Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Probability theory”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Quantum Probability Cancellation Due to a Single-Photon State

When an N-photon state enters a lossless symmetric beamsplitter from one input port, the photon distribution for the two output ports has the form of Bernouli Binormial, with highest probability at equal partition (N/2 at one outport and N/2 at the other). However, injection of a single photon state at the other input port can dramatically change the photon distribution at the outputs, resulting in zero probability at equal partition. Such a strong deviation from classical particle theory stems from quantum probability amplitude cancellation. The effect persists even if the N-photon state is replaced by an arbitrary state of light. A special case is the coherent state which corresponds to homodyne detection of a single photon state and can lead to the measurement of the wave function of a single photon state.

Ou, Z. Y.↗
DOE OSTI2024

Stochastic Trust-Region Algorithm in Random Subspaces with Convergence and Expected Complexity Analyses

Here, this work proposes a framework for large-scale stochastic derivative-free optimization (DFO) by introducing STARS, a trust-region method based on iterative minimization in random subspaces. This framework is both an algorithmic and theoretical extension of a random subspace derivative-free optimization (RSDFO) framework, and an algorithm for stochastic optimization with random models (STORM). Moreover, like RSDFO, STARS achieves scalability by minimizing interpolation models that approximate the objective in low-dimensional affine subspaces, thus significantly reducing per-iteration costs in terms of function evaluations and yielding strong performance on largescale stochastic DFO problems. The user-determined dimension of these subspaces, when the latter are defined, for example, by the columns of so-called Johnson-Lindenstrauss transforms, turns out to be independent of the dimension of the problem. For convergence purposes, inspired by the analyses of RSDFO and STORM, both a particular quality of the subspace and the accuracies of random function estimates and models are required to hold with sufficiently high, but fixed, probabilities. Using martingale theory under the latter assumptions, an almost sure global convergence of STARS to a first-order stationary point is shown, and the expected number of iterations required to reach a desired first-order accuracy is proved to be similar to that of STORM and other stochastic DFO algorithms, up to constants.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1970

The optical scatter channel

Optical scatter channel transmission characteristics, using mathematical model consistent with radiative transfer theory and probability-computing receiver

Holland, A. E.↗
NASA NTRS1977

Storage and retrieval of mass spectral information

Computer handling of mass spectra serves two main purposes: the interpretation of the occasional, problematic mass spectrum, and the identification of the large number of spectra generated in the gas-chromatographic-mass spectrometric (GC-MS) analysis of complex natural and synthetic mixtures. Methods available fall into the three categories of library search, artificial intelligence, and learning machine. Optional procedures for coding, abbreviating and filtering a library of spectra minimize time and storage requirements. Newer techniques make increasing use of probability and information theory in accessing files of mass spectral information.

Hohn, M. E.↗
NASA NTRS1981

Discrimination of form in images corrupted by speckle

The problem investigated is that of a human observer having to distinguish between certain specified geometrical forms corrupted by speckle - an idealization of the problem of a scientist studying a synthetic aperture radar map. Specifically, the cases of two simple alternative forms and of two and four orientations of a simple form have been considered. A theoretical model is developed for the observer's decision process by analogy with optimal receiver theory, and the probability of a correct decision is related to form parameters like size, contrast, and looks. These calculations are verified by psychophysical experiments using computer-simulated pictures.

Korwar, V. N.↗
NASA NTRS1996

Physical Meaning of the Optimum Measurement Process in Quantum Detection Theory

The optimum measurement processes are represented as the optimum detection operators in the quantum detection theory. The error probability by the optimum detection operators goes beyond the standard quantum limit automatically. However the optimum detection operators are given by pure mathematical descriptions. In order to realize a communication system overcoming the standard quantum limit, we try to give the physical meaning of the optimum detection operators.

