European Journal of Applied Mathematics最新文献_第9页

Parametric approach to promote a divergence-free flow in the image-based motion estimation with application to bioirrigation 基于图像的运动估计中促进发散自由流的参数方法及其在生物灌溉中的应用

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2022-06-15 DOI: 10.1017/s095679252200016x

N. Santitissadeekorn, C. Meile, E. Bollt, G. Waldbusser

Flow fields are determined from image sequences obtained in an experiment in which benthic macrofauna, Arenicola marina, causes water flow and the images depict the distribution of a tracer that is carried with the flow. The experimental setup is such that flow is largely two-dimensional, with a localised region where the Arenicola resides, from which flow originates. Here, we propose a novel parametric framework that quantifies such flow that is dominant along the image plane. We adopt a Bayesian framework so that we can impart certain physical constraints on parameters into the estimation process via prior distribution. The primary aim is to approximate the mean of the posterior distribution to present the parameter estimate via Markov Chain Monte Carlo. We demonstrate that the results obtained from the proposed method provide more realistic flows (in terms of divergence magnitude) than those computed from classical approaches such as the multi-resolution Horn–Schunk method. This highlights the usefulness of our approach if motion is largely constrained to the image plane with localised fluid sources.

流场是根据实验中获得的图像序列确定的，在实验中，底栖大型动物Arenicola marina引起水流，图像描绘了随水流携带的示踪剂的分布。实验设置使得流动在很大程度上是二维的，有一个Arenicola所在的局部区域，流动来源于该区域。在这里，我们提出了一种新的参数框架，该框架量化了沿图像平面占主导地位的这种流。我们采用贝叶斯框架，这样我们就可以通过先验分布将参数的某些物理约束赋予估计过程。主要目的是通过马尔可夫链蒙特卡罗来近似后验分布的平均值，以呈现参数估计。我们证明，从所提出的方法获得的结果比从多分辨率Horn–Schunk方法等经典方法计算的结果提供了更真实的流（就发散幅度而言）。如果运动在很大程度上被限制在具有局部流体源的图像平面上，这突出了我们的方法的有用性。

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引用次数: 0

Dynamics and steady state of squirmer motion in liquid crystal 液晶中蠕动运动的动力学与稳态

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2022-06-13 DOI: 10.1017/s0956792523000177

L. Berlyand, Haiyang Chi, M. Potomkin, N. Yip

We analyse a nonlinear partial differential equation system describing the motion of a microswimmer in a nematic liquid crystal environment. For the microswimmer’s motility, the squirmer model is used in which self-propulsion enters the model through the slip velocity on the microswimmer’s surface. The liquid crystal is described using the well-established Beris–Edwards formulation. In previous computational studies, it was shown that the squirmer, regardless of its initial configuration, eventually orients itself either parallel or perpendicular to the preferred orientation dictated by the liquid crystal. Furthermore, the corresponding solution of the coupled nonlinear system converges to a steady state. In this work, we rigorously establish the existence of steady state and also the finite-time existence for the time-dependent problem in a periodic domain. Finally, we will use a two-scale asymptotic expansion to derive a homogenised model for the collective swimming of squirmers as they reach their steady-state orientation and speed.

我们分析了一个描述向列型液晶环境中微游泳器运动的非线性偏微分方程组。对于微游动器的运动，使用蠕动器模型，其中自推进通过微游动器表面的滑动速度进入模型。液晶是使用公认的贝里斯-爱德华兹公式描述的。在之前的计算研究中，已经表明蠕动器，无论其初始配置如何，最终都会将自己定向为平行或垂直于液晶指定的首选定向。此外，耦合非线性系统的相应解收敛到稳态。在这项工作中，我们严格地建立了周期域中含时问题的稳态存在性和有限时间存在性。最后，我们将使用两个尺度的渐近展开来导出蠕动体在达到稳态方向和速度时集体游动的均匀化模型。

引用次数: 1

Steady states of thin-film equations with van der Waals force with mass constraint 具有质量约束的范德华力薄膜方程的稳态

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2022-05-30 DOI: 10.1017/s0956792522000134

Xinfu Chen, Huiqiang Jiang, Guoqing Liu

We consider steady states with mass constraint of the fourth-order thin-film equation with van der Waals force in a bounded domain which leads to a singular elliptic equation for the thickness with an unknown pressure term. By studying second-order nonlinear ordinary differential equation, begin{equation*}h_{rr}+frac{1}{r}h_{r}=frac{1}{alpha}h^{-alpha}-pend{equation*} we prove the existence of infinitely many radially symmetric solutions. Also, we perform rigorous asymptotic analysis to identify the blow-up limit when the steady state is close to a constant solution and the blow-down limit when the maximum of the steady state goes to the infinity.

