A new look at photometry of the Moon

USGS Publications Warehouse

Goguen, J.D.; Stone, T.C.; Kieffer, H.H.; Buratti, B.J.

2010-01-01

We use ROLO photometry (Kieffer, H.H., Stone, T.C. [2005]. Astron. J. 129, 2887-2901) to characterize the before and after full Moon radiance variation for a typical highlands site and a typical mare site. Focusing on the phase angle range 45??. ) to calculate the scattering matrix and solve the radiative transfer equation for I/. F. The mean single scattering albedo is ??=0.808, the asymmetry parameter is ???cos. ?????=0.77 and the phase function is very strongly peaked in both the forward and backward scattering directions. The fit to the observations for the highland site is excellent and multiply scattered photons contribute 80% of I/. F. We conclude that either model, roughness or multiple scattering, can match the observations, but that the strongly anisotropic phase functions of realistic particles require rigorous calculation of many orders of scattering or spurious photometric roughness estimates are guaranteed. Our multiple scattering calculation is the first to combine: (1) a regolith model matched to the measured particle size distribution and index of refraction of the lunar soil, (2) a rigorous calculation of the particle phase function and solution of the radiative transfer equation, and (3) application to lunar photometry with absolute radiance calibration. ?? 2010 Elsevier Inc.

Backscattering from a randomly rough dielectric surface

NASA Technical Reports Server (NTRS)

Fung, Adrian K.; Li, Zongqian; Chen, K. S.

1992-01-01

A backscattering model for scattering from a randomly rough dielectric surface is developed based on an approximate solution of a pair of integral equations for the tangential surface fields. Both like and cross-polarized scattering coefficients are obtained. It is found that the like polarized scattering coefficients contain two types of terms: single scattering terms and multiple scattering terms. The single scattering terms in like polarized scattering are shown to reduce the first-order solutions derived from the small perturbation method when the roughness parameters satisfy the slightly rough conditions. When surface roughnesses are large but the surface slope is small, only a single scattering term corresponding to the standard Kirchhoff model is significant. If the surface slope is large, the multiple scattering term will also be significant. The cross-polarized backscattering coefficients satisfy reciprocity and contain only multiple scattering terms. The difference between vertical and horizontal scattering coefficients is found to increase with the dielectric constant and is generally smaller than that predicted by the first-order small perturbation model. Good agreements are obtained between this model and measurements from statistically known surfaces.

Multiple-scattering coefficients and absorption controlled diffusive processes

NASA Astrophysics Data System (ADS)

Godoy, Salvador; García-Colín, L. S.; Micenmacher, Victor

1999-11-01

Multiple-scattering transmission and reflection coefficients (T,R) are introduced in addition to the diffusion coefficient D for the description of ballistic diffusion in the presence of absorption. For 1D (one-dimensional) systems, the measurement of only one between T and D imposes restrictions on the possible values of the other. If D is measured, then T is bounded between the Landauer and Lambert-Beer equations. Measurements of both (T,D) imply the theoretical knowledge of the microscopic absorption Σa and scattering rΣs cross sections.

Calculation of the angular radiance distribution for a coupled atmosphere and canopy

NASA Technical Reports Server (NTRS)

Liang, Shunlin; Strahler, Alan H.

1993-01-01

The radiative transfer equations for a coupled atmosphere and canopy are solved numerically by an improved Gauss-Seidel iteration algorithm. The radiation field is decomposed into three components: unscattered sunlight, single scattering, and multiple scattering radiance for which the corresponding equations and boundary conditions are set up and their analytical or iterational solutions are explicitly derived. The classic Gauss-Seidel algorithm has been widely applied in atmospheric research. This is its first application for calculating the multiple scattering radiance of a coupled atmosphere and canopy. This algorithm enables us to obtain the internal radiation field as well as radiances at boundaries. Any form of bidirectional reflectance distribution function (BRDF) as a boundary condition can be easily incorporated into the iteration procedure. The hotspot effect of the canopy is accommodated by means of the modification of the extinction coefficients of upward single scattering radiation and unscattered sunlight using the formulation of Nilson and Kuusk. To reduce the computation for the case of large optical thickness, an improved iteration formula is derived to speed convergence. The upwelling radiances have been evaluated for different atmospheric conditions, leaf area index (LAI), leaf angle distribution (LAD), leaf size and so on. The formulation presented in this paper is also well suited to analyze the relative magnitude of multiple scattering radiance and single scattering radiance in both the visible and near infrared regions.

Depolarization and Scattering of Electromagnetic Waves. Appendices.

DTIC Science & Technology

1986-06-30

for both specular point scattering and Bragg scattering in a self-consistent manner is used to express the total cross section of the flake as a...by Arbitrarily Oriented Composite Rough Surfaces. In this work the full wave approach is used to determine the modu- lations of the like and cross...analyze multiple scattering using the equation of radiative transfer with the general Stokes’ parameters. Our ultimate goal is to develop codes which will

Some New Lidar Equations for Laser Pulses Scattered Back from Optically Thick Media Such as Clouds, Dense Aerosol Plumes, Sea Ice, Snow, and Turbid Coastal Waters

NASA Technical Reports Server (NTRS)

Davis, Anthony B.

2013-01-01

I survey the theoretical foundations of the slowly-but-surely emerging field of multiple scattering lidar, which has already found applications in atmospheric and cryospheric optics that I also discuss. In multiple scattering lidar, returned pulses are stretched far beyond recognition, and there is no longer a one-to-one connection between range and return-trip timing. Moreover, one can exploit the radial profile of the diffuse radiance field excited by the laser source that, by its very nature, is highly concentrated in space and collimated in direction. One needs, however, a new class of lidar equations to explore this new phenomenology. A very useful set is derived from radiative diffusion theory, which is found at the opposite asymptotic limit of radiative transfer theory than the conventional (single-scattering) limit used to derive the standard lidar equation. In particular, one can use it to show that, even if the simple time-of-flight-to-range connection is irretrievably lost, multiply-scattered lidar light can be used to restore a unique profiling capability with coarser resolution but much deeper penetration into a wide variety of optical thick media in nature. Several new applications are proposed, including a laser bathymetry technique that should work for highly turbid coastal waters.

Analytical multiple scattering correction to the Mie theory: Application to the analysis of the lidar signal

NASA Technical Reports Server (NTRS)

Flesia, C.; Schwendimann, P.

1992-01-01

The contribution of the multiple scattering to the lidar signal is dependent on the optical depth tau. Therefore, the radar analysis, based on the assumption that the multiple scattering can be neglected is limited to cases characterized by low values of the optical depth (tau less than or equal to 0.1) and hence it exclude scattering from most clouds. Moreover, all inversion methods relating lidar signal to number densities and particle size must be modified since the multiple scattering affects the direct analysis. The essential requests of a realistic model for lidar measurements which include the multiple scattering and which can be applied to practical situations follow. (1) Requested are not only a correction term or a rough approximation describing results of a certain experiment, but a general theory of multiple scattering tying together the relevant physical parameter we seek to measure. (2) An analytical generalization of the lidar equation which can be applied in the case of a realistic aerosol is requested. A pure analytical formulation is important in order to avoid the convergency and stability problems which, in the case of numerical approach, are due to the large number of events that have to be taken into account in the presence of large depth and/or a strong experimental noise.

Use of the Wigner representation in scattering problems

NASA Technical Reports Server (NTRS)

Bemler, E. A.

1975-01-01

The basic equations of quantum scattering were translated into the Wigner representation, putting quantum mechanics in the form of a stochastic process in phase space, with real valued probability distributions and source functions. The interpretative picture associated with this representation is developed and stressed and results used in applications published elsewhere are derived. The form of the integral equation for scattering as well as its multiple scattering expansion in this representation are derived. Quantum corrections to classical propagators are briefly discussed. The basic approximation used in the Monte-Carlo method is derived in a fashion which allows for future refinement and which includes bound state production. Finally, as a simple illustration of some of the formalism, scattering is treated by a bound two body problem. Simple expressions for single and double scattering contributions to total and differential cross-sections as well as for all necessary shadow corrections are obtained.

Surface wave scattering from sharp lateral discontinuities

NASA Astrophysics Data System (ADS)

Pollitz, Fred F.

1994-11-01

The problem of surface wave scattering is re-explored, with quasi-degenerate normal mode coupling as the starting point. For coupling among specified spheroidal and toroidal mode dispersion branches, a set of coupled wave equations is derived in the frequency domain for first-arriving Rayleigh and Love waves. The solutions to these coupled wave equations using linear perturbation theory are surface integrals over the unit sphere covering the lateral distribution of perturbations in Earth structure. For isotropic structural perturbations and surface topographic perturbations, these solutions agree with the Born scattering theory previously obtained by Snieder and Romanowicz. By transforming these surface integrals into line integrals along the boundaries of the heterogeneous regions in the case of sharp discontinuities, and by using uniformly valid Green's functions, it is possible to extend the solution to the case of multiple scattering interactions. The proposed method allows the relatively rapid calculation of exact second order scattered wavefield potentials for scattering by sharp discontinuities, and it has many advantages not realized in earlier treatments. It employs a spherical Earth geometry, uses no far field approximation, and implicitly contains backward as well as forward scattering. Comparisons of asymptotic scattering and an exact solution with single scattering and multiple scattering integral formulations show that the phase perturbation predicted by geometrical optics breaks down for scatterers less than about six wavelengths in diameter, and second-order scattering predicts well both the amplitude and phase pattern of the exact wavefield for sufficiently small scatterers, less than about three wavelengths in diameter for anomalies of a few percent.

An explicit canopy BRDF model and inversion. [Bidirectional Reflectance Distribution Function

NASA Technical Reports Server (NTRS)

Liang, Shunlin; Strahler, Alan H.

1992-01-01

Based on a rigorous canopy radiative transfer equation, the multiple scattering radiance is approximated by the asymptotic theory, and the single scattering radiance calculation, which requires an numerical intergration due to considering the hotspot effect, is simplified. A new formulation is presented to obtain more exact angular dependence of the sky radiance distribution. The unscattered solar radiance and single scattering radiance are calculated exactly, and the multiple scattering is approximated by the delta two-stream atmospheric radiative transfer model. The numerical algorithms prove that the parametric canopy model is very accurate, especially when the viewing angles are smaller than 55 deg. The Powell algorithm is used to retrieve biospheric parameters from the ground measured multiangle observations.

Space-time domain solutions of the wave equation by a non-singular boundary integral method and Fourier transform.

PubMed

Klaseboer, Evert; Sepehrirahnama, Shahrokh; Chan, Derek Y C

2017-08-01

The general space-time evolution of the scattering of an incident acoustic plane wave pulse by an arbitrary configuration of targets is treated by employing a recently developed non-singular boundary integral method to solve the Helmholtz equation in the frequency domain from which the space-time solution of the wave equation is obtained using the fast Fourier transform. The non-singular boundary integral solution can enforce the radiation boundary condition at infinity exactly and can account for multiple scattering effects at all spacings between scatterers without adverse effects on the numerical precision. More generally, the absence of singular kernels in the non-singular integral equation confers high numerical stability and precision for smaller numbers of degrees of freedom. The use of fast Fourier transform to obtain the time dependence is not constrained to discrete time steps and is particularly efficient for studying the response to different incident pulses by the same configuration of scatterers. The precision that can be attained using a smaller number of Fourier components is also quantified.

Spaceborne lidar for cloud monitoring

NASA Astrophysics Data System (ADS)

Werner, Christian; Krichbaumer, W.; Matvienko, Gennadii G.

1994-12-01

Results of laser cloud top measurements taken from space in 1982 (called PANTHER) are presented. Three sequences of land, water, and cloud data are selected. A comparison with airborne lidar data shows similarities. Using the single scattering lidar equation for these spaceborne lidar measurements one can misinterpret the data if one doesn't correct for multiple scattering.

Numerical solution of inverse scattering for near-field optics.

PubMed

Bao, Gang; Li, Peijun

2007-06-01

A novel regularized recursive linearization method is developed for a two-dimensional inverse medium scattering problem that arises in near-field optics, which reconstructs the scatterer of an inhomogeneous medium located on a substrate from data accessible through photon scanning tunneling microscopy experiments. Based on multiple frequency scattering data, the method starts from the Born approximation corresponding to weak scattering at a low frequency, and each update is obtained by continuation on the wavenumber from solutions of one forward problem and one adjoint problem of the Helmholtz equation.

Nonlinear coupled mode approach for modeling counterpropagating solitons in the presence of disorder-induced multiple scattering in photonic crystal waveguides

NASA Astrophysics Data System (ADS)

Mann, Nishan; Hughes, Stephen

2018-02-01

We present the analytical and numerical details behind our recently published article [Phys. Rev. Lett. 118, 253901 (2017), 10.1103/PhysRevLett.118.253901], describing the impact of disorder-induced multiple scattering on counterpropagating solitons in photonic crystal waveguides. Unlike current nonlinear approaches using the coupled mode formalism, we account for the effects of intraunit cell multiple scattering. To solve the resulting system of coupled semilinear partial differential equations, we introduce a modified Crank-Nicolson-type norm-preserving implicit finite difference scheme inspired by the transfer matrix method. We provide estimates of the numerical dispersion characteristics of our scheme so that optimal step sizes can be chosen to either minimize numerical dispersion or to mimic the exact dispersion. We then show numerical results of a fundamental soliton propagating in the presence of multiple scattering to demonstrate that choosing a subunit cell spatial step size is critical in accurately capturing the effects of multiple scattering, and illustrate the stochastic nature of disorder by simulating soliton propagation in various instances of disordered photonic crystal waveguides. Our approach is easily extended to include a wide range of optical nonlinearities and is applicable to various photonic nanostructures where power propagation is bidirectional, either by choice, or as a result of multiple scattering.

Scattered surface wave energy in the seismic coda

USGS Publications Warehouse

Zeng, Y.

2006-01-01

One of the many important contributions that Aki has made to seismology pertains to the origin of coda waves (Aki, 1969; Aki and Chouet, 1975). In this paper, I revisit Aki's original idea of the role of scattered surface waves in the seismic coda. Based on the radiative transfer theory, I developed a new set of scattered wave energy equations by including scattered surface waves and body wave to surface wave scattering conversions. The work is an extended study of Zeng et al. (1991), Zeng (1993) and Sato (1994a) on multiple isotropic-scattering, and may shed new insight into the seismic coda wave interpretation. The scattering equations are solved numerically by first discretizing the model at regular grids and then solving the linear integral equations iteratively. The results show that scattered wave energy can be well approximated by body-wave to body wave scattering at earlier arrival times and short distances. At long distances from the source, scattered surface waves dominate scattered body waves at surface stations. Since surface waves are 2-D propagating waves, their scattered energies should in theory follow a common decay curve. The observed common decay trends on seismic coda of local earthquake recordings particular at long lapse times suggest that perhaps later seismic codas are dominated by scattered surface waves. When efficient body wave to surface wave conversion mechanisms are present in the shallow crustal layers, such as soft sediment layers, the scattered surface waves dominate the seismic coda at even early arrival times for shallow sources and at later arrival times for deeper events.

On the Angular Variation of Solar Reflectance of Snow

NASA Technical Reports Server (NTRS)

Chang, A. T. C.; Choudhury, B. J.

1979-01-01

Spectral and integrated solar reflectance of nonhomogeneous snowpacks were derived assuming surface reflection of direct radiation and subsurface multiple scattering. For surface reflection, a bidirectional reflectance distribution function derived for an isotropic Gaussian faceted surface was considered and for subsurface multiple scattering, an approximate solution of the radiative transfer equation was studied. Solar radiation incident on the snowpack was decomposed into direct and atmospherically scattered radiation. Spectral attenuation coefficients of ozone, carbon dioxide, water vapor, aerosol and molecular scattering were included in the calculation of incident solar radiation. Illustrative numerical results were given for a case of North American winter atmospheric conditions. The calculated dependence of spectrally integrated directional reflectance (or albedo) on solar elevation was in qualitative agreement with available observations.

Magnetotransport of multiple-band nearly antiferromagnetic metals due to hot-spot scattering

DOE PAGES

Koshelev, A. E.

2016-09-30

Multiple-band electronic structure and proximity to antiferromagnetic (AF) instability are the key properties of iron-based superconductors. In this paper, we explore the influence of scattering by the AF spin fluctuations on transport of multiple-band metals above the magnetic transition. A salient feature of scattering on the AF fluctuations is that it is strongly enhanced at the Fermi surface locations where the nesting is perfect (“hot spots” or “hot lines”). We review derivation of the collision integral for the Boltzmann equation due to AF-fluctuations scattering. In the paramagnetic state, the enhanced scattering rate near the hot lines leads to anomalous behaviormore » of electronic transport in magnetic field. We explore this behavior by analytically solving the Boltzmann transport equation with approximate transition rates. This approach accounts for return scattering events and is more accurate than the relaxation-time approximation. The magnetic-field dependences are characterized by two very different field scales: the lower scale is set by the hot-spot width and the higher scale is set by the total scattering amplitude. A conventional magnetotransport behavior is limited to magnetic fields below the lower scale. In the wide range in-between these two scales, the longitudinal conductivity has linear dependence on the magnetic field and the Hall conductivity has quadratic dependence. The linear dependence of the diagonal component reflects growth of the Fermi-surface area affected by the hot spots proportional to the magnetic field. Finally, we discuss applicability of this theoretical framework for describing of anomalous magnetotransport properties in different iron pnictides and chalcogenides in the paramagnetic state.« less

Kaon-nucleus scattering

NASA Technical Reports Server (NTRS)

Hong, Byungsik; Maung, Khin Maung; Wilson, John W.; Buck, Warren W.

1989-01-01

The derivations of the Lippmann-Schwinger equation and Watson multiple scattering are given. A simple optical potential is found to be the first term of that series. The number density distribution models of the nucleus, harmonic well, and Woods-Saxon are used without t-matrix taken from the scattering experiments. The parameterized two-body inputs, which are kaon-nucleon total cross sections, elastic slope parameters, and the ratio of the real to the imaginary part of the forward elastic scattering amplitude, are presented. The eikonal approximation was chosen as our solution method to estimate the total and absorptive cross sections for the kaon-nucleus scattering.

Inverse random source scattering for the Helmholtz equation in inhomogeneous media

NASA Astrophysics Data System (ADS)

Li, Ming; Chen, Chuchu; Li, Peijun

2018-01-01

This paper is concerned with an inverse random source scattering problem in an inhomogeneous background medium. The wave propagation is modeled by the stochastic Helmholtz equation with the source driven by additive white noise. The goal is to reconstruct the statistical properties of the random source such as the mean and variance from the boundary measurement of the radiated random wave field at multiple frequencies. Both the direct and inverse problems are considered. We show that the direct problem has a unique mild solution by a constructive proof. For the inverse problem, we derive Fredholm integral equations, which connect the boundary measurement of the radiated wave field with the unknown source function. A regularized block Kaczmarz method is developed to solve the ill-posed integral equations. Numerical experiments are included to demonstrate the effectiveness of the proposed method.

A microwave backscattering model for precipitation

NASA Astrophysics Data System (ADS)

Ermis, Seda

A geophysical microwave backscattering model for space borne and ground-based remote sensing of precipitation is developed and used to analyze backscattering measurements from rain and snow type precipitation. Vector Radiative Transfer (VRT) equations for a multilayered inhomogeneous medium are applied to the precipitation region for calculation of backscattered intensity. Numerical solution of the VRT equation for multiple layers is provided by the matrix doubling method to take into account close range interactions between particles. In previous studies, the VRT model was used to calculate backscattering from a rain column on a sea surface. In the model, Mie scattering theory for closely spaced scatterers was used to determine the phase matrix for each sublayer characterized by a set of parameters. The scatterers i.e. rain drops within the sublayers were modelled as spheres with complex permittivities. The rain layer was bounded by rough boundaries; the interface between the cloud and the rain column as well as the interface between the sea surface and the rain were all analyzed by using the integral equation model (IEM). Therefore, the phase matrix for the entire rain column was generated by the combination of surface and volume scattering. Besides Mie scattering, in this study, we use T-matrix approach to examine the effect of the shape to the backscattered intensities since larger raindrops are most likely oblique in shape. Analyses show that the effect of obliquity of raindrops to the backscattered wave is related with size of the scatterers and operated frequency. For the ground-based measurement system, the VRT model is applied to simulate the precipitation column on horizontal direction. Therefore, the backscattered reflectivities for each unit range of volume are calculated from the backscattering radar cross sections by considering radar range and effective illuminated area of the radar beam. The volume scattering phase matrices for each range interval are calculated by Mie scattering theory. VRT equations are solved by matrix doubling method to compute phase matrix for entire radar beam. Model results are validated with measured data by X-band dual polarization Phase Tilt Weather Radar (PTWR) for snow, rain, wet hail type precipitation. The geophysical parameters given the best fit with measured reflectivities are used in previous models i.e. Rayleigh Approximation and Mie scattering and compared with the VRT model. Results show that reflectivities calculated by VRT models are differed up to 10 dB from the Rayleigh approximation model and up to 5 dB from the Mie Scattering theory due to both multiple scattering and attenuation losses for the rain rates as high as 80 mm/h.

Radiative transfer in a sphere illuminated by a parallel beam - An integral equation approach. [in planetary atmosphere

NASA Technical Reports Server (NTRS)

Shia, R.-L.; Yung, Y. L.

1986-01-01

The problem of multiple scattering of nonpolarized light in a planetary body of arbitrary shape illuminated by a parallel beam is formulated using the integral equation approach. There exists a simple functional whose stationarity condition is equivalent to solving the equation of radiative transfer and whose value at the stationary point is proportional to the differential cross section. The analysis reveals a direct relation between the microscopic symmetry of the phase function for each scattering event and the macroscopic symmetry of the differential cross section for the entire planetary body, and the interconnection of these symmetry relations and the variational principle. The case of a homogeneous sphere containing isotropic scatterers is investigated in detail. It is shown that the solution can be expanded in a multipole series such that the general spherical problem is reduced to solving a set of decoupled integral equations in one dimension. Computations have been performed for a range of parameters of interest, and illustrative examples of applications to planetary problems as provided.

From Nonradiating Sources to Directionally Invisible Objects

NASA Astrophysics Data System (ADS)

Hurwitz, Elisa

The goal of this dissertation is to extend the understanding of invisible objects, in particular nonradiating sources and directional nonscattering scatterers. First, variations of null-field nonradiating sources are derived from Maxwell's equations. Next, it is shown how to design a nonscattering scatterer by applying the boundary conditions for nonradiating sources to the scalar wave equation, referred to here as the "field cloak method". This technique is used to demonstrate directionally invisible scatterers for an incident field with one direction of incidence, and the influence of symmetry on the directionality is explored. This technique, when applied to the scalar wave equation, is extended to show that a directionally invisible object may be invisible for multiple directions of incidence simultaneously. This opens the door to the creation of optically switchable, directionally invisible objects which could be implemented in couplers and other novel optical devices. Next, a version of the "field cloak method" is extended to the Maxwell's electro-magnetic vector equations, allowing more flexibility in the variety of directionally invisible objects that can be designed. This thesis concludes with examples of such objects and future applications.

On the Discrete Spectrum of the Nonstationary Schrödinger Equation and Multipole Lumps of the Kadomtsev-Petviashvili I Equation

NASA Astrophysics Data System (ADS)

Villarroel, Javier; Ablowitz, Mark J.

The discrete spectrum of the nonstationary Schrödinger equation and localized solutions of the Kadomtsev-Petviashvili-I (KPI) equation are studied via the inverse scattering transform. It is shown that there exist infinitely many real and rationally decaying potentials which correspond to a discrete spectrum whose related eigenfunctions have multiple poles in the spectral parameter. An index or winding number is asssociated with each of these solutions. The resulting localized solutions of KPI behave as collection of individual humps with nonuniform dynamics.

Outer-planet scattering can gently tilt an inner planetary system

NASA Astrophysics Data System (ADS)

Gratia, Pierre; Fabrycky, Daniel

2017-01-01

Chaotic dynamics are expected during and after planet formation, and a leading mechanism to explain large eccentricities of gas giant exoplanets is planet-planet gravitational scattering. The same scattering has been invoked to explain misalignments of planetary orbital planes with respect to their host star's spin. However, an observational puzzle is presented by Kepler-56, which has two inner planets (b and c) that are nearly coplanar with each other, yet are more than 45° inclined to their star's equator. Thus, the spin-orbit misalignment might be primordial. Instead, we further develop the hypothesis in the discovery paper, that planets on wider orbits generated misalignment through scattering, and as a result gently torqued the inner planets away from the equator plane of the star. We integrated the equations of motion for Kepler-56 b and c along with an unstable outer system initialized with either two or three Jupiter-mass planets. We address here whether the violent scattering that generates large mutual inclinations can leave the inner system intact, tilting it gently. In almost all of the cases initially with two outer planets, either the inner planets remain nearly coplanar with each other in the star's equator plane, or they are scattered violently to high mutual inclination and high spin-orbit misalignment. On the contrary, of the systems with three unstable outer planets, a spin-orbit misalignment large enough to explain the observations is generated 28 per cent of the time for coplanar inner planets, which is consistent with the observed frequency of this phenomenon reported so far. We conclude that multiple-planet scattering in the outer parts of the system may account for this new population of coplanar planets hosted by oblique stars.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Xianglin; Wang, Yang; Eisenbach, Markus

One major purpose of studying the single-site scattering problem is to obtain the scattering matrices and differential equation solutions indispensable to multiple scattering theory (MST) calculations. On the other hand, the single-site scattering itself is also appealing because it reveals the physical environment experienced by electrons around the scattering center. In this study, we demonstrate a new formalism to calculate the relativistic full-potential single-site Green's function. We implement this method to calculate the single-site density of states and electron charge densities. Lastly, the code is rigorously tested and with the help of Krein's theorem, the relativistic effects and full potentialmore » effects in group V elements and noble metals are thoroughly investigated.« less

Electromagnetic Scattering by Spheroidal Volumes of Discrete Random Medium

NASA Technical Reports Server (NTRS)

Dlugach, Janna M.; Mishchenko, Michael I.

2017-01-01

We use the superposition T-matrix method to compare the far-field scattering matrices generated by spheroidal and spherical volumes of discrete random medium having the same volume and populated by identical spherical particles. Our results fully confirm the robustness of the previously identified coherent and diffuse scattering regimes and associated optical phenomena exhibited by spherical particulate volumes and support their explanation in terms of the interference phenomenon coupled with the order-of-scattering expansion of the far-field Foldy equations. We also show that increasing non-sphericity of particulate volumes causes discernible (albeit less pronounced) optical effects in forward and backscattering directions and explain them in terms of the same interference/multiple-scattering phenomenon.

On the Mathematical Modeling of Single and Multiple Scattering of Ultrasonic Guided Waves by Small Scatterers: A Structural Health Monitoring Measurement Model

NASA Astrophysics Data System (ADS)

Strom, Brandon William

In an effort to assist in the paradigm shift from schedule based maintenance to conditioned based maintenance, we derive measurement models to be used within structural health monitoring algorithms. Our models are physics based, and use scattered Lamb waves to detect and quantify pitting corrosion. After covering the basics of Lamb waves and the reciprocity theorem, we develop a technique for the scattered wave solution. The first application is two-dimensional, and is employed in two different ways. The first approach integrates a traction distribution and replaces it by an equivalent force. The second approach is higher order and uses the actual traction distribution. We find that the equivalent force version of the solution technique holds well for small pits at low frequencies. The second application is three-dimensional. The equivalent force caused by the scattered wave of an arbitrary equivalent force is calculated. We obtain functions for the scattered wave displacements as a function of equivalent forces, equivalent forces as a function of incident wave, and scattered wave amplitudes as a function of incident amplitude. The third application uses self-consistency to derive governing equations for the scattered waves due to multiple corrosion pits. We decouple the implicit set of equations and solve explicitly by using a recursive series solution. Alternatively, we solve via an undetermined coefficient method which results in an interaction operator and solution via matrix inversion. The general solution is given for N pits including mode conversion. We show that the two approaches are equivalent, and give a solution for three pits. Various approximations are advanced to simplify the problem while retaining the leading order physics. As a final application, we use the multiple scattering model to investigate resonance of Lamb waves. We begin with a one-dimensional problem and progress to a three-dimensional problem. A directed graph enables interpretation of the interaction operator, and we show that a series solution converges due to loss of energy in the system. We see that there are four causes of resonance and plot the modulation depth as a function of spacing between the pits.

Theory of lasing in a multiple-scattering medium

NASA Astrophysics Data System (ADS)

John, Sajeev; Pang, Gendi

1996-10-01

In several recent experiments, isotropic lasing action was observed in paints that contain rhodamine 640 dye molecules in methanol solution as gain media and titania particles as optical scatterers. These so-called paint-on laser systems are extraordinary because they are highly disordered systems. The microscopic mechanism for laser activity and the coherence properties of light emission in this multiple-light-scattering medium have not yet been elucidated. In this paper we derive the emission intensity properties of a model dye system with excited singlet and triplet electronic energy levels, which is immersed in a multiple-scattering medium with transport mean free path l*. Using physically reasonable estimates for the absorption and emission cross section for the singlet and triplet manifolds, and the singlet-triplet intersystem crossing rate, we solve the nonlinear laser rate equations for the dye molecules. This leads to a diffusion equation for the light intensity in the medium with a nonlinear intensity-dependent gain coefficient. Using this model we are able to account for nearly all of the experimentally observed properties of laser paint reported so far when l*>>λ0, the emission wavelength. This includes the dependence of the peak intensity of amplified emission on the mean free path l*, the dye concentration ρ, and the pump intensity characteristics. Our model recaptures the collapse of the emission linewidth at a specific threshold pump intensity and describes how this threshold intensity varies with l*. In addition, our model predicts a dramatic increase in the peak intensity and a further lowering of the lasing threshold for the strong scattering limit l*-->λ0. This suggests a striking enhancement of the characteristics of laser paint near the photon localization threshold in a disordered medium.

Laplace Transform Based Radiative Transfer Studies

NASA Astrophysics Data System (ADS)

Hu, Y.; Lin, B.; Ng, T.; Yang, P.; Wiscombe, W.; Herath, J.; Duffy, D.

2006-12-01

Multiple scattering is the major uncertainty for data analysis of space-based lidar measurements. Until now, accurate quantitative lidar data analysis has been limited to very thin objects that are dominated by single scattering, where photons from the laser beam only scatter a single time with particles in the atmosphere before reaching the receiver, and simple linear relationship between physical property and lidar signal exists. In reality, multiple scattering is always a factor in space-based lidar measurement and it dominates space- based lidar returns from clouds, dust aerosols, vegetation canopy and phytoplankton. While multiple scattering are clear signals, the lack of a fast-enough lidar multiple scattering computation tool forces us to treat the signal as unwanted "noise" and use simple multiple scattering correction scheme to remove them. Such multiple scattering treatments waste the multiple scattering signals and may cause orders of magnitude errors in retrieved physical properties. Thus the lack of fast and accurate time-dependent radiative transfer tools significantly limits lidar remote sensing capabilities. Analyzing lidar multiple scattering signals requires fast and accurate time-dependent radiative transfer computations. Currently, multiple scattering is done with Monte Carlo simulations. Monte Carlo simulations take minutes to hours and are too slow for interactive satellite data analysis processes and can only be used to help system / algorithm design and error assessment. We present an innovative physics approach to solve the time-dependent radiative transfer problem. The technique utilizes FPGA based reconfigurable computing hardware. The approach is as following, 1. Physics solution: Perform Laplace transform on the time and spatial dimensions and Fourier transform on the viewing azimuth dimension, and convert the radiative transfer differential equation solving into a fast matrix inversion problem. The majority of the radiative transfer computation goes to matrix inversion processes, FFT and inverse Laplace transforms. 2. Hardware solutions: Perform the well-defined matrix inversion, FFT and Laplace transforms on highly parallel, reconfigurable computing hardware. This physics-based computational tool leads to accurate quantitative analysis of space-based lidar signals and improves data quality of current lidar mission such as CALIPSO. This presentation will introduce the basic idea of this approach, preliminary results based on SRC's FPGA-based Mapstation, and how we may apply it to CALIPSO data analysis.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koshelev, A. E.

Multiple-band electronic structure and proximity to antiferromagnetic (AF) instability are the key properties of iron-based superconductors. In this paper, we explore the influence of scattering by the AF spin fluctuations on transport of multiple-band metals above the magnetic transition. A salient feature of scattering on the AF fluctuations is that it is strongly enhanced at the Fermi surface locations where the nesting is perfect (“hot spots” or “hot lines”). We review derivation of the collision integral for the Boltzmann equation due to AF-fluctuations scattering. In the paramagnetic state, the enhanced scattering rate near the hot lines leads to anomalous behaviormore » of electronic transport in magnetic field. We explore this behavior by analytically solving the Boltzmann transport equation with approximate transition rates. This approach accounts for return scattering events and is more accurate than the relaxation-time approximation. The magnetic-field dependences are characterized by two very different field scales: the lower scale is set by the hot-spot width and the higher scale is set by the total scattering amplitude. A conventional magnetotransport behavior is limited to magnetic fields below the lower scale. In the wide range in-between these two scales, the longitudinal conductivity has linear dependence on the magnetic field and the Hall conductivity has quadratic dependence. The linear dependence of the diagonal component reflects growth of the Fermi-surface area affected by the hot spots proportional to the magnetic field. Finally, we discuss applicability of this theoretical framework for describing of anomalous magnetotransport properties in different iron pnictides and chalcogenides in the paramagnetic state.« less

Accuracy & Computational Considerations for Wide--Angle One--way Seismic Propagators and Multiple Scattering by Invariant Embedding

NASA Astrophysics Data System (ADS)

Thomson, C. J.

