三维可压缩向列型液晶系统解的衰减率的改进

本文的主要目的在于提高三维可压缩向列型液晶系统解的最高阶(S阶)空间导数的衰减率。如果初值的HS(S≥3)和范数都是有界的,并且其H3范数足够小,则应用纯能量法,我们给出了解的最高阶空间导数L2范数的最优衰减率为(1+t)−(S2+α2),而在魏,李和姚的研究中其衰减率仅为(1+t)−(S−12+α2)。Abstract: The major objective of this thesis lies in improving the decay rates for the highest order (S-order) of spatial derivative of the solutions to the 3D system of compressible nematic liquid crystal. If the norms of both HS(S≥3)and for the initial value are bounded, as well as the norm of H3for that is small enough, with applying pure energy method, we give that the optimal decay rates for the highest order of spatial derivative of the solutions in norm of L2are (1+t)−(S2+α2), while that is just (1+t)−(S−12+α2)in Wei, Li and Yao’s study.

一种单检测器可压缩成像系统设计

采用基于亚高斯随机投影的图像重建方法,得到以稀疏矩阵、非常稀疏投影矩阵作为测量矩阵的仿真结果,设计一种基于数字微镜装置阵列的可压缩成像系统,给出系统结构、各模块之间的联系和核心模块的设计方法。为满足系统对高频弱光信号检测的需要,设计单检测器弱光信号检测模块,实验结果证明该方案速度快、有较高的精度和适应性。

可压缩的Navier-Stokes-Smoluchowski系统解的指数稳定性

研究了泡沫状态下的一维流体-颗粒相互作用模型,该模型描述了分散在粒子演化过程中的粘性可压缩流体。在初始值、物理域和外部势力的合理的物理假设下,利用Sobolev嵌入定理、分部积分、基础不等式等方法建立了一维具有小初始流体密度可压缩的Navier-Stokes-Smoluchowski系统整体古典解的指数稳定性。从而推广了流体-颗粒模型整体古典解存在性的结果。

带阻尼项的一维欧拉系统光滑解的全局存在性

研究了具有大初值一维非等熵带阻尼项的欧拉系统在含尘气体背景下经典解的全局存在性。通过特征线方法,得到局部光滑解的存在性及唯一性,利用解的先验估计,通过经典的延拓方法,获得全局解。

PVT系统的热力学性质

给出了ＰＶＴ系统的物态方程和热力学微分方程，并通过对描述ＰＶＴ系统的四个热力学量Ｐ、Ｖ、Ｔ、Ｓ的偏导数的讨论，确定了为ＰＶＴ系统的三个基本热力学偏导数。

库底饱和淤积砂层对高拱坝地震反应的影响研究

本文中采用时域显式有限元方法,将库底淤积砂层模拟为重流体,以小湾拱坝为例,分析可压缩库水条件下库底饱和淤积砂层对高拱坝地震反应的影响。计算结果表明,从总体上来说饱和淤砂层的存在对高拱坝地震反应影响较小,但是仍有一些局部反应的变化值得注意。

库底非饱和淤砂层对高拱坝地震反应的影响

采用时域显式有限元方法,将库底非饱和淤砂层近似模拟为不同于库水的流体介质。以小湾拱坝为例,分析可压缩库水条件下库底非饱和淤砂层对高拱坝地震反应的影响。计算结果表明非饱和淤砂层的存在有可能使得坝体地震响应增加。

关于热力学基本议程适用条件的教法建议

本文采用在不可逆过程中直接建立热力学基本方法，说明该议程对不可逆过程边疆的两个邻近平衡态也是适用的，从而为解决《热力学》教学中的这一难点，给出了一个比较有效的方法，该方法从学生实际出发，结合具体过程进行讨论，思路清楚，要领明确，易于被学生接受。

On Simultaneous Exact Controllability

We consider a mixed problem for a system describing the evolution of sound in a compressible fluid. We describe how to treat a simultaneous exact boundary controllability problem in the sense proposed by J.L. Lions as well as D. Russell. By using convenient modified multipliers we obtain an observability inequality provided suitable geometric condition on the domain is valid and the speed velocity of the models are related.

