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At least 217 records · Page 12

Bounce-Averaged Hamiltonian for Charged Particles in an Axisymmetric but Nondipolar Model Magnetosphere

In order to facilitate bounce-averaged guiding center simulations of geomagnetically trapped particles, we express the kinetic energy of a particle with magnetic coordinates (L,phi) as an analytic function of the first two adiabatic invariants (M, J) and the L value of the field line. The magnetic field model is axisymmetric, consisting of a dipolar B field plus a uniform southward magnetic field parallel to the dipole moment mu(sub E). This model magnetosphere is surrounded by a circular equatorial neutral line whose radius b is an adjustable parameter. The L value of a field line is (by definition) inversely proportional to the flux enclosed by the corresponding magnetic shell of equatorial radius r(sub 0), and the L value at the neutral line (r(sub 0) = b) is denoted L*. The azimuthal coordinate phi measures magnetic local time. The best functional representation found for the normalized difference (L(exp 3)a(exp 3)/mu(sub E))(B(sub m) - B(sub 0)) between mirror-point field B(sub m) and equatorial field B(sub 0) along any field line is a 5-term expansion in powers (2/3 through 6/3) of the quantity X equivalent to (La/mu(sub E))(exp 1/2)K, where K equivalent to (J(exp 2)/8m(sub 0)M)(exp 1/2) is an adiabatically conserved quantity independent of particle energy, m(sub 0) is the rest mass of the particle, and a is the radius of the Earth. This functional form is motivated by results for limiting cases in which particles mirror very near and very far from the magnetic equator. Expansion coefficients corresponding to various powers of X are obtained from least squares fits to numerically computed results for X as a function of L and B(sub m). These are accurately expressible as fourth-order polynomials in (r(sub 0)/b)(exp 3), hence indirectly as functions of L/L* = 3La/2b. This representation, which leads (except for a manageably small region of parameter space) to better than 1% accuracy in the specification of B(sub m) as a function of K and L, allows bounce-averaged guiding center simulations to be performed without actually tracing the bounce motions of individual particles. Bounce-averaged drifts L' (meridional) and phi' (azimuthal) are proportional to derivatives of the Hamiltonian H (sum of kinetic and potential energies) with respect to phi and L, respectively. Our formulation thus provides a computationally efficient method for tracing the bounce-averaged adiabatic motion (conserving all three invariants) and nonadiabatic transport (violating the third invariant while conserving the first two invariants) of geomagnetically trapped particles in the model magnetosphere.

Schulz, Michael↗

Learning energy-based representations of quantum many-body states

Efficient representation of quantum many-body states on classical computers is a problem of practical importance. An ideal representation of a quantum state combines a succinct characterization informed by the structure and symmetries of the system along with the ability to predict the physical observables of interest. Several machine-learning approaches have been recently used to construct such classical representations, which enable predictions of observables and account for physical symmetries. However, the structure of a quantum state typically gets lost unless a specialized is employed based on prior knowledge of the system. Moreover, most such approaches give no information about what states are easier to learn in comparison with others. Here, we propose a generative energy-based representation of quantum many-body states derived from Gibbs distributions used for modeling the thermal states of classical spin systems. Based on the prior information on a family of quantum states, the energy function can be specified by a small number of parameters using an explicit low-degree polynomial or a generic parametric family such as neural nets and can naturally include the known symmetries of the system. Our results show that such a representation can be efficiently learned from data using exact algorithms in a form that enables the prediction of expectation values of physical observables. Importantly, the structure of the learned energy function provides a natural explanation for the difficulty of learning an energy-based representation of a given class of quantum states when measured in a certain basis. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Space Flight Handbooks, Volume 3 - Planetary Flight Handbook. Part 8 - Jupiter Swingby Missions to Saturn, Uranus, Neptune, and Pluto. Supplement - Tabular Trajectory Data

The trajectory data are presented chronologically and are organized by holding the arrival date constant while varying the Earth departure date in increments of 10 days. Upon completion of the specified range of Earth departure dates, the arrival date is incremented and the range of departure dates is repeated. The range of departure and arrival dates and the corresponding increments are given in Table 5-1 for each launch opportunity. It should be noted that the interval in arrival date is increased in the long flight time region where the variation of the trajectory parameters is relatively small. The criteria used for the selection of these dates are, in general: (i) the minimum Earth departure hyperbolic excess speed (across the Earth departure window) shall not exceed 0.65 EMOS and (2) the periapsis radius at Jupiter shall not be less than 0.95 planet radii.

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FORTRAN read package

Flexible input schemes for digital programs are described. No card format or special order of cards is required. Read package is controlled by small set of parameters which can be changed to account for differences in computers and digital programs.

Diekelman, D. P.↗

An approximate theory of imperfect modeling with application to thermal modeling of spacecraft.

