133 research outputs found
An improved \eps expansion for three-dimensional turbulence: summation of nearest dimensional singularities
An improved \eps expansion in the -dimensional () stochastic
theory of turbulence is constructed by taking into account pole singularities
at in coefficients of the \eps expansion of universal quantities.
Effectiveness of the method is illustrated by a two-loop calculation of the
Kolmogorov constant in three dimensions.Comment: 4 page
Levy flights in quenched random force fields
Levy flights, characterized by the microscopic step index f, are for f<2 (the
case of rare events) considered in short range and long range quenched random
force fields with arbitrary vector character to first loop order in an
expansion about the critical dimension 2f-2 in the short range case and the
critical fall-off exponent 2f-2 in the long range case. By means of a dynamic
renormalization group analysis based on the momentum shell integration method,
we determine flows, fixed point, and the associated scaling properties for the
probability distribution and the frequency and wave number dependent diffusion
coefficient. Unlike the case of ordinary Brownian motion in a quenched force
field characterized by a single critical dimension or fall-off exponent d=2,
two critical dimensions appear in the Levy case. A critical dimension (or
fall-off exponent) d=f below which the diffusion coefficient exhibits anomalous
scaling behavior, i.e, algebraic spatial behavior and long time tails, and a
critical dimension (or fall-off exponent) d=2f-2 below which the force
correlations characterized by a non trivial fixed point become relevant. As a
general result we find in all cases that the dynamic exponent z, characterizing
the mean square displacement, locks onto the Levy index f, independent of
dimension and independent of the presence of weak quenched disorder.Comment: 27 pages, Revtex file, 17 figures in ps format attached, submitted to
Phys. Rev.
Universality of the thermodynamic Casimir effect
Recently a nonuniversal character of the leading spatial behavior of the
thermodynamic Casimir force has been reported [X. S. Chen and V. Dohm, Phys.
Rev. E {\bf 66}, 016102 (2002)]. We reconsider the arguments leading to this
observation and show that there is no such leading nonuniversal term in systems
with short-ranged interactions if one treats properly the effects generated by
a sharp momentum cutoff in the Fourier transform of the interaction potential.
We also conclude that lattice and continuum models then produce results in
mutual agreement independent of the cutoff scheme, contrary to the
aforementioned report. All results are consistent with the {\em universal}
character of the Casimir force in systems with short-ranged interactions. The
effects due to dispersion forces are discussed for systems with periodic or
realistic boundary conditions. In contrast to systems with short-ranged
interactions, for one observes leading finite-size contributions
governed by power laws in due to the subleading long-ranged character of
the interaction, where is the finite system size and is the
correlation length.Comment: 11 pages, revtex, to appear in Phys. Rev. E 68 (2003
Anomalous scaling of passively advected magnetic field in the presence of strong anisotropy
Inertial-range scaling behavior of high-order (up to order N=51) structure
functions of a passively advected vector field has been analyzed in the
framework of the rapid-change model with strong small-scale anisotropy with the
aid of the renormalization group and the operator-product expansion. It has
been shown that in inertial range the leading terms of the structure functions
are coordinate independent, but powerlike corrections appear with the same
anomalous scaling exponents as for the passively advected scalar field. These
exponents depend on anisotropy parameters in such a way that a specific
hierarchy related to the degree of anisotropy is observed. Deviations from
power-law behavior like oscillations or logarithmic behavior in the corrections
to structure functions have not been found.Comment: 15 pages, 18 figure
Anomalous scaling of a passive scalar advected by the turbulent velocity field with finite correlation time and uniaxial small-scale anisotropy
The influence of uniaxial small-scale anisotropy on the stability of the
scaling regimes and on the anomalous scaling of the structure functions of a
passive scalar advected by a Gaussian solenoidal velocity field with finite
correlation time is investigated by the field theoretic renormalization group
and operator product expansion within one-loop approximation. Possible scaling
regimes are found and classified in the plane of exponents ,
where characterizes the energy spectrum of the velocity field in the
inertial range , and is related to the
correlation time of the velocity field at the wave number which is scaled
as . It is shown that the presence of anisotropy does not disturb
the stability of the infrared fixed points of the renormalization group
