380 research outputs found
Direct path from microscopic mechanics to Debye shielding, Landau damping, and wave-particle interaction
The derivation of Debye shielding and Landau damping from the -body
description of plasmas is performed directly by using Newton's second law for
the -body system. This is done in a few steps with elementary calculations
using standard tools of calculus, and no probabilistic setting. Unexpectedly,
Debye shielding is encountered together with Landau damping. This approach is
shown to be justified in the one-dimensional case when the number of particles
in a Debye sphere becomes large. The theory is extended to accommodate a
correct description of trapping and chaos due to Langmuir waves. Shielding and
collisional transport are found to be two related aspects of the repulsive
deflections of electrons, in such a way that each particle is shielded by all
other ones while keeping in uninterrupted motion.Comment: arXiv admin note: substantial text overlap with arXiv:1310.3096,
arXiv:1210.154
Finite thermal conductivity in 1d lattices
We discuss the thermal conductivity of a chain of coupled rotators, showing
that it is the first example of a 1d nonlinear lattice exhibiting normal
transport properties in the absence of an on-site potential. Numerical
estimates obtained by simulating a chain in contact with two thermal baths at
different temperatures are found to be consistent with those ones based on
linear response theory. The dynamics of the Fourier modes provides direct
evidence of energy diffusion. The finiteness of the conductivity is traced back
to the occurrence of phase-jumps. Our conclusions are confirmed by the analysis
of two variants of this model.Comment: 4 pages, 3 postscript figure
Landau model for uniaxial systems with complex order parameter
We study the Landau model for uniaxial incommensurate-commensurate systems of
the I class by keeping Umklapp terms of third and fourth order in the expansion
of the free energy. It applies to systems in which the soft mode minimum lies
between the corresponding commensurate wave numbers. The minimization of the
Landau functional leads to the sine-Gordon equation with two nonlinear terms,
equivalent to the equation of motion for the well-known classical mechanical
problem of two mixing resonances. We calculate the average free energies for
periodic, quasiperiodic and chaotic solutions of this equation, and show that
in the regime of finite strengths of Umklapp terms only periodic solutions are
absolute minima of the free energy, so that the phase diagram contains only
commensurate configurations. The phase transitions between neighboring
configurations are of the first order, and the wave number of ordering goes
through harmless staircase with a finite number of steps. These results are the
basis for the interpretation of phase diagrams for some materials from the I
class of incommensurate-commensurate systems, in particular of those for
ABX and BCCD compounds. Also, we argue that chaotic barriers which
separate metastable periodic solutions represent an intrinsic mechanism for
observed memory effects and thermal hystereses.Comment: 12 pages, 14 figures, LaTeX, to be published in Phys. Rev.
Scaling laws for the largest Lyapunov exponent in long-range systems: A random matrix approach
We investigate the laws that rule the behavior of the largest Lyapunov
exponent (LLE) in many particle systems with long range interactions. We
consider as a representative system the so-called Hamiltonian alpha-XY model
where the adjustable parameter alpha controls the range of the interactions of
N ferromagnetic spins in a lattice of dimension d. In previous work the
dependence of the LLE with the system size N, for sufficiently high energies,
was established through numerical simulations. In the thermodynamic limit, the
LLE becomes constant for alpha greater than d whereas it decays as an inverse
power law of N for alpha smaller than d. A recent theoretical calculation based
on Pettini's geometrization of the dynamics is consistent with these numerical
results (M.-C. Firpo and S. Ruffo, cond-mat/0108158). Here we show that the
scaling behavior can also be explained by a random matrix approach, in which
the tangent mappings that define the Lyapunov exponents are modeled by random
simplectic matrices drawn from a suitable ensemble.Comment: 5 pages, no figure
An approximate renormalization-group transformation for Hamiltonian systems with three degrees of freedom
We construct an approximate renormalization transformation that combines
Kolmogorov-Arnold-Moser (KAM)and renormalization-group techniques, to analyze
instabilities in Hamiltonian systems with three degrees of freedom. This scheme
is implemented both for isoenergetically nondegenerate and for degenerate
Hamiltonians. For the spiral mean frequency vector, we find numerically that
the iterations of the transformation on nondegenerate Hamiltonians tend to
degenerate ones on the critical surface. As a consequence, isoenergetically
degenerate and nondegenerate Hamiltonians belong to the same universality
class, and thus the corresponding critical invariant tori have the same type of
scaling properties. We numerically investigate the structure of the attracting
set on the critical surface and find that it is a strange nonchaotic attractor.