2004-12-01

Pseudodifferential operators (PSDOs) yield in principle exact one--way seismic wave equations, which are attractive both conceptually and for their promise of computational efficiency. The one--way operators can be extended to include multiple--scattering effects, again in principle exactly. In practice approximations must be made and, as an example, the variable--wavespeed Helmholtz equation for scalar waves in two space dimensions is here factorized to give the one--way wave equation. This simple case permits clear identification of a sequence of physically reasonable approximations to be used when the mathematically exact PSDO one--way equation is implemented on a computer. As intuition suggests, these approximations hinge on the medium gradients in the direction transverse to the main propagation direction. A key point is that narrow--angle approximations are to be avoided in the interests of accuracy. Another key consideration stems from the fact that the so--called ``standard--ordering'' PSDO indicates how lateral interpolation of the velocity structure can significantly reduce computational costs associated with the Fourier or plane--wave synthesis lying at the heart of the calculations. The decision on whether a slow or a fast Fourier transform code should be used rests upon how many lateral model parameters are truly distinct. A third important point is that the PSDO theory shows what approximations are necessary in order to generate an exponential one--way propagator for the laterally varying case, representing the intuitive extension of classical integral--transform solutions for a laterally homogeneous medium. This exponential propagator suggests the use of larger discrete step sizes, and it can also be used to approach phase--screen like approximations (though the latter are not the main interest here). Numerical comparisons with finite--difference solutions will be presented in order to assess the approximations being made and to gain an understanding of computation time differences. The ideas described extend to the three--dimensional, generally anisotropic case and to multiple scattering by invariant embedding.

Two-dimensional fast marching for geometrical optics.

PubMed

Capozzoli, Amedeo; Curcio, Claudio; Liseno, Angelo; Savarese, Salvatore

2014-11-03

We develop an approach for the fast and accurate determination of geometrical optics solutions to Maxwell's equations in inhomogeneous 2D media and for TM polarized electric fields. The eikonal equation is solved by the fast marching method. Particular attention is paid to consistently discretizing the scatterers' boundaries and matching the discretization to that of the computational domain. The ray tracing is performed, in a direct and inverse way, by using a technique introduced in computer graphics for the fast and accurate generation of textured images from vector fields. The transport equation is solved by resorting only to its integral form, the transport of polarization being trivial for the considered geometry and polarization. Numerical results for the plane wave scattering of two perfectly conducting circular cylinders and for a Luneburg lens prove the accuracy of the algorithm. In particular, it is shown how the approach is capable of properly accounting for the multiple scattering occurring between the two metallic cylinders and how inverse ray tracing should be preferred to direct ray tracing in the case of the Luneburg lens.

Compactness and robustness: Applications in the solution of integral equations for chemical kinetics and electromagnetic scattering

NASA Astrophysics Data System (ADS)

Zhou, Yajun

This thesis employs the topological concept of compactness to deduce robust solutions to two integral equations arising from chemistry and physics: the inverse Laplace problem in chemical kinetics and the vector wave scattering problem in dielectric optics. The inverse Laplace problem occurs in the quantitative understanding of biological processes that exhibit complex kinetic behavior: different subpopulations of transition events from the "reactant" state to the "product" state follow distinct reaction rate constants, which results in a weighted superposition of exponential decay modes. Reconstruction of the rate constant distribution from kinetic data is often critical for mechanistic understandings of chemical reactions related to biological macromolecules. We devise a "phase function approach" to recover the probability distribution of rate constants from decay data in the time domain. The robustness (numerical stability) of this reconstruction algorithm builds upon the continuity of the transformations connecting the relevant function spaces that are compact metric spaces. The robust "phase function approach" not only is useful for the analysis of heterogeneous subpopulations of exponential decays within a single transition step, but also is generalizable to the kinetic analysis of complex chemical reactions that involve multiple intermediate steps. A quantitative characterization of the light scattering is central to many meteoro-logical, optical, and medical applications. We give a rigorous treatment to electromagnetic scattering on arbitrarily shaped dielectric media via the Born equation: an integral equation with a strongly singular convolution kernel that corresponds to a non-compact Green operator. By constructing a quadratic polynomial of the Green operator that cancels out the kernel singularity and satisfies the compactness criterion, we reveal the universality of a real resonance mode in dielectric optics. Meanwhile, exploiting the properties of compact operators, we outline the geometric and physical conditions that guarantee a robust solution to the light scattering problem, and devise an asymptotic solution to the Born equation of electromagnetic scattering for arbitrarily shaped dielectric in a non-perturbative manner.

A full-potential approach to the relativistic single-site Green's function

DOE PAGES

Liu, Xianglin; Wang, Yang; Eisenbach, Markus; ...

2016-07-07

One major purpose of studying the single-site scattering problem is to obtain the scattering matrices and differential equation solutions indispensable to multiple scattering theory (MST) calculations. On the other hand, the single-site scattering itself is also appealing because it reveals the physical environment experienced by electrons around the scattering center. In this study, we demonstrate a new formalism to calculate the relativistic full-potential single-site Green's function. We implement this method to calculate the single-site density of states and electron charge densities. Lastly, the code is rigorously tested and with the help of Krein's theorem, the relativistic effects and full potentialmore » effects in group V elements and noble metals are thoroughly investigated.« less

On scattering from the one-dimensional multiple Dirac delta potentials

NASA Astrophysics Data System (ADS)

Erman, Fatih; Gadella, Manuel; Uncu, Haydar

2018-05-01

In this paper, we propose a pedagogical presentation of the Lippmann–Schwinger equation as a powerful tool, so as to obtain important scattering information. In particular, we consider a one-dimensional system with a Schrödinger-type free Hamiltonian decorated with a sequence of N attractive Dirac delta interactions. We first write the Lippmann–Schwinger equation for the system and then solve it explicitly in terms of an N × N matrix. Then, we discuss the reflection and the transmission coefficients for an arbitrary number of centres and study the threshold anomaly for the N = 2 and N = 4 cases. We also study further features like the quantum metastable states and resonances, including their corresponding Gamow functions and virtual or antibound states. The use of the Lippmann–Schwinger equation simplifies our analysis enormously and gives exact results for an arbitrary number of Dirac delta potentials.

Some Remarks on GMRES for Transport Theory

NASA Technical Reports Server (NTRS)

Patton, Bruce W.; Holloway, James Paul

2003-01-01

We review some work on the application of GMRES to the solution of the discrete ordinates transport equation in one-dimension. We note that GMRES can be applied directly to the angular flux vector, or it can be applied to only a vector of flux moments as needed to compute the scattering operator of the transport equation. In the former case we illustrate both the delights and defects of ILU right-preconditioners for problems with anisotropic scatter and for problems with upscatter. When working with flux moments we note that GMRES can be used as an accelerator for any existing transport code whose solver is based on a stationary fixed-point iteration, including transport sweeps and DSA transport sweeps. We also provide some numerical illustrations of this idea. We finally show how space can be traded for speed by taking multiple transport sweeps per GMRES iteration. Key Words: transport equation, GMRES, Krylov subspace

Dependent scattering and absorption by densely packed discrete spherical particles: Effects of complex refractive index

NASA Astrophysics Data System (ADS)

Ma, L. X.; Tan, J. Y.; Zhao, J. M.; Wang, F. Q.; Wang, C. A.; Wang, Y. Y.

2017-07-01

Due to the dependent scattering and absorption effects, the radiative transfer equation (RTE) may not be suitable for dealing with radiative transfer in dense discrete random media. This paper continues previous research on multiple and dependent scattering in densely packed discrete particle systems, and puts emphasis on the effects of particle complex refractive index. The Mueller matrix elements of the scattering system with different complex refractive indexes are obtained by both electromagnetic method and radiative transfer method. The Maxwell equations are directly solved based on the superposition T-matrix method, while the RTE is solved by the Monte Carlo method combined with the hard sphere model in the Percus-Yevick approximation (HSPYA) to consider the dependent scattering effects. The results show that for densely packed discrete random media composed of medium size parameter particles (equals 6.964 in this study), the demarcation line between independent and dependent scattering has remarkable connections with the particle complex refractive index. With the particle volume fraction increase to a certain value, densely packed discrete particles with higher refractive index contrasts between the particles and host medium and higher particle absorption indexes are more likely to show stronger dependent characteristics. Due to the failure of the extended Rayleigh-Debye scattering condition, the HSPYA has weak effect on the dependent scattering correction at large phase shift parameters.

Interpretation of light scattering and turbidity measurements in aggregated systems: effect of intra-cluster multiple-light scattering.

PubMed

Soos, Miroslav; Lattuada, Marco; Sefcik, Jan

2009-11-12

In this work we studied the effect of intracluster multiple-light scattering on the scattering properties of a population of fractal aggregates. To do so, experimental data of diffusion-limited aggregation for three polystyrene latexes with similar surface properties but different primary particle diameters (equal to 118, 420, and 810 nm) were obtained by static light scattering and by means of a spectrophotometer. In parallel, a population balance equation (PBE) model, which takes into account the effect of intracluster multiple-light scattering by solving the T-matrix and the mean-field version of T-matrix, was formulated and validated against time evolution of the root mean radius of gyration, , of the zero angle intensity of scattered light, I(0), and of the turbidity, tau. It was found that the mean-field version of the T-matrix theory is able to correctly predict the time evolution of all measured light scattering quantities for all sizes of primary particles without any adjustable parameter. The structure of the aggregates, characterized by fractal dimension, d(f), was independent of the primary particle size and equal to 1.7, which is in agreement with values found in literature. Since the mean-field version of the T-matrix theory used is rather complicated and requires advanced knowledge of cluster structure (i.e., the particle-particle correlation function), a simplified version of the light scattering model was proposed and tested. It was found that within the range of operating conditions investigated, the simplified version of the light scattering model was able to describe with reasonable accuracy the time evolution of all measured light scattering quantities of the cluster mass distribution (CMD) for all three sizes of primary particles and two values of the laser wavelength.

Coherent backscattering of light by complex random media of spherical scatterers: numerical solution

NASA Astrophysics Data System (ADS)

Muinonen, Karri

2004-07-01

Novel Monte Carlo techniques are described for the computation of reflection coefficient matrices for multiple scattering of light in plane-parallel random media of spherical scatterers. The present multiple scattering theory is composed of coherent backscattering and radiative transfer. In the radiative transfer part, the Stokes parameters of light escaping from the medium are updated at each scattering process in predefined angles of emergence. The scattering directions at each process are randomized using probability densities for the polar and azimuthal scattering angles: the former angle is generated using the single-scattering phase function, whereafter the latter follows from Kepler's equation. For spherical scatterers in the Rayleigh regime, randomization proceeds semi-analytically whereas, beyond that regime, cubic spline presentation of the scattering matrix is used for numerical computations. In the coherent backscattering part, the reciprocity of electromagnetic waves in the backscattering direction allows the renormalization of the reversely propagating waves, whereafter the scattering characteristics are computed in other directions. High orders of scattering (~10 000) can be treated because of the peculiar polarization characteristics of the reverse wave: after a number of scatterings, the polarization state of the reverse wave becomes independent of that of the incident wave, that is, it becomes fully dictated by the scatterings at the end of the reverse path. The coherent backscattering part depends on the single-scattering albedo in a non-monotonous way, the most pronounced signatures showing up for absorbing scatterers. The numerical results compare favourably to the literature results for nonabsorbing spherical scatterers both in and beyond the Rayleigh regime.

A Numerical Method for Obtaining Monoenergetic Neutron Flux Distributions and Transmissions in Multiple-Region Slabs

NASA Technical Reports Server (NTRS)

Schneider, Harold

1959-01-01

This method is investigated for semi-infinite multiple-slab configurations of arbitrary width, composition, and source distribution. Isotropic scattering in the laboratory system is assumed. Isotropic scattering implies that the fraction of neutrons scattered in the i(sup th) volume element or subregion that will make their next collision in the j(sup th) volume element or subregion is the same for all collisions. These so-called "transfer probabilities" between subregions are calculated and used to obtain successive-collision densities from which the flux and transmission probabilities directly follow. For a thick slab with little or no absorption, a successive-collisions technique proves impractical because an unreasonably large number of collisions must be followed in order to obtain the flux. Here the appropriate integral equation is converted into a set of linear simultaneous algebraic equations that are solved for the average total flux in each subregion. When ordinary diffusion theory applies with satisfactory precision in a portion of the multiple-slab configuration, the problem is solved by ordinary diffusion theory, but the flux is plotted only in the region of validity. The angular distribution of neutrons entering the remaining portion is determined from the known diffusion flux and the remaining region is solved by higher order theory. Several procedures for applying the numerical method are presented and discussed. To illustrate the calculational procedure, a symmetrical slab ia vacuum is worked by the numerical, Monte Carlo, and P(sub 3) spherical harmonics methods. In addition, an unsymmetrical double-slab problem is solved by the numerical and Monte Carlo methods. The numerical approach proved faster and more accurate in these examples. Adaptation of the method to anisotropic scattering in slabs is indicated, although no example is included in this paper.

Microwave scattering and emission from a half-space anisotropic random medium

NASA Astrophysics Data System (ADS)

Mudaliar, Saba; Lee, Jay Kyoon

1990-12-01

This paper is a sequel to an earlier paper (Lee and Mudaliar, 1988) where the backscattering coefficients of a half-space anisotropic random medium were obtained. Here the bistatic scattering coefficients are calculated by solving the modified radiative transfer equations under a first-order approximation. The effects of multiple scattering on the results are observed. Emissivities are calculated and compared with those obtained using the Born approximation (single scattering). Several interesting properties of the model are brought to notice using numerical examples. Finally, as an application, the theory is used to interpret the passive remote sensing data of multiyear sea ice in the microwave frequency range. A quite close agreement between theoretical prediction and the measured data is found.

GPU acceleration of the Locally Selfconsistent Multiple Scattering code for first principles calculation of the ground state and statistical physics of materials

NASA Astrophysics Data System (ADS)

Eisenbach, Markus; Larkin, Jeff; Lutjens, Justin; Rennich, Steven; Rogers, James H.

2017-02-01

The Locally Self-consistent Multiple Scattering (LSMS) code solves the first principles Density Functional theory Kohn-Sham equation for a wide range of materials with a special focus on metals, alloys and metallic nano-structures. It has traditionally exhibited near perfect scalability on massively parallel high performance computer architectures. We present our efforts to exploit GPUs to accelerate the LSMS code to enable first principles calculations of O(100,000) atoms and statistical physics sampling of finite temperature properties. We reimplement the scattering matrix calculation for GPUs with a block matrix inversion algorithm that only uses accelerator memory. Using the Cray XK7 system Titan at the Oak Ridge Leadership Computing Facility we achieve a sustained performance of 14.5PFlop/s and a speedup of 8.6 compared to the CPU only code.

GPU acceleration of the Locally Selfconsistent Multiple Scattering code for first principles calculation of the ground state and statistical physics of materials

DOE PAGES

Eisenbach, Markus; Larkin, Jeff; Lutjens, Justin; ...

2016-07-12

The Locally Self-consistent Multiple Scattering (LSMS) code solves the first principles Density Functional theory Kohn–Sham equation for a wide range of materials with a special focus on metals, alloys and metallic nano-structures. It has traditionally exhibited near perfect scalability on massively parallel high performance computer architectures. In this paper, we present our efforts to exploit GPUs to accelerate the LSMS code to enable first principles calculations of O(100,000) atoms and statistical physics sampling of finite temperature properties. We reimplement the scattering matrix calculation for GPUs with a block matrix inversion algorithm that only uses accelerator memory. Finally, using the Craymore » XK7 system Titan at the Oak Ridge Leadership Computing Facility we achieve a sustained performance of 14.5PFlop/s and a speedup of 8.6 compared to the CPU only code.« less

New Examination of the Raman Lidar Technique for Water Vapor and Aerosols. Paper 1; Evaluating the Temperature Dependent Lidar Equations

NASA Technical Reports Server (NTRS)

Whiteman, David N.

2003-01-01

The intent of this paper and its companion is to compile together the essential information required for the analysis of Raman lidar water vapor and aerosol data acquired using a single laser wavelength. In this first paper several details concerning the evaluation of the lidar equation when measuring Raman scattering are considered. These details include the influence of the temperature dependence of both pure rotational and vibrational-rotational Raman scattering on the lidar profile. These are evaluated for the first time using a new form of the lidar equation. The results indicate that, for the range of temperatures encountered in the troposphere, the magnitude of the temperature dependent effect can reach 10% or more for narrowband Raman water vapor measurements. Also the calculation of atmospheric transmission is examined carefully including the effects of depolarization. Different formulations of Rayleigh cross section determination commonly used in the lidar field are compared revealing differences up to 5% among the formulations. The influence of multiple scattering on the measurement of aerosol extinction using the Raman lidar technique is considered as are several photon pulse-pileup correction techniques.

Comparison with CLPX II airborne data using DMRT model

USGS Publications Warehouse

Xu, X.; Liang, D.; Andreadis, K.M.; Tsang, L.; Josberger, E.G.

2009-01-01

In this paper, we considered a physical-based model which use numerical solution of Maxwell Equations in three-dimensional simulations and apply into Dense Media Radiative Theory (DMRT). The model is validated in two specific dataset from the second Cold Land Processes Experiment (CLPX II) at Alaska and Colorado. The data were all obtain by the Ku-band (13.95GHz) observations using airborne imaging polarimetric scatterometer (POLSCAT). Snow is a densely packed media. To take into account the collective scattering and incoherent scattering, analytical Quasi-Crystalline Approximation (QCA) and Numerical Maxwell Equation Method of 3-D simulation (NMM3D) are used to calculate the extinction coefficient and phase matrix. DMRT equations were solved by iterative solution up to 2nd order for the case of small optical thickness and full multiple scattering solution by decomposing the diffuse intensities into Fourier series was used when optical thickness exceed unity. It was shown that the model predictions agree with the field experiment not only co-polarization but also cross-polarization. For Alaska region, the input snow structure data was obtain by the in situ ground observations, while for Colorado region, we combined the VIC model to get the snow profile. ??2009 IEEE.

Linearized inversion of multiple scattering seismic energy

NASA Astrophysics Data System (ADS)

Aldawood, Ali; Hoteit, Ibrahim; Zuberi, Mohammad

2014-05-01

Internal multiples deteriorate the quality of the migrated image obtained conventionally by imaging single scattering energy. So, imaging seismic data with the single-scattering assumption does not locate multiple bounces events in their actual subsurface positions. However, imaging internal multiples properly has the potential to enhance the migrated image because they illuminate zones in the subsurface that are poorly illuminated by single scattering energy such as nearly vertical faults. Standard migration of these multiples provides subsurface reflectivity distributions with low spatial resolution and migration artifacts due to the limited recording aperture, coarse sources and receivers sampling, and the band-limited nature of the source wavelet. The resultant image obtained by the adjoint operator is a smoothed depiction of the true subsurface reflectivity model and is heavily masked by migration artifacts and the source wavelet fingerprint that needs to be properly deconvolved. Hence, we proposed a linearized least-square inversion scheme to mitigate the effect of the migration artifacts, enhance the spatial resolution, and provide more accurate amplitude information when imaging internal multiples. The proposed algorithm uses the least-square image based on single-scattering assumption as a constraint to invert for the part of the image that is illuminated by internal scattering energy. Then, we posed the problem of imaging double-scattering energy as a least-square minimization problem that requires solving the normal equation of the following form: GTGv = GTd, (1) where G is a linearized forward modeling operator that predicts double-scattered seismic data. Also, GT is a linearized adjoint operator that image double-scattered seismic data. Gradient-based optimization algorithms solve this linear system. Hence, we used a quasi-Newton optimization technique to find the least-square minimizer. In this approach, an estimate of the Hessian matrix that contains curvature information is modified at every iteration by a low-rank update based on gradient changes at every step. At each iteration, the data residual is imaged using GT to determine the model update. Application of the linearized inversion to synthetic data to image a vertical fault plane demonstrate the effectiveness of this methodology to properly delineate the vertical fault plane and give better amplitude information than the standard migrated image using the adjoint operator that takes into account internal multiples. Thus, least-square imaging of multiple scattering enhances the spatial resolution of the events illuminated by internal scattering energy. It also deconvolves the source signature and helps remove the fingerprint of the acquisition geometry. The final image is obtained by the superposition of the least-square solution based on single scattering assumption and the least-square solution based on double scattering assumption.

Solar system applications of Mie theory and of radiative transfer of polarized light

NASA Technical Reports Server (NTRS)

Whitehill, L. P.

1972-01-01

A theory of the multiple scattering of polarized light is discussed using the doubling method of van de Hulst. The concept of the Stokes parameters is derived and used to develop the form of the scattering phase matrix of a single particle. The diffuse reflection and transmission matrices of a single scattering plane parallel atmosphere are expressed as a function of the phase matrix, and the symmetry properties of these matrices are examined. Four matrices are required to describe scattering and transmission. The scattering matrix that results from the addition of two identical layers is derived. Using the doubling method, the scattering and transmission matrices of layers of arbitrary optical thickness can be derived. The doubling equations are then rewritten in terms of their Fourier components. Computation time is reduced since each Fourier component doubles independently. Computation time is also reduced through the use of symmetry properties.

Forward multiple scattering corrections as function of detector field of view

NASA Astrophysics Data System (ADS)

Zardecki, A.; Deepak, A.

1983-06-01

The theoretical formulations are given for an approximate method based on the solution of the radiative transfer equation in the small angle approximation. The method is approximate in the sense that an approximation is made in addition to the small angle approximation. Numerical results were obtained for multiple scattering effects as functions of the detector field of view, as well as the size of the detector's aperture for three different values of the optical depth tau (=1.0, 4.0 and 10.0). Three cases of aperture size were considered--namely, equal to or smaller or larger than the laser beam diameter. The contrast between the on-axis intensity and the received power for the last three cases is clearly evident.

Electrodynamic multiple-scattering method for the simulation of optical trapping atop periodic metamaterials

NASA Astrophysics Data System (ADS)

Yannopapas, Vassilios; Paspalakis, Emmanuel

2018-07-01

We present a new theoretical tool for simulating optical trapping of nanoparticles in the presence of an arbitrary metamaterial design. The method is based on rigorously solving Maxwell's equations for the metamaterial via a hybrid discrete-dipole approximation/multiple-scattering technique and direct calculation of the optical force exerted on the nanoparticle by means of the Maxwell stress tensor. We apply the method to the case of a spherical polystyrene probe trapped within the optical landscape created by illuminating of a plasmonic metamaterial consisting of periodically arranged tapered metallic nanopyramids. The developed technique is ideally suited for general optomechanical calculations involving metamaterial designs and can compete with purely numerical methods such as finite-difference or finite-element schemes.

Developments in spectrophotometry III: Multiple-field-of-view spectrometer to determine particle-size distribution and refractive index

NASA Technical Reports Server (NTRS)

Fymat, A. L.

1975-01-01

Instrument is based on inverse solution ot equations for light scattered by a transparent medium. Measurements are taken over several angles of incidence rather than over several frequencies. Measurements can be used to simultaneously determine chemical and physical properties of particles in mixed gas or liquid.

Investigation of multiple scattering effects in aerosols

NASA Technical Reports Server (NTRS)

Deepak, A.

1980-01-01

The results are presented of investigations on the various aspects of multiple scattering effects on visible and infrared laser beams transversing dense fog oil aerosols contained in a chamber (4' x 4' x 9'). The report briefly describes: (1) the experimental details and measurements; (2) analytical representation of the aerosol size distribution data by two analytical models (the regularized power law distribution and the inverse modified gamma distribution); (3) retrieval of aerosol size distributions from multispectral optical depth measurements by two methods (the two and three parameter fast table search methods and the nonlinear least squares method); (4) modeling of the effects of aerosol microphysical (coagulation and evaporation) and dynamical processes (gravitational settling) on the temporal behavior of aerosol size distribution, and hence on the extinction of four laser beams with wavelengths 0.44, 0.6328, 1.15, and 3.39 micrometers; and (5) the exact and approximate formulations for four methods for computing the effects of multiple scattering on the transmittance of laser beams in dense aerosols, all of which are based on the solution of the radiative transfer equation under the small angle approximation.

Investigation of multiple scattering effects in aerosols

NASA Astrophysics Data System (ADS)

Deepak, A.

1980-05-01

The results are presented of investigations on the various aspects of multiple scattering effects on visible and infrared laser beams transversing dense fog oil aerosols contained in a chamber (4' x 4' x 9'). The report briefly describes: (1) the experimental details and measurements; (2) analytical representation of the aerosol size distribution data by two analytical models (the regularized power law distribution and the inverse modified gamma distribution); (3) retrieval of aerosol size distributions from multispectral optical depth measurements by two methods (the two and three parameter fast table search methods and the nonlinear least squares method); (4) modeling of the effects of aerosol microphysical (coagulation and evaporation) and dynamical processes (gravitational settling) on the temporal behavior of aerosol size distribution, and hence on the extinction of four laser beams with wavelengths 0.44, 0.6328, 1.15, and 3.39 micrometers; and (5) the exact and approximate formulations for four methods for computing the effects of multiple scattering on the transmittance of laser beams in dense aerosols, all of which are based on the solution of the radiative transfer equation under the small angle approximation.

Fully nonlocal inelastic scattering computations for spectroscopical transmission electron microscopy methods

NASA Astrophysics Data System (ADS)

Rusz, Ján; Lubk, Axel; Spiegelberg, Jakob; Tyutyunnikov, Dmitry

2017-12-01

The complex interplay of elastic and inelastic scattering amenable to different levels of approximation constitutes the major challenge for the computation and hence interpretation of TEM-based spectroscopical methods. The two major approaches to calculate inelastic scattering cross sections of fast electrons on crystals—Yoshioka-equations-based forward propagation and the reciprocal wave method—are founded in two conceptually differing schemes—a numerical forward integration of each inelastically scattered wave function, yielding the exit density matrix, and a computation of inelastic scattering matrix elements using elastically scattered initial and final states (double channeling). Here, we compare both approaches and show that the latter is computationally competitive to the former by exploiting analytical integration schemes over multiple excited states. Moreover, we show how to include full nonlocality of the inelastic scattering event, neglected in the forward propagation approaches, at no additional computing costs in the reciprocal wave method. Detailed simulations show in some cases significant errors due to the z -locality approximation and hence pitfalls in the interpretation of spectroscopical TEM results.

Variational treatment of electron-polyatomic-molecule scattering calculations using adaptive overset grids

NASA Astrophysics Data System (ADS)

Greenman, Loren; Lucchese, Robert R.; McCurdy, C. William

2017-11-01

The complex Kohn variational method for electron-polyatomic-molecule scattering is formulated using an overset-grid representation of the scattering wave function. The overset grid consists of a central grid and multiple dense atom-centered subgrids that allow the simultaneous spherical expansions of the wave function about multiple centers. Scattering boundary conditions are enforced by using a basis formed by the repeated application of the free-particle Green's function and potential Ĝ0+V ̂ on the overset grid in a Born-Arnoldi solution of the working equations. The theory is shown to be equivalent to a specific Padé approximant to the T matrix and has rapid convergence properties, in both the number of numerical basis functions employed and the number of partial waves employed in the spherical expansions. The method is demonstrated in calculations on methane and CF4 in the static-exchange approximation and compared in detail with calculations performed with the numerical Schwinger variational approach based on single-center expansions. An efficient procedure for operating with the free-particle Green's function and exchange operators (to which no approximation is made) is also described.

Multiple-reflection model of human skin and estimation of pigment concentrations

NASA Astrophysics Data System (ADS)

Ohtsuki, Rie; Tominaga, Shoji; Tanno, Osamu

2012-07-01

We describe a new method for estimating the concentrations of pigments in the human skin using surface spectral reflectance. We derive an equation that expresses the surface spectral reflectance of the human skin. First, we propose an optical model of the human skin that accounts for the stratum corneum. We also consider the difference between the scattering coefficient of the epidermis and that of the dermis. We then derive an equation by applying the Kubelka-Munk theory to an optical model of the human skin. Unlike a model developed in a recent study, the present equation considers pigments as well as multiple reflections and the thicknesses of the skin layers as factors that affect the color of the human skin. In two experiments, we estimate the pigment concentrations using the measured surface spectral reflectances. Finally, we confirm the feasibility of the concentrations estimated by the proposed method by evaluating the estimated pigment concentrations in the skin.

Magnetic order at a single-crystal surface in the diffuse-scattering theory

NASA Astrophysics Data System (ADS)

Zasada, I.

2003-06-01

A theoretical description of incoherent spin-dependent multiple scattering of electrons at a magnetically disordered single-crystal surface is reported. A formalism in which the spin operators specify the magnetic state of a surface atom is used for the description of magnetic order at the surface. The theory is based upon the concepts used in multiple scattering spin-dependent diffuse LEED theory (DSPLEED) theory. In the present considerations, this theory is extended to the case of magnetic materials by using the time-independent Dirac equation with an effective magnetic field. Thus, an expression for incoherent spin-dependent intensity for magnetic material is obtained. It depends on the Fourier transform on the surface lattice of the spin-pair correlation function and, as a consequence, on the magnetic properties of the surface. The equations for the description of magnetization and various correlation functions in the frame of effective field theory are derived and the results of the numerical calculations are presented for the particular case of Ni(1 0 0) surface. The spin-orbit induced and exchange asymmetries are calculated. It is found that the magnetic DSPLEED is sensitive to the properties of the surface characterized by the spin-pair correlation functions. Thus, it is demonstrated that the magnetic DSPLEED can be an effective method in the investigation of critical behaviour of magnetic surfaces.

Compacton solutions in a class of generalized fifth-order Korteweg-de Vries equations.

PubMed

Cooper, F; Hyman, J M; Khare, A

2001-08-01

Solitons play a fundamental role in the evolution of general initial data for quasilinear dispersive partial differential equations, such as the Korteweg-de Vries (KdV), nonlinear Schrödinger, and the Kadomtsev-Petviashvili equations. These integrable equations have linear dispersion and the solitons have infinite support. We have derived and investigate a new KdV-like Hamiltonian partial differential equation from a four-parameter Lagrangian where the nonlinear dispersion gives rise to solitons with compact support (compactons). The new equation does not seem to be integrable and only mass, momentum, and energy seem to be conserved; yet, the solitons display almost the same modal decompositions and structural stability observed in integrable partial differential equations. The compactons formed from arbitrary initial data, are nonlinearly self-stabilizing, and maintain their coherence after multiple collisions. The robustness of these compactons and the inapplicability of the inverse scattering tools, that worked so well for the KdV equation, make it clear that there is a fundamental mechanism underlying the processes beyond integrability. We have found explicit formulas for multiple classes of compact traveling wave solutions. When there are more than one compacton solution for a particular set of parameters, the wider compacton is the minimum of a reduced Hamiltonian and is the only one that is stable.

Multiple Volume Scattering in Random Media and Periodic Structures with Applications in Microwave Remote Sensing and Wave Functional Materials

NASA Astrophysics Data System (ADS)

Tan, Shurun

The objective of my research is two-fold: to study wave scattering phenomena in dense volumetric random media and in periodic wave functional materials. For the first part, the goal is to use the microwave remote sensing technique to monitor water resources and global climate change. Towards this goal, I study the microwave scattering behavior of snow and ice sheet. For snowpack scattering, I have extended the traditional dense media radiative transfer (DMRT) approach to include cyclical corrections that give rise to backscattering enhancements, enabling the theory to model combined active and passive observations of snowpack using the same set of physical parameters. Besides DMRT, a fully coherent approach is also developed by solving Maxwell's equations directly over the entire snowpack including a bottom half space. This revolutionary new approach produces consistent scattering and emission results, and demonstrates backscattering enhancements and coherent layer effects. The birefringence in anisotropic snow layers is also analyzed by numerically solving Maxwell's equation directly. The effects of rapid density fluctuations in polar ice sheet emission in the 0.5˜2.0 GHz spectrum are examined using both fully coherent and partially coherent layered media emission theories that agree with each other and distinct from incoherent approaches. For the second part, the goal is to develop integral equation based methods to solve wave scattering in periodic structures such as photonic crystals and metamaterials that can be used for broadband simulations. Set upon the concept of modal expansion of the periodic Green's function, we have developed the method of broadband Green's function with low wavenumber extraction (BBGFL), where a low wavenumber component is extracted and results a non-singular and fast-converging remaining part with simple wavenumber dependence. We've applied the technique to simulate band diagrams and modal solutions of periodic structures, and to construct broadband Green's functions including periodic scatterers.

Ultrasound scatter in heterogeneous 3D microstructures: Parameters affecting multiple scattering

NASA Astrophysics Data System (ADS)

Engle, B. J.; Roberts, R. A.; Grandin, R. J.

