Majorana solution of the Thomas-Fermi equation

We report on an original method, due to Majorana, leading to a semi-analytical series solution of the Thomas-Fermi equation, with appropriate boundary conditions, in terms of only one quadrature. We also deduce a general formula for such a solution which avoids numerical integration, but is expressed in terms of the roots of a given polynomial equation.Comment: RevTex, 5 pages, 1 figur

Multidimensional measurement within adult protective services: design and initial testing of the tool for risk, interventions, and outcomes.

This study describes the development, field utility, reliability, and validity of the multidimensional Tool for Risk, Interventions, and Outcomes (TRIO) for use in Adult Protective Services (APS). The TRIO is designed to facilitate consistent APS practice and collect data related to multiple dimensions of typical interactions with APS clients, including the investigation and assessment of risks, the provision of APS interventions, and associated health and safety outcomes. Initial tests of the TRIO indicated high field utility, social worker "relevance and buy-in," and inter-rater reliability. TRIO concurrent validity was demonstrated via appropriate patterns of TRIO item differentiation based on the type of observed confirmed abuse or neglect; and predictive validity was demonstrated by prediction of the risk of actual APS recurrence. The TRIO is a promising new tool that can help meet the challenges of providing and documenting effective APS practices and identifying those at high risk for future APS recurrence

Time variation of the fine structure constant in decrumpling or TVSD model

Within the framework of a model universe with time variable space dimension (TVSD), known as decrumpling or TVSD model, we study the time variation of the fine structure constant. Using observational bounds on the present time variation of the fine structure constant, we are able to obtain the present time variation of spatial dimensions.Comment: 10 pages, accepted for publication in Int.J.Mod.Phys.

Geometrically Consistent Approach to Stochastic DBI Inflation

Stochastic effects during inflation can be addressed by averaging the quantum inflaton field over Hubble-patch sized domains. The averaged field then obeys a Langevin-type equation into which short-scale fluctuations enter as a noise term. We solve the Langevin equation for a inflaton field with Dirac Born Infeld (DBI) kinetic term perturbatively in the noise and use the result to determine the field value's Probability Density Function (PDF). In this calculation, both the shape of the potential and the warp factor are arbitrary functions, and the PDF is obtained with and without volume effects due to the finite size of the averaging domain. DBI kinetic terms typically arise in string-inspired inflationary scenarios in which the scalar field is associated with some distance within the (compact) extra dimensions. The inflaton's accessible range of field values therefore is limited because of the extra dimensions' finite size. We argue that in a consistent stochastic approach the distance-inflaton's PDF must vanish for geometrically forbidden field values. We propose to implement these extra-dimensional spatial restrictions into the PDF by installing absorbing (or reflecting) walls at the respective boundaries in field space. As a toy model, we consider a DBI inflaton between two absorbing walls and use the method of images to determine its most general PDF. The resulting PDF is studied in detail for the example of a quartic warp factor and a chaotic inflaton potential. The presence of the walls is shown to affect the inflaton trajectory for a given set of parameters.Comment: 20 pages, 3 figure

Surface spin waves in superconducting and insulating ferromagnets

Surface magnetization waves are studied on a semi-infinite magnetic medium in the perpendicular geometry. Both superconducting and insulating ferromagnets are considered. Exchange and dipole energies are taken into account, as well as retardation effects. At large wave vectors, the spectrum for a superconductor and insulator is the same, though for the former the branch is terminated much earlier than for the latter due to excitation of plasmons. At small wave vectors, the surface wave is more robust in the superconductor since it is separated from the bulk continuum by a finite gap.Comment: 4 pages, 2 figure

Oscillating Nernst-Ettingshausen effect in Bismuth across the quantum limit

In elemental Bismuth, 10$^5$ atoms share a single itinerant electron. Therefore, a moderate magnetic field can confine electrons to the lowest Landau level. We report on the first study of metallic thermoelectricity in this regime. The main thermoelectric response is off-diagonal with an oscillating component several times larger than the non-oscillating background. When the first Landau level attains the Fermi Energy, both the Nernst and the Ettingshausen coefficients sharply peak, and the latter attains a temperature-independent maximum. A qualitative agreement with a theory invoking current-carrying edge excitations is observed.Comment: Final published versio

Dissipative flow and vortex shedding in the Painlev\'e boundary layer of a Bose Einstein condensate

Raman et al. have found experimental evidence for a critical velocity under which there is no dissipation when a detuned laser beam is moved in a Bose-Einstein condensate. We analyze the origin of this critical velocity in the low density region close to the boundary layer of the cloud. In the frame of the laser beam, we do a blow up on this low density region which can be described by a Painlev\'e equation and write the approximate equation satisfied by the wave function in this region. We find that there is always a drag around the laser beam. Though the beam passes through the surface of the cloud and the sound velocity is small in the Painlev\'e boundary layer, the shedding of vortices starts only when a threshold velocity is reached. This critical velocity is lower than the critical velocity computed for the corresponding 2D problem at the center of the cloud. At low velocity, there is a stationary solution without vortex and the drag is small. At the onset of vortex shedding, that is above the critical velocity, there is a drastic increase in drag.Comment: 4 pages, 4 figures (with 9 ps files

Some Remarks about Variable Mass Systems

We comment about the general argument given to obtain the rocket equation as it is exposed in standard textbooks. In our opinion, it can induce students to a wrong answer when solving variable mass problems.Comment: 2 page

Approximate Analytic Solution for the Spatiotemporal Evolution of Wave Packets undergoing Arbitrary Dispersion

We apply expansion methods to obtain an approximate expression in terms of elementary functions for the space and time dependence of wave packets in a dispersive medium. The specific application to pulses in a cold plasma is considered in detail, and the explicit analytic formula that results is provided. When certain general initial conditions are satisfied, these expressions describe the packet evolution quite well. We conclude by employing the method to exhibit aspects of dispersive pulse propagation in a cold plasma, and suggest how predicted and experimental effects may be compared to improve the theoretical description of a medium's dispersive properties.Comment: 17 pages, 4 figures, RevTe

Thermodynamic Entropy And The Accessible States of Some Simple Systems

Comparison of the thermodynamic entropy with Boltzmann's principle shows that under conditions of constant volume the total number of arrangements in simple thermodynamic systems with temperature-independent heat capacities is TC/k. A physical interpretation of this function is given for three such systems; an ideal monatomic gas, an ideal gas of diatomic molecules with rotational motion, and a solid in the Dulong-Petit limit of high temperature. T1/2 emerges as a natural measure of the number of accessible states for a single particle in one dimension. Extension to N particles in three dimensions leads to TC/k as the total number of possible arrangements or microstates. The different microstates of the system are thus shown a posteriori to be equally probable, with probability T-C/k, which implies that for the purposes of counting states the particles of the gas are distinguishable. The most probable energy state of the system is determined by the degeneracy of the microstates.Comment: 9 pages, 1 figur