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

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

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.

Organizational factors influencing implementation of evidence-based practices for integrated treatment in behavioral health agencies.

Objective. In recent years, New Mexico has prioritized integrated treatment for cooccurring mental health and substance use disorders within its public behavioral health system. This report describes factors likely to be important when implementing evidence-based practices (EBPs) in community agencies. Methods. Our mixed-method research design consisted of observations, semistructured interviews, and surveys undertaken with employees at 14 agencies at baseline and after 18 months. We developed four-agency typologies based on iterative coding and analysis of observations and interviews. We then examined survey data from employees at the four exemplar agencies to validate qualitative findings. Results. Financial resources and strong leadership impacted agency capacity to train providers and implement EBPs. Quantitative analysis of service provider survey responses from these agencies (N = 38) supported qualitative findings and demonstrated significant mean score differences in leadership, organizational climate, and attitudes toward EBPs in anticipated directions. Conclusion. The availability of strong leadership and financial resources were key components to initial implementation success in this study of community agencies in New Mexico. Reliance only on external funding poses risks for sustainment when demoralizing work climates precipitate employee turnover. Strong agency leadership does not always compensate for deficient financial resources in vulnerable communities

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

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

Radiative damping: a case study

We are interested in the motion of a classical charge coupled to the Maxwell self-field and subject to a uniform external magnetic field, B. This is a physically relevant, but difficult dynamical problem, to which contributions range over more than one hundred years. Specifically, we will study the Sommerfeld-Page approximation which assumes an extended charge distribution at small velocities. The memory equation is then linear and many details become available. We discuss how the friction equation arises in the limit of "small" B and contrast this result with the standard Taylor expansion resulting in a second order equation for the velocity of the charge.Comment: 4 figure

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

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

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