24,225 research outputs found
Strong nonlocality variations in a spherical mean-field dynamo
To explain the large-scale magnetic field of the Sun and other bodies,
mean-field dynamo theory is commonly applied where one solves the averaged
equations for the mean magnetic field. However, the standard approach breaks
down when the scale of the turbulent eddies becomes comparable to the scale of
the variations of the mean magnetic field. Models showing sharp magnetic field
structures have therefore been regarded as unreliable. Our aim is to look for
new effects that occur when we relax the restrictions of the standard approach,
which becomes particularly important at the bottom of the convection zone where
the size of the turbulent eddies is comparable to the depth of the convection
zone itself. We approximate the underlying integro-differential equation by a
partial differential equation corresponding to a reaction-diffusion type
equation for the mean electromotive force, making an approach that is nonlocal
in space and time feasible under conditions where spherical geometry and
nonlinearity are included. In agreement with earlier findings, spatio-temporal
nonlocality lowers the excitation conditions of the dynamo. Sharp structures
are now found to be absent. However, in the surface layers the field remains
similar to before.Comment: 9 pages, 11 figures, 1 table, submitted to Astron Nach
Structure of the exotic nucleus B in the ground state
We investigate the structure of the neutron rich nucleus B through
studies of its breakup in the Coulomb field of a heavy target. The breakup
amplitude is calculated within an adiabatic as well as finite range DWBA
theories of breakup reactions. Both these formalisms allow the use of realistic
wave functions for the relative motion between the fragments in the ground
state of the projectile. The longitudinal momentum distributions of B
(ground state) following the breakup of B on a heavy target at beam
energy of 60 MeV/nucleon, calculated using two possible ground state
configurations of B, have been compared with the recent data. The data
seem to favour B( as the possible ground
state configuration of B with a spectroscopic factor close to unity. We
give our predictions for the neutron angular distributions and the relative
energy spectra in the one-neutron removal reaction of B.Comment: Submitted to Physical Review
Regularizing tunnelling calculations of Hawking temperature
Attempts to understand Hawking radiation as tunnelling across a black hole
horizon require the consideration of singular integrals. Although Schwarzschild
coordinates lead to the standard Hawking temperature, isotropic radial
coordinates may appear to produce an incorrect value. It is demonstrated here
how the proper regularization of singular integrals leads to the standard
temperature for the isotropic radial coordinates as well as for other smooth
transformations of the radial variable, which of course describe the same black
hole.Comment: 4 pages; expande
Stimulated scattering instability in a relativistic plasma
We study the stimulated scattering instabilities of an intense linearly
polarized electromagnetic wave (EMW) in a relativistic plasma with degenerate
electrons. Starting from a relativistic hydrodynamic model and the Maxwell's
equations, we derive coupled nonlinear equations for low-frequency electron and
ion plasma oscillations that are driven by the EMW's ponderomotive force. The
nonlinear dispersion relations are then obtained from the coupled nonlinear
equations which reveal stimulated Raman scattering (SRS), stimulated Brillouin
scattering (SBS), and modulational instabilities (MIs) of EMWs. It is shown
that the thermal pressure of ions and the relativistic degenerate pressure of
electrons significantly modify the characteristics of SRS, SBS, and MIs.Comment: 7 pages, 3 figures. In the revised version, the basic equations are
corrected, and the results and discussion are significantly improved. To
appear in Phys. Plasmas (2018
Random geometric graph description of connectedness percolation in rod systems
The problem of continuum percolation in dispersions of rods is reformulated
in terms of weighted random geometric graphs. Nodes (or sites or vertices) in
the graph represent spatial locations occupied by the centers of the rods. The
probability that an edge (or link) connects any randomly selected pair of nodes
depends upon the rod volume fraction as well as the distribution over their
sizes and shapes, and also upon quantities that characterize their state of
dispersion (such as the orientational distribution function). We employ the
observation that contributions from closed loops of connected rods are
negligible in the limit of large aspect ratios to obtain percolation thresholds
that are fully equivalent to those calculated within the second-virial
approximation of the connectedness Ornstein-Zernike equation. Our formulation
can account for effects due to interactions between the rods, and many-body
features can be partially addressed by suitable choices for the edge
probabilities.Comment: 7 page
Nonlinear Landau damping of wave envelopes in a quantum plasma
The nonlinear theory of Landau damping of electrostatic wave envelopes (WEs)
is revisited in a quantum electron-positron (EP) pair plasma. Starting from a
Wigner-Moyal equation coupled to the Poisson equation and applying the multiple
scale technique, we derive a nonlinear Schr{\"o}dinger (NLS) equation which
governs the evolution of electrostatic WEs. It is shown that the coefficients
of the NLS equation, including the nonlocal nonlinear term, which appears due
to the resonant particles having group velocity of the WEs, are significantly
modified by the particle dispersion. The effects of the quantum parameter
(the ratio of the plasmon energy to the thermal energy densities), associated
with the particle dispersion, are examined on the Landau damping rate of
carrier waves, as well as on the modulational instability of WEs. It is found
that the Landau damping rate and the decay rate of the solitary wave amplitude
are greatly reduced compared to their classical values .Comment: 11 pages, 4 figures; Some typos in Eqs. (6) and (A4) are rectifie
Energy Calculation of Magnetohydrodynamic Waves and Their Stability For Viscous Shearing Flows
A self-consistent, thermodynamic approach is employed to derive the wave
energy of a magnetohydrodynamic system within the harmonic approximation and to
obtain the familiar dispersion relation from the resulting equation of motion.
