Search Results (39)

Landslide deformation monitoring plays a critical role in geohazard prevention and risk mitigation in mountainous regions, where timely and reliable deformation information is essential for early warning and disaster management. Monitoring landslide deformation in mountainous areas remains a persistent challenge, largely due to rugged topography, dense vegetation cover, and low interferometric coherence—factors that substantially limit the effectiveness of conventional InSAR methods. To address these issues, this study aims to develop a robust time-series InSAR framework for enhancing deformation detection and measurement density under low-coherence conditions in complex mountainous terrain, and accordingly introduces the Sequential Estimation and Total Power-Enhanced Expectation–Maximization Inversion (SETP-EMI) approach, which integrates dual-polarization Sentinel-1 SAR time series within a recursive estimation framework, augmented by polarimetric coherence optimization. This methodology allows for dynamic assimilation of SAR data, improves phase quality under low-coherence conditions, and enhances the extraction of distributed scatterers (DS). When applied to Zhenxiong County, Yunnan Province—a region prone to geohazards with complex terrain—the SETP-EMI method achieved a landslide detection rate of 94.1%. It also generated approximately 2.49 million measurement points, surpassing PS-InSAR and SBAS-InSAR results by factors of 22.5 and 3.2, respectively. Validation against ground-based leveling data confirmed the method’s high accuracy and robustness, yielding a standard deviation of 5.21 mm/year. This study demonstrates that the SETP-EMI method, integrated within a DS-InSAR framework, effectively overcomes coherence loss in densely vegetated plateau regions, improving landslide monitoring and early-warning capabilities in complex mountainous terrain. Full article

The nonlinear Schrödinger equation is a classical nonlinear evolution equation with wide applications. This paper explores the asymptotic behavior of solutions to the nonlinear Schrödinger equation with non-zero boundary conditions in the presence of a pair of second-order discrete spectra. We analyze the Riemann–Hilbert problem in the inverse scattering transform by the Deift–Zhou nonlinear steepest descent method. Then we propose a proper deformation to deal with the growing time term and give the conditions for the series in the process of deformation by the Laurent expansion. Finally, we provide the characterization of the interactions between the solitary waves corresponding to second-order discrete spectra and the coherent oscillations produced by the perturbation. Numerical verifications are also performed. Full article

The effects of Ge⁴⁺ substitution on the microwave dielectric properties of inverse spinel Mg₂SnO₄ ceramics were systematically investigated. A series of Mg₂(Sn_1−xGe_x)O₄ (x = 0.00–0.05) ceramics were synthesized via solid-state reaction and sintered at 1450–1600 °C. X-ray diffraction confirmed single-phase inverse spinel structures (Fd-3 m) for compositions up to x = 0.03, while minor MgSnO₃ secondary phases appeared at x = 0.05. Rietveld refinement revealed a linear decrease in lattice parameter from 8.6579 Å (x = 0) to 8.6325 Å (x = 0.05), consistent with Vegard’s law for the substitution of smaller Ge⁴⁺ (0.53 Å, Shannon ionic radius, octahedral coordination) for Sn⁴⁺ (0.69 Å, Shannon ionic radius, octahedral coordination) in octahedral sites. Optimal dielectric properties were achieved at x = 0.03 sintered at 1550 °C; the dielectric constant (ε_r) increased from 7.6 to 8.0, while the quality factor (Qf) improved by 19% from 56,200 to 67,000 GHz, which is attributed to reduced phonon scattering from Ge-induced lattice contraction. The temperature coefficient of resonant frequency (τ_f) remained stable (−64 to −68 ppm/°C) across all compositions. Property degradation at x = 0.05 correlated with the onset of Ge⁴⁺ solubility limit and MgSnO₃ formation. These results demonstrate that controlled Ge⁴⁺ substitution effectively enhances the microwave dielectric performance of Mg₂SnO₄ ceramics for communication applications. Full article

