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A molecular perspective on quantum information 量子信息的分子视角
3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Pub Date : 2023-11-01 DOI: 10.1098/rspa.2023.0599
Gregory D. Scholes
Some of the fundamentals of quantum information science are described, including the concepts of quantum resources, quantum states and mixedness of states. The explanations are detailed and include a combination of basic facts with fully worked examples, and some more advanced topics. The principles of quantum information are illustrated with chemical examples drawn from singlet fission, photophysics of radicals, molecular excitons, electron transfer and so on. Suggestions for prospects and challenges for the field are discussed.
描述了量子信息科学的一些基本原理,包括量子资源、量子态和态混合的概念。解释是详细的,包括基本事实与充分工作的例子,以及一些更高级的主题的组合。从单线态裂变、自由基的光物理、分子激子、电子转移等方面的化学例子说明了量子信息的原理。讨论了该领域的前景和挑战。
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引用次数: 2
Analysis of the energy transfer process for multiple scattering problems involving lossy media 含损介质多重散射问题的能量传递过程分析
3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Pub Date : 2023-11-01 DOI: 10.1098/rspa.2023.0513
Andreas Kalogeropoulos, Nikolaos L. Tsitsas
The energy transfer process for acoustic propagation and scattering in inhomogeneous, lossy media is rigorously investigated. Two problems are considered: an arbitrarily composed cluster of lossy scatterers, excited by a single point source and a layered, lossy medium excited by an internal point-source distribution. Energy conservation laws and optical theorems are established. The connection of active intensity with the scattering cross section and the relation between reactive intensity and Lagrangian density are determined. Furthermore, the influence of the losses of the involved media to the kinetic energy is unveiled. Reductions to lossless media and near-zero frequency values are derived.
研究了非均匀有耗介质中声波传播和散射的能量传递过程。考虑了两个问题:由单点源激发的任意组成的有损散射体簇和由内部点源分布激发的分层有损介质。建立了能量守恒定律和光学定理。确定了有源强度与散射截面的关系以及有源强度与拉格朗日密度的关系。此外,还揭示了所涉及介质的损失对动能的影响。降低到无损介质和接近零的频率值。
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引用次数: 0
Sturm–Liouville systems for the survival probability in first-passage time problems 首次通过时间问题中生存概率的Sturm-Liouville系统
3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Pub Date : 2023-11-01 DOI: 10.1098/rspa.2023.0485
Marcus Dahlenburg, Gianni Pagnini
We derive a Sturm–Liouville system of equations for the exact calculation of the survival probability in first-passage time problems. This system is the one associated with the Wiener–Hopf integral equation obtained from the theory of random walks. The derived approach is an alternative to the existing literature and we tested it against direct calculations from both discrete- and continuous-time random walks in a manageable, but meaningful, example. Within this framework, the Sparre Andersen theorem results to be a boundary condition for the system.
我们导出了一个Sturm-Liouville方程组,用于精确计算首次通过时间问题的生存概率。该系统与由随机游走理论得到的Wiener-Hopf积分方程相关联。导出的方法是现有文献的替代方案,我们在一个可管理但有意义的示例中对离散时间和连续时间随机漫步的直接计算进行了测试。在这个框架内,Sparre Andersen定理可以作为系统的边界条件。
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引用次数: 1
A predictive model of UV-A-riboflavin crosslinking treatment on porcine corneas uv -A-核黄素交联治疗猪角膜的预测模型
3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Pub Date : 2023-11-01 DOI: 10.1098/rspa.2023.0323
Alessandra Bonfanti, Anna Pandolfi
The crosslinking technique (CXL) is an effective low-risk therapeutic treatment of keratoconus and other ectatic disorders of the human cornea. The effect of corneal CXL is to increase the stiffness of the stroma to prevent the progression of the cornea distortion. Several clinical and experimental studies have shown that the stiffening effects predominantly localize on the anterior portion of the stroma and that the in-depth stiffening distribution is highly dependent on the duration of treatment. Yet, how the stiffening effects distribute through the cornea thickness as a function of the treatment duration is an open question. Here, we propose an analytical model of the stiffening profile due to CXL treatment as a function of the irradiation time. We consider linear and nonlinear variations of the crosslinking effects across the thickness and implement them into a finite element model of the porcine cornea. We present a time-dependent in-depth stiffening profile that allows us to predict the post-operative cornea response to physiological intraocular pressure for different irradiation times. We anticipate that this predictive model will support the development of patient specific three-dimensional models that will allow clinicians to design customized CXL treatment, thus enhancing treatment outcomes.