The evolution of the system due to an external perturbation is studied by a
linear response formalism, that also gives the energy absorbed by the
magnetohydrodynamic system from the external field. The calculated wave energy
reveals the presence of positive and negative energy waves, that coalesce
together to give rise to Kelvin - Helmholtz instability of the system. The
threshold value of this instability changes only slightly in the presence of a
small amount of viscosity, thus precluding the dissipative instability of the
negative energy waves. The prediction of such a dissipative instability by
earlier authors turns out to be the result of an erroneous choice of the
viscous drag force, that violates the fundamental law of Galilean invariance.Comment: 27 pages, Latex, Submitted to Jour. Fluid. Mech. (1997
Modulation of kinetic Alfv\'en waves in an intermediate low-beta magnetoplasma
We study the amplitude modulation of nonlinear kinetic Alfv{\'e}n waves
(KAWs) in an intermediate low-beta magnetoplasma. Starting from a set of fluid
equations coupled to the Maxwell's equations, we derive a coupled set of
nonlinear partial differential equations (PDEs) which govern the evolution of
KAW envelopes in the plasma. The modulational instability (MI) of such KAW
envelopes is then studied by a nonlinear Schr{\"o}dinger (NLS) equation derived
from the coupled PDEs. It is shown that the KAWs can evolve into bright
envelope solitons, or can undergo damping depending on whether the
characteristic ratio of the Alfv{\'e}n to ion-acoustic (IA) speeds
remains above or below a critical value. The parameter is also found
to shift the MI domains around the plane, where is the KAW
number perpendicular (parallel) to the external magnetic field. The growth rate
of MI, as well as the frequency shift and the energy transfer rate, are
obtained and analyzed. The results can be useful for understanding the
existence and formation of bright and dark envelope solitons, or damping of KAW
envelopes in space plasmas, e.g., interplanetary space, solar winds etc.Comment: 8 pages, 3 figures; In the revised version, figures are redrawn, the
title, results and discussion are revised; to appear in Phys. Plasmas (2018
Nonlinear Landau damping and modulation of electrostatic waves in a nonextensive electron-positron-pair plasma
The nonlinear theory of amplitude modulation of electrostatic wave envelopes
in a collisionless electron-positron (EP) pair plasma is studied by using a set
of Vlasov-Poisson equations in the context of Tsallis' -nonextensive
statistics. In particular, the previous linear theory of Langmuir oscillations
in EP plasmas [Phys. Rev. E {\bf87}, 053112 (2013)] is rectified and modified.
Applying the multiple scale technique (MST), it is shown that the evolution of
electrostatic wave envelopes is governed by a nonlinear Schr{\"o}dinger (NLS)
equation with a nonlocal nonlinear term [where
denotes the Cauchy principal value, is the small-amplitude electrostatic
(complex) potential, and and are the stretched coordinates in MST]
which appears due to the wave-particle resonance. It is found that a subregion
of superextensivity exists where the carrier wave
frequency can turn over with the group velocity going to zero and then to
negative values. The effects of the nonlocal nonlinear term and the
nonextensive parameter are examined on the modulational instability (MI) of
wave envelopes as well as on the solitary wave solution of the NLS equation. It
is found that the modulated wave packet is always unstable (nonlinear Landau
damping) due to the nonlocal nonlinearity in the NLS equation. Furthermore, the
effect of the nonlinear Landau damping is to slow down the amplitude of the
wave envelope, and the corresponding decay rate can be faster the larger is the
number of superthermal particles in pair plasmas.Comment: 25 pages, 5 figures; In the revised version typos are rectified, long
expressions are given in the Appendices; this version to appear in Phys. Rev.
On the absence of dissipative instability of negative energy waves in hydrodynamic shear flows
Stability criterion for the surface gravity capillary waves in a flowing
two-layered fluid system with viscous dissipation is investigated. It is seen
that the dissipative instability of negative energy waves is absent,- contrary
to what earlier authors have concluded. Their error is identified to arise from
an erroneous choice of the dissipation law, in which the wave profile velocity
is wrongly equated to the particle velocity. Our corrected dissipation law is
also shown to restore Galilean invariance to the stability condition of the
system.Comment: Revtex file, 4 pgs, no fig
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