Reitich, FernandoOverview
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Fernando Reitich
Threephase boundary motions under constant velocities
by F Reitich
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Book
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1 edition published in 1994 in English and held by 1 WorldCat member library worldwide Abstract: "In this paper we deal with the dynamics of material interfaces such as solidliquid, grain or antiphase boundaries. We concentrate on the situation in which these internal surfaces separate three regions in the material with different physical attributes (e.g. grain boundaries in a polycrystal). The basic twodimensional model proposes that the motion of an interface [gamma][subscript ij] between regions i and j (i, j = 1,2,3, i [not =] j) is governed by the equation V[subscript ij] = [mu subscript ij] (f[subscript ij]k[subscript ij] + F[subscript ij]). (0.1) Here V[subscript ij], k[subscript ij], [mu subscript ij] and F[subscript ij] denote, respectively, the normal velocity, the curvature, the mobility and the surface tension of the interface and the numbers F[subscript ij] stand for the (constant) difference in bulk energies. At the point where the three phases coexist, local equilibrium requires that the curves meet at prescribed angles. (0.2) In case the material constants f[subscript ij] are small, f[subscript ij] = [bracket over epsilon f subscript ij] and [epsilon] <<1, previous analyses based on the parabolic nature of the equations (0.1) do not provide good qualitative information on the behavior of solutions. In this case it is more appropriate to consider the singular case with f[subscript ij] = 0. It turns out that this problem, (0.1) with f[subscript ij] = 0, admits infinitely many solutions. Here, we show that a unique solution, 'the vanishing surface tension (VST) solution', is selected by letting [epsilon] > 0. Furthermore, we introduce the concept of weak viscosity solution for the problem with [epsilon] = 0 and show that the VST solution coincides with the unique weak solution. Finally, we give examples showing that, in several cases of physical relevance, the VST solution differs from results proposed previously."
Numerical solution of diffraction problems : a method of variation of boundaries
by Oscar P Bruno
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Book
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1 edition published in 1993 in English and held by 1 WorldCat member library worldwide Abstract: "We present a new numerical method for the solution of the problem of diffraction of light by a doubly periodic surface. This method is based on a high order rigorous perturbative technique, whose application to singly periodic gratings was treated in the first two papers of this series. We briefly discuss the theoretical basis of our algorithm, namely, the property of analyticity of the diffracted fields with respect to variations of the interfaces. While the algebraic derivation of some basic recursive formulae is somewhat involved, it results in expressions which are easy to implement numerically. We present a variety of numerical examples (for bisinusoidal gratings), in order to demonstrate the accuracy exhibited by our method as well as its limited requirements in terms of computing power. Generalization of our computer code to crossed gratings other than bisinusoidal is in principle immediate, but the full domain of applicability of our algorithm remains to be explored. Comparison with results presented previously for actual experimental configurations shows a substantial improvement in the resolution of our numerics over that given by other methods introduced in the past."
Analysis of multiple scattering iterations for highfrequency scatering problems : I: the twodimensional case
by Fatih Ecevit
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1 edition published in 2009 in English and held by 1 WorldCat member library worldwide We present an analysis of a recently proposed integralequation method for the solution of highfrequency electromagnetic and acoustic scattering problems that delivers errorcontrollable solutions in frequencyindependent computational times. Within single scattering configurations the method is based on the use of an appropriate ansatz for the unknown surface densities and on suitable extensions of the method of stationary phase. The extension to multiplescattering configurations, in turn, is attained through consideration of an iterative (Neumann) series that successively accounts for further geometrical wave reflections. As we show, for a collection of twodimensional (cylindrical) convex obstacles, this series can be rearranged into a sum of periodic orbits (of increasing period), each corresponding to contributions arising from waves that reflect off a fixed subset of scatterers when these are transversed sequentially in a periodic manner. Here, we analyze the properties of these periodic orbits in the highfrequency regime, by deriving precise asymptotic expansions for the currents'' (i.e. the normal derivative of the fields) that they induce on the surface of the obstacles. As we demonstrate these expansions can be used to provide accurate estimates of the rate at which their magnitude decreases with increasing number of reflections, which defines the overall rate of convergence of the multiplescattering series. Moreover, we show that the detailed asymptotic knowledge of these currents can be used to accelerate this convergence and, thus, to reduce the number of iterations necessary to attain a prescribed accuracy
Dynamic Simulation of the Temporal Response of Microstructure Formation in Magnetorheological Fluids
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1 edition published in 1999 in English and held by 1 WorldCat member library worldwide Efficient numerical simulations of microstructure development in magnetorheological (MR) fluids are conducted. The simulations, which are based upon a fast multipole algorithm, treat the magnetic inclusions as twodimensional continuum magnetic entities. The development of microstructure is quantified by computing and recording the time evolution of the effective permeability of composite fluid. Such a principle has been previously exploited for the experimental measurements of microstructure development (Jolly, Bender and Mathers, ERMR'97, Yonezawa, Japan 1997). As was observed experimentally, numerical simulations reveal the evolution of microstructure to be multimodal in nature. Unlike the experiments, the numerical simulations afford us the ability to observe the physical mechanisms associated with various modes
Maxwell equations in a nonlinear Kerr medium
by Oscar P Bruno
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Book
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1 edition published in 1993 in English and held by 1 WorldCat member library worldwide Abstract: "In this paper we present an exact calculation of the transfer function associated with the nonlinear FabryPerot resonator. While our exact result cannot be evaluated in terms of elementary functions, it does permit us to obtain a number of simple approximate expressions of various orders of accuracy. In addition, our derivation yields criteria of validity for the approximate formulae. Our approach is to be compared with others in which approximations are introduced in the model itself, either through the equations or through the boundary conditions. Our lowest order approximate formula turns out to be identical, interestingly, with the result obtained from the slowly varying envelope approximation (SVEA). Thus, our validity criteria apply to the SVEA result, and predict well its domain of validity and its breakdown for short wavelengths and for very high intensities and nonlinearities. The simple higher order formulae we present provide improved estimations in such regimes."
