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Mechanical metamaterials are architected manmade materials that allow for unique behaviors not observed in nature, making them promising candidates for a wide range of applications. Existing metamaterials lack tunability as their properties…
Micromorphic theories became an established tool to model size effects in materials like dispersion, localization phenomena or (apparently) size dependent properties. However, the formulation of adequate constitutive relations with its…
In this article, convex optimization is introduced as a promising tool to study Eshelby based inverse micromechanics problems. The focus is on inverse micromechanics using the Eshelby-Mori-Tanaka model given the dielectric constants of the…
This paper aims at the most comprehensive and systematic construction and tabulation of mechanical systems that admit a second invariant, quadratic in velocities, other than the Hamiltonian. The configuration space is in general a 2D…
This article discusses and explains the Hamiltonian formulation for a class of simple gauge invariant mechanical systems consisting of point masses and idealized rods. The study of these models may be helpful to advanced undergraduate or…
We give theoretical analyses of the Magneto-Rayleigh-Taylor instability driven by a rotating magnetic field. Both slab and liner configurations with finite thicknesses are dealt with in the WKB and the non-WKB approximations. Results show…
The paper develops the stiffness relationship between the movements and forces among a system of discrete interacting grains. The approach is similar to that used in structural analysis, but the stiffness matrix of granular material is…
In this talk we present a powerful tool applied to the study of Leptonic Physics. This tool is based on the construction of Weak Basis invariant relations associated to different properties of leptonic models. The rationale behind these…
The purpose of this study is to propose a modified micromorphic continuum model for granular materials based on a micromechanics approach. In this model, Cauchy stress and the couple stress are symmetric conjugated with the symmetric strain…
The last decade has witnessed the emergence of magneto-active polymers (MAPs) as one of the most advanced multi-functional soft composites. Depending on the magnetisation mechanisms and responsive behaviour, MAPs are mainly classified into…
Finite order invariants (Vassiliev invariants) of knots are expressed in terms of weight systems, that is, functions on chord diagrams satisfying the four-term relations. Weight systems have graph analogues, so-called $4$-invariants of…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
In this paper, the problem of the identification of the symmetry class of a given tensor is asked. Contrary to classical approaches which are based on the spectral properties of the linear operator describing the elasticity, our setting is…
Recent developments in the engineering of metamaterials have brought forth a myriad of mesmerizing mechanical properties that do not exist in ordinary solids. Among these, twisting metamaterials, acoustical chirality, or Willis coupling are…
We study invariant measures of continuous contact model in small dimensional spaces ($d =1,2$). Under general conditions we prove that in the critical regime this system has the one-parameter set of invariant measures parametrized by the…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
In general relativity, the motion of an extended body moving in a given spacetime can be described by a particle on a (generally non-geodesic) worldline. In first approximation, this worldline is a geodesic of the underlying spacetime, and…
We have used Monte Carlo simulations to observe the magnetic behaviour of Ising thin-films with cubic lattice structures as a function of temperature and thickness especially in the critical region. The fourth order Binder cumulant is used…
Magnetic gels are composite materials, consisting of a polymer matrix and embedded magnetic particles. Those are mechanically coupled to each other, giving rise to the magnetostrictive effects as well as to a controllable overall elasticity…
Magnetic materials often exhibit complex energy landscapes with multiple local minima, each corresponding to a self-consistent electronic structure solution. Finding the global minimum is challenging, and heuristic methods are not always…