2018-04-01

This paper reports on a computational study of ultrasound propagation in heterogeneous metal microstructures. Random spatial fluctuations in elastic properties over a range of length scales relative to ultrasound wavelength can give rise to scatter-induced attenuation, backscatter noise, and phase front aberration. It is of interest to quantify the dependence of these phenomena on the microstructure parameters, for the purpose of quantifying deleterious consequences on flaw detectability, and for the purpose of material characterization. Valuable tools for estimation of microstructure parameters (e.g. grain size) through analysis of ultrasound backscatter have been developed based on approximate weak-scattering models. While useful, it is understood that these tools display inherent inaccuracy when multiple scattering phenomena significantly contribute to the measurement. It is the goal of this work to supplement weak scattering model predictions with corrections derived through application of an exact computational scattering model to explicitly prescribed microstructures. The scattering problem is formulated as a volume integral equation (VIE) displaying a convolutional Green-function-derived kernel. The VIE is solved iteratively employing FFT-based con-volution. Realizations of random microstructures are specified on the micron scale using statistical property descriptions (e.g. grain size and orientation distributions), which are then spatially filtered to provide rigorously equivalent scattering media on a length scale relevant to ultrasound propagation. Scattering responses from ensembles of media representations are averaged to obtain mean and variance of quantities such as attenuation and backscatter noise levels, as a function of microstructure descriptors. The computational approach will be summarized, and examples of application will be presented.

Inverse scattering transform for the time dependent Schrödinger equation with applications to the KPI equation

NASA Astrophysics Data System (ADS)

Zhou, Xin

1990-03-01

For the direct-inverse scattering transform of the time dependent Schrödinger equation, rigorous results are obtained based on an opertor-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution.

Complex index of refraction estimation from degree of polarization with diffuse scattering consideration.

PubMed

Zhan, Hanyu; Voelz, David G; Cho, Sang-Yeon; Xiao, Xifeng

2015-11-20

The estimation of the refractive index from optical scattering off a target's surface is an important task for remote sensing applications. Optical polarimetry is an approach that shows promise for refractive index estimation. However, this estimation often relies on polarimetric models that are limited to specular targets involving single surface scattering. Here, an analytic model is developed for the degree of polarization (DOP) associated with reflection from a rough surface that includes the effect of diffuse scattering. A multiplicative factor is derived to account for the diffuse component and evaluation of the model indicates that diffuse scattering can significantly affect the DOP values. The scattering model is used in a new approach for refractive index estimation from a series of DOP values that involves jointly estimating n, k, and ρ(d)with a nonlinear equation solver. The approach is shown to work well with simulation data and additive noise. When applied to laboratory-measured DOP values, the approach produces significantly improved index estimation results relative to reference values.

Approximating Reflectance and Transmittance of Vegetation Using Multiple Spectral Invariants

NASA Astrophysics Data System (ADS)

Mottus, M.

2011-12-01

Canopy spectral invariants, eigenvalues of the radiative transfer equation and photon recollision probability are some of the new theoretical tools that have been applied in remote sensing of vegetation and atmosphere. The theoretical approach based on spectral invariants, informally also referred to as the p-theory, owns its attractivity to several factors. Firstly, it provides a rapid and physically-based way of describing canopy scattering. Secondly, the p-theory aims at parameterizing canopy structure in reflectance models using a simple and intuitive concept which can be applied at various structural levels, from shoot to tree crown. The theory has already been applied at scales from the molecular level to forest stands. The most important shortcoming of the p-theory lies in its inability to predict the directionality of scattering. The theory is currently based on only one physical parameter, the photon recollision probability p. It is evident that one parameter cannot contain enough information to reasonably predict the observed complex reflectance patterns produced by natural vegetation canopies. Without estimating scattering directionality, however, the theory cannot be compared with even the most simple (and well-tested) two-stream vegetation reflectance models. In this study, we evaluate the possibility to use additional parameters to fit the measured reflectance and transmittance of a vegetation stand. As a first step, the parameters are applied to separate canopy scattering into reflectance and transmittance. New parameters are introduced following the general approach of eigenvector expansion. Thus, the new parameters are coined higher-order spectral invariants. Calculation of higher-order invariants is based on separating first-order scattering from total scattering. Thus, the method explicitly accounts for different view geometries with different fractions of visible sunlit canopy (e.g., hot-spot). It additionally allows to produce different irradiation levels on leaf surfaces for direct and diffuse incidence, thus (in theory) allowing more accurate calculation of potential photosynthesis rates. Similarly to the p-theory, the use of multiple spectral invariants facilitates easy parametrization of canopy structure and scaling between different structural levels (leaf-shoot-stand). Spectral invariant-based remote sensing approaches are well suited for relatively large pixels even when no detailed ground truth information is available. In a case study, the theory of multiple spectral invariants was applied to measured canopy scattering. Spectral reflectance and transmittance measurements were carried out in gray alder (Alnus incana) plantation at Tartu Observatory, Estonia, in August 2006. The equations produced by the theory of spectral invariants were fitted to measured radiation fluxes. Preliminary results indicate that quantities with invariant-like behavior may indeed be used to approximate canopy scattering directionality.

Robust multiscale field-only formulation of electromagnetic scattering

NASA Astrophysics Data System (ADS)

Sun, Qiang; Klaseboer, Evert; Chan, Derek Y. C.

2017-01-01

We present a boundary integral formulation of electromagnetic scattering by homogeneous bodies that are characterized by linear constitutive equations in the frequency domain. By working with the Cartesian components of the electric E and magnetic H fields and with the scalar functions (r .E ) and (r .H ) where r is a position vector, the problem can be cast as having to solve a set of scalar Helmholtz equations for the field components that are coupled by the usual electromagnetic boundary conditions at material boundaries. This facilitates a direct solution for the surface values of E and H rather than having to work with surface currents or surface charge densities as intermediate quantities in existing methods. Consequently, our formulation is free of the well-known numerical instability that occurs in the zero-frequency or long-wavelength limit in traditional surface integral solutions of Maxwell's equations and our numerical results converge uniformly to the static results in the long-wavelength limit. Furthermore, we use a formulation of the scalar Helmholtz equation that is expressed as classically convergent integrals and does not require the evaluation of principal value integrals or any knowledge of the solid angle. Therefore, standard quadrature and higher order surface elements can readily be used to improve numerical precision for the same number of degrees of freedom. In addition, near and far field values can be calculated with equal precision, and multiscale problems in which the scatterers possess characteristic length scales that are both large and small relative to the wavelength can be easily accommodated. From this we obtain results for the scattering and transmission of electromagnetic waves at dielectric boundaries that are valid for any ratio of the local surface curvature to the wave number. This is a generalization of the familiar Fresnel formula and Snell's law, valid at planar dielectric boundaries, for the scattering and transmission of electromagnetic waves at surfaces of arbitrary curvature. Implementation details are illustrated with scattering by multiple perfect electric conductors as well as dielectric bodies with complex geometries and composition.

Robust iterative method for nonlinear Helmholtz equation

NASA Astrophysics Data System (ADS)

Yuan, Lijun; Lu, Ya Yan

2017-08-01

A new iterative method is developed for solving the two-dimensional nonlinear Helmholtz equation which governs polarized light in media with the optical Kerr nonlinearity. In the strongly nonlinear regime, the nonlinear Helmholtz equation could have multiple solutions related to phenomena such as optical bistability and symmetry breaking. The new method exhibits a much more robust convergence behavior than existing iterative methods, such as frozen-nonlinearity iteration, Newton's method and damped Newton's method, and it can be used to find solutions when good initial guesses are unavailable. Numerical results are presented for the scattering of light by a nonlinear circular cylinder based on the exact nonlocal boundary condition and a pseudospectral method in the polar coordinate system.

Molar mass, radius of gyration and second virial coefficient from new static light scattering equations for dilute solutions: application to 21 (macro)molecules.

PubMed

Illien, Bertrand; Ying, Ruifeng

2009-05-11

New static light scattering (SLS) equations for dilute binary solutions are derived. Contrarily to the usual SLS equations [Carr-Zimm (CZ)], the new equations have no need for the experimental absolute Rayleigh ratio of a reference liquid and solely rely on the ratio of scattered intensities of solutions and solvent. The new equations, which are based on polarizability equations, take into account the usual refractive index increment partial differential n/partial differential rho(2) complemented by the solvent specific polarizability and a term proportional to the slope of the solution density rho versus the solute mass concentration rho(2) (density increment). Then all the equations are applied to 21 (macro)molecules with a wide range of molar mass (0.2500 kg mol(-1)), for which the scattered intensity is no longer independent of the scattering angle, the new equations give the same value of the radius of gyration as the CZ equation and consistent values of the second virial coefficient.

Development of a human eye model incorporated with intraocular scattering for visual performance assessment

NASA Astrophysics Data System (ADS)

Chen, Yi-Chun; Jiang, Chong-Jhih; Yang, Tsung-Hsun; Sun, Ching-Cherng

2012-07-01

A biometry-based human eye model was developed by using the empirical anatomic and optical data of ocular parameters. The gradient refractive index of the crystalline lens was modeled by concentric conicoid isoindical surfaces and was adaptive to accommodation and age. The chromatic dispersion of ocular media was described by Cauchy equations. The intraocular scattering model was composed of volumetric Mie scattering in the cornea and the crystalline lens, and a diffusive-surface model at the retina fundus. The retina was regarded as a Lambertian surface and was assigned its corresponding reflectance at each wavelength. The optical performance of the eye model was evaluated in CodeV and ASAP and presented by the modulation transfer functions at single and multiple wavelengths. The chromatic optical powers obtained from this model resembled that of the average physiological eyes. The scattering property was assessed by means of glare veiling luminance and compared with the CIE general disability glare equation. By replacing the transparent lens with a cataractous lens, the disability glare curve of cataracts was generated to compare with the normal disability glare curve. This model has high potential for investigating visual performance in ordinary lighting and display conditions and under the influence of glare sources.

Multiplicity of transmission coefficients in photonic crystal and split ring resonator waveguides with Kerr nonlinear impurities

NASA Astrophysics Data System (ADS)

Rai, Buddhi; McGurn, Arthur R.

2015-02-01

Photonic crystal and split ring resonator (SRR) metamaterial waveguides with Kerr nonlinear dielectric impurities are studied. The transmission coefficients for two guided modes of different frequencies scattering from the Kerr impurities are computed. The systems are shown to exhibit multiple transmission coefficient solutions arising from the Kerr nonlinearity. Multiple transmission coefficients occur when different input intensities into a waveguide result in the same transmitted output intensities past its nonlinear impurities. (In the case of a single incident guided mode the multiplicity of transmission coefficients is known as optical bistability.) The analytical conditions under which the transmission coefficients are single and multiple valued are determined, and specific examples of both single and multiple valued transmission coefficient scattering are presented. Both photonic crystal and split ring resonator systems are studied as the Kerr nonlinearity enters the photonic crystal and SRR systems in different ways. This allows for an interesting comparison of the differences in behaviors of these two types of system which are described by distinctly different mathematical structures. Both the photonic crystal and SRR models used in the calculations are based on a difference equation approach to the system dynamics. The difference equation approach has been extensively employed in previous papers to model the basic properties of these systems. The paper is a continuation of work on the optical bistability of single guided modes interacting with Kerr impurities in photonic crystals originally considered by McGurn [Chaos 13, 754 (2003), 10.1063/1.1568691] and work on the resonant scattering from Kerr impurities in photonic crystal waveguides considered by McGurn [J. Phys.: Condens. Matter 16, S5243 (2004), 10.1088/0953-8984/16/44/021]. It generalizes this work making the extension to the more complex interaction of two guided modes at different frequencies. It extends the two guided mode treatment by McGurn [Organ. Electron. 8, 227 (2007), 10.1016/j.orgel.2006.06.008] which was limited to a special case of one of the photonic crystal systems considered here.

Spin Filtering in Storage Rings

NASA Astrophysics Data System (ADS)

Nikolaev, N. N.; Pavlov, F. F.

The spin filtering in storage rings is based on a multiple passage of a stored beam through a polarized internal gas target. Apart from the polarization by the spin-dependent transmission, a unique geometrical feature of interaction with the target in such a filtering process, pointed out by H.O. Meyer,1 is a scattering of stored particles within the beam. A rotation of the spin in the scattering process affects the polarization buildup. We derive here a quantum-mechanical evolution equation for the spin-density matrix of a stored beam which incorporates the scattering within the beam. We show how the interplay of the transmission and scattering within the beam changes from polarized electrons to polarized protons in the atomic target. After discussions of the FILTEX results on the filtering of stored protons,2 we comment on the strategy of spin filtering of antiprotons for the PAX experiment at GSI FAIR.3.

Liquid hydrogen mass flow through a multiple orifice Joule-Thomson device

NASA Astrophysics Data System (ADS)

Papell, S. Stephen; Nyland, Ted W.; Saiyed, Naseem H.

Liquid hydrogen mass flow rate, pressure drop, and temperature drop data were obtained for a number of multiple orifice Joule-Thomas devices known as visco jets. The present investigation continues a study to develop an equation for predicting two phase flow of cryogens through these devices. The test apparatus design allowed isenthalpic expansion of the cryogen through the visco jets. The data covered a range of inlet and outlet operating conditions. The mass flow rate range single phase or two phase was 0.015 to 0.98 lbm/hr. The manufacturer's equation was found to overpredict the single phase hydrogen data by 10 percent and the two phase data by as much as 27 percent. Two modifications of the equation resulted in a data correlation that predicts both the single and two phase flow across the visco jet. The first modification was of a theoretical nature, and the second strictly empirical. The former reduced the spread in the two phase data. It was a multiplication factor of 1 - X applied to the manufacturer's equation. The parameter X is the flow quality downstream of the visco jet based on isenthalpic expansion across the device. The latter modification was a 10 percent correction term that correlated 90 percent of the single and two phase data to within +/- 10 percent scatter band.

Liquid hydrogen mass flow through a multiple orifice Joule-Thomson device

NASA Technical Reports Server (NTRS)

Papell, S. S.; Nyland, Ted W.; Saiyed, Naseem H.

1992-01-01

Liquid hydrogen mass flow rate, pressure drop, and temperature drop data were obtained for a number of multiple orifice Joule-Thomson devices known as visco jets. The present investigation continues a study to develop an equation for predicting two phase flow of cryogens through these devices. The test apparatus design allowed isenthalpic expansion of the cryogen through the visco jets. The data covered a range of inlet and outlet operating conditions. The mass flow rate range single phase or two phase was 0.015 to 0.98 lbm/hr. The manufacturer's equation was found to overpredict the single phase hydrogen data by 10 percent and the two phase data by as much as 27 percent. Two modifications of the equation resulted in a data correlation that predicts both the single and two phase flow across the visco jet. The first modification was of a theoretical nature, and the second strictly empirical. The former reduced the spread in the two phase data. It was a multiplication factor of 1-X applied to the manufacturer's equation. The parameter X is the flow quality downstream of the visco jet based on isenthalpic expansion across the device. The latter modification was a 10 percent correction term that correlated 90 percent of the single and two phase data to within +/- 10 percent scatter band.

Liquid hydrogen mass flow through a multiple orifice Joule-Thomson device

NASA Technical Reports Server (NTRS)

Papell, S. Stephen; Nyland, Ted W.; Saiyed, Naseem H.

1992-01-01

Liquid hydrogen mass flow rate, pressure drop, and temperature drop data were obtained for a number of multiple orifice Joule-Thomas devices known as visco jets. The present investigation continues a study to develop an equation for predicting two phase flow of cryogens through these devices. The test apparatus design allowed isenthalpic expansion of the cryogen through the visco jets. The data covered a range of inlet and outlet operating conditions. The mass flow rate range single phase or two phase was 0.015 to 0.98 lbm/hr. The manufacturer's equation was found to overpredict the single phase hydrogen data by 10 percent and the two phase data by as much as 27 percent. Two modifications of the equation resulted in a data correlation that predicts both the single and two phase flow across the visco jet. The first modification was of a theoretical nature, and the second strictly empirical. The former reduced the spread in the two phase data. It was a multiplication factor of 1 - X applied to the manufacturer's equation. The parameter X is the flow quality downstream of the visco jet based on isenthalpic expansion across the device. The latter modification was a 10 percent correction term that correlated 90 percent of the single and two phase data to within +/- 10 percent scatter band.

Liquid hydrogen mass flow through a multiple orifice Joule-Thomson device

NASA Astrophysics Data System (ADS)

Papell, S. S.; Nyland, Ted W.; Saiyed, Naseem H.

1992-07-01

Liquid hydrogen mass flow rate, pressure drop, and temperature drop data were obtained for a number of multiple orifice Joule-Thomson devices known as visco jets. The present investigation continues a study to develop an equation for predicting two phase flow of cryogens through these devices. The test apparatus design allowed isenthalpic expansion of the cryogen through the visco jets. The data covered a range of inlet and outlet operating conditions. The mass flow rate range single phase or two phase was 0.015 to 0.98 lbm/hr. The manufacturer's equation was found to overpredict the single phase hydrogen data by 10 percent and the two phase data by as much as 27 percent. Two modifications of the equation resulted in a data correlation that predicts both the single and two phase flow across the visco jet. The first modification was of a theoretical nature, and the second strictly empirical. The former reduced the spread in the two phase data. It was a multiplication factor of 1-X applied to the manufacturer's equation. The parameter X is the flow quality downstream of the visco jet based on isenthalpic expansion across the device. The latter modification was a 10 percent correction term that correlated 90 percent of the single and two phase data to within +/- 10 percent scatter band.

Coupled atmosphere/canopy model for remote sensing of plant reflectance features

NASA Technical Reports Server (NTRS)

Gerstl, S. A.; Zardecki, A.

1985-01-01

Solar radiative transfer through a coupled system of atmosphere and plant canopy is modeled as a multiple-scattering problem through a layered medium of random scatterers. The radiative transfer equation is solved by the discrete-ordinates finite-element method. Analytic expressions are derived that allow the calculation of scattering and absorption cross sections for any plant canopy layer form measurable biophysical parameters such as the leaf area index, leaf angle distribution, and individual leaf reflectance and transmittance data. An expression for a canopy scattering phase function is also given. Computational results are in good agreement with spectral reflectance measurements directly above a soybean canopy, and the concept of greenness- and brightness-transforms of Landsat MSS data is reconfirmed with the computed results. A sensitivity analysis with the coupled atmosphere/canopy model quantifies how satellite-sensed spectral radiances are affected by increased atmospheric aerosols, by varying leaf area index, by anisotropic leaf scattering, and by non-Lambertian soil boundary conditions. Possible extensions to a 2-D model are also discussed.

Direct observation of the two-plasmon-decay common plasma wave using ultraviolet Thomson scattering.

PubMed

Follett, R K; Edgell, D H; Henchen, R J; Hu, S X; Katz, J; Michel, D T; Myatt, J F; Shaw, J; Froula, D H

2015-03-01

A 263-nm Thomson-scattering beam was used to directly probe two-plasmon-decay (TPD) excited electron plasma waves (EPWs) driven by between two and five 351-nm beams on the OMEGA Laser System. The amplitude of these waves was nearly independent of the number of drive beams at constant overlapped intensity, showing that the observed EPWs are common to the multiple beams. In an experimental configuration where the Thomson-scattering diagnostic was not wave matched to the common TPD EPWs, a broad spectrum of TPD-driven EPWs was observed, indicative of nonlinear effects associated with TPD saturation. Electron plasma waves corresponding to Langmuir decay of TPD EPWs were observed in both Thomson-scattering spectra, suggesting the Langmuir decay instability as a TPD saturation mechanism. Simulated Thomson-scattering spectra from three-dimensional numerical solutions of the extended Zakharov equations of TPD are in excellent agreement with the experimental spectra and verify the presence of the Langmuir decay instability.

Direct observation of the two-plasmon-decay common plasma wave using ultraviolet Thomson scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Follett, R. K.; Edgell, D. H.; Henchen, R. J.

2015-03-26

A 263-nm Thomson-scattering beam was used to directly probe two-plasmon-decay (TPD) excited electron plasma waves (EPWs) driven by between two and five 351-nm beams on the OMEGA Laser System. The amplitude of these waves was nearly independent of the number of drive beams at constant overlapped intensity, showing that the observed EPWs are common to the multiple beams. In an experimental configuration where the Thomson-scattering diagnostic was not wave matched to the common TPD EPWs, a broad spectrum of TPD-driven EPWs was observed, indicative of nonlinear effects associated with TPD saturation. Electron plasma waves corresponding to Langmuir decay of TPDmore » EPWs were observed in both Thomson-scattering spectra, suggesting the Langmuir decay instability as a TPD saturation mechanism. Simulated Thomson-scattering spectra from three-dimensional numerical solutions of the extended Zakharov equations of TPD are in excellent agreement with the experimental spectra and verify the presence of the Langmuir decay instability.« less

Modeling and analysis of multiple scattering of acoustic waves in complex media: application to the trabecular bone.

PubMed

Wojcik, J; Litniewski, J; Nowicki, A

2011-10-01

The integral equations that describe scattering in the media with step-rise changing parameters have been numerically solved for the trabecular bone model. The model consists of several hundred discrete randomly distributed elements. The spectral distribution of scattering coefficients in subsequent orders of scattering has been presented. Calculations were carried on for the ultrasonic frequency ranging from 0.5 to 3 MHz. Evaluation of the contribution of the first, second, and higher scattering orders to total scattering of the ultrasounds in trabecular bone was done. Contrary to the approaches that use the μCT images of trabecular structure to modeling of the ultrasonic wave propagation condition, the 3D numerical model consisting of cylindrical elements mimicking the spatial matrix of trabeculae, was applied. The scattering, due to interconnections between thick trabeculae, usually neglected in trabecular bone models, has been included in calculations when the structure backscatter was evaluated. Influence of the absorption in subsequent orders of scattering is also addressed. Results show that up to 1.5 MHz, the influence of higher scattering orders on the total scattered field characteristic can be neglected while for the higher frequencies, the relatively high amplitude interference peaks in higher scattering orders clearly occur. © 2011 Acoustical Society of America

Some examples of exact and approximate solutions in small particle scattering - A progress report

NASA Technical Reports Server (NTRS)

Greenberg, J. M.

1974-01-01

The formulation of basic equations from which the scattering of radiation by a localized variation in a medium is discussed. These equations are developed in both the differential and the integral form. Primary interest is in the scattering of electromagnetic waves for which the solution of the vector wave equation with appropriate boundary conditions must be considered. Scalar scattering by an infinite homogeneous isotropic circular cylinder, and scattering of electromagnetic waves by infinite circular cylinders are treated, and the case of the finite circular cylinder is considered. A procedure is given for obtaining angular scattering distributions from spheroids.

Invertible propagator for plane wave illumination of forward-scattering structures.

PubMed

Samelsohn, Gregory

2017-05-10

Propagation of directed waves in forward-scattering media is considered. It is assumed that the evolution of the wave field is governed by the standard parabolic wave equation. An efficient one-step momentum-space propagator, suitable for a tilted plane wave illumination of extended objects, is derived. It is expressed in terms of a propagation operator that transforms (the complex exponential of) a linogram of the illuminated object into a set of its diffraction patterns. The invertibility of the propagator is demonstrated, which permits a multiple-shot scatter correction to be performed, and makes the solution especially attractive for either projective or tomographic imaging. As an example, high-resolution tomograms are obtained in numerical simulations implemented for a synthetic phantom, with both refractive and absorptive inclusions.

The forward rainbow scattering of low energy protons by a graphene sheet

NASA Astrophysics Data System (ADS)

Ćosić, M.; Petrović, S.; Nešković, N.

2018-05-01

This article studies the rainbow scattering of 5-keV protons by the single sheet of free-standing graphene and its possible use as a tool for investigation of the ion-graphene interaction. The proton-graphene interaction potential was constructed by using the Doyle-Turner, ZBL, and Molière proton-carbon interaction potentials. The thermal motion of carbon atoms was included by averaging the potentials according to the Debye model. Proton trajectories were obtained by numerical solution of the corresponding Newton equations of motion. They were used to obtain the mapping of the proton initial positions to their scattering angles. Morphological properties of the introduced mapping including its multiplicity and the rainbow singularities were used to explain important features of the obtained angular distributions of transmitted protons.

Photonic Breast Tomography and Tumor Aggressiveness Assessment

DTIC Science & Technology

2011-07-01

incorporates, in optical domain, the vector subspace classification method, Multiple Signal Classification ( MUSIC ). MUSIC was developed by Devaney...and co-workers for finding the location of scattering targets whose size is smaller than the wavelength of acoustic waves or electromagnetic waves...general area of array processing for acoustic and radar time-reversal imaging [12]. The eigenvalue equation of TR matrix is solved, and the signal and

Determination of the spectral values of the real part of the relative refractive index of human blood erythrocytes from the measured directional scattering coefficients

NASA Astrophysics Data System (ADS)

Kugeiko, M. M.; Lisenko, S. A.

2008-07-01

An easily automated method for determining the real part of the refractive index of human blood erythrocytes in the range 0.3 1.2 μm is proposed. The method is operationally and metrologically reliable and is based on the measurement of the coefficients of light scattering from forward and backward hemisphere by two pairs of angles and on the use of multiple regression equations. An engineering solution for constructing a measurement system according to this method is proposed, which makes it possible to maximally reduce the calibration errors and effects of destabilizing factors.

A Hydrodynamic Theory for Spatially Inhomogeneous Semiconductor Lasers: Microscopic Approach

NASA Technical Reports Server (NTRS)

Li, Jianzhong; Ning, C. Z.; Biegel, Bryan A. (Technical Monitor)

2001-01-01

Starting from the microscopic semiconductor Bloch equations (SBEs) including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell's equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole (e-h) and carrier-LO (c-LO) phonon scatterings are directly used to derive the momentum and energy relaxation rates. These rates expressed as functions of temperatures and densities lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma (EHP) to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-h scattering dominates over c-LO phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-h scattering, even though the diffusion coefficients of individual components depend sensitively on the e-h scattering rates. Our discussions lead to new perspectives into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization which in turn couples to the laser field.

Scattering Of Nonplanar Acoustic Waves

NASA Technical Reports Server (NTRS)

Gillman, Judith M.; Farassat, F.; Myers, M. K.

1995-01-01

Report presents theoretical study of scattering of nonplanar acoustic waves by rigid bodies. Study performed as part of effort to develop means of predicting scattering, from aircraft fuselages, of noise made by rotating blades. Basic approach was to model acoustic scattering by use of boundary integral equation to solve equation by the Galerkin method.

Diffusion approximation with polarization and resonance effects for the modelling of seismic waves in strongly scattering small-scale media

NASA Astrophysics Data System (ADS)

Margerin, Ludovic

2013-01-01

This paper presents an analytical study of the multiple scattering of seismic waves by a collection of randomly distributed point scatterers. The theory assumes that the energy envelopes are smooth, but does not require perturbations to be small, thereby allowing the modelling of strong, resonant scattering. The correlation tensor of seismic coda waves recorded at a three-component sensor is decomposed into a sum of eigenmodes of the elastodynamic multiple scattering (Bethe-Salpeter) equation. For a general moment tensor excitation, a total number of four modes is necessary to describe the transport of seismic waves polarization. Their spatio-temporal dependence is given in closed analytical form. Two additional modes transporting exclusively shear polarizations may be excited by antisymmetric moment tensor sources only. The general solution converges towards an equipartition mixture of diffusing P and S waves which allows the retrieval of the local Green's function from coda waves. The equipartition time is obtained analytically and the impact of absorption on Green's function reconstruction is discussed. The process of depolarization of multiply scattered waves and the resulting loss of information is illustrated for various seismic sources. It is shown that coda waves may be used to characterize the source mechanism up to lapse times of the order of a few mean free times only. In the case of resonant scatterers, a formula for the diffusivity of seismic waves incorporating the effect of energy entrapment inside the scatterers is obtained. Application of the theory to high-contrast media demonstrates that coda waves are more sensitive to slow rather than fast velocity anomalies by several orders of magnitude. Resonant scattering appears as an attractive physical phenomenon to explain the small values of the diffusion constant of seismic waves reported in volcanic areas.

A fast invariant imbedding method for multiple scattering calculations and an application to equivalent widths of CO2 lines on Venus

NASA Technical Reports Server (NTRS)

Sato, M.; Kawabata, K.; Hansen, J. E.

1977-01-01

The invariant imbedding method considered is based on an equation which describes the change in the reflected radiation when an optically thin layer is added to the top of the atmosphere. The equation is used to treat the problem of reflection from a planetary atmosphere as an initial value problem. A fast method is discussed for the solution of the invariant imbedding equation. The speed and accuracy of the new method are illustrated by comparing it with the doubling program published by Hansen and Travis (1974). Computations are performed of the equivalent widths of carbon dioxide absorption lines in solar radiation reflected by Venus for several models of the planetary atmosphere.

Finite difference time domain modeling of steady state scattering from jet engines with moving turbine blades

NASA Technical Reports Server (NTRS)

Ryan, Deirdre A.; Langdon, H. Scott; Beggs, John H.; Steich, David J.; Luebbers, Raymond J.; Kunz, Karl S.

1992-01-01

The approach chosen to model steady state scattering from jet engines with moving turbine blades is based upon the Finite Difference Time Domain (FDTD) method. The FDTD method is a numerical electromagnetic program based upon the direct solution in the time domain of Maxwell's time dependent curl equations throughout a volume. One of the strengths of this method is the ability to model objects with complicated shape and/or material composition. General time domain functions may be used as source excitations. For example, a plane wave excitation may be specified as a pulse containing many frequencies and at any incidence angle to the scatterer. A best fit to the scatterer is accomplished using cubical cells in the standard cartesian implementation of the FDTD method. The material composition of the scatterer is determined by specifying its electrical properties at each cell on the scatterer. Thus, the FDTD method is a suitable choice for problems with complex geometries evaluated at multiple frequencies. It is assumed that the reader is familiar with the FDTD method.

Inverse scattering transform and soliton classification of the coupled modified Korteweg-de Vries equation

NASA Astrophysics Data System (ADS)

Wu, Jianping; Geng, Xianguo

2017-12-01

The inverse scattering transform of the coupled modified Korteweg-de Vries equation is studied by the Riemann-Hilbert approach. In the direct scattering process, the spectral analysis of the Lax pair is performed, from which a Riemann-Hilbert problem is established for the equation. In the inverse scattering process, by solving Riemann-Hilbert problems corresponding to the reflectionless cases, three types of multi-soliton solutions are obtained. The multi-soliton classification is based on the zero structures of the Riemann-Hilbert problem. In addition, some figures are given to illustrate the soliton characteristics of the coupled modified Korteweg-de Vries equation.

Electromagnetic inverse scattering

NASA Technical Reports Server (NTRS)

Bojarski, N. N.

1972-01-01

A three-dimensional electromagnetic inverse scattering identity, based on the physical optics approximation, is developed for the monostatic scattered far field cross section of perfect conductors. Uniqueness of this inverse identity is proven. This identity requires complete scattering information for all frequencies and aspect angles. A nonsingular integral equation is developed for the arbitrary case of incomplete frequence and/or aspect angle scattering information. A general closed-form solution to this integral equation is developed, which yields the shape of the scatterer from such incomplete information. A specific practical radar solution is presented. The resolution of this solution is developed, yielding short-pulse target resolution radar system parameter equations. The special cases of two- and one-dimensional inverse scattering and the special case of a priori knowledge of scatterer symmetry are treated in some detail. The merits of this solution over the conventional radar imaging technique are discussed.

Topics Associated with Nonlinear Evolution Equations and Inverse Scattering in Multidimensions,

DTIC Science & Technology

1987-03-01

significant that these concepts can be generalized to 2 spatial plus one time dimension. Here the prototype equation is the Kadomtsev - Petviashvili (K-P...O-193 32 ? T TOPICS ASSOCIATED WITH NONLINEAR E VOLUTION EQUATIONS / AND INVERSE SCATTER! .(U) CLARKSON UNIV POTSDAM NY INST...8217 - Evolution Equations and L Inverse Scattering in Multi- dimensions by _i A ,’I Mark J. Ablowi ClrsnUiest PosaNwYr/37 LaRMFOMON* .F-5 Anwo~~~d kr /ua

Exactly Solvable Multidimensional Nonlinear Equations and Inverse Scattering,

DTIC Science & Technology

1986-12-01

time dimension. Here the prototype euQation is 1 the Kadomtsev - Petviashvili (K-P) equation : .0 6u , x , x - )3,:’u ,’ which is the cop,patliil ity...AD-R193 274 EXACTLY SOLVABLE MULTIDIMENSIONAL NONLINEAR EQUATIONS L/1 AND INVERSE SCATTERING(U) CLARKSON UNIV POTSDAM MY A J MBLOUITZ DEC 86 NSOSI4...ecuations by associating thnm with appropriate compatible linear equations , -ne of which is identified as a Scattering prooD,, ne others(s) serves to

Assessment of polarization effect on aerosol retrievals from MODIS

NASA Astrophysics Data System (ADS)

Korkin, S.; Lyapustin, A.

