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Allowing Wigner’s friend to sequentially measure incompatible observables 允许维格纳之友依次测量不兼容的观测变量
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-04-17 DOI: 10.1098/rspa.2024.0040
Aníbal Utreras-Alarcón, Eric G. Cavalcanti, Howard M. Wiseman

The Wigner’s friend thought experiment has gained a resurgence of interest in recent years thanks to no-go theorems that extend it to Bell-like scenarios. One of these, by us and co-workers, showcased the contradiction that arises between quantum theory and a set of assumptions, weaker than those in Bell’s theorem, which we named ‘Local Friendliness’. Using these assumptions, it is possible to arrive at a set of inequalities for a given scenario, and, in general, some of these inequalities will be harder to violate than the Bell inequalities for the same scenario. A crucial feature of the extended Wigner’s friend scenario in our aforementioned work was the ability of a superobserver to reverse the unitary evolution that gives rise to their friend’s measurement. Here, we present a new scenario where the superobserver can interact with the friend repeatedly in a single experimental instance, either by asking them directly for their result, thus ending that instance, or by reversing their measurement and instructing them to perform a new one. We show that, in these scenarios, the Local Friendliness inequalities will always be the same as Bell inequalities.

近年来,维格纳之友思想实验再次引起人们的兴趣,这要归功于将其扩展到类似贝尔情形的禁区定理。其中一个由我们和合作者提出,展示了量子理论与一组假设之间的矛盾,这组假设比贝尔定理中的假设更弱,我们将其命名为 "局部友好性"。利用这些假设,我们可以得出一组针对给定情景的不等式,而且一般来说,对于同一情景,其中一些不等式比贝尔不等式更难被违反。在我们的上述工作中,维格纳朋友的扩展情景的一个关键特征是超级观测者能够逆转导致其朋友测量的单元演化。在这里,我们提出了一个新方案,超级观察者可以在一个实验实例中与朋友反复互动,要么直接询问他们的结果,从而结束该实验实例,要么逆转他们的测量结果,并指示他们执行新的测量。我们证明,在这些情况下,本地友好度不等式将始终与贝尔不等式相同。
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引用次数: 0
Axisymmetric blockfold origami: a non-flat-foldable Miura variant with self-locking mechanisms and enhanced stiffness 轴对称积木折纸:具有自锁机制和更高刚度的非扁平可折叠三浦变体
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-04-17 DOI: 10.1098/rspa.2023.0956
Xiangxin Dang, Glaucio H. Paulino

Origami foldcores, especially the blockfold cores, have emerged as promising components of high-performance sandwich composites. Inspired by the blockfold origami, we propose the axisymmetric blockfold origami (ABO), which is composed of both rectangular and trapezoidal panels. The ABO inherits the non-flat-foldability of the blockfold origami, and furthermore, displays self-locking mechanisms and enhanced stiffness. The geometry and folding kinematics of the ABO are formulated with respect to the geometric parameters and the folding angle of the assembly. The mathematical conditions are derived for the existence of self-locking mechanisms. We perform compression test simulations to demonstrate enhanced stiffness and increased load-bearing capacity. We find that the existence of rectangular panels not only dominates the non-flat-foldability of the ABO, but also contributes to the enhancement of the stiffness. Our results suggest the potential applications of the ABO for building load-bearing structures with rotational symmetry. Moreover, we discuss the prospects of designing tightly assembled multi-layered origami structures with prestress induced by the mismatch of successive layers to enlighten future research.

折纸芯材,尤其是折纸块芯材,已成为高性能夹层复合材料中极具潜力的组成部分。受折纸的启发,我们提出了轴对称折纸(ABO),它由矩形和梯形板组成。轴对称积木折纸继承了积木折纸的非平面可折叠性,而且还具有自锁机制和更强的刚度。ABO 的几何形状和折叠运动学与组件的几何参数和折叠角度有关。得出了自锁机制存在的数学条件。我们进行了压缩试验模拟,以证明增强的刚度和提高的承载能力。我们发现,矩形面板的存在不仅主导了 ABO 的非平面可折叠性,还有助于增强刚度。我们的研究结果表明,ABO 有可能应用于建造具有旋转对称性的承重结构。此外,我们还讨论了设计紧密组装的多层折纸结构的前景,以及由连续层错配引起的预应力,为未来的研究提供了启迪。
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引用次数: 0
A dynamic trap well model of hydrothermal shape-memory effect in amorphous polymers undergoing tailorable shape recovery behaviour 无定形聚合物中水热形状记忆效应的动态陷井模型,具有可定制的形状恢复行为
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-04-10 DOI: 10.1098/rspa.2023.0615
Jiabin Shi, Galina Gorbacheva, Haibao Lu, Denvid Lau

