Related papers: A rigorous approach to the field recursion method …
In this chapter, the Hilbert space framework in the mathematical theory of composite materials is introduced for studying the properties of effective operators. The goal is to introduce some of the key concepts and fundamental theorems in…
A conducting two-dimensional periodic composite of two anisotropic phases with anisotropic, not necessarily symmetric, conductivity tensors is considered. By finding approximate representations for the relevant operators, an approximation…
We consider the response of a multicomponent body to $n$ fields, such as electric fields, magnetic fields, temperature gradients, concentration gradients, etc., where each component, which is possibly anisotropic, may cross couple the…
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 differential constraints are satisfied in Fourier…
This paper aims at reviewing and analysing the method of reflections. The latter is an iterative procedure designed to linear boundary value problems set in multiply connected domains. Being based on a decomposition of the domain boundary,…
This work establishes a systematic framework for operator construction in the non-relativistic effective field theory, incorporating both the three dimensional Euclidean symmetry and the internal symmetries. By employing double cover of the…
Building on the foundation work of Brown, Milton and Torquato, we present a tractable approach to analyse the effective permittivity of anisotropic two-phase structures. This methodology accounts for successive dipolar interactions,…
This paper considers the iterative solution of linear systems arising from discretization of the anisotropic radiative transfer equation with discontinuous elements on the sphere. In order to achieve robust convergence behavior in the…
We show the power of the algebra of subspace collections developed in Chapter 7 of the book "Extending the Theory of Composites to Other Areas of Science (edited by Milton, 2016). Specifically we accelerate the Fast Fourier Transform…
This paper is concerned with the development and analysis of an iterative solver for high-dimensional second-order elliptic problems based on subspace-based low-rank tensor formats. Both the subspaces giving rise to low-rank approximations…
This is the second paper of a series of three. We construct effective open-closed superstring couplings by classically integrating out massive fields from open superstring field theories coupled to an elementary gauge invariant tadpole…
Higher-order tensors appear in various areas of mechanics as well as physics, medicine or earth sciences. As these tensors are highly complex, most are not well understood. Thus, the analysis and the visualization process form a highly…
In this paper a new general approach is developed to construct and study Lebesgue type decompositions of linear operators $T$ in the Hilbert space setting. The new approach allows to introduce an essentially wider class of Lebesgue type…
A primitive problem of predicting the effective properties of composites is open boundary conditions. In this paper, Eshelby's transformation field method is developed to solve the open boundary problem of two-phase composites having…
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 geometries have the same set of possible effective tensors…
In this paper we investigate dual formulations for massive tensor fields. Usual procedure for construction of such dual formulations based on the use of first order parent Lagrangians in many cases turns out to be ambiguous. We propose to…
We describe a simple, black-box compression format for tensors with a multiscale structure. By representing the tensor as a sum of compressed tensors defined on increasingly coarse grids, we capture low-rank structures on each grid-scale,…
We study the use of transformers to reconstruct the compositions of tensor products of two-dimensional rational conformal field theories (RCFTs) based on their low-energy spectra. The task is challenging due to its combinatorial nature. The…
We study the compositeness of unstable hadrons which lie near the two-hadron threshold. In the framework of the effective field theory, we derive the relation between the compositeness of stable bound states with observables. We then extend…
We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these…