We present the results of an analytical calculation of the distribution of gluons in the state immediately following a heavy ion collision in the quasi–classical limit of QCD given by McLerran–Venugopalan model. We show that the typical transverse energy ET of the produced gluons is of the order of the saturation scale of the nuclei Qs, as predicted by Mueller. We demonstrate that due to multip...

The long-time behaviour of many dynamical systems may be effectively predicted by a low-dimensional model that describes the evolution of a reduced set of variables. We consider the question of how to equip such a low-dimensional model with appropriate initial conditions, so that it faithfully reproduces the long-term behaviour of the original high-dimensional dynamical system. Our method invol...

Our goal is to develop model reduction processes for linear dynamical systems with non-zero initial conditions. Standard model reduction schemes optimize system input/output characteristics but frequently destroy initial condition state space information. Additionally, existing model reduction schemes for initial conditions inappropriately assign weight to initial condition information. We prop...

This paper introduces a systematic treatment of the linear theory of scalar gravitational perturbations in the presence of a fully inhomogeneous magnetic field. The analysis is conducted both in the synchronous and in the conformally Newtonian gauges. The cosmological plasma is assumed to be composed of cold dark mattter, baryons, photons, neutrinos. The problem of super-horizon initial conditi...

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We present several recent results concerning the transition between quantum and classical mechanics, in the situation where the underlying dynamical system has an hyperbolic behaviour. The special role of invariant manifolds will be emphasized, and the long time evolution will show how the quantum non-determinism and the classical chaotic sensitivity to initial conditions can be compared, and i...

Relationships between diverse thermodynamic quantities appropriate to weakly compressible turbulence are derived. It is shown that for turbulence of a nite turbulent Mach number there is a nite eeect of compressibility. A methodology for generating initial conditions for the uctuating pressure, density and dilatational velocity is given which is consistent with nite Mach number eeects. Use of t...

— in spite of the large amount of existing neural models in the literature, there is a lack of a systematic review of the possible effect of choosing different initial conditions on the dynamic evolution of neural systems. In this short review we intend to give insights into this topic by discussing some published examples. First, we briefly introduce the different ingredients of a neural dynam...

Context. The majority of stars form in clusters. Therefore a comprehensive view of star formation requires understanding the initial conditions for cluster formation. Aims. The goal of our study is to shed light on the physical properties of infrared dark clouds (IRDCs) and the role they play in the formation of stellar clusters. This article, the first of a series dedicated to the study of IRD...

We discuss a new algorithm to generate multi-scale initial conditions with multiple levels of refinements for cosmological “zoom-in” simulations. The method uses an adaptive convolution of Gaussian white noise with a real space transfer function kernel together with an adaptive multi-grid Poisson solver to generate displacements and velocities following first (1LPT) or second order Lagrangian p...