13,167 research outputs found

### Nonlinear dynamos at infinite magnetic Prandtl number

The dynamo instability is investigated in the limit of infinite magnetic
Prandtl number. In this limit the fluid is assumed to be very viscous so that
the inertial terms can be neglected and the flow is slaved to the forcing. The
forcing consist of an external forcing function that drives the dynamo flow and
the resulting Lorentz force caused by the back reaction of the magnetic field.
The flows under investigation are the Archontis flow, and the ABC flow forced
at two different scales. The investigation covers roughly three orders of
magnitude of the magnetic Reynolds number above onset. All flows show a weak
increase of the averaged magnetic energy as the magnetic Reynolds number is
increased. Most of the magnetic energy is concentrated in flat elongated
structures that produce a Lorentz force with small solenoidal projection so
that the resulting magnetic field configuration was almost force-free. Although
the examined system has zero kinetic Reynolds number at sufficiently large
magnetic Reynolds number the structures are unstable to small scale
fluctuations that result in a chaotic temporal behavior

### Selective decay by Casimir dissipation in fluids

The problem of parameterizing the interactions of larger scales and smaller
scales in fluid flows is addressed by considering a property of two-dimensional
incompressible turbulence. The property we consider is selective decay, in
which a Casimir of the ideal formulation (enstrophy in 2D flows, helicity in 3D
flows) decays in time, while the energy stays essentially constant. This paper
introduces a mechanism that produces selective decay by enforcing Casimir
dissipation in fluid dynamics. This mechanism turns out to be related in
certain cases to the numerical method of anticipated vorticity discussed in
\cite{SaBa1981,SaBa1985}. Several examples are given and a general theory of
selective decay is developed that uses the Lie-Poisson structure of the ideal
theory. A scale-selection operator allows the resulting modifications of the
fluid motion equations to be interpreted in several examples as parameterizing
the nonlinear, dynamical interactions between disparate scales. The type of
modified fluid equation systems derived here may be useful in modelling
turbulent geophysical flows where it is computationally prohibitive to rely on
the slower, indirect effects of a realistic viscosity, such as in large-scale,
coherent, oceanic flows interacting with much smaller eddies

### Exact solvability of superintegrable Benenti systems

We establish quantum and classical exact solvability for two large classes of
maximally superintegrable Benenti systems in $n$ dimensions with arbitrarily
large $n$. Namely, we solve the Hamilton--Jacobi and Schr\"odinger equations
for the systems in question. The results obtained are illustrated for a model
with the cubic potential.Comment: 15 pages, LaTeX 2e, no figures; in the updated version a number of
typos were fixed and other minor changes were mad

### Helicity Conservation via the Noether Theorem

The conservation of helicity in ideal barotropic fluids is discussed from a
group theoretical point of view. A new symmetry group is introduced i.e. the
alpha group of translations. It is proven via the Noether theorem that this
group generates helicity conservation.Comment: 7 pages of te

### Integrability of one degree of freedom symplectic maps with polar singularities

In this paper, we treat symplectic difference equations with one degree of
freedom. For such cases, we resolve the relation between that the dynamics on
the two dimensional phase space is reduced to on one dimensional level sets by
a conserved quantity and that the dynamics is integrable, under some
assumptions. The process which we introduce is related to interval exchange
transformations.Comment: 10 pages, 2 figure

### On the accuracy of conservation of adiabatic invariants in slow-fast systems

Let the adiabatic invariant of action variable in slow-fast Hamiltonian
system with two degrees of freedom have two limiting values along the
trajectories as time tends to infinity. The difference of two limits is
exponentially small in analytic systems. An iso-energetic reduction and
canonical transformations are applied to transform the slow-fast systems to
form of systems depending on slowly varying parameters in a complexified phase
space. On the basis of this method an estimate for the accuracy of conservation
of adiabatic invariant is given for such systems.Comment: 27 pages, 14 figure

### Degree of randomness: numerical experiments for astrophysical signals

Astrophysical and cosmological signals such as the cosmic microwave
background radiation, as observed, typically contain contributions of different
components, and their statistical properties can be used to distinguish one
from the other. A method developed originally by Kolmogorov is involved for the
study of astrophysical signals of randomness of various degrees. Numerical
performed experiments based on the universality of Kolmogorov distribution and
using a single scaling of the ratio of stochastic to regular components, reveal
basic features in the behavior of generated signals also in terms of a critical
value for that ratio, thus enable the application of this technique for various
observational datasetsComment: 6 pages, 9 figures; Europhys.Letters; to match the published versio

### An Exact Universal Gravitational Lensing Equation

We first define what we mean by gravitational lensing equations in a general
space-time. A set of exact relations are then derived that can be used as the
gravitational lens equations in all physical situations. The caveat is that
into these equations there must be inserted a function, a two-parameter family
of solutions to the eikonal equation, not easily obtained, that codes all the
relevant (conformal) space-time information for this lens equation
construction. Knowledge of this two-parameter family of solutions replaces
knowledge of the solutions to the geodesic equations.
The formalism is then applied to the Schwarzschild lensing problemComment: 12 pages, submitted to Phys. Rev.

### The periodic b-equation and Euler equations on the circle

In this note we show that the periodic b-equation can only be realized as an
Euler equation on the Lie group Diff(S^1) of all smooth and orientiation
preserving diffeomorphisms on the cirlce if b=2, i.e. for the Camassa-Holm
equation. In this case the inertia operator generating the metric on Diff(S^1)
is given by A=1-d^2/dx^2. In contrast, the Degasperis-Procesi equation, for
which b=3, is not an Euler equation on Diff(S^1) for any inertia operator. Our
result generalizes a recent result of B. Kolev.Comment: 8 page

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