In the development of quantum mechanics in the 1920s, both matrix mechanics (developed by Born, Heisenberg and Jordon) and wave mechanics (developed by Schrödinger) prevailed. These early attempts corresponded to the quantum mechanics of particles. Matrix mechanics was found to lead directly to the Schrödinger equation, and the Schrödinger equation could be used to derive the alternative problem for matrix mechanics. Later emphasis lay on the development of the dynamics of fields, where the classical field equations were quantized (see, for example, Weinberg). Today, quantum field theory is one of the most successful physical theories ever developed. The symmetry between particle and wave mechanics is exploited herein. One of the important properties of quantum mechanics is that it is linear, leading to some confusion about how to treat the problem of nonlinear classical field equations. In the present paper we address the case of classical nonlinear soliton equations which are exactly integrable in terms of the periodic/quasiperiodic inverse scattering transform. This means that all physical spectral solutions of the soliton equations can be computed exactly for these specific boundary conditions. Unfortunately, such solutions are highly nonlinear, leading to difficulties in solving the associated quantum mechanical problems. Here we find a strategy for developing the quantum mechanical solutions for soliton dynamics. To address this difficulty, we apply a recently derived result for soliton equations, i.e., that all solutions can be written as quasiperiodic Fourier series. This means that soliton equations, in spite of their nonlinear solutions, are perfectly linearizable with quasiperiodic boundary conditions, the topic of finite gap theory, i.e., the inverse scattering transform with periodic/quasiperiodic boundary conditions. We then invoke the result that soliton equations are Hamiltonian, and we are able to show that the generalized coordinates and momenta also have quasiperiodic Fourier series, a generalized linear superposition law, which is valid in the case of nonlinear, integrable classical dynamics and is here extended to quantum mechanics. Hamiltonian dynamics with the quasiperiodicity of inverse scattering theory thus leads to matrix mechanics. This completes the main theme of our paper, i.e., that classical, nonlinear soliton field equations, linearizable with quasiperiodic Fourier series, can always be quantized in terms of matrix mechanics. Thus, the solitons and their nonlinear interactions are given an explicit description in quantum mechanics. Future work will be formulated in terms of the associated Schrödinger equation. Full article

We address the inverse spectral problem for a PT-symmetric Dirac operator with discontinuity conditions imposed along the entire real axis—a configuration that has not been explicitly solved in prior literature. Our approach constructs fundamental solutions via convergent recursive series expansions and establishes their linear independence through a constant Wronskian. We derive explicit formulas for transmission and reflection coefficients, assemble them into a PT-symmetric scattering matrix, and demonstrate how both spectral and scattering data uniquely determine the underlying complex-valued, discontinuous potentials. Unlike classical treatments, which assume smoothness or limited discontinuities, our framework handles full-axis discontinuities within a non-Hermitian setting, proving uniqueness and providing a constructive recovery algorithm. This method not only generalizes existing inverse scattering theory to PT-symmetric discontinuous operators but also offers direct applicability to optical waveguides, metamaterials, and quantum field models where gain–loss mechanisms and zero-width resonances are critical. Full article

In this study, we investigate the application of the direct sampling method (DSM) to identify small dielectric objects in a limited-aperture inverse scattering problem. Unlike previous studies, we consider the bistatic measurement configuration corresponding to the transmitter location and design indicator functions for both a single source and multiple sources, and we convert the unknown measurement data to a fixed nonzero constant. To explain the applicability and limitation of object detection, we demonstrate that the indicator functions can be expressed by an infinite series of Bessel functions, the material properties of the objects, the bistatic angle, and the converted constant. Based on the theoretical results, we explain how the imaging performance of the DSM is influenced by the bistatic angle and the converted constant. In addition, the results of our analyses demonstrate that a smaller bistatic angle enhances the imaging accuracy and that optimal selection of the converted constant is crucial to realize reliable object detection. The results of the numerical simulations obtained using a two-dimensional Fresnel dataset validate the theoretical findings and illustrate the effectiveness and limitations of the designed indicator functions for small objects. Full article