2010-12-01

Light polarization affects the total intensity of scattered radiation. In this work, we compare aerosol retrievals performed by code MAIAC [1] with and without taking polarization into account. The MAIAC retrievals are based on the look-up tables (LUT). For this work, MAIAC was run using two different LUTs, the first one generated using the scalar code SHARM [2], and the second one generated with the vector code Modified Vector Discrete Ordinates Method (MVDOM). MVDOM is a new code suitable for computations with highly anisotropic phase functions, including cirrus clouds and snow [3]. To this end, the solution of the vector radiative transfer equation (VRTE) is represented as a sum of anisotropic and regular components. The anisotropic component is evaluated in the Small Angle Modification of the Spherical Harmonics Method (MSH) [4]. The MSH is formulated in the frame of reference of the solar beam where z-axis lies along the solar beam direction. In this case, the MSH solution for anisotropic part is nearly symmetric in azimuth, and is computed analytically. In scalar case, this solution coincides with the Goudsmit-Saunderson small-angle approximation [5]. To correct for an analytical separation of the anisotropic part of the signal, the transfer equation for the regular part contains a correction source function term [6]. Several examples of polarization impact on aerosol retrievals over different surface types will be presented. 1. Lyapustin A., Wang Y., Laszlo I., Kahn R., Korkin S., Remer L., Levy R., and Reid J. S. Multi-Angle Implementation of Atmospheric Correction (MAIAC): Part 2. Aerosol Algorithm. J. Geophys. Res., submitted (2010). 2. Lyapustin A., Muldashev T., Wang Y. Code SHARM: fast and accurate radiative transfer over spatially variable anisotropic surfaces. In: Light Scattering Reviews 5. Chichester: Springer, 205 - 247 (2010). 3. Budak, V.P., Korkin S.V. On the solution of a vectorial radiative transfer equation in an arbitrary three-dimensional turbid medium with anisotropic scattering. JQSRT, 109, 220-234 (2008). 4. Budak V.P., Sarmin S.E. Solution of radiative transfer equation by the method of spherical harmonics in the small angle modification. Atmospheric and Oceanic Optics, 3, 898-903 (1990). 5. Goudsmit S., Saunderson J.L. Multiple scattering of electrons. Phys. Rev., 57, 24-29 (1940). 6. Budak V.P, Klyuykov D.A., Korkin S.V. Convergence acceleration of radiative transfer equation solution at strongly anisotropic scattering. In: Light Scattering Reviews 5. Chichester: Springer, 147 - 204 (2010).

Inverse scattering pre-stack depth imaging and it's comparison to some depth migration methods for imaging rich fault complex structure

NASA Astrophysics Data System (ADS)

Nurhandoko, Bagus Endar B.; Sukmana, Indriani; Mubarok, Syahrul; Deny, Agus; Widowati, Sri; Kurniadi, Rizal

2012-06-01

Migration is important issue for seismic imaging in complex structure. In this decade, depth imaging becomes important tools for producing accurate image in depth imaging instead of time domain imaging. The challenge of depth migration method, however, is in revealing the complex structure of subsurface. There are many methods of depth migration with their advantages and weaknesses. In this paper, we show our propose method of pre-stack depth migration based on time domain inverse scattering wave equation. Hopefully this method can be as solution for imaging complex structure in Indonesia, especially in rich thrusting fault zones. In this research, we develop a recent advance wave equation migration based on time domain inverse scattering wave which use more natural wave propagation using scattering wave. This wave equation pre-stack depth migration use time domain inverse scattering wave equation based on Helmholtz equation. To provide true amplitude recovery, an inverse of divergence procedure and recovering transmission loss are considered of pre-stack migration. Benchmarking the propose inverse scattering pre-stack depth migration with the other migration methods are also presented, i.e.: wave equation pre-stack depth migration, waveequation depth migration, and pre-stack time migration method. This inverse scattering pre-stack depth migration could image successfully the rich fault zone which consist extremely dip and resulting superior quality of seismic image. The image quality of inverse scattering migration is much better than the others migration methods.

Nonlinear Waves and Inverse Scattering

DTIC Science & Technology

1990-09-18

to be published Proceedings: conference Chaos in Australia (February 1990). 5. On the Kadomtsev Petviashvili Equation and Associated Constraints by...Scattering Transfoni (IST). IST is a method which alows one to’solve nonlinear wave equations by solving certain related direct and inverse scattering...problems. We use these results to find solutions to nonlinear wave equations much like one uses Fourier analysis for linear problems. Moreover the

Nonlinear Waves and Inverse Scattering

DTIC Science & Technology

1989-01-01

transform provides a linearization.’ Well known systems include the Kadomtsev - Petviashvili , Davey-Stewartson and Self-Dual Yang-Mills equations . The d...which employs inverse scattering theory in order to linearize the given nonlinear equation . I.S.T. has led to new developments in both fields: inverse...scattering and nonlinear wave equations . Listed below are some of the problems studied and a short description of results. - Multidimensional

Multiple Scattering of Electromagnetic Waves in Discrete Random Media.

DTIC Science & Technology

1984-12-31

amplitudes Y and Z: (ka(2 - Kal[ < BM>j --=" YN , ( --) 2Kah,(2ka)jq(2Kal)](13) <c;i>,= Z.. e ... + 24c x2( gMx - 1lhq(2kaxlj( 2Kax) dx (15) Equation...written in terms of the T-matrix of clusters of particles which are then averaged over the positions and relative spacing of the particles in the cluster

A semi-analytical method for near-trapped mode and fictitious frequencies of multiple scattering by an array of elliptical cylinders in water waves

NASA Astrophysics Data System (ADS)

Chen, Jeng-Tzong; Lee, Jia-Wei

2013-09-01

In this paper, we focus on the water wave scattering by an array of four elliptical cylinders. The null-field boundary integral equation method (BIEM) is used in conjunction with degenerate kernels and eigenfunctions expansion. The closed-form fundamental solution is expressed in terms of the degenerate kernel containing the Mathieu and the modified Mathieu functions in the elliptical coordinates. Boundary densities are represented by using the eigenfunction expansion. To avoid using the addition theorem to translate the Mathieu functions, the present approach can solve the water wave problem containing multiple elliptical cylinders in a semi-analytical manner by introducing the adaptive observer system. Regarding water wave problems, the phenomena of numerical instability of fictitious frequencies may appear when the BIEM/boundary element method (BEM) is used. Besides, the near-trapped mode for an array of four identical elliptical cylinders is observed in a special layout. Both physical (near-trapped mode) and mathematical (fictitious frequency) resonances simultaneously appear in the present paper for a water wave problem by an array of four identical elliptical cylinders. Two regularization techniques, the combined Helmholtz interior integral equation formulation (CHIEF) method and the Burton and Miller approach, are adopted to alleviate the numerical resonance due to fictitious frequency.

Phantom Preparation and Optical Property Determination

NASA Astrophysics Data System (ADS)

He, Di; He, Jie; Mao, Heng

2018-12-01

Tissue-like optical phantoms are important in testing new imaging algorithms. Homogeneous optical phantoms with determined optical properties are the first step of making a proper heterogeneous phantom for multi-modality imaging. Typical recipes for such phantoms consist of epoxy resin, hardener, India ink and titanium oxide. By altering the concentration of India ink and titanium oxide, we are able to get multiple homogeneous phantoms with different absorption and scattering coefficients by carefully mixing all the ingredients. After fabricating the phantoms, we need to find their individual optical properties including the absorption and scattering coefficients. This is achieved by solving diffusion equation of each phantom as a homogeneous slab under canonical illumination. We solve the diffusion equation of homogeneous slab in frequency domain and get the formula for theoretical measurements. Under our steady-state diffused optical tomography (DOT) imaging system, we are able to obtain the real distribution of the incident light produced by a laser. With this source distribution we got and the formula we derived, numerical experiments show how measurements change while varying the value of absorption and scattering coefficients. Then we notice that the measurements alone will not be enough for us to get unique optical properties for steady-state DOT problem. Thus in order to determine the optical properties of a homogeneous slab we want to fix one of the coefficients first and use optimization methods to find another one. Then by assemble multiple homogeneous slab phantoms with different optical properties, we are able to obtain a heterogeneous phantom suitable for testing multi-modality imaging algorithms. In this paper, we describe how to make phantoms, derive a formula to solve the diffusion equation, demonstrate the non-uniqueness of steady-state DOT problem by analysing some numerical results of our formula, and finally propose a possible way to determine optical properties for homogeneous slab for our future work.

Characterization of Lorenz number with Seebeck coefficient measurement

DOE PAGES

Kim, Hyun -Sik; Gibbs, Zachary M.; Tang, Yinglu; ...

2015-04-01

In analyzing zT improvements due to lattice thermal conductivity (κ L ) reduction, electrical conductivity (σ) and total thermal conductivity (κ Total ) are often used to estimate the electronic component of the thermal conductivity (κ E ) and in turn κ L from κ L = ~ κ Total - LσT. The Wiedemann-Franz law, κ E = LσT, where L is Lorenz number, is widely used to estimate κ E from σ measurements. It is a common practice to treat L as a universal factor with 2.44 × 10⁻⁸ WΩK⁻² (degenerate limit). However, significant deviations from the degenerate limitmore » (approximately 40% or more for Kane bands) are known to occur for non-degenerate semiconductors where L converges to 1.5 × 10⁻⁸ WΩK⁻² for acoustic phonon scattering. The decrease in L is correlated with an increase in thermopower (absolute value of Seebeck coefficient (S)). Thus, a first order correction to the degenerate limit of L can be based on the measured thermopower, |S|, independent of temperature or doping. We propose the equation: (where L is in 10⁻⁸ WΩK⁻² and S in μV/K) as a satisfactory approximation for L. This equation is accurate within 5% for single parabolic band/acoustic phonon scattering assumption and within 20% for PbSe, PbS, PbTe, Si₀.₈Ge₀.₂ where more complexity is introduced, such as non-parabolic Kane bands, multiple bands, and/or alternate scattering mechanisms. The use of this equation for L rather than a constant value (when detailed band structure and scattering mechanism is not known) will significantly improve the estimation of lattice thermal conductivity. L = 1.5 + exp [-|S|116]« less

Multiple scattering and stop band characteristics of flexural waves on a thin plate with circular holes

NASA Astrophysics Data System (ADS)

Wang, Zuowei; Biwa, Shiro

2018-03-01

A numerical procedure is proposed for the multiple scattering analysis of flexural waves on a thin plate with circular holes based on the Kirchhoff plate theory. The numerical procedure utilizes the wave function expansion of the exciting as well as scattered fields, and the boundary conditions at the periphery of holes are incorporated as the relations between the expansion coefficients of exciting and scattered fields. A set of linear algebraic equations with respect to the wave expansion coefficients of the exciting field alone is established by the numerical collocation method. To demonstrate the applicability of the procedure, the stop band characteristics of flexural waves are analyzed for different arrangements and concentrations of circular holes on a steel plate. The energy transmission spectra of flexural waves are shown to capture the detailed features of the stop band formation of regular and random arrangements of holes. The increase of the concentration of holes is found to shift the dips of the energy transmission spectra toward higher frequencies as well as deepen them. The hexagonal hole arrangement can form a much broader stop band than the square hole arrangement for flexural wave transmission. It is also demonstrated that random arrangements of holes make the transmission spectrum more complicated.

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition. 2; Inclusion of Exchange

NASA Technical Reports Server (NTRS)

Shertzer, Janine; Temkin, Aaron

2004-01-01

The development of a practical method of accurately calculating the full scattering amplitude, without making a partial wave decomposition is continued. The method is developed in the context of electron-hydrogen scattering, and here exchange is dealt with by considering e-H scattering in the static exchange approximation. The Schroedinger equation in this approximation can be simplified to a set of coupled integro-differential equations. The equations are solved numerically for the full scattering wave function. The scattering amplitude can most accurately be calculated from an integral expression for the amplitude; that integral can be formally simplified, and then evaluated using the numerically determined wave function. The results are essentially identical to converged partial wave results.

Loop Integrands for Scattering Amplitudes from the Riemann Sphere

NASA Astrophysics Data System (ADS)

Geyer, Yvonne; Mason, Lionel; Monteiro, Ricardo; Tourkine, Piotr

2015-09-01

The scattering equations on the Riemann sphere give rise to remarkable formulas for tree-level gauge theory and gravity amplitudes. Adamo, Casali, and Skinner conjectured a one-loop formula for supergravity amplitudes based on scattering equations on a torus. We use a residue theorem to transform this into a formula on the Riemann sphere. What emerges is a framework for loop integrands on the Riemann sphere that promises to have a wide application, based on off-shell scattering equations that depend on the loop momentum. We present new formulas, checked explicitly at low points, for supergravity and super-Yang-Mills amplitudes and for n -gon integrands at one loop. Finally, we show that the off-shell scattering equations naturally extend to arbitrary loop order, and we give a proposal for the all-loop integrands for supergravity and planar super-Yang-Mills theory.

Correlation transfer and diffusion of ultrasound-modulated multiply scattered light.

PubMed

Sakadzić, Sava; Wang, Lihong V

2006-04-28

We develop a temporal correlation transfer equation (CTE) and a temporal correlation diffusion equation (CDE) for ultrasound-modulated multiply scattered light. These equations can be applied to an optically scattering medium with embedded optically scattering and absorbing objects to calculate the power spectrum of light modulated by a nonuniform ultrasound field. We present an analytical solution based on the CDE and Monte Carlo simulation results for light modulated by a cylinder of ultrasound in an optically scattering slab. We further validate with experimental measurements the numerical calculations for an actual ultrasound field. The CTE and CDE are valid for moderate ultrasound pressures and on a length scale comparable with the optical transport mean-free path. These equations should be applicable to a wide spectrum of conditions for ultrasound-modulated optical tomography of soft biological tissues.

The effect of dissipative inhomogeneous medium on the statistics of the wave intensity

NASA Technical Reports Server (NTRS)

Saatchi, Sasan S.

1993-01-01

One of the main theoretical points in the theory of wave propagation in random medium is the derivation of closed form equations to describe the statistics of the propagating waves. In particular, in one dimensional problems, the closed form representation of the multiple scattering effects is important since it contributes in understanding such problems like wave localization, backscattering enhancement, and intensity fluctuations. In this the propagation of plane waves in a layer of one-dimensional dissipative random medium is considered. The medium is modeled by a complex permittivity whose real part is a constant representing the absorption. The one dimensional problem is mathematically equivalent to the analysis of a transmission line with randomly perturbed distributed parameters and a single mode lossy waveguide and the results can be used to study the propagation of radio waves through atmosphere and the remote sensing of geophysical media. It is assumed the scattering medium consists of an ensemble of one-dimensional point scatterers randomly positioned in a layer of thickness L with diffuse boundaries. A Poisson impulse process with density lambda is used to model the position of scatterers in the medium. By employing the Markov properties of this process an exact closed form equation of Kolmogorov-Feller type was obtained for the probability density of the reflection coefficient. This equation was solved by combining two limiting cases: (1) when the density of scatterers is small; and (2) when the medium is weakly dissipative. A two variable perturbation method for small lambda was used to obtain solutions valid for thick layers. These solutions are then asymptotically evaluated for small dissipation. To show the effect of dissipation, the mean and fluctuations of the reflected power are obtained. The results were compared with a lossy homogeneous medium and with a lossless inhomogeneous medium and the regions where the effect of absorption is not essential were discussed.

New Examination of the Traditional Raman Lidar Technique II: Temperature Dependence Aerosol Scattering Ratio and Water Vapor Mixing Ratio Equations

NASA Technical Reports Server (NTRS)

Whiteman, David N.; Abshire, James B. (Technical Monitor)

2002-01-01

In a companion paper, the temperature dependence of Raman scattering and its influence on the Raman water vapor signal and the lidar equations was examined. New forms of the lidar equation were developed to account for this temperature sensitivity. Here we use those results to derive the temperature dependent forms of the equations for the aerosol scattering ratio, aerosol backscatter coefficient, extinction to backscatter ratio and water vapor mixing ratio. Pertinent analysis examples are presented to illustrate each calculation.

Photon migration in non-scattering tissue and the effects on image reconstruction

NASA Astrophysics Data System (ADS)

Dehghani, H.; Delpy, D. T.; Arridge, S. R.

1999-12-01

Photon propagation in tissue can be calculated using the relationship described by the transport equation. For scattering tissue this relationship is often simplified and expressed in terms of the diffusion approximation. This approximation, however, is not valid for non-scattering regions, for example cerebrospinal fluid (CSF) below the skull. This study looks at the effects of a thin clear layer in a simple model representing the head and examines its effect on image reconstruction. Specifically, boundary photon intensities (total number of photons exiting at a point on the boundary due to a source input at another point on the boundary) are calculated using the transport equation and compared with data calculated using the diffusion approximation for both non-scattering and scattering regions. The effect of non-scattering regions on the calculated boundary photon intensities is presented together with the advantages and restrictions of the transport code used. Reconstructed images are then presented where the forward problem is solved using the transport equation for a simple two-dimensional system containing a non-scattering ring and the inverse problem is solved using the diffusion approximation to the transport equation.

A novel hybrid scattering order-dependent variance reduction method for Monte Carlo simulations of radiative transfer in cloudy atmosphere

NASA Astrophysics Data System (ADS)

Wang, Zhen; Cui, Shengcheng; Yang, Jun; Gao, Haiyang; Liu, Chao; Zhang, Zhibo

2017-03-01

We present a novel hybrid scattering order-dependent variance reduction method to accelerate the convergence rate in both forward and backward Monte Carlo radiative transfer simulations involving highly forward-peaked scattering phase function. This method is built upon a newly developed theoretical framework that not only unifies both forward and backward radiative transfer in scattering-order-dependent integral equation, but also generalizes the variance reduction formalism in a wide range of simulation scenarios. In previous studies, variance reduction is achieved either by using the scattering phase function forward truncation technique or the target directional importance sampling technique. Our method combines both of them. A novel feature of our method is that all the tuning parameters used for phase function truncation and importance sampling techniques at each order of scattering are automatically optimized by the scattering order-dependent numerical evaluation experiments. To make such experiments feasible, we present a new scattering order sampling algorithm by remodeling integral radiative transfer kernel for the phase function truncation method. The presented method has been implemented in our Multiple-Scaling-based Cloudy Atmospheric Radiative Transfer (MSCART) model for validation and evaluation. The main advantage of the method is that it greatly improves the trade-off between numerical efficiency and accuracy order by order.

Roy-Steiner equations for πN scattering

NASA Astrophysics Data System (ADS)

de Elvira, J. Ruiz; Ditsche, C.; Hoferichter, M.; Kubis, B.; Meißner, U.-G.

2015-10-01

In this talk, we briefly review our ongoing collaboration to precisely determine the low-energy πN scattering amplitude by means of Roy-Steiner equations. After giving a brief overview of this system of dispersive equations and their application to πN scattering, we proceed to solve for the lower partial waves of the s-channel (πN → πN) and the t-channel l( {π π to bar NN} right) sub-problems.

Radiative transfer equation accounting for rotational Raman scattering and its solution by the discrete-ordinates method

NASA Astrophysics Data System (ADS)

Rozanov, Vladimir V.; Vountas, Marco

2014-01-01

Rotational Raman scattering of solar light in Earth's atmosphere leads to the filling-in of Fraunhofer and telluric lines observed in the reflected spectrum. The phenomenological derivation of the inelastic radiative transfer equation including rotational Raman scattering is presented. The different forms of the approximate radiative transfer equation with first-order rotational Raman scattering terms are obtained employing the Cabannes, Rayleigh, and Cabannes-Rayleigh scattering models. The solution of these equations is considered in the framework of the discrete-ordinates method using rigorous and approximate approaches to derive particular integrals. An alternative forward-adjoint technique is suggested as well. A detailed description of the model including the exact spectral matching and a binning scheme that significantly speeds up the calculations is given. The considered solution techniques are implemented in the radiative transfer software package SCIATRAN and a specified benchmark setup is presented to enable readers to compare with own results transparently.

Inverse scattering transform for the KPI equation on the background of a one-line soliton*Inverse scattering transform for the KPI equation on the background of a one-line soliton

NASA Astrophysics Data System (ADS)

Fokas, A. S.; Pogrebkov, A. K.

2003-03-01

We study the initial value problem of the Kadomtsev-Petviashvili I (KPI) equation with initial data u(x1,x2,0) = u1(x1)+u2(x1,x2), where u1(x1) is the one-soliton solution of the Korteweg-de Vries equation evaluated at zero time and u2(x1,x2) decays sufficiently rapidly on the (x1,x2)-plane. This involves the analysis of the nonstationary Schrödinger equation (with time replaced by x2) with potential u(x1,x2,0). We introduce an appropriate sectionally analytic eigenfunction in the complex k-plane where k is the spectral parameter. This eigenfunction has the novelty that in addition to the usual jump across the real k-axis, it also has a jump across a segment of the imaginary k-axis. We show that this eigenfunction can be reconstructed through a linear integral equation uniquely defined in terms of appropriate scattering data. In turn, these scattering data are uniquely constructed in terms of u1(x1) and u2(x1,x2). This result implies that the solution of the KPI equation can be obtained through the above linear integral equation where the scattering data have a simple t-dependence.

Metamaterial Structure Design Optimization: A Study of the Cylindrical Cloak

DTIC Science & Technology

2013-03-01

a Cloaked Cylinder . . . . . . . . . . 112 8.2.2 Optimization with Loss Using Kramers- Kronig Relation . . . . . . 113 8.2.3 Maximize Scatterer...41]. This method creates the overhead of simulating or measuring multiple samples but later in 2010, Szabó et al used the Kramers- Kronig relation to...the passivity constraints of Equation 3.3 and the Kramers- Kronig relation to extract the index of refraction and impedance which can then render the

Reaction formulation for radiation and scattering from plates, corner reflectors and dielectric-coated cylinders

NASA Technical Reports Server (NTRS)

Wang, N. N.

1974-01-01

The reaction concept is employed to formulate an integral equation for radiation and scattering from plates, corner reflectors, and dielectric-coated conducting cylinders. The surface-current density on the conducting surface is expanded with subsectional bases. The dielectric layer is modeled with polarization currents radiating in free space. Maxwell's equation and the boundary conditions are employed to express the polarization-current distribution in terms of the surface-current density on the conducting surface. By enforcing reaction tests with an array of electric test sources, the moment method is employed to reduce the integral equation to a matrix equation. Inversion of the matrix equation yields the current distribution, and the scattered field is then obtained by integrating the current distribution. The theory, computer program and numerical results are presented for radiation and scattering from plates, corner reflectors, and dielectric-coated conducting cylinders.

A multiwave range test for obstacle reconstructions with unknown physical properties

NASA Astrophysics Data System (ADS)

Potthast, Roland; Schulz, Jochen

2007-08-01

We develop a new multiwave version of the range test for shape reconstruction in inverse scattering theory. The range test [R. Potthast, et al., A `range test' for determining scatterers with unknown physical properties, Inverse Problems 19(3) (2003) 533-547] has originally been proposed to obtain knowledge about an unknown scatterer when the far field pattern for only one plane wave is given. Here, we extend the method to the case of multiple waves and show that the full shape of the unknown scatterer can be reconstructed. We further will clarify the relation between the range test methods, the potential method [A. Kirsch, R. Kress, On an integral equation of the first kind in inverse acoustic scattering, in: Inverse Problems (Oberwolfach, 1986), Internationale Schriftenreihe zur Numerischen Mathematik, vol. 77, Birkhauser, Basel, 1986, pp. 93-102] and the singular sources method [R. Potthast, Point sources and multipoles in inverse scattering theory, Habilitation Thesis, Gottingen, 1999]. In particular, we propose a new version of the Kirsch-Kress method using the range test and a new approach to the singular sources method based on the range test and potential method. Numerical examples of reconstructions for all four methods are provided.

The polynomial form of the scattering equations is an H -basis

NASA Astrophysics Data System (ADS)

Bosma, Jorrit; Søgaard, Mads; Zhang, Yang

2016-08-01

We prove that the polynomial form of the scattering equations is a Macaulay H -basis. We demonstrate that this H -basis facilitates integrand reduction and global residue computations in a way very similar to using a Gröbner basis, but circumvents the heavy computation of the latter. As an example, we apply the H -basis to prove the conjecture that the dual basis of the polynomial scattering equations must contain one constant term.

MIMO nonlinear ultrasonic tomography by propagation and backpropagation method.

PubMed

Dong, Chengdong; Jin, Yuanwei

2013-03-01

This paper develops a fast ultrasonic tomographic imaging method in a multiple-input multiple-output (MIMO) configuration using the propagation and backpropagation (PBP) method. By this method, ultrasonic excitation signals from multiple sources are transmitted simultaneously to probe the objects immersed in the medium. The scattering signals are recorded by multiple receivers. Utilizing the nonlinear ultrasonic wave propagation equation and the received time domain scattered signals, the objects are to be reconstructed iteratively in three steps. First, the propagation step calculates the predicted acoustic potential data at the receivers using an initial guess. Second, the difference signal between the predicted value and the measured data is calculated. Third, the backpropagation step computes updated acoustical potential data by backpropagating the difference signal to the same medium computationally. Unlike the conventional PBP method for tomographic imaging where each source takes turns to excite the acoustical field until all the sources are used, the developed MIMO-PBP method achieves faster image reconstruction by utilizing multiple source simultaneous excitation. Furthermore, we develop an orthogonal waveform signaling method using a waveform delay scheme to reduce the impact of speckle patterns in the reconstructed images. By numerical experiments we demonstrate that the proposed MIMO-PBP tomographic imaging method results in faster convergence and achieves superior imaging quality.

Nonlinear Waves and Inverse Scattering

DTIC Science & Technology

1992-01-29

equations include the Kadomtsev - Petviashvili (K-P), Davey-Stewartson (D-S), 2+1 Toda, and Self-Dual Yang-Mills (SDYM) equations . We have uncovered a... Petviashvili Equation and Associated Constraints, M.J. Ablowitz and Javier Villaroel, Studies in Appl. Math. 85, (1991), 195-213. 12. On the Hamiltonian...nonlinear wave equations of physical significance, multidimensional inverse scattering, numer- ically induced instabilities and chaos, and forced

Inverse Scattering Problem For The Schrödinger Equation With An Additional Quadratic Potential On The Entire Axis

NASA Astrophysics Data System (ADS)

Guseinov, I. M.; Khanmamedov, A. Kh.; Mamedova, A. F.

2018-04-01

We consider the Schrödinger equation with an additional quadratic potential on the entire axis and use the transformation operator method to study the direct and inverse problems of the scattering theory. We obtain the main integral equations of the inverse problem and prove that the basic equations are uniquely solvable.

Master equation theory applied to the redistribution of polarized radiation in the weak radiation field limit. III. Theory for the multilevel atom

NASA Astrophysics Data System (ADS)

Bommier, Véronique

2016-06-01

Context. We discuss the case of lines formed by scattering, which comprises both coherent and incoherent scattering. Both processes contribute to form the line profiles in the so-called second solar spectrum, which is the spectrum of the linear polarization of such lines observed close to the solar limb. However, most of the lines cannot be simply modeled with a two-level or two-term atom model, and we present a generalized formalism for this purpose. Aims: The aim is to obtain a formalism that is able to describe scattering in line centers (resonant scattering or incoherent scattering) and in far wings (Rayleigh/Raman scattering or coherent scattering) for a multilevel and multiline atom. Methods: The method is designed to overcome the Markov approximation, which is often performed in the atom-photon interaction description. The method was already presented in the two first papers of this series, but the final equations of those papers were for a two-level atom. Results: We present here the final equations generalized for the multilevel and multiline atom. We describe the main steps of the theoretical development, and, in particular, how we performed the series development to overcome the Markov approximation. Conclusions: The statistical equilibrium equations for the atomic density matrix and the radiative transfer equation coefficients are obtained with line profiles. The Doppler redistribution is also taken into account because we show that the statistical equilibrium equations must be solved for each atomic velocity class.

Seismic reflection imaging, accounting for primary and multiple reflections

NASA Astrophysics Data System (ADS)

Wapenaar, Kees; van der Neut, Joost; Thorbecke, Jan; Broggini, Filippo; Slob, Evert; Snieder, Roel

2015-04-01

Imaging of seismic reflection data is usually based on the assumption that the seismic response consists of primary reflections only. Multiple reflections, i.e. waves that have reflected more than once, are treated as primaries and are imaged at wrong positions. There are two classes of multiple reflections, which we will call surface-related multiples and internal multiples. Surface-related multiples are those multiples that contain at least one reflection at the earth's surface, whereas internal multiples consist of waves that have reflected only at subsurface interfaces. Surface-related multiples are the strongest, but also relatively easy to deal with because the reflecting boundary (the earth's surface) is known. Internal multiples constitute a much more difficult problem for seismic imaging, because the positions and properties of the reflecting interfaces are not known. We are developing reflection imaging methodology which deals with internal multiples. Starting with the Marchenko equation for 1D inverse scattering problems, we derived 3D Marchenko-type equations, which relate reflection data at the surface to Green's functions between virtual sources anywhere in the subsurface and receivers at the surface. Based on these equations, we derived an iterative scheme by which these Green's functions can be retrieved from the reflection data at the surface. This iterative scheme requires an estimate of the direct wave of the Green's functions in a background medium. Note that this is precisely the same information that is also required by standard reflection imaging schemes. However, unlike in standard imaging, our iterative Marchenko scheme retrieves the multiple reflections of the Green's functions from the reflection data at the surface. For this, no knowledge of the positions and properties of the reflecting interfaces is required. Once the full Green's functions are retrieved, reflection imaging can be carried out by which the primaries and multiples are mapped to their correct positions, with correct reflection amplitudes. In the presentation we will illustrate this new methodology with numerical examples and discuss its potential and limitations.

Comment on: Accurate and fast numerical solution of Poisson s equation for arbitrary, space-filling Voronoi polyhedra: Near-field corrections revisited

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gonis, Antonios; Zhang, Xiaoguang

2012-01-01

This is a comment on the paper by Aftab Alam, Brian G. Wilson, and D. D. Johnson [1], proposing the solution of the near-field corrections (NFC s) problem for the Poisson equation for extended, e.g., space filling, charge densities. We point out that the problem considered by the authors can be simply avoided by means of performing certain integrals in a particular order, while their method does not address the genuine problem of NFC s that arises when the solution of the Poisson equation is attempted within multiple scattering theory. We also point out a flaw in their line ofmore » reasoning leading to the expression for the potential inside the bounding sphere of a cell that makes it inapplicable to certain geometries.« less

Comment on ``Accurate and fast numerical solution of Poisson's equation for arbitrary, space-filling Voronoi polyhedra: Near-field corrections revisited''

NASA Astrophysics Data System (ADS)

Gonis, A.; Zhang, X.-G.

2012-09-01

This is a Comment on the paper by Alam, Wilson, and Johnson [Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.84.205106 84, 205106 (2011)], proposing the solution of the near-field corrections (NFCs) problem for the Poisson equation for extended, e.g., space-filling charge densities. We point out that the problem considered by the authors can be simply avoided by means of performing certain integrals in a particular order, whereas, their method does not address the genuine problem of NFCs that arises when the solution of the Poisson equation is attempted within multiple-scattering theory. We also point out a flaw in their line of reasoning, leading to the expression for the potential inside the bounding sphere of a cell that makes it inapplicable for certain geometries.

Particle Scattering in the Resonance Regime: Full-Wave Solution for Axisymmetric Particles with Large Aspect Ratios

NASA Technical Reports Server (NTRS)

Zuffada, Cinzia; Crisp, David

1997-01-01

Reliable descriptions of the optical properties of clouds and aerosols are essential for studies of radiative transfer in planetary atmospheres. The scattering algorithms provide accurate estimates of these properties for spherical particles with a wide range of sizes and refractive indices, but these methods are not valid for non-spherical particles (e.g., ice crystals, mineral dust, and smoke). Even though a host of methods exist for deriving the optical properties of nonspherical particles that are very small or very large compared with the wavelength, only a few methods are valid in the resonance regime, where the particle dimensions are comparable with the wavelength. Most such methods are not ideal for particles with sharp edges or large axial ratios. We explore the utility of an integral equation approach for deriving the single-scattering optical properties of axisymmetric particles with large axial ratios. The accuracy of this technique is shown for spheres of increasing size parameters and an ensemble of randomly oriented prolate spheroids of size parameter equal to 10.079368. In this last case our results are compared with published results obtained with the T-matrix approach. Next we derive cross sections, single-scattering albedos, and phase functions for cylinders, disks, and spheroids of ice with dimensions extending from the Rayleigh to the geometric optics regime. Compared with those for a standard surface integral equation method, the storage requirement and the computer time needed by this method are reduced, thus making it attractive for generating databases to be used in multiple-scattering calculations. Our results show that water ice disks and cylinders are more strongly absorbing than equivalent volume spheres at most infrared wavelengths. The geometry of these particles also affects the angular dependence of the scattering. Disks and columns with maximum linear dimensions larger than the wavelength scatter much more radiation in the forward and backward directions and much less radiation at intermediate phase angles than equivalent volume spheres.

Application of the Finite Element Method in Atomic and Molecular Physics

NASA Technical Reports Server (NTRS)

Shertzer, Janine

2007-01-01

The finite element method (FEM) is a numerical algorithm for solving second order differential equations. It has been successfully used to solve many problems in atomic and molecular physics, including bound state and scattering calculations. To illustrate the diversity of the method, we present here details of two applications. First, we calculate the non-adiabatic dipole polarizability of Hi by directly solving the first and second order equations of perturbation theory with FEM. In the second application, we calculate the scattering amplitude for e-H scattering (without partial wave analysis) by reducing the Schrodinger equation to set of integro-differential equations, which are then solved with FEM.

Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme

NASA Astrophysics Data System (ADS)

Liu, Xianglin; Wang, Yang; Eisenbach, Markus; Stocks, G. Malcolm

2018-03-01

The Green function plays an essential role in the Korringa-Kohn-Rostoker(KKR) multiple scattering method. In practice, it is constructed from the regular and irregular solutions of the local Kohn-Sham equation and robust methods exist for spherical potentials. However, when applied to a non-spherical potential, numerical errors from the irregular solutions give rise to pathological behaviors of the charge density at small radius. Here we present a full-potential implementation of the fully-relativistic KKR method to perform ab initio self-consistent calculation by directly solving the Dirac differential equations using the generalized variable phase (sine and cosine matrices) formalism Liu et al. (2016). The pathology around the origin is completely eliminated by carrying out the energy integration of the single-site Green function along the real axis. By using an efficient pole-searching technique to identify the zeros of the well-behaved Jost matrices, we demonstrated that this scheme is numerically stable and computationally efficient, with speed comparable to the conventional contour energy integration method, while free of the pathology problem of the charge density. As an application, this method is utilized to investigate the crystal structures of polonium and their bulk properties, which is challenging for a conventional real-energy scheme. The noble metals are also calculated, both as a test of our method and to study the relativistic effects.

Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Xianglin; Wang, Yang; Eisenbach, Markus

The Green function plays an essential role in the Korringa–Kohn–Rostoker(KKR) multiple scattering method. In practice, it is constructed from the regular and irregular solutions of the local Kohn–Sham equation and robust methods exist for spherical potentials. However, when applied to a non-spherical potential, numerical errors from the irregular solutions give rise to pathological behaviors of the charge density at small radius. Here we present a full-potential implementation of the fully-relativistic KKR method to perform ab initio self-consistent calculation by directly solving the Dirac differential equations using the generalized variable phase (sine and cosine matrices) formalism Liu et al. (2016). Themore » pathology around the origin is completely eliminated by carrying out the energy integration of the single-site Green function along the real axis. Here, by using an efficient pole-searching technique to identify the zeros of the well-behaved Jost matrices, we demonstrated that this scheme is numerically stable and computationally efficient, with speed comparable to the conventional contour energy integration method, while free of the pathology problem of the charge density. As an application, this method is utilized to investigate the crystal structures of polonium and their bulk properties, which is challenging for a conventional real-energy scheme. The noble metals are also calculated, both as a test of our method and to study the relativistic effects.« less

Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme

DOE PAGES

Liu, Xianglin; Wang, Yang; Eisenbach, Markus; ...

2017-10-28

The Green function plays an essential role in the Korringa–Kohn–Rostoker(KKR) multiple scattering method. In practice, it is constructed from the regular and irregular solutions of the local Kohn–Sham equation and robust methods exist for spherical potentials. However, when applied to a non-spherical potential, numerical errors from the irregular solutions give rise to pathological behaviors of the charge density at small radius. Here we present a full-potential implementation of the fully-relativistic KKR method to perform ab initio self-consistent calculation by directly solving the Dirac differential equations using the generalized variable phase (sine and cosine matrices) formalism Liu et al. (2016). Themore » pathology around the origin is completely eliminated by carrying out the energy integration of the single-site Green function along the real axis. Here, by using an efficient pole-searching technique to identify the zeros of the well-behaved Jost matrices, we demonstrated that this scheme is numerically stable and computationally efficient, with speed comparable to the conventional contour energy integration method, while free of the pathology problem of the charge density. As an application, this method is utilized to investigate the crystal structures of polonium and their bulk properties, which is challenging for a conventional real-energy scheme. The noble metals are also calculated, both as a test of our method and to study the relativistic effects.« less

Simulation study of localization of electromagnetic waves in two-dimensional random dipolar systems.

PubMed

Wang, Ken Kang-Hsin; Ye, Zhen

2003-12-01

We study the propagation and scattering of electromagnetic waves by random arrays of dipolar cylinders in a uniform medium. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is derived from first principles and then solved numerically for electromagnetic fields. For certain ranges of frequencies, spatially localized electromagnetic waves appear in such a simple but realistic disordered system. Dependence of localization on the frequency, radiation damping, and filling factor is shown. The spatial behavior of the total, coherent, and diffusive waves is explored in detail, and found to comply with a physical intuitive picture. A phase diagram characterizing localization is presented, in agreement with previous investigations on other systems.

Nonreciprocal wave scattering on nonlinear string-coupled oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lepri, Stefano, E-mail: stefano.lepri@isc.cnr.it; Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino; Pikovsky, Arkady

2014-12-01

We study scattering of a periodic wave in a string on two lumped oscillators attached to it. The equations can be represented as a driven (by the incident wave) dissipative (due to radiation losses) system of delay differential equations of neutral type. Nonlinearity of oscillators makes the scattering non-reciprocal: The same wave is transmitted differently in two directions. Periodic regimes of scattering are analyzed approximately, using amplitude equation approach. We show that this setup can act as a nonreciprocal modulator via Hopf bifurcations of the steady solutions. Numerical simulations of the full system reveal nontrivial regimes of quasiperiodic and chaoticmore » scattering. Moreover, a regime of a “chaotic diode,” where transmission is periodic in one direction and chaotic in the opposite one, is reported.« less

Scattering from a cylindrical reflector: modified theory of physical optics solution.

PubMed

Yalçin, Ugur

2007-02-01

The problem of scattering from a perfectly conducting cylindrical reflector is examined with the method of the modified theory of physical optics. In this technique the physical optics currents are modified by using a variable unit vector on the scatterer's surface. These current components are obtained for the reflector, which is fed by an offset electric line source. The scattering integral is expressed by using these currents and evaluated asymptotically with the stationary phase method. The results are compared numerically by using physical optics theory, geometrical optics diffraction theory, and the exact solution of the Helmholtz equation. It is found that the modified theory of physical optics scattering field equations agrees with the geometrical optics diffraction theory and the exact solution of the Helmholtz equation.

Temperature Distribution in a Composite of Opaque and Semitransparent Spectral Layers

NASA Technical Reports Server (NTRS)

Siegel, Robert

1997-01-01

The analysis of radiative transfer becomes computationally complex for a composite when there are multiple layers and multiple spectral bands. A convenient analytical method is developed for combined radiation and conduction in a composite of alternating semitransparent and opaque layers. The semi- transparent layers absorb, scatter, and emit radiation, and spectral properties with large scattering are included. The two-flux method is used, and its applicability is verified by comparison with a basic solution in the literature. The differential equation in the two-flux method Is solved by deriving a Green's function. The solution technique is applied to analyze radiation effects in a multilayer zirconia thermal barrier coating with internal radiation shields for conditions in an aircraft engine combustor. The zirconia radiative properties are modeled by two spectral bands. Thin opaque layers within the coating are used to decrease radiant transmission that can degrade the zirconia insulating ability. With radiation shields, the temperature distributions more closely approach the opaque limit that provides the lowest metal wall temperatures.

Polarimetric signatures of a canopy of dielectric cylinders based on first and second order vector radiative transfer theory

NASA Technical Reports Server (NTRS)

Tsang, Leung; Chan, Chi Hou; Kong, Jin AU; Joseph, James

1992-01-01

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.

A boundary integral approach to the scattering of nonplanar acoustic waves by rigid bodies

NASA Technical Reports Server (NTRS)

Gallman, Judith M.; Myers, M. K.; Farassat, F.

1990-01-01

The acoustic scattering of an incident wave by a rigid body can be described by a singular Fredholm integral equation of the second kind. This equation is derived by solving the wave equation using generalized function theory, Green's function for the wave equation in unbounded space, and the acoustic boundary condition for a perfectly rigid body. This paper will discuss the derivation of the wave equation, its reformulation as a boundary integral equation, and the solution of the integral equation by the Galerkin method. The accuracy of the Galerkin method can be assessed by applying the technique outlined in the paper to reproduce the known pressure fields that are due to various point sources. From the analysis of these simpler cases, the accuracy of the Galerkin solution can be inferred for the scattered pressure field caused by the incidence of a dipole field on a rigid sphere. The solution by the Galerkin technique can then be applied to such problems as a dipole model of a propeller whose pressure field is incident on a rigid cylinder. This is the groundwork for modeling the scattering of rotating blade noise by airplane fuselages.

Concept of a Fast and Simple Atmospheric Radiative Transfer Model for Aerosol Retrieval

NASA Astrophysics Data System (ADS)

Seidel, Felix; Kokhanovsky, Alexander A.

2010-05-01

Radiative transfer modelling (RTM) is an indispensable tool for a number of applications, including astrophysics, climate studies and quantitative remote sensing. It simulates the attenuation of light through a translucent medium. Here, we look at the scattering and absorption of solar light on its way to the Earth's surface and back to space or back into a remote sensing instrument. RTM is regularly used in the framework of the so-called atmospheric correction to find properties of the surface. Further, RTM can be inverted to retrieve features of the atmosphere, such as the aerosol optical depth (AOD), for instance. Present-day RTM, such as 6S, MODTRAN, SHARM, RT3, SCIATRAN or RTMOM have errors of only a few percent, however they are rather slow and often not easy to use. We present here a concept for a fast and simple RTM model in the visible spectral range. It is using a blend of different existing RTM approaches with a special emphasis on fast approximative analytical equations and parametrizations. This concept may be helpful for efficient retrieval algorithms, which do not have to rely on the classic look-up-tables (LUT) approach. For example, it can be used to retrieve AOD without complex inversion procedures including multiple iterations. Naturally, there is always a trade-off between speed and modelling accuracy. The code can be run therefore in two different modes. The regular mode provides a reasonable ratio between speed and accuracy, while the optional mode is very fast but less accurate. The normal mode approximates the diffuse scattered light by calculating the first (single scattering) and second order of scattering according to the classical method of successive orders of scattering. The very fast mode calculates only the single scattering approximation, which does not need any slow numerical integration procedure, and uses a simple correction factor to account for multiple scattering. This factor is a parametrization of MODTRAN results, which provide a typical ratio between single and multiple scattered light. A comparison of the presented RTM concept to the widely accepted 6S RTM reveals errors of up to 10% in standard mode. This is acceptable for certain applications. The very fast mode may lead to errors of up to 30%, but it is still able to reproduce qualitatively the results of 6S. An experimental implementation of this RTM concept is written in the common IDL language. It is therefore very flexible and straightforward to be implemented into custom retrieval algorithms of the remote sensing community. The code might also be used to add an atmosphere on top of an existing vegetation-canopy or water RTM. Due to the ease of use of the RTM code and the comprehensibility of the internal equations, the concept might be useful for educational purposes as well. The very fast mode could be of interest for a real-time applications, such as an in-flight instrument performance check for airborne optical sensors. In the future, the concept can be extended to account for scattering according to Mie theory, polarization and gaseous absorption. It is expected that this would reduce the model error to 5% or less.

Regularized wave equation migration for imaging and data reconstruction

NASA Astrophysics Data System (ADS)

Kaplan, Sam T.

The reflection seismic experiment results in a measurement (reflection seismic data) of the seismic wavefield. The linear Born approximation to the seismic wavefield leads to a forward modelling operator that we use to approximate reflection seismic data in terms of a scattering potential. We consider approximations to the scattering potential using two methods: the adjoint of the forward modelling operator (migration), and regularized numerical inversion using the forward and adjoint operators. We implement two parameterizations of the forward modelling and migration operators: source-receiver and shot-profile. For both parameterizations, we find requisite Green's function using the split-step approximation. We first develop the forward modelling operator, and then find the adjoint (migration) operator by recognizing a Fredholm integral equation of the first kind. The resulting numerical system is generally under-determined, requiring prior information to find a solution. In source-receiver migration, the parameterization of the scattering potential is understood using the migration imaging condition, and this encourages us to apply sparse prior models to the scattering potential. To that end, we use both a Cauchy prior and a mixed Cauchy-Gaussian prior, finding better resolved estimates of the scattering potential than are given by the adjoint. In shot-profile migration, the parameterization of the scattering potential has its redundancy in multiple active energy sources (i.e. shots). We find that a smallest model regularized inverse representation of the scattering potential gives a more resolved picture of the earth, as compared to the simpler adjoint representation. The shot-profile parameterization allows us to introduce a joint inversion to further improve the estimate of the scattering potential. Moreover, it allows us to introduce a novel data reconstruction algorithm so that limited data can be interpolated/extrapolated. The linearized operators are expensive, encouraging their parallel implementation. For the source-receiver parameterization of the scattering potential this parallelization is non-trivial. Seismic data is typically corrupted by various types of noise. Sparse coding can be used to suppress noise prior to migration. It is a method that stems from information theory and that we apply to noise suppression in seismic data.

An effective field theory for forward scattering and factorization violation

DOE PAGES

Rothstein, Ira Z.; Stewart, Iain W.

2016-08-03

Starting with QCD, we derive an effective field theory description for forward scattering and factorization violation as part of the soft-collinear effective field theory (SCET) for high energy scattering. These phenomena are mediated by long distance Glauber gluon exchanges, which are static in time, localized in the longitudinal distance, and act as a kernel for forward scattering where |t| << s. In hard scattering, Glauber gluons can induce corrections which invalidate factorization. With SCET, Glauber exchange graphs can be calculated explicitly, and are distinct from graphs involving soft, collinear, or ultrasoft gluons. We derive a complete basis of operators whichmore » describe the leading power effects of Glauber exchange. Key ingredients include regulating light-cone rapidity singularities and subtractions which prevent double counting. Our results include a novel all orders gauge invariant pure glue soft operator which appears between two collinear rapidity sectors. The 1-gluon Feynman rule for the soft operator coincides with the Lipatov vertex, but it also contributes to emissions with ≥ 2 soft gluons. Our Glauber operator basis is derived using tree level and one-loop matching calculations from full QCD to both SCET II and SCET I. The one-loop amplitude’s rapidity renormalization involves mixing of color octet operators and yields gluon Reggeization at the amplitude level. The rapidity renormalization group equation for the leading soft and collinear functions in the forward scattering cross section are each given by the BFKL equation. Various properties of Glauber gluon exchange in the context of both forward scattering and hard scattering factorization are described. For example, we derive an explicit rule for when eikonalization is valid, and provide a direct connection to the picture of multiple Wilson lines crossing a shockwave. In hard scattering operators Glauber subtractions for soft and collinear loop diagrams ensure that we are not sensitive to the directions for soft and collinear Wilson lines. Conversely, certain Glauber interactions can be absorbed into these soft and collinear Wilson lines by taking them to be in specific directions. Finally, we also discuss criteria for factorization violation.« less

Hybrid radiosity-SP3 equation based bioluminescence tomography reconstruction for turbid medium with low- and non-scattering regions

NASA Astrophysics Data System (ADS)

Chen, Xueli; Zhang, Qitan; Yang, Defu; Liang, Jimin

2014-01-01

To provide an ideal solution for a specific problem of gastric cancer detection in which low-scattering regions simultaneously existed with both the non- and high-scattering regions, a novel hybrid radiosity-SP3 equation based reconstruction algorithm for bioluminescence tomography was proposed in this paper. In the algorithm, the third-order simplified spherical harmonics approximation (SP3) was combined with the radiosity equation to describe the bioluminescent light propagation in tissues, which provided acceptable accuracy for the turbid medium with both low- and non-scattering regions. The performance of the algorithm was evaluated with digital mouse based simulations and a gastric cancer-bearing mouse based in situ experiment. Primary results demonstrated the feasibility and superiority of the proposed algorithm for the turbid medium with low- and non-scattering regions.

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II

NASA Technical Reports Server (NTRS)

Shertzer, J.; Temkin, A.

2003-01-01

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE) can be reduced to a 2d partial differential equation (pde), and was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation. The resultant equation can be reduced to a pair of coupled pde's, to which the finite element method can still be applied. The resultant scattering amplitudes, both singlet and triplet, as a function of angle can be calculated for various energies. The results are in excellent agreement with converged partial wave results.

Numerical techniques in radiative heat transfer for general, scattering, plane-parallel media

NASA Technical Reports Server (NTRS)

Sharma, A.; Cogley, A. C.

1982-01-01

The study of radiative heat transfer with scattering usually leads to the solution of singular Fredholm integral equations. The present paper presents an accurate and efficient numerical method to solve certain integral equations that govern radiative equilibrium problems in plane-parallel geometry for both grey and nongrey, anisotropically scattering media. In particular, the nongrey problem is represented by a spectral integral of a system of nonlinear integral equations in space, which has not been solved previously. The numerical technique is constructed to handle this unique nongrey governing equation as well as the difficulties caused by singular kernels. Example problems are solved and the method's accuracy and computational speed are analyzed.

Parametric amplification and bidirectional invisibility in PT -symmetric time-Floquet systems

NASA Astrophysics Data System (ADS)

Koutserimpas, Theodoros T.; Alù, Andrea; Fleury, Romain

2018-01-01

Parity-time (PT )-symmetric wave devices, which exploit balanced interactions between material gain and loss, exhibit extraordinary properties, including lasing and flux-conserving scattering processes. In a seemingly different research field, periodically driven systems, also known as time-Floquet systems, have been widely studied as a relevant platform for reconfigurable active wave control and manipulation. In this article, we explore the connection between PT -symmetry and parametric time-Floquet systems. Instead of relying on material gain, we use parametric amplification by considering a time-periodic modulation of the refractive index at a frequency equal to twice the incident signal frequency. We show that the scattering from a simple parametric slab, whose dynamics follows the Mathieu equation, can be described by a PT -symmetric scattering matrix, whose PT -breaking threshold corresponds to the Mathieu instability threshold. By combining different parametric slabs modulated out of phase, we create PT -symmetric time-Floquet systems that feature exceptional scattering properties, such as coherent perfect absorption (CPA)-laser operation and bidirectional invisibility. These bidirectional properties, rare for regular PT -symmetric systems, are related to a compensation of parametric amplification due to multiple scattering between two parametric systems modulated with a phase difference.

Extending generalized Kubelka-Munk to three-dimensional radiative transfer.

PubMed

Sandoval, Christopher; Kim, Arnold D

2015-08-10

The generalized Kubelka-Munk (gKM) approximation is a linear transformation of the double spherical harmonics of order one (DP₁) approximation of the radiative transfer equation. Here, we extend the gKM approximation to study problems in three-dimensional radiative transfer. In particular, we derive the gKM approximation for the problem of collimated beam propagation and scattering in a plane-parallel slab composed of a uniform absorbing and scattering medium. The result is an 8×8 system of partial differential equations that is much easier to solve than the radiative transfer equation. We compare the solutions of the gKM approximation with Monte Carlo simulations of the radiative transfer equation to identify the range of validity for this approximation. We find that the gKM approximation is accurate for isotropic scattering media that are sufficiently thick and much less accurate for anisotropic, forward-peaked scattering media.

Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism

NASA Astrophysics Data System (ADS)

Alam, Aftab; Khan, Suffian N.; Smirnov, A. V.; Nicholson, D. M.; Johnson, Duane D.

2014-11-01

The Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an efficient site-centered, electronic-structure technique for addressing an assembly of N scatterers. Wave functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number Lmax=(l,mmax), while scattering matrices, which determine spectral properties, are truncated at Lt r=(l,mt r) where phase shifts δl >ltr are negligible. Historically, Lmax is set equal to Lt r, which is correct for large enough Lmax but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for Lmax>Lt r with δl >ltr set to zero [X.-G. Zhang and W. H. Butler, Phys. Rev. B 46, 7433 (1992), 10.1103/PhysRevB.46.7433]. We present a numerically efficient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R3 process with rank N (ltr+1 ) 2 ] and includes higher-L contributions via linear algebra [R2 process with rank N (lmax+1) 2 ]. The augmented-KKR approach yields properly normalized wave functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe, and L 1 0 CoPt and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus Lmax for a given Lt r.

Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism

DOE PAGES

Alam, Aftab; Khan, Suffian N.; Smirnov, A. V.; ...

2014-11-04

Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an ecient sitecentered, electronic-structure technique for addressing an assembly of N scatterers. Wave-functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number L max = (l,m) max, while scattering matrices, which determine spectral properties, are truncated at L tr = (l,m) tr where phase shifts δl>l tr are negligible. Historically, L max is set equal to L tr, which is correct for large enough L max but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for L maxmore » > L tr with δl>l tr set to zero [Zhang and Butler, Phys. Rev. B 46, 7433]. We present a numerically ecient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R 3 process with rank N(l tr + 1) 2] and includes higher-L contributions via linear algebra [R 2 process with rank N(l max +1) 2]. Augmented-KKR approach yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe and L1 0 CoPt, and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus L max for a given L tr.« less

Characterization of Lorenz number with Seebeck coefficient measurement

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Hyun-Sik; Materials Research Center, Samsung Advanced Institute of Technology, Samsung Electronics, Suwon 443-803; Gibbs, Zachary M.

2015-04-01

In analyzing zT improvements due to lattice thermal conductivity (κ{sub L}) reduction, electrical conductivity (σ) and total thermal conductivity (κ{sub Total}) are often used to estimate the electronic component of the thermal conductivity (κ{sub E}) and in turn κ{sub L} from κ{sub L} = ∼ κ{sub Total} − LσT. The Wiedemann-Franz law, κ{sub E} = LσT, where L is Lorenz number, is widely used to estimate κ{sub E} from σ measurements. It is a common practice to treat L as a universal factor with 2.44 × 10{sup −8} WΩK{sup −2} (degenerate limit). However, significant deviations from the degenerate limit (approximatelymore » 40% or more for Kane bands) are known to occur for non-degenerate semiconductors where L converges to 1.5 × 10{sup −8} WΩK{sup −2} for acoustic phonon scattering. The decrease in L is correlated with an increase in thermopower (absolute value of Seebeck coefficient (S)). Thus, a first order correction to the degenerate limit of L can be based on the measured thermopower, |S|, independent of temperature or doping. We propose the equation: L=1.5+exp[−(|S|)/(116) ] (where L is in 10{sup −8} WΩK{sup −2} and S in μV/K) as a satisfactory approximation for L. This equation is accurate within 5% for single parabolic band/acoustic phonon scattering assumption and within 20% for PbSe, PbS, PbTe, Si{sub 0.8}Ge{sub 0.2} where more complexity is introduced, such as non-parabolic Kane bands, multiple bands, and/or alternate scattering mechanisms. The use of this equation for L rather than a constant value (when detailed band structure and scattering mechanism is not known) will significantly improve the estimation of lattice thermal conductivity.« less

Simulation electromagnetic scattering on bodies through integral equation and neural networks methods

NASA Astrophysics Data System (ADS)

Lvovich, I. Ya; Preobrazhenskiy, A. P.; Choporov, O. N.

2018-05-01

The paper deals with the issue of electromagnetic scattering on a perfectly conducting diffractive body of a complex shape. Performance calculation of the body scattering is carried out through the integral equation method. Fredholm equation of the second time was used for calculating electric current density. While solving the integral equation through the moments method, the authors have properly described the core singularity. The authors determined piecewise constant functions as basic functions. The chosen equation was solved through the moments method. Within the Kirchhoff integral approach it is possible to define the scattered electromagnetic field, in some way related to obtained electrical currents. The observation angles sector belongs to the area of the front hemisphere of the diffractive body. To improve characteristics of the diffractive body, the authors used a neural network. All the neurons contained a logsigmoid activation function and weighted sums as discriminant functions. The paper presents the matrix of weighting factors of the connectionist model, as well as the results of the optimized dimensions of the diffractive body. The paper also presents some basic steps in calculation technique of the diffractive bodies, based on the combination of integral equation and neural networks methods.

A fast and well-conditioned spectral method for singular integral equations

NASA Astrophysics Data System (ADS)

Slevinsky, Richard Mikael; Olver, Sheehan

2017-03-01

We develop a spectral method for solving univariate singular integral equations over unions of intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the equations as almost-banded infinite-dimensional systems. This is accomplished by utilizing low rank approximations for sparse representations of the bivariate kernels. The resulting system can be solved in O (m2 n) operations using an adaptive QR factorization, where m is the bandwidth and n is the optimal number of unknowns needed to resolve the true solution. The complexity is reduced to O (mn) operations by pre-caching the QR factorization when the same operator is used for multiple right-hand sides. Stability is proved by showing that the resulting linear operator can be diagonally preconditioned to be a compact perturbation of the identity. Applications considered include the Faraday cage, and acoustic scattering for the Helmholtz and gravity Helmholtz equations, including spectrally accurate numerical evaluation of the far- and near-field solution. The JULIA software package SingularIntegralEquations.jl implements our method with a convenient, user-friendly interface.

Roy-Steiner equations for πN scattering

NASA Astrophysics Data System (ADS)

Ruiz de Elvira, J.; Ditsche, C.; Hoferichter, M.; Kubis, B.; Meißner, U.-G.

2014-06-01

In this talk, we present a coupled system of integral equations for the πN → πN (s-channel) and ππ → N̅N (t-channel) lowest partial waves, derived from Roy-Steiner equations for pion-nucleon scattering. After giving a brief overview of this system of equations, we present the solution of the t-channel sub-problem by means of Muskhelishvili-Omnès techniques, and solve the s-channel sub-problem after finding a set of phase shifts and subthreshold parameters which satisfy the Roy-Steiner equations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rothstein, Ira Z.; Stewart, Iain W.

Starting with QCD, we derive an effective field theory description for forward scattering and factorization violation as part of the soft-collinear effective field theory (SCET) for high energy scattering. These phenomena are mediated by long distance Glauber gluon exchanges, which are static in time, localized in the longitudinal distance, and act as a kernel for forward scattering where |t| << s. In hard scattering, Glauber gluons can induce corrections which invalidate factorization. With SCET, Glauber exchange graphs can be calculated explicitly, and are distinct from graphs involving soft, collinear, or ultrasoft gluons. We derive a complete basis of operators whichmore » describe the leading power effects of Glauber exchange. Key ingredients include regulating light-cone rapidity singularities and subtractions which prevent double counting. Our results include a novel all orders gauge invariant pure glue soft operator which appears between two collinear rapidity sectors. The 1-gluon Feynman rule for the soft operator coincides with the Lipatov vertex, but it also contributes to emissions with ≥ 2 soft gluons. Our Glauber operator basis is derived using tree level and one-loop matching calculations from full QCD to both SCET II and SCET I. The one-loop amplitude’s rapidity renormalization involves mixing of color octet operators and yields gluon Reggeization at the amplitude level. The rapidity renormalization group equation for the leading soft and collinear functions in the forward scattering cross section are each given by the BFKL equation. Various properties of Glauber gluon exchange in the context of both forward scattering and hard scattering factorization are described. For example, we derive an explicit rule for when eikonalization is valid, and provide a direct connection to the picture of multiple Wilson lines crossing a shockwave. In hard scattering operators Glauber subtractions for soft and collinear loop diagrams ensure that we are not sensitive to the directions for soft and collinear Wilson lines. Conversely, certain Glauber interactions can be absorbed into these soft and collinear Wilson lines by taking them to be in specific directions. Finally, we also discuss criteria for factorization violation.« less

Generalized Rayleigh scattering. I. Basic theory.

NASA Astrophysics Data System (ADS)

Ivanov, V. V.

1995-11-01

The classsical problem of multiple molecular (in particular, Rayleigh) scattering in plane-parallel atmospheres is considered from a somewhat broader viewpoint than usual. The general approach and ideology are borrowed from non-LTE line formation theory. The main emphasis is on the depth dependence of the corresponding source matrix rather than on the emergent radiation. We study the azimuth-averaged radiation field of polarized radiation in a semi-infinite atmosphere with embedded primary sources. The corresponding 2x2 phase matrix of molecular scattering is P=(1-W) P_I_+W P_R_, where P_I_ and P_R_ are the phase matrices of the scalar isotropic scattering and of the Rayleigh scattering, respectively, and W is the depolarization parameter. Contrary to the usual assumption that W{in}[0,1], we assume W{in} [0,{infinity}) and call this generalized Rayleigh scattering (GRS). Using the factorization of P which is intimately related to its diadic expansion, we reduce the problem to an integral equation for the source matrix S(τ) with a matrix displacement kernel. In operator form this equation is S={LAMBDA}S+S^*^, where {LAMBDA} is the matrix {LAMBDA}-operator and S^*^ is the primary source term. This leads to a new concept, the matrix albedo of single scattering λ =diag(λ_I_,λ_Q_), where λ_I_ is the usual (scalar) single scattering albedo and λ_Q_=0.7Wλ_I_. Its use enables one to formulate matrix equivalents of many of the results of the scalar theory in exactly the same form as in the scalar case. Of crucial importance is the matrix equivalent of the sqrt(ɛ) law of the scalar theory. Another useful new concept is the λ-plane, i.e., the plane with the axes (λ_I_,λ_Q_). Systematic use of the matrix sqrt(ɛ) law and of the λ-plane proved to be a useful instrument in classifying various limiting and particular cases of GRS and in discussing numerical data on the matrix source functions (to be given in Paper II of the series).

Particle Acceleration and Heating by Turbulent Reconnection

NASA Astrophysics Data System (ADS)

Vlahos, Loukas; Pisokas, Theophilos; Isliker, Heinz; Tsiolis, Vassilis; Anastasiadis, Anastasios

2016-08-01

Turbulent flows in the solar wind, large-scale current sheets, multiple current sheets, and shock waves lead to the formation of environments in which a dense network of current sheets is established and sustains “turbulent reconnection.” We constructed a 2D grid on which a number of randomly chosen grid points are acting as scatterers (I.e., magnetic clouds or current sheets). Our goal is to examine how test particles respond inside this large-scale collection of scatterers. We study the energy gain of individual particles, the evolution of their energy distribution, and their escape time distribution. We have developed a new method to estimate the transport coefficients from the dynamics of the interaction of the particles with the scatterers. Replacing the “magnetic clouds” with current sheets, we have proven that the energization processes can be more efficient depending on the strength of the effective electric fields inside the current sheets and their statistical properties. Using the estimated transport coefficients and solving the Fokker-Planck (FP) equation, we can recover the energy distribution of the particles only for the stochastic Fermi process. We have shown that the evolution of the particles inside a turbulent reconnecting volume is not a solution of the FP equation, since the interaction of the particles with the current sheets is “anomalous,” in contrast to the case of the second-order Fermi process.

PARTICLE ACCELERATION AND HEATING BY TURBULENT RECONNECTION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vlahos, Loukas; Pisokas, Theophilos; Isliker, Heinz

2016-08-10

Turbulent flows in the solar wind, large-scale current sheets, multiple current sheets, and shock waves lead to the formation of environments in which a dense network of current sheets is established and sustains “turbulent reconnection.” We constructed a 2D grid on which a number of randomly chosen grid points are acting as scatterers (i.e., magnetic clouds or current sheets). Our goal is to examine how test particles respond inside this large-scale collection of scatterers. We study the energy gain of individual particles, the evolution of their energy distribution, and their escape time distribution. We have developed a new method tomore » estimate the transport coefficients from the dynamics of the interaction of the particles with the scatterers. Replacing the “magnetic clouds” with current sheets, we have proven that the energization processes can be more efficient depending on the strength of the effective electric fields inside the current sheets and their statistical properties. Using the estimated transport coefficients and solving the Fokker–Planck (FP) equation, we can recover the energy distribution of the particles only for the stochastic Fermi process. We have shown that the evolution of the particles inside a turbulent reconnecting volume is not a solution of the FP equation, since the interaction of the particles with the current sheets is “anomalous,” in contrast to the case of the second-order Fermi process.« less

Predicting X-ray diffuse scattering from translation–libration–screw structural ensembles

PubMed Central

Van Benschoten, Andrew H.; Afonine, Pavel V.; Terwilliger, Thomas C.; Wall, Michael E.; Jackson, Colin J.; Sauter, Nicholas K.; Adams, Paul D.; Urzhumtsev, Alexandre; Fraser, James S.

2015-01-01

Identifying the intramolecular motions of proteins and nucleic acids is a major challenge in macromolecular X-ray crystallography. Because Bragg diffraction describes the average positional distribution of crystalline atoms with imperfect precision, the resulting electron density can be compatible with multiple models of motion. Diffuse X-ray scattering can reduce this degeneracy by reporting on correlated atomic displacements. Although recent technological advances are increasing the potential to accurately measure diffuse scattering, computational modeling and validation tools are still needed to quantify the agreement between experimental data and different parameterizations of crystalline disorder. A new tool, phenix.diffuse, addresses this need by employing Guinier’s equation to calculate diffuse scattering from Protein Data Bank (PDB)-formatted structural ensembles. As an example case, phenix.diffuse is applied to translation–libration–screw (TLS) refinement, which models rigid-body displacement for segments of the macromolecule. To enable the calculation of diffuse scattering from TLS-refined structures, phenix.tls_as_xyz builds multi-model PDB files that sample the underlying T, L and S tensors. In the glycerophos­phodiesterase GpdQ, alternative TLS-group partitioning and different motional correlations between groups yield markedly dissimilar diffuse scattering maps with distinct implications for molecular mechanism and allostery. These methods demonstrate how, in principle, X-ray diffuse scattering could extend macromolecular structural refinement, validation and analysis. PMID:26249347

Predicting X-ray diffuse scattering from translation–libration–screw structural ensembles

DOE PAGES

Van Benschoten, Andrew H.; Afonine, Pavel V.; Terwilliger, Thomas C.; ...