我们考虑了在有界域中具有范德华力的四阶薄膜方程的质量约束稳态，这导致了具有未知压力项的厚度的奇异椭圆方程。通过研究二阶非线性常微分方程{r}h_{r} 我们证明了无穷多个径向对称解的存在性。此外，我们进行了严格的渐近分析，以确定当稳态接近常解时的爆破极限和当稳态的最大值达到无穷大时的爆破限制。

引用次数: 0

Extended symmetry analysis of remarkable (1+2)-dimensional Fokker–Planck equation 显著(1+2)维Fokker-Planck方程的扩展对称性分析

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2022-05-26 DOI: 10.1017/S0956792523000074

Serhii D. Koval, Alexander Bihlo, R. Popovych

Abstract We carry out the extended symmetry analysis of an ultraparabolic Fokker–Planck equation with three independent variables, which is also called the Kolmogorov equation and is singled out within the class of such Fokker–Planck equations by its remarkable symmetry properties. In particular, its essential Lie invariance algebra is eight-dimensional, which is the maximum dimension within the above class. We compute the complete point symmetry pseudogroup of the Fokker–Planck equation using the direct method, analyse its structure and single out its essential subgroup. After listing inequivalent one- and two-dimensional subalgebras of the essential and maximal Lie invariance algebras of this equation, we exhaustively classify its Lie reductions, carry out its peculiar generalised reductions and relate the latter reductions to generating solutions with iterative action of Lie-symmetry operators. As a result, we construct wide families of exact solutions of the Fokker–Planck equation, in particular, those parameterised by an arbitrary finite number of arbitrary solutions of the (1+1)-dimensional linear heat equation. We also establish the point similarity of the Fokker–Planck equation to the (1+2)-dimensional Kramers equations whose essential Lie invariance algebras are eight-dimensional, which allows us to find wide families of exact solutions of these Kramers equations in an easy way.

摘要本文对具有三个自变量的超抛物型Fokker-Planck方程进行了扩展对称分析，该方程又称为Kolmogorov方程，因其显著的对称性而在该类Fokker-Planck方程中被挑选出来。特别地，它的本质李不变代数是八维的，这是上述类中的最大维数。用直接法计算了Fokker-Planck方程的完全点对称伪群，分析了它的结构，并找出了它的本质子群。在列出该方程的本质和极大李不变代数的等价一二维子代数之后，我们详尽地分类了它的李约简，进行了它特有的广义约简，并将后者的约简与李对称算子的迭代作用生成解联系起来。因此，我们构造了Fokker-Planck方程的广泛精确解族，特别是那些由任意有限数量的(1+1)维线性热方程的任意解参数化的解族。我们还建立了Fokker-Planck方程与(1+2)维Kramers方程的点相似性，这些Kramers方程的基本李不变代数是8维的，这使得我们可以很容易地找到这些Kramers方程的广泛的精确解族。

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引用次数: 4

A distributionally ambiguous two-stage stochastic approach for investment in renewable generation 可再生能源发电投资的一种分布模糊两阶段随机方法

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2022-05-12 DOI: 10.1017/S0956792522000122

Pedro Borges, C. Sagastizábal, M. Solodov, A. Tomasgard

The optimal expansion of a power system with reduced carbon footprint entails dealing with uncertainty about the distribution of the random variables involved in the decision process. Optimisation under ambiguity sets provides a mechanism to suitably deal with such a setting. For two-stage stochastic linear programs, we propose a new model that is between the optimistic and pessimistic paradigms in distributionally robust stochastic optimisation. When using Wasserstein balls as ambiguity sets, the resulting optimisation problem has nonsmooth convex constraints depending on the number of scenarios and a bilinear objective function. We propose a decomposition method along scenarios that converges to a solution, provided a global optimisation solver for bilinear programs with polyhedral feasible sets is available. The solution procedure is applied to a case study on expansion of energy generation that takes into account sustainability goals for 2050 in Europe, under uncertain future market conditions.