Multi-angle remote sensing observations play an important role in the remote sensing of solar radiation absorbed by land surfaces. Currently, the Moderate Resolution Imaging Spectroradiometer (MODIS) and Visible Infrared Imaging Radiometer Suite (VIIRS) teams have successively applied the Ross–Li kernel-driven bidirectional reflectance distribution function (BRDF) model to integrate multi-angle observations to produce long time series BRDF model parameter products (MCD43 and VNP43), which can be used for the inversion of various surface parameters and the angle correction of remote sensing data. Even though the MODIS and VIIRS BRDF products originate from sensors and algorithms with similar designs, the consistency between BRDF parameters for different sensors is still unknown, and this likely affects the consistency and accuracy of various downstream parameter inversions. In this study, we applied BRDF model parameter time-series data from the overlapping period of the MODIS and VIIRS services to systematically analyze the temporal and spatial differences between the BRDF parameters and derived indices of the two sensors from the site scale to the region scale in the red band and NIR band, respectively. Then, we analyzed the sensitivity of the BRDF parameters to variations in Normalized Difference Hotspot–Darkspot (NDHD) and examined the spatiotemporal distribution of zero-valued pixels in the BRDF parameter products generated by the constraint method in the Ross–Li model from both sensors, assessing their potential impact on NDHD derivation. The results confirm that among the three BRDF parameters, the isotropic scattering parameters of MODIS and VIIRS are more consistent, whereas the volumetric and geometric-optical scattering parameters are more sensitive and variable; this performance is more pronounced in the red band. The indices derived from the MODIS and VIIRS BRDF parameters were compared, revealing increasing discrepancies between the albedo and typical directional reflectance and the NDHD. The isotropic scattering parameter and the volumetric scattering parameter show responses that are very sensitive to increases in the equal interval of the NDHD, indicating that the differences between the MODIS and VIIRS products may strongly influence the consistency of NDHD estimation. In addition, both MODIS and VIIRS have a large proportion of zero-valued pixels (volumetric and geometric-optical parameter layers), whereas the spatiotemporal distribution of zero-valued pixels in VIIRS is more widespread. While the zero-valued pixels have a minor influence on reflectance and albedo estimation, such pixels should be considered with attention to the estimation accuracy of the vegetation angular index, which relies heavily on anisotropic characteristics, e.g., the NDHD. This study reveals the need in optimizing the Clumping Index (CI)-NDHD algorithm to produce VIIRS CI product and highlights the importance of considering BRDF product quality flags for users in their specific applications. The method used in this study also helps improve the theoretical framework for cross-sensor product consistency assessment and clarify the uncertainty in high-precision ecological monitoring and various remote sensing applications. Full article

A bi-Gamma distribution model is proposed to determine the probability density function (PDF) of broadband non-Gaussian random stress rainflow ranges during vibration fatigue. A series of stress Power Spectral Densities (PSD) are provided, and the corresponding Gaussian random stress time histories are generated using the inverse Fourier transform and time-domain randomization methods. These Gaussian random stress time histories are then transformed into non-Gaussian random stress time histories. The probability density values of the stress ranges are obtained using the rainflow counting method, and then the bi-Gamma distribution PDF model is fitted to these values to determine the model’s parameters. The PSD parameters and the kurtosis, along with their corresponding model parameters, constitute the neural network input–output dataset. The neural network model established after training can directly provide the parameter values of the bi-Gamma model based on the input PSD parameters and kurtosis, thereby obtaining the PDF of the stress rainflow ranges. The predictive capability of the neural network model is verified and the effects of non-Gaussian random stress with different kurtosis on the structural fatigue life are compared for the same stress PSD. And all life predicted results were within the second scatter band. Full article