Osaki, Masao↗
NASA NTRS1998

Energetics and Dynamics of GaAs Epitaxial Growth via Quantum Wave Packet Studies

The dynamics of As(sub 2) molecule incorporation into the flat Ga-terminated GaAs(100) surface is studied computationally. The time-dependent Schrodinger equation is solved on a two-dimensional potential energy surface obtained using density functional theory calculations. The probabilities of trapping and subsequent dissociation of the molecular As(sub 2) bond are calculated as a function of beam translational energy and vibrational quantum number of As(sub 2).

Dzegilenko, Fedor N.↗
NASA NTRS2002

NASA Participated in the Japan 2001 Science, Creativity and the Young Mind Workshop

During the week of July 23, 2001, a workshop called the Japan 2001 Science, Creativity and the Young Mind took place at Bristol University in Bristol, England. Coordinated by the Clifton Scientific Trust, it brought together 60 British and Japanese students and provided them with a forum for learning and interacting. All the students were chosen from geographical areas of social deprivation, where university education is not seen as a natural progression for students. One of the aims of the workshop was to give the combined group a new view of themselves as potential scientists and an ambition to succeed at the highest level. Members of the Glenn Research Center's Learning Technologies Project participated with six of the students and their team leaders as a Space Science Team. Four interactive videoconferencing sessions were held between the NASA Glenn Research Center and Bristol University on four consecutive days. During the sessions, students raised questions concerning various theories about the probable formation of volcanoes on Mars. Of specific interest was if the great Tharsis volcanoes might be the result of an ancient collision of planetary proportions, or if plate tectonic movement, evidence for which was recently discovered by NASA's Mars Global Surveyor Spacecraft, might account for them.

Kolecki, Joseph C.↗
NASA NTRS1992

The Pekeris problem, and the interior of the pulsating sphere, first success of exact ray theory, and what rays?

This paper presents what is probably the first application of exact ray theory to provide nontrivial exact solutions of the Helmholtz equation. First, the Pekeris problem is considered. This is followed by consideration of the problem of the field maintained within a uniformly pulsating sphere. In the Pekeris problem, an iterative solution provides the exact solution on the second iteration. In the second problem, it is shown that the exact ray theory eliminates the focus of the geometric theory.

Mcaninch, Gerry L.↗
NASA NTRS1967

Theory of atomic transitions

Transition probabilities of atomic collisions, elastic scattering of electrons, and excitation functions

ELECTRON COLLISION↗
NASA NTRS1975

A review of the theory of interstellar communication

The probability is analyzed that intelligent civilizations capable of interstellar communication exist in the galaxy. Drake's (1960) equation for the prevalence of communicative civilization is used in the calculations, and attempts are made to place limits on the search range that must be covered to contact other civilizations, the longevity of the communicative phase of such civilizations, and the possible number of two-way exchanges between civilizations in contact with each other. The minimum estimates indicate that some 100,000 civilizations probably coexist within several tens of astronomical units of each other and that some 1,000,000 probably coexist within 10 light years of each other. Attempts to detect coherent signals characteristic of intelligent life are briefly noted, including Projects Ozma and Cyclops as well as some Soviet attempts. Recently proposed American and Soviet programs for interstellar communication are outlined.

Billingham, J.↗
NASA NTRS1976

Heavy ion fragmentation experiments at the bevatron

Collaborative research efforts to study the fragmentation processes of heavy nuclei in matter using heavy ion beams of the Bevatron/Bevalac are described. The goal of the program is to obtain the single particle inclusive spectra of secondary nuclei produced at 0 deg by the fragmentation of heavy ion beam projectiles. The process being examined is B+T yields F + anything, where B is the beam nucleus, T is the target nucleus, and F is the detected fragment. The fragments F are isotopically identified by experimental procedures involving magnetic analysis, energy loss and time-of-flight measurements. Effects were also made to: (a) study processes of heavy nuclei in matter, (b) measure the total and partial production cross section for all isotopes, (c) test the applicability of high energy multiparticle interaction theory to nuclear fragmentation, (d) apply the cross section data and fragmentation probabilities to cosmic ray transport theory, and (e) search for systematic behavior of fragment production as a means to improve existing semi-empirical theories of cross-sections.

