Polarization of tightly focused laser beams

The polarization properties of monochromatic light beams are studied. In contrast to the idealization of an electromagnetic plane wave, finite beams which are everywhere linearly polarized in the same direction do not exist. Neither do beams which are everywhere circularly polarized in a fixed plane. It is also shown that transversely finite beams cannot be purely transverse in both their electric and magnetic vectors, and that their electromagnetic energy travels at less than c. The electric and magnetic fields in an electromagnetic beam have different polarization properties in general, but there exists a class of steady beams in which the electric and magnetic polarizations are the same (and in which energy density and energy flux are independent of time). Examples are given of exactly and approximately linearly polarized beams, and of approximately circularly polarized beams.Comment: 9 pages, 6 figure

Task Force Development to Provide Education and Leadership to the Meat Goat Industry

Chevon is the most frequently consumed meat in the world. Meat goat production is increasing because of the economic value of goats as efficient converters of low-quality forages into quality meat, milk, and hide products for specialty markets of health conscious, ethnic, and faith based consumers. Estimates of national marketing indicate that U.S. meat goat production is nearly 500,000 head less than demand. Where resources are limited, meat goats can be raised efficiently and profitably on small farms, so the country could become self-sufficient in meat goats

Effect of atmospheric turbulence on propagation properties of optical vortices formed by using coherent laser beam arrays

In this paper, we consider the effect of the atmospheric turbulence on the propagation of optical vertex formed from the radial coherent laser beam array, with the initially well-defined phase distribution. The propagation formula of the radial coherent laser array passing through the turbulent atmosphere is analytically derived by using the extended Huygens-Fresnel diffraction integral. Based on the derived formula, the effect of the atmospheric turbulence on the propagation properties of such laser arrays has been studied in great detail. Our main results show that the atmospheric turbulence may result in the prohibition of the formation of the optical vortex or the disappearance of the formed optical vortex, which are very different from that in the free space. The formed optical vortex with the higher topological charge may propagate over a much longer distance in the moderate or weak turbulent atmosphere. After the sufficient long-distance atmospheric propagation, all the output beams (even with initially different phase distributions) finally lose the vortex property and gradually become the Gaussian-shaped beams, and in this case the output beams actually become incoherent light fields due to the decoherence effect of the turbulent atmosphere.Comment: 10 pages, 5 figure

The demand for unfair gambles: Why illegal lotteries persist

We show how cheating in illegal gambling can be sustained in equilibrium, even when gamblers are aware of it. Not only is cheating profit-maximizing for operators, but it can also be utility-maximizing if it provides gamblers the opportunity to engage in other related activities that generate non-monetary rewards, such as practicing superstitions. This, in turn, suggests why legalizing gambling might not fully capture the gains from the illegal market - operators and gamblers both prefer cheating, but this would be harder to hide in a legalized environment. We illustrate the model, generate results, and verify them empirically, using the example of jueteng, an illegal numbers game in the Philippines

Combined vitamin B6-magnesium treatment in autism spectrum disorder

Background The use of mega-vitamin intervention began in the 1950s with the treatment of schizophrenic patients. Pyroxidine (vitamin B6) was first used with children diagnosed with autism syndrome when speech and language improvement was observed in some children as a result of large doses of B6. A number of studies attempted to assess the effects of vitamin B6-Magnesium (Mg) was found to reduce undesirable side effects from B6) on characteristics such as verbal communication, non-verbal communication, interpersonal skills, and physiological function, in individuals with autism. Objectives To determine the efficacy of vitamin B6 and magnesium (B6-Mg) for treating social, communication, and behavioural responses of children and adults with autism. Search strategy We searched the Cochrane Controlled Trials Register (Cochrane Library, Issue 2, 2002), MEDLINE (1966 to January 2002), EMBASE (1980 to January 2002), PsycINFO (1887 to January 2002), Dissertation Abstracts International (1861 to January 2002). The search engine FirstSearch was also used (January 2002). All searches were updated in April 2005. Reference lists for all the obtained studies and other review articles were examined for additional studies. Selection criteria All studies in which the participants had been diagnosed with autistic spectrum disorder were randomly allocated prior to intervention and in which outcomes were compared to either a placebo or non-treated group were included. Data collection and analysis Two reviewers independently evaluated and extracted data from all potential studies identified for inclusion. Main results This update includes a new trial (Kuriyama 2002) to bring the total of included studies to three (total n = 33). One study, which used a cross-over design (Tolbert 1993) provided insufficient data to conduct an analysis. Another crossover study (Findling 1997) yielded no significant differences between treatment and placebo group performances following the B6 intervention on measures of social interaction, communication, compulsivity, impulsivity, or hyperactivity. The latest study (Kuriyama 2002) was motivated by evidence from epilepsy research and was focussed on a subgroup of children with pervasive developmental disorders (PDDs) who exhibited clinical features similar to those with pyroxidine-dependent epilepsy. This small study (n = 8) only measured IQ and \u27Social Quotient\u27 and found a statistically significant benefit for IQ (5.2, 95% CI = [0.2 to 10.3]) when in the treated group, by using change scores. Authors\u27 conclusions Due to the small number of studies, the methodological quality of studies, and small sample sizes, no recommendation can be advanced regarding the use of B6-Mg as a treatment for autism

