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1.
Uncertainty forecasting in orbital mechanics is an essential but difficult task, primarily because the underlying Fokker–Planck equation (FPE) is defined on a relatively high dimensional (6-D) state–space and is driven by the nonlinear perturbed Keplerian dynamics. In addition, an enormously large solution domain is required for numerical solution of this FPE (e.g. encompassing the entire orbit in the \(x-y-z\) subspace), of which the state probability density function (pdf) occupies a tiny fraction at any given time. This coupling of large size, high dimensionality and nonlinearity makes for a formidable computational task, and has caused the FPE for orbital uncertainty propagation to remain an unsolved problem. To the best of the authors’ knowledge, this paper presents the first successful direct solution of the FPE for perturbed Keplerian mechanics. To tackle the dimensionality issue, the time-varying state pdf is approximated in the CANDECOMP/PARAFAC decomposition tensor form where all the six spatial dimensions as well as the time dimension are separated from one other. The pdf approximation for all times is obtained simultaneously via the alternating least squares algorithm. Chebyshev spectral differentiation is employed for discretization on account of its spectral (“super-fast”) convergence rate. To facilitate the tensor decomposition and control the solution domain size, system dynamics is expressed using spherical coordinates in a noninertial reference frame. Numerical results obtained on a regular personal computer are compared with Monte Carlo simulations. 相似文献
2.
This work investigates the applicability of several dimensionality reduction techniques for large-scale solar data analysis. Using a solar benchmark dataset that contains images of multiple types of phenomena, we investigate linear and nonlinear dimensionality reduction methods in order to reduce our storage and processing costs and maintain a good representation of our data in a new vector space. We present a comparative analysis of several dimensionality reduction methods and different numbers of target dimensions by utilizing different classifiers in order to determine the degree of data dimensionality reduction that can be achieved with these methods, and to discover the method that is the most effective for solar images. After determining the optimal number of dimensions, we then present preliminary results on indexing and retrieval of the dimensionally reduced data. 相似文献
3.
The precision of the rates of the photolysis processes initiating the complex chemistry of Titan’s upper atmosphere conditions strongly the predictivity of photochemical models. Recent studies in sensitivity analysis of such models point out photolysis rate constants as key parameters. However, they have been treated approximately so far. We deal here directly with uncertainty in the absorption cross-sections to derive the uncertain altitude-dependent photolysis rate constants. We observe that the uncertainty on the photolysis rate constants of the major species, N2 and CH4, varies strongly with altitude and rather surprisingly vanishes at specific altitudes. We propose a simple model to interpret these features and we demonstrate that they are transferable to any major absorber distributed barometrically in an atmosphere. 相似文献
4.
5.
Prasenjit Sengupta 《Celestial Mechanics and Dynamical Astronomy》2007,99(1):13-22
This paper presents a method for the truncation of infinite Fourier–Bessel representations for functions requiring a solution
to Kepler’s equation. Use is made of the Lambert W function to solve for the desired index that bounds the remainder terms of the series, within the prescribed tolerance. The
enforcement of a maximum on the number of Bessel functions is also useful in truncating the Bessel functions themselves, resulting
in an analytical representation of the solution to a desired tolerance, without the use of infinite series. 相似文献
6.
A possible mechanism for the formation and heating of coronal loops through the propagation and damping of fast mode waves is proposed and studied in detail. Loop-like field structures are represented by a dipole field with the point dipole at a given distance below the solar surface. The density of the medium is determined by hydrostatic equilibrium along the field lines in an isothermal atmosphere. The fast mode waves propagating outward from the coronal base are refracted into regions with a low Alfvén speed and suffer collisionless damping when the gas pressure becomes comparable to the magnetic pressure. The propagation and damping of these waves are studied for three different cases: a uniform density at the coronal base, a density depletion within a given flux tube, and a density enhancement within a given flux tube. The fast mode waves are found to be important in the formation and heating of the loops if the wave energy flux density is of the order 105 ergs cm-2 s-1 at the coronal base.The National Center for Atmospheric Research is sponsored by the National Science Foundation. 相似文献
7.
The Cherenkov Telescopes Array (CTA) is planned as the future instrument for very-high-energy (VHE) gamma-ray astronomy with a wide energy range of four orders of magnitude and an improvement in sensitivity compared to current instruments of about an order of magnitude. Monte Carlo simulations are a crucial tool in the design of CTA. The ultimate goal of these simulations is to find the most cost-effective solution for given physics goals and thus sensitivity goals or to find, for a given cost, the solution best suited for different types of targets with CTA. Apart from uncertain component cost estimates, the main problem in this procedure is the dependence on a huge number of configuration parameters, both in specifications of individual telescope types and in the array layout. This is addressed by simulation of a huge array intended as a superset of many different realistic array layouts, and also by simulation of array subsets for different telescope parameters. Different analysis methods – in use with current installations and extended (or developed specifically) for CTA – are applied to the simulated data sets for deriving the expected sensitivity of CTA. In this paper we describe the current status of this iterative approach to optimize the CTA design and layout. 相似文献
8.
