4,669 research outputs found

### Absolute and convective instabilities of an inviscid compressible mixing layer: Theory and applications

This study aims to examine the effect of compressibility on unbounded and parallel shear flow linear instabilities. This analysis is of interest for industrial, geophysical, and astrophysical flows. We focus on the stability of a wavepacket as opposed to previous single-mode stability studies. We consider the notions of absolute and convective instabilities first used to describe plasma instabilities. The compressible-flow modal theory predicts instability whatever the Mach number. Spatial and temporal growth rates and Reynolds stresses nevertheless become strongly reduced at high Mach numbers. The evolution of disturbances is driven by Kelvin -Helmholtz instability that weakens in supersonic flows. We wish to examine the occurrence of absolute instability, necessary for the appearance of turbulent motions in an inviscid and compressible two-dimensional mixing layer at an arbitrary Mach number subject to a three-dimensional disturbance. The mixing layer is defined by a parametric family of mean-velocity and temperature profiles. The eigenvalue problem is solved with the help of a spectral method. We ascertain the effects of the distribution of temperature and velocity in the mixing layer on the transition between convective and absolute instabilities. It appears that, in most cases, absolute instability is always possible at high Mach numbers provided that the ratio of slow-stream temperature over fast-stream temperature may be less than a critical maximal value but the temporal growth rate present in the absolutely unstable zone remains small and tends to zero at high Mach numbers. The transition toward a supersonic turbulent regime is therefore unlikely to be possible in the linear theory. Absolute instability can be also present among low-Mach-number coflowing mixing layers provided that this same temperature ratio may be small, but nevertheless, higher than a critical minimal value. Temperature distribution within the mixing layer also has an effect on the growth rate, this diminishes when the slow stream is heated. These results are applied to the dynamics of mixing layers in the interstellar medium and to the dynamics of the heliopause, frontier between the interstellar medium, and the solar wind. (C) 2009 American Institute of Physics

### Non-Perturbative Renormalization Group for Simple Fluids

We present a new non perturbative renormalization group for classical simple
fluids. The theory is built in the Grand Canonical ensemble and in the
framework of two equivalent scalar field theories as well. The exact mapping
between the three renormalization flows is established rigorously. In the Grand
Canonical ensemble the theory may be seen as an extension of the Hierarchical
Reference Theory (L. Reatto and A. Parola, \textit{Adv. Phys.}, \textbf{44},
211 (1995)) but however does not suffer from its shortcomings at subcritical
temperatures. In the framework of a new canonical field theory of liquid state
developed in that aim our construction identifies with the effective average
action approach developed recently (J. Berges, N. Tetradis, and C. Wetterich,
\textit{Phys. Rep.}, \textbf{363} (2002))

### How Multivalency controls Ionic Criticality

To understand how multivalency influences the reduced critical temperatures,
Tce (z), and densities, roce (z), of z : 1 ionic fluids, we study equisized
hard-sphere models with z = 1-3. Following Debye, Hueckel and Bjerrum,
association into ion clusters is treated with, also, ionic solvation and
excluded volume. In good accord with simulations but contradicting
integral-equation and field theories, Tce falls when z increases while roce
rises steeply: that 80-90% of the ions are bound in clusters near T_c serves to
explain these trends. For z \neq 1 interphase Galvani potentials arise and are
evaluated.Comment: 4 pages, 4 figure

### Monte Carlo simulation method for Laughlin-like states in a disk geometry

We discuss an alternative accurate Monte Carlo method to calculate the
ground-state energy and related quantities for Laughlin states of the
fractional quantum Hall effect in a disk geometry. This alternative approach
allows us to obtain accurate bulk regime (thermodynamic limit) values for
various quantities from Monte Carlo simulations with a small number of
particles (much smaller than that needed with standard Monte Carlo approaches).Comment: 13 pages, 6 figures, 2 table

### Discretization Dependence of Criticality in Model Fluids: a Hard-core Electrolyte

Grand canonical simulations at various levels, $\zeta=5$-20, of fine- lattice
discretization are reported for the near-critical 1:1 hard-core electrolyte or
RPM. With the aid of finite-size scaling analyses it is shown convincingly
that, contrary to recent suggestions, the universal critical behavior is
independent of $\zeta$ (\grtsim 4); thus the continuum $(\zeta\to\infty)$ RPM
exhibits Ising-type (as against classical, SAW, XY, etc.) criticality. A
general consideration of lattice discretization provides effective
extrapolation of the {\em intrinsically} erratic $\zeta$-dependence, yielding
(\Tc^ {\ast},\rhoc^{\ast})\simeq (0.0493_{3},0.075) for the $\zeta=\infty$
RPM.Comment: 4 pages including 4 figure