A dynamic trap well model is developed to describe the complex relaxations of functional segments, and explore the working principles behind the hydrothermal coupling effect in shape memory polymers (SMPs). A constitutive relationship among shape fixity strain, shape recovery strain and relaxation time has been formulated to characterize the hydrothermal coupling effect using geometrical parameters (i.e. width and height) of trap wells. Moreover, effects of temperature and solvent absorption on dynamic relaxation behaviours of SMPs have been formulated based on the Flory-Huggins theory and Fokker-Plank probability equation. The trap well model effectively analyzes the shape fixity ratio and shape recovery ratio within ranges of 50–100% and 0–100%, respectively. Finally, an extended Maxwell model is proposed to formulate the dynamic mechanical behaviours of SMPs with hydrothermal shape-memory effect (SME), and the analytical results have been verified using the experimental results reported in literature. A good agreement between the analytical results obtained from the proposed model and the experimental data is present, where the correlation coefficient (R2) is 95%. The present study firstly introduces the dynamic trap well model for shape memory behaviours and intricate relaxations, and then accurately predicts the dynamic shape recovery of SMP in response to hydrothermal stimulus.

本研究建立了一个动态陷井模型来描述功能片段的复杂弛豫,并探索形状记忆聚合物(SMP)中水热耦合效应背后的工作原理。在形状固定应变、形状恢复应变和弛豫时间之间建立了构成关系,从而利用陷井的几何参数(即宽度和高度)来描述水热耦合效应。此外,基于 Flory-Huggins 理论和 Fokker-Plank 概率方程,还提出了温度和溶剂吸收对 SMP 动态弛豫行为的影响。捕集井模型分别有效地分析了 50-100% 和 0-100% 范围内的形状固定率和形状恢复率。最后,提出了一个扩展的麦克斯韦模型来描述具有热液形状记忆效应(SME)的 SMP 的动态力学行为,并利用文献报道的实验结果验证了分析结果。根据提出的模型得出的分析结果与实验数据之间存在良好的一致性,相关系数(R2)达到 95%。本研究首先介绍了形状记忆行为和复杂弛豫的动态陷井模型,然后准确预测了 SMP 在水热刺激下的动态形状恢复。
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引用次数: 0
Describing financial crisis propagation through epidemic modelling on multiplex networks 通过多路网络上的流行病建模来描述金融危机的传播
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-04-10 DOI: 10.1098/rspa.2023.0787
Malvina Bozhidarova, Frank Ball, Yves van Gennip, Reuben D. O’Dea, Gilles Stupfler

This paper proposes a novel framework for modelling the spread of financial crises in complex networks, combining financial data, Extreme Value Theory and an epidemiological transmission model. We accommodate two key aspects of contagion modelling: fundamentals-based contagion, where the transmission is due to direct financial linkages, and pure contagion, where a crisis might trigger additional crises due to global effects. We use stock price, geographical location and economic sector data for a set of 398 companies to construct multiplex networks of four layers, on which a susceptible-infected-recovered transmission model is defined, in order to model the spread of financial shocks between companies by accounting for their interconnected nature. By utilizing stock price data for the 2008 and 2020 financial crises, we investigate and assess the effectiveness of our model in forecasting the propagation of financial shocks through the network, where a shock is detected by measuring stock price volatility. The results suggest that the proposed framework is effective in predicting the spread of financial crises. Our findings demonstrate the significance of each layer of the multiplex network structure, which differentiates between various transmission pathways, for predicting the number of affected companies, as well as for company-, sector- or location-specific predictions.

本文结合金融数据、极值理论和流行病学传播模型,提出了一个新颖的框架,用于模拟金融危机在复杂网络中的蔓延。我们将传染建模的两个关键方面结合起来:基于基本面的传染,即传染是由于直接的金融联系造成的;纯粹的传染,即一场危机可能会由于全球效应引发其他危机。我们利用一组 398 家公司的股价、地理位置和经济部门数据构建了四层多路网络,并在此基础上定义了易感-感染-恢复传播模型,以便通过考虑公司之间的相互关联性来模拟金融冲击在公司之间的传播。通过利用 2008 年和 2020 年金融危机的股票价格数据,我们研究并评估了我们的模型在预测金融冲击通过网络传播方面的有效性。结果表明,所提出的框架能有效预测金融危机的传播。我们的研究结果表明,多路复用网络结构的每一层(区分各种传播途径)对于预测受影响公司的数量以及针对公司、行业或地点的预测都具有重要意义。
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引用次数: 0
A rigorous mathematical theory for topological phases and edge modes in spring-mass mechanical systems 弹簧-质量机械系统拓扑相位和边缘模式的严格数学理论
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-04-10 DOI: 10.1098/rspa.2023.0910
Ridvan Ozdemir, Junshan Lin

