玻壳成型过程诱导残余应力的数值预测

建立了玻壳压制成型固化过程中残余应力预测的数值模拟模型,采用平行平板间玻璃熔体的固化问题来描述成型过程中残余应力形成的机理,并假定材料为热流变简单粘弹性材料．基于板壳理论,将产品视为平板单元的组合,并采用有限元法来求解,这种方法可以象全三维计算一样一层层地计算残余应力,非常适合复杂形状的薄压制成型产品．最后通过实验比较验证了所提出的模型和方法．     

Quantization for a Ginzburg-Landau type energy related to superconductivity with normal impurity inclusion

The author applies Pohozaev identity to research the quantization for a Ginzburg-Landau type functional related to superconductivity with normal impurity inclusion. Under the different assumptions, the author obtains the quantization results by dealing with the defect on the junction.     

Dynamics of Stochastic Ginzburg-Landau Equations Driven by Colored Noise on Thin Domains

This work is concerned with the asymptotic behaviors of solutions to a class of non-autonomous stochastic Ginzburg-Landau equations driven by colored noise and deterministic non-autonomous terms defined on thin domains. The existence and uniqueness of tempered pullback random attractors are proved for the stochastic Ginzburg-Landau systems defined on $(n+1)$-dimensional narrow domain. Furthermore, the upper semicontinuity of these attractors is established, when a family of $(n+1)$-dimensional thin domains collapses onto an $n$-dimensional domain.     

MODERATE DEVIATIONS FROM HYDRODYNAMIC LIMIT OF A GINZBURG-LANDAU MODEL

The authors consider the moderate deviations of hydrodynamic limit for Ginzburg-Landau models. The moderate deviation principle of hydrodynamic limit for a specific Ginzburg-Landau model is obtained and an explicit formula of the rate function is derived.     

A model for variable thickness superconducting thin films

A model for superconductivity in thin films having variable thickness is derived through an averaging process across the film. When the film is of uniform thickness the model is identical to a model for superconducting cylinders as the Ginzburg-Landau parameter tends to . This means that all superconducting materials, whether type I or type II in bulk, behave as type-II superconductors when made into sufficiently thin films. When the film is of non-uniform thickness the variations in thickness appear as spatially varying coefficients in the thin-film differential equations. After providing a formal derivation of the model, some results about solutions of the variable thickness model are given. In particular, it is shown that solutions obtained from the new model are an appropriate limit of a sequence of averages of solutions of the three-dimensional Ginzburg-Landau model as the thickness of the film tends to zero. An application of the variable thickness thin film model to flux pinning is then provided. In particular, the results of a numerical calculation are given that show that the vortex-like structures present in superconductors are attracted to relatively thin regions.Supported by British Nuclear Electric Fuels Research Fellowship.Supported by the Department of Energy under grant number DE-FG02-93ER25172.Supported by the Department of Energy under grant number DE-FG05-93ER25175.     

The Mathematical Model and Research Progress of the Boundary Layer Flashback in Premixed Combustion北大核心CSCD

Flashback is a key problem influencing the normal operation of power equipment such as gas turbines. As one of the main mechanisms that cause flashback, the boundary layer flashback has an important effect on the design and operation of gas turbine combustors and other combustion devices. Since the critical gradient model for the boundary layer flashback was put forward by Lewis et al. in 1945, the theoretical models for the boundary layer flashback, such as the Peclet number model, the Damköhler number model and the flame angle theory, were developed one after another. However, these theoretical models still need improvements. Until now, the theoretical models for the boundary layer flashback are still in continuous development and modification. The history of the boundary layer flashback was reviewed, and the background, pertinence and shortcomings of the theoretical models were elucidated in the order of the model establishment time. In addition, the development status and research progress of the theoretical models for the boundary layer flashback in recent years were summarized, especially the progress made with new methods such as numerical simulation and statistical analysis. Further, the theoretical research direction and breakthrough points of the combustion boundary layer flashback at present and in the future were put forward. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Wave-field asymptotics in the problem of diffraction by a planar junction of thin layers and boundary-contact conditions

The problem of diffraction by a planar junction of thin layers covering a perfectly conducting substratum is considered, and its asymptotic solution is constructed. The wave field in the vicinity of the junction of the layers is described by a function of the boundary layer. Based on the asymptotics obtained, the generalized impedance boundary condition, which simulates thin layers, and the contact conditions are derived. The uniqueness of the solution of a model problem is discussed. Bibliography: 6 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 230, 1995, pp. 157–171. Original Translated by M. A. Lyalinov.     

