Solving the time-dependent Schr\"odinger equation with absorbing boundary conditions and source terms in Mathematica 6.0

In recent decades a lot of research has been done on the numerical solution of the time-dependent Schr\"odinger equation. On the one hand, some of the proposed numerical methods do not need any kind of matrix inversion, but source terms cannot be easily implemented into this schemes; on the other, some methods involving matrix inversion can implement source terms in a natural way, but are not easy to implement into some computational software programs widely used by non-experts in programming (e.g. Mathematica). We present a simple method to solve the time-dependent Schr\"odinger equation by using a standard Crank-Nicholson method together with a Cayley's form for the finite-difference representation of evolution operator. Here, such standard numerical scheme has been simplified by inverting analytically the matrix of the evolution operator in position representation. The analytical inversion of the N x N matrix let us easily and fully implement the numerical method, with or without source terms, into Mathematica or even into any numerical computing language or computational software used for scientific computing.Comment: 15 pages, 7 figure

Low Speed Aerodynamics of the X-38 CRV

This project was performed in support of the engineering development of the NASA X-38 Crew Return Vehicle (CRV)system. Wind tunnel experiments were used to visualize various aerodynamic phenomena encountered by the CRV during the final stages of descent and landing. Scale models of the CRV were used to visualize vortex structures above and below the vehicle, and in its wake, and to quantify their trajectories. The effect of flaperon deflection on these structures was studied. The structure and dynamics of the CRV's wake during the drag parachute deployment stage were measured. Regions of high vorticity were identified using surveys conducted in several planes using a vortex meter. Periodic shedding of the vortex sheets from the sides of the CRV was observed using laser sheet videography as the CRV reached high angles of attack during the quasi-steady pitch-up prior to parafoil deployment. Using spectral analysis of hot-film anemometer data, the Strouhal number of these wake fluctuations was found to be 0.14 based on the model span. Phenomena encountered in flight test during parafoil operation were captured in scale-model tests, and a video photogrammetry technique was implemented to obtain parafoil surface shapes during flight in the tunnel. Forces on the parafoil were resolved using tension gages on individual lines. The temporal evolution of the phenomenon of leading edge collapse was captured. Laser velocimetry was used to demonstrate measurement of the porosity of the parafoil surface. From these measurements, several physical explanations have been developed for phenomena observed at various stages of the X-38 development program. Quantitative measurement capabilities have also been demonstrated for continued refinement of the aerodynamic technologies employed in the X-38 project. Detailed results from these studies are given in an AIAA Paper, two slide presentations, and other material which are given on a Web-based archival resource. This is the Digital Library of the Georgia Tech Experimental Aerodynamics Group

Interactions of asbestos-activated macrophages with an experimental fibrosarcoma

Supernatants from in vivo asbestos-activated macrophages failed to show any cytostatic activity against a syngeneic fibrosarcoma cell line in vitro. UICC chrysotile-induced peritoneal exudate cells also failed to demonstrate any growth inhibitory effect on the same cells in Winn assays of tumor growth. Mixing UICC crocidolite with inoculated tumor cells resulted in a dose-dependent inhibition of tumor growth; this could, however, be explained by a direct cytostatic effect on the tumor cells of high doses of crocidolite, which was observed in vitro

The TD50: a proposed general convention for the numerical description of the carcinogenic potency of chemicals in chronic-exposure animal experiments.

A generally accepted format for the numerical description of the carcinogenic potency of a particular chemical in a particular strain of animals is desirable so that statements from different sources about potency and attempts by different authors to correlate potency with particular laboratory measurements will be comparable. The choice of an appropriate standard format is to a certain extent arbitrary. In this paper we recommend that the TD50 (tumorigenic dose rate 50) be used. TD50 can be calculated for a single target site or combination of sites. The TD50, in analogy with the LD50, is defined as that chronic dose rate (in mg/kg body weight/day) which would halve the actuarially adjusted percentage of tumor-free animals at the end of a standard experiment time--the "standard lifespan" for the species. This paper consists of a brief discussion of the TD50, sufficient to make the general reader familiar with the properties of such an index, an appendix discussing methods for its estimation and certain conventions we have adopted for use in analyzing "nonstandard" experiments. A major problem in calculating any index of carcinogenic potency is that much published material gives only the final crude percentage of tumor-bearing animals at each dose, instead of percentages adjusted for the effects of intercurrent mortality or data from which these adjusted percentages can be derived. If the dose level administered to the animals is toxic, then premature death from nonneoplastic causes may prevent some dosed animals that would have developed tumors from actually doing so. This will particularly affect the high-dose group.(ABSTRACT TRUNCATED AT 250 WORDS

