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A. R. Rastegar

Publications and source records attributed to A. R. Rastegar.

7 recordsLinked to original sources
arXiv1999

Forced Burgers Turbulence in 3-Dimensions

We investigate non-perturbative results of inviscid forced Burgers equation supplemented to continuity equation in three-dimensions. The exact two-point correlation function of density is calculated in three-dimensions. The two-point correlator $<ρ(\bf x_1) ρ(\bf x_2)>$ behaves as $ |{\bf {x_1 - x_2}}|^{-α_3}$ and in the universal region $α_3 = 7/2$ while in the non-universal region $α_3 = 3$. In the non-universal region we drive a Kramers-Moyal equation governing the evolution of the probability density function (PDF) of longitudinal velocity increments for three dimensional Burgers turbulence. In this region we prove Yakhot's conjecture {[Phys. Rev. E {\bf 57}, 1737 (1998)]} for the equation of PDF for three dimensional Burgers turbulence. We also derive the intermittency exponents for the longitudinal structure functions and show that in the inertial regime one point $U_{rms}$ enters in the PDF of velocity difference.

chao-dyn↗
arXiv1999

Tunneling in $Λ$ Decaying Cosmologies and the Cosmological Constant Problem

The tunneling rate, with exact prefactor, is calculated to first order in $\hbar$ for an empty closed Friedmann-Robertson-Walker (FRW) universe with decaying cosmological term $Λ\sim R^{-m}$ ($R$ is the scale factor and $m$ is a parameter $0\leq m \leq 2$). This model is equivalent to a cosmology with the equation of state $p_χ=(m/3 -1)ρ_χ$. The calculations are performed by applying the dilute-instanton approximation on the corresponding Duru-Kleinert path integral. It is shown that the highest tunneling rate occurs for $m=2$ corresponding to the cosmic string matter universe. The obtained most probable cosmological term, like one obtained by Strominger, accounts for a possible solution to the cosmological constant problem.

gr-qc↗
arXiv1998

On Duru-Kleinert Path Integral In Quantum Cosmology

We show that the Duru-Kleinert fixed energy amplitude leads to the path integral for the propagation amplitude in the closed FRW quantum cosmology with scale factor as one degree of freedom. Then, using the Duru-Kleinert equivalence of corresponding actions, we calculate the tunneling rate, with exact prefactor, through the dilute-instanton approximation to first order in \hbar.

gr-qc↗
arXiv1998

Tunneling in a Cosmological Model with Violation of Strong Energy Condition

The tunneling rate, with exact prefactor, is calculated to first order in \hbar for a closed FRW universe filled with perfect fluid violating the strong energy condition. The calculations are performed by applying the dilute-instanton approximation on the corresponding Duru-Kleinert path integral. It is shown that a closed FRW universe filled with a perfect fluid with small violation of strong energy condition is more probable to tunnel than the same universe with large violation of strong energy condition.

gr-qc↗
arXiv1998

Exact Two-Point Correlation Functions of Turbulence Without Pressure in Three-Dimensions

We investigate exact results of isotropic turbulence in three-dimensions when the pressure gradient is negligible. We derive exact two-point correlation functions of density in three-dimensions and show that the density-density correlator behaves as $ |{x_1 - x_2}|^{-α_3}$, where $α_3 = 2 + \frac{\sqrt{33}}{6}$. It is shown that, in three-dimensions, the energy spectrum $E(k)$ in the inertial range scales with exponent $ 2 - \frac {\sqrt{33}}{12} \simeq 1.5212$. We also discuss the time scale for which our exact results are valid for strong 3D--turbulence in the presence of the pressure. We confirm our predictions by using the recent results of numerical calculations and experiment.

hep-th↗
arXiv1996

Turbulence With Pressure

We investigate the exact results of the Navier-Stokes equations using the methods developed by Polyakov. It is shown that when the velocity field and the density are not independent, the Burgers equation is obtained leading to exact N-point generating functions of velocity field. Our results show that, the operator product expansion has to be generalized both in the absence and the presence of pressure. We find a method to determine the extra terms in the operator product expansion and derive its coefficients and find the first correction to probablity distribuation function. In the general case and for small pressure, we solve the problem perturbatively and find the probablity distribuation function for the Navier-Stokes equation in the mean field approximation.

hep-th↗