2015-07-28

Identifying the intramolecular motions of proteins and nucleic acids is a major challenge in macromolecular X-ray crystallography. Because Bragg diffraction describes the average positional distribution of crystalline atoms with imperfect precision, the resulting electron density can be compatible with multiple models of motion. Diffuse X-ray scattering can reduce this degeneracy by reporting on correlated atomic displacements. Although recent technological advances are increasing the potential to accurately measure diffuse scattering, computational modeling and validation tools are still needed to quantify the agreement between experimental data and different parameterizations of crystalline disorder. A new tool, phenix.diffuse, addresses this need by employing Guinier'smore » equation to calculate diffuse scattering from Protein Data Bank (PDB)-formatted structural ensembles. As an example case, phenix.diffuse is applied to translation–libration–screw (TLS) refinement, which models rigid-body displacement for segments of the macromolecule. To enable the calculation of diffuse scattering from TLS-refined structures, phenix.tls_as_xyz builds multi-model PDB files that sample the underlying T, L and S tensors. In the glycerophosphodiesterase GpdQ, alternative TLS-group partitioning and different motional correlations between groups yield markedly dissimilar diffuse scattering maps with distinct implications for molecular mechanism and allostery. In addition, these methods demonstrate how, in principle, X-ray diffuse scattering could extend macromolecular structural refinement, validation and analysis.« less

Integral Equations and Scattering Solutions for a Square-Well Potential.

ERIC Educational Resources Information Center

Bagchi, B.; Seyler, R. G.

1979-01-01

Derives Green's functions and integral equations for scattering solutions subject to a variety of boundary conditions. Exact solutions are obtained for the case of a finite spherical square-well potential, and properties of these solutions are discussed. (Author/HM)

Utilization of the multiple scattering model for the conception of heterogeneous materials with specific electromagnetic properties

NASA Astrophysics Data System (ADS)

Vignéras-Lefebvre, V.; Miane, J. L.; Parneix, J. P.

1993-03-01

A modelisation of the behaviour of heterogeneous structures, made with spherical particles, submitted to microwave fields, using multiple scattering, is presented. First of all, we expose the principle of scattering by a single sphere, using Mie's equations represented in the form of a transfer matrix. This matrix, generalized to a distribution of particles, allows the translation of an average behaviour of the material. As part of the limit of Rayleigh, the value of the effective permittivity thus obtained is compared to experimental results. Une modélisation du comportement de structures hétérogènes composées de particules sphériques, soumises à des champs hyperfréquences, utilisant la multidiffusion, est présentée. Dans un premier temps, nous exposons le principe de la diffusion par une seule sphère en utilisant les équations de Mie représentées sous forme matricielle. Cette matrice généralisée à une distribution de particules permet de traduire un comportement moyen du matériau. Dans le cadre de l'approximation de Rayleigh, la valeur de la permittivité ainsi calculée est comparée à des résultats expérimentaux.

Scattering and Emission from Inhomogeneous Vegetation Canopy and Alien Target by Using Three-Dimensional Vector Radiative Transfer (3D-VRT) Equation

NASA Astrophysics Data System (ADS)

Jin, Ya-Qiu; Liang, Zichang

2005-01-01

To solve 3D-VRT equation for the model of spatially inhomogeneous scatter media, the finite enclosure of the scatter media is geometrically divided, in both the vertical z and horizontal (x,y) directions, to form very thin multi-boxes. The zero-th order emission, first-order Mueller matrix of each thin box and an iterative approach of high-order radiative transfer are applied to deriving high-order scattering and emission of whole inhomogeneous scatter media. Numerical results of polarized brightness temperature at microwave frequency and under different radiometer's resolutions from inhomogeneous scatter model such as vegetation canopy and embedded alien target are simulated and discussed.

Application of linear multifrequency-grey acceleration to preconditioned Krylov iterations for thermal radiation transport

DOE PAGES

Till, Andrew T.; Warsa, James S.; Morel, Jim E.

2018-06-15

The thermal radiative transfer (TRT) equations comprise a radiation equation coupled to the material internal energy equation. Linearization of these equations produces effective, thermally-redistributed scattering through absorption-reemission. In this paper, we investigate the effectiveness and efficiency of Linear-Multi-Frequency-Grey (LMFG) acceleration that has been reformulated for use as a preconditioner to Krylov iterative solution methods. We introduce two general frameworks, the scalar flux formulation (SFF) and the absorption rate formulation (ARF), and investigate their iterative properties in the absence and presence of true scattering. SFF has a group-dependent state size but may be formulated without inner iterations in the presence ofmore » scattering, while ARF has a group-independent state size but requires inner iterations when scattering is present. We compare and evaluate the computational cost and efficiency of LMFG applied to these two formulations using a direct solver for the preconditioners. Finally, this work is novel because the use of LMFG for the radiation transport equation, in conjunction with Krylov methods, involves special considerations not required for radiation diffusion.« less

Radiative transfer theory for a random distribution of low velocity spheres as resonant isotropic scatterers

NASA Astrophysics Data System (ADS)

Sato, Haruo; Hayakawa, Toshihiko

2014-10-01

Short-period seismograms of earthquakes are complex especially beneath volcanoes, where the S wave mean free path is short and low velocity bodies composed of melt or fluid are expected in addition to random velocity inhomogeneities as scattering sources. Resonant scattering inherent in a low velocity body shows trap and release of waves with a delay time. Focusing of the delay time phenomenon, we have to consider seriously multiple resonant scattering processes. Since wave phases are complex in such a scattering medium, the radiative transfer theory has been often used to synthesize the variation of mean square (MS) amplitude of waves; however, resonant scattering has not been well adopted in the conventional radiative transfer theory. Here, as a simple mathematical model, we study the sequence of isotropic resonant scattering of a scalar wavelet by low velocity spheres at low frequencies, where the inside velocity is supposed to be low enough. We first derive the total scattering cross-section per time for each order of scattering as the convolution kernel representing the decaying scattering response. Then, for a random and uniform distribution of such identical resonant isotropic scatterers, we build the propagator of the MS amplitude by using causality, a geometrical spreading factor and the scattering loss. Using those propagators and convolution kernels, we formulate the radiative transfer equation for a spherically impulsive radiation from a point source. The synthesized MS amplitude time trace shows a dip just after the direct arrival and a delayed swelling, and then a decaying tail at large lapse times. The delayed swelling is a prominent effect of resonant scattering. The space distribution of synthesized MS amplitude shows a swelling near the source region in space, and it becomes a bell shape like a diffusion solution at large lapse times.

A plane wave model for direct simulation of reflection and transmission by discretely inhomogeneous plane parallel media

NASA Astrophysics Data System (ADS)

Mackowski, Daniel; Ramezanpour, Bahareh

2018-07-01

A formulation is developed for numerically solving the frequency domain Maxwell's equations in plane parallel layers of inhomogeneous media. As was done in a recent work [1], the plane parallel layer is modeled as an infinite square lattice of W × W × H unit cells, with W being a sample width of the layer and H the layer thickness. As opposed to the 3D volume integral/discrete dipole formulation, the derivation begins with a Fourier expansion of the electric field amplitude in the lateral plane, and leads to a coupled system of 1D ordinary differential equations in the depth direction of the layer. A 1D dyadic Green's function is derived for this system and used to construct a set of coupled 1D integral equations for the field expansion coefficients. The resulting mathematical formulation is considerably simpler and more compact than that derived, for the same system, using the discrete dipole approximation applied to the periodic plane lattice. Furthermore, the fundamental property variable appearing in the formulation is the Fourier transformed complex permittivity distribution in the unit cell, and the method obviates any need to define or calculate a dipole polarizability. Although designed primarily for random media calculations, the method is also capable of predicting the single scattering properties of individual particles; comparisons are presented to demonstrate that the method can accurately reproduce, at scattering angles not too close to 90°, the polarimetric scattering properties of single and multiple spheres. The derivation of the dyadic Green's function allows for an analytical preconditioning of the equations, and it is shown that this can result in significantly accelerated solution times when applied to densely-packed systems of particles. Calculation results demonstrate that the method, when applied to inhomogeneous media, can predict coherent backscattering and polarization opposition effects.

Fluorescence lifetime measurements in heterogeneous scattering medium

NASA Astrophysics Data System (ADS)

Nishimura, Goro; Awasthi, Kamlesh; Furukawa, Daisuke

2016-07-01

Fluorescence lifetime in heterogeneous multiple light scattering systems is analyzed by an algorithm without solving the diffusion or radiative transfer equations. The algorithm assumes that the optical properties of medium are constant in the excitation and emission wavelength regions. If the assumption is correct and the fluorophore is a single species, the fluorescence lifetime can be determined by a set of measurements of temporal point-spread function of the excitation light and fluorescence at two different concentrations of the fluorophore. This method is not dependent on the heterogeneity of the optical properties of the medium as well as the geometry of the excitation-detection on an arbitrary shape of the sample. The algorithm was validated by an indocyanine green fluorescence in phantom measurements and demonstrated by an in vivo measurement.

A Non-Perturbative, Finite Particle Number Approach to Relativistic Scattering Theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lindesay, James V

2001-05-11

We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a non-perturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the non-relativistic limit to the non-relativistic Faddeev equations. The aim of this program is to develop equations which explicitly depend upon physically observable input variables, and do not require ''renormalization'' ormore » ''dressing'' of these parameters to connect them to the boundary states.« less

Surface roughness scattering of electrons in bulk mosfets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zuverink, Amanda Renee

2015-11-01

Surface-roughness scattering of electrons at the Si-SiO 2 interface is a very important consideration when analyzing Si metal-oxide-semiconductor field-effect transistors (MOSFETs). Scattering reduces the mobility of the electrons and degrades the device performance. 250-nm and 50-nm bulk MOSFETs were simulated with varying device parameters and mesh sizes in order to compare the effects of surface-roughness scattering in multiple devices. The simulation framework includes the ensemble Monte Carlo method used to solve the Boltzmann transport equation coupled with a successive over-relaxation method used to solve the two-dimensional Poisson's equation. Four methods for simulating the surface-roughness scattering of electrons were implemented onmore » both devices and compared: the constant specularity parameter, the momentum-dependent specularity parameter, and the real-space-roughness method with both uniform and varying electric fields. The specularity parameter is the probability of an electron scattering speculariy from a rough surface. It can be chosen as a constant, characterizing partially diffuse scattering of all electrons from the surface the same way, or it can be momentum dependent, where the size of rms roughness and the normal component of the electron wave number determine the probability of electron-momentum randomization. The real-space rough surface method uses the rms roughness height and correlation length of an actual MOSFET to simulate a rough interface. Due to their charge, electrons scatter from the electric field and not directly from the surface. If the electric field is kept uniform, the electrons do not perceive the roughness and scatter as if from a at surface. However, if the field is allowed to vary, the electrons scatter from the varying electric field as they would in a MOSFET. These methods were implemented for both the 50-nm and 250-nm MOSFETs, and using the rms roughness heights and correlation lengths for real devices. The current-voltage and mobility-electric field curves were plotted for each method on the two devices and compared. The conclusion is that the specularity-parameter methods are valuable as simple models for relatively smooth interfaces. However, they have limitations, as they cannot accurately describe the drastic reduction in the current and the electron mobility that occur in MOSFETs with very rough Si-SiO 2 interfaces.« less

Modeling lidar waveforms with time-dependent stochastic radiative transfer theory for remote estimations of forest structure

NASA Astrophysics Data System (ADS)

Kotchenova, Svetlana Y.; Shabanov, Nikolay V.; Knyazikhin, Yuri; Davis, Anthony B.; Dubayah, Ralph; Myneni, Ranga B.

2003-08-01

Large footprint waveform-recording laser altimeters (lidars) have demonstrated a potential for accurate remote sensing of forest biomass and structure, important for regional and global climate studies. Currently, radiative transfer analyses of lidar data are based on the simplifying assumption that only single scattering contributes to the return signal, which may lead to errors in the modeling of the lower portions of recorded waveforms in the near-infrared spectrum. In this study we apply time-dependent stochastic radiative transfer (RT) theory to model the propagation of lidar pulses through forest canopies. A time-dependent stochastic RT equation is formulated and solved numerically. Such an approach describes multiple scattering events, allows for realistic representation of forest structure including foliage clumping and gaps, simulates off-nadir and multiangular observations, and has the potential to provide better approximations of return waveforms. The model was tested with field data from two conifer forest stands (southern old jack pine and southern old black spruce) in central Canada and two closed canopy deciduous forest stands (with overstory dominated by tulip poplar) in eastern Maryland. Model-simulated signals were compared with waveforms recorded by the Scanning Lidar Imager of Canopies by Echo Recovery (SLICER) over these regions. Model simulations show good agreement with SLICER signals having a slow decay of the waveform. The analysis of the effects of multiple scattering shows that multiply scattered photons magnify the amplitude of the reflected signal, especially that originating from the lower portions of the canopy.

Accuracy and efficiency considerations for wide-angle wavefield extrapolators and scattering operators

NASA Astrophysics Data System (ADS)

Thomson, C. J.

2005-10-01

Several observations are made concerning the numerical implementation of wide-angle one-way wave equations, using for illustration scalar waves obeying the Helmholtz equation in two space dimensions. This simple case permits clear identification of a sequence of physically motivated approximations of use when the mathematically exact pseudo-differential operator (PSDO) one-way method is applied. As intuition suggests, these approximations largely depend on the medium gradients in the direction transverse to the main propagation direction. A key point is that narrow-angle approximations are to be avoided in the interests of accuracy. Another key consideration stems from the fact that the so-called `standard-ordering' PSDO indicates how lateral interpolation of the velocity structure can significantly reduce computational costs associated with the Fourier or plane-wave synthesis lying at the heart of the calculations. A third important point is that the PSDO theory shows what approximations are necessary in order to generate an exponential one-way propagator for the laterally varying case, representing the intuitive extension of classical integral-transform solutions for a laterally homogeneous medium. This exponential propagator permits larger forward stepsizes. Numerical comparisons with Helmholtz (i.e. full) wave-equation finite-difference solutions are presented for various canonical problems. These include propagation along an interfacial gradient, the effects of a compact inclusion and the formation of extended transmitted and backscattered wave trains by model roughness. The ideas extend to the 3-D, generally anisotropic case and to multiple scattering by invariant embedding. It is concluded that the method is very competitive, striking a new balance between simplifying approximations and computational labour. Complicated wave-scattering effects are retained without the need for expensive global solutions, providing a robust and flexible modelling tool.

Multiple magnetic scattering in small-angle neutron scattering of Nd-Fe-B nanocrystalline magnet.

PubMed

Ueno, Tetsuro; Saito, Kotaro; Yano, Masao; Ito, Masaaki; Shoji, Tetsuya; Sakuma, Noritsugu; Kato, Akira; Manabe, Akira; Hashimoto, Ai; Gilbert, Elliot P; Keiderling, Uwe; Ono, Kanta

2016-06-20

We have investigated the influence of multiple scattering on the magnetic small-angle neutron scattering (SANS) from a Nd-Fe-B nanocrystalline magnet. We performed sample-thickness- and neutron-wavelength-dependent SANS measurements, and observed the scattering vector dependence of the multiple magnetic scattering. It is revealed that significant multiple scattering exists in the magnetic scattering rather than the nuclear scattering of Nd-Fe-B nanocrystalline magnet. It is considered that the mean free path of the neutrons for magnetic scattering is rather short in Nd-Fe-B magnets. We analysed the SANS data by the phenomenological magnetic correlation model considering the magnetic microstructures and obtained the microstructural parameters.

Multiple magnetic scattering in small-angle neutron scattering of Nd–Fe–B nanocrystalline magnet

PubMed Central

Ueno, Tetsuro; Saito, Kotaro; Yano, Masao; Ito, Masaaki; Shoji, Tetsuya; Sakuma, Noritsugu; Kato, Akira; Manabe, Akira; Hashimoto, Ai; Gilbert, Elliot P.; Keiderling, Uwe; Ono, Kanta

2016-01-01

We have investigated the influence of multiple scattering on the magnetic small-angle neutron scattering (SANS) from a Nd–Fe–B nanocrystalline magnet. We performed sample-thickness- and neutron-wavelength-dependent SANS measurements, and observed the scattering vector dependence of the multiple magnetic scattering. It is revealed that significant multiple scattering exists in the magnetic scattering rather than the nuclear scattering of Nd–Fe–B nanocrystalline magnet. It is considered that the mean free path of the neutrons for magnetic scattering is rather short in Nd–Fe–B magnets. We analysed the SANS data by the phenomenological magnetic correlation model considering the magnetic microstructures and obtained the microstructural parameters. PMID:27321149

Nonlinear Problems in Fluid Dynamics and Inverse Scattering

DTIC Science & Technology

1993-05-31

nonlinear Kadomtsev - Petviashvili (KP) equations , have solutions which will become infinite in finite time. This phenomenon is sometimes referred to as...40 (November 1992). 4 7. Wave Collapse and Instability of Solitary Waves of a Generalized Nonlinear Kaoiomtsev- Petviashvili Equation , X.P. Wang, M.J...words) The inverse scattering of a class of differential-difference equations and multidimensional operators has been constructed. Solutions of nonlinear

Parallel Solver for Diffuse Optical Tomography on Realistic Head Models With Scattering and Clear Regions.

PubMed

Placati, Silvio; Guermandi, Marco; Samore, Andrea; Scarselli, Eleonora Franchi; Guerrieri, Roberto

2016-09-01

Diffuse optical tomography is an imaging technique, based on evaluation of how light propagates within the human head to obtain the functional information about the brain. Precision in reconstructing such an optical properties map is highly affected by the accuracy of the light propagation model implemented, which needs to take into account the presence of clear and scattering tissues. We present a numerical solver based on the radiosity-diffusion model, integrating the anatomical information provided by a structural MRI. The solver is designed to run on parallel heterogeneous platforms based on multiple GPUs and CPUs. We demonstrate how the solver provides a 7 times speed-up over an isotropic-scattered parallel Monte Carlo engine based on a radiative transport equation for a domain composed of 2 million voxels, along with a significant improvement in accuracy. The speed-up greatly increases for larger domains, allowing us to compute the light distribution of a full human head ( ≈ 3 million voxels) in 116 s for the platform used.

Hydraulic Properties of Closely Spaced Dipping Open Fractures Intersecting a Fluid-Filled Borehole Derived From Tube Wave Generation and Scattering

NASA Astrophysics Data System (ADS)

Minato, Shohei; Ghose, Ranajit; Tsuji, Takeshi; Ikeda, Michiharu; Onishi, Kozo

2017-10-01

Fluid-filled fractures and fissures often determine the pathways and volume of fluid movement. They are critically important in crustal seismology and in the exploration of geothermal and hydrocarbon reservoirs. We introduce a model for tube wave scattering and generation at dipping, parallel-wall fractures intersecting a fluid-filled borehole. A new equation reveals the interaction of tube wavefield with multiple, closely spaced fractures, showing that the fracture dip significantly affects the tube waves. Numerical modeling demonstrates the possibility of imaging these fractures using a focusing analysis. The focused traces correspond well with the known fracture density, aperture, and dip angles. Testing the method on a VSP data set obtained at a fault-damaged zone in the Median Tectonic Line, Japan, presents evidences of tube waves being generated and scattered at open fractures and thin cataclasite layers. This finding leads to a new possibility for imaging, characterizing, and monitoring in situ hydraulic properties of dipping fractures using the tube wavefield.

A microwave scattering model for layered vegetation

NASA Technical Reports Server (NTRS)

Karam, Mostafa A.; Fung, Adrian K.; Lang, Roger H.; Chauhan, Narinder S.

1992-01-01

A microwave scattering model was developed for layered vegetation based on an iterative solution of the radiative transfer equation up to the second order to account for multiple scattering within the canopy and between the ground and the canopy. The model is designed to operate over a wide frequency range for both deciduous and coniferous forest and to account for the branch size distribution, leaf orientation distribution, and branch orientation distribution for each size. The canopy is modeled as a two-layered medium above a rough interface. The upper layer is the crown containing leaves, stems, and branches. The lower layer is the trunk region modeled as randomly positioned cylinders with a preferred orientation distribution above an irregular soil surface. Comparisons of this model with measurements from deciduous and coniferous forests show good agreements at several frequencies for both like and cross polarizations. Major features of the model needed to realize the agreement include allowance for: (1) branch size distribution, (2) second-order effects, and (3) tree component models valid over a wide range of frequencies.

Scattering for the 3D Gross-Pitaevskii Equation

NASA Astrophysics Data System (ADS)

Guo, Zihua; Hani, Zaher; Nakanishi, Kenji

2017-11-01

We study the Cauchy problem for the 3D Gross-Pitaevskii equation. The global well-posedness in the natural energy space was proved by Gérard (Ann. Inst. H. Poincaré Anal. Non Linéaire 23(5):765-779, 2006). In this paper we prove scattering for small data in the same space with some additional angular regularity, and in particular in the radial case we obtain small energy scattering.

Inherent and Apparent Scattering Properties of Coated or Uncoated Spheres Embedded in an Absorbing Host Medium

NASA Technical Reports Server (NTRS)

Yang, P.; Gao, B.-C.; Wiscombe, W. J.; Mishchenko, M. I.; Platnick, S.; Huang, H.-L.; Baum, B. A.; Hu, Y. X.; Winkler, D,; Tsay, S.-C.;

Light scattering from an atomic gas under conditions of quantum degeneracy

NASA Astrophysics Data System (ADS)

Porozova, V. M.; Gerasimov, L. V.; Havey, M. D.; Kupriyanov, D. V.

2018-05-01

Elastic light scattering from a macroscopic atomic sample existing in the Bose-Einstein condensate phase reveals a unique physical configuration of interacting light and matter waves. However, the joint coherent dynamics of the optical excitation induced by an incident photon is influenced by the presence of incoherent scattering channels. For a sample of sufficient length the excitation transports as a polariton wave and the propagation Green's function obeys the scattering equation which we derive. The polariton dynamics could be tracked in the outgoing channel of the scattered photon as we show via numerical solution of the scattering equation for one-dimensional geometry. The results are analyzed and compared with predictions of the conventional macroscopic Maxwell theory for light scattering from a nondegenerate atomic sample of the same density and size.

A new treatment of nonlocality in scattering process

NASA Astrophysics Data System (ADS)

Upadhyay, N. J.; Bhagwat, A.; Jain, B. K.

2018-01-01

Nonlocality in the scattering potential leads to an integro-differential equation. In this equation nonlocality enters through an integral over the nonlocal potential kernel. The resulting Schrödinger equation is usually handled by approximating r,{r}{\\prime }-dependence of the nonlocal kernel. The present work proposes a novel method to solve the integro-differential equation. The method, using the mean value theorem of integral calculus, converts the nonhomogeneous term to a homogeneous term. The effective local potential in this equation turns out to be energy independent, but has relative angular momentum dependence. This method is accurate and valid for any form of nonlocality. As illustrative examples, the total and differential cross sections for neutron scattering off 12C, 56Fe and 100Mo nuclei are calculated with this method in the low energy region (up to 10 MeV) and are found to be in reasonable accord with the experiments.

Impurity-limited resistance and phase interference of localized impurities under quasi-one dimensional nano-structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sano, Nobuyuki, E-mail: sano@esys.tsukuba.ac.jp

2015-12-28

The impurity-limited resistance and the effect of the phase interference among localized multiple impurities in the quasi-one dimensional (quasi-1D) nanowire structures are systematically investigated under the framework of the scattering theory. We derive theoretical expressions of the impurity-limited resistance in the nanowire under the linear response regime from the Landauer formula and from the Boltzmann transport equation (BTE) with the relaxation time approximation. We show that the formula from the BTE exactly coincides with that from the Landauer approach with the weak-scattering limit when the energy spectrum of the in-coming electrons from the reservoirs is narrow and, thus, point outmore » a possibility that the distinction of the impurity-limited resistances derived from the Landauer formula and that of the BTE could be made clear. The derived formulas are applied to the quasi-1D nanowires doped with multiple localized impurities with short-range scattering potential and the validity of various approximations on the resistance are discussed. It is shown that impurity scattering becomes so strong under the nanowire structures that the weak-scattering limit breaks down in most cases. Thus, both phase interference and phase randomization simultaneously play a crucial role in determining the impurity-limited resistance even under the fully coherent framework. When the impurity separation along the wire axis direction is small, the constructive phase interference dominates and the resistance is much greater than the average resistance. As the separation becomes larger, however, it approaches the series resistance of the single-impurity resistance due to the phase randomization. Furthermore, under the uniform configuration of impurities, the space-average resistance of multiple impurities at room temperature is very close to the series resistance of the single-impurity resistance, and thus, each impurity could be regarded as an independent scattering center. The physical origin of this “self-averaging” under the fully coherent environments is attributed to the broadness of the energy spectrum of the in-coming electrons from the reservoirs.« less

A conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gamba, Irene M.; ICES, The University of Texas at Austin, 201 E. 24th St., Stop C0200, Austin, TX 78712; Haack, Jeffrey R.

2014-08-01

We present the formulation of a conservative spectral method for the Boltzmann collision operator with anisotropic scattering cross-sections. The method is an extension of the conservative spectral method of Gamba and Tharkabhushanam [17,18], which uses the weak form of the collision operator to represent the collisional term as a weighted convolution in Fourier space. The method is tested by computing the collision operator with a suitably cut-off angular cross section and comparing the results with the solution of the Landau equation. We analytically study the convergence rate of the Fourier transformed Boltzmann collision operator in the grazing collisions limit tomore » the Fourier transformed Landau collision operator under the assumption of some regularity and decay conditions of the solution to the Boltzmann equation. Our results show that the angular singularity which corresponds to the Rutherford scattering cross section is the critical singularity for which a grazing collision limit exists for the Boltzmann operator. Additionally, we numerically study the differences between homogeneous solutions of the Boltzmann equation with the Rutherford scattering cross section and an artificial cross section, which give convergence to solutions of the Landau equation at different asymptotic rates. We numerically show the rate of the approximation as well as the consequences for the rate of entropy decay for homogeneous solutions of the Boltzmann equation and Landau equation.« less

Kinetics of Electrons from Plasma Discharge in a Latent Track Region Induced by Swift Heavy ION Irradiation

NASA Astrophysics Data System (ADS)

Minárik, Stanislav

2015-08-01

While passing swift heavy ion through a material structure, it produces a region of radiation affected material which is known as a "latent track". Scattering motions of electrons interacting with a swift heavy ion are dominant in the latent track region. These phenomena include the electron impurity and phonon scattering processes modified by the interaction with the ion projectile as well as the Coulomb scattering between two electrons. In this paper, we provide detailed derivation of a 3D Boltzmann scattering equation for the description of the relative scattering motion of such electrons. Phase-space distribution function for this non-equilibrioum system of scattering electrons can be found by the solution of mentioned equation.

Scattering and emission from inhomogeneous vegetation canopy and alien target beneath by using three-dimensional vector radiative transfer (3D-VRT) equation

NASA Astrophysics Data System (ADS)

Jin, Ya-Qiu; Liang, Zichang

2005-05-01

To solve the 3D-VRT equation for the model of spatially inhomogeneous scatter media, the finite enclosure of the scatter media is geometrically divided, in both vertical z and transversal (x,y) directions, to form very thin multi-boxes. The zeroth order emission, first-order Mueller matrix of each thin box and an iterative approach of high-order radiative transfer are applied to derive high-order scattering and emission of whole inhomogeneous scatter media. Numerical results of polarized brightness temperature at microwave frequency and under different radiometer resolutions from inhomogeneous scatter model such as vegetation canopy and alien target beneath canopy are simulated and discussed.

Solution of the relativistic asymptotic equations in electron-ion scattering

NASA Astrophysics Data System (ADS)

Young, I. G.; Norrington, P. H.

1994-12-01

Two asymptotic expansions are suggested for the solution of the coupled equations for the radial channel wavefunctions arising from the treament of electron-ion scattering using the Dirac Hamiltonian. The recurrence relations obtained for the expansions coefficients are given. A method is suggested for calculation of the one-electron Dirac-Coulomb functions used in the second expansion using solutions of the non-relativistic Coulomb equation with complex arguments.

Inclusion of exact exchange in the noniterative partial-differential-equation method of electron-molecule scattering - Application to e-N2

NASA Technical Reports Server (NTRS)

Weatherford, C. A.; Onda, K.; Temkin, A.

1985-01-01

The noniterative partial-differential-equation (PDE) approach to electron-molecule scattering of Onda and Temkin (1983) is modified to account for the effects of exchange explicitly. The exchange equation is reduced to a set of inhomogeneous equations containing no integral terms and solved noniteratively in a difference form; a method for propagating the solution to large values of r is described; the changes in the polarization potential of the original PDE method required by the inclusion of exact static exchange are indicated; and the results of computations for e-N2 scattering in the fixed-nuclei approximation are presented in tables and graphs and compared with previous calculations and experimental data. Better agreement is obtained using the modified PDE method.

Inverse scattering in 1-D nonhomogeneous media and recovery of the wave speed

NASA Astrophysics Data System (ADS)

Aktosun, Tuncay; Klaus, Martin; van der Mee, Cornelis

1992-04-01

The inverse scattering problem for the 1-D Schrödinger equation d2ψ/dx2 + k2ψ= k2P(x)ψ + Q(x)ψ is studied. This equation is equivalent to the 1-D wave equation with speed 1/√1-P(x) in a nonhomogeneous medium where Q(x) acts as a restoring force. When Q(x) is integrable with a finite first moment, P(x)<1 and bounded below and satisfies two integrability conditions, P(x) is recovered uniquely when the scattering data and Q(x) are known. Some explicitly solved examples are provided.

Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Luo, Xu-Dan; Musslimani, Ziad H.

2018-01-01

In 2013, a new nonlocal symmetry reduction of the well-known AKNS (an integrable system of partial differential equations, introduced by and named after Mark J. Ablowitz, David J. Kaup, and Alan C. Newell et al. (1974)) scattering problem was found. It was shown to give rise to a new nonlocal PT symmetric and integrable Hamiltonian nonlinear Schrödinger (NLS) equation. Subsequently, the inverse scattering transform was constructed for the case of rapidly decaying initial data and a family of spatially localized, time periodic one-soliton solutions was found. In this paper, the inverse scattering transform for the nonlocal NLS equation with nonzero boundary conditions at infinity is presented in four different cases when the data at infinity have constant amplitudes. The direct and inverse scattering problems are analyzed. Specifically, the direct problem is formulated, the analytic properties of the eigenfunctions and scattering data and their symmetries are obtained. The inverse scattering problem, which arises from a novel nonlocal system, is developed via a left-right Riemann-Hilbert problem in terms of a suitable uniformization variable and the time dependence of the scattering data is obtained. This leads to a method to linearize/solve the Cauchy problem. Pure soliton solutions are discussed, and explicit 1-soliton solution and two 2-soliton solutions are provided for three of the four different cases corresponding to two different signs of nonlinearity and two different values of the phase difference between plus and minus infinity. In another case, there are no solitons.

Differences between the MEMLS and the multiple-layer HUT model and their comparisons with in-situ snowpack observations

NASA Astrophysics Data System (ADS)

Pan, J.; Durand, M. T.; Sandells, M. J.; Lemmetyinen, J.; Kim, E. J.

2013-12-01

Application of passive microwave (PM) brightness temperature for snow water equivalent retrieval requires deep understanding of snow emission models, not only for their performance to reproduce in-situ PM observations, but also for their theoretical differences to approximate radiative transfer theory. In this paper, differences between the multiple-layer HUT (or TKK) model and the Microwave Emission Model of Layered Snowpacks (MEMLS) were listed, and the two models were compared with snow ground-based PM observations at Streamboat Springs, Colorado, USA; Churchill, Canada; and Sodankyla, Finland. The two models were chosen for their multiple-layer schemes are close to actual layer-by-layer snow measurements. Both the two models are semi-empirical models; whereas the HUT model uses the mean snow grain size, MEMLS uses the correlation length to relate the snow microstructure with the scattering coefficients. The two parameters are related according to previous studies. The Specific Surface Area (SSA) was measured at three test sites to derive the correlation length, while the mean snow grain sizes was available at Stream Springs and Sodankyla. It was shown that with different apparent forms of radiative transfer equations, the different parts of the two models have one-to-one correspondence however, and intermediate parameters are comparable. Regarding the multiple-layer structure of the models, it was found that the HUT model considers the internal reflectivity of each snow layer to be zero. The two-flux radiative transfer equations of the two models were compared, and the correspondence of the semi-empirical parameter q in the HUT model was found in the MEMLS. The effect of consideration of transverse radiation scattered into the direction under consideration via the six-flux approximation in MEMLS is compared. Based on model comparisons, we analyzed the differences of TB predictions at the three test sites.

Scattering of electromagnetic plane wave from a perfect electric conducting strip placed at interface of topological insulator-chiral medium

NASA Astrophysics Data System (ADS)

Shoukat, Sobia; Naqvi, Qaisar A.

