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Front Matter |
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Abstract
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Abstract
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Pure, Applied, and Industrial Mathematics: Strength Through Connections |
A. Friedman |
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Abstract
It gives me great pleasure to participate in the 60th birthday celebration of Karl-Heinz Hoffmann. Professor Hoffmann is known worldwide through his research in applied mathematics. He is also recognized for his leadership role in making connections between mathematics and the sciences, and between mathematical research in academia and industrial problems which lend themselves to mathematical modeling. I recall travelling with Professor Hoffmann to companies such as BASF and SIEMENS to discuss and identify problems of interest to these companies. I also recall attending his lectures in international conferences. In these lectures, he developed models in areas such as smart materials and phase transition, and presented innovative mathematical analysis as well as effective numerical simulations.
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On ,,-Matrices |
W. Hackbusch,B. Khoromskij,S. A. Sauter |
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Abstract
A class of matrices (.-matrices) has recently been introduced by one of the authors. These matrices have the following properties: (i) They are sparse in the sense that only few data are needed for their representation, (ii) The matrix-vector multiplication is of almost linear complexity, (iii) In general, sums and products of these matrices are no longer in the same set, but their truncations to the .-matrix format are again of almost linear complexity, (iv) The same statement holds for the inverse of an .-matrix..The term “almost linear complexity” used above means that estimates are given by .(.log..). The logarithmic factor can be avoided by a further improvement, which is described in the present paper. We prove that the storage requirements and the cost of the matrix-vector multiplication is strictly linear in the dimension ., while still (full) system matrices of the boundary element method can be approximated up to the discretization error.
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On the Stability of Microstructure for General Martensitic Transformations |
M. Luskin |
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Abstract
We describe a general theory for the stability of the laminated microstructure for martensitic crystals. Our theory has been applied to the orthorhombic to monoclinic transformation, the cubic to tetragonal transformation, the tetragonal to monoclinic transformation, and the cubic to orthorhombic transformation.
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Dissipative Evolution of Microstructure in Shape Memory Alloys |
T. Roubíček |
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Abstract
This contribution surveys models for evolution of twinning and inelastic response of crystallic materials due to martensitic phase transformations. Then a focus is devoted to a “mesoscopical” evolution model in a scalar situation based on a simple 2nd-order evolution variational inequality. A rate-independent dissipation mechanism is involved and shown by computer experiments to make possible a modelling of inelastic response of crystallic materials like shape-memory effects.
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A Phase Diagram of Integration and Segregation in a Population of Hawks and Doves |
I. Müller |
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Abstract
The contest strategy of a population may be used to define a population energy as a function of the composition of the population. The minimum of such an energy corresponds to the composition of the evolutionarily stable strategy which is approached by natural selection..If, however, the composition is fixed, the population may alter its strategy. If it has two strategies to choose from it will choose the one that is energetically more favourable. This choice can mean an integrated or a segregated population depending on the value of the resource for which different groups of the population compete.
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Existence and Asymptotic Behaviour in Phase-Field Models with Hysteresis |
P. Krejčí,J. Sprekels,S. Zheng |
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Abstract
Phase field systems as mathematical models for phase transitions have drawn increasing attention in recent years. However, while being capable of capturing many of the experimentally observed phenomena, they give only a simplified picture of intrinsic hysteresis effects occurring in phase transition processes. To overcome this shortcoming, the first two authors have recently proposed a new approach in a series of papers which is based on the mathematical theory of hysteresis operators developed in the past fifteen years, and obtained results on existence, uniqueness and regularity of solutions for a class of phase-field systems with hysteresis that includes among others the relaxed Stefan problem and hysteretic analogues of the models due to Caginalp and Penrose-Fife for nonconserved order parameters with zero interfacial energy. Here, we give a brief account of the method, with a special focus on new results obtained by the authors of the present paper and related to the asymptotic behaviour of the system as . → +∞.
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On a New Class of Nonlocal Unilateral Problems in Thermomechanics |
J.-F Rodrigues |
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Abstract
In this study we consider the equilibrium of an elastic membrane over a rigid obstacle subjected to a temperature field strongly depending on the contact with the obstacle. This problem can be formulated as an unilateral problem coupled with a heat diffusion equation with a discontinuous function depending on the contact region. It corresponds to an interior free boundary problem in thermoelasticity of different type with respect to the boundary unilateral contact problem, or the thermal Signorini problem, considered in [2] with mollification of the discontinuous heat source.
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Dynamics of Diffusive Phase Transitions Driven by Coupled Mechanisms |
M. Niezgódka |
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Abstract
The paper gives an overview of basic set-ups for modelling dynamic phase separation phenomena in binary systems governed by various driving mechanisms coupled with diffusion. In particular, non-isothermal situations axe treated and two-scale systems with conserved macroscopic order parameters while including non-conserved mesoscopic components are considered.
