非定常Navier-Stokes方程基于两重网格离散的有限元并行算法

基于两重网格离散和区域分解技巧，提出三种求解非定常Navier-Stokes方程的有限元并行算法.算法的基本思想是在每一时间迭代步，在粗网格上采用Oseen迭代法求解非线性问题，在细网格上分别并行求解Oseen、Newton、Stokes线性问题以校正粗网格解.对于空间变量采用有限元离散，时间变量采用向后Euler格式离散.数值实验验证了算法的有效性.     

基于简单MOPA结构实现3.08 kW全光纤窄线宽线偏振激光输出

基于简单的主振荡功率放大结构,演示了一种高功率窄线宽线性偏振全光纤激光器,其最大输出功率为3.08 kW,3 dB线宽为0.2 nm。在整个功率缩放过程中,偏振消光比约为94%,光束质量M 2约为1.4。这是国内外首次实现3 kW全保偏光纤激光输出,与基于相位调制的窄线宽激光器相比,该激光器可实现近似的线宽,同时具有受激布里渊散射阈值高、系统结构简单、成本低等特点。     

某型机进近段高精度相对姿态实时测量技术

某型机在飞行训练过程中，进近段的二维相对姿态数据对于该型机安全着陆有着至关重要的作用。基于无线网络电台的双向数据传输系统能够实时获取进近段飞机相对理想着陆点的水平、垂直相对位置数据。通过上行链路上传着陆点的姿态数据，下行链路实时下传动动差分后的差分数据,最后在中心控制站进行二次数据处理。该技术获得的进近段二维相对姿态精度达到厘米级，满足飞行训练的需求。同时结合飞机显控数据以及视景图，以多角化动态关联的方式将实时获取的姿态数据等呈现给指挥员，更好地辅助指挥员进行着陆指挥工作。     

分数阶Schrodinger—Kirchhoff方程无穷多高能量解的存在性

本文研究如下带有变号势函数的分数阶Schrodinger Kirchhoff方程(a+b∫∫R^N|u(x)-u(y)|^p/|x-y|^N+p^sdxdy)^p-1(-△)p^su+λV(x)|u|^p-2u=f(x,u)-μg(x)|u|^q-2u,x∈R^N.其中s∈(0,1),p∈[2,∞),q∈(l,p),a,b>0,λ,μ>0均为正常数,在V,f,g等函数合适的条件下,运用喷泉定理获得该系统无穷多高能量解的存在性.     

Properties of bounded stochastic processes employed in biophysics

Abstract

Realistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated within a solid mathematical ground. Four families are object of investigation: the Sine-Wiener (SW), the Doering–Cai–Lin (DCL), the Tsallis–Stariolo–Borland (TSB), and the Kessler–Sørensen (KS) families. We address mathematical questions on existence and uniqueness of the processes defined through Stochastic Differential Equations, which often conceal non-obvious behavior, and we explore the behavior of the solutions near the boundaries of the state space. The expression of the time-dependent probability density of the Sine-Wiener noise is provided in closed form, and a close connection with the Doering–Cai–Lin noise is shown. Further relationships among the different families are explored, pathwise and in distribution. Finally, we illustrate an analogy between the Kessler–Sørensen family and Bessel processes, which allows to relate the respective local times at the boundaries.     

Aharonov–Bohm effect for bound states on spin-0 massive charged particles in a Gödel-type space–time with Coulomb potential

In this paper, we investigate the relativistic quantum dynamics of spin-0 massive charged particles in a Gödel-type space–time with electromagnetic interactions. We derive the radial wave equation of the Klein–Gordon equation with an internal magnetic flux field and Coulomb-type potential in the Som–Raychaudhuri space–time with cosmic string. We solve this equation and analyze the analog effect in relation to the Aharonov–Bohm effect for bound states.     

Analytical solution of stochastic differential equation by multilayer perceptron neural network approximation of Fokker–Planck equation

The Fokker–Planck equation is a useful tool to analyze the transient probability density function of the states of a stochastic differential equation. In this paper, a multilayer perceptron neural network is utilized to approximate the solution of the Fokker–Planck equation. To use unconstrained optimization in neural network training, a special form of the trial solution is considered to satisfy the initial and boundary conditions. The weights of the neural network are calculated by Levenberg–Marquardt training algorithm with Bayesian regularization. Three practical examples demonstrate the efficiency of the proposed method.     

Torsional vibration of functionally graded nano-rod under magnetic field supported by a generalized torsional foundation based on nonlocal elasticity theory

Abstract

This article contains the nonlocal elasticity theory to capture size effects in functionally graded (FG) nano-rod under magnetic field supported by a torsional foundation. Torque effect of an axial magnetic field on an FG nano-rod has been defined using Maxwell’s relation. The material properties were assumed to vary according to the power law in radial direction. The Navier equation and boundary conditions of the size-dependent FG nano-rod were derived by the Hamilton’s principle. These equations were solved by employing the generalized differential quadrature method (GDQM). Presented model has the ability to turn into the classical model if the material length scale parameter is taken to be zero. The effects of some parameters, such as inhomogeneity constant, magnetic field and small-scale parameter, were studied. As an important result of this study can be stated that an FG nano-rod model based on the nonlocal elasticity theory behaves softer and has smaller natural frequency.