交联技术(CXL)是一种有效的低风险治疗圆锥角膜和其他人类角膜扩张疾病的方法。角膜CXL的作用是增加角膜基质的硬度,防止角膜畸变的发展。一些临床和实验研究表明,硬化效应主要局限于基质的前部,而深度硬化分布高度依赖于治疗的持续时间。然而,硬化效应如何通过角膜厚度作为治疗持续时间的函数分布是一个悬而未决的问题。在这里,我们提出了一个解析模型的强化轮廓由于CXL处理作为辐照时间的函数。我们考虑了交联效应在厚度上的线性和非线性变化,并将其实现到猪角膜的有限元模型中。我们提出了一个时间依赖的深度硬化剖面,使我们能够预测手术后角膜对不同照射时间的生理眼内压的反应。我们预计该预测模型将支持患者特定三维模型的发展,这将允许临床医生设计定制的CXL治疗,从而提高治疗效果。
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引用次数: 0
Shear and flexural deformations in flextegrity segmental beams inspired by Leonardo’s triangular masonry construction 受列奥纳多的三角形砌体结构启发,柔性整体分段梁的剪切和弯曲变形
3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Pub Date : 2023-11-01 DOI: 10.1098/rspa.2023.0453
Claudio Boni, Gianni Royer-Carfagni
In Tabula XCI verso of Codex Atlanticus, Leonardo da Vinci presents an ingenious masonry structure composed of segments in the shape of inverted triangles. These are assembled by contact in a chain to obtain a lintel or jack arch, where they are pressed together by the thrust of the end constraints. Drawing inspiration from Leonardo’s sketches, we show that, by connecting the segments in pair through elastic tendons, this system represents a new type of flextegrity beam. In a classical flextegrity, the contact surfaces of the segments are curved conjugate profiles, imposing a pure rolling motion along properly designed pitch lines: the consequent elongation of the tendon dictates the constitutive response as a function of the relative rotation of the segments. Here, the contact is through plane surfaces, so that the kinematics, besides the relative rotation, is characterized by segmental shearing. This system is theoretically analysed and a continuum model is derived as the length of the segments becomes small. Comparisons with experiments on three-dimensional-printed prototypes confirm the theoretical findings and highlight the possible competition between rotational and sliding types of deformation. Apart from the historical value, this type of construction can be used in innovative structures or metamaterials.
在《大西洋抄本》的XCI版中,列奥纳多·达·芬奇展示了一个由倒三角形状的分段组成的巧妙的砖石结构。它们通过接触在链中组装以获得门楣或千斤顶拱,在那里它们被末端约束的推力压在一起。从列奥纳多的草图中得到灵感,我们展示了,通过弹性腱连接成对的部分,这个系统代表了一种新型的柔性整体梁。在经典柔性整体中,节段的接触面是弯曲的共轭轮廓,沿着适当设计的节距线施加纯滚动运动:随后的肌腱伸长决定了本构响应作为节段相对旋转的函数。在这里,接触是通过平面进行的,因此运动学除了相对旋转之外,还具有分段剪切的特征。对该系统进行了理论分析,并推导出了随着段长变小的连续统模型。与三维打印原型的实验比较证实了理论发现,并强调了旋转变形和滑动变形之间可能存在的竞争。除了历史价值,这种类型的建筑可以用于创新结构或超材料。
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引用次数: 1
Parametric solutions to the kinematics of developable degree-4 rigid origami vertices 可展次4刚性折纸顶点运动学的参数解
3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Pub Date : 2023-11-01 DOI: 10.1098/rspa.2023.0319
Yucai Hu, Changjun Zheng, Chuanxing Bi, Haiyi Liang
Developable degree-4 (DD4) vertices have four facets and four creases and can be unfolded flat. The rigid-folding kinematics of DD4 vertices is rich in that it generally has two folding modes and can get stuck when two facets bind together. To study the full spectrum of the kinematics of DD4 vertices, parametric solutions for fold angles in terms of the cotangents of half-angles are derived from the opposite and adjacent fold angle relationships. It is shown that any two fold angles of a general DD4 vertex are related by the equation of a hyperbola. When the vertex has collinear creases or is flat-foldable, the pertinent hyperbola equations degenerate into linear relationships. Meanwhile, when DD4 vertices are classified into three categories according to Grashof’s criterion, both unique and binding folds can be readily located from the facet with the largest or smallest sector angle. The rigid-folding kinematics of typical vertices is then investigated. In addition to the flat state, the two folding modes can also be switched at the binding states if self-intersection is permitted. The results provide new formulae and clear geometric views on the rigid-folding kinematics of DD4 vertices, which are fundamental for constructing larger origami patterns.