An operator splitting approach for the interaction between a fluid and a multilayered poroelastic structure

We develop a loosely coupled fluid‐structure interaction finite element solver based on the Lie operator splitting scheme. The scheme is applied to the interaction between an incompressible, viscous, Newtonian fluid, and a multilayered structure, which consists of a thin elastic layer and a thick poroelastic material. The thin layer is modeled using the linearly elastic Koiter membrane model, while the thick poroelastic layer is modeled as a Biot system. We prove a conditional stability of the scheme and derive error estimates. Theoretical results are supported with numerical examples. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1054–1100, 2015     

Averaging in Cascade Junctions with a “Wide” Transmission Domain

We consider a boundary-value problem for the Poisson equation in a dense multilevel junction consisting of a body of the junction and many periodically situated thin rectangles connected with the body by a transmission layer with a periodic boundary. It is supposed that the rectangles have finite lengths and the transmission layer has a small width that is much greater than the period. Nonhomogeneous Neumann boundary conditions are imposed upon the boundary of the transmission layer. An addition parameter of perturbation is included in these boundary conditions. Averaged problems are constructed and convergence theorems for solution and energy integrals are proved as a function of that parameter.     

A Model for Predicting the Production Yield of Integrated Circuits

In the production of integrated circuits (I.C.s), the ability to estimate the yield of working devices, or die, is economically important. This yield depends on the distribution of material and processing defects across the surface of the wafer of devices.A number of models have been proposed to explain the distribution of point defects on I.C.s. Most of these models are based on the Poisson distribution for describing the number of defects expected on a die. These models do not inherently allow for dependence between the number of defects expected on two adjacent die.This paper develops a model for generating an I.C. defect distribution that allows for dependence in the number of defects on die that are near one another. The correlation matrix and yields of observed data are found to compare favourably with theoretical results of the proposed dependent model. Simulation results are used to compare the new dependent model to a previously proposed independent model. These dependent-model simulations show defective die clustered near each other on the wafer, a property that has been observed on real wafers. Methods of parameter and yield estimation in the dependent model are discussed.     

Global Jacobian and Γ-convergence in a two-dimensional Ginzburg-Landau model for boundary vortices

In the theory of 2D Ginzburg-Landau vortices, the Jacobian plays a crucial role for the detection of topological singularities. We introduce a related distributional quantity, called the global Jacobian that can detect both interior and boundary vortices for a 2D map u. We point out several features of the global Jacobian, in particular, we prove an important stability property. This property allows us to study boundary vortices in a 2D Ginzburg-Landau model arising in thin ferromagnetic films, where a weak anchoring boundary energy penalising the normal component of u at the boundary competes with the usual bulk potential energy. We prove an asymptotic expansion by Γ-convergence at the second order for this mixed boundary/interior energy in a regime where boundary vortices are preferred. More precisely, at the first order of the limiting expansion, the energy is quantised and determined by the number of boundary vortices detected by the global Jacobian, while the second order term in the limiting energy expansion accounts for the interaction between the boundary vortices.     

Mathematical Modeling and Simulation of Antibubble Dynamics

In this study, we propose a mathematical model and perform numerical simulations for the antibubble dynamics. An antibubble is a droplet of liquid surrounded by a thin film of a lighter liquid, which is also in a heavier surrounding fluid. The model is based on a phase-field method using a conservative Allen-Cahn equation with a space-time dependent Lagrange multiplier and a modified Navier-Stokes equation. In this model, the inner fluid, middle fluid and outer fluid locate in specific diffusive layer regions according to specific phase filed (order parameter) values. If we represent the antibubble with conventional binary or ternary phase-field models, then it is difficult to have stable thin film. However, the proposed approach can prevent nonphysical breakup of fluid film during the simulation. Various numerical tests are performed to verify the efficiency of the proposed model.     

Models of superconducting–normal–superconducting junctions

A time-dependent Ginzburg–Landau-type model of a superconducting–normal–superconducting junction is presented. The existence and the uniqueness of the solutions are proved. When the data of the model are symmetric of some kinds, the solutions turns out to be symmetric of some kinds. In this symmetric case, an approximate model with the small thickness of the normal material in the middle of the junction as coefficients of a differential system is established for the sake of numerical computations. And also the existence and the uniqueness of the solution to this approximate model are set up. © 1998 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.     