减少碳足迹的电力系统的最佳扩展需要处理决策过程中涉及的随机变量分布的不确定性。模糊集下的优化提供了一种适当处理这种设置的机制。对于两阶段随机线性规划，我们在分布鲁棒随机优化中提出了一个介于乐观和悲观范式之间的新模型。当使用Wasserstein球作为模糊集时，得到的优化问题具有非光滑凸约束，这取决于场景的数量和双线性目标函数。我们提出了一种沿着场景的分解方法，该方法收敛于一个解，前提是具有多面体可行集的双线性程序的全局优化求解器是可用的。该解决方案程序适用于一项关于扩大能源生产的案例研究，该研究考虑了欧洲在不确定的未来市场条件下2050年的可持续发展目标。

引用次数: 0

Asymptotic and transient dynamics of SEIR epidemic models on weighted networks 加权网络上SEIR流行病模型的渐近和瞬态动力学

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2022-04-26 DOI: 10.1017/s0956792522000109

CANRONG TIAN, ZUHAN LIU, SHIGUI RUAN

We study the effect of population mobility on the transmission dynamics of infectious diseases by considering a susceptible-exposed-infectious-recovered (SEIR) epidemic model with graph Laplacian diffusion, that is, on a weighted network. First, we establish the existence and uniqueness of solutions to the SEIR model defined on a weighed graph. Then by constructing Liapunov functions, we show that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity and the endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than unity. Finally, we apply our generalized weighed graph to Watts–Strogatz network and carry out numerical simulations, which demonstrate that degrees of nodes determine peak numbers of the infectious population as well as the time to reach these peaks. It also indicates that the network has an impact on the transient dynamical behaviour of the epidemic transmission.

通过考虑一个具有拉普拉斯扩散图的SEIR流行病模型，即在加权网络上，研究了人口流动对传染病传播动力学的影响。首先，我们建立了在加权图上定义的SEIR模型解的存在唯一性。然后通过构造Liapunov函数，证明了当基本繁殖数小于1时无病平衡是全局渐近稳定的，当基本繁殖数大于1时地方病平衡是全局渐近稳定的。最后，我们将广义加权图应用于Watts-Strogatz网络，并进行了数值模拟，结果表明节点度决定了感染群体的峰值数量以及到达这些峰值的时间。这也表明网络对流行病传播的瞬态动力学行为有影响。

引用次数: 0

Asymptotic and transient dynamics of SEIR epidemic models on weighted networks 加权网络上SEIR流行病模型的渐近和瞬态动力学

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2022-04-26 DOI: 10.1017/s0956792522000109

CANRONG TIAN, ZUHAN LIU, SHIGUI RUAN

We study the effect of population mobility on the transmission dynamics of infectious diseases by considering a susceptible-exposed-infectious-recovered (SEIR) epidemic model with graph Laplacian diffusion, that is, on a weighted network. First, we establish the existence and uniqueness of solutions to the SEIR model defined on a weighed graph. Then by constructing Liapunov functions, we show that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity and the endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than unity. Finally, we apply our generalized weighed graph to Watts–Strogatz network and carry out numerical simulations, which demonstrate that degrees of nodes determine peak numbers of the infectious population as well as the time to reach these peaks. It also indicates that the network has an impact on the transient dynamical behaviour of the epidemic transmission.

通过考虑一个具有拉普拉斯扩散图的SEIR流行病模型，即在加权网络上，研究了人口流动对传染病传播动力学的影响。首先，我们建立了在加权图上定义的SEIR模型解的存在唯一性。然后通过构造Liapunov函数，证明了当基本繁殖数小于1时无病平衡是全局渐近稳定的，当基本繁殖数大于1时地方病平衡是全局渐近稳定的。最后，我们将广义加权图应用于Watts-Strogatz网络，并进行了数值模拟，结果表明节点度决定了感染群体的峰值数量以及到达这些峰值的时间。这也表明网络对流行病传播的瞬态动力学行为有影响。

引用次数: 0

Steady state diffusion in tubular structures: Assessment of one-dimensional models 管状结构的稳态扩散:一维模型的评估

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2022-04-25 DOI: 10.1017/s0956792522000110

P. A. MARTIN, A. T. SKVORTSOV

Steady-state diffusion in long axisymmetric structures is considered. The goal is to assess one-dimensional approximations by comparing them with axisymmetric eigenfunction expansions. Two problems are considered in detail: a finite tube with one end that is partly absorbing and partly reflecting; and two finite coaxial tubes with different cross-sectional radii joined together abruptly. Both problems may be modelled using effective boundary conditions, containing a parameter known as the trapping rate. We show that trapping rates depend on the lengths of the finite tubes (and that they decay slowly as these lengths increase) and we show how trapping rates are related to blockage coefficients, which are well known in the context of potential flow along tubes of infinite length.

