Related papers: Phenomena in Gravitational Clustering
Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here,…
The interplay between gravitational and dispersive forces in a multi-streamed medium leads to an effect which is exposed in the present note as the genuine driving force of stabilization of large-scale structure. The conception of `adhesive…
Can local fluctuations of a ``Quintessence'' scalar field play a dynamical role in the gravitational clustering and cosmic structure formation process? We address this question in the general framework of scalar-tensor theories of gravity.…
The authors study the method of scaling in the context of the study of automorphism groups of complex domains in multiple dimensions. Various types of scaling techniques are compared and contrasted. Applications are given in a number of…
A new approach to study the scaling behavior of the scalar theory near the Gaussian fixed point in $d$-dimensions is presented. For a class of initial data an explicit use of the Green's function of the evolution equation is made. It is…
I review the theory of hierarchical clustering, starting with an historical overview and moving on to a discussion of those aspects of dissipationless clustering under gravity which are most relevant to galaxy formation. I conclude with…
We consider the problem of gravitational clustering in a D-dimensional expanding Universe and derive scaling relations connecting the exact mean two-point correlation function with the linear mean correlation function, in the quasi-linear…
In this paper we consider extensions of the gradient elasticity models proposed earlier by the second author to describe materials with fractional non-locality and fractality using the techniques developed recently by the first author. We…
The understanding of the large-scale structure formation requires the resolution of coupled nonlinear equations describing the cosmic density and velocity fields. This is a complicated problem that, for the last decade, has been essentially…
We review several aspects of clusters of galaxies and their application to cosmology. We present first results of numerical simulations of the dynamics of the intra-cluster gas and of different interaction processes between cluster galaxies…
Research done during the previous century established our Standard Cosmological Model. There are many details still to be filled in, but few would seriously doubt the basic premise. Past surveys have revealed that the large-scale…
Graphs are commonly used to represent and visualize causal relations. For a small number of variables, this approach provides a succinct and clear view of the scenario at hand. As the number of variables under study increases, the graphical…
The process of formation of fractal structure in one-dimensional self-gravitating system is examined numerically. It is clarified that structures created in small spatial scale grow up to larger scale through clustering of clusters, and…
The study of granular crystals, metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics,…
We discuss the differences and analogies of gravitational clustering in finite and infinite systems. The process of collective, or violent, relaxation leading to the formation of quasi-stationary states is one of the distinguished features…
There is evidence of a scale-invariant matter distribution up to scales over 10 Megaparsecs. We review scaling (fractal or multifractal) models of large scale structure and their observational evidence. We conclude that the dynamics of…
The largest uncertainty for cosmological studies using clusters of galaxies is introduced by our limited knowledge of the statistics of galaxy cluster structure, and of the scaling relations between observables and cluster mass. A large…
Galaxy clusters are sources of gravitational radiation. The main aim of this paper is to give numerical estimates and theoretical description of the relevant features of the gravitational radiation coming from an appropriate spatial…
Graph clustering is a fundamental problem in unsupervised learning, with numerous applications in computer science and in analysing real-world data. In many real-world applications, we find that the clusters have a significant high-level…
Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation…