152 research outputs found
Models of Passive and Reactive Tracer Motion: an Application of Ito Calculus
By means of Ito calculus it is possible to find, in a straight-forward way,
the analytical solution to some equations related to the passive tracer
transport problem in a velocity field that obeys the multidimensional Burgers
equation and to a simple model of reactive tracer motion.Comment: revised version 7 pages, Latex, to appear as a letter to J. of
Physics
A non-perturbative renormalization group study of the stochastic Navier--Stokes equation
We study the renormalization group flow of the average action of the
stochastic Navier--Stokes equation with power-law forcing. Using Galilean
invariance we introduce a non-perturbative approximation adapted to the zero
frequency sector of the theory in the parametric range of the H\"older exponent
of the forcing where real-space local interactions are
relevant. In any spatial dimension , we observe the convergence of the
resulting renormalization group flow to a unique fixed point which yields a
kinetic energy spectrum scaling in agreement with canonical dimension analysis.
Kolmogorov's -5/3 law is, thus, recovered for as also predicted
by perturbative renormalization. At variance with the perturbative prediction,
the -5/3 law emerges in the presence of a \emph{saturation} in the
-dependence of the scaling dimension of the eddy diffusivity at
when, according to perturbative renormalization, the velocity
field becomes infra-red relevant.Comment: RevTeX, 18 pages, 5 figures. Minor changes and new discussion
Pressure and intermittency in passive vector turbulence
We investigate the scaling properties a model of passive vector turbulence
with pressure and in the presence of a large-scale anisotropy. The leading
scaling exponents of the structure functions are proven to be anomalous. The
anisotropic exponents are organized in hierarchical families growing without
bound with the degree of anisotropy. Nonlocality produces poles in the
inertial-range dynamics corresponding to the dimensional scaling solution. The
increase with the P\'{e}clet number of hyperskewness and higher odd-dimensional
ratios signals the persistence of anisotropy effects also in the inertial
range.Comment: 4 pages, 1 figur
Passive scalar turbulence in high dimensions
Exploiting a Lagrangian strategy we present a numerical study for both
perturbative and nonperturbative regions of the Kraichnan advection model. The
major result is the numerical assessment of the first-order -expansion by
M. Chertkov, G. Falkovich, I. Kolokolov and V. Lebedev ({\it Phys. Rev. E},
{\bf 52}, 4924 (1995)) for the fourth-order scalar structure function in the
limit of high dimensions 's. %Two values of the velocity scaling exponent
have been considered: % and . In the first case, the
perturbative regime %takes place at , while in the second at , %in agreement with the fact that the relevant small parameter %of the
theory is . In addition to the perturbative results, the
behavior of the anomaly for the sixth-order structure functions {\it vs} the
velocity scaling exponent, , is investigated and the resulting behavior
discussed.Comment: 4 pages, Latex, 4 figure
Manifestation of anisotropy persistence in the hierarchies of MHD scaling exponents
The first example of a turbulent system where the failure of the hypothesis
of small-scale isotropy restoration is detectable both in the `flattening' of
the inertial-range scaling exponent hierarchy, and in the behavior of odd-order
dimensionless ratios, e.g., skewness and hyperskewness, is presented.
Specifically, within the kinematic approximation in magnetohydrodynamical
turbulence, we show that for compressible flows, the isotropic contribution to
the scaling of magnetic correlation functions and the first anisotropic ones
may become practically indistinguishable. Moreover, skewness factor now
diverges as the P\'eclet number goes to infinity, a further indication of
small-scale anisotropy.Comment: 4 pages Latex, 1 figur
On the strong anomalous diffusion
The superdiffusion behavior, i.e. , with , in general is not completely characherized by a unique exponent. We study
some systems exhibiting strong anomalous diffusion, i.e. where and is not a linear function of .
This feature is different from the weak superdiffusion regime, i.e.
, as in random shear flows. The strong anomalous diffusion
can be generated by nontrivial chaotic dynamics, e.g. Lagrangian motion in
time-dependent incompressible velocity fields, symplectic maps and
intermittent maps. Typically the function is piecewise linear. This
corresponds to two mechanisms: a weak anomalous diffusion for the typical
events and a ballistic transport for the rare excursions. In order to have
strong anomalous diffusion one needs a violation of the hypothesis of the
central limit theorem, this happens only in a very narrow region of the control
parameters space.Comment: 27 pages, 14 figure
Neuromuscular excitability changes produced by sustained voluntary contraction and response to mexiletine in myotonia congenita
Objective: To investigate the cause of transient weakness in myotonia congenita (MC) and the mechanism of action of mexiletine in reducing weakness. Methods: The changes in neuromuscular excitability produced by 1. min of maximal voluntary contractions (MVC) were measured on the amplitude of compound muscle action potentials (CMAP) in two patients with either recessive or dominant MC, compared to control values obtained in 20 healthy subjects. Measurements were performed again in MC patients after mexiletine therapy. Results: Transient reduction in maximal CMAP amplitude lasting several minutes after MVC was evident in MC patients, whereas no change was observed in controls. Mexiletine efficiently reduced this transient CMAP depression in both patients. Discussion: Transient CMAP depression following sustained MVC may represent the electrophysiological correlate of the weakness clinically experienced by the patients. In MC, the low chloride conductance could induce self-sustaining action potentials after MVC, determining progressive membrane depolarization and a loss of excitability of muscle fibers, thus resulting in transient paresis. Mexiletine may prevent conduction block due to excessive membrane depolarization, thus reducing the transient CMAP depression following sustained MVC
On the canonically invariant calculation of Maslov indices
After a short review of various ways to calculate the Maslov index appearing
in semiclassical Gutzwiller type trace formulae, we discuss a
coordinate-independent and canonically invariant formulation recently proposed
by A Sugita (2000, 2001). We give explicit formulae for its ingredients and
test them numerically for periodic orbits in several Hamiltonian systems with
mixed dynamics. We demonstrate how the Maslov indices and their ingredients can
be useful in the classification of periodic orbits in complicated bifurcation
scenarios, for instance in a novel sequence of seven orbits born out of a
tangent bifurcation in the H\'enon-Heiles system.Comment: LaTeX, 13 figures, 3 tables, submitted to J. Phys.
Eddy diffusivity of quasi-neutrally-buoyant inertial particles
We investigate the large-scale transport properties of quasi-neutrally-buoyant inertial particles carried by incompressible zero-mean periodic or steady ergodic flows. We show howto compute large-scale indicators such as the inertial-particle terminal velocity and eddy diffusivity from first principles in a perturbative expansion around the limit of added-mass factor close to unity. Physically, this limit corresponds to the case where the mass density of the particles is constant and close in value to the mass density of the fluid, which is also constant. Our approach differs from the usual over-damped expansion inasmuch as we do not assume a separation of time scales between thermalization and small-scale convection effects. For a general flow in the class of incompressible zero-mean periodic velocity fields, we derive closed-form cell equations for the auxiliary quantities determining the terminal velocity and effective diffusivity. In the special case of parallel flows these equations admit explicit analytic solution. We use parallel flows to show that our approach sheds light onto the behavior of terminal velocity and effective diffusivity for Stokes numbers of the order of unity.Peer reviewe
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