Related papers: A critique of scaling behaviour in non-linear stru…
We have investigated the scale-invariant solutions of the BBGKY equations for spatial correlation functions of cosmological density fluctuations and the mean relative peculiar velocity in the strongly nonlinear regime. It is found that the…
We investigate stability of the scale-invariant solutions of the BBGKY equations for two-point spatial correlation functions of the density fluctuations in the strongly non-linear regime. In the case that the background skewness of the…
We have investigated the relation between the two-point spatial correlation function and the density profile of the dark matter halo in the strongly non-linear regime. It is well known that when the density fluctuation grows into dark…
We investigate non-linear scaling relations for two-dimensional gravitational collapse in an expanding background using a 2D TreePM code and study the strongly non-linear regime ($\bar\xi \leq 200$) for power law models. Evolution of these…
The growth of density perturbations in an expanding universe in the non-linear regime is investigated. The underlying equations of motion are cast in a suggestive form, and motivate a conjecture that the scaled pair velocity, $h(a,x)\equiv…
We use the BBGKY hierarchy equations to calculate, perturbatively, the lowest order nonlinear correction to the two point correlation and the pair velocity for Gaussian initial conditions in a critical density matter dominated cosmological…
Using an ensemble of high resolution 2D numerical simulations, we explore the scaling properties of cosmological density fluctuations in the non-linear regime. We study the scaling behaviour of the usual $N$--point volume-averaged…
It is known that radial collapse around density peaks can explain the key features of evolution of correlation function in gravitational clustering in three dimensions. The same model also makes specific predictions for two dimensions. In…
We present results for the cosmic non-linear density-fluctuation power spectrum based on the analytical formalism developed in [1] which allows us to study cosmic structure formation based on Newtonian particle dynamics in phase-space. This…
Studies of a class of infinite one dimensional self-gravitating systems have highlighted that, on the one hand, the spatial clustering which develops may have scale invariant (fractal) properties, and, on the other, that they display…
Large scale simulations of two-dimensional bidisperse granular fluids allow us to determine spatial correlations of slow particles via the four-point structure factor $S_4(q,t)$. Both cases, elastic ($\varepsilon=1$) as well as inelastic…
We investigate the nonlinear instability of a smooth steady density profile solution of the threedimensional nonhomogeneous incompressible Navier-Stokes equations in the presence of a uniform gravitational field, including a Rayleigh-Taylor…
We continue our exploration of the wiggly generalisation of the Velocity-Dependent One Scale Model for cosmic strings, through the study of its allowed asymptotic scaling solutions. We extend the work of a previous paper [Almeida $\&$…
Bouncing solutions are obtained from a generally covariant action characterized by a potential which is a nonlocal functional of the dilaton field at two separated space-time points. Gradient instabilities are shown to arise in this context…
An exact nonlinear scaling transformation is presented for the local three-dimensional dynamical equations of motion for differentially rotating disks. The result is relevant to arguments that have been put forth claiming that numerical…
We consider Vlasov-type scaling for the Glauber dynamics in continuum with a positive integrable potential, and construct rescaled and limiting evolutions of correlation functions. Convergence to the limiting evolution for the positive…
We present a study of dynamical scaling and front motion in a one dimensional system that describes Rayleigh-Benard convection in a rotating cell. We use a model of three competing modes proposed by Busse and Heikes to which spatial…
We propose new scaling laws for the properties of planetary dynamos. In particular, the Rossby number, the magnetic Reynolds number, the ratio of magnetic to kinetic energy, the Ohmic dissipation timescale and the characteristic aspect…
The cosmological evolution of topological defect networks can broadly be divided into two stages. At early times they are friction-dominated due to particle scattering and therefore non-relativistic, and may either be conformally stretched…
At the jamming transition, amorphous packings are known to display anomalous vibrational modes with a density of states (DOS) that remains constant at low frequency. The scaling of the DOS at higher densities remains, however, unclear. One…