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Free Boundary Problems and their Stabilisation |
J. R. Ockendon |
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Abstract
Free boundary problems (FBPs) are those in which some partial differential equations have to be solved in a region with a boundary whose position is to be found as part of the problem. This article will briefly review some of the theory and folklore concerning such problems and their stabilisation with the aim of highlighting the major open problems that currently confront mathematicians working in the area. It is a subject with which Prof. Hoffmann has been intimately involved over the past three decades and it is a pleasure to acknowledge the contributions he has made to our understanding of problems ranging from the Stefan problem, which created so much excitement in the 1970’s, to FBPs in superconductivity which are currently ”all the rage”. Of course I must also include Prof. Hoffmann’s involvement with the more political applications of ”les frontières libres”.
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A New Model for the Dynamics of Dispersions in a Batch Reactor |
A. Fasano,F. Rosso |
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Abstract
A new model for coalescence and breakage of liquid-liquid dispersion is presented. The main features are: (i) the introduction of an efficiency factor which controls the time rate of the various processes affecting the size distribution function of droplets, (ii) a new effect — that we call volume scattering — which is consistent with the experimentally observed circumstance of the existence of a top size limit for droplets depending on the general dynamical conditions. The model is proved to be mathematically and physically correct by proving existence and uniqueness of a regular solution to the Cauchy problem.
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Optimal Control Problems for the Navier-Stokes Equations |
A. Fürsikov,M. Gunzburger,L. S. Hou,S. Manservisi |
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Abstract
Optimal boundary control problems and related inhomogeneous boundary value problems for the Navier-Stokes equations are considered. The control is the data in the Dirichlet boundary condition. The objective functional is the drag on a body immersed in the fluid. The size of the control is limited through the application of explicit bounds or through penalization of the drag functional. A necessary step in the analysis of both the control problems and the related boundary value problems is the characterization of traces of solenoidal vector fields. Such characterization results are given in two and three dimensions as are existence results about solutions of the boundary value problems. Results about the existence of solutions of the optimal control problem are given in the two-dimensional case, as are results concerning the numerical approximation of optimal solutions.
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Structural Identification of Nonlinear Coefficient Functions in Transport Processes through Porous M |
P. Knabner,B. Igler |
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Abstract
Mathematical models provide the starting point for the simulation of complex processes, which arise in the natural and engineering sciences. Characteristic properties of the considered systems are represented by model parameters or coefficients. These have to be determined by experiments. If the coefficients are not measured directly, as direct measurements are not possible or do not lead to satisfying results, numerical identification procedures have to be applied.
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Abstract
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Development of Innovative Osteosynthesis Techniques by Numerical and In Vitro Simulation of the Mast |
A. Neff,A. Kuhn,H. Schieferstein,A. M. Hinz,E. Wilczok,G. Mühlberger,H.-F. Zeilhofer,R. Sader,H. Dep |
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Abstract
Maxillofacial surgery still faces a considerable number of biomechanical questions. An attempt to cope with the complexity of the masticatory system is introduced: synchronizing numerical simulation and in vitro experiments for mutual validation in order to clarify some events out of the vast number of unknown variables in the chewing process, such as muscle forces, bone stress and strain. This interdisciplinary project can be considered a promising approach based on the latest technology in medicine, mathematics and mechanical engineering. In addition, the application of adaptive materials will help to optimize maxillofacial surgery.
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Rate Independent Hysteresis |
M. Brokate |
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Abstract
We outline some basic features of the mathematical theory of hysteresis operators and indicate connections to applications, in particular magnetics and mechanics.
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The Oxidation Process of Silicon |
W. Merz |
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Abstract
In electronic devices the electrical insulation of different areas is often achieved by layers of silicon-dioxide. These are usually created by exposing the silicon wafers at process temperatures between 700–1200°C to a gas flow containing oxygen or to a stream. Using different oxygen isotrops tracer experiments have shown that the new oxide is created at the interface between silicon and silicon-dioxide.
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The Growth of Vapor Deposited Amorphous Zr65Al7.5Cu27.5-Alloy Films: Experiment and Simulation |
S. G. Mayr,M. Moske,K. Samwer |
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Abstract
The surface structures of amorphous Zr.Al.Cu.-alloy films prepared by ultra high vacuum physical vapor deposition are investigated with scanning tunneling microscopy to identify the major surface mechanisms for amorphous film growth. A fourier analysis of the STM images shows that curvature induced surface diffusion and a non-smoothing surface mechanism is present. Numerical simulations using a Monte-Carlo and a continuum model which includes adatom concentration triggered surface diffusion as additional coarsing mechanism are in excellent agreement with the experimental results.
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Modelling, Simulation, and Control of Electrorheological Fluid Devices |
R. H. W. Hoppe,G. Mazurkevitch,U. Rettig,O. von Stryk |
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Abstract
The new generation of electrorheological fluids (ERFs) offers a wide range of applicability in fluid mechatronics with automotive ERF devices such as ERF shock absorbers mentioned at first place. The optimal design of such tools requires the proper modelling and simulation both of the operational behaviour of the device itself as well as its impact on the dynamics of the complete vehicle. This paper addresses these issues featuring an extended Bingham fluid model and its numerical solution as well as substitutive models of viscoeleastic-plastic system behaviour. Also control issues for optimal semi-active suspension of vehicles with controllable ERF shock absorbers are discussed.
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发表于 2025-3-21 17:22:54
