Pattern Formation of Dunes

Dunes are aerodynamic instabilities of a mobile ground. Only recently, the equations of motion of a free granular surface born by air and gravity have been established. I will present the equations and analyze their stability. A numerical solution gives very good quantitative agreement with field measurements. As function of wind velocity and the amount of sand, various patterns are reproduced. I will discuss in particular barchan dunes that under certain conditions behave like solitons and can in other cases breed offspring. Also practical applications like protection against desertification will be discussed.     

Periodic Solutions of an Autonomous Reaction-Diffusion System—A Model System

We describe the dynamics of an autonomous system of two reaction-diffusion equations which can be looked at as a model system for more general reaction-diffusion systems. In our system all solutions tend to zero or to (finitely many) periodic orbits which can be fully described—including their stability properties. Furthermore, we construct invariant sets for the period map and show how a new invariant called torsion number is related to our model system.     

Particle transport method for convection problems with reaction and diffusion

The paper is devoted to the further development of the particle transport method for the convection problems with diffusion and reaction. Here, the particle transport method for a convection–reaction problem is combined with an Eulerian finite‐element method for diffusion in the framework of the operator‐splitting approach. The technique possesses a special spatial adaptivity to resolve solution singularities possible due to convection and reaction terms. A monotone projection technique is used to transfer the solution of the convection–reaction subproblem from a moving set of particles onto a fixed grid to initialize the diffusion subproblem. The proposed approach exhibits good mass conservation and works with structured and unstructured meshes. The performance of the presented algorithm is tested on one‐ and two‐dimensional benchmark problems. The numerical results confirm that the method demonstrates good accuracy for the convection‐dominated as well as for convection–diffusion problems. Copyright © 2007 John Wiley & Sons, Ltd.     

Control strategies for timestep selection in finite element simulation of incompressible flows and coupled reaction–convection–diffusion processes

We propose two timestep selection algorithms, based on feedback control theory, for finite element simulation of steady state and transient 2D viscous flow and coupled reaction–convection–diffusion processes. To illustrate performance of the schemes in practice, we solve Rayleigh–Benard–Marangoni flows, flow across a backward‐facing step, unsteady flow around a circular cylinder and chemical reaction systems. Numerical experiments confirm that the feedback controllers produce in some cases a very smooth stepsize variation, suggesting that robust control algorithms are possible. These experiments also show that parameter selection can improve timesteps when co‐ordinated with the convergence control of non‐linear iterations. Further, computational cost of the selection procedures is negligible, since they involve only storing a few extra vectors, computation of norms and evaluation of kinetic energy. Copyright © 2004 John Wiley & Sons, Ltd.     

Fully computable a posteriori error bounds for stabilised FEM approximations of convection–reaction–diffusion problems in three dimensions

Fully computable upper bounds are developed for the discretisation error measured in the natural (energy) norm for convection–reaction–diffusion problems in three dimensions. The upper bounds are genuine upper bounds in the sense that the numerical value of the estimated error exceeds the actual numerical value of the true error regardless of the coarseness of the mesh or the nature of the data for the problem. All constants appearing in the bounds are fully specified. Examples show the estimator to be reliable and accurate even in the case of complicated three‐dimensional problems. Copyright © 2013 John Wiley & Sons, Ltd.     

Uniqueness of the Bistable Traveling Wave for Mutualist Species

For a system of reaction–diffusion equations that models the interaction of n mutualist species, the existence of the bistable traveling wave solution has been proved where the nonlinear reaction terms possess a certain type of monotonicity. However the problem of whether there can be two distinct traveling waves remains open. In this paper we use a homotopy approach incorporated with the Liapunov–Schmidt method to show that the bistable traveling wave solution is unique. Our method developed in this paper can also be applied to study the existence and uniqueness of traveling wave solutions for some competition models.     

组合超弹性材料中的空穴生成与增长

本文研究了一种组合不可压超弹性材料圆柱体中空穴的生成与增长问题，得到了这种材料受表面均布拉伸死荷载和轴向拉压共同作用下空穴生成问题的解析解，得到了不同组合情况下圆柱体中空穴生成时的临界载荷及分叉曲线，发现组合材料可以发生右分叉，也可以发生左分叉；给出了空穴生成后的应力分布，并讨论了所存在的应力间断和应力集中问题；通过能量比较分析了解的稳定性，讨论了发生右分叉或左分叉的条件，并分析了材料中预存微孔的增长情况。     

Existence of Standing Pulse Solutions to an Inhomogeneous Reaction–Diffusion System

We prove the existence of locally unique, symmetric standing pulse solutions to homogeneous and inhomogeneous versions of a certain reaction–diffusion system. This system models the evolution of photoexcited carrier density and temperature inside the cavity of a semiconductor Fabry–Pérot interferometer. Such pulses represent the fundamental nontrivial mode of pattern formation in this device. Our results follow from a geometric singular perturbation approach, based largely on Fenichel's theorems and the Exchange Lemma.     

