Related papers: On energy consistent vector hysteresis operators
In this note we provide a full conjugacy and subdifferential calculus for convex convex-composite functions in finite-dimensional space. Our approach, based on infimal convolution and cone-convexity, is straightforward and yields the…
A new local and gauge invariant quantum vortex operator is constructed in three-dimensional gauge field theories. The correlation functions of this operator are evaluated exactly in pure Maxwell theory and by means of a loop expansion in…
In this monograph we develop magnetic pseudodifferential theory for operator-valued and equivariant operator-valued functions and distributions from first principles. These have found plentiful applications in mathematical physics,…
We present results about minimization of convex functionals defined over a finite set of vectors in a finite dimensional Hilbert space, that extend several known results for the Benedetto-Fickus frame potential. Our approach depends on…
We perform computer simulations to probe the magnetic hysteresis in a two-dimensional ($L^{}_x\times L^{}_y$) assembly of magnetic nanoparticles as a function of dipolar interaction strength $h^{}_d$, temperature $T$, aspect ratio…
This habilitation thesis centres on linearisation of vector-valued functions which means that vector-valued functions are represented by continuous linear operators. The first question we face is which vector-valued functions may be…
In a watt balance experiment, separate measurements of magnetic force and induced electric potential in a conductor in a magnetic field allow for a virtual comparison between mechanical and electrical powers, which leads to and an accurate…
An analysis of one and two point functions of the energy momentum tensor on homogeneous spaces of constant curvature is undertaken. The possibility of proving a $c$-theorem in this framework is discussed, in particular in relation to the…
We reconsider the Equivalence Theorem from an algebraic viewpoint, using an extended BRST symmetry. This version of the Equivalence Theorem is then used to reexpress the Abelian Higgs model action, originally written in terms of undesirable…
We propose a new approach to model electrical machines based on energy considerations and construction symmetries of the motor. We detail the approach on the Permanent-Magnet Synchronous Motor and show that it can be extended to Synchronous…
Three magnetic relativistic Schr\"odinger operators corresponding to the classical relativistic Hamiltonian symbol with magnetic vector and electric scalar potentials are considered, dependent on how to quantize the kinetic energy term…
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…
Hysteresis is an important issue in modeling piezoelectric materials, for example, in applications to energy harvesting, where hysteresis losses may influence the efficiency of the process. The main problem in numerical simulations is the…
Finite Cartesian products of operators play a central role in monotone operator theory and its applications. Extending such products to arbitrary families of operators acting on different Hilbert spaces is an open problem, which we address…
In this paper, we prove that a kind of second order stochastic differential operator can be represented by the limit of solutions of BSDEs with uniformly continuous coefficients. This result is a generalization of the representation for the…
Understanding the dynamics of magnetic vortices has emerged as an important challenge regarding the recent development of spin-torque vortex oscillators. Either micromagnetic simulations or the analytical Thiele equation approach are…
We present a kinetic energy tensor that unifies a scalar kinetic energy density commonly used in meta-Generalized Gradient Approximation functionals and the vorticity density that appears in paramagnetic current-density-functional theory.…
Ferromagnetic materials exhibit anisotropy, saturation, and hysteresis. We here study the incorporation of an incremental vector hysteresis model representing such complex behavior into nonlinear magnetic field problems both, from a…
A geometric theory of the irreducible tensor operators of quantum spin systems. It is based upon the Maxwell-Sylvester geometric representation of the multipolar electrostatic potential. In the latter, an order-$\ell$ multipolar potential…
The concept of energy-dependent forces in quantum mechanics is re-analysed. We suggest a simplification of their study via the representation of each self-adjoint and energy-dependent Hamiltonian H=H(E) with real spectrum by an auxiliary…