Exact Solution to the Scattering of Waves from a Rough Surface
Exact solution for scattering of arbitrary scalar wave from rough surface adapted to solution of Neumann and Dirichlet problems
NEUMANN PROBLEM↗
SEARCH · Search NASA
Results for “Solution scattering”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Backscattering from a Gaussian distributed, perfectly conducting, rough surface
The problem of scattering by random surfaces possessing many scales of roughness is analyzed. The approach is applicable to bistatic scattering from dielectric surfaces, however, this specific analysis is restricted to backscattering from a perfectly conducting surface in order to more clearly illustrate the method. The surface is assumed to be Gaussian distributed so that the surface height can be split into large and small scale components, relative to the electromagnetic wavelength. A first order perturbation approach is employed wherein the scattering solution for the large scale structure is perturbed by the small scale diffraction effects. The scattering from the large scale structure is treated via geometrical optics techniques. The effect of the large scale surface structure is shown to be equivalent to a convolution in k-space of the height spectrum with the following: the shadowing function, a polarization and surface slope dependent function, and a Gaussian factor resulting from the unperturbed geometrical optics solution. This solution provides a continuous transition between the near normal incidence geometrical optics and wide angle Bragg scattering results.
Brown, G. S.↗
Albedos of homogeneous semi-infinite canopies - Comparison of two-stream analytic and numerical solutions
The albedo of plant canopies is treated as a problem in radiative transfer. Albedos calcualted from an iterative multistream numerical model are compared with those calculated with an analytic two-stream solution. With the assumption of a randomly homogeneous distribution of leaf positions and orientations and isotropic scattering by individual leaves, the single-scattering albedo of the canopy can be found analytically. This single-scattering solution is incorporated into the two-stream solution and used to benchmark the multistream numerical model in the single-scattering limit. Relative errors so established in the multistream model are O(0.3 percent) or less. The two-stream model is also found to be remarkably accurate, with the error in multiply scattered radiation O(5 percent) or less, corresponding to absolute errors in visible albedo of less than 0.001 and near-infrared albedo of less than or equal to 0.01. Thus the two-stream model should be adequate for many purposes, such as climate modeling, provided the assumptions of homogeneous canopy and isotropic scattering are not too unrealistic.
Dickinson, Robert E.↗
Machine learning-assisted profiling of a kinked ladder polymer structure using scattering
Ladder polymers consisting of fused rings in the backbone have very limited conformational freedom, which results in very different properties from traditional linear polymers. However, accurately determining their size and chain conformations from solution scattering remains a challenge. Their chain conformations of kinked ladder polymers are largely governed by the structures and relative orientations or configurations of the repeat units, unlike conventional polymer chains whose bending angles between repeat units follow a unimodal Gaussian distribution. Meanwhile, traditional scattering models for polymer chains do not account for these unique structural features. This work introduces a novel approach that integrates machine learning with Monte Carlo simulations to construct a model that can describe the geometry of a type of kinked CANAL ladder polymers. We first develop a Monte Carlo simulation model for sampling the configuration space of CANAL ladder polymers, where each repeat unit is modeled as a biaxial segment. Then, we establish a machine learning-assisted scattering analysis framework based on Gaussian Process Regression. Finally, we conduct small-angle neutron scattering experiments on a CANAL ladder polymer solution to apply our approach. Our method uncovers structural features of such ladder polymers that conventional methods fail to capture.
Ding, Lijie [Oak Ridge National Laboratory (ORNL),↗
Parallel decomposition methods for the solution of electromagnetic scattering problems
This paper contains a overview of the methods used in decomposing solutions to scattering problems onto coarse-grained parallel processors. Initially, a short summary of relevant computer architecture is presented as background to the subsequent discussion. After the introduction of a programming model for problem decomposition, specific decompositions of finite difference time domain, finite element, and integral equation solutions to Maxwell's equations are presented. The paper concludes with an outline of possible software-assisted decomposition methods and a summary.