We detail the investigation of the first application of several dissimilarity measures for large-scale solar image data analysis. Using a solar-domain-specific benchmark dataset that contains multiple types of phenomena, we analyzed combinations of image parameters with different dissimilarity measures to determine the combinations that will allow us to differentiate between the multiple solar phenomena from both intra-class and inter-class perspectives, where by class we refer to the same types of solar phenomena. We also investigate the problem of reducing data dimensionality by applying multi-dimensional scaling to the dissimilarity matrices that we produced using the previously mentioned combinations. As an early investigation into dimensionality reduction, we investigate by applying multidimensional scaling (MDS) how many MDS components are needed to maintain a good representation of our data (in a new artificial data space) and how many can be discarded to enhance our querying performance. Finally, we present a comparative analysis of several classifiers to determine the quality of the dimensionality reduction achieved with this combination of image parameters, similarity measures, and MDS. 相似文献
9.
We propose a special representation for the secular part of the perturbing function describing the mutual attraction of satellites. In contrast to the known representations, it has a single analytical form for any ratio between the semimajor axes of the perturbed and perturbing satellites. The resulting expression is a partial sum of a power series with respect to the small eccentricities and planet-equatorial inclinations of the satellites’ orbits. This sum includes terms up to and including the fourth degree with respect to these small parameters. The proposed expansion is compared with one of the known expansions for the secular part of the perturbing function. 相似文献
10.
M. Bahmanabadi A. Anvari G. Rastegarzadeh J. Samimi M. Lamehi Rachti 《Experimental Astronomy》1998,8(3):211-229
We have carried out a series of measurements with twenty-one light enclosures of different geometry and inside finishes to compare their performance for use in extensive air shower experiments. It is found that for light enclosures with white inside finish there is an inherent induced uncertainty in time measurement, in addition to the uncertainty arising from the uncertain transit location of the shower particle in a large area scintillator. Both of these uncertainties which can not be improved with better electronics limit the angular resolution of EAS arrays. 相似文献
11.
Paul D. Kiel Jarrod R. Hurley 《Monthly notices of the Royal Astronomical Society》2006,369(3):1152-1166
We perform binary population-synthesis calculations to investigate the incidence of low-mass X-ray binaries (LMXBs) and their birth rate in the Galaxy. We use a binary-evolution algorithm that models all the relevant processes including tidal circularization and synchronization. Parameters in the evolution algorithm that are uncertain and may affect X-ray binary formation are allowed to vary during the investigation. We agree with previous studies that under standard assumptions of binary evolution the formation rate and number of black hole (BH) LMXBs predicted by the model are more than an order of magnitude less than what is indicated by observations. We find that the common-envelope process cannot be manipulated to produce significant numbers of BH LMXBs. However, by simply reducing the mass-loss rate from helium stars adopted in the standard model, to a rate that agrees with the latest data, we produce a good match to the observations. Including LMXBs that evolve from intermediate-mass systems also leads to favourable results. We stress that constraints on the X-ray binary population provided by observations are used here merely as a guide as surveys suffer from incompleteness and much uncertainty is involved in the interpretation of results. 相似文献
12.
本文综述了电离层、对流层中电波折射引起的射电天文观测及卫星测地中的各种误差及各种改正方法和它们的精度。 对流层影响的主要改正方法是实测大气温度、压力等参数,用数学模型计算。电离层影响的改正目前有三种方法:一是实时测量电离层主要参数——电子总含量的变化,然后用数学模型方法改正。二是采用双频同时观测的手段来消除电离层折射的影响。三是采用自校准方法。文中还比较了两种不同的自校准方法——常规自校准方法和多余量自校准方法。 相似文献
13.
G. F. Roach 《Astrophysics and Space Science》1981,80(1):237-247
A method, involving boundary integral equations of the first kind is offered for obtaining exact representations for solutions to interior and exterior harmonic problems. The method is constructive and a representation can be obtained to any degree of accuracy. The determination of Roche harmonics appears as a special case. 相似文献
14.
P. Donald Ariel 《Astrophysics and Space Science》1992,196(1):153-166
The stability of an infinitely conducting plasma of variable density has been investigated taking into account the finiteness of the ion Larmor radius. The perturbations propagating along the ambient magnetic field are considered. It is established that, in general,n
2 is necessarily real, wheren is the growth rate of disturbance, thus ruling out the possibility of overstability or damped oscillations. The solution is shown to be characterized by a variational principle, which provides the basis for obtaining an approximate solution of the problem. Two density distributions are considered: (i) a continuously stratified plasma layer and (ii) two semi-infinitely extending plasmas of constant densities separated by a horizontal interface. In both cases it has been shown that for the said disturbances the stability criterion remains unaffected by the inclusion of finite Larmor radius effects, though the amplified motion is strongly inhibited due to their inclusion. 相似文献
15.
