Related papers: Geophysical modelling with Colombeau functions: Mi…
Atmospheric flows exhibit fluctuations of all scales (space -time) ranging from turbulence (millimeters-seconds) to climate (thousands of kilometers-years). The apparently random fluctuations however exhibit long-range spatio-temporal…
We derive new general expressions for the fluctuating electromagnetic field outside a homogeneous material surface. The analysis is based on general results from the thermodynamics of irreversible processes, and requires no consideration of…
A wavelet-like model for distributions of objects in natural and man-made terrestrial environments is developed. The model is constructed in a self-similar fashion, with the sizes, amplitudes, and numbers of objects occurring at a constant…
The class $\mathfrak C $ relative to countably compact topological spaces and the class $\mathfrak P$ relative to pseudocompact spaces introduced by Z. Frol\'ik are naturally generalized relative to every topological property. We provide a…
Seismic vulnerability analysis of existing buildings requires basic information on their structural behaviour. The ambient vibrations of buildings and the modal parameters (frequencies, damping ration and modal shapes) that can be extracted…
Scaling analysis of seismicity in the space-time-magnitude domain very often starts from the relation N(m,L)=a(L)*10**(-bm)*L**c for the rate of seismic events of magnitude M>m in an area of size L. There is some evidence in favor of…
We discuss correlation properties of a general mass density field introducing a classification of structures based on their complexity. Standard cosmological models for primordial mass fluctuations are characterized by a sort of large-scale…
A categorical formalism is introduced for studying various features of the symplectic geometry of Lefschetz fibrations and the algebraic geometry of Tyurin degenerations. This approach is informed by homological mirror symmetry, derived…
Minkowski functionals constitute a family of order parameters which discriminate spatial patterns according to size, shape and connectivity. Here we point out, that these scalar descriptors can be complemented by vector-valued curvature…
The study reports a systematic evaluation of the role of spatially correlated mechanical elements on failure behavior of heterogeneous materials represented by fiber bundle models (FBM) with different load redistribution rules. The increase…
Cosmological models that are locally consistent with general relativity and the standard model in which an object transported around the universe undergoes P, C and CP transformations, are constructed. This leads to generalization of the…
We review the present status of our research and understanding regarding the dynamics and the statistical properties of earthquakes, mainly from a statistical physical viewpoint. Emphasis is put both on the physics of friction and fracture,…
A framework is developed enabling the global analysis of the stability of cosmological models using the local geometric characteristics of the infinite-dimensional superspace, i.e. using the generalised Jacobi equation reformulated for…
Discoveries of the scale-free and small-world features are reported on a network constructed from the seismic data. It is shown that the connectivity distribution decays as a power law, and the value of the degrees of separation, i.e., the…
Independent of specific local features, global spatio-temporal structures in diverse phenomena around bifurcation points are described by the complex Ginzburg-Landau equation (CGLE) derived using the reductive perturbation method, which…
The method of passive imaging in seismology has been developped recently in order to image the earth crust from recordings of the seismic noise. This method is founded on the computation of correlations of the seismic noise. In this paper,…
We introduce a new notion of "regularity structure" that provides an algebraic framework allowing to describe functions and / or distributions via a kind of "jet" or local Taylor expansion around each point. The main novel idea is to…
The fluctuations of spacetime geometries at finite temperature are evaluated within the linearized theory of gravity. These fluctuations are described by the probability distribution of various configurations of the gravitational field. The…
We compute characteristic functionals of Dirichlet-Ferguson measures over a locally compact Polish space and prove continuous dependence of the random measure on the parameter measure. In finite dimension, we identify the dynamical symmetry…
The subject of the paper is the geometry and topology of cosmological spacetimes and vector bundles thereon, which are used to model physical fields propagating in the universe. Global hyperbolicity and factorization properties of the…