In this work, we examine the topological phases of the spring-mass lattices when the spatial inversion symmetry of the system is broken and prove the existence of edge modes when two lattices with different topological phases are glued together. In particular, for the one-dimensional lattice consisting of an infinite array of masses connected by springs, we show that the Zak phase of the lattice is quantized, only taking the value 0 or π. We also prove the existence of an edge mode when two semi-infinite lattices with distinct Zak phases are connected. For the two-dimensional honeycomb lattice, we characterize the valley Chern numbers of the lattice when the masses on the lattice vertices are uneven. The existence of edge modes is proved for a joint honeycomb lattice formed by gluing two semi-infinite lattices with opposite valley Chern numbers together.

在这项工作中,我们研究了当系统的空间反转对称性被打破时弹簧-质量点阵的拓扑相位,并证明了当两个拓扑相位不同的点阵粘合在一起时边缘模式的存在。特别是,对于由弹簧连接的无限质量阵列组成的一维网格,我们证明了网格的 Zak 相是量子化的,只取 0 或 π 值。对于二维蜂巢晶格,我们描述了当晶格顶点上的质量不均匀时晶格的谷切尔恩数。我们证明了将两个具有相反谷切尔恩数的半无限晶格粘合在一起所形成的联合蜂窝晶格存在边缘模式。
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引用次数: 0
Stability of penetrative convective currents in local thermal non-equilibrium 局部热非均衡状态下穿透性对流的稳定性
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-04-10 DOI: 10.1098/rspa.2023.0820
Giuseppe Arnone, Florinda Capone, Jacopo Alfonso Gianfrani

The aim of this paper is to investigate the onset of penetrative convection in a Darcy–Brinkman porous medium under the hypothesis of local thermal non-equilibrium. For the problem at stake, the strong form of the principle of exchange of stabilities has been proved, i.e. convective motions can occur only through secondary stationary motions. We perform linear and nonlinear stability analyses of the basic state, with particular regard to the behaviour of stability thresholds with respect to the relevant physical parameters characterizing the problem. The Chebyshev-τ method and the shooting method are employed and accurately implemented to solve the differential eigenvalue problems arising from linear and nonlinear analyses to determine critical Rayleigh numbers. Via numerical simulations, the stabilizing effect of the upper bounding plane temperature, of the Darcy number and of the interaction coefficient for the heat exchange, is demonstrated.

本文旨在研究达西-布林克曼(Darcy-Brinkman)多孔介质在局部热非均衡假设下发生的穿透性对流。对于所涉及的问题,已经证明了稳定性交换原理的强形式,即对流运动只能通过次级静止运动发生。我们对基本状态进行了线性和非线性稳定性分析,特别关注了稳定性临界值与问题相关物理参数的关系。我们采用并精确实施了切比雪夫-τ 法和射击法,以解决线性和非线性分析中产生的微分特征值问题,从而确定临界瑞利数。通过数值模拟,证明了上界平面温度、达西数和热交换交互系数的稳定作用。
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引用次数: 0
Free propagation of resonant waves in nonlinear dissipative metamaterials 非线性耗散超材料中共振波的自由传播
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-04-10 DOI: 10.1098/rspa.2023.0759
Alessandro Fortunati, Andrea Arena, Marco Lepidi, Andrea Bacigalupo, Walter Lacarbonara

This paper deals with the free propagation problem of resonant and close-to-resonance waves in one-dimensional lattice metamaterials endowed with nonlinearly viscoelastic resonators. The resonators' constitutive and geometric nonlinearities imply a cubic coupling with the lattice. The analytical treatment of the nonlinear wave propagation equations is carried out via a perturbation approach. In particular, after a suitable reformulation of the problem in the Hamiltonian setting, the approach relies on the well-known resonant normal form techniques from Hamiltonian perturbation theory. It is shown how the constructive features of the Lie Series formalism can be exploited in the explicit computation of the approximations of the invariant manifolds. A discussion of the metamaterial dynamic stability, either in the general or in the weak dissipation case, is presented.

