Convergence of a Stochastic Method for the Modeling of Polymeric Fluids

We present a convergence analysis of a stochastic method for numerical modeling of complex fluids using Brownian configuration fields (BCF) for shear flows. The analysis takes into account the special structure of the stochastic partial differential equations for shear flows. We establish the optimal rate of convergence. We also analyze the nature of the error by providing its leading order asymptotics.     

Minimum action method for the study of rare events

The least action principle from the Wentzell‐Freidlin theory of large deviations is exploited as a numerical tool for finding the optimal dynamical paths in spatially extended systems driven by a small noise. The action is discretized and a preconditioned BFGS method is used to optimize the discrete action. Applications are presented for thermally activated reversal in the Ginzburg‐Landau model in one and two dimensions, and for noise induced excursion events in the Brusselator taken as an example of non‐gradient system arising in chemistry. In the Ginzburg‐Landau model, the reversal proceeds via interesting nucleation events, followed by propagation of domain walls. The issue of nucleation versus propagation is discussed and the scaling for the number of nucleation events as a function of the reversal time and other material parameters is computed. Good agreement is found with the numerical results. In the Brusselator, whose deterministic dynamics has a single stable equilibrium state, the presence of noise is shown to induce large excursions by which the system cycles out of this equilibrium state. © 2004 Wiley Periodicals, Inc.     

Well-Posedness for the Dumbbell Model of Polymeric Fluids

The dumbbell model is a coupled hydrodynamic-kinetic model for polymeric fluids in which the configurations of the dumbbells are described by stochastic differential equations. We prove well-posedness of this model by deriving directly a priori estimates on the stochastic model. Our results can be used to analyze stochastic simulation methods such as the ones that are based on Brownian configuration fields.Supported by ONR grant N00014-01-1-0674 and National Science Foundation of China through a Class B Award for Distinguished Young Scholars 10128102.Partially supported by the special funds for Major State Research Projects G1999032804 and National Science Foundation of China for Distinguished Young Scholars 10225103.     

Reconstruction of electron-phonon interaction function from temperature dependence of electrical resistivity for metals

The determination of the electron-phonon interaction function (EPIF) from the temperature dependence of the electrical resistivity (TDER) for metals within a selected moderate temperature range is numerically demonstrated based on the general theory of the amplitude-phase-retrieval problem and an iterative algorithm. From the model calculation, the convergent solution can be obtained; however, the profile of the recovered EPIF depends on the initial frequency distribution used in the algorithm since this inversion problem is inherently ill-posed. In order to get reasonable result, it is necessary to introduce additional information about the feature of the EPIF for guiding the choice of the initial distribution. The algorithm can also furnish a robust reconstruction of EPIF from TDER contaminated with random noise. It means that this algorithm is relatively stable and insensitive to external perturbation; therefore in a sense, the presented algorithm overcomes the ill-posedness of the inversion problem.     

Analysis of the heterogeneous multiscale method for elliptic homogenization problems

A comprehensive analysis is presented for the heterogeneous multiscale method (HMM for short) applied to various elliptic homogenization problems. These problems can be either linear or nonlinear, with deterministic or random coefficients. In most cases considered, optimal estimates are proved for the error between the HMM solutions and the homogenized solutions. Strategies for retrieving the microstructural information from the HMM solutions are discussed and analyzed.

     

基于FPGA的四轴飞行控制器的硬件系统设计

为提高四轴飞行器的数据采集与数据处理能力,降低四轴飞行器的功耗,研制了一种基于FPGA的四轴飞行控制器。飞行控制器以NIOS II处理器为控制核心,结合嵌入的SPI、I2C、UART等IP核实现了数据的实时采集与快速处理,并提出并行处理PPM解码和编码、超声波检测与控制、蜂鸣器控制的设计方案,利用VerilogHDL语言在FPGA上设计了这些并行处理功能模块,这些功能模块通过PIO核与NIOS II处理器连接,能够自主完成所规定的处理功能。经过多次飞行测试,四轴飞行器能够稳定的起飞和降落,快速的飞行,转弯,上升和下降,也能够避开障碍物,验证了四轴飞行控制器功能稳定,功耗较低,已达到设计的要求。     

Generalized variational principles,global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics

We study systems of conservation laws arising in two models of adhesion particle dynamics. The first is the system of free particles which stick under collision. The second is a system of gravitationally interacting particles which also stick under collision. In both cases, mass and momentum are conserved at the collisions, so the dynamics is described by 2×2 systems of conservations laws. We show that for these systems, global weak solutions can be constructed explicitly using the initial data by a procedure analogous to the Lax-Oleinik variational principle for scalar conservation laws. However, this weak solution is not unique among weak solutions satisfying the standard entropy condition. We also study a modified gravitational model in which, instead of momentum, some other weighted velocity is conserved at collisions. For this model, we prove both existence and uniqueness of global weak solutions. We then study the qualitative behavior of the solutions with random initial data. We show that for continuous but nowhere differentiable random initial velocities, all masses immediately concentrate on points even though they were continuously distributed initially, and the set of shock locations is dense.     

Propagation of socillations in the Solutions of 1-D Compressible Fluid Equations

We study the propagation of initial osillations in the solutions of one-dimensional inviscid gas dynamic equations and the compressible Navier-Stokes equations. Using Multiple scale analysis, we derivbe the homogenized equations which take the form of n averaged system coupled with a dynamic cell-problem. We prove rigorous error estimates to justify the validity of these equations. We also show that the weak limits of the osicllatory solytions satisfy gas dynamic equations with an equation of state depeding on the microstructurer of the inital data     

Preservation of the Morphology of a Self‐Encapsulated Thin Titania Film in a Functional Multilayer Stack: An X‐Ray Scattering Study

Looks matter: Generally, the morphology of titania thin films is crucial for their performance, hence much effort is spent to tailor the desired morphology. X‐ray scattering enables the monitoring of the crystalline titania layer morphology during build‐up of the functional multilayer stack (see Figure). Herein evidence is provided that the morphology is preserved throughout the fabrication process.

     

A multiscale coupling method for the modeling of dynamics of solids with application to brittle cracks

We present a multiscale model for numerical simulations of dynamics of crystalline solids. The method combines the continuum nonlinear elasto-dynamics model, which models the stress waves and physical loading conditions, and molecular dynamics model, which provides the nonlinear constitutive relation and resolves the atomic structures near local defects. The coupling of the two models is achieved based on a general framework for multiscale modeling – the heterogeneous multiscale method (HMM). We derive an explicit coupling condition at the atomistic/continuum interface. Application to the dynamics of brittle cracks under various loading conditions is presented as test examples.