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In this work, a complete first order analytical solution, which includes the short periodic terms, for the problem of optimal low-thrust limited-power transfers between arbitrary elliptic coplanar orbits in a Newtonian central gravity field is obtained through Hamilton-Jacobi theory and a perturbation method based on Lie series.
Frozen orbits of the Hill problem are determined in the double averaged problem, where short and long period terms are removed by means of Lie transforms. The computation of initial conditions of corresponding quasi periodic solutions in the non-averaged problem is straightforward for the perturbation method used provides the explicit equations of the transformation that connects the averaged and non-averaged models. A fourth order analytical theory reveals necessary for the accurate computation of quasi periodic, frozen orbits.
Baroreflex sensitivity (BRS) decreases during spaceflight and simulated spaceflight (head down bed rest [BR]). However, previous studies have only examined BRS in response to a limited blood pressure (BP) range or to a single sudden change in BP. PURPOSE: The purpose of this study was to examine BRS during 90 days of 6deg head-down tilt BR over a broad range of BP perturbations. METHODS: Nineteen normal volunteers (12M, 7F) were tested one day before BR, and then near BR days 30, 60 and 90. BP was pharmacologically altered by continuous infusions of phenylephrine (PE) and sodium nitroprusside (SNP). Electrocardiogram and continuous BP were collected during 10 min of normal saline (NS), followed by increasing concentrations of PE (10 min each of 0.4, 0.8 and 1.6 micro-g/kg/min). After a 20 min break, NS was infused again for 10 min, followed by increasing concentrations of SNP (10 min each of 0.4, 0.8, 1.2 micro-g/kg/min). Baroreceptor sensitivity was measured as the slope of a sequence of 3 or more beats in which the systolic BP and following R-R interval (RR) both increased or decreased. Spectral heart rate variability (HRV) and mean RR were analyzed using data from only the NS infusions. Two-way repeated-measures analysis of variance was performed to examine the effects of BR and gender. RESULTS: RR decreased (p<0.001) from pre- BR across BR days. High frequency in normalized units, a measure of parasympathetic activity, decreased with BR (p=0.027) and was lower (p=0.046) in men (0.39+/-0.02, mean+/-SEM) than women (0.48+/-0.02). The spontaneous baroreflex slope, our measure of BRS, increased with PE and decreased with SNP across BR (p<0.001). The percentage decrease in BRS from pre- to post-BR appeared to be larger in women (43.6+/-7.0%) than in men (31.3+/-3.9%, p=0.06). CONCLUSION: Parasympathetic activity and baroreflex sensitivity decrease during 90 days of BR, and BRS tends to diminish more in women than in men.
This paper addresses the problem of controlling a nonlinear plant with a slow actuator using singular perturbation method. For the known plant-actuator cascaded system the proposed scheme achieves tracking of a given reference model with considerably less control demand than would otherwise result when using conventional design techniques. This is the consequence of excluding the small parameter from the actuator dynamics via time scale separation. The resulting tracking error is within the order of this small parameter. For the unknown system the adaptive counterpart is developed based on the prediction model, which is driven towards the reference model by the control design. It is proven that the prediction model tracks the reference model with an error proportional to the small parameter, while the prediction error converges to zero. The resulting closed-loop system with all prediction models and adaptive laws remains stable. The benefits of the approach are demonstrated in simulation studies and compared to conventional control approaches.
A flight trajectory optimization algorithm with fuel and contrails models, which develops alternative flight paths, provides policy makers the necessary data to make tradeoffs between persistent contrails mitigation and aircraft fuel consumption. This study develops an algorithm that calculates wind-optimal trajectories for cruising aircraft while avoiding the regions of airspace prone to persistent contrails formation. The optimal trajectory is derived using Singular Perturbation Method. The regions of airspace favorable to persistent contrails formation are modeled as high-risk areas that aircraft should avoid and are adjustable. The tradeoffs between persistent contrails formation and additional travel time are investigated for wind-optimal trajectories and various contrails-avoidance trajectories at 10 different cruising altitudes for flights departing from Chicago and San Diego to New York. The additional travel times required for avoiding 100% persistent contrails formation at various flight altitudes ranged from approximately 0% to 4.3% for flights from Chicago to New York. For flights between San Diego and New York, additional traveling times vary between 1.3% and 5% depending on the cruise altitude and the percentage of contrail avoidance. Talk will present the results of aircraft fuel consumptions that are proportional to the travel time for cruising aircraft.
Global monitoring of sea surface salinity from space requires an accurate model for the dielectric constant of sea water as a function of salinity and temperature to characterize the emissivity of the surface. Measurements are being made at 1.413 GHz, the center frequency of the Aquarius radiometers, using a resonant cavity and the perturbation method. The cavity is operated in a transmission mode and immersed in a liquid bath to control temperature. Multiple measurements are made at each temperature and salinity. Error budgets indicate a relative accuracy for both real and imaginary parts of the dielectric constant of about 1%.
