高雷诺数下非混相Rayleigh-Taylor不稳定性的格子Boltzmann方法模拟

本文采用相场格子Boltzmann方法研究了竖直微通道内中等Atwoods数流体的单模Rayleigh-Taylor不稳定性问题,系统分析了雷诺数对相界面动力学行为以及扰动在各发展阶段演化规律的影响.数值结果表明高雷诺数条件下,不稳定性界面扰动的增长经历了四个不同的发展阶段,包括线性增长阶段、饱和速度阶段、重加速阶段及混沌混合阶段.在线性增长阶段,我们计算获得的气泡与尖钉振幅符合线性稳定性理论,并且线性增长率随着雷诺数的增加而增大.在第二个阶段,我们观察到气泡与尖钉将以恒定的速度增长,获得的尖钉饱和速度略高于Goncharov经典势能模型的解析解[Phys.Rev.Lett.200288134502],这归因于系统中产生了多个尺度的旋涡,而涡之间的相互作用促进了尖钉的增长.随着横向速度和纵向速度的差异扩大,气泡和尖钉界面演化诱导产生的Kelvin–Helmholtz不稳定性逐渐增强,从而流体混合区域出现许多不同层次的涡结构,加速了气泡与尖钉振幅的演化速度,并在演化后期阶段,导致界面发生多层次卷起、剧烈变形、混沌破裂等行为,最终形成了非常复杂的拓扑结构.此外,我们还统计了演化后期气泡与尖钉的无量纲加速度,发现气泡和尖钉的振幅在后期呈现二次增长规律,其增长率系数分别为0.045与0.233.而在低雷诺条件下,重流体在不稳定性后期以尖钉的形式向下运动而轻流体以气泡的形式向上升起.在整个演化过程中,界面变得足够光滑,气泡与尖钉在后期的演化速度接近于常数,未观察到后期的重加速与混沌混合阶段.     

宽体液腔Janus-Helmholtz换能器

本文使用有限元方法对宽体液腔Janus-Helmholtz(JH)换能器进行了仿真分析,得出了壳体宽度拓展增量对JH换能器工作性能的影响规律。使用三维建模的方式,分析了连接部分对换能器性能的影响及宽体壳体的的模态,证明了三维建模的必要性。依据仿真优化结构设计了一款宽体液腔JH换能器并进行了湖上测试。最终测试结果与仿真结果有很好的一致性,相较直筒JH换能器其谐振频率降低300Hz,发射电压响应最高可达144dB。     

Identifying the viscoelastic properties of soft matter from the indentation response of a hard film-soft substrate system

The indentation technique is widely used in measuring the mechanical properties of soft matter at the microscale or nanoscale,but still faces challenges by these unique properties as well as the consequent strong surface adhesion, including the strong nonlinear effect, unclear judgment of the contact point, difficulties in estimating the contact area, and the risk of the indenter piercing the sample. Here we propose a two-step method to solve these problems: lay a hard film on a soft matter, and obtain the viscoelastic properties of this soft matter through the indentation response of this composite structure. We first establish a theoretical indentation model of the hard film-soft substrate system based on the theory of plates, elastic-viscoelastic correspondence principle and Boltzmann superposition principle. To verify the correctness of this method, we measure the mechanical properties of the methyl vinyl silicone rubber(MVSR) covered by a Cu nanofilm. Finally, we test the effectiveness and error sensitivity of this method with the finite element method(FEM). The results show that our method can accurately measure the mechanical properties of soft matter, while effectively circumventing the problems of the traditional indentation technique.     

Sufficient Conditions for a Digraph to be Supereulerian

A (di)graph is supereulerian if it contains a spanning eulerian sub(di)graph. This property is a relaxation of hamiltonicity. Inspired by this analogy with hamiltonian cycles and by similar results in supereulerian graph theory, we analyze a number of sufficient Ore type conditions for a digraph to be supereulerian. Furthermore, we study the following conjecture due to Thomassé and the first author: if the arc‐connectivity of a digraph is not smaller than its independence number, then the digraph is supereulerian. As a support for this conjecture we prove it for digraphs that are semicomplete multipartite or quasitransitive and verify the analogous statement for undirected graphs.     

形状记忆合金椭圆孔口问题的有限单元法

基于Lagoudas形状记忆合金(SMA)三维本构模型,假设材料为各向同性,推导了SMA平面应力状态的增量型本构方程,继而编写了ABAQUS用户自定义材料(UMAT)子程序,研究了在双向拉伸情况下,外载荷、温度、椭圆孔口长短轴之比对超弹性SMA椭圆孔口板中应力诱发马氏体相变区的影响。数值结果表明:应力诱发马氏体相变首先发生在椭圆孔口长轴端点部位,在外加载荷作用下逐渐扩展到板内,并由内向外形成马氏体相区、相变混合区和奥氏体相区;SMA板内应力诱发马氏体完全相变区面积与施加外载荷成正相关,与温度成负相关;随着椭圆孔口长短轴之比增大,SMA板内应力诱发马氏体完全相变区面积呈现出先减小后增大的趋势;拉应力差值相同时,相较于拉应力沿椭圆孔口长轴方向较大的情况,当拉应力沿椭圆孔口短轴方向较大时,SMA板内完全相变区面积较大,椭圆孔口周边应力集中现象更明显。     

Mathematical analysis of the dynamics of COVID-19 in Africa under the influence of asymptomatic cases and re-infection

Coronavirus pandemic (COVID-19) hit the world in December 2019, and only less than 5% of the 15 million cases were recorded in Africa. A major call for concern was the significant rise from 2% in May 2020 to 4.67% by the end of July 15, 2020. This drastic increase calls for quick intervention in the transmission and control strategy of COVID-19 in Africa. A mathematical model to theoretically investigate the consequence of ignoring asymptomatic cases on COVID-19 spread in Africa is proposed in this study. A qualitative analysis of the model is carried out with and without re-infection, and the reproduction number is obtained under re-infection. The results indicate that increasing case detection to detect asymptomatically infected individuals will be very effective in containing and reducing the burden of COVID-19 in Africa. In addition, the fact that it has not been confirmed whether a recovered individual can be re-infected or not, then enforcing a living condition where recovered individuals are not allowed to mix with the susceptible or exposed individuals will help in containing the spread of COVID-19.     

The minimum forcing number of perfect matchings in the hypercube

Let $M$ be a perfect matching in a graph. A subset $S$ of $M$ is said to be a forcing set of $M$, if $M$ is the only perfect matching in the graph that contains $S$. The minimum size of a forcing set of $M$ is called the forcing number of $M$. Pachter and Kim (1998) conjectured that the forcing number of every perfect matching in the $n$-dimensional hypercube is $2^{n?2}$, for all $n\ge 2$. This was revised by Riddle (2002), who conjectured that it is at least $2^{n?2}$, and proved it for all even $n$. We show that the revised conjecture holds for all $n\ge 2$. The proof is based on simple linear algebra.     

Multistrain edge‐based compartmental model on networks

Multistrain diseases, which are infected through individual contacts, pose severe public health threat nowadays. In this paper, we build competitive and mutative two‐strain edge‐based compartmental models using probability generation function (PGF) and pair approximation (PA). Both of them are ordinary differential equations. Their basic reproduction numbers and final size formulas are explicitly derived. We show that the formula gives a unique positive final epidemic size when the reproduction number is larger than unity. We further consider competitive and mutative multistrain diseases spreading models and compute their basic reproduction numbers. We perform numerical simulations that show some dynamical properties of the competitive and mutative two‐strain models.