77 research outputs found
Critical exponents in zero dimensions
In the vicinity of the onset of an instability, we investigate the effect of
colored multiplicative noise on the scaling of the moments of the unstable mode
amplitude. We introduce a family of zero dimensional models for which we can
calculate the exact value of the critical exponents for all the
moments. The results are obtained through asymptotic expansions that use the
distance to onset as a small parameter. The examined family displays a variety
of behaviors of the critical exponents that includes anomalous exponents:
exponents that differ from the deterministic (mean-field) prediction, and
multiscaling: non-linear dependence of the exponents on the order of the
moment
Anomalous exponents at the onset of an instability
Critical exponents are calculated exactly at the onset of an instability,
using asymptotic expansiontechniques. When the unstable mode is subject to
multiplicative noise whose spectrum at zero frequency vanishes, we show that
the critical behavior can be anomalous, i.e. the mode amplitude X scales with
departure from onset \mu as with an exponent
different from its deterministic value. This behavior is observed in a direct
numerical simulation of the dynamo instability and our results provide a
possible explanation to recent experimental observations
On the magnetic fields generated by experimental dynamos
We review the results obtained by three successful fluid dynamo experiments
and discuss what has been learnt from them about the effect of turbulence on
the dynamo threshold and saturation. We then discuss several questions that are
still open and propose experiments that could be performed to answer some of
them.Comment: 40 pages, 13 figure
Effects of the low frequencies of noise on On-Off intermittency
A bifurcating system subject to multiplicative noise can exhibit on-off
intermittency close to the instability threshold. For a canonical system, we
discuss the dependence of this intermittency on the Power Spectrum Density
(PSD) of the noise. Our study is based on the calculation of the Probability
Density Function (PDF) of the unstable variable. We derive analytical results
for some particular types of noises and interpret them in the framework of
on-off intermittency. Besides, we perform a cumulant expansion for a random
noise with arbitrary power spectrum density and show that the intermittent
regime is controlled by the ratio between the departure from the threshold and
the value of the PSD of the noise at zero frequency. Our results are in
agreement with numerical simulations performed with two types of random
perturbations: colored Gaussian noise and deterministic fluctuations of a
chaotic variable. Extensions of this study to another, more complex, system are
presented and the underlying mechanisms are discussed.Comment: 13pages, 13 figure
On the localized phase of a copolymer in an emulsion: supercritical percolation regime
In this paper we study a two-dimensional directed self-avoiding walk model of
a random copolymer in a random emulsion. The copolymer is a random
concatenation of monomers of two types, and , each occurring with
density 1/2. The emulsion is a random mixture of liquids of two types, and
, organised in large square blocks occurring with density and ,
respectively, where . The copolymer in the emulsion has an energy
that is minus times the number of -matches minus times the
number of -matches, where without loss of generality the interaction
parameters can be taken from the cone . To make the model mathematically tractable, we assume that the
copolymer is directed and can only enter and exit a pair of neighbouring blocks
at diagonally opposite corners.
In \cite{dHW06}, it was found that in the supercritical percolation regime , with the critical probability for directed bond percolation on
the square lattice, the free energy has a phase transition along a curve in the
cone that is independent of . At this critical curve, there is a transition
from a phase where the copolymer is fully delocalized into the -blocks to a
phase where it is partially localized near the -interface. In the present
paper we prove three theorems that complete the analysis of the phase diagram :
(1) the critical curve is strictly increasing; (2) the phase transition is
second order; (3) the free energy is infinitely differentiable throughout the
partially localized phase.Comment: 43 pages and 10 figure
Bounds on dissipation in magnetohydrodynamic problems in plane shear geometry
The total dissipation rate for magnetohydrodynamic (MHD) flows in plane geometry with both velocity and magnetic shear is studied. For some boundary conditions it is shown that the lower bound on the dissipation rate is achieved by the equivalent of Stokes flow for MHD. Using the background method [Doering and Constantin, Phys. Rev. Lett. 69, 1648 (1992)] upper bounds for the dissipation rate are calculated. For a shear layer, with both velocity and magnetic shear, parameter dependence of the upper bound is obtained. As a by-product of this calculation, an energy stability domain is calculated. A sheet pinch is also studied, and it is shown that the upper bound tends to zero as the resistivity tends to zero. Thus, an antiturbulence result is obtained. © 2003 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70246/2/PHPAEN-10-11-4314-1.pd
Transport of magnetic field by a turbulent flow of liquid sodium
We study the effect of a turbulent flow of liquid sodium generated in the von
K\'arm\'an geometry, on the localized field of a magnet placed close to the
frontier of the flow. We observe that the field can be transported by the flow
on distances larger than its integral length scale. In the most turbulent
configurations, the mean value of the field advected at large distance
vanishes. However, the rms value of the fluctuations increases linearly with
the magnetic Reynolds number. The advected field is strongly intermittent.Comment: 4 pages, 6 figure
Chaotic magnetic field reversals in turbulent dynamos
We present direct numerical simulations of reversals of the magnetic field
generated by swirling flows in a spherical domain. In agreement with a recent
model, we observe that coupling dipolar and quadrupolar magnetic modes by an
asymmetric forcing of the flow generates field reversals. In addition, we show
that this mechanism strongly depends on the value of the magnetic Prandtl
number.Comment: 4 pages, 5 figure
Generation of magnetic field by dynamo action in a turbulent flow of liquid sodium
We report the observation of dynamo action in the VKS experiment, i.e., the
generation of magnetic field by a strongly turbulent swirling flow of liquid
sodium. Both mean and fluctuating parts of the field are studied. The dynamo
threshold corresponds to a magnetic Reynolds number Rm \sim 30. A mean magnetic
field of order 40 G is observed 30% above threshold at the flow lateral
boundary. The rms fluctuations are larger than the corresponding mean value for
two of the components. The scaling of the mean square magnetic field is
compared to a prediction previously made for high Reynolds number flows.Comment: 4 pages, 5 figure
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