29 research outputs found
Lectures on random polymers
These lecture notes are a guided tour through the fascinating world of polymer chains interacting with themselves and/or with their environment. The focus is on the mathematical description of a number of physical and chemical phenomena, with particular emphasis on phase transitions and space-time scaling. The topics covered, though only a selection, are typical for the area. Sections 1â3 describe models of polymers without disorder, Sections 4â6 models of polymers with disorder. Appendices AâE contain tutorials in which a number of key techniques are explained in more detail
Magnetic field reversals in an experimental turbulent dynamo
We report the first experimental observation of reversals of a dynamo field
generated in a laboratory experiment based on a turbulent flow of liquid
sodium. The magnetic field randomly switches between two symmetric solutions B
and -B. We observe a hierarchy of time scales similar to the Earth's magnetic
field: the duration of the steady phases is widely distributed, but is always
much longer than the time needed to switch polarity. In addition to reversals
we report excursions. Both coincide with minima of the mechanical power driving
the flow. Small changes in the flow driving parameters also reveal a large
variety of dynamo regimes.Comment: 5 pages, 4 figure
A numerical model of the VKS experiment
We present numerical simulations of the magnetic field generated by the flow
of liquid sodium driven by two counter-rotating impellers (VKS experiment).
Using a dynamo kinematic code in cylindrical geometry, it is shown that
different magnetic modes can be generated depending on the flow configuration.
While the time averaged axisymmetric mean flow generates an equatorial dipole,
our simulations show that an axial field of either dipolar or quadrupolar
symmetry can be generated by taking into account non-axisymmetric components of
the flow. Moreover, we show that by breaking a symmetry of the flow, the
magnetic field becomes oscillatory. This leads to reversals of the axial dipole
polarity, involving a competition with the quadrupolar component.Comment: 6 pages, 5 figure
Susceptibility divergence, phase transition and multistability of a highly turbulent closed flow
Using time-series of stereoscopic particle image velocimetry data, we study
the response of a turbulent von K\'{a}rm\'{a}n swirling flow to a continuous
breaking of its forcing symmetry. Experiments are carried over a wide Reynolds
number range, from laminar regime at to highly turbulent regime
near . We show that the flow symmetry can be quantitatively
characterized by two scalars, the global angular momentum and the mixing
layer altitude , which are shown to be statistically equivalent.
Furthermore, we report that the flow response to small forcing dissymetry is
linear, with a slope depending on the Reynolds number: this response
coefficient increases non monotonically from small to large Reynolds number and
presents a divergence at a critical Reynolds number . This divergence coincides with a change in the statistical properties
of the instantaneous flow symmetry : its pdf changes from Gaussian to
non-Gaussian with multiple maxima, revealing metastable non-symmetrical states.
For symmetric forcing, a peak of fluctuations of is also observed at
: these fluctuations correspond to time-intermittencies between
metastable states of the flow which, contrary to the very-long-time-averaged
mean flow, spontaneously and dynamically break the system symmetry. We show
that these observations can be interpreted in terms of divergence of the
susceptibility to symmetry breaking, revealing the existence of a phase
transition. An analogy with the ferromagnetic-paramagnetic transition in
solid-state physics is presented and discussed.Comment: to appear in Journal of Statistical Mechanic
Open questions about homogeneous fluid dynamos: the VKS experiments
We consider several problems that arise in the context of homogeneous fluid dynamos
such as the e ect of turbulence on the dynamo threshold, the saturation level of the
generated magnetic eld above the threshold and its dynamics. We compare some of our
predictions with the recent experimental results of the Karlsruhe and Riga experiments.
Finally, we present the VKS experiment that we have designed to answer some of the
remaining open questions. We study, in particular, the response of a turbulent flow to
an external magnetic eld
Nonlinear magnetic induction by helical motion in a liquid sodium turbulent flow
We report an experimental study of the magnetic field ~BB induced by a turbulent swirling flow of liquid sodium submitted to a transverse magnetic field ~BB0. We show that the induced field can behave nonlinearly as a function of the magnetic Reynolds number, Rm. At low Rm, the induced mean field along the axis of the flow, hBxi, and the one parallel to ~BB0, hByi, first behave like R2
m, whereas the third component, hBzi, is linear in Rm. The sign of hBxi is determined by the flow helicity. At higher Rm, ~BB
strongly depends on the local geometry of the mean flow: hBxi decreases to zero in the core of the swirling flow but remains finite outside. We compare the experimental results with the computed magnetic induction due to the mean flow alone
MHD measurements in the von KĂĄrmĂĄn sodium experiment
We study the magnetic induction in a confined swirling flow of liquid sodium, at integral magnetic
Reynolds numbers up to 50. More precisely, we measure in situ the magnetic field induced by the
flow motion in the presence of a weak external field. Because of the very small value of the
magnetic Prandtl number of all liquid metals, flows with even modest Rm are strongly turbulent.
Large mean induction effects are observed over a fluctuating background. As expected from the von
KĂĄrmĂĄn flow geometry, the induction is strongly anisotropic. The main contributions are the
generation of an azimuthal induced field when the applied field is in the axial direction ~an V effect!
and the generation of axial induced field when the applied field is the transverse direction ~as in a
large scale a effect!. Strong fluctuations of the induced field, due to the flow nonstationarity, occur
over time scales slower than the flow forcing frequency. In the spectral domain, they display a f21
spectral slope. At smaller scales ~and larger frequencies! the turbulent fluctuations are in agreement
with a Kolmogorov modeling of passive vector dynamics