研究了长轴对称结构中的稳态扩散问题。目标是通过比较一维近似与轴对称特征函数展开来评估一维近似。详细考虑了两个问题:一端部分吸收部分反射的有限管;两个具有不同截面半径的有限同轴管突然连接在一起。这两个问题都可以用有效的边界条件来模拟，其中包含一个称为捕获率的参数。我们展示了捕获速率取决于有限管道的长度(并且随着长度的增加它们会缓慢衰减)，我们展示了捕获速率如何与堵塞系数相关，这在沿着无限长度管道的势流的背景下是众所周知的。

引用次数: 0

Steady state diffusion in tubular structures: Assessment of one-dimensional models 管状结构的稳态扩散:一维模型的评估

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2022-04-25 DOI: 10.1017/s0956792522000110

P. A. MARTIN, A. T. SKVORTSOV

Steady-state diffusion in long axisymmetric structures is considered. The goal is to assess one-dimensional approximations by comparing them with axisymmetric eigenfunction expansions. Two problems are considered in detail: a finite tube with one end that is partly absorbing and partly reflecting; and two finite coaxial tubes with different cross-sectional radii joined together abruptly. Both problems may be modelled using effective boundary conditions, containing a parameter known as the trapping rate. We show that trapping rates depend on the lengths of the finite tubes (and that they decay slowly as these lengths increase) and we show how trapping rates are related to blockage coefficients, which are well known in the context of potential flow along tubes of infinite length.

研究了长轴对称结构中的稳态扩散问题。目标是通过比较一维近似与轴对称特征函数展开来评估一维近似。详细考虑了两个问题:一端部分吸收部分反射的有限管;两个具有不同截面半径的有限同轴管突然连接在一起。这两个问题都可以用有效的边界条件来模拟，其中包含一个称为捕获率的参数。我们展示了捕获速率取决于有限管道的长度(并且随着长度的增加它们会缓慢衰减)，我们展示了捕获速率如何与堵塞系数相关，这在沿着无限长度管道的势流的背景下是众所周知的。

引用次数: 0

On the Lie symmetries of characteristic function hierarchy in compressible turbulence 关于可压缩湍流中特征函数层次的Lie对称性

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2022-04-11 DOI: 10.1017/S0956792522000092

D. S. Praturi, D. Plümacher, M. Oberlack

We compute the Lie symmetries of characteristic function (CF) hierarchy of compressible turbulence, ignoring the effects of viscosity and heat conductivity. In the probability density function (PDF) hierarchy, a typical non-local nature is observed, which is naturally eliminated in the CF hierarchy. We observe that the CF hierarchy retains all the symmetries satisfied by compressible Euler equations. Broadly speaking, four types of symmetries can be discerned in the CF hierarchy: (i) symmetries corresponding to coordinate system invariance, (ii) scaling/dilation groups, (iii) projective groups and (iv) statistical symmetries, where the latter define measures of intermittency and non-gaussianity. As the multi-point CFs need to satisfy additional constraints such as the reduction condition, the projective symmetries are only valid for monatomic gases, that is, the specific heat ratio, $gamma = 5/3$ . The linearity of the CF hierarchy results in the statistical symmetries due to the superposition principle. For all of the symmetries, the global transformations of the CF and various key compressible statistics are also presented.

我们计算了可压缩湍流特征函数(CF)层次的李氏对称性，忽略了粘度和导热性的影响。在概率密度函数(PDF)层次结构中，观察到典型的非局部性质，而在CF层次结构中自然消除了非局部性质。我们观察到CF层次保留了所有可压缩欧拉方程所满足的对称性。广义地说，在CF层次中可以识别出四种对称类型:(i)对应于坐标系不变性的对称，(ii)缩放/扩张群，(iii)投影群和(iv)统计对称，后者定义了间歇性和非高斯性的度量。由于多点CFs需要满足约化条件等附加约束，因此投影对称性只对单原子气体有效，即比热比$gamma = 5/3$。由于叠加原理，CF层次的线性导致统计对称性。对于所有的对称，还给出了CF的全局变换和各种关键可压缩统计量。

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引用次数: 0