A selection of open problems in the theory of composites is presented. Particular attention is
drawn to the question of whether two-dimensional, two-phase composites with general …

Iterative fast Fourier transform methods are useful for calculating the fields in composite
materials and their macroscopic response. By iterating back and forth until convergence, the …

Examples of non-quasiconvex functions that are rank-one convex are rare. In this paper we
construct a family of such functions by means of the algebraic methods of the theory of exact …

We prove a realization theorem for rational functions of several complex variables which
extends the main theorem of Bessmertnyĭ (in: Alpay, Gohberg, Vinnikov (eds) Interpolation …

Using a Hilbert space framework inspired by the methods of orthogonal projections and
Hodge decompositions, we study a general class of problems (called Z-problems) that arise …

Electrochemical impedance spectra of composite materials contain information on the
topological arrangement, volume fraction, and shape of particles, as well as the dielectric …

A body Θ containing two phases, which may form a periodic composite with microstructure
much smaller that the body, or which may have structure on a length scale comparable to …

In this thesis, we consider a class of Z-problems and their associated effective operators on
Hilbert spaces which arise in effective media theory, especially within the theory of …

In two‐phase materials, each phase having a non‐local response in time, it has been found
that for some driving fields the response somehow untangles at specific times, and allows …

Here we obtain bounds on the generalized spectrum of that operator whose inverse, when it
exists, gives Green's function. We consider the wide range of physical problems that can be …