Search Results (20)

Electrically charged particles present in this layer of the Earth’s atmosphere can alter radio waves, such as those from GPS, Galileo, or BeiDou, resulting in non-estimated errors with respect to the available navigation models for the end user. For most positioning algorithms based in sequential filters, this effect is translated into a slow convergence towards a solution around the decimeter error level. If we consider that the ionosphere’s effect varies based on the user’s location and solar activity due to the atmosphere particle composition, it becomes clear that a global accurate model, valid across wide areas accounting for different seasons and timespans, is, at the very least, quite challenging. The focus of this paper is the demonstration of a global ionosphere model designed to improve the positioning accuracy of the end user through the estimation of ionospheric corrections to the broadcasted navigation message. Mathematically, this method is based on a spherical harmonic expansion model. This approach has the advantage of reducing the dependency from a highly densified station network where the ionosphere delay must be constantly estimated in dozens of locations, in favor of a simplified model that barely needs to be adjusted with a limited set of real-time data (around 40 stations). In this case, GMV’s global station network was used, which comprises geodetic-grade receivers tracking the signal in open-sky locations around the globe. The global ionospheric model is configured to process signals from GPS and Galileo constellations. To evaluate the performances of this model on the final user position estimation, several precise point positioning (PPP) solutions were computed at different locations. The results were compared with PPP solutions calculated without ionospheric corrections at the same stations. The goal of this paper is to show the significant performance improvement observed with the implementation of the global model. Full article

Fourier ptychography (FP) can break through the limitations of existing optical systems with a single aperture and realize large field-of-view (FOV) and high-resolution (HR) imaging simultaneously by aperture synthesis in the frequency domain. The method has potential applications for remote sensing and space-based imaging. However, the aperture stop of the imaging system was generally set to be much smaller than the system with an adjustable diaphragm, so it failed to make full use of the imaging capability of the system. In this paper, a reflective remote FP with full aperture is proposed, and the optical aperture of the camera is set to be the maximum according to the sample-matching condition, which can further improve the imaging resolution by exploring the whole capability of the system. Firstly, the physical model of the remote FP is established using oblique illumination of a convergent spherical wave. Then, the sampling characteristics of the low-resolution (LR) intensity image are analyzed. Assuming diffraction-limited imaging, the size of the aperture of the optical system needs to match the sampling of the detector. An experimental setup with an imaging distance of 2.4 m is built, and a series of LR images is collected by moving the camera for the diffused samples, including the USAF resolution test target and the banknote, where the diameter of the single aperture is set to the maximum to match the size of the CCD pixel under the practical minimum F^# of the camera of 2.8. The high-resolution image is reconstructed by applying the iterative phase retrieval algorithm. The experimental results show that the reconstructed resolution is improved to 2.5×. This verifies that remote FP with full aperture can effectively improve the imaging resolution using only the present single-aperture optical system. Full article

We describe a family of paraxial and quasi-monochromatic optical wave packets with finite energy and smoothly shaped amplitude in space and time that develops a singularity in the intensity when spatio-temporally focused by imparting a converging spherical wavefront and a negative temporal chirp. This singular behavior upon ideal focusing is manifested in actual focusing with finite apertures and in media with high-order dispersion with “exploding” behavior featuring an indefinitely increasing concentration of the energy when opening the aperture radius, thus exercising continuous control on the focal intensity and spatial and temporal resolution. These wave packets offer a new way of focusing that outperforms what can be achieved with standard Gaussian wave packets in terms of focal intensity and resolution, providing new possibilities in applications where energy concentration and its control are crucial. Full article

