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Steklov eigenvalues of nearly hyperspherical domains 近超球面域的斯特克洛夫特征值
IF 3.5 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Pub Date : 2024-04-03 DOI: 10.1098/rspa.2023.0734
Chee Han Tan, Robert Viator

We consider Steklov eigenvalues of nearly hyperspherical domains in Rd+1 with d3. In previous work, treating such domains as perturbations of the ball, we proved that the Steklov eigenvalues are analytic functions of the domain perturbation parameter. Here, we compute the first-order term of the asymptotic expansion and show that the first-order perturbations are eigenvalues of a Hermitian matrix, whose entries can be written explicitly in terms of Pochhammer’s and Wigner 3j-symbols. We analyse the asymptotic expansion and show the following isoperimetric results among domains with fixed volume: (i) for an infinite subset of Steklov eigenvalues, the ball is not optimal and (ii) for a different infinite subset of Steklov eigenvalues, the ball is a stationary point.

我们考虑的是 Rd+1 中 d≥3 的近超球面域的 Steklov 特征值。在以前的工作中,我们将此类域视为球的扰动,证明了斯特克洛夫特征值是域扰动参数的解析函数。在这里,我们计算了渐近展开的一阶项,并证明一阶扰动是一个赫米矩阵的特征值,其项可以用波哈默和维格纳 3j 符号明确写出。我们对渐近展开进行了分析,并展示了具有固定体积的域之间的以下等周结果:(i) 对于斯特克洛夫特征值的一个无限子集,球不是最优的;(ii) 对于斯特克洛夫特征值的另一个无限子集,球是一个静止点。
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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 MULTIDISCIPLINARY SCIENCES 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 MULTIDISCIPLINARY SCIENCES 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 MULTIDISCIPLINARY SCIENCES 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 MULTIDISCIPLINARY SCIENCES 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 MULTIDISCIPLINARY SCIENCES 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 MULTIDISCIPLINARY SCIENCES 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 MULTIDISCIPLINARY SCIENCES 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 MULTIDISCIPLINARY SCIENCES 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
Jamming problems and the effects of compliance in dual peg-hole disassembly 双钉孔拆卸中的干扰问题和顺应性的影响
IF 3.5 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Pub Date : 2024-03-20 DOI: 10.1098/rspa.2023.0364
Farzaneh Goli, Yongquan Zhang, Mo Qu, Yue Zang, Mozafar Saadat, Duc Truong Pham, Yongjing Wang

Disassembly is a crucial step in remanufacturing and is currently mainly performed by humans. Automating disassembly can reduce labour costs and make remanufacturing more economically attractive. This paper focuses on identifying and characterizing a common disassembly task, dual peg-hole disassembly, with the aim of building a robotic disassembly system for this task. We enumerate the possible contact states and their geometric conditions during the extraction of two studs in a dual peg-hole. This paper focuses on jamming in the extraction and conducts geometrical and quasi-static analyses to determine the boundary conditions of jamming. Based on the analyses, this paper also investigates the role of active compliance as a solution to avoid jamming. We also simulate critical variables and examine key parameters such as the degree of compliance, the location of the compliance centre and initial position errors. Finally, we conduct experimental studies on dual peg-hole extraction with different compliance centres obtained using active compliance.

拆卸是再制造的关键步骤,目前主要由人工完成。拆卸自动化可以降低劳动力成本,使再制造更具经济吸引力。本文的重点是识别和描述常见的拆卸任务--双钉孔拆卸,目的是为这一任务构建一个机器人拆卸系统。我们列举了在双钉孔中拔出两个螺柱时可能出现的接触状态及其几何条件。本文重点关注拔出过程中的卡住现象,并进行了几何和准静态分析,以确定卡住的边界条件。在分析的基础上,本文还研究了主动顺应性作为避免卡塞解决方案的作用。我们还模拟了关键变量,并研究了关键参数,如顺从度、顺从中心位置和初始位置误差。最后,我们对使用主动顺应性获得的不同顺应性中心的双钉孔提取进行了实验研究。
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引用次数: 0
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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
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