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In the framework of linearized elasticity, we study thin elastic composite plates with thickness $\delta$. The plates contain small, rigid rectangular plates distributed periodically along $\varepsilon$. Between two neighboring rigid plates…
Let $M$ be a cancellative and commutative monoid. A non-invertible element of $M$ is called an atom (or irreducible element) if it cannot be factored into two non-invertible elements, while an atom $a$ of $M$ is called strong if $a^n$ has a…
A new formalism is used for a Monte Carlo determination of the elastic constants of a two-dimensional net of fixed connectivity. The net is composed of point-like atoms each of which is tethered to six neighbors by a bond limiting the…
We study the local dimension of the convolution of two measures. We give conditions for bounding the local dimension of the convolution on the basis of the local dimension of one of them. Moreover, we give a formula for the local dimension…
We consider periodic domain structures which appear due to the magnetoelastic interaction if the antiferromagnetic crystal is attached to an elastic substrate. The peculiar behavior of such structures in an external magnetic field is…
The dimensions of sets of matrices of various types, with specified eigenvalue multiplicities, are determined. The dimensions of the sets of matrices with given Jordan form and with given singular value multiplicities are also found. Each…
By following the ideas underpinning the well-established ``homogeneous model'' of an $n$-dimensional Euclidean space, we investigate whether the motion group or the weak motion group of an $n$-dimensional affine metric space on a vector…
We numerically validate the Virtual Element Method of order k for general second order elliptic problems with variable coefficients in three dimensions. Moreover, we investigate numerically also the Serendipity version of the VEM (in three…
The purpose of this note is to study some algebraic properties of irreducible ideals of monoids. We establish relations between irreducible, prime, and semiprime ideals. We explore some properties of irreducible ideals in local, Noetherian,…
In recent years molecular elasticity has emerged as an active area of research: there are experiments that probe mechanical properties of single biomolecules such as DNA and Actin, with a view to understanding the role of elasticity of…
We study an elasticity model for compressed protein monolayers or particle rafts at a liquid interface. Based on the microscopic view of hard-core particles with soft shells, a bead-spring model is formulated and analyzed in terms of…
This paper is devoted to the study of codimension two holomorphic foliations and distributions. We prove the stability of complete intersection of codimension two distributions and foliations in the local case. Converserly we show the…
In this paper we analyze a virtual element method for the two dimensional elasticity spectral problem allowing small edges. Under this approach, and with the aid of the theory of compact operators, we prove convergence of the proposed VEM…
We introduce the notion of solid monoid and rigid monoid in monoidal categories and study the formal properties of these objects in this framework. We show that there is a one to one correspondence between solid monoids, smashing…
In dimension two, we study complete monomial ideals combinatorially, their Rees algebras and develop effective means to find their defining equations.
The packing of elastic bodies has emerged as a paradigm for the study of macroscopic disordered systems. However, progress is hampered by the lack of controlled experiments. Here we consider a model experiment for the isotropic…
The topological Weyl semimetal MoTe2, in the orthorhombic phase, is an important system both from the point of view of fundamental physics and potential applications. In this study we have investigated the elastic, electronic, bonding and…
We study the dynamics of rigid spheres embedded in viscoelastic media and address two questions of importance to microrheology. First we calculate the complete response to an external force of a single bead in a homogeneous elastic network…
The elastic properties of a material with spherical voids of equal volume are analysed using a new model, with particular attention paid to the hexagonal close-packed and the face-centred cubic arrangement of voids. Void fractions well…
In this paper we consider the stability issue for the inverse problem of determining an unknown inclusion contained in an elastic body by all the pairs of measurements of displacement and traction taken at the boundary of the body. Both the…