Hyperfine structure constants have many applications, but are often hard to calculate accurately due to large and canceling contributions from different terms of the hyperfine interaction operator, and also from different closed and spherically symmetric core subshells that break up due to electron correlation effects. In multiconfiguration calculations, the wave functions are expanded in terms of configuration state functions (CSFs) built from sets of one-electron orbitals. The orbital sets are typically enlarged within the layer-by-layer approach. The calculations are energy-driven, and orbitals in each new layer of correlation orbitals are spatially localized in regions where the weighted total energy decreases the most, overlapping and breaking up different closed core subshells in an irregular pattern. As a result, hyperfine structure constants, computed as expectation values of the hyperfine operators, often show irregular or oscillating convergence patterns. Large orbital sets, and associated large CSF expansions, are needed to obtain converged values of the hyperfine structure constants. We analyze the situation for the states of the $\{2s^{2}2p^3,2s^{2}2p^{2}3p,2s^{2}2p^{2}4p\}$ odd and $\{2s^{2}2p^{2}3s,2s2p^4,2s^{2}2p^{2}4s,2s^{2}2p^{2}3d\}$ even configurations in N I, and show that the convergence with respect to the increasing sets of orbitals is radically improved by introducing separately optimized orbital sets targeted for describing the spin- and orbital-polarization effects of the $1s$ and $2s$ core subshells that are merged with, and orthogonalized against, the ordinary energy-optimized orbitals. In the layer-by-layer approach, the spectroscopic orbitals are kept frozen from the initial calculation and are not allowed to relax in response to the introduced layers of correlation orbitals. To compensate for this lack of variational freedom, the orbitals are transformed to natural orbitals prior to the final calculation based on single and double substitutions from an increased multireference set. The use of natural orbitals has an important impact on the states of the $2s^{2}2p^{2}3s$ configuration, bringing the corresponding hyperfine interaction constants in closer agreement with experiment. Relying on recent progress in methodology, the multiconfiguration calculations are based on configuration state function generators, cutting down the time for spin-angular integration by factors of up to 50, compared to ordinary calculations. Full article

We present a new explicit quasi-Lagrangian integration scheme with the three-dimensional cubic spline function transform (transform = fitting + interpolation, referred to as the “spline format”) on a spherical quasi-uniform longitude–latitude grid. It is a consistent longitude–latitude grid, and to verify the feasibility, accuracy, convergence, and stability of the spline format interpolation scheme for the upstream point on the longitude–latitude grid, which may map a quasi-uniform longitude–latitude grid, a set of ideal, exact test schemes is adopted, which are recognized and proven to be effective internationally. The equilibrium flow test, cross-polar flow test, and Rossby–Haurwitz wave test are used to illustrate the spline scheme uniformity to the linear scheme and to overcome the over-dense grid in the polar region and the non-singularity of the poles. The cross-polar flow test demonstrates that the geostrophic wind crosses the polar area correctly, including the South Pole and North Pole. A non-hydrostatic, fully compressible dynamic core is used to complete the density flow test, demonstrating the existence of a time-varying reference atmosphere and that the spline format can simulate highly nonlinear fine-scale transient flows. It can be compared for the two results of the density flow test between the solution with the spline format and the benchmark reference solution with the linear format. Based on the findings, the non-hydrostatic dynamic core with the spline format is recommended for adoption. When simulated for the flow over an ideal mountain, through the “topographic gravity wave test”, the bicubic surface terrain and terrain-following height coordinates, time-split integration, and vector discrete decomposition can be derived successfully. These may serve as the foundations for a global, unified spline-format numerical model in the future. Full article

The Richards–Wolf formulas not only adequately describe a light field at a tight focus, but also make it possible to describe a light field immediately behind an ideal spherical lens, that is, on a converging spherical wave front. Knowing all projections of light field strength vectors behind the lens, the longitudinal components of spin and orbital angular momenta (SAM and OAM) can be found. In this case, the longitudinal projection of the SAM immediately behind the lens either remains zero or decreases. This means that the Spin–Orbital Conversion (SOC) effect where part of the “spin goes into orbit” takes place immediately behind the lens. And the sum of longitudinal projections of SAM and OAM is preserved. As for the spin Hall effect, it does not form right behind the lens, but appears as focusing occurs. That is, there is no Hall effect immediately behind the lens, but it is maximum at the focus. This happens because two optical vortices with topological charges (TCs) 2 and −2 and with spins of different signs (with left and right circular polarization) are formed right behind the lens. However, the total spin is zero since amplitudes of these vortices are the same. The amplitude of optical vortices becomes different while focusing and at the focus itself, and therefore regions with spins of different signs (Hall effect) appear. A general form of initial light fields which longitudinal field component is zero at the focus was found. In this case, the SAM vector can only have a longitudinal component that is nonzero. The SAM vector elongated only along the optical axis at the focus is used in magnetization task. Full article

