Enclosure of the Numerical Range of a Class of Non-Selfadjoint Rational Operator Functions

In this paper we introduce an enclosure of the numerical range of a class of rational operator functions. In contrast to the numerical range the presented enclosure can be computed exactly in the infinite dimensional case as well as in the finite dimensional case. Moreover, the new enclosure is minimal given only the numerical ranges of the operator coefficients and many characteristics of the numerical range can be obtained by investigating the enclosure. We introduce a pseudonumerical range and study an enclosure of this set. This enclosure provides a computable upper bound of the norm of the resolvent.Comment: 31 page

Structural information of composites from complex-valued measured bulk properties

This paper is concerned with the estimation of the volume fraction and the anisotropy of a two-component composite from measured bulk properties. An algorithm that takes into account that measurements have errors is developed. This algorithm is used to study data from experimental measurements with an unknown microstructure. The dependence on the microstructure is quantified in terms of a measure in the representation formula introduced by D. Bergman. We use composites with known microstructures to illustrate the dependence on the underlying measure and show how errors in the measurements affect the estimations of the structural parameters

A comparison of two numerical methods for homogenization of Maxwell's equations

When the wavelength is much larger than the typical scale of the microstructure in a material, it is possible to define effective or homogenized material coefficients. The classical way of determination of the homogenized coeffi- cients consists of solving an elliptic problem in a unit cell. This method and the Floquet-Bloch method, where an eigenvalue problem is solved, are numerically compared with respect to accuracy and contrast sensitivity. The Floquet-Bloch method is shown to be a good alternative to the classical homogenization method, when the contrast is modest

A spectral projection based method for the numerical solution of wave equations with memory

In this paper, we compare two approaches to numerically approximate the solution of second-order Gurtin-Pipkin type of integro-dierential equations. Both methods are based on a high-order Discontinous Galerkin approximation in space and the numerical inverse Laplace transform. In the first approach, we use functional calculus and the inverse Laplace transform to represent the solution. The spectral projections are then numerically computed and the approximation of the solution of the time-dependent problem is given by a summation of terms that are the product of projections of the data and the inverse Laplace transform of scalar functions. The second approach is the standard inverse Laplace transform technique. We show that the approach based on spectral projections can be very ecient when several time points are computed, and it is particularly interesting for parameter-dependent problems where the data or the kernel depends on a parameter

Comparison of Static and Driving Simulator Venues for the Tactile Detection Response Task

The general objective of the present study was to validate a low-cost, static, version of the Tactile Detection Response Task (TDRT) intended for driver-vehicle interface evaluation in industrial settings. The static TDRT venue was compared to the more commonly used driving simulator venue, where the TDRT and the secondary task under evaluation are performed during simulated driving. The results indicated that the effect of venue was additive over a range of visual-manual and cognitive secondary tasks, which offers preliminary support for the static TDRT venue as a surrogate for the driving simulator TDRT venue. However, a more detailed analysis revealed a counterintuitive effect for one of the visual-manual secondary tasks (SuRT), where the easier version of the task (as confirmed by subjective workload ratings) yielded a stronger effect on the TDRT than the more difficult version. Possible explanations and implications for the TDRT and its application to driver-vehicle interface evaluation are discussed

Numerical solution of distributed-order time-fractional diffusion-wave equations using Laplace transforms

In this paper, we consider the numerical inverse Laplace transform for distributed order time-fractional equations, where a discontinuous Galerkin scheme is used to discretize the problem in space. The success of Talbot’s approach for the computation of the inverse Laplace transform depends critically on the problem’s spectral properties and we present a method to numerically enclose the spectrum and compute resolvent estimates independent of the problem size. The new results are applied to time-fractional wave and diffusion-wave equations of distributed order