The Raman Spectra and Molecular Constants of Phosphorus Trifluoride and Phosphine

The Raman frequencies of PF3(l) were found to be omega1(1), 890 cm^-1; omega2(1), 531 cm^-1; omega3(2), 840 cm^-1; and omega4(2), 486 cm^-1, indicating a regular pyramid structure of the molecule. Three frequencies were observed for PH3(l): 2306 cm^-1, 1115 cm^-1 and 979 cm^-1. With the aid of electron diffraction data the standard virtual entropies of PF3(g), PCl3(g), AsF3(g), and AsCl3(g) at 25°C are calculated to be 64.2, 74.7, 69.2, and 78.2 cal./deg., respectively; that of PH3(g) is estimated to be 50.5 cal./deg. These data lead to the following free energies of formation at 25°C: AsCl3(g), -62,075 cal.; PH3(g), 2750 cal.; PCl3(g), -62,220 cal

Physics of the Pseudogap State: Spin-Charge Locking

The properties of the pseudogap phase above Tc of the high-Tc cuprate superconductors are described by showing that the Anderson-Nambu SU(2) spinors of an RVB spin gap 'lock' to those of the electron charge system because of the resulting improvement of kinetic energy. This enormously extends the range of the vortex liquid state in these materials. As a result it is not clear that the spinons are ever truly deconfined. A heuristic description of the electrodynamics of this pseudogap-vortex liquid state is proposed.Comment: Submitted to Phys Rev Letter

The BSSN formulation is a partially constrained evolution system

Relativistic simulations in 3+1 dimensions typically monitor the Hamiltonian and momentum constraints during evolution, with significant violations of these constraints indicating the presence of instabilities. In this paper we rewrite the momentum constraints as first-order evolution equations, and show that the popular BSSN formulation of the Einstein equations explicitly uses the momentum constraints as evolution equations. We conjecture that this feature is a key reason for the relative success of the BSSN formulation in numerical relativity.Comment: 8 pages, minor grammatical correction

Reading, Writing and Raisinets: Are School Finances Contributing to Children's Obesity?

The proportion of adolescents in the United States who are obese has nearly tripled over the last two decades. At the same time, schools, often citing financial pressures, have given students greater access to "junk" foods, using proceeds from the sales to fund school programs. We examine whether schools under financial pressure are more likely to adopt potentially unhealthful food policies. We find that a 10 percentage point increase in the probability of access to junk food leads to about a one percent increase in students' body mass index (BMI). However, this average effect is entirely driven by adolescents who have an overweight parent, for whom the effect of such food policies is much larger (2.2%). This suggests that those adolescents who have a genetic or family susceptibility to obesity are most affected by the school food environment. A rough calculation suggests that the increase in availability of junk foods in schools can account for about one-fifth of the increase in average BMI among adolescents over the last decade.

A hybrid perturbation-Galerkin technique for partial differential equations

A two-step hybrid perturbation-Galerkin technique for improving the usefulness of perturbation solutions to partial differential equations which contain a parameter is presented and discussed. In the first step of the method, the leading terms in the asymptotic expansion(s) of the solution about one or more values of the perturbation parameter are obtained using standard perturbation methods. In the second step, the perturbation functions obtained in the first step are used as trial functions in a Bubnov-Galerkin approximation. This semi-analytical, semi-numerical hybrid technique appears to overcome some of the drawbacks of the perturbation and Galerkin methods when they are applied by themselves, while combining some of the good features of each. The technique is illustrated first by a simple example. It is then applied to the problem of determining the flow of a slightly compressible fluid past a circular cylinder and to the problem of determining the shape of a free surface due to a sink above the surface. Solutions obtained by the hybrid method are compared with other approximate solutions, and its possible application to certain problems associated with domain decomposition is discussed

Formation of Chimneys in Mushy Layers: Experiment and Simulation

In this fluid dyanmics video, we show experimental images and simulations of chimney formation in mushy layers. A directional solidification apparatus was used to freeze 25 wt % aqueous ammonium chloride solutions at controlled rates in a narrow Hele-Shaw cell (1mm gap). The convective motion is imaged with schlieren. We demonstrate the ability to numerically simulate mushy layer growth for direct comparison with experiments

Gravitational waveforms from the evaporating ACO cosmic string loop

The linearly polarized gravitational waveforms from a certain type of rotating, evaporating cosmic string - the Allen-Casper-Ottewill loop - are constructed and plotted over the lifetime of the loop. The formulas for the waveforms are simple and exact, and describe waves which attenuate self-similarly, with the amplitude and period of the waves falling off linearly with time.Comment: 30 pages, 16 figure