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, $N \rightarrow \infty$, 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