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This paper provides results on local and global existence for a class of solutions to the Euler equations for an incompressible, inviscid fluid. By considering a class of solutions which exhibits a characteristic growth at infinity we…
The large-scale structure of the Universe formed from initially small perturbations in the cosmic density field, leading to galaxy clusters with up to 10^15 Msun at the present day. Here, we review the formation of structures in the…
Closed, singularity-free, inflationary cosmological models have recently been studied in the context of general relativity. Despite their appeal, these so called emergent models suffer from a number of limitations. These include the fact…
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…
Clusters of galaxies, the most massive virialized systems known, provide a powerful tool for studying the structure, the mass density, and the cosmology of our universe. Clusters furnish one of the best estimates of the dynamical mass…
Estimating the age of the Universe is an old problem. Rapid progress in observational cosmology in recent years has led to more accurate values of the fundamental parameters. The current most popular model is a flat Universe, with about 30%…
We study the evolution of matter density perturbations in the framework of massive conformal gravity (MCG). Starting from the conservation of the energy-momentum tensor, we find the continuity and Euler equations for the conformal perfect…
We apply a unique gas fraction estimator to published X-ray cluster properties and we compare the derived gas fractions of observed clusters to simulated ones. The observations are consistent with a universal gas fraction of…
We obtain the specific heat in the third constraint scenario for a canonical ensemble of a nonextensive extreme relativistic ideal gas in a closed form. The canonical ensemble of N particles in D dimensions is well-defined for the choice of…
Observational evidence indicates that the role of gas is secondary to that of gravity in the formation of the most luminous spheroids inhabiting the centres of galaxy associations, as originally conjectured in the late 80's/early 90's.…
We outline a new model in which generalised uncertainty relations, that govern the behaviour of microscopic world, and dark energy, that determines the large-scale evolution of the Universe, are intrinsically linked via the quantum…
The general relativity is the base for any exact evolutionary theory of large scale structures. We calculate the universal 2+1-dimensional plane equations of gravitational field in general relativity. Based on the equations, the evolutions…
In this paper, we investigate the effects of a new version of the generalized uncertainty principle (modified GUP) on the dynamics of the Universe. As the modified GUP will modify the relation between the entropy and area of the apparent…
We review the observed properties of globular cluster systems and their implications for models of galaxy formation. Observations show that globular clusters form in gas-rich mergers, and that bimodal metallicity distributions are common in…
A general framework for an emergent universe scenario has been given which makes use of an equation of state. The general features of the model have also been studied and possible primordial composition of the universe have been suggested.
The interstellar medium (ISM) can be thought of as the galactic atmosphere which fills the space between stars. When clouds within the ISM collapse, stars are born. When the stars die, they return their matter to the surrounding gas.…
Self-gravitating systems such as elliptical galaxies appear to have a constant specific entropy and obey a scaling law relating their potential energy to their mass. These properties can be interpreted as due to the physical processes…
In these notes we show that any projective subspace arrangement can be realized as a generalized star configuration variety. This type of interpolation result may be useful in designing linear codes with prescribed codewords of minimum…
We show that all closed $2$-dimensional singularities for higher codimension mean curvature flow that cannot be perturbed away have uniform entropy bounds and lie in a linear subspace of small dimension. The entropy and dimension of the…
In a large scale view of the universe, galaxies are the basic unit of structure. A typical bright galaxy may contain 100 billion stars and span tens of thousands of light years, but the empty expanses between the galaxies are much larger…