As more and more numerical and analytical solutions to the linear neutron transport equation become available, verification of the numerical results becomes increasingly important. This presentation concerns the development of another benchmark for the linear neutron transport equation in a benchmark series, each employing a different method of solution. In 1D, there are numerous ways of analytically solving the monoenergetic transport equation, such as the Wiener–Hopf method, based on the analyticity of the solution, the method of singular eigenfunctions, inversion of the Laplace and Fourier transform solutions, and analytical discrete ordinates in the limit, which is arguably one of the most straightforward, to name a few. Another potential method is the PN (Legendre polynomial order N) method, where one expands the solution in terms of full-range orthogonal Legendre polynomials, and with orthogonality and series truncation, the moments form an open set of first-order ODEs. Because of the half-range boundary conditions for incoming particles, however, full-range Legendre expansions are inaccurate near material discontinuities. For this reason, a double PN (DPN) expansion in half-range Legendre polynomials is more appropriate, where one separately expands incoming and exiting flux distributions to preserve the discontinuity at material interfaces. Here, we propose and demonstrate a new method of solution for the DPN equations for an isotropically scattering medium. In comparison to a well-established fully analytical response matrix/discrete ordinate solution (RM/DOM) benchmark using an entirely different method of solution for a non-absorbing 1 mfp thick slab with both isotropic and beam sources, the DPN algorithm achieves nearly 8- and 7-place precision, respectively. Full article

The Bessel function of the first kind $J_N\left(kx\right)$ is expanded in a Fourier–Legendre series, as is the modified Bessel function of the first kind $I_N\left(kx\right)$. The purpose of these expansions in Legendre polynomials was not an attempt to rival established numerical methods for calculating Bessel functions but to provide a form for $J_N\left(kx\right)$ useful for analytical work in the area of strong laser fields, where analytical integration over scattering angles is essential. Despite their primary purpose, one can easily truncate the series at 21 terms to provide 33-digit accuracy that matches the IEEE extended precision in some compilers. The analytical theme is furthered by showing that infinite series of like-powered contributors (involving ${ }_1{F}_2$ hypergeometric functions) extracted from the Fourier–Legendre series may be summed, having values that are inverse powers of the eight primes $1/\left(2^i{3}^j{5}^k{7}^l{11}^m{13}^n{17}^o{19}^p\right)$ multiplying powers of the coefficient k. Full article

The versatile Generalized Retrieval of Aerosol and Surface Properties (GRASP) algorithm exploits the advantages of synergic ground-based aerosol observations such as radiometric (sensitive to columnar aerosol optical and microphysical properties) and lidar (sensitive to vertical distribution of the optical properties) observations. The synergy is possible when the complementary data is mutually constrained by GRASP parametrization that includes, for the first time ever, the degree of linear polarization (DoLP) parameter measured by a polarized sun-sky-lunar AERONET photometer (380, 440, 500, 675, 870, 1020, and 1640 nm) in synergy with the vertical profiles from an elastic lidar (355, 532, and 1064 nm). First, a series of numerical tests is performed using simulated data generated using a climatology of data and ground-based measurements. The inversions are performed with and without random noise for five different combinations of input data, starting from the AERONET-like dataset and increasing to the complex one by adding more information for three aerosol scenarios: I—high aerosol optical depth (AOD) with dominant coarse mode; II—low AOD with dominant coarse mode; III—high AOD with dominant fine mode. The inclusion of DoLP improves (i) the retrieval accuracy of the fine-mode properties when it is not dominant; (ii) the retrieval accuracy of the coarse-mode properties at longer wavelengths and that of the fine-mode properties at shorter wavelengths; (iii) the retrieval accuracy of the coarse-mode real part of the refractive index (up to 36% reduction), but has no effect on the retrieval of the imaginary part; (iv) reduces up to 83% the bias of the sphere fraction (SF) retrieval in coarse-mode dominated regimes; and (v) the root mean square error (RMSE) of the retrieval for most of the parameters in all scenarios. In addition, the addition of more photometer channels in synergy with a three-wavelength elastic lidar reduces the RMSE for the real part (67% in the coarse mode) and the imaginary part (35% in the fine mode) of the refractive index, the single scattering albedo (38% in the fine mode), the lidar ratio (20% in the coarse mode), and the SF (43%). Full article

In this paper, an approach to solving direct and inverse scattering problems on the half-line for a one-dimensional Schrödinger equation with a complex-valued potential that is exponentially decreasing at infinity is developed. It is based on a power series representation of the Jost solution in a unit disk of a complex variable related to the spectral parameter by a Möbius transformation. This representation leads to an efficient method of solving the corresponding direct scattering problem for a given potential, while the solution to the inverse problem is reduced to the computation of the first coefficient of the power series from a system of linear algebraic equations. The approach to solving these direct and inverse scattering problems is illustrated by several explicit examples and numerical testing. Full article