Cwik, Tom↗
Light transmission and reflection in perennially ice-covered Lake Hoare, Antarctica
We have investigated the transmission and albedo of the perennial ice cover on Lake Hoare, Antarctica. Our database consists of year-round measurements of the photosynthetically active radiation (400-700 nm) under the ice, measurements of the spatial variation of the under-ice light in midsummer, and spectrally resolved measurements from 400 to 700 nm of the albedo and transmission of the ice cover in early (November) and in midsummer (January). Our results show that the transmission decreases in the first part of summer, dropping by a factor of approximately 4 from November to January. We suggest that this is due to heating in the upper layers of the ice cover and the formation of Tyndall figures. Later in the summer when a significant liquid water fraction occurs within the ice cover, the transmission increases. In the fall when the ice cover freezes solid the transmission drops markedly. The spectrally resolved measurements from 400 to 700 nm show that approximately 2-5% of the incident light in this spectral region penetrates the 3.5-m thick ice cover. We have analyzed the spectral data using a two-stream scattering solution to the radiative transfer equation with three vertical layers in the ice cover. A surficial glaze of scattering ice 1 cm thick overlies a layer of sandy, bubbly ice about a meter thick, and below this is a thick layer of sand-free ice with bubbles. We find that the ice cover is virtually opaque at wavelengths longer than 800 nm. The net transmission of solar energy is approximately 2%. Significant changes in the thickness of the ice cover have been reported at Lake Hoare. These are due primarily to changes in the thickness of the bottom layer only. Because this layer is relatively clear, the effect on the transmission through the ice cover from these changes is less than would be predicted assuming a homogeneous ice cover.
Mckay, C. P.↗
Tracking structural solvent reorganization and recombination dynamics following e – photoabstraction from aqueous I – with femtosecond x-ray spectroscopy and scattering
Here we present a sub-picosecond resolved investigation of the structural solvent reorganization and geminate recombination dynamics following 400 nm two-photon excitation and photodetachment of a valence p electron from the aqueous atomic solute, I–(aq). The measurements utilized time-resolved X-ray Absorption Near Edge Structure (TR-XANES) spectroscopy and X-ray Solution Scattering (TR-XSS) at the Linac Coherent Light Source x-ray free electron laser in a laser pump/x-ray probe experiment. The XANES measurements around the L 1 -edge of the generated nascent iodine atoms (I 0 ) yield an average electron ejection distance from the iodine parent of 7.4 ± 1.5 Å with an excitation yield of about 1/3 of the 0.1M NaI aqueous solution. The kinetic traces of the XANES measurement are in agreement with a purely diffusion-driven geminate iodine–electron recombination model without the need for a long-lived (I 0 :e–) contact pair. Nonequilibrium classical molecular dynamics simulations indicate a delayed response of the caging H 2 O solvent shell and this is supported by the structural analysis of the XSS data: We identify a two-step process exhibiting a 0.1 ps delayed solvent shell reorganization time within the tight H-bond network and a 0.3 ps time constant for the mean iodine–oxygen distance changes. The results indicate that most of the reorganization can be explained classically by a transition from a hydrophilic cavity with a well-ordered first solvation shell (hydrogens pointing toward I–) to an expanded cavity around I 0 with a more random orientation of the H 2 O molecules in a broadened first solvation shell.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Theory of microwave remote sensing
Active and passive microwave remote sensing of earth terrains is studied. Electromagnetic wave scattering and emission from stratified media and rough surfaces are considered with particular application to the remote sensing of soil moisture. Radiative transfer theory for both the random and discrete scatterer models is examined. Vector radiative transfer equations for nonspherical particles are developed for both active and passive remote sensing. Single and multiple scattering solutions are illustrated with applications to remote sensing problems. Analytical wave theory using the Dyson and Bethe-Salpeter equations is employed to treat scattering by random media. The backscattering enhancement effects, strong permittivity fluctuation theory, and modified radiative transfer equations are addressed. The electromagnetic wave scattering from a dense distribution of discrete scatterers is studied. The effective propagation constants and backscattering coefficients are calculated and illustrated for dense media.
