight. Included are graphical results for several illustrative values of surface structure parameters.

在当前的科学和技术领域,表面波在结构化界面上的透射率研究在超表面、电子边波、晶体晶界等方面的应用中获得了一些进展。本文介绍的结果揭示了材料不均匀性对表面波传播的影响。在经典力学框架内,采用了类似于古尔廷-默多克模型的方法,假定表面的弹性特性与主体不同。限于原型方格半平面上的标量波,被考虑的结构表面上的粒子具有片断恒定质量和跨界面点的表面力常数。体格中的粒子与近邻粒子相互作用时,平行于表面的力常数与法向力常数不相等。这种晶格结构存在一个表面波带,波形在半平面内呈指数衰减。根据半平面上的精确解法给出了表面波透射率公式,因此,之前的工作(Sharma & Eremeyev 2019 Int.J. Eng.Sci. 143, 33-38 (doi:10.1016/j.ijengsci.2019.06.007) )进行了扩展。通过体波泄露的能量流入部分的明确表达是一大亮点。文中还包含了几个表面结构参数值的图解结果。
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引用次数: 0
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