Continuum models of rarefied gas flows in problems of hypersonic aerothermodynamics

The limits of applicability of continuum flow models in the problem of the hypersonic rarefied gas flow over blunt bodies are determined by an asymptotic analysis of the Navier–Stokes equations, the numerical solution of the viscous shock layer equations and the numerical and asymptotic solution of the thin viscous shock layer equations for low Reynolds numbers. It is shown that the thin viscous shock layer model gives correct values of the skin friction coefficient and the heat transfer coefficient in the transitional to free-molecule flow regime. The asymptotic solutions, the numerical solutions obtained within the framework of different continuum models, and the results of a calculation by Direct Simulation Monte Carlo method are compared.     

High-order accurate thin layer approximations for time-domain electromagnetics, Part II: Transmission layers

We continue the development of high-order accurate thin layer approximations for time-domain electromagnetics and focus in this paper on a new family of models for thin transmission layers. The thin transmission layer approximations are valid for general isotropic materials and certain types of anisotropic materials. The models also allow the inclusion of smoothly curved layers. Both dielectric and magnetic materials can be considered. These models are non-trivial and we discuss their formulation, properties, and implementation in the context of discontinuous Galerkin methods which emerge as being particularly well suited for this family of models. The range of validity, accuracy, and stability of the models and numerical approximations is demonstrated through one- and two-dimensional examples.     

Modeling of the nonlinear vibrations of a stiffened moderately thick plate

We consider a multi-structure consisting of a plate reinforced by a thin stiffener on a portion of its boundary. The model we consider for this structure (viewed as a heterogeneous plate) is nonlinear and takes into account the transverse shear effects. Our aim is to model this junction and reproduce the effect of the thin stiffener by means of approximate boundary conditions on the junction region.     

A comparative analysis of approaches for investigating hypersonic flow over blunt bodies in a transitional regime

Hypersonic flows of a viscous perfect rarefied gas over blunt bodies in a transitional flow regime from continuum to free molecular, characteristic when spacecraft re-enter Earth's atmosphere at altitudes above 90-100 km, are considered. The two-dimensional problem of hypersonic flow is investigated over a wide range of free stream Knudsen numbers using both continuum and kinetic approaches: by numerical and analytical solutions of the continuum equations, by numerical solution of the Boltzmann kinetic equation with a model collision integral in the form of the S-model, and also by the direct simulation Monte Carlo method. The continuum approach is based on the use of asymptotically correct models of a thin viscous shock layer and a viscous shock layer. A refinement of the condition for a temperature jump on the body surface is proposed for the viscous shock layer model. The continuum and kinetic solutions, and also the solutions obtained by the Monte Carlo method are compared. The effectiveness, range of application, advantages and disadvantages of the different approaches are estimated.     

On the minimizers of the Ginzburg-Landau energy for high kappa: the axially symmetric case

The Ginzburg-Landau theory of superconductivity is examined in the case of a special geometry of the sample, the infinite cylinder. We restrict to axially symmetric solutions and consider models with and without vortices. First putting the Ginzburg-Landau parameter κ formally equal to infinity, the existence of a minimizer of this reduced Ginzburg-Landau energy is proved. Then asymptotic behaviour for large κ of minimizers of the full Ginzburg-Landau energy is analyzed and different convergence results are obtained. Our main result states that, when κ is large, the minimum of the energy is reached when there are about κ vortices at the center of the cylinder. Numerical computations illustrate the various behaviours.     

On the shape of a plastic layer compressed by parallel planes

The problem of the shape of the contour which bounds a thin layer made of an ideally plastic material is investigated. The layer is compressed by parallel planes which approach one another along a common normal (a spreading problem). New formulations of the problems are presented together with the traditional formulation. In all cases, they reduce to a Cauchy problem for non-linear evolutionary equations and the study is carried out in the class of self-similar solutions. Using the method proposed in this paper, new solutions are obtained in both the traditional and new formulations.     

Microscale mechanics for metal thin film delamination along ceramic substrates

The metal thin film delamination along metal/ceramic interface in the case of large scale yielding is studied by employing the strain gradient plasticity theory and the material microscale effects are considered. Two different fracture process models are used in this study to describe the nonlinear delamination phenomena for metal thin films. A set of experiments have been done on the mechanism of copper films delaminating from silica substrates, based on which the peak interface separation stress and the micro-length scale of material, as well as the dislocation-free zone size are predicted.