可展开度为4 (DD4)的顶点有四个切面和四个折痕,可以平展开。DD4顶点的刚性折叠运动学是丰富的,因为它通常有两种折叠模式,当两个面结合在一起时可能会卡住。为了研究DD4顶点的全谱运动学,从对角和邻角的对折角关系中导出了半角的等距的对折角的参数解。证明了一般DD4顶点的任意两个夹角是由双曲线方程联系起来的。当顶点有共线折痕或可平折时,相关双曲线方程退化为线性关系。同时,根据Grashof准则将DD4顶点分为三类时,可以很容易地从扇形角最大或最小的面定位到唯一褶皱和绑定褶皱。然后研究了典型顶点的刚性折叠运动学。除了平面状态外,如果允许自交,两种折叠模式也可以在结合状态下进行切换。这些结果为DD4顶点的刚性折叠运动学提供了新的公式和清晰的几何视图,为构造更大的折纸图案奠定了基础。
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引用次数: 0
Anisotropy distorts the spreading of a fixed volume porous gravity current 各向异性扭曲了固定体积多孔重力电流的扩散
3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Pub Date : 2023-11-01 DOI: 10.1098/rspa.2023.0271
Graham P. Benham
We consider the release and subsequent gravity-driven spreading of a dense finite volume of fluid in an anisotropic porous medium bounded by an impermeable substrate. When the permeability in the vertical direction is much smaller than in the horizontal direction, as is the case in many real geological reservoirs, this restricts the spread of the current to a very thin layer near the impermeable base. Using a combination of asymptotic analysis and finite difference computations of Darcy flow, we show that there exist two distinct flow regimes. At early times, the bulk of the current descends slowly and uniformly, injecting fluid into thin finger-like regions near the base. At much later times, the current transitions to the classical gravity-driven solution and continues to spread with a self-similar shape. One interesting consequence is that the swept volume of the current grows differently depending on the anisotropy of the medium. This has important consequences for managing contaminant spills, where it is important to minimize the contacted volume of the aquifer, or during geological CO 2 sequestration where a larger contacted volume results in more CO 2 being stored.
我们考虑了由不透水基材包围的各向异性多孔介质中致密有限体积流体的释放和随后的重力驱动扩散。当垂直方向的渗透率远小于水平方向时,就像在许多真实的地质储层中一样,这限制了电流在不透水基底附近的非常薄的一层。利用渐近分析和有限差分计算相结合的方法,我们证明了达西流存在两种不同的流型。在早期,大部分电流缓慢而均匀地下降,将液体注入基部附近的细手指状区域。在很晚的时候,电流转变为经典的重力驱动的解决方案,并继续以自相似的形状传播。一个有趣的结果是,电流的扫过体积随着介质的各向异性而变化。这对管理污染物泄漏具有重要的影响,在这种情况下,重要的是尽量减少含水层的接触体积,或者在地质二氧化碳封存期间,较大的接触体积导致更多的二氧化碳被储存。
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引用次数: 0
Plane and axisymmetric problems of an interfacial crack in a power-law graded material 幂律梯度材料界面裂纹的平面和轴对称问题
3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Pub Date : 2023-11-01 DOI: 10.1098/rspa.2023.0630
Y. A. Antipov
Plane and axisymmetric problems of interfacial cracks in a power-law graded infinite medium are examined. It is shown that the models are governed by integral equations of Mellin’s convolution type whose kernels are expressed through the hypergeometric function. Exact solutions are derived by the method of orthogonal Jacobi polynomials in a series form and by the Wiener–Hopf method by quadratures. Mode-I stress intensity factors and the associated weight functions for power-law graded materials in the plane and axisymmetric cases are introduced and evaluated. It is shown that, although the displacement jump and the normal traction component have power singularities at the crack tip different from 1/2, the strain energy variation is proportional to the crack length change as in the case of homogeneous materials. A Griffith-type criterion of crack propagation in power-law graded materials is proposed and results of numerical tests are reported.
