4,895 research outputs found
On the mean field dynamo with Hall effect
We study in the present paper how Hall effect modifies the quenching process
of the electromotive force (e.m.f.) in Mean Field Dynamo (MFD) theories. We
write down the evolution equations for the e.m.f. and for the large and small
scale magnetic helicity, treat Hall effect as a perturbation and integrate the
resulting equations assuming boundary conditions such that the total
divergencies vanish. For force-free large scale magnetic fields, Hall effect
acts by coupling the small scale velocity and magnetic fields. For the range of
parameters considered, the overall effect is a stronger quenching of the e.m.f.
than in standard MHD and a damping of the inverse cascade of magnetic helicity.
In astrophysical environments characterized by the parameters considered here,
Hall effect would produce an earlier quenching of the e.m.f. and consequently a
weaker large scale magnetic field.Comment: 8 pages, 4 figures. Accepted by A&
Asymptotics of capture zone distributions in a fragmentation-based model of submonolayer deposition
We consider the asymptotics of the distribution of the capture zones associated with the islands nucleated during submonolayer deposition onto a one-dimensional substrate. We use a convolution of the distribution of inter-island gaps, the asymptotics of which is known for a class of nucleation models, to derive the asymptotics for the capture zones. The results are in broad agreement with published Monte Carlo simulation data (O'Neill et al., 2012) [13]
Accretion Disks and Dynamos: Toward a Unified Mean Field Theory
Conversion of gravitational energy into radiation in accretion discs and the
origin of large scale magnetic fields in astrophysical rotators have often been
distinct topics of research. In semi-analytic work on both problems it has been
useful to presume large scale symmetries, necessarily resulting in mean field
theories. MHD turbulence makes the underlying systems locally asymmetric and
nonlinear. Synergy between theory and simulations should aim for the
development of practical mean field models that capture essential physics and
can be used for observational modeling. Mean field dynamo (MFD) theory and
alpha-viscosity accretion theory exemplify such ongoing pursuits. 21st century
MFD theory has more nonlinear predictive power compared to 20th century MFD
theory, whereas accretion theory is still in a 20th century state. In fact,
insights from MFD theory are applicable to accretion theory and the two are
artificially separated pieces of what should be a single theory. I discuss
pieces of progress that provide clues toward a unified theory. A key concept is
that large scale magnetic fields can be sustained via local or global magnetic
helicity fluxes or via relaxation of small scale magnetic fluctuations, without
the kinetic helicity driver of 20th century textbooks. These concepts may help
explain the formation of large scale fields that supply non-local angular
momentum transport via coronae and jets in a unified theory of accretion and
dynamos. In diagnosing the role of helicities and helicity fluxes in disk
simulations, each disk hemisphere should be studied separately to avoid being
misled by cancelation that occurs as a result of reflection asymmetry. The
fraction of helical field energy in disks is expected to be small compared to
the total field in each hemisphere as a result of shear, but can still be
essential for large scale dynamo action.Comment: For the Proceedings of the Third International Conference and
Advanced School "Turbulent Mixing and Beyond," TMB-2011 held on 21 - 28
August 2011 at the Abdus Salam International Centre for Theoretical Physics,
Trieste, http://users.ictp.it/~tmb/index2011.html Italy, To Appear in Physica
Scripta (corrected small items to match version in print
Molecular gyroscopes and biological effects of weak ELF magnetic fields
Extremely-low-frequency magnetic fields are known to affect biological
systems. In many cases, biological effects display `windows' in biologically
effective parameters of the magnetic fields: most dramatic is the fact that
relatively intense magnetic fields sometimes do not cause appreciable effect,
while smaller fields of the order of 10--100 T do. Linear resonant
physical processes do not explain frequency windows in this case. Amplitude
window phenomena suggest a nonlinear physical mechanism. Such a nonlinear
mechanism has been proposed recently to explain those `windows'. It considers
quantum-interference effects on protein-bound substrate ions. Magnetic fields
cause an interference of ion quantum states and change the probability of
ion-protein dissociation. This ion-interference mechanism predicts specific
magnetic-field frequency and amplitude windows within which biological effects
occur. It agrees with a lot of experiments. However, according to the
mechanism, the lifetime of ion quantum states within a protein
cavity should be of unrealistic value, more than 0.01 s for frequency band
10--100 Hz. In this paper, a biophysical mechanism has been proposed that (i)
retains the attractive features of the ion interference mechanism and (ii) uses
the principles of gyroscopic motion and removes the necessity to postulate
large lifetimes. The mechanism considers dynamics of the density matrix of the
molecular groups, which are attached to the walls of protein cavities by two
covalent bonds, i.e., molecular gyroscopes. Numerical computations have shown
almost free rotations of the molecular gyros. The relaxation time due to van
der Waals forces was about 0.01 s for the cavity size of 28 angstr\"{o}ms.Comment: 10 pages, 7 figure
Finite-Size Scaling in the Energy-Entropy Plane for the 2D +- J Ising Spin Glass
For square lattices with the 2D Ising spin glass with
+1 and -1 bonds is found to have a strong correlation between the energy and
the entropy of its ground states. A fit to the data gives the result that each
additional broken bond in the ground state of a particular sample of random
bonds increases the ground state degeneracy by approximately a factor of 10/3.
For (where is the fraction of negative bonds), over this range of
, the characteristic entropy defined by the energy-entropy correlation
scales with size as . Anomalous scaling is not found for the
characteristic energy, which essentially scales as . When , a
crossover to scaling of the entropy is seen near . The results
found here suggest a natural mechanism for the unusual behavior of the low
temperature specific heat of this model, and illustrate the dangers of
extrapolating from small .Comment: 9 pages, two-column format; to appear in J. Statistical Physic
Mean magnetic field generation in sheared rotators
A generalized mean magnetic field induction equation for differential
rotators is derived, including a compressibility, and the anisotropy induced on
the turbulent quantities from the mean magnetic field itself and a mean
velocity shear. Derivations of the mean field equations often do not emphasize
that there must be anisotropy and inhomogeneity in the turbulence for mean
field growth. The anisotropy from shear is the source of a term involving the
product of the mean velocity gradient and the cross-helicity correlation of the
isotropic parts of the fluctuating velocity and magnetic field,
\lb{\bfv}\cdot{\bfb}\rb^{(0)}. The full mean field equations are derived to
linear order in mean fields, but it is also shown that the cross-helicity term
survives to all orders in the velocity shear. This cross-helicity term can
obviate the need for a pre-existing seed mean magnetic field for mean field
growth: though a fluctuating seed field is necessary for a non-vanishing
cross-helicity, the term can produce linear (in time) mean field growth of the
toroidal field from zero mean field. After one vertical diffusion time, the
cross-helicity term becomes sub-dominant and dynamo exponential
amplification/sustenance of the mean field can subsequently ensue. The
cross-helicity term should produce odd symmetry in the mean magnetic field, in
contrast to the usually favored even modes of the dynamo amplification in
sheared discs. This may be important for the observed mean field geometries of
spiral galaxies. The strength of the mean seed field provided by the cross-
helicity depends linearly on the magnitude of the cross-helicity.Comment: 15 pages, LaTeX, matches version accepted to ApJ, minor revision
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