Derivation of the paraxial form of the angular momentum of the electromagnetic field from the general form

It is shown how the standard forms for the spin and orbital components of the angular momentum of a paraxial wave of electromagnetic radiation are obtained from the general expressions for the angular momentum that have been derived recently. This result will enable the general expressions for angular momentum to be applied with confidence to the many configurations of electromagnetic fields that are more complicated than plane or paraxial waves.Comment: typos corrected 6 page

Comparison of different forms for the "spin" and "orbital" components of the angular momentum of light

We compare three attempts that have been made to decompose the angular momentum of the electromagnetic field into components of an "orbital" and "spin" nature. All three expressions are different and it appears, on the basis of classical electrodynamics, that there is no preferred way of decomposing the angular momentum of the electromagnetic field into orbital and spin components, even in an inertial frame.Comment: Some clarifications. 7 pages pdf. Earlier version published in International Journal of Optics: http://www.hindawi.com/journals/ijo/aip/728350

Longitudinal and transverse components of a vector field

A unified account, from a pedagogical perspective, is given of the longitudinal and transverse projective delta functions proposed by Belinfante and of their relation to the Helmholtz theorem for the decomposition of a three-vector field into its longitudinal and transverse components. It is argued that the results are applicable to fields that are time-dependent as well as fields that are time-independent.Comment: 9 pages pdf format. Includes derivation and extension of the Frahm relation and volume integrals of projector

Interatomic forces, phonons, the Foreman-Lomer Theorem and the Blackman Sum Rule

Foreman and Lomer proposed in 1957 a method of estimating the harmonic forces between parallel planes of atoms of primitive cubic crystals by Fourier transforming the squared frequencies of phonons propagating along principal directions. A generalized form of this theorem is derived in this paper and it is shown that it is more appropriate to apply the method to certain combinations of the phonon dispersion relations rather than to individual dispersion relations themselves. Further, it is also shown how the method may be extended to the non-primitive hexagonal close packed and diamond lattices. Explicit, exact and general relations in terms of atomic force constants are found for deviations from the Blackman sum rule which itself is shown to be derived from the generalized Foreman-Lomer theorem.Comment: 13 pages pd

Gauge-invariant Formulation of the Second-order Cosmological Perturbations

Gauge invariant treatments of the second order cosmological perturbation in a four dimensional homogeneous isotropic universe filled with the perfect fluid are completely formulated without any gauge fixing. We derive all components of the Einstein equations in the case where the first order vector and tensor modes are negligible. These equations imply that the tensor and the vector mode of the second order metric perturbations may be generated by the scalar-scalar mode coupling of the linear order perturbations as the result of the non-linear effects of the Einstein equations.Comment: 5 pages, no figure. RevTeX; short letter version of gr-qc/0605108; some details of explanations are adde

Adaptive digital signal processing Java teaching tool

This publication presents a JAVA program for teaching the rudiments of adaptive digital signal processing (DSP) algorithms and techniques. Adaptive DSP is on of the most important areas of signal processsing, and provides the core algorithmic means to implement applications ranging from mobile telephone speech coding, to noise cancellation, to communication channel equalization. Over the last 30 years adaptive digital signal processing has progressed from being a strictly graduate level advanced class in signal processing theory to a topic that is part of the core curriculum for many undergraduate signal processing classes. The JAVA applet presented in this publication has been devised for students to use in combination with lecture notes and/or one of the recognised textbooks such that they can quickly and conveniently simulate algorithms such as the LMS (least mean squares), RLS (recursive least squares) and so on in a variety of applications without requiring to write programs or scripts or using any special purpose software. By the very nature of the JAVA code therefore, the applet can be run from any browser, even over a low bandwidth modem connection

Collisions Between Gravity-Dominated Bodies: 1. Outcome Regimes and Scaling Laws

Collisions are the core agent of planet formation. In this work, we derive an analytic description of the dynamical outcome for any collision between gravity-dominated bodies. We conduct high-resolution simulations of collisions between planetesimals; the results are used to isolate the effects of different impact parameters on collision outcome. During growth from planetesimals to planets, collision outcomes span multiple regimes: cratering, merging, disruption, super-catastrophic disruption, and hit-and-run events. We derive equations (scaling laws) to demarcate the transition between collision regimes and to describe the size and velocity distributions of the post-collision bodies. The scaling laws are used to calculate maps of collision outcomes as a function of mass ratio, impact angle, and impact velocity, and we discuss the implications of the probability of each collision regime during planet formation. The analytic collision model presented in this work will significantly improve the physics of collisions in numerical simulations of planet formation and collisional evolution. (abstract abridged)Comment: Version 3, accepted to ApJ in Nov. 2011 published online Dec. 2011. Abstract abridge

Demographic Trends in National Forest, Recreational, Retirement, and Amenity Areas

Those who live near national forests are both potential forest visitors and neighbors who feel the impact of many forest management decisions. This paper provides some insights about those proximate populations. It does so by measuring the proportion of national forest land within each county and then combining that with an analysis of the patterns of demographic change over the past several decades. Because there is considerable overlap between counties that contain national forests and those designated as recreational, high amenity, and retirement destination counties, demographic trends in such counties are compared. A total of 757 of the 3,141 U.S. counties contain national forest land. More than 66.1 million people resided in these counties in 2000, some 24% of the U.S. total. The population in national forest counties grew by 19% between 1990 and 2000 compared to 13% for the nation as a whole. Most of the population gain in national forest areas resulted from net in-migration. Population gains in national forest counties were slightly smaller than those in recreational and natural amenity counties and significantly less than those in retirement destination counties; however, the gains were considerably larger than those in other counties. National forest counties that are metropolitan have significantly more Hispanics than other metropolitan counties but fewer Blacks and Whites. Nonmetropolitan national forest counties contain a much larger proportion of non-Hispanic Whites than their metropolitan counterparts, a finding consistent with that for nonmetropolitan counties in general. Knowledge about the changing size and demographic structure of the population in national forest counties has particular relevance to Forest Service planners and policymakers