Related papers: Tessellations and Descartes disk configurations
Skeletal polyhedra and polygonal complexes are finite or infinite periodic structures in 3-space with interesting geometric, combinatorial, and algebraic properties. These structures can be viewed as finite or infinite periodic graphs…
Shape grammars compute over shapes which are defined in the universe $U^*$. Shapes in the universe $U^*$ are analogous to line drawings that can be physically realized in the plane. Any shape is embedded or contained in an arrangement of…
After reviewing the Lounesto spinor field classification, according to the bilinear covariants associated to a spinor field, we call attention and unravel some prominent features involving unexpected properties about spinor fields under…
We provide a minimal continuum model for mesoscale plasticity, explaining the cellular dislocation structures observed in deformed crystals. Our dislocation density tensor evolves from random, smooth initial conditions to form self-similar…
The connection between symmetries and linearizations of discrete-time dynamical systems is being inverstigated. It is shown, that existence of semigroup structures related to the vector field and having linear representations enables…
We prove an analogue for Stokes torsors of Deligne's skeleton conjecture and deduce from it the representability of the functor of relative Stokes torsors by an affine scheme of finite type over C. This provides, in characteristic 0, a…
We present an overview of recent experimental and theoretical advances in our understanding of the spin structure of protons and neutrons.
We study the near horizon geometry of generic Killing horizons constructing suitable coordinates and taking the appropriate scaling limit. We are able to show that the geometry will always show an enhancement of symmetries, and, in the…
It is argued that the main characteristic features of displacive relaxor ferrolectrics of the form ${\rm{A(B,B')}\rm{O}}_3$ with isovalent ${\rm{B,B'}}$ can be explained and understood in terms of a soft-pseudospin analogue of conventional…
Optically thin dusty disks around Main Sequence stars consist of debris from catastrophic collisions or from low erosion of long-lived planetesimals. Resolved observations of dusty disks have systematically evidenced asymmetries and annular…
This present work is based on our previous publications, which all together trigger our "Killing spinor programme". Other significant spinor fields are injected into the scheme and the intricate relations between them and their bilinears…
Icosahedral tilings, although non-periodic, are known to be characterized by their configurations of some finite size. This characterization has also been expressed in terms of a simple alternation condition. We provide an alternative proof…
In this paper we study multilinear morphisms between commutative group schemes and the associated tensor constructions. We will also do some explicit calculations and give examples that show that this theory behaves in a way that one would…
A general theory is developed for describing the nonlinear relaxation of spin systems from a strongly nonequilibrium initial state, when, in addition, the sample is coupled to a resonator. Such processes are characterized by nonlinear…
Spin glasses are disordered magnetic systems that exhibit a variety of properties that are characteristic of complex systems. After a brief review of basic spin glass concepts, their use in areas such as computer science, biology, and other…
We establish a theoretical correspondence between spin-one antiferromagnetic spinor condensates in an external magnetic field and quantum rotor models in an external potential. We show that the rotor model provides a conceptually clear…
Some ideas relating to a bracket formulation for dissipative systems are considered. The formulation involves a bracket that is analogous to a generalized Poisson bracket, but possesses a symmetric component. Such a bracket is presented for…
The stagnation point flow toward a rotating disk of finite radius is known to develop -- near the edge of the disk -- into a triple deck structure when the flow is strictly a stagnation point flow, and into a double deck structure when the…
A special approach to examine spinor structure of 3-space is proposed. It is based on the use of the concept of a spatial spinor defined through taking the square root of a real-valued 3-vector. Two sorts of spatial spinor according to…
This paper studies the configuration space of all possible positions of a linkage in R^n. For example, it shows that for every compact algebraic set, there is a linkage whose configuration space is analytically isomorphic to a finite number…