Related papers: Physical structures. Forming physical fields and m…

A class of two dimensional field theories, based on (generically degenerate) Poisson structures and generalizing gravity-Yang-Mills systems, is presented. Locally, the solutions of the classical equations of motion are given. A general…

The growth and dynamics of solid surfaces displays a multitude of power law relationships, which are often associated with geometric self-similarity. In many cases the mechanisms behind these power laws are comparatively trivial, and…

Are symmetries discovered or rather invented by humans ? The stand you may take firmly here reveals a lot of your epistemological position. Conversely, the arguments you may forge for answering to this question, or to one of its numerous…

In the field theories with twistor structure particles can be identified with (spacially bounded) caustics of null geodesic congruences defined by the twistor field. As a realization, we consider the ``algebrodynamical'' approach based on…

Plasmons are usually described in terms of macroscopic quantities such as electric fields and currents. However as fundamental excitations of metals they are also quantum objects with internal structure. We demonstrate that this can induce…

The structure of the multiverse is determined by information flow.

A correspondence between different $Pin$-type structures on a compact surface and quadratic (linear) forms on its homology is constructed. Addition of structures is defined and expressed in terms of these quadratic forms.

We prove that the set of orthogonal separable coordinates on an arbitrary (pseudo-)Riemannian manifold carries a natural structure of a projective variety, equipped with an action of the isometry group. This leads us to propose a new,…

In the last years there has been a growing interest in the understanding a vast variety of scale invariant and critical phenomena occurring in nature. Experiments and observations indeed suggest that many physical systems develop…

We survey a decade worth of work pertaining to the nodal structures of random fields, with emphasis on the transformative techniques that shaped the field.

We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. In the route, we also discover new characterizations of…

We discuss and compare several geometric structures which imply an upper bound to the acceleration of a particle measured in its rest system. While all of them have the same implications on the motion of a point particle, they differ in…

We use the geometry of the space of fields for gauged supersymmetric mechanics to construct the twisted differential equivariant K-theory of a manifold with an action by a finite group.

This paper collects some characteristic aspects of the general model-building framework of the mechanics of complex bodies, that are bodies in which the material substructure influences prominently the gross behavior through interactions…

A system of linear equations over a skew field has properties similar to properties of a system of linear equations over a field. Even noncommutativity of a product creates a new picture the properties of system of linear equations and of…

Scalar fields, strongly coupled to matter, can be present in nature and still be invisible to local experiments if they are subject to a screening mechanism. The symmetron is one such mechanism which relies on restoration of a spontaneously…

Accretion of mineralized thin wall-like structures via localized growth along their edges is observed in a range of physical and biological systems ranging from molluscan and brachiopod shells to carbonate-silica composite precipitates. To…

We study some properties of quadratic forms with values in a field whose underlying vector spaces are endowed with the structure of right vector spaces over a division ring extension of that field. Some generalized notions of isotropy,…

In this paper we first show that the usual three dimensionality of space, which is taken for granted, results from the spinorial behaviour of Fermions, which constitute the material content of the universe. It is shown that the resulting…

This paper describes the foundations of a differential geometry of a quaternionic curves. The Frenet-Serret equations and the evolutes and evolvents of a particular quaternionic curve are accordingly determined. This new formulation takes…