119 research outputs found
About coherent structures in random shell models for passive scalar advection
A study of anomalous scaling in models of passive scalar advection in terms
of singular coherent structures is proposed. The stochastic dynamical system
considered is a shell model reformulation of Kraichnan model. We extend the
method introduced in \cite{DDG99} to the calculation of self-similar instantons
and we show how such objects, being the most singular events, are appropriate
to capture asymptotic scaling properties of the scalar field. Preliminary
results concerning the statistical weight of fluctuations around these optimal
configurations are also presented.Comment: 4 pages, 2 postscript figures, submitted to PR
Phases of the 2D Hubbard model at low doping
We show that the planar spiral phase of the 2D Hubbard model at low doping,
x, is unstable towards a noncoplanar spin configuration. The novel equilibrium
state we found at low doping is incommensurate with the inverse pitch of the
spiral varying as x^(1/2), but nevertheless has a dominant peak in the
susceptibility at (\pi,\pi). Relevance to the NMR and neutron scattering
experiments in La_2-xSr_xCuO_4 is disccussed.Comment: 12 pages, emtex v.3.
Computation of the radiation amplitude of oscillons
The radiation loss of small amplitude oscillons (very long-living, spatially
localized, time dependent solutions) in one dimensional scalar field theories
is computed in the small-amplitude expansion analytically using matched
asymptotic series expansions and Borel summation. The amplitude of the
radiation is beyond all orders in perturbation theory and the method used has
been developed by Segur and Kruskal in Phys. Rev. Lett. 58, 747 (1987). Our
results are in good agreement with those of long time numerical simulations of
oscillons.Comment: 22 pages, 9 figure
Outliers, Extreme Events and Multiscaling
Extreme events have an important role which is sometime catastrophic in a
variety of natural phenomena including climate, earthquakes and turbulence, as
well as in man-made environments like financial markets. Statistical analysis
and predictions in such systems are complicated by the fact that on the one
hand extreme events may appear as "outliers" whose statistical properties do
not seem to conform with the bulk of the data, and on the other hands they
dominate the (fat) tails of probability distributions and the scaling of high
moments, leading to "abnormal" or "multi"-scaling. We employ a shell model of
turbulence to show that it is very useful to examine in detail the dynamics of
onset and demise of extreme events. Doing so may reveal dynamical scaling
properties of the extreme events that are characteristic to them, and not
shared by the bulk of the fluctuations. As the extreme events dominate the
tails of the distribution functions, knowledge of their dynamical scaling
properties can be turned into a prediction of the functional form of the tails.
We show that from the analysis of relatively short time horizons (in which the
extreme events appear as outliers) we can predict the tails of the probability
distribution functions, in agreement with data collected in very much longer
time horizons. The conclusion is that events that may appear unpredictable on
relatively short time horizons are actually a consistent part of a multiscaling
statistics on longer time horizons.Comment: 11 pages, 14 figures included, PRE submitte
Polarization of superfluid turbulence
We show that normal fluid eddies in turbulent helium II polarize the tangle
of quantized vortex lines present in the flow, thus inducing superfluid
vorticity patterns similar to the driving normal fluid eddies. We also show
that the polarization is effective over the entire inertial range. The results
help explain the surprising analogies between classical and superfluid
turbulence which have been observed recently.Comment: 3 figure
Superconducting Spiral Phase in the two-dimensional t-J model
We analyse the t-t'-t''-J model, relevant to the superconducting cuprates. By
using chiral perturbation theory we have determined the ground state to be a
spiral for small doping \delta << 1 near half filling. In this limit the
solution does not contain any uncontrolled approximations. We evaluate the
spin-wave Green's functions and address the issue of stability of the spiral
state, leading to the phase diagram of the model. At t'=t''=0 the spiral state
is unstable towards a local enhancement of the spiral pitch, and the nature of
the true ground state remains unclear. However, for values of t' and t''
corresponding to real cuprates the (1,0) spiral state is stabilized by quantum
fluctuations (``order from disorder'' effect). We show that at \delta = 0.119
the spiral is commensurate with the lattice with a period of 8 lattice
spacings. It is also demonstrated that spin-wave mediated superconductivity
develops in the spiral state and a lower limit for the superconducting gap is
derived. Even though one cannot classify the gap symmetry according to the
lattice representations (s,p,d,...) since the symmetry of the lattice is
spontaneously broken by the spiral, the gap always has lines of nodes along the
(1,\pm 1) directions.Comment: 17 pages, 11 figure
Pulses in the Zero-Spacing Limit of the GOY Model
We study the propagation of localised disturbances in a turbulent, but
momentarily quiescent and unforced shell model (an approximation of the
Navier-Stokes equations on a set of exponentially spaced momentum shells).
These disturbances represent bursts of turbulence travelling down the inertial
range, which is thought to be responsible for the intermittency observed in
turbulence. Starting from the GOY shell model, we go to the limit where the
distance between succeeding shells approaches zero (``the zero spacing limit'')
and helicity conservation is retained. We obtain a discrete field theory which
is numerically shown to have pulse solutions travelling with constant speed and
with unchanged form. We give numerical evidence that the model might even be
exactly integrable, although the continuum limit seems to be singular and the
pulses show an unusual super exponential decay to zero as when , where is the {\em
golden mean}. For finite momentum shell spacing, we argue that the pulses
should accelerate, moving to infinity in a finite time. Finally we show that
the maximal Lyapunov exponent of the GOY model approaches zero in this limit.Comment: 27 pages, submitted for publicatio
A hidden Goldstone mechanism in the Kagom\'e lattice antiferromagnet
In this paper, we study the phases of the Heisenberg model on the \kagome
lattice with antiferromagnetic nearest neighbour coupling and
ferromagnetic next neighbour coupling . Analysing the long wavelength, low
energy effective action that describes this model, we arrive at the phase
diagram as a function of . The interesting part of
this phase diagram is that for small , which includes , there is
a phase with no long range spin order and with gapless and spin zero low lying
excitations. We discuss our results in the context of earlier, numerical and
experimental work.Comment: 21 pages, latex file with 5 figure
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