Related papers: Representation of Material Elements and Geometry o…
Magnetism primarily describes the physics and materials science of systems presenting a magnetization -- a macroscopic order parameter characterizing electron angular momentum. The order parameter is associated with the electronic exchange…
A brief survey of the author's works on the quantum theory of magnetism. Theoretical foundation and applications of the generalized spin-fermion (sp-d) exchange lattice model to various magnetic systems, e.g., rare-earth metals and…
Th is paper is motivated by the growing importance of better understanding of the phenomena and consequences of high- intensity energetic particle beam interactions with accelerator, generic target , and detector components. It reviews the…
Quadratic surfaces gain more and more attention among the Geometric Algebra community and some frameworks were proposed in order to represent, transform, and intersect these quadratic surfaces. As far as the authors know, none of these…
A geometrical interpretation of the $G$-structures associated to elastic material bodies is given. In addition, characterizations of their integrability are obtained. Since the lack of integrability is a geometrical measure of the lack of…
The mathematical formalisms used to model biological systems induce both latent and ambiguous assumptions that can limit or distort their representational capabilities. Developing formalisms that can represent systems more precisely is…
Most emergent properties of the materials discovered since the 1980s are related to the existence of electron-electron interactions which are large with respect to the kinetic energies and could not be thoroughly studied before. The…
The electronic structure of heavy elements, when described in a space-time which the metric is affected by the electromagnetic interaction, presents instabilities. These instabilities increase with the atomic number, and above a critical…
Hysterons are elementary units of hysteresis that underlie many complex behaviors of non-equilibrium matter. Because models of interacting hysterons can describe disordered matter, this suggests that artificial systems could respond to…
This presentation explains why models with a dynamical symmetry often work extraordinarily well even in the presence of large symmetry breaking interactions. A model may be a caricature of a more realistic system with a "quasi-dynamical"…
The elements of micromaser physics are reviewed in a tutorial way. The emphasis is on the basic theoretical concepts, not on technical details or experimental subtleties. After a brief treatment of the atom-photon interaction according to…
Urban systems are composed by complex couplings of several components, and more particularly between the built environment and transportation networks. Their interaction is involved in the emergence of the urban form. We propose in this…
Mechanical metamaterials leverage geometric design to achieve unconventional properties, such as high strength at low density, efficient wave guiding, and complex shape morphing. The ability to control shape changes builds on the complex…
The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
An elementary understanding of the relevant length, mass and energy scales at the molecular level can be used to explain the order of magnitude of material properties such as mass density, latent heat, surface tension, elastic moduli and…
The main theme of this workshop (Dagstuhl seminar 04351) is `Spatial Representation: Continuous vs. Discrete'. Spatial representation has two contrasting but interacting aspects (i) representation of spaces' and (ii) representation by…
In the paper a self-consistent theoretical description of the lattice and magnetic properties of a model system with magnetoelastic interaction is presented. The dependence of magnetic exchange integrals on the distance between interacting…
This is the first in a series of papers where we develop new structural elements on singular area minimizing hypersurfaces, the skin structures. They disclose previously unapproachable and largely unexpected geometric and analytic…
Complex networks have become the main paradigm for modelling the dynamics of interacting systems. However, networks are intrinsically limited to describing pairwise interactions, whereas real-world systems are often characterized by…