We propose a model with
3-dimensional spatial sections, constructed from hyperbolic cusp space glued to
Seifert manifolds which are in this case homology spheres. The topological part
of this research is based on Thurston’s conjecture which states that any
3-dimensional manifold has a canonical decomposition into parts, each of which
has a particular geometric structure. In our case, each part is either a
Seifert fibered or a cusp hyperbolic space. In our construction we remove tubular
neighbourhoods of singular orbits in areas of Seifert fibered manifolds using a
splice operation and replace each with a cusp hyperbolic space. We thus
achieve elimination of all singularities, which appear in the standard-like
cosmological models, replacing them by “a torus to infinity”. From this
construction, we propose an alternative manifold for cosmology with finite
volume and without Friedmann-like singularities. This manifold was used for
calculating coupling constants. Obtaining in this way a theoretical explanation
for fundamental forces is at least in the sense of the hierarchy.

Abstract:
In this paper we present a new derivation of the $H$-theorem and the corresponding collisional equilibrium velocity distributions, within the framework of Tsallis' nonextensive thermostatistics. Unlike previous works, in our derivation we do not assume any modification on the functional form of Boltzmann's original "molecular chaos hypothesis". Rather, we explicitly introduce into the collision scenario, the existence of statistical dependence between the molecules before the collision has taken place, through a conditional distribution $f(\vec{v}_2|\vec{v}_1)$. In this approach, different equilibrium scenarios emerge depending on the value of the nonextensive entropic parameter.

Abstract:
This paper presents the preliminary results of the characterization of pattern evolution in the process of cosmic structure formation. We are applying on N-body cosmological simulations data the technique proposed by Rosa, Sharma & Valdivia (1999) and Ramos et al. (2000) to estimate the time behavior of asymmetries in the gradient field. The gradient pattern analysis is a well tested tool, used to build asymmetrical fragmentation parameters estimated over a gradient field of an image matrix able to quantify a complexity measure of nonlinear extended systems. In this investigation we work with the high resolution cosmological data simulated by the Virgo consortium, in different time steps, in order to obtain a diagnostic of the spatio-temporal disorder in the matter density field. We perform the calculations of the gradient vectors statistics, such as mean, variance, skewness, kurtosis, and correlations on the gradient field. Our main goal is to determine different dynamical regimes through the analysis of complex patterns arising from the evolutionary process of structure formation. The results show that the gradient pattern technique, specially the statistical analysis of second and third gradient moment, may represent a very useful tool to describe the matter clustering in the Universe.

Abstract:
We study an alternative geometrical approach on the problem of classical cosmological singularity. It is based on a generalized function $f (x, y) = x^{2} + y^{2} = (1 - z)z^{n}$ which consists of a cusped coupled isosurface. Such a geometry is computed and discussed into the context of Friedmann singularity-free cosmology where a pre-big bang scenario is considered. Assuming that the mechanism of cusp formation is described by non-linear oscillations of a pre-big bang extended very high energy density field ($> 3 \times 10^{94} kg/m^{3} $), we show that the action under the gravitational field follows a tautochrone of revolution, understood here as the primary projected geometry that alternatively replaces the Friedmann singularity in the standard big bang theory. As shown here this new approach allows us to interpret the nature of both matter and dark energy from first geometric principles.

Abstract:
this paper describes an innovative technique, the gradient pattern analysis (gpa), for analysing spatially extended dynamics. the measures obtained from gpa are based on the spatio-temporal correlations between large and small amplitude fluctuations of the structure represented as a dynamical gradient pattern. by means of four gradient moments it is possible to quantify the relative fluctuations and scaling coherence at a dynamical numerical lattice and this is a set of proper measures of the pattern complexity and equilibrium. the gpa technique is applied for the first time in 3d-simulated molecular chains with the objective of characterizing small symmetry breaking, amplitude and phase disorder due to spatio-temporal fluctuations driven by the spatially extended dynamics of a relaxation regime.

Abstract:
This paper describes an innovative technique, the gradient pattern analysis (GPA), for analysing spatially extended dynamics. The measures obtained from GPA are based on the spatio-temporal correlations between large and small amplitude fluctuations of the structure represented as a dynamical gradient pattern. By means of four gradient moments it is possible to quantify the relative fluctuations and scaling coherence at a dynamical numerical lattice and this is a set of proper measures of the pattern complexity and equilibrium. The GPA technique is applied for the first time in 3D-simulated molecular chains with the objective of characterizing small symmetry breaking, amplitude and phase disorder due to spatio-temporal fluctuations driven by the spatially extended dynamics of a relaxation regime.

Abstract:
In this paper, we analyze the probability density function (PDF) of solar wind velocity and proton density, based on generalized thermostatistics (GT) approach, comparing theoretical results with observational data. The time series analyzed were obtained from the SOHO satellite mission where measurements were sampled every hour. We present in the investigations data for two years of different solar activity: (a) moderate activity (MA) period (1997) and (b) high activity (HA) period (2000). For the MA period, the results show good agreement between experimental data and GT model. For the HA period, the agreement between experimental and theoretical PDFs was fairly good, but some distortions were observed, probably due to intermittent characteristics of turbulent processes. As a complementary analysis, the Global Wavelet Spectrum (GWS) was obtained allowing the characterization of the predominant temporal variability scales for both the periods and the stochastics aspects of the nonlinear solar wind variability are discussed.

Abstract:
We investigate two important questions about the use of the nonextensive thermostatistics (NETS) formalism in the context of nonlinear galaxy clustering in the Universe. Firstly, we define a quantitative criterion for justifying nonextensivity at different physical scales. Then, we discuss the physics behind the ansatz of the entropic parameter $q(r)$. Our results suggest the approximate range where nonextensivity can be justified and, hence, give some support to the applicability of NETS to the study of large scale structures.

Abstract:
In this paper we describe two new computational operators, called complex entropic form (CEF) and generalized complex entropic form (GEF), for pattern characterization of spatially extended systems. Besides of being a measure of regularity, both operators permit to quantify the degree of phase disorder associated with a given gradient field. An application of CEF and GEF to the analysis of the gradient pattern dynamics of a logistic Coupled Map Lattice is presented. Simulations using a Gaussian and random initial condition, provide interesting insights on the the system gradual transition from order/symmetry to disorder/randomness.

Abstract:
In this paper, we discuss the impact of a rain forest canopy on the statistical characteristics of atmospheric turbulence. This issue is of particular interest for understanding on how the Amazon terrestrial biosphere interact with the atmosphere. For this, we used a probability density function model of velocity and temperature differences based on Tsallis' non-extensive thermostatistics. We compared theoretical results with experimental data measured in a 66 m micrometeorological tower, during the wet-season campaign of the Large Scale Biosphere-Atmosphere Experiment in Amazonia (LBA). Particularly, we investigated how the value of the entropic parameter is affected when one moves into the canopy, or when one passes from day/unstable to night/stable conditions. We show that this new approach provides interesting insights on turbulence in a complex environment such as the Amazon forest.