24,446 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
Revisiting the ABC flow dynamo
The ABC flow is a prototype for fast dynamo action, essential to the origin
of magnetic field in large astrophysical objects. Probably the most studied
configuration is the classical 1:1:1 flow. We investigate its dynamo properties
varying the magnetic Reynolds number Rm. We identify two kinks in the growth
rate, which correspond respectively to an eigenvalue crossing and to an
eigenvalue coalescence. The dominant eigenvalue becomes purely real for a
finite value of the control parameter. Finally we show that even for Rm =
25000, the dominant eigenvalue has not yet reached an asymptotic behaviour. Its
still varies very significantly with the controlling parameter. Even at these
very large values of Rm the fast dynamo property of this flow cannot yet be
established
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
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 dimensions with arbitrarily
large . 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
Primordial magnetic fields constrained by CMB anisotropies and dynamo cosmology
Magneto-curvature stresses could deform magnetic field lines and this would
give rise to back reaction and restoring magnetic stresses [Tsagas, PRL
(2001)]. Barrow et al [PRD (2008)] have shown in Friedman universe the
expansion to be slow down in spatial section of negative Riemann curvatures.
From Chicone et al [CMP (1997)] paper, proved that fast dynamos in compact 2D
manifold implies negatively constant Riemannian curvature, here one applies the
Barrow-Tsagas ideas to cosmic dynamos. Fast dynamo covariant stretching of
Riemann slices of cosmic Lobachevsky plane is given. Inclusion of advection
term on dynamo equations [Clarkson et al, MNRAS (2005)] is considered. In
absence of advection a fast dynamo is also obtained. Viscous and restoring
forces on stretching particles decrease, as magnetic rates increase. From COBE
data (), one computes stretching
.
Zeldovich et al has computed the maximum magnetic growth rate as
. From COBE data one computes
a lower growth rate for the magnetic field as
, well-within Zeldovich et al
estimate. Instead of the Harrison value one obtains the
lower primordial field which yields the
at the Big Bang time.Comment: Dept of theoretical physics-UERJ-Brasi
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
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.
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