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At least 937 records · Page 52
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Simultaneous Momentum and Position Measurement and the Instrumental Weyl-Heisenberg Group

The canonical commutation relation, [Q,P]=iℏ, stands at the foundation of quantum theory and the original Hilbert space. The interpretation of P and Q as observables has always relied on the analogies that exist between the unitary transformations of Hilbert space and the canonical (also known as contact) transformations of classical phase space. Now that the theory of quantum measurement is essentially complete (this took a while), it is possible to revisit the canonical commutation relation in a way that sets the foundation of quantum theory not on unitary transformations but on positive transformations. This paper shows how the concept of simultaneous measurement leads to a fundamental differential geometric problem whose solution shows us the following. The simultaneous P and Q measurement (SPQM) defines a universal measuring instrument, which takes the shape of a seven-dimensional manifold, a universal covering group we call the instrumental Weyl-Heisenberg (IWH) group. The group IWH connects the identity to classical phase space in unexpected ways that are significant enough that the positive-operator-valued measure (POVM) offers a complete alternative to energy quantization. Five of the dimensions define processes that can be easily recognized and understood. The other two dimensions, the normalization and phase in the center of the IWH group, are less familiar. The normalization, in particular, requires special handling in order to describe and understand the SPQM instrument.

47 OTHER INSTRUMENTATION↗
DOE OSTI2017

Solar Energetic Particle Acceleration by a Shock Wave Accompanying a Coronal Mass Ejection in the Solar Atmosphere

Solar energetic particle acceleration by a shock wave accompanying a coronal mass ejection (CME) is studied. The description of the accelerated particle spectrum evolution is based on the numerical calculation of the diffusive transport equation with a set of realistic parameters. The relation between the CME and shock speeds, which depend on the initial CME radius, is determined. Depending on the initial CME radius, its speed, and the magnetic energy of the scattering Alfvén waves, the accelerated particle spectrum is established 10–60 minutes from the beginning of CME motion. The maximum energies of particles reach 0.1–10 GeV. The CME radii of 3–5 R{sub ⊙} and the shock radii of 5–10 R{sub ⊙} agree with observations. The calculated particle spectra agree with the observed ones in events registered by ground-based detectors if the turbulence spectrum in the solar corona significantly differs from the Kolmogorov one.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Numerical investigation of microbial quorum sensing under various flow conditions

Microorganisms efficiently coordinate phenotype expressions through a decision-making process known as quorum sensing (QS). We investigated QS amongst distinct, spatially distributed microbial aggregates under various flow conditions using a process-driven numerical model. Model simulations assess the conditions suitable for QS induction and quantify the importance of advective transport of signaling molecules. In addition, advection dilutes signaling molecules so that faster flow conditions require higher microbial densities, faster signal production rates, or higher sensitivities to signaling molecules to induce QS. However, autoinduction of signal production can substantially increase the transport distance of signaling molecules in both upstream and downstream directions. We present empirical approximations to the solutions of the advection–diffusion–reaction equation that describe the concentration profiles of signaling molecules for a wide range of flow and reaction rates. These empirical relationships, which predict the distribution of dissolved solutes along pore channels, allow to quantitatively estimate the effective communication distances amongst multiple microbial aggregates without further numerical simulations.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1974

Finite-amplitude thermal convection in a spherical shell

The properties of finite-amplitude thermal convection for a Boussinesq fluid contained in a spherical shell are investigated. All nonlinear terms are retained in the equations, and both axisymmetric and nonaxisymmetric solutions are studied. The velocity is expanded in terms of poloidal and toroidal vectors. Spherical surface harmonics resolve the horizontal structure of the flow, but finite differences are used in the vertical. With a few modifications, the transform method developed by Orszag (1970) is used to calculate the nonlinear terms, while Green's function techniques are applied to the poloidal equation and diffusion terms.

Young, R. E.↗
NASA NTRS1974

Vibrationally excited nitrogen in stable auroral red arcs and its effect on ionospheric recombination

The time-dependent continuity equations, including diffusion, were solved for the first six energy levels of molecular nitrogen for conditions in the thermosphere corresponding to stable auroral red (SAR) arcs. The results show that molecular nitrogen is excited vibrationally to the degree that the rate constant for the ionospheric loss process, O(+) + N2 yields NO(+) + N, is increased by as much as a factor of 7.6 at F2 region altitudes. It was found that deviations from the energetically equivalent Boltzmann distribution were large, causing the rate constant to be as much as 1.6 times the rate constant calculated for the Boltzmann distribution. These results indicate that SAR arc intensities as small as 58 R can produce noticeable increases in the ionosphere ion-atom interchange reaction rate and hence in the rate of loss of ionospheric electrons. It is suggested that the observed decrease of electron density in the F2 region in SAR arcs can probably be explained by enhanced reaction rates for ion-atom interchange between O(+) and N2 caused by vibrational excitation of molecular nitrogen by electron impact.

Newton, G. P.↗
NASA NTRS1977

Systems improved numerical differencing analyzer

Analyzer is software system that possesses capabilities which make it well suited for solving lumped-parameter representations of physical problems governed by diffusion-type equations, such as Fourier, Poisson, or La Place.

Fink, L. C.↗
NASA NTRS1980

Systems improved numerical differencing analyzer

Program solves physical problems governed by diffusion-type equations, provided that equations can be modeled by lumped-parameter representation. Program is used for thermal analysis, and could be adapted to solve Fourier, Poisson, and Laplace differential equations. Program is in FORTRAN IV and Assembler for execution on UNIVAC 1100-series or CYBER 175.

