Related papers: Some open problems in the theory of composites
Tensors are multidimensional analogs of matrices. In this paper, based on degree-theoretic ideas, we study homogeneous nonlinear complementarity problems induced by tensors. By specializing this to $Z$-tensors (which are tensors with…
High-entropy alloys, which exist in the high-dimensional composition space, provide enormous unique opportunities for realizing unprecedented structural and functional properties. A fundamental challenge, however, lies in how to predict the…
We investigate the following three consistency conditions for constructing string theories on orbifolds: i) the invariance of the energy-momentum tensors under twist operators, ii) the duality of amplitudes and iii) modular invariance of…
Exactly solvable models are interesting for science and education, since they help in scientific search and in understanding of phenomena. Some exact solutions for simple quantum-mechanical models are considered. The models include two…
We present a short overview of the recent results in the theory of diffusion and wave equations with generalised derivative operators. We give generic examples of such generalised diffusion and wave equations, which include time-fractional,…
We use curvature decompositions to construct generating sets for the space of algebraic curvature tensors and for the space of tensors with the same symmetries as those of a torsion free, Ricci symmetric connection; the latter naturally…
The discrete periodic lattice of masses and springs with line and point defects is considered. The dispersion equations for propagative, guided and localised waves are obtained. The detailed analysis of example with three masses is…
The ``spatial interpretation of compositeness'', presented and discussed in [1,2] in the context of non-relativistic potential scattering, is extended to higher partial waves. A particular set of basis states is used to arrive at a slightly…
We point out four problems which have arisen during the recent research in the domain of Combinatorial Physics.
In this thesis we deal with the specific collective phenomena in condensed matter - striped-structures formation. Such structures are observed in different branches of condensed matter physics, like surface physics or physics of…
Explicit expressions for the behavior of statistically isotropic composites with viscoelastic matrices and linear elastic inclusions are determined by application of the correspondence principle. The behavior of the matrix is linear in…
This paper presents a new concept of geometric multipole expansion for the conductivity or anti-plane elasticity problem in two dimensions by using the Faber polynomials. As an application, we construct semi-neutral inclusions of general…
It is shown that a general two-component feedback loop can be viewed as a deformed Hamiltonian system. Some of the implications of using ideas from theoretical physics to study biological processes are discussed.
We define new norms for symmetric tensors over ordered normed spaces; these norms are defined by considering linear combinations of tensor products or powers of positive elements only. Relations between the different norms are studied. The…
We introduce combinatorial types of arrangements of convex bodies, extending order types of point sets to arrangements of convex bodies, and study their realization spaces. Our main results witness a trade-off between the combinatorial…
This is a broad reviw of some of the fundamental results of research on the Bechgaard salts.To a lesser extent Q2D salts will also be discussed.Apart from known results,based on the author's work and the literature,some open problems will…
A survey of some recent and important results which have to do with integrable equations and their relationship with the theory of surfaces is given. Some new results are also presented. The concept of the moving frame is examined, and it…
A dual-continuum model can offer a practical approach to understanding first-order behaviours of poromechanically coupled multiscale systems. To close the governing equations, constitutive equations with models to calculate effective…
We give a brief review of some generalized continuum theories applied to the crystals with complicated microscopic structure. Three different ways of generalization of the classical elasticity theory are discussed. One is the high-gradient…
We review some aspects of theories with compact extra dimensions. We consider the motivation and the theoretical basis of Large, Universal and Warped Extra Dimensions. We focus on those aspects that are potentially relevant in the…