Oscar P. Bruno

Transient heat transfer effects on the pseudoelastic behavior of shape-memory wires

Abstract Experimental results of a displacement-controlled elongation of a shape-memory wire of nickel-titanium are presented. It is observed that the hysteretic strain-stress curves depend strongly on the strain rates at which the wire is extended. A theoretical model is proposed to explain this phenomenon. This model couples the fully time-dependent heat transfer in the wire to its quasi-static mechanical behavior through the temperature dependence of the transformation stress of the alloy. It accounts quantitatively for experimentally observed changes in the pseudoelastic hysteresis. The model presented here is different from others proposed in the literature, as it does not make use of a kinetic relation and accounts for the observed changes in the pseudoelastic hysteresis without parameter fitting. The results show that a model consisting of a single moving austenite-martensite interface is sufficient to predict the response of the wire over several decades of strain rate.

Numerical solution of diffraction problems: a method of variation of boundaries

Previously ( Proc. R. Soc. Edinburgh122A, 317– 340, 1992) we established that solutions to problems of diffraction of light in a periodic structure behave analytically with respect to variations of the interface. We present an algorithm based on this observation for the numerical solution of the problem. The principal component of the algorithm is a simple recursive formula for the derivatives of the efficiencies with respect to the height of the grating. A conformal mapping mechanism is introduced to enhance the convergence of the series. This allows us to deal with the types of profile and wavelength usually considered in practice. To illustrate our method, we give numerical results for sinusoidal and echelette gratings.

Prescribed error tolerances within fixed computational times for scattering problems of arbitrarily high frequency: the convex case

We present a new algorithm for the numerical solution of problems of electromagnetic or acoustic scattering by large, convex obstacles. 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. We include numerical results illustrating the high-order convergence of our algorithm as well as its asymptotically bounded computational cost as the frequency increases.

On the magneto-elastic properties of elastomer–ferromagnet composites

Abstract We study the macroscopic magneto-mechanical behavior of composite materials consisting of a random, statistically homogeneous distribution of ferromagnetic, rigid inclusions embedded firmly in a non-magnetic elastic matrix. Specifically, for given applied elastic and magnetic fields, we calculate the overall deformation and stress–strain relation for such a composite, correct to second order in the particle volume fraction. Our solution accounts for the fully coupled magneto-elastic interactions; the distribution of magnetization in the composite is calculated from the basic minimum energy principle of magneto-elasticity.

Numerical solution of diffraction problems: a method of variation of boundaries. III. Doubly periodic gratings

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 [ J. Opt. Soc. Am. A10, 1168, 2307 ( 1993)]. 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 formulas is somewhat involved, it results in expressions that 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.

Solution of a boundary value problem for the Helmholtz equation via variation of the boundary into the complex domain

In this paper we deal with the problem of diffraction of electromagnetic waves by a periodic interface between two materials. This corresponds to a two-dimensional quasi-periodic boundary value problem for the Helmholtz equation. We prove that solutions behave analytically with respect to variations of the interface. The interest of this result is both theoretical – the legitimacy of power series expansions in the parameters of the problem has indeed been questioned – and, perhaps more importantly, practical: we have found that the solution can be computed on the basis of this observation. The simple algorithm that results from such boundary variations is described. To establish the property of analyticity of the solution for the grating with respect to the height δ, we present a holomorphic formulation of the problem using surface potentials. We show that the densities entering into the potential theoretic formulation are analytic with respect to variations of the boundary, or, in other words, that the integral operator that results from the transmission conditions at the interface is invertible in a space of holomorphic functions of the variables ( x , y , δ). This permits us to conclude, in particular, that the partial derivatives of u with respect to δ at δ = 0 satisfy certain boundary value problems for the Helmholtz equation, in regions with plane boundaries, which can be solved in a closed form.

Numerical solution of diffraction problems: a method of variation of boundaries. II. Finitely conducting gratings, Padé approximants, and singularities

We recently introduced a method of variation of boundaries for the solution of diffraction problems [ J. Opt. Soc. Am. A10, 1168 ( 1993)]. This method, which is based on a theorem of analyticity of the electromagnetic field with respect to variations of the interfaces, has been successfully applied in problems of diffraction of light by perfectly conducting gratings. We continue our investigation of diffraction problems. Using our previous results on analytic dependence with respect to the grating groove depth, we present a new numerical algorithm that applies to dielectric and metallic gratings. We also incorporate Pade approximation in our numerics. This addition enlarges the domain of applicability of our methods, and it results in computer codes that can predict more accurately the response of diffraction gratings in the resonance region. In many cases results are obtained that are several orders of magnitude more accurate than those given by other methods available at present, such as the integral or differential formalisms. We present a variety of numerical applications, including examples for several types of grating profile and for wavelengths of light ranging from microwaves to ultraviolet, and we compare our results with experimental data. We also use Pade approximants to gain insight into the analytic structure and the spectrum of singularities of the fields as functions of the groove depth. Finally, we discuss some connections between Pade approximation and another summation mechanism, enhanced convergence, which we introduced in the earlier paper. It is argued that, provided that certain numerical difficulties can be overcome, the performance of our algorithms could be further improved by a combination of these summation methods.

Surface scattering in three dimensions: an accelerated high-order solver

We present a new algorithm for the numerical solution of problems of acoustic scattering by surfaces in three–dimensional space. This algorithm evaluates scattered fields through fast, high–order, accurate solution of the corresponding boundary integral equation. The high–order accuracy of our solver is achieved through use of partitions of unityI together with analytical resolution of kernel singularities. The acceleration, in turn, results from use of high–order equivalent source approximations, which allow for fast evaluation of non–adjacent interactions by means of the three–dimensional fast Fourier transform (FFT). Our acceleration scheme has dramatically lower memory requirements and yields much higher accuracy than existing FFT–accelerated techniques. The present algorithm computes one matrix–vector multiply in O(N6/5logN) to O(N4/3logN) operations (depending on the geometric characteristics of the scattering surface), it exhibits super–algebraic convergence, and it does not suffer from accuracy breakdowns of any kind. We demonstrate the efficiency of our method through a variety of examples. In particular, we show that the present algorithm can evaluate accurately, on a personal computer, scattering from bodies of acoustical sizes (ka) of several hundreds.

On the O(1) solution of multiple-scattering problems

In this paper, we present a multiple-scattering solver for nonconvex geometries such as those obtained as the union of a finite number of convex surfaces. For a prescribed error tolerance, this algorithm exhibits a fixed computational cost for arbitrarily high frequencies. At the core of the method is an extension of the method of stationary phase, together with the use of an ansatz for the unknown density in a combined-field boundary integral formulation.

Fast, High-Order, High-Frequency Integral Methods for Computational Acoustics and Electromagnetics

We review a set of algorithms and methodologies developed recently for the numerical solution of problems of scattering by complex bodies in three-dimensional space. These methods, which are based on integral equations, high-order integration, Fast Fourier Transforms and highly accurate high-frequency integrators, can be used in the solution of problems of electromagnetic and acoustic scattering by surfaces and penetrable scatterers — even in cases in which the scatterers contain geometric singularities such as comers and edges. All of the solvers presented here exhibit high-order convergence, they run on low memories and reduced operation counts, and they result in solutions with a high degree of accuracy. In particular, our approach to direct solution of integral equations results in algorithms that can evaluate accurately in a personal computer scattering from hundred-wavelength-long objects — a goal, otherwise achievable today only by super-computing. The high-order high-frequency methods we present, in turn, are efficient where our direct methods become costly, thus leading to an overall computational methodology which is applicable and accurate throughout the electromagnetic spectrum.