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Facets shadowing test is time-consuming and inefficient in calculation of radar cross section utilizing physical optics (PO). A novel method is proposed in this paper by covering the target by overlapped spheres which divide the facets to several consistent groups. In order to ensure that every facet is included by at least one sphere, the adjacent spheres must have a common area and some facets may be included by more than one sphere. Spheres’ shadowing tests are conducted before the facets’ tests. If one sphere does not shadow the facet under testing, then the facet cannot be shadowed by any facet within the sphere. Otherwise, every facet within the sphere should be judged whether to shadow the facet. Numerical simulation is conducted to validate the efficiency and accuracy of the algorithm. The spheres’ size on performance of the algorithm is also discussed in this paper and an optional choice of the parameter is achieved resulting 89% time saving. [ABSTRACT FROM AUTHOR]

A computational scheme is presented that takes into account the topography, i.e. the shadowing and hence the local emission angle of the electrons when evaluating AR-XPS data of macroscopic rough surfaces. The topography of the sample surface is supposed to be recorded by atomic force microscopy and/or opticalmicroscopy. The emitted photoelectrons are simulated based on an extension of the Beer-Lambert law that includes the shadowing, the current local emission angle, and the geometrical instrument setup. The obtained angle-resolved XPS spectra are optimized in accordance with experimental ones via a self-consistentminimization algorithmthat also allows one to determine the layer thicknesses of the corrugated sample. In order to validate the proposed numerical scheme, the simulationprogram simulationof electron spectra for surface analysis is used. An additional analysis is then performed considering only experimental data. The numerical scheme gives good agreement in simulation-simulation as well as simulation-experiment comparisons and permits a comprehensible interpretation of themeasured data. [ABSTRACT FROM AUTHOR]

We prove that the two-sided limit shadowing property is among the strongest known notions of pseudo-orbit tracing. It implies shadowing, average shadowing, asymptotic average shadowing and specification properties. We also introduce a weaker notion that is called two-sided limit shadowing with a gap and prove that it implies shadowing and transitivity. We show that those two properties allow to characterize topological transitivity and mixing in a class of expansive homeomorphisms and hence they characterize transitive (mixing) shifts of finite type. [ABSTRACT FROM AUTHOR]

Abstract: Shadowing occurs for the groove zone plate when radiation origin from one zone of the zone plate must pass through another before reaching the focus point. Using the vector diffraction theory, we study the influence of the shadowing on the focusing properties of binary phase Fresnel zone plates (FZPs). The results show that a low-numerical-aperture (NA) FZP can be treated as an ideal in-plane FZP and the shadowing effect can be neglected. For a high-NA FZP, however, the shadowing effect from the etch depth has to be considered. Owing to the shadowing, the intensity of focusing spot decreases markedly and the size of focusing spot increases slightly in a high-NA FZP. The optimal etching depth of an actual FZP is smaller than that of an ideal FZP. [Copyright &y& Elsevier]

SUMMARY An existing elevation dependent shadowing model for high-altitude platform (HAP) mobile communication in built-up areas is employed to perform the area coverage probability analysis and fading margin computation for HAP mobile communication systems. A generalized expression for the PDF of the received signal power in the HAP coverage is derived. The shadowing fade margin model that can characterize different types of built-up area is developed. Theoretical relations between shadowing fade margin and outage probability and cell coverage probability are given. Numerical simulation for isoflux coverage HAP-based system shows that there is great difference in the value of shadowing fade margin under line-of-sight and non-line-of-sight conditions for the same outage probability. It is also found that the cell coverage probability is insensitive to the variance of the shadowing fade margin in suburban environment whatever the size of the cell and for small cells in urban high-rise environments.Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Let M be a closed smooth manifold M, and let f: M → M be a diffeomorphism. In this paper, we consider a nontrivial transitive set Λ of f. We show that if f has the C-stably average shadowing property on Λ, then Λ admits a dominated splitting. [ABSTRACT FROM AUTHOR]

Abstract: The standard Fock functions that are the point of departure for this study are used in diffraction theory to describe the surface current on perfectly conducting convex scatterers. They are fairly accurate near the shadow boundary and in the shadow. There is also a reformulation in terms of these functions that describes the field in the lit region. In this study, a uniform counterpart to these functions is obtained for cylindrical geometry by means of integral representations. The numerical aspects of the evaluation of these integrals are discussed. High accuracy is achieved, also for the lit region. Asymptotic approximations for the uniform functions are obtained in the high frequency limit. These expansions could provide the same accuracy as the integral representation inside the lit domain of the scatterer. [Copyright &y& Elsevier]

Abstract: The influence of mask error enhancement factor (MEEF) on the mask shadowing effect was investigated for extreme ultraviolet lithography. Imaging properties including horizontal–vertical (H–V) CD (critical dimension) bias and MEEF change through the pitch according to absorber thickness and process condition were studied using aerial image simulation. The mask structure used in this study consisted of tantalum nitride (TaN) absorber and 2nm ruthenium (Ru) capping layer on the 40 pair of Mo–Si multilayer. As the absorber thickness increased and the pattern pitch decreased, both H–V CD bias and MEEF increased. At the illumination condition of 0.32 numerical aperture (NA), the H–V CD bias variation through the pitch was negligible and slightly increased at 1:1 pitch, while it steeply increased at 1:1.2 and 1:1 pitch for NA of 0.25. The MEEF value was below 1.5 for all calculated absorber thicknesses when the pitch was from 1:1.2 to 1:5, whereas it was 3 with 64nm thick TaN for 1:1 pitch at vertical pattern. With the increment of absorber thickness, the MEEF difference between the horizontal and vertical pattern increased. We also calculated the H–V overlapping process window (PW) according to TaN thickness using 22nm 1:1 line and space (L/S) pattern. As absorber thickness decreased, the overlapping zone in the EL of the focus–exposure plots between the horizontal and vertical features increased. Enough image contrast and H–V overlapping PW could be achieved by applying 38nm thick TaN. [ABSTRACT FROM AUTHOR]