We compute exponents that characterize its universality class.Comment: 10 pages typeset using REVTeX, 7 PS figure
Foliar lead uptake by lettuce exposed to atmospheric fallouts
Metal uptake by plants occurs by soil−root transfer but also by direct transfer of contaminants from the atmosphere to the shoots. This second pathway may be particularly important in kitchen gardens near industrial plants. The mechanisms of foliar uptake of lead by lettuce (Lactuca sativa) exposed to the atmospheric fallouts of a lead-recycling plant were studied. After 43 days of exposure, the thoroughly washed leaves contained 335 ± 50 mg Pb kg−1 (dry weight). Micro-X-ray fluorescence mappings evidenced Pb-rich spots of a few hundreds of micrometers in diameter located in necrotic zones. These spots were more abundant at the base of the central nervure. Environmental scanning electron microscopy coupled with energy dispersive X-ray microanalysis showed that smaller particles (a few micrometers in diameter) were also present in other regions of the leaves, often located beneath the leaf surface. In addition, submicrometric particles were observed inside stomatal openings. Raman microspectrometry analyses of the leaves identified smelter-originated Pb minerals but also secondary phases likely resulting from the weathering of original particles. On the basis of these observations, several pathways for foliar lead uptake are discussed. A better understanding of these mechanisms may be of interest for risk assessment of population exposure to atmospheric metal contamination
Landau Model for Commensurate-Commensurate Phase Transitions in Uniaxial Improper Ferroelectric Crystals
We propose the Landau model for lock-in phase transitions in uniaxially
modulated improper ferroelectric incommensurate-commensurate systems of class
I. It includes Umklapp terms of third and fourth order and secondary order
parameter representing the local polarization. The corresponding phase diagram
has the structure of harmless staircase, with the allowed wave numbers obeying
the Farey tree algorithm. Among the stable commensurate phases only those with
periods equal to odd number of lattice constants have finite macroscopic
polarizations. These results are in excellent agreement with experimental
findings in some A2BX4 compounds.Comment: 9 pages, 5 figures, revtex, to be published in Journal of Physics:
Cond. Matter as a Letter to the Edito
Statistical features of edge turbulence in RFX-mod from Gas Puffing Imaging
Plasma density fluctuations in the edge plasma of the RFX-mod device are
measured through the Gas Puffing Imaging Diagnostics. Statistical features of
the signal are quantified in terms of the Probability Distribution Function
(PDF), and computed for several kinds of discharges. The PDFs from discharges
without particular control methods are found to be adequately described by a
Gamma function, consistently with the recent results by Graves et al [J.P.
Graves, et al, Plasma Phys. Control. Fusion 47, L1 (2005)]. On the other hand,
pulses with external methods for plasma control feature modified PDFs. A first
empirical analysis suggests that they may be interpolated through a linear
combination of simple functions. An inspection of the literature shows that
this kind of PDFs is common to other devices as well, and has been suggested to
be due to the simultaneous presence of different mechanisms driving
respectively coherent bursts and gaussian background turbulence. An attempt is
made to relate differences in the PDFs to plasma conditions such as the local
shift of the plasma column. A simple phenomenological model to interpret the
nature of the PDF and assign a meaning to its parameters is also developed.Comment: 27 pages. Published in PPC
Stochastic ionization through noble tori: Renormalization results
We find that chaos in the stochastic ionization problem develops through the
break-up of a sequence of noble tori. In addition to being very accurate, our
method of choice, the renormalization map, is ideally suited for analyzing
properties at criticality. Our computations of chaos thresholds agree closely
with the widely used empirical Chirikov criterion
Riemannian theory of Hamiltonian chaos and Lyapunov exponents
This paper deals with the problem of analytically computing the largest
Lyapunov exponent for many degrees of freedom Hamiltonian systems. This aim is
succesfully reached within a theoretical framework that makes use of a
geometrization of newtonian dynamics in the language of Riemannian geometry. A
new point of view about the origin of chaos in these systems is obtained
independently of homoclinic intersections. Chaos is here related to curvature
fluctuations of the manifolds whose geodesics are natural motions and is
described by means of Jacobi equation for geodesic spread. Under general
conditions ane effective stability equation is derived; an analytic formula for
the growth-rate of its solutions is worked out and applied to the
Fermi-Pasta-Ulam beta model and to a chain of coupled rotators. An excellent
agreement is found the theoretical prediction and the values of the Lyapunov
exponent obtained by numerical simulations for both models.Comment: RevTex, 40 pages, 8 PostScript figures, to be published in Phys. Rev.
E (scheduled for November 1996
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