1,116 research outputs found
Early nonlinear regime of MHD internal modes: the resistive case
It is shown that the critical layer analysis, involved in the linear theory
of internal modes, can be extended continuously into the early nonlinear
regime. For the m=1 resistive mode, the dynamical analysis involves two small
parameters: the inverse of the magnetic Reynolds number S and the m=1 mode
amplitude A, that measures the amount of nonlinearities in the system. The
location of the instantaneous critical layer and the dominant dynamical
equations inside it are evaluated self-consistently, as A increases and crosses
some S-dependent thresholds. A special emphasis is put on the influence of the
initial q-profile on the early nonlinear behavior. Predictions are given for a
family of q-profiles, including the important low shear case, and shown to be
consistent with recent experimental observations
Kinetic limit of N-body description of wave-particle self- consistent interaction
A system of N particles eN=(x1,v1,...,xN,vN) interacting self-consistently
with M waves Zn=An*exp(iTn) is considered. Hamiltonian dynamics transports
initial data (eN(0),Zn(0)) to (eN(t),Zn(t)). In the limit of an infinite number
of particles, a Vlasov-like kinetic equation is generated for the distribution
function f(x,v,t), coupled to envelope equations for the M waves. Any initial
data (f(0),Z(0)) with finite energy is transported to a unique (f(t),Z(t)).
Moreover, for any time T>0, given a sequence of initial data with N particles
distributed so that the particle distribution fN(0)-->f(O) weakly and with
Zn(0)-->Z(O) as N tends to infinity, the states generated by the Hamiltonian
dynamics at all time 0<t<T are such that (eN(t),Zn(t)) converges weakly to
(f(t),Z(t)). Comments: Kinetic theory, Plasma physics.Comment: 18 pages, LaTe
Chaos suppression in the large size limit for long-range systems
We consider the class of long-range Hamiltonian systems first introduced by
Anteneodo and Tsallis and called the alpha-XY model. This involves N classical
rotators on a d-dimensional periodic lattice interacting all to all with an
attractive coupling whose strength decays as r^{-alpha}, r being the distances
between sites. Using a recent geometrical approach, we estimate for any
d-dimensional lattice the scaling of the largest Lyapunov exponent (LLE) with N
as a function of alpha in the large energy regime where rotators behave almost
freely. We find that the LLE vanishes as N^{-kappa}, with kappa=1/3 for alpha/d
between 0 and 1/2 and kappa=2/3(1-alpha/d) for alpha/d between 1/2 and 1. These
analytical results present a nice agreement with numerical results obtained by
Campa et al., including deviations at small N.Comment: 10 pages, 3 eps figure
Occupational Tasks and Changes in the Wage Structure
This paper argues that changes in the returns to occupational tasks have contributed to changes in the wage distribution over the last three decades. Using Current Population Survey (CPS) data, we first show that the 1990s polarization of wages is explained by changes in wage setting between and within occupations, which are well captured by tasks measures linked to technological change and offshorability. Using a decomposition based on Firpo, Fortin, and Lemieux (2009), we find that technological change and deunionization played a central role in the 1980s and 1990s, while offshorability became an important factor from the 1990s onwards.wage inequality, polarization, occupational tasks, offshoring, RIF-regressions
Unconditional Quantile Regressions
We propose a new regression method to estimate the impact of explanatory variables on quantiles of the unconditional distribution of an outcome variable. The proposed method consists of running a regression of the (recentered) influence function (RIF) of the unconditional quantile on the explanatory variables. The influence function is a widely used tool in robust estimation that can easily be computed for each quantile of interest. We show how standard partial effects, as well as policy effects, can be estimated using our regression approach. We propose three different regression estimators based on a standard OLS regression (RIFOLS), a Logit regression (RIF-Logit), and a nonparametric Logit regression (RIFNP). We also discuss how our approach can be generalized to other distributional statistics besides quantiles.Influence Functions, Unconditional Quantile, Quantile Regressions.
Unveiling the nature of out-of-equilibrium phase transitions in a system with long-range interactions
Recently, there has been some vigorous interest in the out-of-equilibrium
quasistationary states (QSSs), with lifetimes diverging with the number N of
degrees of freedom, emerging from numerical simulations of the ferromagnetic XY
Hamiltonian Mean Field (HMF) starting from some special initial conditions.
Phase transitions have been reported between low-energy magnetized QSSs and
large-energy unexpected, antiferromagnetic-like, QSSs with low magnetization.
This issue is addressed here in the Vlasov N \rightarrow \infty limit. It is
argued that the time-asymptotic states emerging in the Vlasov limit can be
related to simple generic time-asymptotic forms for the force field. The
proposed picture unveils the nature of the out-of-equilibrium phase transitions
reported for the ferromagnetic HMF: this is a bifurcation point connecting an
effective integrable Vlasov one-particle time-asymptotic dynamics to a partly
ergodic one which means a brutal open-up of the Vlasov one-particle phase
space. Illustration is given by investigating the time-asymptotic value of the
magnetization at the phase transition, under the assumption of a sufficiently
rapid time-asymptotic decay of the transient force field
Equilibrium statistical mechanics for single waves and wave spectra in Langmuir wave-particle interaction
Under the conditions of weak Langmuir turbulence, a self-consistent
wave-particle Hamiltonian models the effective nonlinear interaction of a
spectrum of M waves with N resonant out-of-equilibrium tail electrons. In order
to address its intrinsically nonlinear time-asymptotic behavior, a Monte Carlo
code was built to estimate its equilibrium statistical mechanics in both the
canonical and microcanonical ensembles. First the single wave model is
considered in the cold beam/plasma instability and in the O'Neil setting for
nonlinear Landau damping. O'Neil's threshold, that separates nonzero
time-asymptotic wave amplitude states from zero ones, is associated to a second
order phase transition. These two studies provide both a testbed for the Monte
Carlo canonical and microcanonical codes, with the comparison with exact
canonical results, and an opportunity to propose quantitative results to
longstanding issues in basic nonlinear plasma physics. Then the properly
speaking weak turbulence framework is considered through the case of a large
spectrum of waves. Focusing on the small coupling limit, as a benchmark for the
statistical mechanics of weak Langmuir turbulence, it is shown that Monte Carlo
microcanonical results fully agree with an exact microcanonical derivation. The
wave spectrum is predicted to collapse towards small wavelengths together with
the escape of initially resonant particles towards low bulk plasma thermal
speeds. This study reveals the fundamental discrepancy between the long-time
dynamics of single waves, that can support finite amplitude steady states, and
of wave spectra, that cannot.Comment: 15 pages, 7 figures, to appear in Physics of Plasma
Linear theory and violent relaxation in long-range systems: a test case
In this article, several aspects of the dynamics of a toy model for longrange
Hamiltonian systems are tackled focusing on linearly unstable unmagnetized
(i.e. force-free) cold equilibria states of the Hamiltonian Mean Field (HMF).
For special cases, exact finite-N linear growth rates have been exhibited,
including, in some spatially inhomogeneous case, finite-N corrections. A random
matrix approach is then proposed to estimate the finite-N growth rate for some
random initial states. Within the continuous, , approach,
the growth rates are finally derived without restricting to spatially
homogeneous cases. All the numerical simulations show a very good agreement
with the different theoretical predictions. Then, these linear results are used
to discuss the large-time nonlinear evolution. A simple criterion is proposed
to measure the ability of the system to undergo a violent relaxation that
transports it in the vicinity of the equilibrium state within some linear
e-folding times
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