Various representations of the Jordan-Brans-Dicke (JBD) theory arising in conformal transformations of the metric are considered. Propositions are formulated that establish the mathematical equivalence of these representations, making it possible from known exact solutions in one representation to generate new ones in another. It is shown, in particular, how to obtain new solutions in the general theory of relativity from known solutions in the JBD theory and vice versa. 相似文献
16.
The Advanced Space-based Solar Observatory(ASO-S) mission aims to explore the two most spectacular eruptions on the Sun: solar flares and coronal mass ejections(CMEs), and their magnetism.For the study of CMEs, the payload Lyman-alpha Solar Telescope(LST) has been proposed. It includes a traditional white-light coronagraph and a Lyman-alpha coronagraph which opens a new window to CME observations. Polarization measurements taken by white-light coronagraphs are crucial for deriving fundamental physical parameters of CMEs. To make such measurements, there are two options for a Stokes polarimeter which have been applied by existing white-light coronagraphs for space missions. One uses a single or triple linear polarizer, the other involves both a half-wave plate and a linear polarizer. We find that the former option is subject to less uncertainty in the derived Stokes vector propagating from detector noise.The latter option involves two plates which are prone to internal reflections and may have a reduced transmission factor. Therefore, the former option is adopted as our Stokes polarimeter scheme for LST. Based on the parameters of the intended linear polarizer(s) colorPol provided by CODIXX and the half-wave plate 2-APW-L2-012 C by Altechna, it is further shown that the imperfect maximum transmittance of the polarizer significantly increases the variance amplification of Stokes vector by at least about 50% when compared with the ideal case. The relative errors of Stokes vector caused by the imperfection of colorPol polarizer and the uncertainty due to the polarizer assembly in the telescope are estimated to be about 5%. Among the considered parameters, we find that the dominant error comes from the uncertainty in the maximum transmittance of the polarizer. 相似文献
17.
This paper deals with the closed-form representation of the non-resonant nuclear reaction rate taking into account electron screening effects for the reacting particles. The basic physical principles concerning nuclear reactions in dense astrophysical plasmas are applied to derive the representation of the screened nuclear reaction rate integral. Taking advantage of the theory of Meijer'sG-function it is shown that both the reaction rate integrals with and without screening corrections can be represented in closed form. Mathematical approximations for the reaction rate integral, till now considered as inevitable in the literature, are avoided and exact computable representations given. 相似文献
18.
Considering mode coupling as a consequence of the matching of boundary conditions at an infinitesimal discontinuity, a concept introduced by the same authors earlier, we derive explicit expressions for the coupling coefficients for electromagnetic waves propagating in a rather general direction in an inhomogeneous magnetized plasma. Some special cases of the theory are discussed. 相似文献
19.
Roger Gendrin 《Astrophysics and Space Science》1974,28(1):245-266
We consider the movement of individual electrons in a magnetized plasma in which a monochromatic wave is propagating in the whistler mode. We derive simple expressions which give the displacement of the electrons as a function of time, the phase angle that their velocity vector makes with the magnetic component of the wave, their pitch angle and energy changes. A useful formula is obtained which gives the velocity range over which particles remain trapped inside the wave, as a function of the wave intensity and of the initial phase angle of the particle. It is shown that even strictly resonant particles can escape from the wave when their initial phase angle is very small. From the derived expressions, it is possible to compute the phase-bunching effect which occurs approximately at one trapping wavelength behind the leading edge of the interaction region. We deduce also the total amount of energy which is taken from (or given to) the wave by magnetospheric electrons in both cases of naturally existing or artificially injected particles. It is shown that these non-linear amplification processes can lead to very large VLF amplitude in the magnetosphere. 相似文献
20.
Jaap D. Bregman 《Experimental Astronomy》2004,17(1-3):365-380
Investigating the requirements for an aperture synthesis array that optimise the performance for surveying shows that, next to collecting area and system temperature, the field-of-view (FoV) is key parameter. However, the effective sensitivity not only depends on bandwidth and integration time but could be seriously limited by side lobe confusion and by gain errors that determine the effective dynamic range. From the basic sensitivity equation for a radiometric system we derive an optimum cost ratio between collecting area and processing electronics, where the latter should be less than a third of the total cost. For an instrument that has to cover a fraction of sky larger than its field-of-view, the FoV enters the equation for survey sensitivity and we identify the number of independent feed systems per unit collecting area as a key parameter. Then the optimum cost distribution allows the electronics to account for up to half the total cost. Further analysis of the sensitivity formula shows that there is an optimum design frequency for a survey instrument below 1 GHz. We discuss the impact of station size and array configuration on self-calibration, side lobe confusion and effective sensitivity and conclude that a minimum station size of 20 m diameter is required at 0.3 GHz as long as multi-patch self-calibration procedures need, per baseline, a signal-to-noise ratio of more than two for each ionospheric coherence patch. 相似文献