Radar Scattering includes: Surface Characteristics, Geometric Properties, Dielectric Properties, Rough Surface Scattering, Geometrical Optics and Small Perturbation Method Solutions, Integral Equation Method, Magellan Image of Pancake Domes on Venus, Dickinson Impact Crater on Venus (Magellan), Lakes on Titan (Cassini Radar, Longitudinal Dunes on Titan (Cassini Radar), Rough Surface Scattering: Effect of Dielectric Constant, Vegetation Scattering, Effect of Soil Moisture. Polarimetric Radar includes: Principles of Polarimetry: Field Descriptions, Wave Polarizations: Geometrical Representations, Definition of Ellipse Orientation Angles, Scatter as Polarization Transformer, Scattering Matrix, Coordinate Systems, Scattering Matrix, Covariance Matrix, Pauli Basis and Coherency Matrix, Polarization Synthesis, Polarimeter Implementation.
During the course of a literature survey concerning resonance charge exchange, an unusual degree of agreement was noted between an extrapolation of the data reported by Kushnir, Palyukh, and Sena and the data reported by Ziegler. The data of Kushnir et al. are for ion-atom relative energies from 10 to 1000 ev, while the data of Ziegler are for a relative energy of about 1 ev. Extrapolation of the data of Kushnir et al. was made in accordance with Holstein's theory, 3 which is a combination of time-dependent perturbation methods and classical orbit theory. The results of this theory may be discussed in terms of a critical impact parameter b(sub c).
We present a robust initialization scheme that estimates parameter values for the numerical solution of a two-point boundary value problem. The two-point boundary value problem formulation stems from the optimization of a cost functional subject to the dynamics of a simplified lateral aircraft model and other constraints. Leveraging regular perturbation methods, initial parameter estimates are analytically determined and used to initialize a gradient descent optimization routine which is shown to rapidly converge over a range of initial aircraft positions and heading angles. Additionally, the velocity of the aircraft is optimized to ensure the trajectory of the aircraft terminates within a desired region in both time and space.
To guide development of microwave process technology that could be used during in situ construction on the Moon, we measured the high-temperature basic dielectric properties (εʹ and εʺ) of 17 lunar simulants and related materials. In order to confidently use these data one needs to understand the data’s strengths and weaknesses. Therefore, a goal of this publication is to provide insights into the comparative effects of sample composition, pre-treatments, experimental variables, high temperatures, and other factors on the measured response. The dielectric measurements were performed using the cavity perturbation method over a temperature range between room temperature to 1000 °C, or higher, and provided the real and imaginary components of permittivity at six frequencies. The utility of the original values was limited by the varying density of the pellets used in the measurement. Therefore, all of the εʹ and εʺ measurements at the frequency of 2466 MHz have been scaled to a constant density, 1.75 g/cm 3 . Here the data are presented as graphs chosen to aid analysis within and across simulant groups. To gain additional insight into the processes happening at the elevated temperatures in the dielectric measurements, heat capacity data was obtained using differential scanning calorimetry (DSC) on several of the simulant materials. Our data show that over the frequency range 397 MHz – 2985 MHz a material’s behavior does not greatly change, as compared to the scale of differences observed between lunar mare and highland simulants at high temperatures. For example at 1000 °C, the mare simulant JSC-1A absorbs 10 times more power than the highland simulant NUW-LHT-5M. We observe that as melting temperatures are reached both permittivity and dielectric loss rise non-linearly, helping to explain thermal runaway during microware heating. Our data show that even less than a few weight % of many non-lunar minerals, and the use of mixtures in simulants can affect the dielectric behavior at higher temperatures. A comparison of our results with published dielectric data for Apollo samples and with remote sensing of the Moon supports the conclusion the simulants and lunar material at room temperature have very similar dielectric values.
Nuclear structure physics is on the threshold of confronting several long-standing problems such as the origin of shell structure from basic nucleon-nucleon and three-nucleon interactions. At the same time those interactions are being developed with increasing contact to QCD, the underlying theory of the strong interactions, using effective field theory. The motivation is clear - QCD offers the promise of great predictive power spanning phenomena on multiple scales from quarks and gluons to nuclear structure. However, new tools that involve non-perturbative methods are required to build bridges from one scale to the next. We present an overview of recent theoretical and computational progress with a Hamiltonian approach to build these bridges and provide illustrative results for the nuclear structure of light nuclei and quantum field theory.
In nuclear science, gamma and neutron spectra are counted energy by energy, and then particle by particle. Until recently, few studies have been performed on how exactly those energy spectra are counted, or how those counts are correlated. Because of lack of investigation, cross section covariance and correlation matrices are usually estimated using perturbation method. We will discuss a statistical counting scheme that shall mimic the gamma and neutron counting process used in nuclear science. From this counting scheme, the cross section covariance and correlation can be statistically derived.
