226 research outputs found
Stochastic magnetohydrodynamic turbulence in space dimensions
Interplay of kinematic and magnetic forcing in a model of a conducting fluid
with randomly driven magnetohydrodynamic equations has been studied in space
dimensions by means of the renormalization group. A perturbative
expansion scheme, parameters of which are the deviation of the spatial
dimension from two and the deviation of the exponent of the powerlike
correlation function of random forcing from its critical value, has been used
in one-loop approximation. Additional divergences have been taken into account
which arise at two dimensions and have been inconsistently treated in earlier
investigations of the model. It is shown that in spite of the additional
divergences the kinetic fixed point associated with the Kolmogorov scaling
regime remains stable for all space dimensions for rapidly enough
falling off correlations of the magnetic forcing. A scaling regime driven by
thermal fluctuations of the velocity field has been identified and analyzed.
The absence of a scaling regime near two dimensions driven by the fluctuations
of the magnetic field has been confirmed. A new renormalization scheme has been
put forward and numerically investigated to interpolate between the
expansion and the double expansion.Comment: 12 pages, 4 figure
Functional Methods in Stochastic Systems
Field-theoretic construction of functional representations of solutions of
stochastic differential equations and master equations is reviewed. A generic
expression for the generating function of Green functions of stochastic systems
is put forward. Relation of ambiguities in stochastic differential equations
and in the functional representations is discussed. Ordinary differential
equations for expectation values and correlation functions are inferred with
the aid of a variational approach.Comment: Plenary talk presented at Mathematical Modeling and Computational
Science. International Conference, MMCP 2011, Star\'a Lesn\'a, Slovakia, July
4-8, 201
Contribution of non-work and work-related risk factors to the association between income and mental disorders in a working population: the Health 2000 Study
Reaction, Levy Flights, and Quenched Disorder
We consider the A + A --> emptyset reaction, where the transport of the
particles is given by Levy flights in a quenched random potential. With a
common literature model of the disorder, the random potential can only increase
the rate of reaction. With a model of the disorder that obeys detailed balance,
however, the rate of reaction initially increases and then decreases as a
function of the disorder strength. The physical behavior obtained with this
second model is in accord with that for reactive turbulent flow, indicating
that Levy flight statistics can model aspects of turbulent fluid transport.Comment: 6 pages, 5 pages. Phys. Rev. E. 65 (2002) 011109--1-
Dynamics of particles and manifolds in a quenched random force field
We study the dynamics of a directed manifold of internal dimension D in a
d-dimensional random force field. We obtain an exact solution for and a Hartree approximation for finite d. They yield a Flory-like
roughness exponent and a non trivial anomalous diffusion exponent
continuously dependent on the ratio of divergence-free ()
to potential () disorder strength. For the particle (D=0) our results
agree with previous order RG calculations. The time-translational
invariant dynamics for smoothly crosses over to the previously
studied ultrametric aging solution in the potential case.Comment: 5 pages, Latex fil
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