In linear inverse scattering, the performance of the imaging system is sometimes evaluated in terms of its resolution, i.e., its capability to reconstruct a point-like scatterer. However, there is still a lack of analytical studies on the achievable resolution. To address this, we consider the point spread function (PSF) evaluation of the scattered near field for the single frequency and multi-view/multi-static case in homogeneous medium. Instead of numerically computing the PSF, we propose and discuss an approximate closed form under series expansions according to the angular ranges of both source and receiver location. In order to assess the effectiveness of the proposed approximation, we consider two cases including both full and limited view angles for the incident field and observation ranges. In addition, we provide a localization application to show the usefulness of the theoretical discussion. Numerical results confirmed the analytical investigations. Full article

Tunneling work, including the construction of municipal tunnels and metro lines, may disturb the structural health of aging buildings in densely built urban areas. Deformation monitoring and risk assessments of aging buildings are crucial to mitigate incidents and prevent losses of people’s lives and properties. Time-series InSAR reveals spatio-temporal information about observed targets by extracting persistent scatterers of the structures, which can achieve the wide-range monitoring of buildings and infrastructure. However, solely relying on InSAR-derived general parameters (deformation rates and time series of specific points) cannot objectively assess the safety conditions of buildings. To address this issue, this study proposes an InSAR Nonuniform Settlement Index. First, the point targets of buildings are extracted through time-series InSAR processing. Then, using the points as inputs, the Nonuniform Settlement Index calculates the 3D settlement plane and the inclination angle of the plane corresponding to each building. In this way, the proposed Nonuniform Settlement Index acts as a subsequent analysis method of time-series InSAR to characterize the safety statuses of buildings. In our study, 147 scenes of COSMO-SkyMed images from 2013 to 2022 were used to inverse the nine-year deformation evolution of the tested area. After time-series InSAR processing and index analysis based on the above SAR datasets, cross-validation was implemented with static-level and manual investigation data. The approach was to use one aging, collapsed building affected by tunneling work, as well as the eight adjacent aging buildings. The results showed high consistency with the in situ data, which proves the efficiency of the proposed approach. Full article

Internal multiple prediction remains a high-priority problem in seismic data processing, such as subsurface imaging and quantitative amplitude analysis and inversion, particularly in the common-midpoint (CMP) gathers, which contain multicoverage reflection information of the subsurface. Internal multiples, generated by unknown reflectors in complex environments, can be reconstructed with certain combinations of seismic reflection events using the inverse scattering series internal multiple prediction algorithm, which is usually applied to shot records in source–receiver coordinates. The computational overhead is one of the major challenges limiting the strength of the multidimensional implementation of the prediction algorithm, even in the coupled plane-wave domain. In this paper, we first comprehensively review the plane-wave domain inverse scattering series internal multiple prediction algorithm, and we propose a new scheme of achieving 2D multiple attenuation using a 1.5D prediction algorithm in the CMP domain, which significantly reduces the computational burden. Moreover, we quantify the difference in behavior of the 1.5D prediction algorithm for the shot/receiver and the CMP gathers on tilted strata. Numerical analysis of prediction errors shows that the 1.5D algorithm is more capable of handling dipping generators in the CMP domain than in the shot/receiver gathers, and it is able to predict the accredited traveltimes of internal multiples caused by dipping reflectors with small inclinations. For more complex cases with large inclination, using the 1.5D prediction algorithm, internal multiple predictions fail both in the CMP domain and in the shot/receiver gathers, which require the full 2D prediction algorithm. To attenuate internal multiples in the CMP gathers generated by large-dipping strata, a modified version is proposed based on the full 2D plane-wave domain internal multiple prediction algorithm. The results show that the traveltimes of internal multiples caused by dipping generators seen in the simple benchmark example are correctly predicted in the CMP domain using the modified 2D prediction algorithm. Full article