研究了幂律梯度无限介质中界面裂纹的平面和轴对称问题。结果表明,该模型是由Mellin卷积型积分方程控制的,其核用超几何函数表示。用级数形式的正交雅可比多项式法和正交的Wiener-Hopf法推导了精确解。介绍并评价了幂律梯度材料在平面和轴对称情况下的i型应力强度因子和相关权函数。结果表明,虽然位移跳变和法向牵引分量在裂纹尖端处存在不同于1/2的幂奇点,但在均质材料情况下,应变能变化与裂纹长度变化成正比。提出了幂律梯度材料裂纹扩展的griffith型判据,并报道了数值试验结果。
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引用次数: 0
Exact hydrodynamics and onset of phase separation for an active exclusion process 主动排除过程的精确流体力学和相分离的开始
3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Pub Date : 2023-11-01 DOI: 10.1098/rspa.2023.0524
James Mason, Clément Erignoux, Robert L. Jack, Maria Bruna
We consider a lattice model of active matter with exclusion and derive its hydrodynamic description exactly. The hydrodynamic limit leads to an integro-differential equation for the density of particles with a given orientation. Volume exclusion results in nonlinear mobility dependent on spatial density. Such models of active matter can support motility-induced phase separation, which occurs despite the absence of attractive interactions. We study the onset of phase separation with linear stability analysis and numerical simulations.
我们考虑了不相容活性物质的晶格模型,并准确地推导了它的流体力学描述。水动力极限导致了给定方向的粒子密度的积分微分方程。体积排斥导致依赖于空间密度的非线性迁移。这种活性物质的模型可以支持运动诱导的相分离,尽管缺乏吸引力的相互作用。我们用线性稳定性分析和数值模拟研究了相分离的开始。
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引用次数: 0
Two-layer gravity currents of generalized Newtonian fluids 广义牛顿流体的两层重力流
3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Pub Date : 2023-11-01 DOI: 10.1098/rspa.2023.0429
Ian Christy, Edward M. Hinton
We examine gravity-driven two-layer flow of generalized Newtonian fluids. The two layers have different densities and constitutive laws, and the flow is assumed to be shallow and inertia-less. A depth-integrated model for flow over one-dimensional topography is derived with the volume fluxes written in terms of functions that depend only on the fluids’ rheology. The model enables two-layer flows of any combination of generalized Newtonian fluids to be computed without explicit knowledge of the velocity profile. For viscoplastic layers, the formulation provides a convenient way to determine the layer evolution without having to analyse the multiple yield surfaces that may occur. Motivated by the lubricated flow of ice sheets, we analyse the case in which the lower layer is relatively thin. The model reduces to a one-layer flow with an effective slip law that encapsulates the thickness and generalized Newtonian rheology of the lower layer. For flow over two-dimensional topography, a depth-integrated two-layer model cannot generally be derived because the direction of the shear stress varies across the lower layer. Progress is possible in the special cases that the lower layer is Newtonian or is relatively thin.
我们研究了广义牛顿流体的重力驱动两层流。两层具有不同的密度和本构律,流假定为浅流和无惯性流。导出了一维地形上流动的深度积分模型,其中体积通量用仅依赖于流体流变学的函数表示。该模型使任何广义牛顿流体组合的两层流动无需明确的速度分布知识即可计算。对于粘塑性层,该公式提供了一种方便的方法来确定层的演变,而不必分析可能出现的多个屈服面。受冰盖润滑流动的影响,我们分析了下层相对较薄的情况。该模型简化为具有有效滑移律的单层流动,该滑移律包含了下层的厚度和广义牛顿流变学。对于二维地形上的流动,由于剪切应力的方向在下层发生变化,通常无法推导出深度积分的两层模型。在较低的层是牛顿的或相对较薄的特殊情况下,进展是可能的。
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引用次数: 0
期刊
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
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