Tsang, L.↗
Structure and ultrafast dynamics of tri-nuclear Ag-/Tl–Pt 2 POP 4 complexes in solution
The energetics and dynamics of ion assembly in solution has broad influence in nanomaterials and inorganic synthesis. To investigate the fundamental processes involved, we present a time-resolved x-ray solution scattering (TR-XSS) study of the trinuclear silver and thallium complexes of the diplatinum ion PtPOP [Pt 2 (H 2 P 2 O 5 )$_4^{4−}$] in aqueous solution. These complexes, their structural properties, and their electronic structure are not well understood and afford a unique opportunity to study the metal–metal bond formation that influences molecular and material assembly in solution. We present model-independent analysis of the observed dynamics as well as an analysis incorporating time-resolved structural refinements of key bond lengths with $<$100 fs time resolution. We find that upon photoexcitation, the Pt atoms contract ∼0.25 Å toward the center of both the Ag- and the Tl-PtPOP complexes, as previously observed for the PtPOP anion. For the AgPtPOP system, an ultrafast Ag-Pt bond expansion of ∼0.2 Å is observed, whereas in contrast, the TlPtPOP system exhibits a Tl-Pt bond contraction of ∼0.3 Å upon photoexcitation. For both complexes, the change in electronic state leads to coherent (“wave-packet”) oscillations along the metal–Pt coordinates. Based on these structural dynamics, we propose an electronic structure model that describes the metal–metal bonding behavior in both the ground and excited state for both complexes.
Lenzen, Philipp [Technical Univ. of Denmark, Lyngb↗
BioXTAS RAW 2 : new developments for a free open-source program for small-angle scattering data reduction and analysis
BioXTAS RAW is a free open-source program for reduction, analysis and modelling of biological small-angle scattering data. Here, the new developments in RAW version 2 are described. These include improved data reduction using pyFAI ; updated automated Guinier fitting and D max finding algorithms; automated series ( e.g. size-exclusion chromatography coupled small-angle X-ray scattering or SEC-SAXS) buffer- and sample-region finding algorithms; linear and integral baseline correction for series; deconvolution of series data using regularized alternating least squares ( REGALS ); creation of electron-density reconstructions using electron density via solution scattering ( DENSS ); a comparison window showing residuals, ratios and statistical comparisons between profiles; and generation of PDF reports with summary plots and tables for all analysis. Furthermore, there is now a RAW API, which can be used without the graphical user interface (GUI), providing full access to all of the functionality found in the GUI. In addition to these new capabilities, RAW has undergone significant technical updates, such as adding Python 3 compatibility, and has entirely new documentation available both online and in the program.
97 MATHEMATICS AND COMPUTING↗
Vibrational wavepacket dynamics in Fe carbene photosensitizer determined with femtosecond X-ray emission and scattering
Abstract The non-equilibrium dynamics of electrons and nuclei govern the function of photoactive materials. Disentangling these dynamics remains a critical goal for understanding photoactive materials. Here we investigate the photoinduced dynamics of the [Fe(bmip) 2 ] 2+ photosensitizer, where bmip = 2,6-bis(3-methyl-imidazole-1-ylidine)-pyridine, with simultaneous femtosecond-resolution Fe Kα and Kβ X-ray emission spectroscopy (XES) and X-ray solution scattering (XSS). This measurement shows temporal oscillations in the XES and XSS difference signals with the same 278 fs period oscillation. These oscillations originate from an Fe-ligand stretching vibrational wavepacket on a triplet metal-centered ( 3 MC) excited state surface. This 3 MC state is populated with a 110 fs time constant by 40% of the excited molecules while the rest relax to a 3 MLCT excited state. The sensitivity of the Kα XES to molecular structure results from a 0.7% average Fe-ligand bond length shift between the 1 s and 2p core-ionized states surfaces.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Polarimetric signatures of a canopy of dielectric cylinders based on first and second order vector radiative transfer theory
Complete polarimetric signatures of a canopy of dielectric cylinders overlying a homogeneous half space are studied with the first and second order solutions of the vector radiative transfer theory. The vector radiative transfer equations contain a general nondiagonal extinction matrix and a phase matrix. The energy conservation issue is addressed by calculating the elements of the extinction matrix and the elements of the phase matrix in a manner that is consistent with energy conservation. Two methods are used. In the first method, the surface fields and the internal fields of the dielectric cylinder are calculated by using the fields of an infinite cylinder. The phase matrix is calculated and the extinction matrix is calculated by summing the absorption and scattering to ensure energy conservation. In the second method, the method of moments is used to calculate the elements of the extinction and phase matrices. The Mueller matrix based on the first order and second order multiple scattering solutions of the vector radiative transfer equation are calculated. Results from the two methods are compared. The vector radiative transfer equations, combined with the solution based on method of moments, obey both energy conservation and reciprocity. The polarimetric signatures, copolarized and depolarized return, degree of polarization, and phase differences are studied as a function of the orientation, sizes, and dielectric properties of the cylinders. It is shown that second order scattering is generally important for vegetation canopy at C band and can be important at L band for some cases.
