2,351 research outputs found
Nonlinear magnetoacoustic waves in a cold plasma
The equations describing planar magnetoacoustic waves of permanent form in a cold plasma are rewritten so as to highlight the presence of a naturally small parameter equal to the ratio of the electron and ion masses. If the magnetic field is not nearly perpendicular to the direction of wave propagation, this allows us to use a multiple-scale expansion to demonstrate the existence and nature of nonlinear wave solutions. Such solutions are found to have a rapid oscillation of constant amplitude superimposed on the underlying large-scale variation. The approximate equations for the large-scale variation are obtained by making an adiabatic approximation and in one limit, new explicit solitary pulse solutions are found. In the case of a perpendicular magnetic field, conditions for the existence of solitary pulses are derived. Our results are consistent with earlier studies which were restricted to waves having a velocity close to that of long-wavelength linear magnetoacoustic waves
A solitary-wave solution to a perturbed KdV equation
We derive the approximate form and speed of a solitary-wave solution to a perturbed KdV equation. Using a conventional perturbation expansion, one can derive a first-order correction to the solitary-wave speed, but at the next order, algebraically secular terms appear, which produce divergences that render the solution unphysical. These terms must be treated by a regrouping procedure developed by us previously. In this way, higher-order corrections to the speed are obtained, along with a form of solution that is bounded in space. For this particular perturbed KdV equation, it is found that there is only one possible solitary wave that has a form similar to the unperturbed soliton solution
Nonlocal spectral properties of disordered alloys
A general method is proposed for calculating a fully k-dependent, continuous,
and causal spectral function A(k,E) within the recently introduced nonlocal
version of the coherent-potential approximation (NLCPA). The method involves
the combination of both periodic and anti-periodic solutions to the associated
cluster problem and also leads to correct bulk quantities for small cluster
sizes. We illustrate the method by investigating the Fermi surface of a
two-dimensional alloy. Dramatically, we find a smeared electronic topological
transition not predicted by the conventional CPA.Comment: 17 pages, 5 figures, Submitted to: J. Phys.: Condens. Matter
Editorial receipt 25 May 200
Weakly nonlinear waves in magnetized plasma with a slightly non-Maxwellian electron distribution. Part 2, Stability of cnoidal waves
We determine the growth rate of linear instabilities resulting from long-wavelength transverse perturbations applied to periodic nonlinear wave solutions to the Schamel–Korteweg–de Vries–Zakharov–Kuznetsov (SKdVZK) equation which governs weakly nonlinear waves in a strongly magnetized cold-ion plasma whose electron distribution is given by two Maxwellians at slightly different temperatures. To obtain the growth rate it is necessary to evaluate non-trivial integrals whose number is kept to a minimum by using recursion relations. It is shown that a key instance of one such relation cannot be used for classes of solution whose minimum value is zero, and an additional integral must be evaluated explicitly instead. The SKdVZK equation contains two nonlinear terms whose ratio b increases as the electron distribution becomes increasingly flat-topped. As b and hence the deviation from electron isothermality increases, it is found that for cnoidal wave solutions that travel faster than long-wavelength linear waves, there is a more pronounced variation of the growth rate with the angle θ at which the perturbation is applied. Solutions whose minimum values are zero and which travel slower than long-wavelength linear waves are found, at first order, to be stable to perpendicular perturbations and have a relatively narrow range of θ for which the first-order growth rate is not zero
Investigation of the nonlocal coherent-potential approximation
Recently the nonlocal coherent-potential approximation (NLCPA) has been
introduced by Jarrell and Krishnamurthy for describing the electronic structure
of substitutionally disordered systems. The NLCPA provides systematic
corrections to the widely used coherent-potential approximation (CPA) whilst
preserving the full symmetry of the underlying lattice. Here an analytical and
systematic numerical study of the NLCPA is presented for a one-dimensional
tight-binding model Hamiltonian, and comparisons with the embedded cluster
method (ECM) and molecular coherent potential approximation (MCPA) are made.Comment: 18 pages, 5 figure
The Role of Projection in the Control of Bird Flocks
Swarming is a conspicuous behavioural trait observed in bird flocks, fish
shoals, insect swarms and mammal herds. It is thought to improve collective
awareness and offer protection from predators. Many current models involve the
hypothesis that information coordinating motion is exchanged between neighbors.
We argue that such local interactions alone are insufficient to explain the
organization of large flocks of birds and that the mechanism for the exchange
of long-ranged information necessary to control their density remains unknown.
We show that large flocks self-organize to the maximum density at which a
typical individual is still just able to see out of the flock in many
directions. Such flocks are marginally opaque - an external observer can also
just still see a substantial fraction of sky through the flock. Although
seemingly intuitive we show that this need not be the case; flocks could easily
be highly diffuse or entirely opaque. The emergence of marginal opacity
strongly constrains how individuals interact with each other within large
swarms. It also provides a mechanism for global interactions: An individual can
respond to the projection of the flock that it sees. This provides for faster
information transfer and hence rapid flock dynamics, another advantage over
local models. From a behavioural perspective it optimizes the information
available to each bird while maintaining the protection of a dense, coherent
flock.Comment: PNAS early edition published online at
http://www.pnas.org/cgi/doi/10.1073/pnas.140220211
Electric field generation by the electron beam filamentation instability: Filament size effects
The filamentation instability (FI) of counter-propagating beams of electrons
is modelled with a particle-in-cell simulation in one spatial dimension and
with a high statistical plasma representation. The simulation direction is
orthogonal to the beam velocity vector. Both electron beams have initially
equal densities, temperatures and moduli of their nonrelativistic mean
velocities. The FI is electromagnetic in this case. A previous study of a small
filament demonstrated, that the magnetic pressure gradient force (MPGF) results
in a nonlinearly driven electrostatic field. The probably small contribution of
the thermal pressure gradient to the force balance implied, that the
electrostatic field performed undamped oscillations around a background
electric field. Here we consider larger filaments, which reach a stronger
electrostatic potential when they saturate. The electron heating is enhanced
and electrostatic electron phase space holes form. The competition of several
smaller filaments, which grow simultaneously with the large filament, also
perturbs the balance between the electrostatic and magnetic fields. The
oscillations are damped but the final electric field amplitude is still
determined by the MPGF.Comment: 14 pages, 10 plots, accepted for publication in Physica Script
On the effect of Ti on Oxidation Behaviour of a Polycrystalline Nickel-based Superalloy
Titanium is commonly added to nickel superalloys but has a well-documented
detrimental effect on oxidation resistance. The present work constitutes the
first atomistic-scale quantitative measurements of grain boundary and bulk
compositions in the oxide scale of a current generation polycrystalline nickel
superalloy performed through atom probe tomography. Titanium was found to be
particularly detrimental to oxide scale growth through grain boundary
diffusion
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