Abrupt grain boundary melting in ice

The effect of impurities on the grain boundary melting of ice is investigated through an extension of Derjaguin-Landau-Verwey-Overbeek theory, in which we include retarded potential effects in a calculation of the full frequency dependent van der Waals and Coulombic interactions within a grain boundary. At high dopant concentrations the classical solutal effect dominates the melting behavior. However, depending on the amount of impurity and the surface charge density, as temperature decreases, the attractive tail of the dispersion force interaction begins to compete effectively with the repulsive screened Coulomb interaction. This leads to a film-thickness/temperature curve that changes depending on the relative strengths of these interactions and exhibits a decrease in the film thickness with increasing impurity level. More striking is the fact that at very large film thicknesses, the repulsive Coulomb interaction can be effectively screened leading to an abrupt reduction to zero film thickness.Comment: 8 pages, 1 figur

Modeling the iron oxides and oxyhydroxides for the prediction of environmentally sensitive phase transformations

Iron oxides and oxyhydroxides are challenging to model computationally as competing phases may differ in formation energies by only several kJ/mol, they undergo magnetization transitions with temperature, their structures may contain partially occupied sites or long-range ordering of vacancies, and some loose structures require proper description of weak interactions such as hydrogen bonding and dispersive forces. If structures and transformations are to be reliably predicted under different chemical conditions, each of these challenges must be overcome simultaneously, while preserving a high level of numerical accuracy and physical sophistication. Here we present comparative studies of structure, magnetization, and elasticity properties of iron oxides and oxyhydroxides using density functional theory calculations with plane-wave and locally-confined-atomic-orbital basis sets, which are implemented in VASP and SIESTA packages, respectively. We have selected hematite, maghemite, goethite, lepidocrocite, and magnetite as model systems from a total of 13 known iron oxides and oxyhydroxides; and use same convergence criteria and almost equivalent settings in order to make consistent comparisons. Our results show both basis sets can reproduce the energetic stability and magnetic ordering, and are in agreement with experimental observations. There are advantages to choosing one basis set over the other, depending on the intended focus. In our case, we find the method using PW basis set most appropriate, and combine our results to construct the first phase diagram of iron oxides and oxyhydroxides in the space of competing chemical potentials, generated entirely from first principlesComment: 46 pages - Accepted for publication in PRB (19 journal pages), January 201

Valley degeneracy in biaxially strained aluminum arsenide quantum wells

This paper details a complete formalism for calculating electron subband energy and degeneracy in strained multi-valley quantum wells grown along any orientation with explicit results for the AlAs quantum well case. A standardized rotation matrix is defined to transform from the conventional- cubic-cell basis to the quantum-well-transport basis whereby effective mass tensors, valley vectors, strain matrices, anisotropic strain ratios, and scattering vectors are all defined in their respective bases. The specific cases of (001)-, (110)-, and (111)-oriented aluminum arsenide (AlAs) quantum wells are examined, as is the unconventional (411) facet, which is of particular importance in AlAs literature. Calculations of electron confinement and strain in the (001), (110), and (411) facets determine the critical well width for crossover from double- to single-valley degeneracy in each system. The notation is generalized to include miscut angles, and can be adapted to other multi-valley systems. To help classify anisotropic inter-valley scattering events, a new primitive unit cell is defined in momentum space which allows one to distinguish purely in-plane inter-valley scattering events from those that requires an out-of-plane momentum scattering component.Comment: 17 pages, 4 figures, 2 table

Local probing of ionic diffusion by electrochemical strain microscopy: spatial resolution and signal formation mechanisms

Electrochemical insertion-deintercalation reactions are typically associated with significant change of molar volume of the host compound. This strong coupling between ionic currents and strains underpins image formation mechanisms in electrochemical strain microscopy (ESM), and allows exploring the tip-induced electrochemical processes locally. Here we analyze the signal formation mechanism in ESM, and develop the analytical description of operation in frequency and time domains. The ESM spectroscopic modes are compared to classical electrochemical methods including potentiostatic and galvanostatic intermittent titration (PITT and GITT), and electrochemical impedance spectroscopy (EIS). This analysis illustrates the feasibility of spatially resolved studies of Li-ion dynamics on the sub-10 nanometer level using electromechanical detection.Comment: 49 pages, 17 figures, 4 tables, 3 appendices, to be submitted to J. Appl. Phys