A New Path-Integral Representation of the TT-Matrix in Potential Scattering

We employ the method used by Barbashov and collaborators in Quantum Field Theory to derive a path-integral representation of the $T$-matrix in nonrelativistic potential scattering which is free of functional integration over fictitious variables as was necessary before. The resulting expression serves as a starting point for a variational approximation applied to high-energy scattering from a Gaussian potential. Good agreement with exact partial-wave calculations is found even at large scattering angles. A novel path-integral representation of the scattering length is obtained in the low-energy limit.Comment: 9 pages, 1 figure, Latex with amsmath, amssym; v2: some typos corrected, matches published versio

Index theorems on manifolds with straight ends

We study Fredholm properties and index formulas for Dirac operators over complete Riemannian manifolds with straight ends. An important class of examples of such manifolds are complete Riemannian manifolds with pinched negative sectional curvature and finite volume

The Virginia Chesapeake Bay: recent sedimentation and paleodrainage

A comparison of the bathymetric surveys of the 1850-series and 1950-series indicated an average sedimentation rate for the Virginia Chesapeake Bay of 0.55 m (1.81 ft) for the last century. A statistically significant relationship between the depth of water and the rate of sedimentation was found where high rates of sedimentation exist in extremely shallow water (0 to 2 m) and in intermediate depths (6 to 13 m), while low rates exist between 2 m and 6 m, and in some cases in water deeper than 13 m. The results of 900 km of continuous seismic reflection profiles taken in the Virginia and lower-Maryland Chesapeake Bay indicate that the ancestral Rappahannock, Piankatank, York, and James rivers were not tributary to the ancestral Susquehanna River during the Wisconsin Glaciation as was previously believed. The ancestral Rappahannock, Piankatank, and York rivers converge and flow out of the present bay area through a paleochannel located under Tail of the Horseshoe Shoal on the south side of the Bay entrance. These combined rivers probably converged with the ancestral James River somewhere on the present continental shelf. A paleochannel in the Mainstem of the Bay north of the Potomac River mouth has an apparent thalweg depth of -42 m (-138 ft), whereas a much deeper channel at -61 m (-200 ft) has been reported by Ryan (1953) in the upper bay reaches. This suggests that the Susquehanna did not flow in the Mainstem region during the Wisconsinan Glaciation and most probably flowed in the Tangier Sound region. No evidence was found to support theories concerning the existence of significant Post-Tertiary crustal movement in the lower Bay region

Children’s Perceptions of Cohesion

The general purpose of the two studies reported here was to examine perceptions of team cohesiveness in children aged 9 to 12 years. In Study 1, focus groups were used to examine individual perceptions of cohesion from the perspective of group integration—the group as a totality. In Study 2, open-ended questionnaires were used to examine individual perceptions of cohesion from the perspective of individual attractions to the group. The results showed that children as young as nine years understand the phenomenon known as cohesion. They can discuss the group as a totality, the characteristics of cohesive and non-cohesive teams, and identify the major factors attracting them to and maintaining their involvement in the group. Also, the ability to clearly distinguish between task and social cohesion is present. The results provide insight into the world of child sport and emphasise the importance of group cohesion, affiliation, and other social constructs in children’s involvement and adherence to sport groups

Variational approximations in a path integral description of potential scattering

Abstract.: Using a recent path integral representation for the T -matrix in nonrelativistic potential scattering we investigate new variational approximations in this framework. By means of the Feynman-Jensen variational principle and the most general ansatz quadratic in the velocity variables --over which one has to integrate functionally-- we obtain variational equations which contain classical elements (trajectories) as well as quantum-mechanical ones (wave spreading). We analyse these equations and solve them numerically by iteration, a procedure best suited at high energy. The first correction to the variational result arising from a cumulant expansion is also evaluated. Comparison is made with exact partial-wave results for scattering from a Gaussian potential and better agreement is found at large scattering angles where the standard eikonal-type approximations fai

Cantilever-based Resonant Gas Sensors with Integrated Recesses for Localized Sensing Layer Deposition

This work presents mass-sensitive hammerhead resonators with integrated recesses as a gas-phase chemical microsensor platform. Recesses are etched into the head region of the resonator to locally deposit chemically sensitive polymers by ink-jet printing. This permits the sensing films to be confined to areas that (a) are most effective in detecting mass loading and (b) are not strained during the in-plane vibrations of the resonator. As a result of the second point, even 5-μm thick polymer coatings on resonators with a 9-12 μm silicon thickness barely affect the Q-factor in air. This translates into higher frequency stability and ultimately higher sensor resolution compared to uniformly coated devices

Phase Diagram and Incommensurate Phases in Undoped Manganites

We study the existence of incommensurate phases in the phase diagram of the two orbital double exchange model coupled with Jahn-Teller phonons and with superexchange interactions. In agreement with experimental results, we find that undoped manganites $RMnO_3$ ($R$ being some rare earth element) show temperature induced commensurate-incommensurate phase transitions. In the incommensurate phase the magnetic wave vector varies with temperature. The incommensurate phase arises from the competition between the short range antiferromagnetic superexchange interaction and the long range ferromagnetic double exchange interaction