Tsang, Leung↗
The Liquid Jet Endstation for Hard X-ray Scattering and Spectroscopy at the Linac Coherent Light Source
The ability to study chemical dynamics on ultrafast timescales has greatly advanced with the introduction of X-ray free electron lasers (XFELs) providing short pulses of intense X-rays tailored to probe atomic structure and electronic configuration. Fully exploiting the full potential of XFELs requires specialized experimental endstations along with the development of techniques and methods to successfully carry out experiments. The liquid jet endstation (LJE) at the Linac Coherent Light Source (LCLS) has been developed to study photochemistry and biochemistry in solution systems using a combination of X-ray solution scattering (XSS), X-ray absorption spectroscopy (XAS), and X-ray emission spectroscopy (XES). The pump–probe setup utilizes an optical laser to excite the sample, which is subsequently probed by a hard X-ray pulse to resolve structural and electronic dynamics at their intrinsic femtosecond timescales. The LJE ensures reliable sample delivery to the X-ray interaction point via various liquid jets, enabling rapid replenishment of thin samples with millimolar concentrations and low sample volumes at the 120 Hz repetition rate of the LCLS beam. This paper provides a detailed description of the LJE design and of the techniques it enables, with an emphasis on the diagnostics required for real-time monitoring of the liquid jet and on the spatiotemporal overlap methods used to optimize the signal. Additionally, various scientific examples are discussed, highlighting the versatility of the LJE.
EXAFS↗
Aqueous Zr/Hf IV ‐Oxo Cluster Speciation and Separation
Abstract Many industrial separations of chemically‐similar elements are achieved by solvent extraction, exploiting differences in speciation and solubility across aqueous‐organic interfaces. We recently identified [OM 4 (OH) 6 (SCN) 12 ] 4− (OM 4 , M=Zr/Hf IV ) tetrahedral oxoclusters as the main species in industrial processes that produce nuclear‐grade Zr and Hf from crude ore. However, isostructural/isoelectronic OM 4 ‐oxoclusters do not explain selective extraction of Hf into the organic phase. Here we have characterized heterometal Hf−Zr clusters in solution and the solid‐state yielding key information about their fundamentally different chemistry that engenders separation. Clusters prepared with both ammonium (industrial process) and tetramethylammonium counter cations revealed that 1) heterometal clusters (instead of a mixture of homometal clusters) assemble, and 2) Hf‐rich OM 4 selectively precipitates over Zr‐rich OM 4 , providing a separation process that does not require an organic extractant. Mass spectrometry, small‐angle X‐ray scattering, solution‐state 1 H nuclear magnetic resonance (NMR) spectroscopy, and solid‐state 17 O NMR evidence both mixed‐metal speciation and selective Hf‐precipitation. Raman spectroscopy suggests greater Zr‐ligand lability than Hf‐ligand lability, consistent with higher aqueous solubility of Zr‐rich clusters, enabling both extraction and precipitation‐based separation. Fundamentally, we also identify a key difference between these chemically similar elements that has enabled diversification of Zr‐polyoxocation chemistry over the last decade, while Hf‐polyoxocation chemistry lags.