Proposal of a new concept of model testing which makes use of imperfect models and is based on the heuristic argument of representing the error states in a multidimensional Euclidean space when the errors in the modeling parameter are sufficiently small. By a separation of these errors into positive and negative groups, and from a consideration of the error paths in the hyperspaces, it is shown that the global effect of these errors may be evaluated with a good degree of approximation. Conditions under which the procedure would yield satisfactory results are discussed. To test the usefulness of the theory a computer experiment was conducted for the prediction of both transient and steady state thermal behavior of a hypothetical spacecraft using perfect, as well as imperfect, models.

Chao, B. T.↗

Proton dose approximation in arbitrary convex geometry

An expansion is derived for the solution to the transport equation in two dimensions subject to boundary conditions given for an arbitrary convex region. Questions of high-energy transport are considered along with the properties of the dose response function. The expansion of the solution of the transport equation is presented in terms of a parameter which measures the lateral dispersion of an unidirectional beam. This parameter is usually small and the expansion is expected to converge rapidly. The dominant term in the expansion is related to fluence-to-dose conversion factors in a semiinfinite slab for normal incidence. A convenient parameterization of the conversion factors is provided along with numerical examples.

Wilson, J. W.↗

Application of a parameter identification technique to a hingeless helicopter rotor

A mathematical model of a gyro-controlled, three-bladed hingeless helicopter rotor was developed and parameters of the model were estimated using a parameter identification technique. The flapping and feathering degrees of freedom of the blades were modeled. The equations of the model contain time-varying, periodic coefficients due to the forward speed of the rotor. A digital simulation of the analytical model was compared with wind-tunnel measurements to establish the validity of the model. Comparisons of steady-state and transient solutions of the analytical model with the tunnel measurements gave reasonably good matching of gyro angle but less satisfactory matching of hub moment measurements. Further improvements were obtained by use of a parameter identification technique to adjust as many as 10 parameters of the analytical model. The sensitivity of the blade response to small changes in the parameters was also calculated.

Kanning, G.↗

Measurement scanning schemes for terrain modeling

A scanning scheme for the laser rangefinder aboard an autonomous Mars Rover is developed. The rover is expected to be able to traverse an incline of slope up to 25% deg positive or negative. The total azimuth angle of the rangefinder is calculated so that the rangefinder can scan a width of 3 m at a distance of 3 m. A combination of two approaches is considered: scanning the field with a data point spacing appropriate for the terrain modeling technique, followed by zoom scanning with reduced spacing aimed at an obstacle location indicated in a previous terrain scan. It is found that the scan time and total number of data points can be reduced by dividing the field into corridors. The scan is divided into two subscans: the initial scan covering the entire field, and a corridor scan. The corridor scan method reduces the core required in the on-board computer. Hardware changes are expected to be small since the parameters of the corridor are fixed and a continuously variable point spacing is not necessary.

Friedman, M.↗

Automatic vehicle monitoring systems study. Report of phase O. Volume 1: Executive summary

A set of planning guidelines is presented to help law enforcement agencies and vehicle fleet operators decide which automatic vehicle monitoring (AVM) system could best meet their performance requirements. Improvements in emergency response times and resultant cost benefits obtainable with various operational and planned AVM systems may be synthesized and simulated by means of special computer programs for model city parameters applicable to small, medium, and large urban areas. Design characteristics of various AVM systems and the implementation requirements are illustrated and cost estimated for the vehicles, the fixed sites, and the base equipments. Vehicle location accuracies for different RF links and polling intervals are analyzed.

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Automatic vehicle monitoring systems study. Report of phase O. Volume 2: Problem definition and derivation of AVM system selection techniques

A set of planning guidelines is presented to help law enforcement agencies and vehicle fleet operators decide which automatic vehicle monitoring (AVM) system could best meet their performance requirements. Improvements in emergency response times and resultant cost benefits obtainable with various operational and planned AVM systems may be synthesized and simulated by means of special computer programs for model city parameters applicable to small, medium and large urban areas. Design characteristics of various AVM systems and the implementation requirements are illustrated and cost estimated for the vehicles, the fixed sites and the base equipments. Vehicle location accuracies for different RF links and polling intervals are analyzed. Actual applications and coverage data are tabulated for seven cities whose police departments actively cooperated in the study.

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Annoyance due to simulated blade-slap noise

The effects of several characteristics of blade slap noise on annoyance response were studied. These characteristics or parameters were the sound pressure level of the continuous noise used to simulate helicopter broadband noise, the ratio of impulse peak to broadband noise or crest factor, the number of pressure excursions comprising an impulse event, the rise and fall time of the individual impulses, and the repetition frequency of the impulses. Analyses were conducted to determine the correlation between subjective response and various physical measures for the range of parameters studied. A small but significant improvement in the predictive ability of PNL was provided by an A-weighted crest factor correlation. No significant improvement in predictive ability was provided by a rate correction.