Nonlinear transport of Bose-Einstein condensates through mesoscopic waveguides

We study the coherent flow of interacting Bose-condensed atoms in mesoscopic waveguide geometries. Analytical and numerical methods, based on the mean-field description of the condensate, are developed to study both stationary as well as time-dependent propagation processes. We apply these methods to the propagation of a condensate through an atomic quantum dot in a waveguide, discuss the nonlinear transmission spectrum and show that resonant transport is generally suppressed due to an interaction-induced bistability phenomenon. Finally, we establish a link between the nonlinear features of the transmission spectrum and the self-consistent quasi-bound states of the quantum dot.Comment: 23 pages, 16 figure

Group analysis and exact solutions of a class of variable coefficient nonlinear telegraph equations

A complete group classification of a class of variable coefficient (1+1)-dimensional telegraph equations $f(x)u_{tt}=(H(u)u_x)_x+K(u)u_x$, is given, by using a compatibility method and additional equivalence transformations. A number of new interesting nonlinear invariant models which have non-trivial invariance algebras are obtained. Furthermore, the possible additional equivalence transformations between equations from the class under consideration are investigated. Exact solutions of special forms of these equations are also constructed via classical Lie method and generalized conditional transformations. Local conservation laws with characteristics of order 0 of the class under consideration are classified with respect to the group of equivalence transformations.Comment: 23 page

Intense physical activity is associated with cognitive performance in the elderly

Numerous studies have reported positive impacts of physical activity on cognitive function. However, the majority of these studies have utilised physical activity questionnaires or surveys, thus results may have been influenced by reporting biases. Through the objective measurement of routine levels of physical activity via actigraphy, we report a significant association between intensity, but not volume, of physical activity and cognitive functioning. A cohort of 217 participants (aged 60–89 years) wore an actigraphy unit for 7 consecutive days and underwent comprehensive neuropsychological assessment. The cohort was stratified into tertiles based on physical activity intensity. Compared with individuals in the lowest tertile of physical activity intensity, those in the highest tertile scored 9%, 9%, 6% and 21% higher on the digit span, digit symbol, Rey Complex Figure Test (RCFT) copy and Rey Figure Test 30-min recall test, respectively. Statistically, participants in the highest tertile of physical activity intensity performed significantly better on the following cognitive tasks: digit symbol, RCFT copy and verbal fluency test (all P<0.05). The results indicate that intensity rather than quantity of physical activity may be more important in the association between physical activity and cognitive function

First Penning-trap mass measurement in the millisecond half-life range: the exotic halo nucleus 11Li

In this letter, we report a new mass for $^{11}$Li using the trapping experiment TITAN at TRIUMF's ISAC facility. This is by far the shortest-lived nuclide, $t_{1/2} = 8.8 \rm{ms}$, for which a mass measurement has ever been performed with a Penning trap. Combined with our mass measurements of $^{8,9}$Li we derive a new two-neutron separation energy of 369.15(65) keV: a factor of seven more precise than the best previous value. This new value is a critical ingredient for the determination of the halo charge radius from isotope-shift measurements. We also report results from state-of-the-art atomic-physics calculations using the new mass and extract a new charge radius for $^{11}$Li. This result is a remarkable confluence of nuclear and atomic physics.Comment: Formatted for submission to PR

Conservation laws of semidiscrete canonical Hamiltonian equations

There are many evolution partial differential equations which can be cast into Hamiltonian form. Conservation laws of these equations are related to one-parameter Hamiltonian symmetries admitted by the PDEs. The same result holds for semidiscrete Hamiltonian equations. In this paper we consider semidiscrete canonical Hamiltonian equations. Using symmetries, we find conservation laws for the semidiscretized nonlinear wave equation and Schrodinger equation.Comment: 19 pages, 2 table