The conductivity tensor is obtained directly from the perturbed Vlasov equation for a plasma in an inhomogeneous magnetic field. The conductivity tensor elements are obtained consistently to all orders in the "pe...
The conductivity tensor is obtained directly from the perturbed Vlasov equation for a plasma in an inhomogeneous magnetic field. The conductivity tensor elements are obtained consistently to all orders in the "perpendicular wavenumbers" and to first order in the equilibrium magnetic field gradient. Conditions on the parallel wavenumber and the magnetic field gradient for which such a method is valid are given. The wave differential operator is obtained from the conductivity tensor using Maxwell's equations. The coupled differential equations are then truncated to second order to model the case of minority and second harmonic ion cyclotron heating. The forms of the electromagnetic and kinetic power flows and the minority and majority cyclotron damping are obtained simply. The differential equations are solved numerically as a linear combination of boundary value problems for the perturbing electric fields using standard NAG library routines, and the transmission, reflection and mode conversion are calculated for a range of k(y) and k(z) values. On setting k(y) to zero, excellent agreement is found between the results obtained from our code and published results from codes by other authors.
The existence of Killing vectors in conformally flat perfect fluid spacetimes in general relativity is considered. In particular Killing vectors which are neither orthogonal nor parallel to the fluid velocity vector a...
The existence of Killing vectors in conformally flat perfect fluid spacetimes in general relativity is considered. In particular Killing vectors which are neither orthogonal nor parallel to the fluid velocity vector are considered and stationary fields in which the fluid velocity vector is not parallel to the timelike Killing vector field are shown to exist. This class of solutions is shown to include several stationary (but non-static) axisymmetric fields, thus providing counter-examples to a theorem of Collinson (1976). In the case when the fluid is non-expanding, the number of spacelike Killing vectors is shown to depend on the rank of four functions of time which appear in the metric. Some examples of stationary but non-static fields are presented in closed form.
The author obtains the propagator for a charged particle in the presence of a constant magnetic field and any positive definite quadratic potential. The trace is then calculated and the eigenvalues of the Hamiltonian ...
The author obtains the propagator for a charged particle in the presence of a constant magnetic field and any positive definite quadratic potential. The trace is then calculated and the eigenvalues of the Hamiltonian concerned are obtained.
A formal derivation is presented of an efficient algorithm for comput.ng the "sums" of all segments, of a given length, of a sequence. Here, "sums" refers to the continued application of a binary o...
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A formal derivation is presented of an efficient algorithm for comput.ng the "sums" of all segments, of a given length, of a sequence. Here, "sums" refers to the continued application of a binary operator of which associativity is the only known property. Recurrence relations are used to separate two concerns, viz. characterisation of the values to be comput.d and choosing the order in which these values will be comput.d.
This article addresses the following problem. Given a set S of clauses and a set of constant and function symbols F that occur in the clauses of S, obtain a fully quantified (closed) formula S' from S by replacing...
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This article addresses the following problem. Given a set S of clauses and a set of constant and function symbols F that occur in the clauses of S, obtain a fully quantified (closed) formula S' from S by replacing expressions starting with symbols in F with existentially quantified variables. S' must be unsatisfiable if and only if S is unsatisfiable. A sound (but not complete) solution is given in the form of an outline of an algorithm.
A technique is proposed for aiding photointerpreters in detecting man-made features in aerial reconnaissance images. The technique, which uses a metric called fractal error, is based on the observed propensity of natu...
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A technique is proposed for aiding photointerpreters in detecting man-made features in aerial reconnaissance images. The technique, which uses a metric called fractal error, is based on the observed propensity of natural image features to fit a fractional Brownian motion model. Man-made features usually do not fit this model well, and consequently the fractal error metric may be used as a discriminant function for detecting man-made scene features.
The author obtains an expression for the stochastic Lagrangian as used in stochastic mechanics in a straightforward manner without obtaining the singular terms of Guerra et. at. (1983). He then presents a new derivati...
The author obtains an expression for the stochastic Lagrangian as used in stochastic mechanics in a straightforward manner without obtaining the singular terms of Guerra et. at. (1983). He then presents a new derivation of the Schrodinger equation.
One of the problems in linearized seismic inverse scattering, which has received little attention so far, is the existence of large gaps in the acquisition geometry due to the use of a limited number of sources and re...
One of the problems in linearized seismic inverse scattering, which has received little attention so far, is the existence of large gaps in the acquisition geometry due to the use of a limited number of sources and receivers. Frequently used Born inversion methods do not take this kind of sampling effect into account. Therefore, especially for three-dimensional problems, the results may suffer from serious artefacts. These problems are partially overcome by using iterative methods, based on the minimization of an error norm. For two-dimensional test problems, we have found that iterative methods give significantly more accurate results for sparsely sampled data. For large-scale seismic inverse problems, the rate of convergence of any iterative method is extremely important. We have found that fast convergence rates can be achieved with the aid of methods that are preconditioned with the Born inverse scattering operator. In particular, the rate of convergence of the preconditioned successive overrelaxation method and the preconditioned Krylov subspace method have been found to be much faster than the widely used conjugate gradient method. With these new methods, we have obtained acceptable results for problems containing as many as 90 000 unknowns, after only four iterations.
We prove the result that any perfect fluid solution of Einstein's field equations satisfying a barotropic equation of state p = p(mu) and the condition mu + p not-equal 0, which admits a proper conformal Killing v...
We prove the result that any perfect fluid solution of Einstein's field equations satisfying a barotropic equation of state p = p(mu) and the condition mu + p not-equal 0, which admits a proper conformal Killing vector (CKV) parallel to the fluid 4-velocity, is locally a Friedmann-Robertson-Walker model. Generalizations of this result to the case p not-equal p(mu) are then investigated. Finally, the consequences of the result are discussed and related to previous work on inheriting CKV, on asymptotic Friedmann-like CKV, on a conjecture that shear-free, perfect fluid models necessarily have either zero vorticity or zero expansion, and previous results from relativistic kinetic theory.
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