Related papers: Physical structures. Forming physical fields and m…
Let M be a manifold, and G a Lie group which satisfies the unique extension property. An (M,G) manifold N is a manifold endowed with an atlas (U_i,f_i) where f_i is a diffeomorphism between U_i and an open set of M such that the coordinates…
The role of tidal shear in the formation of structure in the Universe is explored. To illustrate the possible and sometimes dramatic impact of tidal fields we focus on the evolution of voids. We firstly analyze the role of tidal fields both…
The connection between Jacobi fields and odular structures of affine manifold is established. It is shown that the Jacobi fields generate the natural geoodular structure of affinely connected manifolds.
The mechanics of the structured particles develops. The substantiation of applicability of such mechanics for the description of processes of evolution in open nonequilibrium systems is offered. The consequences following from the equations…
We describe the geometric structures involved in the variational formulation of physical theories. In presence of these structures, the constitutive set of a physical system can be generated by a family of functions. We discuss conditions,…
Morphogenetic patterns are highly sophisticated dissipative structures. Are they governed by the same general mechanisms as chemical and hydrodynamic patterns? Turing's symmetry breaking and Wolpert's signalling provide alternative…
Observations are inconsistent with a homogeneous and isotropic universe with ordinary matter and gravity. The universe is far from exact homogeneity and isotropy at late times, and the effect of the non-linear structures has to be…
The mechanics of structured particles (SP) consisting from potentially interacting material points are discussed. For this purpose the derivation of the SP equation motion in the field of external forces is submitted. The differences…
It is proposed that the mathematical models for any physical systems that are based in first principles, such as conservation laws or balance principles, have some common elements, namely, a space of kinematical states, a space of dynamical…
Geological materials are often seen as the antithesis of soft; rocks are hard. However, during the formation of minerals and rocks, all the systems we shall discuss, indeed geological materials in general, pass through a stage where they…
Geometric evolution represents a fundamental aspect of many physical phenomena. In this paper we consider the geometric evolution of structures that undergo topological changes. Topological changes occur when the shape of an object evolves…
Physical geometry studies mutual disposition of geometrical objects and points in space, or space-time, which is described by the distance function d, or by the world function \sigma =d^{2}/2. One suggests a new general method of the…
This note provides a variational description of the most basic differential geometric structures on a smooth manifold.
The paper develops an earlier proposition that the physical universe is a finite system co-ordinatised by a very large finite field $\mathrm{F}_\mathfrak{p}$ which looks like the field of complex numbers to an observer. We construct a place…
We briefly review the structure and properties of self-dual field actions.
The analysis of images (of obtained in various ranges of the lengths of waves) of luminous objects in the Universe by means of a method of multilevel dynamic contrasting led author to the conclusions: a) the structures of all observable…
Identical relations occur in various branches of mathematics and mathematical physics. The Cauchy-Riemann relations, characteristical and canonical relations, the Bianchi identities and others are examples of identical relations. It can be…
Measures in the context of Category Theory lead to various relations, even differential relations, of categories that are independent of the mathematical structure forming objects of a category. Such relations, which are independent of…
The space-time geometry is considered to be a physical geometry, i.e. a geometry described completely by the world function. All geometrical concepts and geometric objects are taken from the proper Euclidean geometry. They are expressed via…
The study of integrability of the mathematical physics equations showed that the differential equations describing real processes are not integrable without additional conditions. This follows from the functional relation that is derived…