本文讨论了共振波和接近共振波在装有非线性粘弹性谐振器的一维晶格超材料中的自由传播问题。谐振器的构成和几何非线性意味着与晶格的立方耦合。非线性波传播方程的分析处理是通过扰动方法进行的。特别是,在哈密顿设置中对问题进行适当重述后,该方法依赖于哈密顿扰动理论中著名的共振法线形式技术。研究表明,在显式计算不变流形的近似值时,如何利用列数列形式主义的构造特征。此外,还讨论了超材料在一般或弱耗散情况下的动态稳定性。
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引用次数: 0
Droplet evaporation on curved surfaces: transients of internal and external transport phenomena 曲面上的液滴蒸发:内部和外部传输现象的瞬变
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-04-03 DOI: 10.1098/rspa.2023.0613
Arnov Paul, Subhadeep Mondal, Purbarun Dhar

We explore the transient evolution of thermo-fluid-dynamics of evaporating sessile droplets over curved substrates in the liquid and gaseous domains. A computational model using the Arbitrary Lagrangian-Eulerian framework is adopted. The governing equations in both liquid and gaseous domains are solved in a fully coupled manner, considering coupled effects of evaporative cooling and heat advection due to bulk fluid motion. This bulk motion in the liquid domain is caused by natural advection due to thermal actuations such as thermal Marangoni flow and buoyancy-driven convection. For the gaseous domain, the additional effects of solutal convection (due to vapour-concentration variation), Stefan flow and interfacial viscous stresses are also considered. To depict a generalized role of substrate curvature, both concave and convex surfaces with curvatures over a wide range are studied. The surface wettability effects are also explored by varying the true contact angle of the droplets. Computational predictions on evaporation rate and internal flow field are validated against experimental results from literature. The interplay of wetting state and substrate curvature is noted to substantially affect the evaporation process and its thermo-fluidics. The convex curvature significantly augments internal advection while the same is weakened over concave substrates due to altered mass loss rate. Consequently, the duration of multi-vortex Marangoni flows in the development stages of evaporation and the advection in the external gaseous domain is markedly different for different curvatures. Further, on superhydrophobic curved surfaces, the effects of re-distributed evaporative fluxes play a major role. In such cases, the reduced mass flux over a large interfacial area near the periphery expedites the stable state Marangoni and external flow features.

我们探讨了在液态和气态领域,无柄液滴在弯曲基底上蒸发的热流体动力学瞬态演化。计算模型采用任意拉格朗日-欧勒框架。以完全耦合的方式求解液态和气态域中的控制方程,并考虑到蒸发冷却和散装流体运动引起的热平流的耦合效应。液态域中的体运动是由热马兰戈尼流和浮力驱动对流等热作用引起的自然平流造成的。对于气态域,还考虑了溶质对流(由于蒸汽浓度变化)、斯特凡流和界面粘性应力的额外影响。为了描述基底曲率的一般作用,研究了曲率范围较大的凹面和凸面。此外,还通过改变液滴的真实接触角探讨了表面润湿性的影响。对蒸发率和内部流场的计算预测与文献中的实验结果进行了验证。润湿状态和基底曲率的相互作用对蒸发过程及其热流体学产生了重大影响。凸面曲率极大地增强了内部平流,而凹面基底则由于质量损失率的改变而削弱了内部平流。因此,在蒸发的发展阶段,多涡马兰戈尼流的持续时间和外部气态域的平流在不同曲率下明显不同。此外,在超疏水的曲面上,重新分布的蒸发通量的影响起着重要作用。在这种情况下,外围附近大面积界面上减少的质量通量会加速稳定状态马兰戈尼和外部流动特征的形成。
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引用次数: 0
Elastic response of a cylinder loaded by a Hertzian contact pressure and maintained in equilibrium by its inertia 由赫兹接触压力加载并由惯性维持平衡的圆柱体的弹性响应
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-04-03 DOI: 10.1098/rspa.2023.0891
Pierric Mora, Fabien Treyssède, Laurent Laguerre

We derive the compliance of an elastic cylinder submitted to a line Hertzian contact. The cylinder is maintained in static equilibrium by bulk forces that are proportional to rigid body motions. Displacements are measured by setting integral gauges that amount to prescribing zero net linear and angular momentum, if the problem were to depend upon time. Various cases are covered, representing either infinitesimal or finite contact displacements, including partial slip. The developments are illustrated by revisiting a classical example in what could be called The heavy cylinder on a vibrating soil. The four contact resonances and forced response of the system are given in closed form in the quasi-static approximation, and compared against a reference numerical solution. The formulae can also be used as building blocks to assemble the compliance matrix of a system comprising several cylinders.

我们推导了线赫兹接触弹性圆柱体的顺应性。圆柱体通过与刚体运动成比例的体力保持静态平衡。位移是通过设置积分量规测量的,如果问题取决于时间,积分量规相当于规定净线性动量和角动量为零。研究涵盖了代表无限小或有限接触位移(包括部分滑移)的各种情况。通过重温一个可称为 "振动土壤上的重圆柱体 "的经典示例,对这一发展进行了说明。以准静态近似的封闭形式给出了系统的四个接触共振和受迫响应,并与参考数值解进行了比较。这些公式还可用作组合由多个圆柱体组成的系统的顺应性矩阵的构件。
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引用次数: 0
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 Mathematics 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
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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
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