Simulations for gas flows in microgeometries using the direct simulation Monte Carlo method

Micro gas flows are often encountered in MEMS devices and classical CFD could not accurately predict the flow and thermal behavior due to the high Knudsen number. Therefore, the gas flow in microgeometries was investigated using the direct simulation Monte Carlo (DSMC) method. New treatments for boundary conditions are verified by simulations of micro-Poiseuille flow, compared with the previous boundary treatments, and slip analytical solutions of the continuum theory. The orifice flow and the corner flow in microchannels are simulated using the modified DSMC codes. The predictions were compared with existing experimental phenomena as well as predictions using continuum theory. The results showed that the channel geometry significantly affects the microgas flow. In the orifice flow, the flow separation occurred at very small Reynolds numbers. In the corner flow, no flow separation occurred even with a high driving pressure. The DSMC results agreed well with existing experimental information.     

Simulating pedestrian flow through narrow exits

Introduction: The flow of pedestrians through narrow doorways is one of the most common features of crowd motions and evacuations. It is particularly an important aspect of pedestrian simulations models since their accuracy depends highly on their ability to produce realistic exit flow rates. The problem has been extensively studied in the literature, but many aspects of it have remained controversial with mixed (and often contradictory) evidence emerging from different studies and different methods. Methods: We discuss the significance of parameter calibration for accurate simulation of pedestrian flow through narrow exits using social force model. Based on sensitivity analyses, we show how simulated exit throughput rate can vastly differ by changing the value of certain parameters. We identify the two parameters that are most critical, and then calibrate them based on a set of experimental observations (at macro level). Using these calibrated parameters, we then re-examine three fundamental questions related to pedestrian flow at bottlenecks, (1) the relation between desired velocity and simulated egress time; (2) the effect of barricade at exits; and (3) the effect of exit in the corner versus the middle. Results: Our numerical analyses showed that, with the calibrated parameters, increasing the desired velocity in the social-force model results in monotonically shorter egress times (at a marginal rate that rapidly diminishes as the desired velocity increases). We showed that placing a panel-like barricade at exit can facilitate the outflow and reduces the egress time, but its effect depends on the widths of exit, as well as the size of the barricade and its distance to exit. We show that the positioning the exit in the corner is also effective in terms of reducing egress time, but only for very narrow exits. The benefit diminishes quickly as the exit becomes wider. Applications: These outcomes demonstrated the significance of parameter calibration for accurate simulation of crowd flows. The findings may also help to identify simple modifications that can facilitate crowd flows at narrow bottlenecks.     

Generalized Hopf bifurcation emerged from a corner in general planar piecewise smooth systems

We investigate a generalized Hopf bifurcation emerged from a corner located at the origin which is the intersection of n$n$ discontinuity boundaries in planar piecewise smooth dynamical systems with the Jacobian matrix of each smooth subsystem having either two different nonzero real eigenvalues or a pair of complex conjugate eigenvalues. We obtain a novel result that the generalized Hopf bifurcation can occur even when the Jacobian matrix of each smooth subsystem has two different nonzero real eigenvalues. According to the eigenvalues of the Jacobian matrices and the number of smooth subsystems, we provide a general method and prove some generalized Hopf bifurcation theorems by studying the associated Poincaré map.     

半线性方程ROBIN问题的角层解(英文)

本文讨论了一类半线性方程Robin边值问题.利用微分不等式理论,研究了边值问题角层解的存在性和渐近性态.     

Dilatometric studies of Y2W3O12 with added Al2O3

Y₂W₃O₁₂ exhibits negative thermal expansion along the three crystallographic directions due to the transverse thermal vibrations perpendicular to the Y-O-W linkage. It is highly hygroscopic and forms a trihydrate structure at room temperature. Dilatometric studies of Y₂W₃O₁₂ show large thermal expansion hysteresis due to large grain size and a large initial positive thermal expansion due to the removal of water molecules. Al₂O₃ has been added to Y₂W₃O₁₂ upto 10 wt% in an attempt to overcome the hygroscopicity and reduce the particle size and thereby the thermal expansion hysteresis. Thermo gravimetric, dilatometric and electron microscopic studies are presented to support these observations. Dedicated to Professor C N R Rao on his 70th birthday     