2016-12-01

In this manuscript, scattering from a perfect electric conducting strip located at planar interface of topological insulator (TI)-chiral medium is investigated using the Kobayashi Potential method. Longitudinal components of electric and magnetic vector potential in terms of unknown weighting function are considered. Use of related set of boundary conditions yields two algebraic equations and four dual integral equations (DIEs). Integrand of two DIEs are expanded in terms of the characteristic functions with expansion coefficients which must satisfy, simultaneously, the discontinuous property of the Weber-Schafheitlin integrals, required edge and boundary conditions. The resulting expressions are then combined with algebraic equations to express the weighting function in terms of expansion coefficients, these expansion coefficients are then substituted in remaining DIEs. The projection is applied using the Jacobi polynomials. This treatment yields matrix equation for expansion coefficients which is solved numerically. These unknown expansion coefficients are used to find the scattered field. The far zone scattering width is investigated with respect to different parameters of the geometry, i.e, chirality of chiral medium, angle of incidence, size of the strip. Significant effects of different parameters including TI parameter on the scattering width are noted.

Adjoint Sensitivity Analysis of Radiative Transfer Equation: Temperature and Gas Mixing Ratio Weighting Functions for Remote Sensing of Scattering Atmospheres in Thermal IR

NASA Technical Reports Server (NTRS)

Ustinov, E.

1999-01-01

Sensitivity analysis based on using of the adjoint equation of radiative transfer is applied to the case of atmospheric remote sensing in the thermal spectral region with non-negligeable atmospheric scattering.

Achieving a strongly negative scattering asymmetry factor in random media composed of dual-dipolar particles

NASA Astrophysics Data System (ADS)

Wang, B. X.; Zhao, C. Y.

2018-02-01

Understanding radiative transfer in random media like micro- or nanoporous and particulate materials, allows people to manipulate the scattering and absorption of radiation, as well as opens new possibilities in applications such as imaging through turbid media, photovoltaics, and radiative cooling. A strong-backscattering phase function, i.e., a negative scattering asymmetry parameter g , is of great interest, which can possibly lead to unusual radiative transport phenomena, for instance, Anderson localization of light. Here we demonstrate that by utilizing the structural correlations and second Kerker condition for a disordered medium composed of randomly distributed silicon nanoparticles, a strongly negative scattering asymmetry factor (g ˜-0.5 ) for multiple light scattering can be realized in the near infrared. Based on the multipole expansion of Foldy-Lax equations and quasicrystalline approximation (QCA), we have rigorously derived analytical expressions for the effective propagation constant and scattering phase function for a random system containing spherical particles, by taking the effect of structural correlations into account. We show that as the concentration of scattering particles rises, the backscattering is also enhanced. Moreover, in this circumstance, the transport mean free path is largely reduced and even becomes smaller than that predicted by independent scattering approximation. We further explore the dependent scattering effects, including the modification of electric and magnetic dipole excitations and far-field interference effect, both induced and influenced by the structural correlations, for volume fraction of particles up to fv˜0.25 . Our results have profound implications in harnessing micro- or nanoscale radiative transfer through random media.

Geant4 simulations of soft proton scattering in X-ray optics. A tentative validation using laboratory measurements

NASA Astrophysics Data System (ADS)

Fioretti, Valentina; Mineo, Teresa; Bulgarelli, Andrea; Dondero, Paolo; Ivanchenko, Vladimir; Lei, Fan; Lotti, Simone; Macculi, Claudio; Mantero, Alfonso

2017-12-01

Low energy protons (< 300 keV) can enter the field of view of X-ray telescopes, scatter on their mirror surfaces at small incident angles, and deposit energy on the detector. This phenomenon can cause intense background flares at the focal plane decreasing the mission observing time (e.g. the XMM-Newton mission) or in the most extreme cases, damaging the X-ray detector. A correct modelization of the physics process responsible for the grazing angle scattering processes is mandatory to evaluate the impact of such events on the performance (e.g. observation time, sensitivity) of future X-ray telescopes as the ESA ATHENA mission. The Remizovich model describes particles reflected by solids at glancing angles in terms of the Boltzmann transport equation using the diffuse approximation and the model of continuous slowing down in energy. For the first time this solution, in the approximation of no energy losses, is implemented, verified, and qualitatively validated on top of the Geant4 release 10.2, with the possibility to add a constant energy loss to each interaction. This implementation is verified by comparing the simulated proton distribution to both the theoretical probability distribution and with independent ray-tracing simulations. Both the new scattering physics and the Coulomb scattering already built in the official Geant4 distribution are used to reproduce the latest experimental results on grazing angle proton scattering. At 250 keV multiple scattering delivers large proton angles and it is not consistent with the observation. Among the tested models, the single scattering seems to better reproduce the scattering efficiency at the three energies but energy loss obtained at small scattering angles is significantly lower than the experimental values. In general, the energy losses obtained in the experiment are higher than what obtained by the simulation. The experimental data are not completely representative of the soft proton scattering experienced by current X-ray telescopes because of the lack of measurements at low energies (< 200 keV) and small reflection angles, so we are not able to address any of the tested models as the one that can certainly reproduce the scattering behavior of low energy protons expected for the ATHENA mission. We can, however, discard multiple scattering as the model able to reproduce soft proton funnelling, and affirm that Coulomb single scattering can represent, until further measurements at lower energies are available, the best approximation of the proton scattered angular distribution at the exit of X-ray optics.

A Theory of Exoplanet Transits with Light Scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Robinson, Tyler D., E-mail: tydrobin@ucsc.edu

Exoplanet transit spectroscopy enables the characterization of distant worlds, and will yield key results for NASA's James Webb Space Telescope . However, transit spectra models are often simplified, omitting potentially important processes like refraction and multiple scattering. While the former process has seen recent development, the effects of light multiple scattering on exoplanet transit spectra have received little attention. Here, we develop a detailed theory of exoplanet transit spectroscopy that extends to the full refracting and multiple scattering case. We explore the importance of scattering for planet-wide cloud layers, where the relevant parameters are the slant scattering optical depth, themore » scattering asymmetry parameter, and the angular size of the host star. The latter determines the size of the “target” for a photon that is back-mapped from an observer. We provide results that straightforwardly indicate the potential importance of multiple scattering for transit spectra. When the orbital distance is smaller than 10–20 times the stellar radius, multiple scattering effects for aerosols with asymmetry parameters larger than 0.8–0.9 can become significant. We provide examples of the impacts of cloud/haze multiple scattering on transit spectra of a hot Jupiter-like exoplanet. For cases with a forward and conservatively scattering cloud/haze, differences due to multiple scattering effects can exceed 200 ppm, but shrink to zero at wavelength ranges corresponding to strong gas absorption or when the slant optical depth of the cloud exceeds several tens. We conclude with a discussion of types of aerosols for which multiple scattering in transit spectra may be important.« less

Global linear gyrokinetic simulations for LHD including collisions

NASA Astrophysics Data System (ADS)

Kauffmann, K.; Kleiber, R.; Hatzky, R.; Borchardt, M.

2010-11-01

The code EUTERPE uses a Particle-In-Cell (PIC) method to solve the gyrokinetic equation globally (full radius, full flux surface) for three-dimensional equilibria calculated with VMEC. Recently this code has been extended to include multiple kinetic species and electromagnetic effects. Additionally, a pitch-angle scattering operator has been implemented in order to include collisional effects in the simulation of instabilities and to be able to simulate neoclassical transport. As a first application of this extended code we study the effects of collisions on electrostatic ion-temperature-gradient (ITG) instabilities in LHD.

Wavefunction Engineering of Spintronic devices in ZnO/MgO and GaN/AlN Quantum Structures Doped with Transition Metal Ions

DTIC Science & Technology

2006-08-01

2005). 7. " Dependence of the interband transitions on the In mole-fraction and the applied electric field in InxGaj_xAs/In0. 52Al0.48As multiple... tunneling boundary conditions for open structures. The boundary conditions at interfaces require the maintenance of derivative operator ordering...computational methods for the solution of Schr6dinger’s equations for scattering/ tunneling structures as well as for the eigenvalue problems that arise for

A single-sided homogeneous Green's function representation for holographic imaging, inverse scattering, time-reversal acoustics and interferometric Green's function retrieval

NASA Astrophysics Data System (ADS)

Wapenaar, Kees; Thorbecke, Jan; van der Neut, Joost

2016-04-01

Green's theorem plays a fundamental role in a diverse range of wavefield imaging applications, such as holographic imaging, inverse scattering, time-reversal acoustics and interferometric Green's function retrieval. In many of those applications, the homogeneous Green's function (i.e. the Green's function of the wave equation without a singularity on the right-hand side) is represented by a closed boundary integral. In practical applications, sources and/or receivers are usually present only on an open surface, which implies that a significant part of the closed boundary integral is by necessity ignored. Here we derive a homogeneous Green's function representation for the common situation that sources and/or receivers are present on an open surface only. We modify the integrand in such a way that it vanishes on the part of the boundary where no sources and receivers are present. As a consequence, the remaining integral along the open surface is an accurate single-sided representation of the homogeneous Green's function. This single-sided representation accounts for all orders of multiple scattering. The new representation significantly improves the aforementioned wavefield imaging applications, particularly in situations where the first-order scattering approximation breaks down.

First-Principles Modeling Of Electromagnetic Scattering By Discrete and Discretely Heterogeneous Random Media

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.

2016-01-01

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell- Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of the first principles formalism enabling accurate calculations of monochromatic and quasi-monochromatic scattering by static and randomly varying multiparticle groups. We illustrate how this general framework can be coupled with state-of-the-art computer solvers of the Maxwell equations and applied to direct modeling of electromagnetic scattering by representative random multi-particle groups with arbitrary packing densities. This first-principles modeling yields general physical insights unavailable with phenomenological approaches. We discuss how the first-order-scattering approximation, the radiative transfer theory, and the theory of weak localization of electromagnetic waves can be derived as immediate corollaries of the Maxwell equations for very specific and well-defined kinds of particulate medium. These recent developments confirm the mesoscopic origin of the radiative transfer, weak localization, and effective-medium regimes and help evaluate the numerical accuracy of widely used approximate modeling methodologies.

First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media.

PubMed

Mishchenko, Michael I; Dlugach, Janna M; Yurkin, Maxim A; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R Lee; Travis, Larry D; Yang, Ping; Zakharova, Nadezhda T

2016-05-16

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ , or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell-Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of the first-principles formalism enabling accurate calculations of monochromatic and quasi-monochromatic scattering by static and randomly varying multiparticle groups. We illustrate how this general framework can be coupled with state-of-the-art computer solvers of the Maxwell equations and applied to direct modeling of electromagnetic scattering by representative random multi-particle groups with arbitrary packing densities. This first-principles modeling yields general physical insights unavailable with phenomenological approaches. We discuss how the first-order-scattering approximation, the radiative transfer theory, and the theory of weak localization of electromagnetic waves can be derived as immediate corollaries of the Maxwell equations for very specific and well-defined kinds of particulate medium. These recent developments confirm the mesoscopic origin of the radiative transfer, weak localization, and effective-medium regimes and help evaluate the numerical accuracy of widely used approximate modeling methodologies.

First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media

PubMed Central

Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.

2018-01-01

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell’s equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell–Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell–Lorentz equations, we trace the development of the first-principles formalism enabling accurate calculations of monochromatic and quasi-monochromatic scattering by static and randomly varying multiparticle groups. We illustrate how this general framework can be coupled with state-of-the-art computer solvers of the Maxwell equations and applied to direct modeling of electromagnetic scattering by representative random multi-particle groups with arbitrary packing densities. This first-principles modeling yields general physical insights unavailable with phenomenological approaches. We discuss how the first-order-scattering approximation, the radiative transfer theory, and the theory of weak localization of electromagnetic waves can be derived as immediate corollaries of the Maxwell equations for very specific and well-defined kinds of particulate medium. These recent developments confirm the mesoscopic origin of the radiative transfer, weak localization, and effective-medium regimes and help evaluate the numerical accuracy of widely used approximate modeling methodologies. PMID:29657355

Parallel CARLOS-3D code development

DOE Office of Scientific and Technical Information (OSTI.GOV)

Putnam, J.M.; Kotulski, J.D.

1996-02-01

CARLOS-3D is a three-dimensional scattering code which was developed under the sponsorship of the Electromagnetic Code Consortium, and is currently used by over 80 aerospace companies and government agencies. The code has been extensively validated and runs on both serial workstations and parallel super computers such as the Intel Paragon. CARLOS-3D is a three-dimensional surface integral equation scattering code based on a Galerkin method of moments formulation employing Rao- Wilton-Glisson roof-top basis for triangular faceted surfaces. Fully arbitrary 3D geometries composed of multiple conducting and homogeneous bulk dielectric materials can be modeled. This presentation describes some of the extensions tomore » the CARLOS-3D code, and how the operator structure of the code facilitated these improvements. Body of revolution (BOR) and two-dimensional geometries were incorporated by simply including new input routines, and the appropriate Galerkin matrix operator routines. Some additional modifications were required in the combined field integral equation matrix generation routine due to the symmetric nature of the BOR and 2D operators. Quadrilateral patched surfaces with linear roof-top basis functions were also implemented in the same manner. Quadrilateral facets and triangular facets can be used in combination to more efficiently model geometries with both large smooth surfaces and surfaces with fine detail such as gaps and cracks. Since the parallel implementation in CARLOS-3D is at high level, these changes were independent of the computer platform being used. This approach minimizes code maintenance, while providing capabilities with little additional effort. Results are presented showing the performance and accuracy of the code for some large scattering problems. Comparisons between triangular faceted and quadrilateral faceted geometry representations will be shown for some complex scatterers.« less

Enhanced backscattering of optical waves due to densely distributed scatterers

NASA Astrophysics Data System (ADS)

Ma, Yushieh; Varadan, Vijay K.; Varadan, Vasundara V.

1988-01-01

Using multiple scattering theory, the T matrix of a pair of scatterers which takes all back-and-forth scattering between the pair members into account and considers multiple scattering effects in the intensity calculation is used to calculate the magnitude and the width of the backscattered intensity peak. Generally, at low concentrations, both the magnitude of the scattered intensity and multiple scattering contributions are not sufficiently strong to reach the enhanced-backscattering threshold. The results obtained are consistent with those yielded by optical experiments.

On a partial differential equation method for determining the free energies and coexisting phase compositions of ternary mixtures from light scattering data.

PubMed

Ross, David S; Thurston, George M; Lutzer, Carl V

2008-08-14

In this paper we present a method for determining the free energies of ternary mixtures from light scattering data. We use an approximation that is appropriate for liquid mixtures, which we formulate as a second-order nonlinear partial differential equation. This partial differential equation (PDE) relates the Hessian of the intensive free energy to the efficiency of light scattering in the forward direction. This basic equation applies in regions of the phase diagram in which the mixtures are thermodynamically stable. In regions in which the mixtures are unstable or metastable, the appropriate PDE is the nonlinear equation for the convex hull. We formulate this equation along with continuity conditions for the transition between the two equations at cloud point loci. We show how to discretize this problem to obtain a finite-difference approximation to it, and we present an iterative method for solving the discretized problem. We present the results of calculations that were done with a computer program that implements our method. These calculations show that our method is capable of reconstructing test free energy functions from simulated light scattering data. If the cloud point loci are known, the method also finds the tie lines and tie triangles that describe thermodynamic equilibrium between two or among three liquid phases. A robust method for solving this PDE problem, such as the one presented here, can be a basis for optical, noninvasive means of characterizing the thermodynamics of multicomponent mixtures.

Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres

NASA Technical Reports Server (NTRS)

Mishchenko, M. I.; Lacis, A. A.; Travis, L. D.

1994-01-01

Although neglecting polarization and replacing the rigorous vector radiative transfer equation by its approximate scalar counterpart has no physical background, it is a widely used simplification when the incident light is unpolarized and only the intensity of the reflected light is to be computed. We employ accurate vector and scalar multiple-scattering calculations to perform a systematic study of the errors induced by the neglect of polarization in radiance calculations for a homogeneous, plane-parallel Rayleigh-scattering atmosphere (with and without depolarization) above a Lambertian surface. Specifically, we calculate percent errors in the reflected intensity for various directions of light incidence and reflection, optical thicknesses of the atmosphere, single-scattering albedos, depolarization factors, and surface albedos. The numerical data displayed can be used to decide whether or not the scalar approximation may be employed depending on the parameters of the problem. We show that the errors decrease with increasing depolarization factor and/or increasing surface albedo. For conservative or nearly conservative scattering and small surface albedos, the errors are maximum at optical thicknesses of about 1. The calculated errors may be too large for some practical applications, and, therefore, rigorous vector calculations should be employed whenever possible. However, if approximate scalar calculations are used, we recommend to avoid geometries involving phase angles equal or close to 0 deg and 90 deg, where the errors are especially significant. We propose a theoretical explanation of the large vector/scalar differences in the case of Rayleigh scattering. According to this explanation, the differences are caused by the particular structure of the Rayleigh scattering matrix and come from lower-order (except first-order) light scattering paths involving right scattering angles and right-angle rotations of the scattering plane.

Laser induced heat source distribution in bio-tissues

NASA Astrophysics Data System (ADS)

Li, Xiaoxia; Fan, Shifu; Zhao, Youquan

2006-09-01

During numerical simulation of laser and tissue thermal interaction, the light fluence rate distribution should be formularized and constituted to the source term in the heat transfer equation. Usually the solution of light irradiative transport equation is given in extreme conditions such as full absorption (Lambert-Beer Law), full scattering (Lubelka-Munk theory), most scattering (Diffusion Approximation) et al. But in specific conditions, these solutions will induce different errors. The usually used Monte Carlo simulation (MCS) is more universal and exact but has difficulty to deal with dynamic parameter and fast simulation. Its area partition pattern has limits when applying FEM (finite element method) to solve the bio-heat transfer partial differential coefficient equation. Laser heat source plots of above methods showed much difference with MCS. In order to solve this problem, through analyzing different optical actions such as reflection, scattering and absorption on the laser induced heat generation in bio-tissue, a new attempt was made out which combined the modified beam broaden model and the diffusion approximation model. First the scattering coefficient was replaced by reduced scattering coefficient in the beam broaden model, which is more reasonable when scattering was treated as anisotropic scattering. Secondly the attenuation coefficient was replaced by effective attenuation coefficient in scattering dominating turbid bio-tissue. The computation results of the modified method were compared with Monte Carlo simulation and showed the model provided reasonable predictions of heat source term distribution than past methods. Such a research is useful for explaining the physical characteristics of heat source in the heat transfer equation, establishing effective photo-thermal model, and providing theory contrast for related laser medicine experiments.

Frequency-domain method for measuring spectral properties in multiple-scattering media: methemoglobin absorption spectrum in a tissuelike phantom

NASA Astrophysics Data System (ADS)

Fishkin, Joshua B.; So, Peter T. C.; Cerussi, Albert E.; Gratton, Enrico; Fantini, Sergio; Franceschini, Maria Angela

1995-03-01

We have measured the optical absorption and scattering coefficient spectra of a multiple-scattering medium (i.e., a biological tissue-simulating phantom comprising a lipid colloid) containing methemoglobin by using frequency-domain techniques. The methemoglobin absorption spectrum determined in the multiple-scattering medium is in excellent agreement with a corrected methemoglobin absorption spectrum obtained from a steady-state spectrophotometer measurement of the optical density of a minimally scattering medium. The determination of the corrected methemoglobin absorption spectrum takes into account the scattering from impurities in the methemoglobin solution containing no lipid colloid. Frequency-domain techniques allow for the separation of the absorbing from the scattering properties of multiple-scattering media, and these techniques thus provide an absolute

Exploring the feasibility of focusing CW light through a scattering medium into closely spaced twin peaks via numerical solutions of Maxwell’s equations

NASA Astrophysics Data System (ADS)

Tseng, Snow H.; Chang, Shih-Hui

2018-04-01

Here we present a numerical simulation to analyze the effect of scattering on focusing light into closely-spaced twin peaks. The pseudospectral time-domain (PSTD) is implemented to model continuous-wave (CW) light propagation through a scattering medium. Simulations show that CW light can propagate through a scattering medium and focus into closely-spaced twin peaks. CW light of various wavelengths focusing into twin peaks with sub-diffraction spacing is simulated. In advance, light propagation through scattering media of various number densities is simulated to decipher the dependence of CW light focusing phenomenon on the scattering medium. The reported simulations demonstrate the feasibility of focusing CW light into twin peaks with sub-diffraction dimensions. More importantly, based upon numerical solutions of Maxwell’s equations, research findings show that the sub-diffraction focusing phenomenon can be achieved with scarce or densely-packed scattering media.

Fast two-stream method for computing diurnal-mean actinic flux in vertically inhomogeneous atmospheres

NASA Technical Reports Server (NTRS)

Filyushkin, V. V.; Madronich, S.; Brasseur, G. P.; Petropavlovskikh, I. V.

1994-01-01

Based on a derivation of the two-stream daytime-mean equations of radiative flux transfer, a method for computing the daytime-mean actinic fluxes in the absorbing and scattering vertically inhomogeneous atmosphere is suggested. The method applies direct daytime integration of the particular solutions of the two-stream approximations or the source functions. It is valid for any duration of period of averaging. The merit of the method is that the multiple scattering computation is carried out only once for the whole averaging period. It can be implemented with a number of widely used two-stream approximations. The method agrees with the results obtained with 200-point multiple scattering calculations. The method was also tested in runs with a 1-km cloud layer with optical depth of 10, as well as with aerosol background. Comparison of the results obtained for a cloud subdivided into 20 layers with those obtained for a one-layer cloud with the same optical parameters showed that direct integration of particular solutions possesses an 'analytical' accuracy. In the case of the source function interpolation, the actinic fluxes calculated above the one-layer and 20-layer clouds agreed within 1%-1.5%, while below the cloud they may differ up to 5% (in the worst case). The ways of enhancing the accuracy (in a 'two-stream sense') and computational efficiency of the method are discussed.

Spacecraft self-contamination due to back-scattering of outgas products

NASA Technical Reports Server (NTRS)

Robertson, S. J.

1976-01-01

The back-scattering of outgas contamination near an orbiting spacecraft due to intermolecular collisions was analyzed. Analytical tools were developed for making reasonably accurate quantitative estimates of the outgas contamination return flux, given a knowledge of the pertinent spacecraft and orbit conditions. Two basic collision mechanisms were considered: (1) collisions involving only outgas molecules (self-scattering) and (2) collisions between outgas molecules and molecules in the ambient atmosphere (ambient-scattering). For simplicity, the geometry was idealized to a uniformly outgassing sphere and to a disk oriented normal to the freestream. The method of solution involved an integration of an approximation of the Boltzmann kinetic equation known as the BGK (or Krook) model equation. Results were obtained in the form of simple equations relating outgas return flux to spacecraft and orbit parameters. Results were compared with previous analyses based on more simplistic models of the collision processes.

Predicting X-ray diffuse scattering from translation–libration–screw structural ensembles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Van Benschoten, Andrew H.; Afonine, Pavel V.; Terwilliger, Thomas C.

2015-07-28

A method of simulating X-ray diffuse scattering from multi-model PDB files is presented. Despite similar agreement with Bragg data, different translation–libration–screw refinement strategies produce unique diffuse intensity patterns. Identifying the intramolecular motions of proteins and nucleic acids is a major challenge in macromolecular X-ray crystallography. Because Bragg diffraction describes the average positional distribution of crystalline atoms with imperfect precision, the resulting electron density can be compatible with multiple models of motion. Diffuse X-ray scattering can reduce this degeneracy by reporting on correlated atomic displacements. Although recent technological advances are increasing the potential to accurately measure diffuse scattering, computational modeling andmore » validation tools are still needed to quantify the agreement between experimental data and different parameterizations of crystalline disorder. A new tool, phenix.diffuse, addresses this need by employing Guinier’s equation to calculate diffuse scattering from Protein Data Bank (PDB)-formatted structural ensembles. As an example case, phenix.diffuse is applied to translation–libration–screw (TLS) refinement, which models rigid-body displacement for segments of the macromolecule. To enable the calculation of diffuse scattering from TLS-refined structures, phenix.tls-as-xyz builds multi-model PDB files that sample the underlying T, L and S tensors. In the glycerophosphodiesterase GpdQ, alternative TLS-group partitioning and different motional correlations between groups yield markedly dissimilar diffuse scattering maps with distinct implications for molecular mechanism and allostery. These methods demonstrate how, in principle, X-ray diffuse scattering could extend macromolecular structural refinement, validation and analysis.« less

Intrinsic and scattering attenuation of high-frequency S-waves in the central part of the External Dinarides

NASA Astrophysics Data System (ADS)

Majstorović, Josipa; Belinić, Tena; Namjesnik, Dalija; Dasović, Iva; Herak, Davorka; Herak, Marijan

2017-09-01

The central part of the External Dinarides (CED) is a geologically and tectonically complex region formed in the collision between the Adriatic microplate and the European plate. In this study, the contributions of intrinsic and scattering attenuation ( Q i - 1 and Q sc - 1 , respectively) to the total S-wave attenuation were calculated for the first time. The multiple lapse-time window analysis (MLTWA method), based on the assumptions of multiple isotropic scattering in a homogeneous medium with uniformly distributed scatterers, was applied to seismograms of 450 earthquakes recorded at six seismic stations. Selected events have hypocentral distances between 40 and 90 km with local magnitudes between 1.5 and 4.7. The analysis was performed over 11 frequency bands with central frequencies between 1.5 and 16 Hz. Results show that the seismic albedo of the studied area is less than 0.5 and Q i - 1 > Q sc - 1 at all central frequencies and for all stations. These imply that the intrinsic attenuation dominates over scattering attenuation in the whole study area. Calculated total S-wave and expected coda wave attenuation for CED are in a very good agreement with the ones measured in previous studies using the coda normalization and the coda-Q methods. All estimated attenuation factors decrease with increasing frequency. The intrinsic attenuation for CED is among the highest observed elsewhere, which could be due to the highly fractured and fluid-filled carbonates in the upper crust. The scattering and the total S-wave attenuation for CED are close to the average values obtained in other studies performed worldwide. In particular, good agreement of frequency dependence of total attenuation in CED and in the regions that contributed most strong-motion records for ground motion prediction equations used in PSHA in Croatia indicates that those were well chosen and applicable to this area as far as their attenuation properties are concerned.

High-order integral equation methods for problems of scattering by bumps and cavities on half-planes.

PubMed

Pérez-Arancibia, Carlos; Bruno, Oscar P

2014-08-01

This paper presents high-order integral equation methods for the evaluation of electromagnetic wave scattering by dielectric bumps and dielectric cavities on perfectly conducting or dielectric half-planes. In detail, the algorithms introduced in this paper apply to eight classical scattering problems, namely, scattering by a dielectric bump on a perfectly conducting or a dielectric half-plane, and scattering by a filled, overfilled, or void dielectric cavity on a perfectly conducting or a dielectric half-plane. In all cases field representations based on single-layer potentials for appropriately chosen Green functions are used. The numerical far fields and near fields exhibit excellent convergence as discretizations are refined-even at and around points where singular fields and infinite currents exist.

A single-scattering correction for the seismo-acoustic parabolic equation.

PubMed

Collins, Michael D

2012-04-01

An efficient single-scattering correction that does not require iterations is derived and tested for the seismo-acoustic parabolic equation. The approach is applicable to problems involving gradual range dependence in a waveguide with fluid and solid layers, including the key case of a sloping fluid-solid interface. The single-scattering correction is asymptotically equivalent to a special case of a single-scattering correction for problems that only have solid layers [Küsel et al., J. Acoust. Soc. Am. 121, 808-813 (2007)]. The single-scattering correction has a simple interpretation (conservation of interface conditions in an average sense) that facilitated its generalization to problems involving fluid layers. Promising results are obtained for problems in which the ocean bottom interface has a small slope.

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II: Inclusion of Exchange

NASA Technical Reports Server (NTRS)

Shertzer, Janine; Temkin, A.

2003-01-01

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE), which can be reduced to a 2d partial differential equation (pde), was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation, which is reducible to a pair of coupled pde's. The resultant scattering amplitudes, both singlet and triplet, calculated as a function of energy are in excellent agreement with converged partial wave results.

TH-C-19A-01: Analytic Design Method to Make a 2D Planar, Segmented Ion Chamber Water-Equivalent for Proton Dose Measurements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Harris, W; Hollebeek, R; Teo, B

2014-06-15

Purpose: Quality Assurance (QA) measurements of proton therapy fields must accurately measure steep longitudinal dose gradients as well as characterize the dose distribution laterally. Currently, available devices for two-dimensional field measurements perturb the dose distribution such that routine QA measurements performed at multiple depths require multiple field deliveries and are time consuming. Methods: A design procedure for a two-dimensional detector array is introduced whereby the proton energy loss and scatter are adjusted so that the downstream dose distribution is maintained to be equivalent to that which would occur in uniform water. Starting with the design for an existing, functional two-dimensionalmore » segmented ion chamber prototype, a compensating material is introduced downstream of the detector to simultaneously equate the energy loss and lateral scatter in the detector assembly to the values in water. An analytic formalism and procedure is demonstrated to calculate the properties of the compensating material in the general case of multiple layers of arbitrary material. The resulting design is validated with Monte Carlo simulations. Results: With respect to the specific prototype design considered, the results indicate that a graphite compensating layer of the proper dimensions can yield proton beam range perturbation less than 0.1mm and beam sigma perturbation less than 2% across the energy range of therapeutic proton beams. Conclusion: We have shown that, for a 2D gas-filled detector array, a graphite-compensating layer can balance the energy loss and multiple Coulomb scattering relative to uniform water. We have demonstrated an analytic formalism and procedure to determine a compensating material in the general case of multiple layers of arbitrary material. This work was supported by the US Army Medical Research and Materiel Command under Contract Agreement No. DAMD17-W81XWH-04-2-0022. Opinions, interpretations, conclusions and recommendations are those of the author and are not necessarily endorsed by the US Army.« less

Antiplane wave scattering from a cylindrical cavity in pre-stressed nonlinear elastic media

PubMed Central

Shearer, Tom; Parnell, William J.; Abrahams, I. David

2015-01-01

The effect of a longitudinal stretch and a pressure-induced inhomogeneous radial deformation on the scattering of antiplane elastic waves from a cylindrical cavity is determined. Three popular nonlinear strain energy functions are considered: the neo-Hookean, the Mooney–Rivlin and a two-term Arruda–Boyce model. A new method is developed to analyse and solve the governing wave equations. It exploits their properties to determine an asymptotic solution in the far-field, which is then used to derive a boundary condition to numerically evaluate the equations local to the cavity. This method could be applied to any linear ordinary differential equation whose inhomogeneous coefficients tend to a constant as its independent variable tends to infinity. The effect of the pre-stress is evaluated by considering the scattering cross section. A longitudinal stretch is found to decrease the scattered power emanating from the cavity, whereas a compression increases it. The effect of the pressure difference depends on the strain energy function employed. For a Mooney–Rivlin material, a cavity inflation increases the scattered power and a deflation decreases it; for a neo-Hookean material, the scattering cross section is unaffected by the radial deformation; and for a two-term Arruda–Boyce material, both inflation and deflation are found to decrease the scattered power. PMID:26543398

Electromagnetic scattering and emission by a fixed multi-particle object in local thermal equilibrium: General formalism.

PubMed

Mishchenko, Michael I

2017-10-01

The majority of previous studies of the interaction of individual particles and multi-particle groups with electromagnetic field have focused on either elastic scattering in the presence of an external field or self-emission of electromagnetic radiation. In this paper we apply semi-classical fluctuational electrodynamics to address the ubiquitous scenario wherein a fixed particle or a fixed multi-particle group is exposed to an external quasi-polychromatic electromagnetic field as well as thermally emits its own electromagnetic radiation. We summarize the main relevant axioms of fluctuational electrodynamics, formulate in maximally rigorous mathematical terms the general scattering-emission problem for a fixed object, and derive such fundamental corollaries as the scattering-emission volume integral equation, the Lippmann-Schwinger equation for the dyadic transition operator, the multi-particle scattering-emission equations, and the far-field limit. We show that in the framework of fluctuational electrodynamics, the computation of the self-emitted component of the total field is completely separated from that of the elastically scattered field. The same is true of the computation of the emitted and elastically scattered components of quadratic/bilinear forms in the total electromagnetic field. These results pave the way to the practical computation of relevant optical observables.

Cloud Effects in Hyperspectral Imagery from First-Principles Scene Simulations

DTIC Science & Technology

2009-01-01

SPIE. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, or distribution to multiple locations...scattering and absorption, scattering events, surface scattering with material-dependent bidirectional reflectances, multiple surface adjacency...aerosols or clouds, they may be absorbed, or they may reflect off the ground or an object. A given photon may undergo multiple scattering events

Λ scattering equations

NASA Astrophysics Data System (ADS)

Gomez, Humberto

2016-06-01

The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter Λ controlling the opening of a branch cut. The new representation of scattering amplitudes possesses an enhanced redundancy which can be used to fix, modulo branches, the location of four punctures while promoting Λ to a variable. Via residue theorems we show how CHY formulas break up into sums of products of smaller (off-shell) ones times a propagator. This leads to a powerful way of evaluating CHY integrals of generic rational functions, which we call the Λ algorithm.

Scattering by a slab containing randomly located cylinders: comparison between radiative transfer and electromagnetic simulation.

