Related papers: New extremal inclusions and their applications to …
The description of the collective magnetorheological effect induced by magnetic field in magnetoactive elastomers is proposed. The condition of consistency is used between magnetic and mechanic momenta of forces exerted on magnetically…
The goal of this thesis is the search for integrable and superintegrable systems with magnetic field. We formulate the quantum mechanical determining equations for second order integrals of motion in the cylindrical coordinates and we find…
This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine…
We derive a model for the finite motion of a magneto-elastic rod reinforced with isotropic (spherical) or anisotropic (ellipsoidal) inclusions. The particles are assumed weakly and uniformly magnetised, rigid and firmly embedded into the…
This paper presents a novel multi-scale method for elliptic partial differential equations with arbitrarily rough coefficients. In the spirit of numerical homogenization, the method constructs problem-adapted ansatz spaces with uniform…
Entanglement entropies have revealed, in the last years, to be a powerful tool to extract information about the physics of condensed-matter systems. In the first part of this thesis, we show how to extract essential details about the…
Exact solutions are derived for the problem of a two-dimensional, infinitely anisotropic, linear-elastic medium containing a periodic lattice of voids. The matrix material possesses either one infinitely soft, or one infinitely hard loading…
Mathematics demonstrates that an ideally evolving magnetic field has an exponentially increasing sensitivity to non-ideal effects for all but truly exceptional evolutions. On a time scale that depends only logarithmically on the magnitude…
We propose to introduce the concept of exceptional points in intermediate courses on mathematics and classical mechanics by means of simple textbook examples. The first one is an ordinary second-order differential equation with constant…
Consider a 2D composites with non-overlapping equal inclusions imbedded in a host material of the normalized unit conductivity. The conductivity of inclusions takes two values $\sigma_1$ and $\sigma_2$ with the probabilities $p$ and $1-p$,…
Many results that are difficult can be found more easily by using a generalization in the complex plane of Einstein's addition law of parallel velocities. Such a generalization is a natural way to add quantities that are limited to bounded…
Hamiltonian models based on a localized basis set are widely used in condensed matter physics, as, for example, for the calculation of electronic structures or transport properties. The presence of a weak and homogeneous magnetic field can…
We consider the Lame system of linear elasticity with periodically distributed inclusions whose elastic parameters have high contrast compared to the background media. We develop a unified method based on layer potential techniques to…
A new fully discrete linearized $H^1$-conforming Lagrange finite element method is proposed for solving the two-dimensional magneto-hydrodynamics equations based on a magnetic potential formulation. The proposed method yields numerical…
The aim of this article is to elaborate and rigorously analyze a topological derivative based imaging framework for locating an electromagnetic inclusion of diminishing size from boundary measurements of the tangential component of…
We consider the equilibrium equations for a linearized Cosserat material and provide two perspectives concerning well-posedness. First, the system can be viewed as the Hodge Laplace problem on a differential complex. On the other hand, we…
A transverse multipole expansion is derived, including the longitudinal components necessarily present in regions of varying magnetic field profile. It can be used for exact numerical orbit following through the fringe field regions of…
We investigate the two-dimensional elastostatic inclusion problem in an unbounded medium. Building on the recent developments for rigid inclusions \cite{Mattei:2021:EAS} and conductivity inclusions \cite{Jung:2021:SEL}, we extend these…
We propose two classes of mixed finite elements for linear elasticity of any order, with interior penalty for nonconforming symmetric stress approximation. One key point of our method is to introduce some appropriate nonconforming…
We consider the perturbation of an electric potential due to an insulating inclusion with corners. This perturbation is known to admit a multipole expansion whose coefficients are linear combinations of generalized polarization tensors. We…