Ergodic stationary distribution and practical application of a hybrid stochastic cholera transmission model with waning vaccine-induced immunity under nonlinear regime switching

Considering the effect of stochasticity including white noise and colored noise, this paper aims to study a hybrid stochastic cholera epidemic model with waning vaccine-induced immunity and nonlinear telegraph perturbations. First, we derive a critical value ${?}_0^C$ related to the basic reproduction number ${?}_0$ of the deterministic model. The key aim of this paper is to generalize the θ-stochastic criterion method proposed by the recent work (Han et al. in Chaos Solit Fract 140:110238, 2020) to eliminate nonlinear telegraph perturbations. Next, via constructing several θ-stochastic Lyapunov functions and using the generalized method, we further prove that the stochastic model have a unique ergodic stationary distribution under ${?}_0^C>1$. Results show that the prevention and control of cholera epidemic depend on low transmission rate and small telegraph perturbations. Finally, the corresponding numerical simulations are performed to illustrate our analytical results and a practical application on the Somalia cholera outbreak is shown at the end of this paper.     

Strategy to mitigate single event upset in 14-nm CMOS bulk FinFET technology

Three-dimensional (3D) TCAD simulations demonstrate that reducing the distance between the well boundary and N-channel metal-oxide semiconductor (NMOS) transistor or P-channel metal-oxide semiconductor (PMOS) transistor can mitigate the cross section of single event upset (SEU) in 14-nm complementary metal-oxide semiconductor (CMOS) bulk FinFET technology. The competition of charge collection between well boundary and sensitive nodes, the enhanced restoring currents and the change of bipolar effect are responsible for the decrease of SEU cross section. Unlike dual-interlock cell (DICE) design, this approach is more effective under heavy ion irradiation of higher LET, in the presence of enough taps to ensure the rapid recovery of well potential. Besides, the feasibility of this method and its effectiveness with feature size scaling down are discussed.     

配合参数对单晶炉驱动系统的影响分析

光伏产业的发展使得对硅材料的需求日益增加,同时硅单晶生产行业竞争也日趋激烈。作为生产硅单晶的重要装备,单晶炉的稳定性和可靠性关系到硅单晶生产效率的提升和成本的下降,因此其驱动系统的设计和优化成为装备制造的关键环节。本文以NVT-HG2000-V1型硅单晶生长炉的驱动系统为研究对象,用SolidWorks三维建模实现虚拟装配,采用ADAMS建立其动力学仿真模型,并对驱动系统的运动过程进行仿真模拟。采用控制变量法定量分析了铜套与升降轴的配合间隙及丝杠参数对驱动力和驱动力矩的影响规律,进而在提高硅单晶生长炉装备稳定性和可靠性方面给出合理的技术建议。结果表明,铜套与升降轴的配合间隙达到0.071 mm后能有效降低驱动系统运行所需驱动力矩,丝杠倾斜度、螺纹螺距与螺纹间摩擦系数的增大均会导致驱动系统运行所需力矩大幅增加。     

Time reversal for obstacle location in elastodynamics from acoustic recording

The Note is concerned with a feasibility study of time reversal in a non-homogeneous elastic medium, from data recorded in an acoustic medium. Our aim here is to determine the presence and some physical properties of elastic “inclusions” (unknown, not observable solid objects, characterized by their elastic properties) from partial observations of acoustic waves scattered by these inclusions. A finite element numerical method, based on a variational acousto-elastodynamics formulation, is derived and used to solve the forward, and then, the time-reversed problem. A criterion, derived from the reverse time migration framework, is introduced, to help construct images of the inclusions to be determined. Numerical illustrations on configurations that mimic the breast cancer configuration are proposed, and show that one can differentiate between two inclusions, even with different properties.     

The martingale problem for a class of nonlocal operators of diagonal type

We consider systems of stochastic differential equations of the form $$\begin{array}{c}\hfill d{X}_t^i=\sum _{j=1}^d{A}_{ij}\left(X_{t?}\right)d{Z}_t^j\end{array}$$ for $i=1,?,d$ with continuous, bounded and non‐degenerate coefficients. Here $Z_t^1,?,Z_t^d$ are independent one‐dimensional stable processes with ${\alpha }_1,?,{\alpha }_d\in (0,2)$. In this article we research on uniqueness of weak solutions to such systems by studying the corresponding martingale problem. We prove the uniqueness of weak solutions in the case of diagonal coefficient matrices.     

Poisson discretizations of Wiener functionals and Malliavin operators with Wasserstein estimates

This article proposes a global, chaos-based procedure for the discretization of functionals of Brownian motion into functionals of a Poisson process with intensity $\lambda >0$. Under this discretization we study the weak convergence, as the intensity of the underlying Poisson process goes to infinity, of Poisson functionals and their corresponding Malliavin-type derivatives to their Wiener counterparts. In addition, we derive a convergence rate of $O\left({\lambda }^{?1∕4}\right)$ for the Poisson discretization of Wiener functionals by combining the multivariate Chen–Stein method with the Malliavin calculus. Our proposed sufficient condition for establishing the mentioned convergence rate involves the kernel functions in the Wiener chaos, yet we provide examples, especially the discretization of some common path dependent Wiener functionals, to which our results apply without committing the explicit computations of such kernels. To the best our knowledge, these are the first results in the literature on the universal convergence rate of a global discretization of general Wiener functionals.     

A MODAL TESTING METHOD FOR CANTILEVER BEAM1)

基于欧拉-伯努利梁理论得到悬臂梁自由振动的振型函数。通过数值计算得出实验用的悬臂梁前五阶振型的节点位置及其与梁长的比值。考虑传感器对悬臂梁固有频率的影响,建立梁-传感器模型进行仿真分析并得出悬臂梁前五阶固有频率。基于节点位置和测点位置,在实验中选择激励点。将具体实验的结果与梁-传感器仿真模型结果进行对比,通过前五阶固有频率的误差分析,发现仿真分析结果与实验结果误差最高为 1.3%。研究完整地叙述了悬臂梁的模态测试流程,可为工程技术人员的模态测试起一定的指导作用。     

Distribution dependent stochastic differential equations

Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include the correspondence of weak solutions and nonlinear Fokker-Planck equations, the well-posedness, regularity estimates, exponential ergodicity, long time large deviations, and comparison theorems.     

Mechanical property and deformation mechanism of gold nanowire with non-uniform distribution of twinned boundaries:A molecular dynamics simulation study

The mechanical property and deformation mechanism of twinned gold nanowire with non-uniform distribution of twinned boundaries(TBs) are studied by the molecular dynamics(MD) method. It is found that the twin boundary spacing(TBS) has a great effect on the strength and plasticity of the nanowires with uniform distribution of TBs. And the strength enhances with the decrease of TBS, while its plasticity declines. For the nanowires with non-uniform distribution of TBs, the differences in distribution among different TBSs have little effect on the Young's modulus or strength, and the compromise in strength appears. But the differences have a remarkable effect on the plasticity of twinned gold nanowire. The twinned gold nanowire with higher local symmetry ratio has better plasticity. The initial dislocations always form in the largest TBS and the fracture always appears at or near the twin boundaries adjacent to the smallest TBS. Some simulation results are consistent with the experimental results.