Turbo-Coded Modulation of EVRC Speech Encoder with Unequal Error Protection for Fading Channels

The Enhanced Variable Rate Codec (EVRC) is a standard for the Speech Service Option 3 for Wideband Spread Spectrum Digital System, which has been employed in both IS-95 cellular systems and ANSI J-STC-008 PCS (Personal Communications Systems). This paper investigated the combination of turbo codes with Unequal Error Protection (UEP) and 16-QAM modulation for EVRC codec of Rate 1 to get power and bandwidth efficient coding scheme. The results show that the UEP system outperforms the Equal Error Protection (EEP) one by 1.45 dB at BER of 10 -5.

半导体非等熵Euler-Poisson系统非常数平衡解的稳定性

本文考虑源自半导体材料科学中的非等熵可压缩Euler-Poisson系统.借助时空混合导数迭代方法和对称子技巧,研究了三维空间环上的周期问题;在初值为一个非常数平衡态的小摄动前提下,证明了当时间趋于无穷大时,该问题的整体光滑解按指数速率衰减至平衡态.这种粒子输运现象反映了等熵与非等熵系统的本质联系.

Zero dielectric constant limit to the non-isentropic compressible Euler-Maxwell system

We investigate the zero dielectric constant limit to the non-isentropic compressible Euler-Maxwell system.We justify this singular limit rigorously in the framework of smooth solutions and obtain the nonisentropic compressible magnetohydrodynamic equations as the dielectric constant tends to zero.

Numerical Simulation of the Supersonic Flows in the Second Throat Ejector-Diffuser Systems

The supersonic ejector-diffuser system with a second throat was simulated using CFD. A fully implicit finite volume scheme was applied to solve the axisymmetric Navier-Stokes equations and a standard k-E turbulence model was used to close the governing equations. The flow field in the supersonic ejectordiffuser system was investigated by changing the ejector throat area ratio and the secondary mass flow ratio at a fixed operating pressure ratio of 10. A convergent-divergent nozzle with a design Mach number of 2.11 was selected to give the supersonic operation of the ejector-diffuser system. For the constant area mixing tube the secondary mass flow seemed not to significantly change the flow field in the ejector-diffuser systems. It was, however, found that the flow in the ejector-diffuser systems having the second throat is strongly dependent on the secondary mass flow.

Simulating coupled dynamics of a rigid-flexible multibody system and compressible fluid

As a subsequent work of previous studies of authors, a new parallel computation approach is proposed to simulate the coupled dynamics of a rigid-flexible multibody system and compressible fluid. In this approach, the smoothed particle hydrodynamics(SPH) method is used to model the compressible fluid, the natural coordinate formulation(NCF) and absolute nodal coordinate formulation(ANCF) are used to model the rigid and flexible bodies, respectively. In order to model the compressible fluid properly and efficiently via SPH method, three measures are taken as follows. The first is to use the Riemann solver to cope with the fluid compressibility, the second is to define virtual particles of SPH to model the dynamic interaction between the fluid and the multibody system, and the third is to impose the boundary conditions of periodical inflow and outflow to reduce the number of SPH particles involved in the computation process. Afterwards, a parallel computation strategy is proposed based on the graphics processing unit(GPU) to detect the neighboring SPH particles and to solve the dynamic equations of SPH particles in order to improve the computation efficiency. Meanwhile, the generalized-alpha algorithm is used to solve the dynamic equations of the multibody system. Finally, four case studies are given to validate the proposed parallel computation approach.

Global well-posedness of 3-D density-dependent Navier-Stokes system with variable viscosity

Given initial data(ρ0, u0) satisfying 0 < m ρ0≤ M, ρ0- 1 ∈ L2∩˙W1,r(R3) and u0 ∈˙H-2δ∩ H1(R3) for δ∈ ]1/4, 1/2[ and r ∈ ]6, 3/1- 2δ[, we prove that: there exists a small positive constant ε1,which depends on the norm of the initial data, so that the 3-D incompressible inhomogeneous Navier-Stokes system with variable viscosity has a unique global strong solution(ρ, u) whenever‖ u0‖ L2 ‖▽u0 ‖L2 ≤ε1 and ‖μ(ρ0)- 1‖ L∞≤ε0 for some uniform small constant ε0. Furthermore, with smoother initial data and viscosity coefficient, we can prove the propagation of the regularities for such strong solution.