The code is used to provide an unfolded/adjusted energy-dependent fission reactor neutron spectrum based upon an input trial spectrum and a set of measured activities. This is part of a neutron environment characterization that supports doing testing in a given reactor environment. An iterative perturbation method is used to obtain a "best fit" neutron flux spectrum for a given input set of infinitely dilute foil activities. The calculational procedure consists of the selection of a trial flux spectrum to serve as the initial approximation to the solution, and subsequent iteration to a form acceptable as an appropriate solution. The solution is specified either as time-integrated flux (fluence) for a pulsed environment or as a flux for a steady-state neutron environment.
In 2008, an UO{sub 2} fuel rod was irradiated up to ∼ 3.5 GWd/tHL in the CEA/Saclay research reactor Osiris through the MERCI experiment. Some rod's pellets were analysed. Experimental results were obtained: - fuel rod decay heat measurement by calorimetry (cooling times from 27 minutes to 42 days), - evaluation of the amounts of some nuclei (U, Pu, Cs, Nd...) by isotopic dilution mass spectrometry, - nuclide activities. Comparison of type (C - M)/M where C is the calculated decay heat and M the experimentally measured decay heat was reported in reference. Neutronics flux was computed by CEA TRIPOLI-4 Monte-Carlo or APOLLO2 deterministic transport code system. Irradiation and cooling phases were simulated with CEA DARWIN/PEPIN2 code system. Good agreements were globally shown between numerical simulation results and experimental measurements on total decay heat. Uncertainty propagation in this previous work was established from Rebah's studies. These last years, within the framework of supports to its industrial partners EDF and Areva, the CEA/DEN has implemented two different approaches to propagate nuclear data uncertainties to depletion code outputs. A direct forward deterministic perturbation method using sensitivity profiles was implemented in the French industrial depletion code system DARWIN/PEPIN2. Meanwhile, a propagation based on Monte Carlo correlated sampling was achieved using the CEA uncertainty platform URANIE and the new generation depletion code MENDEL. Both methods will be described in this article. Uncertainties on nuclear data (independent fission yields, multigroup microscopic cross sections, radioactive decay constants, radioactive decay branching ratio and radioactive decay energies) are propagated to decay heat and isotopic concentrations. To match MERCI first study, flux computation is realized by APOLLO2. Furthermore, uncertainty quantification (UQ) is re-evaluated by both DARWIN/PEPIN2 and MENDEL codes. It is an important stage in the process of validating both depletion codes with their respective data library. (authors)
Purpose: Dosimetric effect and discrepancy according to the rectum definition methods and dose perturbation by air cavity in an endo-rectal balloon (ERB) were verified using rectal-wall (Rwall) dose maps considering systematic errors in dose optimization and calculation accuracy in intensity-modulated radiation treatment (IMRT) for prostate cancer patients. Methods: When the inflated ERB having average diameter of 4.5 cm and air volume of 100 cc is used for patient, Rwall doses were predicted by pencil-beam convolution (PBC), anisotropic analytic algorithm (AAA), and AcurosXB (AXB) with material assignment function. The errors of dose optimization and calculation by separating air cavity from the whole rectum (Rwhole) were verified with measured rectal doses. The Rwall doses affected by the dose perturbation of air cavity were evaluated using a featured rectal phantom allowing insert of rolled-up gafchromic films and glass rod detectors placed along the rectum perimeter. Inner and outer Rwall doses were verified with reconstructed predicted rectal wall dose maps. Dose errors and extent at dose levels were evaluated with estimated rectal toxicity. Results: While AXB showed insignificant difference of target dose coverage, Rwall doses underestimated by up to 20% in dose optimization for the Rwhole than Rwall at all dose range except for the maximum dose. As dose optimization for Rwall was applied, the Rwall doses presented dose error less than 3% between dose calculation algorithm except for overestimation of maximum rectal dose up to 5% in PBC. Dose optimization for Rwhole caused dose difference of Rwall especially at intermediate doses. Conclusion: Dose optimization for Rwall could be suggested for more accurate prediction of rectal wall dose prediction and dose perturbation effect by air cavity in IMRT for prostate cancer. This research was supported by the Leading Foreign Research Institute Recruitment Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (MSIP) (Grant No. 200900420)
Numerical integration of long-range lunar effects in the motion of artificial satellites by extension of halperns method of secular perturbations
Some methods for calculation of local perturbations of neutron fields and reactivity effects accompanying them are considered. Existence, uniqueness, properties and methods for finding solutions to the considered problems are discussed.
Hill method of secular perturbations and determination of zero-rank effects in nonsingular vectorial elements of motion of planets, comets, and satellites