Heckman, H. H.↗
NASA NTRS1975

Heavy Ion Fragmentation Experiments at the Bevatron

Fragmentation processes of heavy nuclei in matter using the heavy-ion capability of the Bevatron were studied. The purpose was to obtain the single particle inclusive spectra of secondary nuclei produced at 0 deg by the fragmentation of heavy ion beam projectiles. The process being examined is B+T yields F + anything, where B is the beam nucleus, T is the target nucleus, and F is the detected fragment. The fragments F are isotopically identified by experimental procedures involving magnetic analysis, energy loss and time-of-flight measurements. Attempts were also made to: (1) measure the total and partial production cross section for all isotopes, (2) test the applicability of high-energy multi-particle interaction theory to nuclear fragmentation, (3) apply the cross-section data and fragmentation probabilities to cosmic ray transport theory, and (4) search for systematic behavior of fragment production as a means to improve existing semi-empirical theories of cross sections.

Heckman, H. H.↗
NASA NTRS1984

Spatial estimation from remotely sensed data via empirical Bayes models

Multichannel satellite image data, available as LANDSAT imagery, are recorded as a multivariate time series (four channels, multiple passovers) in two spatial dimensions. The application of parametric empirical Bayes theory to classification of, and estimating the probability of, each crop type at each of a large number of pixels is considered. This theory involves both the probability distribution of imagery data, conditional on crop types, and the prior spatial distribution of crop types. For the latter Markov models indexed by estimable parameters are used. A broad outline of the general theory reveals several questions for further research. Some detailed results are given for the special case of two crop types when only a line transect is analyzed. Finally, the estimation of an underlying continuous process on the lattice is discussed which would be applicable to such quantities as crop yield.

Hill, J. R.↗
NASA NTRS2005

What Information Theory Says about Bounded Rational Best Response

Probability Collectives (PC) provides the information-theoretic extension of conventional full-rationality game theory to bounded rational games. Here an explicit solution to the equations giving the bounded rationality equilibrium of a game is presented. Then PC is used to investigate games in which the players use bounded rational best-response strategies. Next it is shown that in the continuum-time limit, bounded rational best response games result in a variant of the replicator dynamics of evolutionary game theory. It is then shown that for team (shared-payoff) games, this variant of replicator dynamics is identical to Newton-Raphson iterative optimization of the shared utility function.

Wolpert, David H.↗
DOE OSTI2025

Calculation of ion–ion mutual neutralization rate constants using Landau–Zener theory coupled with trajectory simulations for Ar + –Cl − , Br − , I −

In this computational study, we self-consistently calculate the rate constants of mutual neutralization reactions by incorporating the electron transfer probability, using Landau–Zener state transition theory with inputs derived from ab initio quantum chemistry calculations, into classical trajectory simulations. Electronic structure calculations are done using correlation consistent basis sets with multi-reference configuration interaction to map all the molecular electronic states below the ion-dissociation limit as a function of the distance between the reacting species. Our electronic structure calculations have been significantly improved from our previous work through improved selection of molecular electronic configurations maintaining a fine grid of 1a 0 over a wide range of bond lengths and accurate treatment of spin–orbit couplings. Non-adiabatic coupling matrix elements are calculated with the three-point central difference method near each avoided crossing to estimate the exact crossing point R x and coupling parameter H if , which are inputs to the multi-channel Landau–Zener theory to calculate the electron transition probability. Our approach is applied to estimate the mutual neutralization rate constants for the following ion pairs: Ar + –Cl − , Ar + –Br − , Ar + –I − at ∼133 Pa. Furthermore, our predictions are compared against the experimental data reported. It is seen that the improvement in the electronic structure calculation results in excellent agreement between the simulation results and the available experimental data to within a factor of ∼2 or ∼±50%.

Complete-active space self-consistent field↗