Heterostructures overgrown on GaAs corner substrates

By choosing suitable crystal facets we are able to epitaxially overgrow a precleaved corner-substrate. We are using GaAs (1 1 0)-like facets and growth conditions such that no accumulation or depletion of deposited material near the corner is observed, avoiding morphological changes at the corner during the growth process. So we achieve high-quality layer growth across the corner. With this technique we demonstrate a new type of quantum confinement structure consisting of a GaAs/AlGaAs heterostructure overgrown on top of this precleaved corner-substrate.     

Initiation of fracture at the interface corner of bi-material joints

Within the context of linear elasticity, a stress singularity of the form Hr^λ−1 may exist at the interface corner of a bi-material joint, where r is the radial distance from the corner, H is the stress intensity factor and λ−1 is the order of the singularity. Recent experimental results in the literature support the use of a critical value of the intensity factor H=H_c as a fracture initiation criterion at the interface corner. In this paper, we examine the validity and limitations of this criterion for predicting the onset of fracture in a butt joint consisting of a thin layer of an elastic-plastic adhesive layer sandwiched between two elastic adherends. The evolution of plastic deformation at the corner is determined theoretically and by the finite element method, and the solution is compared with the extent of the elastic singular field. It is shown that H_c is a valid fracture parameter if h>B(H_c/σ_Y)^1/(1−λ) where the non-dimensional constant B=100 for β=0 and B=13 for β=α/4. Here, h is the thickness of the adhesive layer, σ_Y is the uniaxial yield stress of the bulk adhesive and (α,β) are Dundurs’ parameters (Dundurs, J., J. Appl. Mech. 36 (1969) 650). Experimental results for aluminium/epoxy/aluminium and brass/solder/brass sandwiched joints are used to assess the role of plastic deformation on the validity of the failure criterion.     

Hyperbolic Distortion of Conformal Maps at Corners

We consider conformal self-maps φ of the unit disk onto simply connected domains. We assume φ is continuous in a neighborhood of a point , with φ(ζ) of modulus one, and that has a corner at φ(ζ). We prove that the modulus of the hyperbolic derivative of φ tends to a limit along certain simple curves in the disk that end at ζ non-tangentially. Moreover, we prove that the value of this limit depends only on the geometry of the corner and on the angle of approach to ζ. Our proof is based on a constructive approximation of the domain by more special domains. This research in its different stages was supported partially by MEC grants MTM2006-14449-C02-02 and MTM2006-26627-E (Acciones Complementarias), Spain; and also by “Ingenio Mathematica (i-MATH)” CSD2006-00032 (Consolider—Ingenio 2010), from MCyT, Spain; as well as by the MEC/Fulbright Fellowship 2007-0752.     

基于角点的红外与可见光图像自动配准方法

针对红外图像与可见光图像的自动配准问题,提出了一种基于图像角点特征以及仿射变换模型的方法.利用Harris因子分别在红外图像和可见光图像上检测角点,并对两幅图像进行边缘检测,得到其边缘图像.通过角点邻域在边缘图像上的相关性,实现角点的粗匹配;通过角点的细匹配,从匹配的角点中选择两对匹配最佳的点作为仿射变换的控制点,得到仿射变换模型,并对待配准图像进行仿射变换,从而实现图像配准.实验结果表明:该方法运算速度快,可以很好地完成红外与可见光图像的自动配准.     

A new auxiliary variable formulation of high-order local radiation boundary conditions: corner compatibility conditions and extensions to first-order systems

We present a new auxiliary variable formulation of high-order radiation boundary conditions for the numerical simulation of waves on unbounded domains. Retaining the flexibility of Higdon’s wave-product conditions, our approach allows arbitrary-order implementations. When applied to the scalar wave equation, the proposed method leads to balanced, symmetrizable systems of wave equations on the boundary. It can also be extended to first-order systems. Corner compatibility conditions are derived for the auxiliary variable equations. They are shown experimentally to lead to stable, accurate results.