Order and Pattern Formation in Psychotherapy

In an empirical analysis of the dynamics of psychotherapy processes, concepts and tools from self-organization theory are applied. Our focus is on pattern formation in the therapy system, i.e. the system constituted by the interaction dynamics of therapist and patient. The hypothesis of pattern formation explored is based on data sets of 28 psychotherapy courses (10 behavioral, 3 client-centered, 9 heuristic, 6 schema-oriented; 40 to 90 weekly sessions). Patients' and therapists' therapy session records are analyzed (33 variables addressing various aspects of the therapeutic relationship, of progress within and outside the therapy setting). Multivariate methods are implemented to test the key hypothesis of self-organization theory, namely the reduction of degrees of freedom of a system. Consistent with this hypothesis, a significant reduction of degrees of freedom is found when the initial and final sessions of the therapies are compared. Correspondingly, Landsberg order increased significantly in the course of therapies. Given these findings, the explorative question of how this self-organizing property relates to therapy outcome is investigated. We find a significant positive association with various outcome measures, such as: therapist's and client's evaluations of success (direct change measures), feelings of guilt, anxiety, social potence, depression (pre-post effect sizes), and others. These results suggest that order is related to therapy outcome. In our interpretation, order is a dynamical attribute of the therapeutic alliance to be considered as a promising therapy process variable.     

光机械式红外探测器中镜面弯曲对探测灵敏度的影响(英文)

光学读出式红外成像技术是近年来研究的热点,本文讨论了镜面弯曲对光学检测灵敏度的影响。由双材料微悬臂梁组成的非致冷焦平面阵列通过体刻蚀工艺加工而成,由于残余应力的影响,制成的焦平面阵列将会发生弯曲,应力导致的镜面弯曲将会降低光学探测灵敏度。本文通过傅立叶光学模拟了镜面弯曲对光学探测灵敏度的影响,并通过实验验证了该模型。实验和模拟结果表明,在镜面曲率为0 .1mm-1时,光学探测灵敏度将会降低到理想情况的40 %。最后我们用这个模型评价了通过表面修饰来提高光学性能的效果。     

The Effect of Chemical Equilibrium on the Formation of Stable Stratification

The formation of a stable stratification, rather than a uniformly mixed state, is shown to depend critically on the equation of state (EOS) or mixing rule for the density as a function of the solution constitution. For instance, ideal solutions can form any stable stratification at hydrostatic equilibrium, although molecular diffusion will eventually make the concentration of solute uniform. Several other types of EOS are considered at hydrostatic equilibrium, resulting in two and three layer stratifications. In the presence of convective mixing, however, the EOS serves only as a guide, since the dynamics of, for example, turbulent dispersion, significantly alter the formation of stratifications. The case of recirculating flows, however, can be simply treated and results in two layer stratifications for an EOS which is superjacent to the ideal solution. The example of stratification formation in a Burt separator is given.     

光机械式红外探测器中镜面弯曲对探测灵敏度的影响

光学读出式红外成像技术是近年来研究的热点，本文讨论了镜面弯曲对光学检测灵敏度的影响。由双材料微悬臂梁组成的非致冷焦平面阵列通过体刻蚀工艺加工而成，由于残余应力的影响，制成的焦平面阵列将会发生弯曲，应力导致的镜面弯曲将会降低光学探测灵敏度。本文通过傅立叶光学模拟了镜面弯曲对光学探测灵敏度的影响，并通过实验验证了该模型。实验和模拟结果表明，在镜面曲率为0．1mm-1时，光学探测灵敏度将会降低到理想情况的40％。最后我们用这个模型评价了通过表面修饰来提高光学性能的效果。     

利用激光剪切干涉术和塔宝效应获得实时等曲率条纹

本文研究了一种新的获得镜状表面试件实时等曲率条纹的方法。这种方法是利用激光光栅剪切干涉仪和塔宝效应实现的。曲率测量灵敏度达每条纹10~(-6)/mm。本文提供了理论分析和实验结果。     