On the global existence of weak solutions for the Cucker-Smale-Navier-Stokes system with shear thickening

We study the large-time dynamics of Cucker-Smale(C-S)flocking particles interacting with nonNewtonian incompressible fluids.Dynamics of particles and fluids were modeled using the kinetic Cucker-Smale equation for particles and non-Newtonian Navier-Stokes system for fluids,respectively and these two systems are coupled via the drag force,which is the main flocking(alignment)mechanism between particles and fluids.We present a global existence theory for weak solutions to the coupled Cucker-Smale-Navier-Stokes system with shear thickening.We also use a Lyapunov functional approach to show that sufficiently regular solutions approach flocking states exponentially fast in time.

Large time behavior of solutions to 3D compressible Navier-Stokes-Poisson system

We consider the three-dimensional compressible Navier-Stokes-Poisson system where the electric field of the internal electrostatic potential force is governed by the self-consistent Poisson equation.If the Fourier modes of the initial data are degenerate at the low frequency or the initial data decay fast at spatial infinity,we show that the density converges to its equilibrium state at the L 2-rate (1+t)(-7/4) or L ∞-rate (1+t)(-5/2),and the momentum decays at the L 2-rate (1+t)(-5/4) or L ∞-rate (1+t)(-2).These convergence rates are shown to be optimal for the compressible Navier-Stokes-Poisson system.

Examples of Boundary Layers Associated with the Incompressible Navier-Stokes Equations

The author surveys a few examples of boundary layers for which the Prandtl boundary layer theory can be rigorously validated.All of them are associated with the incompressible Navier-Stokes equations for Newtonian fluids equipped with various Dirichlet boundary conditions(specified velocity).These examples include a family of(nonlinear 3D) plane parallel flows,a family of(nonlinear) parallel pipe flows,as well as flows with uniform injection and suction at the boundary.We also identify a key ingredient in establishing the validity of the Prandtl type theory,i.e.,a spectral constraint on the approximate solution to the Navier-Stokes system constructed by combining the inviscid solution and the solution to the Prandtl type system.This is an additional difficulty besides the wellknown issue related to the well-posedness of the Prandtl type system.It seems that the main obstruction to the verification of the spectral constraint condition is the possible separation of boundary layers.A common theme of these examples is the inhibition of separation of boundary layers either via suppressing the velocity normal to the boundary or by injection and suction at the boundary so that the spectral constraint can be verified.A meta theorem is then presented which covers all the cases considered here.

Two-Dimensional Riemann Problems for the Compressible Euler System

Riemann problems for the compressible Euler system in two space dimensions are complicated and difficult,but a viable alternative remains missing.The author lists merits of one-dimensional Riemann problems and compares them with those for the current two-dimensional Riemann problems,to illustrate their worthiness.Two-dimensional Riemann problems are approached via the methodology promoted by Andy Majda in the spirits of modern applied mathematics;that is,simplified model is built via asymptotic analysis,numerical simulation and theoretical analysis.A simplified model called the pressure gradient system is derived from the full Euler system via an asymptotic process.State-of-the-art numerical methods in numerical simulations are used to discern small-scale structures of the solutions,e.g.,semi-hyperbolic patches.Analytical methods are used to establish the validity of the structure revealed in the numerical simulation.The entire process,used in many of Majda's programs,is shown here for the two-dimensional Riemann problems for the compressible Euler systems of conservation laws.

Initial-boundary value problem of three phase flow in porous media

We study the mathematical model of three phase compressible flows through porous media. Under the condition that the rock, water and oil are incompressible, and the compressibility of gas is small, we present a finite element scheme to the initial-boundary value problem of the nonlinear system of equations, then by the convergence of the scheme we prove that the problem admits a weak solution.