### Hypernetted-chain study of broken rotational symmetry states for the $\bm{\nu}$ = 1/3 fractional quantum Hall effect and other fractionally filled Landau levels

We investigate broken rotational symmetry (BRS) states for the fractional
quantum Hall effect (FQHE) at 1/3-filling of the valence Landau level (LL).
Recent Monte Carlo calculations by Musaelian and Joynt [J. Phys.: Condens.\
Matter {\bf 8}, L105 (1996)] suggest that Laughlin's state becomes unstable to
a BRS state for some critical finite thickness value. We study in detail the
properties of such state by performing a hypernetted-chain calculation that
gives results in the thermodynamic limit, complementing other methods which are
limited to a finite number of particles. Our results indicate that while
Laughlin's state is stable in the lowest LL, in higher LLs a BRS instability
occurs, perhaps indicating the absence of FQHE at partial fillings of higher
LLs. Possible connections to the newly discovered liquid crystalline phases in
higher LLs are also discussed.Comment: 7 pages including 3 eps figure

### Equation of state in the fugacity format for the two-dimensional Coulomb gas

We derive the exact general form of the equation of state, in the fugacity
format, for the two-dimensional Coulomb gas. Our results are valid in the
conducting phase of the Coulomb gas, for temperatures above the
Kosterlitz-Thouless transition. The derivation of the equation of state is
based on the knowledge of the general form of the short-distance expansion of
the correlation functions of the Coulomb gas. We explicitly compute the
expansion up to order $O(\zeta^6)$ in the activity $\zeta$. Our results are in
very good agreement with Monte Carlo simulations at very low density

### Scalar Casimir Effect on a D-dimensional Einstein Static Universe

We compute the renormalised energy momentum tensor of a free scalar field
coupled to gravity on an (n+1)-dimensional Einstein Static Universe (ESU),
RxS^n, with arbitrary low energy effective operators (up to mass dimension
n+1). A generic class of regulators is used, together with the Abel-Plana
formula, leading to a manifestly regulator independent result. The general
structure of the divergences is analysed to show that all the gravitational
couplings (not just the cosmological constant) are renormalised for an
arbitrary regulator. Various commonly used methods (damping function,
point-splitting, momentum cut-off and zeta function) are shown to, effectively,
belong to the given class. The final results depend strongly on the parity of
n. A detailed analytical and numerical analysis is performed for the behaviours
of the renormalised energy density and a quantity `sigma' which determines if
the strong energy condition holds for the `quantum fluid'. We briefly discuss
the quantum fluid back-reaction problem, via the higher dimensional Friedmann
and Raychaudhuri equations, observe that equilibrium radii exist and unveil the
possibility of a `Casimir stabilisation of Einstein Static Universes'.Comment: 37 pages, 15 figures, v2: minor changes in sections 1, 2.5, 3 and 4;
version published in CQ

### The density functional theory of classical fluids revisited

We reconsider the density functional theory of nonuniform classical fluids
from the point of view of convex analysis. From the observation that the
logarithm of the grand-partition function $\log \Xi [\phi]$ is a convex
functional of the external potential $\phi$ it is shown that the Kohn-Sham free
energy ${\cal A}[\rho]$ is a convex functional of the density $\rho$. $\log \Xi
[\phi]$ and ${\cal A}[\rho]$ constitute a pair of Legendre transforms and each
of these functionals can therefore be obtained as the solution of a variational
principle. The convexity ensures the unicity of the solution in both cases. The
variational principle which gives $\log \Xi [\phi]$ as the maximum of a
functional of $\rho$ is precisely that considered in the density functional
theory while the dual principle, which gives ${\cal A}[\rho]$ as the maximum of
a functional of $\phi$ seems to be a new result.Comment: 10 page

### Exchange-correlation vector potentials and vorticity-dependent exchange-correlation energy densities in two-dimensional systems

We present a new approach how to calculate the scalar exchange-correlation
potentials and the vector exchange-correlation potentials from current-carrying
ground states of two-dimensional quantum dots. From these exchange-correlation
potentials we derive exchange-correlation energy densities and examine their
vorticity (or current) dependence. Compared with parameterizations of
current-induced effects in literature we find an increased significance of
corrections due to paramagnetic current densities.Comment: 5 figures, submitted to PR

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