考虑范德华力曲率效应的双壁碳纳米管外压屈曲

针对双壁碳纳米管外压屈曲问题,研究了层间范德华力的曲率效应对临界外压的影响。应用弹性双层圆柱壳模型,考虑层间范德华力不仅与层间距有关而且与挠度曲率的变化有关,导出了外压屈曲临界压力解析公式。计算得出在不同半径、不同长细比下,外压屈曲临界压力的数值结果,并与经典壳的结果和忽略范德华力曲率效应的结果做了比较。结果显示,对于小半径的双壁碳纳米管曲率效应对外压屈曲有效明显的影响。     

Chemically Reacting Flows and Continuous Flow Stirred Tank Reactors: The Large Diffusivity Limit

In this paper we consider the relationship between chemically reacting flows and continuous flow stirred tank reactors (CSTR). In particular, we show that in the limit as the chemical and thermal diffusivities go to infinity, the solutions of the reacting flow PDE approach the solutions to the CSTR ODE. We further show that the global attractors for the reacting flow come arbitrarily close top the CSTR global attractor as the diffusivities go to infinity. An important feature of the reacting flow model we use is Robin–Neumann boundary conditions for the chemistry and temperature, which we use to mimic the CSTR inflow and outflow terms. The key in our analysis is an examination of how the Laplacian with Robin–Neumann boundary conditions converges to the Laplacian with Neumann boundary conditions as the diffusivity goes to infinity.     

Effect of Streamline Curvature on Intensity of Streamwise Vortices in the Mixing Layer of Supersonic Jets

The structure of supersonic nonisobaric jets with Mach numbers M_a = 1 and 2 is considered experimentally to find the effect of streamline curvature on the evolution of streamwise vortices in the mixing layer. The spatial development of steady streamwise vortices in the mixing layer of supersonic jets is considered. A method for generation of steady streamwise vortices by applying microroughness elements of controlled size onto the inner surface of the nozzle is developed. Radial profiles and azimuthal variations of total pressure are obtained; the mixinglayer thickness and the curvature of streamlines in supersonic jets are determined. A significant effect of microroughness elements of prescribed shape located on the nozzle surface on the behavior of total pressure in the mixing layer of supersonic jets, as compared to natural disturbances, is obtained.     

正交曲线坐标系下紊流数学模型的曲率修正

考虑弯曲边界曲率效应对水流水力特性的影响,建立了正交曲线坐标系下的素流数学模型。通过计算实例说明,该数学模型能够很好地帷有复杂边界的流线弯曲水流的水力特性。     

Subcritical Growth of an Internal Circular Crack in an Aging Viscoelastic Laminated Composite

Delayed fracture of a laminated composite under tensile loads applied at infinity is studied. The composite consists of alternating elastic and aging viscoelastic layers and contains an internal penny-shaped mode I macrocrack located in parallel to the layers. A modified Leonov–Panasyuk–Dugdale crack model and the critical crack-tip opening criterion constitute a fracture model. The subcritical crack growth equations are derived using the Volterra principle and the method of operator continued fractions. The laws governing delayed fracture are studied for a specific composite material     

列车编组对桥梁振动响应影响的试验研究

通过对两座桥梁振动测试结果的分析，发现列车编组对桥梁振动响应很有影响，且这一现象过去常常被忽略。本文详细研究了列车编组与桥梁横向振动响应之间的关系，同时还就一座桥梁加固后的试验结果进行分析，指出用改善列车编组的方法提高桥梁动态性能的必要性和可行性。     

Development of a convection–diffusion‐reaction magnetohydrodynamic solver on non‐staggered grids

This paper presents a convection–diffusion‐reaction (CDR) model for solving magnetic induction equations and incompressible Navier–Stokes equations. For purposes of increasing the prediction accuracy, the general solution to the one‐dimensional constant‐coefficient CDR equation is employed. For purposes of extending this discrete formulation to two‐dimensional analysis, the alternating direction implicit solution algorithm is applied. Numerical tests that are amenable to analytic solutions were performed in order to validate the proposed scheme. Results show good agreement with the analytic solutions and high rate of convergence. Like many magnetohydrodynamic studies, the Hartmann–Poiseuille problem is considered as a benchmark test to validate the code. Copyright © 2004 John Wiley & Sons, Ltd.