Anomalous spin Hall and inverse spin Hall effects in magnetic systems

Spin current is a very important tensor quantity in spintronics. However, the well-known spin-Hall effect (SHE) can only generate a few of its components whose propagating and polarization directions are perpendicular with each other and to an applied charge current. It is highly desirable in applications to generate spin currents whose polarization can be in any possible direction. Here anomalous SHE and inverse spin-Hall effect (ISHE) in magnetic systems are predicted. Spin currents, whose polarisation and propagation are collinear or orthogonal with each other and along or perpendicular to the charge current, can be generated, depending on whether the applied charge current is along or perpendicular to the order parameter. In anomalous ISHEs, charge currents proportional to the order parameter can be along or perpendicular to the propagating or polarization directions of the spin current.

Influence of Shape Spread in an Ensemble of Metal Nanoparticles on Their Optical Properties

The theoretical basis of the work consists in that the dissipative processes in non-spherical nanoparticles, whose sizes are smaller than the mean free path of electrons, are characterized by a tensor quantity, whose diagonal elements together with the depolarization coefficients determine the half-widths of plasma resonances. Accordingly, the averaged characteristics are obtained for an ensemble of metal nanoparticles with regard for the influence of the nanoparticle shape on the depolarization coefficients and the components of the optical conductivity tensor. Three original variants of the nanoparticle shape distribution function are proposed on the basis of the joint application of the Gauss and “cap” functions.

The separation of the Hamilton-Jacobi equation for the Kerr metric

We discuss the separability of the Hamilton-Jacobi equation for the Kerr metric. We use a recent theorem which says that a completely integrable geodesic equation has a fully separable Hamilton-Jacobi equation if and only if the Lagrangian is a composite of the involutive first integrals. We also discuss the physical significance of Carter's fourth constant in terms of the symplectic reduction of the Schwarzschild metric via SO(3), showing that the Killing tensor quantity is the remnant of the square of angular momentum.

Stress

Stress is a tensor quantity that describes the mechanical force density (force per unit area) on the complete surface of a domain inside a material body. A stress exists wherever one part of a body exerts a force on neighboring parts. Its orientation is not tied to any particular directions that are intrinsic to the material like, say, crystallographic axes. It is thus distinct from the matter tensors that were discussed in the preceding chapter, all of which have definitive orientations within a crystal or other anisotropic material; it is called a field tensor (and so is strain). The definition of stress depends on the concept of a continuum. Let f(xi) be a single-valued function defined for every point xi in a region. This function is said to be continuous at the point xi if the following holds for all paths of approach of xi to °xi:. . . f(xi) → f(°xi) as xi → °xi (4.1)· . . . Equivalently, for any number ∊, no matter how small, there exists a neighborhood of nonzero radius around the point xi in which: . . . . 〈f(xi) − f(°xi)〉2 < ∊,­ (4.2) . . . for all points xi in that neighborhood. A continuum is an idealized material whose physical attributes are continuous functions of position. Thus neighboring points remain neighbors, and a continuum cannot have gaps or jumps (discontinuities) in its properties. Surfaces bounding gaps or defining discontinuities must be specially treated in continuum mechanics. Examples are surfaces between two fluids of differing density or viscosity, or between solids with different thermal conductivity or elastic properties. Real materials are never continua; they are discontinuous at the atomic scale, and often at larger scales as well. The notion of a continuum is, therefore, only a macroscopic approximation, but it allows useful mathematical approaches to the treatment of real phenomena.

MOVING‐BASE GRAVITY GRADIOMETER SURVEYS AND INTERPRETATION

Moving‐base gravity gradiometers are currently under development at Bell Aerospace Co., Charles Stark Draper Laboratory, and Hughes Aircraft Co. In principle, these instruments can be mounted on stable platforms in aircraft or marine survey ships. Unlike a conventional gravimeter, the gradiometer is insensitive to vertical (heave) accelerations of the vehicle and does not require an Eötvös correction. Gradiometers thereby offer an overwhelming improvement in the speed and accuracy of gravity surveys. In addition, a gradiometer provides more information than a gravimeter because a tensor quantity is measured, rather than a scalar. How should the gradient data be used? The simplest approach is to convert the gradients into gravity anomalies by integrating along the vehicle path, and then apply conventional interpretation models. This approach is sound if the survey tracks are closely spaced because continuous two‐dimensional gravity anomalies completely define the gravity field outside the earth, according to potential theory. On the other hand, one can widen the survey tracks considerably if a more sophisticated approach is adopted that exploits the extra information in the gradients. In this paper, we compare the “simple” approach and a more elaborate (“optimal”) one that uses the entire gradient tensor. The comparison is based on information theory concepts: How much information is in the gradient data? How much is lost if the gradients are converted to gravity anomalies? Statistical models are fitted to Bouguer residual gravity anomalies from a salt dome field in the Louisiana Gulf Coast, and the interpretation rms errors are evaluated for each approach based on optimal estimation theory. The results show that a gradiometric survey with 18-km spacing contains the same information as a gravimetric survey with 8-km spacing. The sensitivities of the results to the following survey parameters are determined: track spacing, gradiometer noise, vehicle speed, and aircraft altitude.