The focus of this work is to determine at which threshold can the results for both plane and spherical wave incidence assumptions either converge or deviate when performing multiple diffraction attenuation calculations. The analysis has been carried out—for various millimeter-wave frequencies, inter-obstacle spacings, and angles of incidence—by employing a pair of two-dimensional (2D) hybrid formulations based on both the uniform theory of diffraction and physical optics (UTD-PO). This way, we seek to demonstrate under which circumstances each wave incidence assumption can be valid in environments that entail millimeter-wave bands. Based on this, we may ensure the minimum necessary distance from the transmitter to the first diffracting obstacle for the convergence of the spherical wave incidence solution onto that of the plane wave with a relative error below 0.1%. Our results demonstrate that for less than four diffracting elements, the minimum necessary distance engages in quasi-linear behavior under variations in both the angle of incidence and obstacle spacing. Notably, the considered frequencies (60–100 GHz) have almost no bearing on the results. Our findings will facilitate the simplified, more accurate and realistic planning of millimeter-wave radio communication systems, with multiple diffractions across various obstacles. Full article

The controlled source extremely low frequency (CSELF) method bears the potential for deep resource exploitation utilizing the skywave. The “Skywave” denotes the electromagnetic wave propagating through the waveguide formed by the Earth and ionosphere. It has a considerable penetration depth into the lithosphere due to its low-frequency band. Previous research on extremely low-frequency electromagnetic fields with the coupled lithosphere, atmosphere, and planar ionosphere models ignored the effect of the Earth’s curvature. Thus, we aimed to present the exact formulas for horizontal electric dipoles (HED) in a spherical “Earth-ionosphere” model. These new formulas consider the Earth’s curvature as a multilayer medium rather than a homogeneous underground. We introduce three techniques: function combination pairs, addition and subtraction terms, and Padé approximants, to handle slow convergence in numerical calculation. In the spherical waveguide, electromagnetic fields are mutually interfered with and produce oscillations, which is different from the planar model. The influence of Earth’s curvature cannot be neglected with the increase in source–receiver distance, though it is negligible within 3000 km. Furthermore, it is worth noting that apparent resistivity ρ_θφ enters the waveguide area earlier than ρ_φθ. This method can be used as Green’s function to simulate the electromagnetic field of actual antennas and 3-D models. Full article

In the framework of Generalized Lorenz–Mie theory (GLMT), based on the expansion results of electromagnetic field radiation components of Bessel pincer light sheets beam acting on dielectric particles of arbitrary size, the expression of radiation force components in a Cartesian coordinate system is obtained by using the Maxwell stress tensor method. On the one hand, the effects of the refractive index and the equivalent radius of spherical particles on the distribution of radiation force are discussed; On the other hand, the influence of beam scaling parameter and beam order of Bessel pincer light sheets beam on the distribution of radiation force are investigated. The results indicate that the changes of particle’s refractive index and effective radius only affect the distribution of radiation force. However, the beam scaling parameter and beam order of Bessel pincer light sheets beam have a very sharp impact on the convergence position, distribution range and bending degree far away from the wave source of the radiation force. Single-beam optical tweezers using the self-focusing and self-bending Bessel pincer light-sheets beam are crucial for applications such as single molecule biophysics, optical manipulation and particle separation/clearing. Full article

The aspheric light emitted from a pinhole restrains the reconstruction quality of a digital in-line hologram. Herein, the Fresnel-diffracted spot from the first step converging spherical wave diffracted at a rough circular aperture is collimated and expanded to generate an even plane wave, which is converged again by an objective lens and matching a minimum aperture while the central spot is varying from light to dark. We observed that the collected background hologram is filled with a round spot with high contrast as an ideal spherical wave. The resolution board and biology experimental results demonstrated a distinctively reconstructed image without any image processing in a single exposure. The adjustable field of view and magnification, single exposure, and noncontact make it suitable for an online microscope. Full article

Despite the high capital requirements, offshore wind and wave energy integrated stations (WWS) are an emerging and potential solution to optimize efficiency in renewable energy development. Decisions about installation location significantly influence their efficiency. This study examines and determines highly efficient and sustainable locations based on quantitative indicators and qualitative criteria. For this purpose, a novel dual-side behavioral spherical fuzzy multi-criteria decision-making (MCDM) approach was developed and applied for the case study of Vietnam. In the first stage, the behavioral Data Envelopment Analysis (B-DEA) model, constructed based on prospect theory, is applied to analyze locations according to quantitative indicators under decision makers’ psychological behavior consideration. In the second stage, a spherical fuzzy extension of the integration composed of the DEMATEL (decision-making trial and evaluation laboratory) and the EDAS (evaluation based on distance from average solution) methods helped to evaluate the locations. Based on the convergence in qualitative and quantitative analysis results, efficiency–sustainability positioning maps are established. The research provides recommendations for appropriate WWS locations from that visualization. The research compared findings with current development projects, plans, and policies in Vietnam for validation. Full article

