Fisher Information and Kinetic-energy Functionals: A Dequantization Approach

We strengthen the connection between Information Theory and quantum-mechanical systems using a recently developed dequantization procedure whereby quantum fluctuations latent in the quantum momentum are suppressed. The dequantization procedure results in a decomposition of the quantum kinetic energy as the sum of a classical term and a purely quantum term. The purely quantum term, which results from the quantum fluctuations, is essentially identical to the Fisher information. The classical term is complementary to the Fisher information and, in this sense, it plays a role analogous to that of the Shannon entropy. We demonstrate the kinetic energy decomposition for both stationary and nonstationary states and employ it to shed light on the nature of kinetic-energy functionals.Comment: 13 pages, 3 figures. To appear in J. Comput. Appl. Mat

Infrared diode laser spectroscopy of the fundamental band of NF(a1Δ)

Thirty-one lines of the fundamental vibration–rotation band of the NF free radical in its a 1 state have been detected in absorption near 8.6 µm using a tunable infrared diode laser. Linewidths were Doppler limited and several transitions were accompanied by resolved hyperfine structure due to fluorine and nitrogen nuclear moments. Wave number calibration using accurately determined N2O lines yielded v0 = 1165.952±0.001 cm^−1 for the band center. Rotational and centrifugal distortion constants for both v = 0 and 1 states have also been determined

Diffusion algorithms and data reduction routine for onsite launch predictions for the transport of Titan 3 C exhaust effluents

The NASA/MSFC multilayer diffusion algorithms have been specialized for the prediction of the surface impact for the dispersive transport of the exhaust effluents from the launch of a Titan 3 vehicle. This specialization permits these transport predictions to be made at the launch range in real time so that the effluent monitoring teams can optimize their monitoring grids. Basically, the data reduction routine requires just the meteorology profiles for the thermodynamics and kinematics of the atmosphere as an input. These profiles are graphed along with the resulting exhaust cloud rise history, the center line concentrations and dosages, and the hydrogen chloride isopleths

Debris about asteroids: Where and how much?

We summarize several recent findings on the size and shape of the region within which material can stably orbit an asteroid. If the asteroid (with assumed density 2.38 g/cu cm) circles the Sun at 2.55 AU, co-planar prograde material will remain trapped whenever started on unperturbed circular orbits at less than about 220 R(sub A) (asteroid radii); co-planar retrograde particles are stable out twice as far. Our 3-D stability surface, which encloses several hundred numerically calculated orbits that start with various inclinations, is shaped like a sphere with its top and bottom sliced off; its dimensions scale like the Hill radius =(mu/3)(exp 1/3)R, where mu is the asteroid-to-solar mass ratio and R is the asteroid's orbital radius. If the asteroid moves along an elliptical orbit, a fairly reliable indicator of the dimensions of the hazard zone is the size of its Hill sphere at the orbit's pericenter. Grains with radii less than a few mm will be lost through the action of radiation forces which can induce escape or cause collisions with the asteroid on times scales of a few years; interplanetary micrometeoroids produce collisional break-up of these particles in approximately 10(exp 4) yrs. The effects of Jupiter and of asteroids that pass close to the target asteroid allow particles to diffuse from the system, again shrinking the hazard zone. None of the considered sources-primordial formation, debris spalled off the asteroid during micrometeoroid impact, captured interplanetary particles, feeder satellites, etc., seem capable of densely populating distant orbits from the asteroid. No certain detections of debris clouds or of binary asteroids have been made. Thus, it seems highly unlikely that a spacecraft fly-by targeted at 100 R(sub A) from the asteroid over its orbital pole would encounter any material

Evaluating the influence of lake morphology, trophic status and diagenesis on geochemical profiles in lake sediments

Recent geochemical studies provide evidence that changes in vertical distributions of nutrients in lake sediments are driven by anthropogenic activities, based primarily on trends of increasing concentrations in upper sediment layers. However, we show that vertical concentration profiles of carbon (C), nitrogen (N) and phosphorus (P) in lake sediments can be higher in the upper, most recently deposited sediment strata, driven largely by natural diagenetic processes and not eutrophication alone. We examined sediment cores from 14 different lakes in New Zealand and China ranging from oligotrophic to highly eutrophic and shallow to deep, and found that the shape of vertical profiles of total P, a key nutrient for lake productivity, can be similar in sediments across gradients of widely differing trophic status. We derived and applied empirical and mechanistic diagenesis steady state profile models to describe the vertical distribution of C, N and P in the sediments. These models, which focus on large scale temporal (decades) and spatial (up to 35 cm in the vertical) processes, revealed that density-differentiated burial and biodiffusive mixing, were strongly correlated with vertical concentration gradients of sediment C, N and P content, whereas lake trophic status was not. A sensitivity analysis of parameters included in the diagenetic model further showed that the processes including flux of organic matter to the sediment-water interface, burial (net sedimentation), breakdown of organic matter and biodiffusion all significantly can influence the vertical distribution of sediment P content. We conclude that geochemical studies attempting to evaluate drivers of the vertical distribution of sediment C, N, and P content in lake sediments should also account for the natural diagenetic drivers of vertical concentration gradients, assisted with application of similar models to those presented in this study. This would include quantification of key sediment diagenesis model parameters to separate out the influence of anthropogenic activities

The conic-gearing image of a complex number and a spinor-born surface geometry

Quaternion (Q-) mathematics formally contains many fragments of physical laws; in particular, the Hamiltonian for the Pauli equation automatically emerges in a space with Q-metric. The eigenfunction method shows that any Q-unit has an interior structure consisting of spinor functions; this helps us to represent any complex number in an orthogonal form associated with a novel geometric image (the conic-gearing picture). Fundamental Q-unit-spinor relations are found, revealing the geometric meaning of spinors as Lam\'e coefficients (dyads) locally coupling the base and tangent surfaces.Comment: 7 pages, 1 figur

Temporal and spatial variations in phytoplankton productivity in surface waters of a warm-temperate, monomictic lake in New Zealand

Surface phytoplankton productivity measurements were carried out in morphologically complex Lake Rotoiti with the objective of defining variations between sites and seasons, and the dominant environmental drivers of these variations. Measurements were carried out monthly at two depths at each of three morphologically diverse stations for 1 year throughout the lake. Productivity at the surface of the shallow embayment was significantly higher in most months of the year compared with the surface of the other two stations but there were no significant differences from September to December 2004. There were no relationships between measured environmental variables and primary productivity or specific production. Inorganic nutrient concentrations at the surface of the shallow station were low throughout the whole year but at the other two stations they showed a typical pattern for monomictic lakes of higher levels during winter mixing and declining concentrations during thermal stratification. The high variability between sites found in this study indicates that it is important to account for local differences in productivity in morphologically diverse lakes, and that whole lake productivity estimates may vary greatly depending on the location and depth of productivity measurements