A survey of impulsive trajectories Final report

Literature survey of astrodynamics problems on intercept, transfer, and rendezvous trajectorie

Density functional study of the adsorption of K on the Ag(111) surface

Full-potential gradient corrected density functional calculations of the adsorption of potassium on the Ag(111) surface have been performed. The considered structures are Ag(111) (root 3 x root 3) R30degree-K and Ag(111) (2 x 2)-K. For the lower coverage, fcc, hcp and bridge site; and for the higher coverage all considered sites are practically degenerate. Substrate rumpling is most important for the top adsorption site. The bond length is found to be nearly identical for the two coverages, in agreement with recent experiments. Results from Mulliken populations, bond lengths, core level shifts and work functions consistently indicate a small charge transfer from the potassium atom to the substrate, which is slightly larger for the lower coverage.Comment: to appear in Phys Rev

Moments of spectral functions: Monte Carlo evaluation and verification

The subject of the present study is the Monte Carlo path-integral evaluation of the moments of spectral functions. Such moments can be computed by formal differentiation of certain estimating functionals that are infinitely-differentiable against time whenever the potential function is arbitrarily smooth. Here, I demonstrate that the numerical differentiation of the estimating functionals can be more successfully implemented by means of pseudospectral methods (e.g., exact differentiation of a Chebyshev polynomial interpolant), which utilize information from the entire interval $(-\beta \hbar / 2, \beta \hbar/2)$. The algorithmic detail that leads to robust numerical approximations is the fact that the path integral action and not the actual estimating functional are interpolated. Although the resulting approximation to the estimating functional is non-linear, the derivatives can be computed from it in a fast and stable way by contour integration in the complex plane, with the help of the Cauchy integral formula (e.g., by Lyness' method). An interesting aspect of the present development is that Hamburger's conditions for a finite sequence of numbers to be a moment sequence provide the necessary and sufficient criteria for the computed data to be compatible with the existence of an inversion algorithm. Finally, the issue of appearance of the sign problem in the computation of moments, albeit in a milder form than for other quantities, is addressed.Comment: 13 pages, 2 figure

Convergence Characteristics of the Cumulant Expansion for Fourier Path Integrals

The cumulant representation of the Fourier path integral method is examined to determine the asymptotic convergence characteristics of the imaginary-time density matrix with respect to the number of path variables $N$ included. It is proved that when the cumulant expansion is truncated at order $p$, the asymptotic convergence rate of the density matrix behaves like $N^{-(2p+1)}$. The complex algebra associated with the proof is simplified by introducing a diagrammatic representation of the contributing terms along with an associated linked-cluster theorem. The cumulant terms at each order are expanded in a series such that the the asymptotic convergence rate is maintained without the need to calculate the full cumulant at order $p$. Using this truncated expansion of each cumulant at order $p$, the numerical cost in developing Fourier path integral expressions having convergence order $N^{-(2p+1)}$ is shown to be approximately linear in the number of required potential energy evaluations making the method promising for actual numerical implementation.Comment: 47 pages, 2 figures, submitted to PR

An Infinite Swapping Approach to the Rare-Event Sampling Problem

We describe a new approach to the rare-event Monte Carlo sampling problem. This technique utilizes a symmetrization strategy to create probability distributions that are more highly connected and thus more easily sampled than their original, potentially sparse counterparts. After discussing the formal outline of the approach and devising techniques for its practical implementation, we illustrate the utility of the technique with a series of numerical applications to Lennard-Jones clusters of varying complexity and rare-event character.Comment: 24 pages, 16 figure

Surface Enhancement of Superconductivity in Tin

The possibility of surface enhancement of superconductivity is examined experimentally. It is shown that single crystal tin samples with cold-worked surfaces represent a superconductor with a surface-enhanced order parameter (or negative surface extrapolation length b), whose magnitude can be controlled.Comment: 8 pages, 4 figure

Streambed and Water Profile Response to In-Channel Restoration Structures in a Laboratory Meandering Stream

In-channel structures are often installed in alluvial rivers during restoration to steer currents, but they also modify the streambed morphology and water surface profile, and alter hydraulic gradients driving ecologically important hyporheic exchange. Although river features before and after restoration need to be compared, few studies have collected detailed observations to facilitate this comparison. We created a laboratory mobile-bed alluvial meandering river and collected detailed measurements in the highly sinuous meander before and after installation of in-channel structures, which included one cross vane and six J-hooks situated along 1 bar unit. Measurements of streambed and water surface elevation with sub-millimeter vertical accuracy and horizontal resolution were obtained using close-range photogrammetry. Compared to the smooth gradually varied water surface profile for control runs without structures, the structures created rapidly varied flow with subcritical to supercritical flow transitions, as well as backwater and forced-morphology pools, which increased volumetric storage by 74% in the entire stream reach. The J-hooks, located along the outer bank of the meander bend and downstream of the cross vane, created stepwise patterns in the streambed and water surface longitudinal profiles. The pooling of water behind the cross vane increased the hydraulic gradient across the meander neck by 1% and increased local groundwater gradients by 4%, with smaller increases across other transects through the intrameander zone. Scour pools developed downstream of the cross vane and around the J-hooks situated near the meander apex. In-channel structures significantly changed meander bend hydraulic gradients, and the detailed streambed and water surface 3-D maps provide valuable data for computational modeling of changes to hyporheic exchange

Precise Measurement of Magnetic Field Gradients from Free Spin Precession Signals of 3^{3}He and 129^{129}Xe Magnetometers

We report on precise measurements of magnetic field gradients extracted from transverse relaxation rates of precessing spin samples. The experimental approach is based on the free precession of gaseous, nuclear spin polarized $^3$He and $^{129}$Xe atoms in a spherical cell inside a magnetic guiding field of about 400 nT using LT$_C$ SQUIDs as low-noise magnetic flux detectors. The transverse relaxation rates of both spin species are simultaneously monitored as magnetic field gradients are varied. For transverse relaxation times reaching 100 h, the residual longitudinal field gradient across the spin sample could be deduced to be$|\vec{\nabla}B_z|=(5.6 \pm 0.4)$ pT/cm. The method takes advantage of the high signal-to-noise ratio with which the decaying spin precession signal can be monitored that finally leads to the exceptional accuracy to determine magnetic field gradients at the sub pT/cm scale