The excitation cross-sections of the nS states of atomic hydrogen, n = 2 to 6, by electron impact on the ground state of atomic hydrogen were calculated using the variational polarized-orbital method at various incident electron energies in the range 10 to 122 eV. Converged excitation cross-sections were obtained using sixteen partial waves (L = 0 to 15). Excitation cross-sections to 2S state, calculated earlier, were calculated at higher energies than before. Results obtained using the hybrid theory (variational polarized orbital method) are compared to those obtained using other approaches such as the Born–Oppenheimer, close-coupling, R-matrix, and complex-exterior scaling methods using only the spherical symmetric wave functions. Phase shifts and elastic cross-sections are given at various energies and angular momenta. Excitation rate coefficients were calculated at various electron temperatures, which are required for plasma diagnostics in solar and astrophysics to infer plasma parameters. Excitation cross-sections are compared with those obtained by positron impact excitation. Full article

An analysis of multiple scattering by two Perfect Electric Conducting (PEC) spheres using translation Addition Theorem (AT) for spherical vector wave functions is presented. Specifically, the Cruzan formalism is used to represent the AT for spherical harmonics, which introduces the translation coefficients for transformation of spherical harmonics from one coordinate to another. The adoption of these coefficients with the use of two PEC spheres in a near zone region makes the calculation of multiple scattering electric fields very efficient. As an illustration, the mathematical formation using advanced computational approaches was inspected. Then, the generic truncation criteria in the scattered electric field by two PEC spheres was deeply investigated using translation AT. However, the numerical validation was obtained using Comsol simulation software. This approach will allow to evaluate the scattering from macro-structures composed of spherical particles, i.e., biological molecules, clouds of airborne particles, etc. An original and fully general solution to the problem using vector quantities is introduced, and the convergence of the solution in several numerical examples is also demonstrated. This approach takes into account the effect of multiple scattering by two PEC spheres for spherical vector function. Full article

Ocean modeling and simulation are important for understanding the dynamic processes in the geophysical system, and the simulation of tidal dynamics is of great significance for understanding the dynamic evolution of the ocean. However, there are some problems in existing simulations, including lack of specific standards to produce a desirable discrete spherical mesh for global ocean modelling. Many global ocean numerical models based on conventional longitude-latitude (LL) coordinates suffer from the “pole problem” in regions adjacent to the North Pole due to the convergence of meridians, which seriously hinders global ocean simulations. In this paper, a new longitude-latitude spherical grid coupled with rotated coordinate mapping is proposed to overcome the problem. In the design of the numerical model, for spatial approximation, the finite volume method on staggered C grid is proposed to solve the two-dimensional tidal wave equations for the global ocean. For temporal integration, the third-order Adams-Bashforth method is used to explicitly extrapolate the value on the next time interval half layer, and then the fourth-order implicit Adams-Moulton method is used to correct the water level. Finally, the constructed model is used to simulate the dynamics of two-dimensional tidal waves in the global ocean, and the co-tidal maps of two major diurnal tide and semidiurnal tide components are shown. The results demonstrate that the proposed model can support the simulation of tidal dynamics in the global ocean, especially for the Arctic Ocean. Full article

Spiral pattern is formed for coaxial interference between two vortex beams with different radii of wavefront curvatures and different topological charges (TCs). A theoretical model considering various parameters (such as phase difference, radius of wavefront curvature, and TCs) is established to predict all kinds of interference patterns. An improved Mach-Zehnder interferometer is set up in an experiment to generate different kinds of spiral patterns and verify the theoretical model. The number of spiral lobes is determined by the absolute value of TCs’ difference between two vortex beams, and the twist direction relates to the sign of TCs’ difference and the difference of reciprocals for the radii of wavefront curvature, clockwise for the same sign, and counterclockwise for the opposite signs. The twist direction of the spiral pattern reverses and the lobes direction near the core of the pattern changes obviously when the spherical wave changes from convergence to divergence. Full article