Electromagnetic Scattering
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1 edition published in 2001 in English and held by 1 WorldCat member library worldwide The problems and techniques addressed under the present contract deal with issues of analysis and computation in electromagnetics. The primary goal consists of the development of efficient numerical tools for the prediction of scattered fields in a number of practical configurations. For this, substantial effort will be devoted to the extension and enhancement 0 the Method of Variation of Boundaries (MVB). Specific objectives in connection with MVB include: (1) advancement and implementation of algorithmic improvements for very highorder calculations; (2) application to the solution of eigenvalue problems (related to cavities, resonators and waveguides); to the calculation of electromagnetic scattering from damaged objects and rough terrain; and to inverse scattering problems. (3) Concurrent with these endeavors the program will pursue the incorporation of the boundaryvariation approach in more classical computational techniques, such as the finiteelement methods (FEM). A first instance of such interactions will be sought through the implementation of highorder boundary perturbation approximations to computational radiation conditions (typically imposed on separable geometries). To enable and enhance such applications, the plan includes the development of new (highorder) discontinuous Galerkin (DG) finite element approach to electromagnetic scattering calculations which is expected to provide an advantageous setting for adaptivity and parallelization. Alternative highorder methods (e.g., based on integral equation formulations) will also be considered
A new approach to the solution of problems of scattering by bounded obstacles
by Oscar P Bruno
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1 edition published in 1995 in English and held by 1 WorldCat member library worldwide
Parameter identification in reactiondiffusion models
by University of Minnesota
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Book
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1 edition published in 1991 in English and held by 1 WorldCat member library worldwide
Evaluation of HighFrequency Electromagnetic Scattering via HighOrder MultipleScattering Integral Asymptotics
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1 edition published in 2003 in English and held by 1 WorldCat member library worldwide Report developed under STTR contract for topic AFOlTOO9. We introduced a new algorithm for the numerical solution of problems of electromagnetic or acoustic scattering in the highfrequency regime. This algorithm combines the use of an ansatz for the unknown density in a boundary integral formulation of the scattering problem with an extension of the ideas of the method of stationary phase. In particular, we obtained numerical results illustrating the high order convergence of our algorithm as well as its asymptotically bounded computational cost as the frequency increases
Local existence and uniqueness of solutions of the Stefan problem with surface tension and kinetic undercooling
by University of Minnesota
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Book
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1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
Rapidly stretching plastic jets: the linearized problem
by University of Minnesota
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Book
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1 edition published in 1988 in English and held by 1 WorldCat member library worldwide
The overall elastic energy of polycrystalline martensitic solids
by University of Minnesota
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Book
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1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
Mathematical modeling in industry
by University of Minnesota
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Book
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1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
A highorder perturbation approach to profile reconstruction. I: perfectly conducting gratings
by University of Minnesota
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Book
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1 edition published in 1997 in English and held by 1 WorldCat member library worldwide
Computational Electromagnetics
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1 edition published in 2004 in English and held by 1 WorldCat member library worldwide The objective of the effort sponsored by the present contract consists of the development of a suite of numerical algorithms, founded on a rigorous mathematical basis for the accurate and efficient prediction of electromagnetic scattering returns. The techniques are based on Integral equations, perturbation theory and high frequency approximations; general numerical methods will be sought through suitable combinations of these
A hyperbolic inverse problem arising in the evolution of combustion aerosol
by University of Minnesota
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Book
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1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
Solution of a boundary value problem for Helmholtz equation via variation of the boundary into the complex domain
by University of Minnesota
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Book
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1 edition published in 1991 in English and held by 1 WorldCat member library worldwide
Analysis of a mathematical model for the growth of tumors
by University of Minnesota
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Book
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1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
The Stefan problem with small surface tension
by University of Minnesota
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Book
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1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
Partial Differential Equations from the Materials Sciences: Analysis and Computation
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1 edition published in 1998 in English and held by 1 WorldCat member library worldwide This report describes accomplishments in the areas of electromagnetic scattering and smart materials achieved under Grant No. F496209510113. With regards to problems of wave propagation, advances in the development of highorder perturbation methods are reported. These include the derivation and coding of algorithms for the numerical solution of the scalar and vector forward scattering problems for two and threedimensional configurations and the formulation of corresponding approaches to inverse scattering calculations and to the estimation of normal and quasinormal cavity modes. Concurrent achievements in the study of smart materials are also recounted here. They include the development of nonlinear homogenization theories intended to capture overall elastic behaviors (e.g., of shapememory alloys, SMA), or magnetic and rheological responses (such as those of magnetorheological fluids, MRF). The latter project was undertaken in collaboration with scientists at the Lord Corporation, the worldwide leader in MRF technology, and was geared towards the incorporation of advanced mathematical modeling and simulations into the design of MRF more
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Reitich, Fernando
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