Roseborough, Alexander [Department of Chemistry Or↗
INVESTIGATING THE FEASIBILITY AND STABILITY FOR MODELING ACOUSTIC WAVE SCATTERING USING A TIME-DOMAIN BOUNDARY INTEGRAL EQUATION WITH IMPEDANCE BOUNDARY CONDITION
Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet and environmentally friendly aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for aircraft noise reduction and are characterized by a frequency-dependent impedance. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering by geometric bodies treated with acoustic liners. This work considers using either an impedance or an admittance (inverse of impedance) boundary condition to allow for acoustic scattering problems to be modeled with geometries consisting of both un-lined and lined surfaces. Three acoustic liner models are discussed: the Extended Helmholtz Resonator Model, the Three-Parameter Impedance Model, and the Broadband Impedance Model. In both the Helmholtz and Three-Parameter models, liner impedance is specified at a given frequency, whereas the Broadband model allows for the investigation of multiple frequencies simultaneously. The impedance and admittance boundary conditions for acoustic liners are derived for each model and coupled with a time-domain boundary integral equation. The scattering solution is obtained iteratively using a boundary element method with constant spatial and third-order temporal basis functions. Time-domain boundary integral equations are unfortunately prone to numerical instabilities due to resonant frequencies resulting from non-trivial solutions in the interior domain. When reformulated with the Burton-Miller method, the instabilities are eliminated. Using a Burton-Miller reformulation, the stability of the boundary element method assuming a liner boundary condition is assessed using eigenvalue analysis. The stability of each liner model is discussed, and it is shown that the Three-Parameter and Broadband models are sufficient for modeling an acoustic liner on the surface of scattering bodies. The Helmholtz model demonstrates strict limitations for stability, whereas the Three-Parameter and Broadband models are stable for most cases. Also included in this work is an assessment of the spatial accuracy of the time-domain boundary element method with respect to the surface element basis functions, as well as a performance study of the numerical algorithm.
computational mathematics↗
Small-angle X-ray microdiffraction from fibrils embedded in tissue thin sections
Small-angle X-ray scattering (SAXS) from fibrils embedded in a fixed, thin section of tissue includes contributions from the fibrils, the polymeric matrix surrounding the fibrils, other constituents of the tissue, and cross-terms due to the spatial correlation between fibrils and neighboring molecules. This complex mixture severely limits the amount of information that can be extracted from scattering studies. However, availability of micro- and nano-beams has made the measurement of scattering from very small volumes possible, which, in some cases, may be dominated by a single fibrillar constituent. In such cases, information about the predominant species may be accessible. Nevertheless, even in these cases, the correlations between the positions of fibrils and other constituents have a significant impact on the observed scattering. Here, strategies are proposed to extract partial information about fibril structure and tissue organization on the basis of SAXS from samples of this type. It is shown that the spatial correlation function of the fibril in the direction perpendicular to the fibril axis can be computed and contains information about the predominant fibril structure and the organization of the surrounding tissue matrix. This has significant advantages over approaches based on techniques developed for X-ray solution scattering. Examples of correlation calculations in different types of samples are given to demonstrate the information that can be obtained from these measurements.
36 MATERIALS SCIENCE↗
A periodic moment method solution for TM scattering from lossy dielectric bodies with application to wedge absorber
The periodic moment method (PMM) solution for the scattering from two-dimensional lossy dielectric bodies is developed in this paper. The purpose is to design microwave wedge absorber for low reflectivity so that one can improve the performance of anechoic chamber measurements. With PMM, the reflection and transmission coefficients of periodically distributed bodies illuminated by a plane wave have been accurately calculated using a Cray Y-MP supercomputer. Through these studies, some wedge absorber configurations have been designed, fabricated, and then tested in the OSU/ESL compact range measurement facility. Two 8 in. commercial wedges, a curved wedge, and a four-layer wedge are studied in this paper. In all cases, good agreement between calculations and measurements has been obtained.
Yang, Chang-Fa↗
Fast emulation of quantum three-body scattering
Here, we develop a class of emulators for solving quantum three-body scattering problems. They are based on combining the variational method for scattering observables and the recently proposed eigenvector continuation concept. The emulators are first trained by the exact scattering solutions of the governing Hamiltonian at a small number of points in its parameter space, and then employed to make interpolations and extrapolations in that space. Through a schematic nuclear-physics model with finite-range two and three-body interactions, we demonstrate the emulators to be extremely accurate and efficient. The computing time for emulation is on the scale of milliseconds (on a laptop), with relative errors ranging from 10 –13 to 10 –4 depending on the case. The emulators also require little memory. We argue that these emulators can be generalized to even more challenging scattering problems. Furthermore, this general strategy may be applicable for building the same type of emulators in other fields, wherever variational methods can be developed for evaluating physical models.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