equations which are directly related to the corresponding scaling regimes. The
influence of anisotropy on the anomalous scaling of the structure functions of
the passive scalar field is studied as a function of the fixed point value of
the parameter which represents the ratio of turnover time of scalar field
and velocity correlation time. It is shown that the corresponding one-loop
anomalous dimensions, which are the same (universal) for all particular models
with concrete value of in the isotropic case, are different (nonuniversal)
in the case with the presence of small-scale anisotropy and they are continuous
functions of the anisotropy parameters, as well as the parameter . The
dependence of the anomalous dimensions on the anisotropy parameters of two
special limits of the general model, namely, the rapid-change model and the
frozen velocity field model, are found when and ,
respectively.Comment: revtex, 25 pages, 37 figure
An improved \eps expansion for three-dimensional turbulence: two-loop renormalization near two dimensions
An improved \eps expansion in the -dimensional () stochastic
theory of turbulence is constructed at two-loop order which incorporates the
effect of pole singularities at in coefficients of the \eps
expansion of universal quantities. For a proper account of the effect of these
singularities two different approaches to the renormalization of the powerlike
correlation function of the random force are analyzed near two dimensions. By
direct calculation it is shown that the approach based on the mere
renormalization of the nonlocal correlation function leads to contradictions at
two-loop order. On the other hand, a two-loop calculation in the
renormalization scheme with the addition to the force correlation function of a
local term to be renormalized instead of the nonlocal one yields consistent
results in accordance with the UV renormalization theory. The latter
renormalization prescription is used for the two-loop renormalization-group
analysis amended with partial resummation of the pole singularities near two
dimensions leading to a significant improvement of the agreement with
experimental results for the Kolmogorov constant.Comment: 23 pages, 2 figure
Generalized Central Limit Theorem and Renormalization Group
We introduce a simple instance of the renormalization group transformation in
the Banach space of probability densities. By changing the scaling of the
renormalized variables we obtain, as fixed points of the transformation, the
L\'evy strictly stable laws. We also investigate the behavior of the
transformation around these fixed points and the domain of attraction for
different values of the scaling parameter. The physical interest of a
renormalization group approach to the generalized central limit theorem is
discussed.Comment: 16 pages, to appear in J. Stat. Phy
Effects of turbulent mixing on critical behaviour in the presence of compressibility: Renormalization group analysis of two models
Critical behaviour of two systems, subjected to the turbulent mixing, is
studied by means of the field theoretic renormalization group. The first
system, described by the equilibrium model A, corresponds to relaxational
dynamics of a non-conserved order parameter. The second one is the strongly
non-equilibrium reaction-diffusion system, known as Gribov process and
equivalent to the Reggeon field theory. The turbulent mixing is modelled by the
Kazantsev-Kraichnan "rapid-change" ensemble: time-decorrelated Gaussian
velocity field with the power-like spectrum k^{-d-\xi}. Effects of
compressibility of the fluid are studied. It is shown that, depending on the
relation between the exponent \xi and the spatial dimension d, the both systems
exhibit four different types of critical behaviour, associated with four
possible fixed points of the renormalization group equations. The most
interesting point corresponds to a new type of critical behaviour, in which the
nonlinearity and turbulent mixing are both relevant, and the critical exponents
depend on d, \xi and the degree of compressibility. For the both models,
compressibility enhances the role of the nonlinear terms in the dynamical
equations: the region in the d-\xi plane, where the new nontrivial regime is
stable, is getting much wider as the degree of compressibility increases. In
its turn, turbulent transfer becomes more efficient due to combined effects of
the mixing and the nonlinear terms.Comment: 25 pages, 4 figure
Glassy trapping of manifolds in nonpotential random flows
We study the dynamics of polymers and elastic manifolds in non potential
static random flows. We find that barriers are generated from combined effects
of elasticity, disorder and thermal fluctuations. This leads to glassy trapping
even in pure barrier-free divergenceless flows
(). The physics is described by a new RG fixed point at finite
temperature. We compute the anomalous roughness and dynamical
exponents for directed and isotropic manifolds.Comment: 5 pages, 3 figures, RevTe
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