Related papers: Phenomena in Gravitational Clustering
Scaling relations for the mass, angular momentum and other properties of a wide range of self-similar structures in the universe are seen to have universal features. As a consequence of the ideas elaborated in earlier papers these relations…
These lecture notes concentrate on a few specific topics concerning the distribution of galaxies on scales from 0.1 to nearly 1000/h Mpc. The main aim is to provide the students with the information and tools to familiarize with a few basic…
In this paper, we will study the large scale structure formation using the gravitational partition function. We will assertively argue that the system of gravitating galaxies can be analyzed using the Tsallis statistical mechanics. The…
We consider the influence of a power-law deviation from the critical coupling such that the system is critical at its surface. We develop a scaling theory showing that such a perturbation introduces a new length scale which governs the…
We give a brief introduction to (upper) cluster algebras and their quantization using examples. Then we present several important families of bases for these algebras using topological models. We also discuss tropical properties of these…
We consider gravitational clustering from primoridal non-Gaussian fluctuations provided by a $\chi^2$ model, as motivated by some models of inflation. The emphasis is in signatures that can be used to constrain this type of models from…
q-deformed nonlinear field equations are constructed including Klein-Gordon and Maxwell equations. The q-deformation is interpreted as mathematical structure describing specific nonlinearity for which frequency of vibration exponentially…
Linear rate equations are used to describe the cascading decay of an initial heavy cluster into fragments. We consider moments of arbitrary orders of the mass multiplicity spectrum and derive scaling properties pertaining to their time…
The observation of scaling in processes in which a weakly interacting probe delivers large momentum ${\bf q}$ to a many-body system simply reflects the dominance of incoherent scattering off target constituents. While a suitably defined…
A fourth-order and a second-order nonlinear diffusion models in spectral space are proposed to describe gravitational wave turbulence in the approximation of strongly local interactions. We show analytically that the model equations satisfy…
We propose a possible relation between complex networks and gravity. Our guide in our proposal is the power-law distribution of the node degree in network theory and the information approach to gravity. The established bridge may allow us…
Cosmic structures at large scales represent the earliest and most extended form of matter condensation. In this lecture we review the application of the methods and concepts of modern statistical physics to these structures. This leads to a…
Macroscopic equations arising out of stochastic particle systems in detailed balance (called dissipative systems or gradient flows) have a natural variational structure, which can be derived from the large-deviation rate functional for the…
An overview of recent results with CLAS is presented with emphasis on nucleon resonance studies, nucleon spin structure, and generalized parton distributions.
This note aims to offer a non-technical and self-contained introduction to gravitational algebras and their applications in the nonequilibrium physics of gravitational systems. We begin by presenting foundational concepts from operator…
We probe gravitational clustering in N-body simulations using geometrical descriptors sensitive to `connectedness': the genus curve, percolation and shape statistics. We find that both genus and percolation curves provide complementary…
We study the large-scale structure formation in the Universe in the frame of scalar-tensor theories as an alternative to general relativity. We review briefly the Newtonian limit of non-minimally coupled scalar-tensor theories and the…
Scalar fields are crucial components in high energy physics and extensions of General Relativity. The fact they are not observed in the solar system may be due to a mechanism which screens their presence in high dense regions. We show how…
Theory of matrix factorizations is useful to study hypersurfaces in commutative algebra. To study noncommutative hypersurfaces, which are important objects of study in noncommutative algebraic geometry, we introduce a notion of…
Geometric constraints impact the formation of a broad range of spatial networks, from amino acid chains folding to proteins structures to rearranging particle aggregates. How the network of interactions dynamically self-organizes in such…