Gravitational collapse of a charged and radiating fluid ball in the diffusion limit

1996 ◽  
Vol 28 (6) ◽  
pp. 735-747 ◽  
Author(s):  
W. Barreto ◽  
A. Da Silva
Keyword(s):  
Gravitational Collapse ◽  
Diffusion Limit ◽  
Fluid Ball

Introduction

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Gravitational Collapse ◽  
Present State ◽  
Strong Gravity ◽  
Shape Dynamics

Shape Dynamics (SD) is a field theory that describes gravity in a different way than General Relativity (GR): it assumes a preferred notion of simultaneity, and the dynamical content of the theory consists of conformal 3- geometries. SD coincides with (GR) in most situations, in particular in the experimentally well-tested regimes, but it departs from it in some strong-gravity situations, for example at cosmological singularities or upon gravitational collapse. This chapter provides a quick introduction to the theory and a brief description of its present state.

scholarly journals Steady-State Analysis of the Join-the-Shortest-Queue Model in the Halfin–Whitt Regime

2020 ◽  
Vol 45 (3) ◽  
pp. 1069-1103
Author(s):  
Anton Braverman
Keyword(s):  
Steady State ◽  
Diffusion Limit ◽  
Fluid Limit ◽  
Time Intervals ◽  
Dimensional Diffusion ◽  
Queue Model ◽  
Join The Shortest Queue ◽  
Shortest Queue ◽  
Process Level ◽  
General Tool

This paper studies the steady-state properties of the join-the-shortest-queue model in the Halfin–Whitt regime. We focus on the process tracking the number of idle servers and the number of servers with nonempty buffers. Recently, Eschenfeldt and Gamarnik proved that a scaled version of this process converges, over finite time intervals, to a two-dimensional diffusion limit as the number of servers goes to infinity. In this paper, we prove that the diffusion limit is exponentially ergodic and that the diffusion scaled sequence of the steady-state number of idle servers and nonempty buffers is tight. Combined with the process-level convergence proved by Eschenfeldt and Gamarnik, our results imply convergence of steady-state distributions. The methodology used is the generator expansion framework based on Stein’s method, also referred to as the drift-based fluid limit Lyapunov function approach in Stolyar. One technical contribution to the framework is to show how it can be used as a general tool to establish exponential ergodicity.

scholarly journals Generalized fractional Poisson process and related stochastic dynamics

2020 ◽  
Vol 23 (3) ◽  
pp. 656-693 ◽  
Author(s):  
Thomas M. Michelitsch ◽  
Alejandro P. Riascos
Keyword(s):  
Poisson Process ◽  
Continuous Time ◽  
Counting Process ◽  
Stochastic Dynamics ◽  
Waiting Times ◽  
Fractional Diffusion ◽  
Diffusion Limit ◽  
Fractional Operators ◽  
Fractional Poisson Process ◽  
Erlang Process

AbstractWe survey the ‘generalized fractional Poisson process’ (GFPP). The GFPP is a renewal process generalizing Laskin’s fractional Poisson counting process and was first introduced by Cahoy and Polito. The GFPP contains two index parameters with admissible ranges 0 < β ≤ 1, α > 0 and a parameter characterizing the time scale. The GFPP involves Prabhakar generalized Mittag-Leffler functions and contains for special choices of the parameters the Laskin fractional Poisson process, the Erlang process and the standard Poisson process. We demonstrate this by means of explicit formulas. We develop the Montroll-Weiss continuous-time random walk (CTRW) for the GFPP on undirected networks which has Prabhakar distributed waiting times between the jumps of the walker. For this walk, we derive a generalized fractional Kolmogorov-Feller equation which involves Prabhakar generalized fractional operators governing the stochastic motions on the network. We analyze in d dimensions the ‘well-scaled’ diffusion limit and obtain a fractional diffusion equation which is of the same type as for a walk with Mittag-Leffler distributed waiting times. The GFPP has the potential to capture various aspects in the dynamics of certain complex systems.

Diffusion limit of a Boltzmann–Poisson system with nonlinear equilibrium state

2019 ◽  
Vol 16 (01) ◽  
pp. 131-156
Author(s):  
Lanoir Addala ◽  
Mohamed Lazhar Tayeb
Keyword(s):  
Nonlinear Diffusion ◽  
Collision Operator ◽  
Nonlinear Diffusion Equation ◽  
One Dimension ◽  
Diffusion Limit ◽  
Poisson System ◽  
Nonlinear Relaxation ◽  
Contraction Property ◽  
Hilbert Expansion ◽  
Nonlinear Equilibrium

The diffusion approximation for a Boltzmann–Poisson system is studied. Nonlinear relaxation type collision operator is considered. A relative entropy is used to prove useful [Formula: see text]-estimates for the weak solutions of the scaled Boltzmann equation (coupled to Poisson) and to prove the convergence of the solution toward the solution of a nonlinear diffusion equation coupled to Poisson. In one dimension, a hybrid Hilbert expansion and the contraction property of the operator allow to exhibit a convergence rate.

scholarly journals Magnetic field amplification in newly-born neutron stars

1996 ◽  
Vol 160 ◽  
pp. 435-436
Author(s):  
H.-J. Wiebicke ◽  
U. Geppert
Keyword(s):  
Magnetic Field ◽  
Neutron Stars ◽  
Gravitational Collapse ◽  
Dipole Field ◽  
Numerical Calculations ◽  
Selection Effects ◽  
Thermoelectric Effects ◽  
Field Amplification ◽  
Seed Field ◽  
Flux Conservation

AbstractWe present a scenario of magnetic field (MF) evolution of newly-born neutron stars (NSs). Numerical calculations show that in the hot phase of young NSs the MF can be amplified by thermoelectric effects, starting from a moderately strong seed-field. Therefore, there is no need to assume a 1012G dipole field immediately after the gravitational collapse of the supernova (SN) event. The widely accepted scenario for such a field to be produced by flux conservation during the collapse is critically discussed. Instead, it can be generated by amplification and selection effects in the first 104yrs, and by the subsequent fast ohmic decay of higher multipole components, when the NS cools down.

scholarly journals Examining gravitational collapse with test scalar fields

2010 ◽  
Vol 27 (16) ◽  
pp. 165019 ◽  
Author(s):  
Ryo Saotome ◽  
Ratindranath Akhoury ◽  
David Garfinkle
Keyword(s):  
Gravitational Collapse ◽  
Scalar Fields

scholarly journals Conformal mapping of the Misner–Sharp mass from gravitational collapse

2016 ◽  
Vol 25 (07) ◽  
pp. 1650081 ◽  
Author(s):  
Fayçal Hammad
Keyword(s):  
Conformal Mapping ◽  
Gravitational Collapse ◽  
Conformal Transformation ◽  
Conformal Mappings ◽  
Conformal Transformations ◽  
Theories Of Gravity ◽  
Definition Of ◽  
Geometric Definition

The conformal transformation of the Misner–Sharp mass is reexamined. It has recently been found that this mass does not transform like usual masses do under conformal mappings of spacetime. We show that when it comes to conformal transformations, the widely used geometric definition of the Misner–Sharp mass is fundamentally different from the original conception of the latter. Indeed, when working within the full hydrodynamic setup that gave rise to that mass, i.e. the physics of gravitational collapse, the familiar conformal transformation of a usual mass is recovered. The case of scalar–tensor theories of gravity is also examined.

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