On the vanishing electron-mass limit in plasma hydrodynamics in unbounded media

We consider the zero-electron-mass limit for the Navier-Stokes-Poisson system in unbounded spatial domains. Assuming smallness of the viscosity coefficient and ill-prepared initial data, we show that the asymptotic limit is represented by the incompressible Navier-Stokes system, with a Brinkman damping, in the case when viscosity is proportional to the electron-mass, and by the incompressible Euler system provided the viscosity is dominated by the electron mass. The proof is based on the RAGE theorem and dispersive estimates for acoustic waves, and on the concept of suitable weak solutions for the compressible Navier-Stokes system

Low Mach number limit for the Quantum-Hydrodynamics system

In this paper we deal with the low Mach number limit for the system of quantum-hydrodynamics, far from the vortex nucleation regime. More precisely, in the framework of a periodic domain and ill-prepared initial data we prove strong convergence of the solutions towards regular solutions of the incompressible Euler system. In particular we will perform a detailed analysis of the time oscillations and of the relative entropy functional related to the system.Comment: To appear in Research in the Mathematical Science

Hydrodynamic Methods and Exact Solutions in Application to the Electromagnetic Field Theory in Medium

The new Vavilov-Cherenkov radiation theory which is based on the relativistic generalization of the Landau theory for superfluid threshold velocity and Abraham theory of the electromagnetic field (EMF) in medium is represented. The new exact solution of the Cauchy problem in unbounded space is obtained for the n-dimensional Euler-Helmholtz (EH) equation in the case of a nonzero-divergence velocity field for an ideal compressible medium. The solution obtained describes the inertial vortex motion and coincides with the exact solution to the n-dimensional Hopf equation which simulates turbulence without pressure. Due to the introduction of a fairly large external friction or by introducing an arbitrary small effective volume viscosity, a new analytic solution of the Cauchy problem for the three-dimensional Navier-Stokes (NS) equation is obtained for compressible flows. This gives the positive solution to the Clay problem (www.clamath.org) generalization on the compressible NS equation. This solution also gives the possibility to obtain a new class of regular solutions to the n-dimensional modification of the Kuramoto-Sivashinsky equation, which is ordinarily used for the description of the nonlinear propagation of fronts in active media. The example for potential application of the new exact solution to the Hopf equation is considered in the connection of nonlinear geometrical optics with weak nonlinear medium at the nonlocality of the small action radii

Recent results in relativistic heavy ion collisions: from ``a new state of matter'' to "the perfect fluid"

Experimental Physics with Relativistic Heavy Ions dates from 1992 when a beam of 197Au of energy greater than 10A GeV/c first became available at the Alternating Gradient Synchrotron (AGS) at Brookhaven National Laboratory (BNL) soon followed in 1994 by a 208Pb beam of 158A GeV/c at the Super Proton Synchrotron (SPS) at CERN (European Center for Nuclear Research). Previous pioneering measurements at the Berkeley Bevalac in the late 1970's and early 1980's were at much lower bombarding energies (~ 1 A GeV/c) where nuclear breakup rather than particle production is the dominant inelastic process in A+A collisions. More recently, starting in 2000, the Relativistic Heavy Ion Collider (RHIC) at BNL has produced head-on collisions of two 100A GeV beams of fully stripped Au ions, corresponding to nucleon-nucleon center-of-mass energy, sqrt(sNN)=200 GeV, total c.m. energy 200A GeV. The objective of this research program is to produce nuclear matter with extreme density and temperature, possibly resulting in a state of matter where the quarks and gluons normally confined inside individual nucleons (r < 1 fm) are free to act over distances an order of magnitude larger. Progress from the period 1992 to the present will be reviewed, with reference to previous results from light ion and proton-proton collisions where appropriate. Emphasis will be placed on the measurements which formed the basis for the announcements by the two major laboratories: "A new state of matter", by CERN on Feb 10, 2000 and "The perfect fluid", by BNL on April 19, 2005.Comment: 62 pages, 39 figures. Review article published in Reports on Progress in Physics on June 23, 2006. In this published version, mistakes, typographical errors, and citations have been corrected and a subsection has been adde

Non-Isobaric Thermal Instability

Multiphase media have very complex structure and evolution. Accurate numerical simulations are necessary to make advances in our understanding of this rich physics. Because simulations can capture both the linear and nonlinear evolution of perturbations with a relatively wide range of sizes, it is important to thoroughly understand the stability of condensation and acoustic modes between the two extreme wavelength limits of isobaric and isochoric instability as identified by Field. Partially motivated by a recent suggestion that large non-isobaric clouds can shatter into tiny cloudlets, we revisit the linear theory to survey all possible regimes of thermal instability. We uncover seven regimes in total, one of which allows three unstable condensation modes. Using the code Athena++, we determine the numerical requirements to properly evolve small amplitude perturbations of the entropy mode into the nonlinear regime. Our 1D numerical simulations demonstrate that for a typical AGN cooling function, the nonlinear evolution of a single eigenmode in an isobarically unstable plasma involves increasingly larger amplitude oscillations in cloud size, temperature, and density as the wavelength increases. Such oscillations are the hallmark behavior of non-isobaric multiphase gas dynamics and may be observable as correlations between changes in brightness and the associated periodic redshifts and blueshifts in systems that can be spatially resolved. Intriguingly, we discuss regimes and derive characteristic cloud sizes for which the saturation process giving rise to these oscillations can be so energetic that the cloud may indeed break apart. However, we dub this process splattering instead of shattering, as it is a different fragmentation mechanism that is triggered when the cloud suddenly lands on the stable cold branch of the equilibrium curve