Powell, C. A.↗

Global enclosure fire modeling with applications

A brief review of LERC (Limiting Energy Release Criteria) is presented. Application of LERC to JSC/Boeing ignition source full-scale tests and to JSC/Dacfir math-model validation tests is outlined. It is concluded that: (1) a complete LERC application to the JSC/Boeing tests verifies the fuel load criterion as the limiting constraint; (2) the variability of magnitude and form of the results of repeated tests with and without small variations in parameters emphasizes the significance of the local flow, species concentration, and heat transfer distribution; and (3) weight loss measurements of recent JSC tests show consistent results with prior methods, fuel load constrained.

Stuart, J. W.↗

Automated vehicle guidance using discrete reference markers

Techniques for providing steering control for an automated vehicle using discrete reference markers fixed to the road surface are investigated analytically. Either optical or magnetic approaches can be used for the sensor, which generates a measurement of the lateral offset of the vehicle path at each marker to form the basic data for steering control. Possible mechanizations of sensor and controller are outlined. Techniques for handling certain anomalous conditions, such as a missing marker, or loss of acquisition, and special maneuvers, such as u-turns and switching, are briefly discussed. A general analysis of the vehicle dynamics and the discrete control system is presented using the state variable formulation. Noise in both the sensor measurement and in the steering servo are accounted for. An optimal controller is simulated on a general purpose computer, and the resulting plots of vehicle path are presented. Parameters representing a small multipassenger tram were selected, and the simulation runs show response to an erroneous sensor measurement and acquisition following large initial path errors.

Johnston, A. R.↗

Multifunctional transducer

Several parameters of a small region of a muscle tissue or other object, can be simultaneously measured using with minimal traumatizing or damage of the object, a trifunctional transducer which can determine the force applied by a muscle fiber, the displacement of the fiber, and the change in thickness of the fiber. The transducer has three legs with inner ends joined together and outer ends formed to piece the tissue and remain within it. Two of the legs are relatively stiff, to measure force applied by the tissue, and a third leg is relatively flexible to measure displacement of the tissue relative to one or both stiff legs, and with the three legs lying in a common plane so that the force and displacement measurements all relate to the same direction of muscle movements. A flexible loop is attached to one of the stiff legs to measure changes in muscle thickness, with the upper end of the loop fixed to the leg and the lower end of the loop bearing against the surface of the tissue and being free to slide on the leg.

Feldstein, C.↗

On the equivalence between semiempirical fracture analyses and R-curves

The relationship between the R-curves and semiempirical fracture analyses (SEFA) is investigated theoretically using a hypothetical material. Equivalent R-curves (ERC) are developed for real materials using data from the literature. It is shown that for each SEFA there is an ERC whose magnitude and shape are determined by the SEFA formulation and its empirical parameters. The ERC is equivalent in that it predicts exactly the same relationship between the fracture stress and the initial crack length (residual strength) as the SEFA. If the effective R-curve is unique, then the various empirical parameters cannot be constant, and vice versa. However, for one of the SEFA examined, Newman's SEFA, parameter variations are small enough to be within the range of normal data scatter for real materials.

Orange, T. W.↗

Orbits of the Tethys Lagrangian bodies

Preliminary libration parameters are derived for the objects found in 1980 at the triangular libration points of Tethys. The parameters are obtained from an orbit analysis of ground-based and Voyager I data obtained in 1980 for the separation from Saturn along the ring major axis, the projected separations from the Tethys L4 and L5 points and the separations from Tethys in orbital longitude. The best fitting libration parameters indicate a small (approximately 2 deg) libration amplitude for the L4 body. Data for the object at the L5 point may be fit either by orbits with libration amplitudes greater than 50 deg, or with small libration amplitudes, which are in agreement with recent Voyager II observations.

Reitsema, H. J.↗

Lagged average forecasting, some operational considerations

The Lagged Average Forecast (LAF) method differs from the Monte Carlo Forecast (MCF) method in the definition of the ensemble of initial states which are used to generate the ensemble of forecasts. The LAF initial states are the current analysis and the forecasts made from previous analyses verifying the current time. Thus the LAF ensemble is composed of forecasts which are made by a regular operational system of numerical weather prediction and the LAF method is therefore operationally attractive. The application of the authors' previous ideas and results to an operational model requires the resolution of what might be called the degrees of freedom problem, i.e., how to obtain a homogeneous sample large enough to calculate stable statistics. It is suggested that this problem may be solved by carefully modeling the required statistics in terms of a small set of parameters and then estimating only these few parameters from the data. It is noted that there may be considerable information in each initial ensemble relating to the predictability of each particular case, and that this information may be incorporated in the model of the statistics.

Hoffman, R. N.↗