Land mobile satellite (LMS) channels at the L (1/2 GHz) and S (2/4 GHz) frequency bands are mainly affected by propagation effects due to the local environment of a mobile terminal, such as multipath, shadowing, and blockage. Future systems for mobile satellite services (MSS) will operate at higher frequency bands, such as Ku (12/14 GHz) and Ka (20/30 GHz), where the tropospheric propagation effects also play an important role. Experimental campaigns conducted so far for Ku/Ka-band LMS channels have not considered any possible correlation between the tropospheric and local environment propagation effects. However, recent experimental work has indicated that these fading effects are not independent. As a first analytical approach to this open problem, a novel statistical analysis is presented in this paper. Emphasis is put on Ku/Ka-band LMS channels whose fading events can be modeled by the Ricean distribution with a relatively high K-factor. A novel analytical relationship between the Ricean K-factor and the rain attenuation effects is derived, and based on them, an analytical statistical prediction model for the distribution of the Ricean K-factor is derived. Particular attention is paid to the rainfall spatial inhomogeneity, as well as to the different effects of the climatic area of interest (temperate versus tropical) on the Ricean K-factor statistics. Thus, the presented analysis considers both spatially correlated bivariate lognormal and gamma statistics for the accurate characterization of rain attenuation. The proposed models are flexible and incorporate the impact of several critical operational, climatic, and geometrical parameters of an LMS channel on its multipath behavior under rainfall conditions. Useful numerical results are provided, specific future planned work is outlined, and the need for further experimental verification data is also pointed out. [ABSTRACT FROM AUTHOR]

Abstract: Matrices resulting from wavelet transforms have a special “shadow” block structure, that is, their small upper left blocks contain their lower frequency information. Numerical solutions of linear systems with such matrices require special care. We propose shadow block iterative methods for solving linear systems of this type. Convergence analysis for these algorithms are presented. We apply the algorithms to three applications: linear systems arising in the classical regularization with a single parameter for the signal de-blurring problem, multilevel regularization with multiple parameters for the same problem and the Galerkin method of solving differential equations. We also demonstrate the efficiency of these algorithms by numerical examples in these applications. [Copyright &y& Elsevier]

An exact trajectory of a dynamical system lying close to a numerical trajectory is called a shadow. We present a general-purpose method for proving the existence of finite-time shadows of numerical ODE integrations of arbitrary dimension in which some measure of hyperbolicity is present and there are either 0 or 1 expanding modes, or 0 or 1 contracting modes. Much of the rigor is provided automatically by interval arithmetic and validated ODE integration software that is freely available. The method is a generalization of a previously published containment process that was applicable only to two-dimensional maps. We extend it to handle maps of arbitrary dimension with the above restrictions, and finally to ODEs. The method involves building n-cubes around each point of the discrete numerical trajectory through which the shadow is guaranteed to pass at appropriate times. The proof consists of two steps: first, the rigorous computational verification of a simple geometric property, which we call the inductive containment property, and second, a simple geometric argument showing that this property implies the existence of a shadow. The computational step is almost entirely automated and easily adaptable to any ODE problem. The method allows for the rescaling of time, which is a necessary ingredient for successfully shadowing ODEs. Finally, the method is local, in the sense that it builds the shadow inductively, requiring information only from the most recent integration step, rather than more global information typical of several other methods. The method produces shadows of comparable length and distance to all currently published results. Finally, we conjecture that the inductive containment property implies the existence of a shadow without restriction on the number of expanding and contracting modes, although proof currently eludes us. [ABSTRACT FROM AUTHOR]

Areas of high concentrations of particulates in the urban atmosphere are hypothesized to strongly influence the solar receipt in nearby nonpolluted regions. Reductions of solar radiation in oonpolluted areas by upsun high aerosol regions are computed using a three-dimensional multi-scattering radiation model for specified solar-elevation classes. Numerical simulations from this model indicate that reductions exceeding 10 percent can occur several kilometers downsun of even moderately polluted regions in the early morning (i.e., periods of low solar-elevation angle). Although the reductions in global radiation are quite pronounced in the early day, they are generally overwhelmed in the daily total because of the relatively small amount of radiation associated with low-elevation angles. A series of simulations for three representative latitudes (33°N, 43°N and 53°N) demonstrate that the areal extent of the shadowing is highly dependent on latitude. Reductions in solar radiation exceeding 3 percent occur 15 km down range of the center of pollution for high-latitude (53°N) locations during early-morning, low-elevation angle periods. Such excessive solar attenuation in nonpolluted regions may affect the site selection of solar power facilities, the planning and siting of parks, golf courses and other recreational activities, the migration and tourism trends in areas experiencing seasonal population changes (i.e., the sunbelt states), and the temperature regime of the region. [ABSTRACT FROM AUTHOR]