Source record↗
NASA NTRS1981

Parameterization of linear wave chemical transport in planetary atmospheres by eddy diffusion

Two-dimensional transport by linear waves is parameterized by wave velocity and temperature correlations and nonconservative properties of the atmosphere in a residual Eulerian framework. Explicit expressions derived for the eddy tracer flux vector are written in eddy diffusion tensor form, but it is demonstrated that strong coupling of chemistry and temperature through the rate constants, as is the case for ozone, requires additional terms proportional to the mixing ratio and not to its gradient. A variety of limiting cases are discussed. In the residual Eulerian framework the K(yz), K(zy) components are nonzero for a nonconservative atmosphere and/or a reactive tracer. Tracers have common transport coefficients in the limit where their chemistry is negligible in comparison to transience. It is shown that the usual one-dimensional vertical eddy diffusion continuity equation is rigorously valid only when the temperature dependence of the rate constants is negligible and the tracer has strong vertical stratification relative to its horizontal variability.

Strobel, D. F.↗
NASA NTRS1982

Jacchia-Lineberry upper atmosphere density model

A series of increasingly accurate models which are a careful blend of empirical and theoretical formulae were developed. The exospheric temperature is assumed to be a function of: (1) the average and daily variations in the solar flux, (2) the average and three hourly variations in the geomagnetic index, (3) the angle between the position vector and the axis of the unsymmetric atmospheric bulge, and (4) the angle between the position vector and the geomagnetic pole. The exospheric temperature is related to the density by the solution of the diffusion equilibrium equations for the different constituents of the atmosphere as a function of altitude. Other variations are modeled directly as changes in the density. They are: (1) changes due to the semiannual effect, and (2) changes due to the seasonal latitudinal effect. The causes for these variations are not exactly known but may be modeled sufficiently by empirical formulae. The Jacchia model is assumed to be valid over the altitude range of 90 to 2500 km. The residuals between the observed density from satellite drag observations and the computed densities show the mean relative error to be generally less than 10 percent with occasional peak errors near 50 percent.

Mueller, A. C.↗
NASA NTRS1983

Acceleration and transport processes - Verification and observations

The general problem of diffusive transport and acceleration of energetic charged particles is considered. The transport of solar-flare particles, solar modulation of galactic cosmic rays and shock acceleration processes on the solar wind are examined and observational tests are summarized. It is concluded that the basic diffusive transport equation is a useful approximation in situations like the solar wind, where turbulent scattering by magnetic irregularities is sufficient to maintain near isotropy. The application of this equation to the interstellar medium andd other, more distant astrophysical regimes is then discussed and implications for gamma-ray astrophysics are outlined. Finally the evidence for interstellar turbulence is reviewed and its consequences briefly discussed.

Jokipii, J. R.↗
NASA NTRS1988

SINDA - Systems Improved Numerical Differencing Analyzer

Capability to model fluid flow added. SINDA is software system developed to solve physical problems governed by diffusion-type equations mathematically modeled by lumped-parameter representations. Used as general thermal analyzer with resistor-and-capacitor-network representations. Adapted to wide range of problems represented by Fourier, Possion, Laplace, or other differential equations. Written in FORTRAN and Assembler.

Damico, Steve J.↗
NASA NTRS1988

Finite element procedures for time-dependent convection-diffusion-reaction systems

New finite element procedures based on the streamline-upwind/Petrov-Galerkin formulations are developed for time-dependent convection-diffusion-reaction equations. These procedures minimize spurious oscillations for convection-dominated and reaction-dominated problems. The results obtained for representative numerical examples are accurate with minimal oscillations. As a special application problem, the single-well chemical tracer test (a procedure for measuring oil remaining in a depleted field) is simulated numerically. The results show the importance of temperature effects on the interpreted value of residual oil saturation from such tests.

Tezduyar, T. E.↗
NASA NTRS1990

SINDA '85/FLUINT, Version 2.2

SINDA, Systems Improved Numerical Differencing Analyzer, software system developed for solving physical problems governed by diffusion-type equations modeled by lumped-parameter representations. Used as general thermal analyzer with resistor-and-capacitor-network representations, adapted to wide range of problems represented by such differential equations as Fourier, Poisson, or LaPlace. Software system updated. FLUINT, FLUid INTegrator, is advanced, one-dimensional fluid-analysis program solving equations of arbitrary fluid-flow networks. Written in FORTRAN and ASSEMBLER.

Cullimore, Brent↗
NASA NTRS1989

Tau approximation techniques for identification of coefficients in parabolic PDE

A variant of the Tau method, called the weak Tau method, is developed on the basis of the weak form of the PDE for use in least-squares parameter estimation; also presented is a suitable abstract convergence framework. The emphasis is on the theoretical framework that allows treatment of the weak Tau method when it is applied to a wide class of inverse problems, including those for diffusion-advection equations, the Fokker-Planck model for population dynamics, and damped beam equations. Extensive numerical testing of the weak Tau method has demonstrated that it compares quite favorably with existing methods.

Banks, H. T.↗
NASA NTRS1991

A simple estimate of funneling-assisted charge collection

Funneling is qualitatively discussed in detail, and a quantitative analysis is given for the total (time-integrated) collected charge. It is shown that, for an n(+)/p junction, the total collected charge QT is given by QT = (1 + mu-n/mu-p) QD + 2Q(diff), where QD is the charge initially liberated in the depletion region and Qdiff is charge collected by diffusion. This equation does not apply to very short ion tracks or to devices having a thin epilayer. A numerical example is presented, and a comparison is made with PISCES results.

Edmonds, Larry D.↗