PubMed

Roux, L; Mareschal, P; Vukadinovic, N; Thibaud, J B; Greffet, J J

2001-02-01

This study is devoted to the examination of scattering of waves by a slab containing randomly located cylinders. For the first time to our knowledge, the complete transmission problem has been solved numerically. We have compared the radiative transfer theory with a numerical solution of the wave equation. We discuss the coherent effects, such as forward-scattering dip and backscattering enhancement. It is seen that the radiative transfer equation can be used with great accuracy even for optically thin systems whose geometric thickness is comparable with the wavelength. We have also shown the presence of dependent scattering.

Impressed sources and fields in the volume-integral-equation formulation of electromagnetic scattering by a finite object: A tutorial

NASA Astrophysics Data System (ADS)

Mishchenko, Michael I.; Yurkin, Maxim A.

2018-07-01

Although free space cannot generate electromagnetic waves, the majority of existing accounts of frequency-domain electromagnetic scattering by particles and particle groups are based on the postulate of existence of an impressed incident field, usually in the form of a plane wave. In this tutorial we discuss how to account for the actual existence of impressed source currents rather than impressed incident fields. Specifically, we outline a self-consistent theoretical formalism describing electromagnetic scattering by an arbitrary finite object in the presence of arbitrarily distributed impressed currents, some of which can be far removed from the object and some can reside in its vicinity, including inside the object. To make the resulting formalism applicable to a wide range of scattering-object morphologies, we use the framework of the volume integral equation formulation of electromagnetic scattering, couple it with the notion of the transition operator, and exploit the fundamental symmetry property of this operator. Among novel results, this tutorial includes a streamlined proof of fundamental symmetry (reciprocity) relations, a simplified derivation of the Foldy equations, and an explicit analytical expression for the transition operator of a multi-component scattering object.

A multichannel model for the self-consistent analysis of coherent transport in graphene nanoribbons.

PubMed

Mencarelli, Davide; Pierantoni, Luca; Farina, Marco; Di Donato, Andrea; Rozzi, Tullio

2011-08-23

In this contribution, we analyze the multichannel coherent transport in graphene nanoribbons (GNRs) by a scattering matrix approach. We consider the transport properties of GNR devices of a very general form, involving multiple bands and multiple leads. The 2D quantum transport over the whole GNR surface, described by the Schrödinger equation, is strongly nonlinear as it implies calculation of self-generated and externally applied electrostatic potentials, solutions of the 3D Poisson equation. The surface charge density is computed as a balance of carriers traveling through the channel at all of the allowed energies. Moreover, formation of bound charges corresponding to a discrete modal spectrum is observed and included in the model. We provide simulation examples by considering GNR configurations typical for transistor devices and GNR protrusions that find an interesting application as cold cathodes for X-ray generation. With reference to the latter case, a unified model is required in order to couple charge transport and charge emission. However, to a first approximation, these could be considered as independent problems, as in the example. © 2011 American Chemical Society

New Examination of the Traditional Raman Lidar Technique II: Evaluating the Ratios for Water Vapor and Aerosols

NASA Technical Reports Server (NTRS)

Whiteman, David N.

2003-01-01

In a companion paper, the temperature dependence of Raman scattering and its influence on the Raman and Rayleigh-Mie lidar equations was examined. New forms of the lidar equation were developed to account for this temperature sensitivity. Here those results are used to derive the temperature dependent forms of the equations for the water vapor mixing ratio, aerosol scattering ratio, aerosol backscatter coefficient, and extinction to backscatter ratio (Sa). The error equations are developed, the influence of differential transmission is studied and different laser sources are considered in the analysis. The results indicate that the temperature functions become significant when using narrowband detection. Errors of 5% and more can be introduced in the water vapor mixing ratio calculation at high altitudes and errors larger than 10% are possible for calculations of aerosol scattering ratio and thus aerosol backscatter coefficient and extinction to backscatter ratio.

Application and development of the Schwinger multichannel scattering theory and the partial differential equation theory of electron-molecule scattering

NASA Technical Reports Server (NTRS)

Weatherford, Charles A.

1993-01-01

One version of the multichannel theory for electron-target scattering based on the Schwinger variational principle, the SMC method, requires the introduction of a projection parameter. The role of the projection parameter a is investigated and it is shown that the principal-value operator in the SMC equation is Hermitian regardless of the value of a as long as it is real and nonzero. In a basis that is properly orthonormalizable, the matrix representation of this operator is also Hermitian. The use of such basis is consistent with the Schwinger variational principle because the Lippmann-Schwinger equation automatically builds in the correct boundary conditions. Otherwise, an auxiliary condition needs to be introduced, and Takatsuka and McKoy's original value of a is one of the three possible ways to achieve Hermiticity. In all cases but one, a can be uncoupled from the Hermiticity condition and becomes a free parameter. An equation for a based on the variational stability of the scattering amplitude is derived; its solution has an interesting property that the scattering amplitude from a converged SMC calculation is independent of the choice of a even though the SMC operator itself is a-dependent. This property provides a sensitive test of the convergence of the calculation. For a static-exchange calculation, the convergence requirement only depends on the completeness of the one-electron basis, but for a general multichannel case, the a-invariance in the scattering amplitude requires both the one-electron basis and the N plus 1-electron basis to be complete. The role of a in the SMC equation and the convergence property are illustrated using two examples: e-CO elastic scattering in the static-exchange approximation, and a two-state treatment of the e-H2 Chi(sup 1)Sigma(sub g)(+) yields b(sup 3)Sigma(sub u)(+) excitation.

Oblique scattering from radially inhomogeneous dielectric cylinders: An exact Volterra integral equation formulation

NASA Astrophysics Data System (ADS)

Tsalamengas, John L.

2018-07-01

We study plane-wave electromagnetic scattering by radially and strongly inhomogeneous dielectric cylinders at oblique incidence. The method of analysis relies on an exact reformulation of the underlying field equations as a first-order 4 × 4 system of differential equations and on the ability to restate the associated initial-value problem in the form of a system of coupled linear Volterra integral equations of the second kind. The integral equations so derived are discretized via a sophisticated variant of the Nyström method. The proposed method yields results accurate up to machine precision without relying on approximations. Numerical results and case studies ably demonstrate the efficiency and high accuracy of the algorithms.

Scattering transform for nonstationary Schroedinger equation with bidimensionally perturbed N-soliton potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.

2006-12-15

In the framework of the extended resolvent approach the direct and inverse scattering problems for the nonstationary Schroedinger equation with a potential being a perturbation of the N-soliton potential by means of a generic bidimensional smooth function decaying at large spaces are introduced and investigated. The initial value problem of the Kadomtsev-Petviashvili I equation for a solution describing N wave solitons on a generic smooth decaying background is then linearized, giving the time evolution of the spectral data.

Solution of the Wang Chang-Uhlenbeck equation for molecular hydrogen

NASA Astrophysics Data System (ADS)

Anikin, Yu. A.

2017-06-01

Molecular hydrogen is modeled by numerically solving the Wang Chang-Uhlenbeck equation. The differential scattering cross sections of molecules are calculated using the quantum mechanical scattering theory of rigid rotors. The collision integral is computed by applying a fully conservative projection method. Numerical results for relaxation, heat conduction, and a one-dimensional shock wave are presented.

The Scattering of Partially Coherent Electromagnetic Beam Illumination from Statistically Rough Surfaces

DTIC Science & Technology

2014-06-19

scattering research performed by the radio - frequency /microwave and visible/near-infrared communities for synthetic aperture radar and remote...Rough Surfaces with Arbitrary Slope and Frequency ,” IEEE Trans. Antennas Propag. 28, 11 - 21 (1980). 76. E. Bahar, “Full-Wave Solutions for the...equations ..................................................................................... 11 2.2.1 Electric-field integral equations

Fitting Data to Model: Structural Equation Modeling Diagnosis Using Two Scatter Plots

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Hayashi, Kentaro

2010-01-01

This article introduces two simple scatter plots for model diagnosis in structural equation modeling. One plot contrasts a residual-based M-distance of the structural model with the M-distance for the factor score. It contains information on outliers, good leverage observations, bad leverage observations, and normal cases. The other plot contrasts…

Scattering and bound states of spinless particles in a mixed vector-scalar smooth step potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garcia, M.G.; Castro, A.S. de

2009-11-15

Scattering and bound states for a spinless particle in the background of a kink-like smooth step potential, added with a scalar uniform background, are considered with a general mixing of vector and scalar Lorentz structures. The problem is mapped into the Schroedinger-like equation with an effective Rosen-Morse potential. It is shown that the scalar uniform background present subtle and trick effects for the scattering states and reveals itself a high-handed element for formation of bound states. In that process, it is shown that the problem of solving a differential equation for the eigenenergies is transmuted into the simpler and moremore » efficient problem of solving an irrational algebraic equation.« less

Dissipative quantum transport in silicon nanowires based on Wigner transport equation

NASA Astrophysics Data System (ADS)

Barraud, Sylvain

2011-11-01

In this work, we present a one-dimensional model of quantum electron transport for silicon nanowire transistor that makes use of the Wigner function formalism and that takes into account the carrier scattering. Effect of scattering on the current-voltage (I-V) characteristics is assessed using both the relaxation time approximation and the Boltzmann collision operator. Similarly to the classical transport theory, the scattering mechanisms are included in the Wigner formulation through the addition of a collision term in the Liouville equation. As compared to the relaxation time, the Boltzmann collision operator approach is considered to be more realistic because it provides a better description of the scattering events. Within the Fermi golden rule approximation, the standard collision term is described for both acoustic phonon and surface-roughness interactions. It is introduced in the discretized version of the Liouville equation to obtain the Wigner distribution function and the current density. The model is then applied to study the impact of each scattering mechanism on short-channel electrical performance of silicon nanowire transistors for different gate lengths and nanowire widths.

Treatment of late time instabilities in finite-difference EMP scattering codes

NASA Astrophysics Data System (ADS)

Simpson, L. T.; Holland, R.; Arman, S.

1982-12-01

Constraints applicable to a finite difference mesh for solution of Maxwell's equations are defined. The equations are applied in the time domain for computing electromagnetic coupling to complex structures, e.g., rectangular, cylindrical, or spherical. In a spatially varying grid, the amplitude growth of high frequency waves becomes exponential through multiple reflections from the outer boundary in cases of late-time solution. The exponential growth of the numerical noise exceeds the value of the real signal. The correction technique employs an absorbing surface and a radiating boundary, along with tailored selection of the grid mesh size. High frequency noise is removed through use of a low-pass digital filter, a linear least squares fit is made to thy low frequency filtered response, and the original, filtered, and fitted data are merged to preserve the high frequency early-time response.

A split-step method to include electron–electron collisions via Monte Carlo in multiple rate equation simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huthmacher, Klaus; Molberg, Andreas K.; Rethfeld, Bärbel

2016-10-01

A split-step numerical method for calculating ultrafast free-electron dynamics in dielectrics is introduced. The two split steps, independently programmed in C++11 and FORTRAN 2003, are interfaced via the presented open source wrapper. The first step solves a deterministic extended multi-rate equation for the ionization, electron–phonon collisions, and single photon absorption by free-carriers. The second step is stochastic and models electron–electron collisions using Monte-Carlo techniques. This combination of deterministic and stochastic approaches is a unique and efficient method of calculating the nonlinear dynamics of 3D materials exposed to high intensity ultrashort pulses. Results from simulations solving the proposed model demonstrate howmore » electron–electron scattering relaxes the non-equilibrium electron distribution on the femtosecond time scale.« less

Crystallographic effects during radiative melting of semitransparent materials

NASA Astrophysics Data System (ADS)

Webb, B. W.; Viskanta, R.

1987-10-01

Experiments have been performed to illustrate crystallogrpahic effects during radiative melting of unconfined vertical layers of semitransparent material. Radiative melting of a polycrystalline paraffin was performed and the instantaneous layer weight and transmittance were measured using a cantilever beam technique and thermopile radiation detector, respectively. The effects of radiative flux, initial solid subcooling, spectral distribution of the irradiation, and crystal structure of the solid as determined qualitatively by the sample solidification rate were studied. Experimental results show conclusively the dominant influence of cystallographic effects in the form of multiple internal scattering of radiation during the melting process. A theoretical model is formulated to predict the melting rate of the material. Radiation transfer is treated by solving the one-dimensional radiative transfer equation for an absorbing-scattering medium using the discrete ordinates method. Melting rate and global layer reflectance as predicted by the model agree well with experimental data. Parametric studies conducted with the model illustrate the sensitivity of the melting behavior to such variables as incident radiative flux, initial layer opacity (material extinction coefficient), and scattering asymmetry factor.

Modeling silica aerogel optical performance by determining its radiative properties

NASA Astrophysics Data System (ADS)

Zhao, Lin; Yang, Sungwoo; Bhatia, Bikram; Strobach, Elise; Wang, Evelyn N.

2016-02-01

Silica aerogel has been known as a promising candidate for high performance transparent insulation material (TIM). Optical transparency is a crucial metric for silica aerogels in many solar related applications. Both scattering and absorption can reduce the amount of light transmitted through an aerogel slab. Due to multiple scattering, the transmittance deviates from the Beer-Lambert law (exponential attenuation). To better understand its optical performance, we decoupled and quantified the extinction contributions of absorption and scattering separately by identifying two sets of radiative properties. The radiative properties are deduced from the measured total transmittance and reflectance spectra (from 250 nm to 2500 nm) of synthesized aerogel samples by solving the inverse problem of the 1-D Radiative Transfer Equation (RTE). The obtained radiative properties are found to be independent of the sample geometry and can be considered intrinsic material properties, which originate from the aerogel's microstructure. This finding allows for these properties to be directly compared between different samples. We also demonstrate that by using the obtained radiative properties, we can model the photon transport in aerogels of arbitrary shapes, where an analytical solution is difficult to obtain.

Scatter characterization and correction for simultaneous multiple small-animal PET imaging.

PubMed

Prasad, Rameshwar; Zaidi, Habib

2014-04-01

The rapid growth and usage of small-animal positron emission tomography (PET) in molecular imaging research has led to increased demand on PET scanner's time. One potential solution to increase throughput is to scan multiple rodents simultaneously. However, this is achieved at the expense of deterioration of image quality and loss of quantitative accuracy owing to enhanced effects of photon attenuation and Compton scattering. The purpose of this work is, first, to characterize the magnitude and spatial distribution of the scatter component in small-animal PET imaging when scanning single and multiple rodents simultaneously and, second, to assess the relevance and evaluate the performance of scatter correction under similar conditions. The LabPET™-8 scanner was modelled as realistically as possible using Geant4 Application for Tomographic Emission Monte Carlo simulation platform. Monte Carlo simulations allow the separation of unscattered and scattered coincidences and as such enable detailed assessment of the scatter component and its origin. Simple shape-based and more realistic voxel-based phantoms were used to simulate single and multiple PET imaging studies. The modelled scatter component using the single-scatter simulation technique was compared to Monte Carlo simulation results. PET images were also corrected for attenuation and the combined effect of attenuation and scatter on single and multiple small-animal PET imaging evaluated in terms of image quality and quantitative accuracy. A good agreement was observed between calculated and Monte Carlo simulated scatter profiles for single- and multiple-subject imaging. In the LabPET™-8 scanner, the detector covering material (kovar) contributed the maximum amount of scatter events while the scatter contribution due to lead shielding is negligible. The out-of field-of-view (FOV) scatter fraction (SF) is 1.70, 0.76, and 0.11% for lower energy thresholds of 250, 350, and 400 keV, respectively. The increase in SF ranged between 25 and 64% when imaging multiple subjects (three to five) of different size simultaneously in comparison to imaging a single subject. The spill-over ratio (SOR) increases with increasing the number of subjects in the FOV. Scatter correction improved the SOR for both water and air cold compartments of single and multiple imaging studies. The recovery coefficients for different body parts of the mouse whole-body and rat whole-body anatomical models were improved for multiple imaging studies following scatter correction. The magnitude and spatial distribution of the scatter component in small-animal PET imaging of single and multiple subjects simultaneously were characterized, and its impact was evaluated in different situations. Scatter correction improves PET image quality and quantitative accuracy for single rat and simultaneous multiple mice and rat imaging studies, whereas its impact is insignificant in single mouse imaging.

Determination of surface reflectance and estimates of atmospheric optical depth and single scattering albedo from Landsat Thematic Mapper data

NASA Technical Reports Server (NTRS)

Conel, James E.

1990-01-01

Groound-reflectance data on selected targets for calbiration of a Landsat TM image of Wind River Basin, Wyoming, acquired November 21, 1982 were examined. Field-derived calibration relationships together with Landsat radiometric calibration data are used to convert scanner DN values to spectral radiance for the TM bands and (together with a simplified homogeneous atmospheric model) to obtain estimates of single-scattering albedo and optical depth consistent with the derived path radiance and transmission properties of the atmosphere. These estimates are used to study the problems of evaluation of the magnitude of adjacency effects for reference targets, the assumption of isotropic properties, and the aggregate magnitude of multiple reflections between sky and ground. The radiance calibration equations are also used together with preflight measured signal/noise properties of the TM-4 system to estimate the noise-equivalent reflectance recoverable in practice from the system.

Flux-limited diffusion in a scattering medium. [such as accretion-disk coronae

NASA Technical Reports Server (NTRS)

Melia, Fulvio; Zylstra, Gregory J.

1991-01-01

A diffusion equation (FDT) is presented with a coefficient that reduces to the appropriate limiting form in the streaming and near thermodynamic limits for a moving fluid in which the dominant source of opacity is Thomson scattering. The present results are compared to those obtained with the corresponding equations for an absorptive medium. It is found that FDT for a scattering medium is accurate to better than less than about 17 percent over the range of optical depths of tau in the range of about 0 to 3.

Scattering Theory for the Acoustic Wave Equation in an Arbitrary Exterior Domain

DTIC Science & Technology

1976-08-30

65) will be further studied in the follow-up article. REFERENCES 1. C.H. Wilcox, Scattering Theory for the d - Alembert Equation in Exterior Domains...Exterior Domain Naval Research Lab Washington D C 30 Aug 76 254060 NRL Report 8030 Scattering Theory for the Acoustic Wave SEquation in an Arbitrary...STATEMENT (of the .b.Ia te ntere., d in loc k 10. If diferegn from R pr)A. 16 SUPPLEMENTARY NOTES IS KEY WORDS (Co.n.v onl r*eers Od*e ifftoneemy and

Einstein-Yang-Mills scattering amplitudes from scattering equations

NASA Astrophysics Data System (ADS)

Cachazo, Freddy; He, Song; Yuan, Ellis Ye

2015-01-01

We present the building blocks that can be combined to produce tree-level S-matrix elements of a variety of theories with various spins mixed in arbitrary dimensions. The new formulas for the scattering of n massless particles are given by integrals over the positions of n points on a sphere restricted to satisfy the scattering equations. As applications, we obtain all single-trace amplitudes in Einstein-Yang-Mills (EYM) theory, and generalizations to include scalars. Also in EYM but extended by a B-field and a dilaton, we present all double-trace gluon amplitudes. The building blocks are made of Pfaffians and Parke-Taylor-like factors of subsets of particle labels.

Method and apparatus for fiber optic multiple scattering suppression

NASA Technical Reports Server (NTRS)

Ackerson, Bruce J. (Inventor)

2000-01-01

The instant invention provides a method and apparatus for use in laser induced dynamic light scattering which attenuates the multiple scattering component in favor of the single scattering component. The preferred apparatus utilizes two light detectors that are spatially and/or angularly separated and which simultaneously record the speckle pattern from a single sample. The recorded patterns from the two detectors are then cross correlated in time to produce one point on a composite single/multiple scattering function curve. By collecting and analyzing cross correlation measurements that have been taken at a plurality of different spatial/angular positions, the signal representative of single scattering may be differentiated from the signal representative of multiple scattering, and a near optimum detector separation angle for use in taking future measurements may be determined.

A Markov Chain-based quantitative study of angular distribution of photons through turbid slabs via isotropic light scattering

NASA Astrophysics Data System (ADS)

Li, Xuesong; Northrop, William F.

2016-04-01

This paper describes a quantitative approach to approximate multiple scattering through an isotropic turbid slab based on Markov Chain theorem. There is an increasing need to utilize multiple scattering for optical diagnostic purposes; however, existing methods are either inaccurate or computationally expensive. Here, we develop a novel Markov Chain approximation approach to solve multiple scattering angular distribution (AD) that can accurately calculate AD while significantly reducing computational cost compared to Monte Carlo simulation. We expect this work to stimulate ongoing multiple scattering research and deterministic reconstruction algorithm development with AD measurements.

A new formulation of electromagnetic wave scattering using an on-surface radiation boundary condition approach

NASA Technical Reports Server (NTRS)

Kriegsmann, Gregory A.; Taflove, Allen; Umashankar, Koradar R.

1987-01-01

A new formulation of electromagnetic wave scattering by convex, two-dimensional conducting bodies is reported. This formulation, called the on-surface radiation condition (OSRC) approach, is based upon an expansion of the radiation condition applied directly on the surface of a scatterer. It is now shown that application of a suitable radiation condition directly on the surface of a convex conducting scatterer can lead to substantial simplification of the frequency-domain integral equation for the scattered field, which is reduced to just a line integral. For the transverse magnetic case, the integrand is known explicitly. For the transverse electric case, the integrand can be easily constructed by solving an ordinary differential equation around the scatterer surface contour. Examples are provided which show that OSRC yields computed near and far fields which approach the exact results for canonical shapes such as the circular cylinder, square cylinder, and strip. Electrical sizes for the examples are ka = 5 and ka = 10. The new OSRC formulation of scattering may present a useful alternative to present integral equation and uniform high-frequency approaches for convex cylinders larger than ka = 1. Structures with edges or corners can also be analyzed, although more work is needed to incorporate the physics of singular currents at these discontinuities. Convex dielectric structures can also be treated using OSRC.

On a generalized Ablowitz-Kaup-Newell-Segur hierarchy in inhomogeneities of media: soliton solutions and wave propagation influenced from coefficient functions and scattering data

NASA Astrophysics Data System (ADS)

Zhang, Sheng; Hong, Siyu

2018-07-01

In this paper, a generalized Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy in inhomogeneities of media described by variable coefficients is investigated, which includes some important nonlinear evolution equations as special cases, for example, the celebrated Korteweg-de Vries equation modeling waves on shallow water surfaces. To be specific, the known AKNS spectral problem and its time evolution equation are first generalized by embedding a finite number of differentiable and time-dependent functions. Starting from the generalized AKNS spectral problem and its generalized time evolution equation, a generalized AKNS hierarchy with variable coefficients is then derived. Furthermore, based on a systematic analysis on the time dependence of related scattering data of the generalized AKNS spectral problem, exact solutions of the generalized AKNS hierarchy are formulated through the inverse scattering transform method. In the case of reflectionless potentials, the obtained exact solutions are reduced to n-soliton solutions. It is graphically shown that the dynamical evolutions of such soliton solutions are influenced by not only the time-dependent coefficients but also the related scattering data in the process of propagations.

The Three-Component Defocusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions

NASA Astrophysics Data System (ADS)

Biondini, Gino; Kraus, Daniel K.; Prinari, Barbara

2016-12-01

We present a rigorous theory of the inverse scattering transform (IST) for the three-component defocusing nonlinear Schrödinger (NLS) equation with initial conditions approaching constant values with the same amplitude as {xto±∞}. The theory combines and extends to a problem with non-zero boundary conditions three fundamental ideas: (i) the tensor approach used by Beals, Deift and Tomei for the n-th order scattering problem, (ii) the triangular decompositions of the scattering matrix used by Novikov, Manakov, Pitaevski and Zakharov for the N-wave interaction equations, and (iii) a generalization of the cross product via the Hodge star duality, which, to the best of our knowledge, is used in the context of the IST for the first time in this work. The combination of the first two ideas allows us to rigorously obtain a fundamental set of analytic eigenfunctions. The third idea allows us to establish the symmetries of the eigenfunctions and scattering data. The results are used to characterize the discrete spectrum and to obtain exact soliton solutions, which describe generalizations of the so-called dark-bright solitons of the two-component NLS equation.

Acoustic scattering by arbitrary distributions of disjoint, homogeneous cylinders or spheres.

PubMed

Hesford, Andrew J; Astheimer, Jeffrey P; Waag, Robert C

2010-05-01

A T-matrix formulation is presented to compute acoustic scattering from arbitrary, disjoint distributions of cylinders or spheres, each with arbitrary, uniform acoustic properties. The generalized approach exploits the similarities in these scattering problems to present a single system of equations that is easily specialized to cylindrical or spherical scatterers. By employing field expansions based on orthogonal harmonic functions, continuity of pressure and normal particle velocity are directly enforced at each scatterer using diagonal, analytic expressions to eliminate the need for integral equations. The effect of a cylinder or sphere that encloses all other scatterers is simulated with an outer iterative procedure that decouples the inner-object solution from the effect of the enclosing object to improve computational efficiency when interactions among the interior objects are significant. Numerical results establish the validity and efficiency of the outer iteration procedure for nested objects. Two- and three-dimensional methods that employ this outer iteration are used to measure and characterize the accuracy of two-dimensional approximations to three-dimensional scattering of elevation-focused beams.

Scattering on two Aharonov-Bohm vortices

NASA Astrophysics Data System (ADS)

Bogomolny, E.

2016-12-01

The problem of two Aharonov-Bohm (AB) vortices for the Helmholtz equation is examined in detail. It is demonstrated that the method proposed by Myers (1963 J. Math. Phys. 6 1839) for slit diffraction can be generalised to obtain an explicit solution for AB vortices. Due to the singular nature of AB interaction the Green function and scattering amplitude for two AB vortices obey a series of partial differential equations. Coefficients entering these equations, fulfil ordinary non-linear differential equations whose solutions can be obtained by solving the Painlevé III equation. The asymptotics of necessary functions for very large and very small vortex separations are calculated explicitly. Taken together, this means that the problem of two AB vortices is exactly solvable.

Dielectric response in Bloch’s hydrodynamic model of an electron-ion plasma

NASA Astrophysics Data System (ADS)

Ishikawa, K.; Felderhof, B. U.

The linear response of an electron-ion plasma to an applied oscillating electric field is studied within the framework of Bloch’s classical hydrodynamic model. The ions are assumed to be fixed in space and distributed according to a known probability distribution. The linearized equations of motion for electron density and flow velocity are studied with the aid of a multiple scattering analysis and cluster expansion. This allows systematic reduction of the many-ion problem to a composition of few-ion problems, and shows how the longitudinal dielectric response function can in principle be calculated.

Theory of Multiple Coulomb Scattering from Extended Nuclei

DOE R&D Accomplishments Database

Cooper, L. N.; Rainwater, J.

1954-08-01

Two independent methods are described for calculating the multiple scattering distribution for projected angle scattering resulting when very high energy charged particles traverse a thick scatterer. The results are compared with the theories of Moliere and Olbert.

GPU Acceleration of the Locally Selfconsistent Multiple Scattering Code for First Principles Calculation of the Ground State and Statistical Physics of Materials

NASA Astrophysics Data System (ADS)

Eisenbach, Markus

The Locally Self-consistent Multiple Scattering (LSMS) code solves the first principles Density Functional theory Kohn-Sham equation for a wide range of materials with a special focus on metals, alloys and metallic nano-structures. It has traditionally exhibited near perfect scalability on massively parallel high performance computer architectures. We present our efforts to exploit GPUs to accelerate the LSMS code to enable first principles calculations of O(100,000) atoms and statistical physics sampling of finite temperature properties. Using the Cray XK7 system Titan at the Oak Ridge Leadership Computing Facility we achieve a sustained performance of 14.5PFlop/s and a speedup of 8.6 compared to the CPU only code. This work has been sponsored by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Material Sciences and Engineering Division and by the Office of Advanced Scientific Computing. This work used resources of the Oak Ridge Leadership Computing Facility, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725.

Consistent radiative transfer modeling of active and passive observations of precipitation

NASA Astrophysics Data System (ADS)

Adams, Ian

2016-04-01

Spaceborne platforms such as the Tropical Rainfall Measurement Mission (TRMM) and the Global Precipitation Measurement (GPM) mission exploit a combination of active and passive sensors to provide a greater understanding of the three-dimensional structure of precipitation. While "operationalized" retrieval algorithms require fast forward models, the ability to perform higher fidelity simulations is necessary in order to understand the physics of remote sensing problems by testing assumptions and developing parameterizations for the fast models. To ensure proper synergy between active and passive modeling, forward models must be consistent when modeling the responses of radars and radiometers. This work presents a self-consistent transfer model for simulating radar reflectivities and millimeter wave brightness temperatures for precipitating scenes. To accomplish this, we extended the Atmospheric Radiative Transfer Simulator (ARTS) version 2.3 to solve the radiative transfer equation for active sensors and multiple scattering conditions. Early versions of ARTS (1.1) included a passive Monte Carlo solver, and ARTS is capable of handling atmospheres of up to three dimensions with ellipsoidal planetary geometries. The modular nature of ARTS facilitates extensibility, and the well-developed ray-tracing tools are suited for implementation of Monte Carlo algorithms. Finally, since ARTS handles the full Stokes vector, co- and cross-polarized reflectivity products are possible for scenarios that include nonspherical particles, with or without preferential alignment. The accuracy of the forward model will be demonstrated with precipitation events observed by TRMM and GPM, and the effects of multiple scattering will be detailed. The three-dimensional nature of the radiative transfer model will be useful for understanding the effects of nonuniform beamfill and multiple scattering for spatially heterogeneous precipitation events. The targets of this forward model are GPM (the Dual-wavelength Precipitation Radar (DPR) and GPM Microwave Imager (GMI)).

Sharp threshold of blow-up and scattering for the fractional Hartree equation

NASA Astrophysics Data System (ADS)

Guo, Qing; Zhu, Shihui

2018-02-01

We consider the fractional Hartree equation in the L2-supercritical case, and find a sharp threshold of the scattering versus blow-up dichotomy for radial data: If M[u0 ]s -sc/sc E [u0 ] < M[ Q ]s -sc/sc E [ Q ] and M[u0 ]s -sc/sc ‖u0‖ H˙s 2 < M[ Q ]s -sc/sc ‖Q‖ H˙s 2 , then the solution u (t) is globally well-posed and scatters; if M[u0 ]s -sc/sc E [u0 ] < M[ Q ]s -sc/sc E [ Q ] and M[u0 ]s -sc/sc ‖u0‖ H˙s 2 > M[ Q ]s -sc/sc ‖Q‖ H˙s 2 , the solution u (t) blows up in finite time. This condition is sharp in the sense that the solitary wave solution eit Q (x) is global but not scattering, which satisfies the equality in the above conditions. Here, Q is the ground-state solution for the fractional Hartree equation.

Accurate radiative transfer calculations for layered media.

PubMed

Selden, Adrian C

2016-07-01

Simple yet accurate results for radiative transfer in layered media with discontinuous refractive index are obtained by the method of K-integrals. These are certain weighted integrals applied to the angular intensity distribution at the refracting boundaries. The radiative intensity is expressed as the sum of the asymptotic angular intensity distribution valid in the depth of the scattering medium and a transient term valid near the boundary. Integrated boundary equations are obtained, yielding simple linear equations for the intensity coefficients, enabling the angular emission intensity and the diffuse reflectance (albedo) and transmittance of the scattering layer to be calculated without solving the radiative transfer equation directly. Examples are given of half-space, slab, interface, and double-layer calculations, and extensions to multilayer systems are indicated. The K-integral method is orders of magnitude more accurate than diffusion theory and can be applied to layered scattering media with a wide range of scattering albedos, with potential applications to biomedical and ocean optics.

Extrinsic extinction cross-section in the multiple acoustic scattering by fluid particles

NASA Astrophysics Data System (ADS)

Mitri, F. G.

2017-04-01

Cross-sections (and their related energy efficiency factors) are physical parameters used in the quantitative analysis of different phenomena arising from the interaction of waves with a particle (or multiple particles). Earlier works with the acoustic scattering theory considered such quadratic (i.e., nonlinear) quantities for a single scatterer, although a few extended the formalism for a pair of scatterers but were limited to the scattering cross-section only. Therefore, the standard formalism applied to viscous particles is not suitable for the complete description of the cross-sections and energy balance of the multiple-particle system because both absorption and extinction phenomena arise during the multiple scattering process. Based upon the law of the conservation of energy, this work provides a complete comprehensive analysis for the extrinsic scattering, absorption, and extinction cross-sections (i.e., in the far-field) of a pair of viscous scatterers of arbitrary shape, immersed in a nonviscous isotropic fluid. A law of acoustic extinction taking into consideration interparticle effects in wave propagation is established, which constitutes a generalized form of the optical theorem in multiple scattering. Analytical expressions for the scattering, absorption, and extinction cross-sections are derived for plane progressive waves with arbitrary incidence. The mathematical expressions are formulated in partial-wave series expansions in cylindrical coordinates involving the angle of incidence, the addition theorem for the cylindrical wave functions, and the expansion coefficients of the scatterers. The analysis shows that the multiple scattering cross-section depends upon the expansion coefficients of both scatterers in addition to an interference factor that depends on the interparticle distance. However, the extinction cross-section depends on the expansion coefficients of the scatterer located in a particular system of coordinates, in addition to the interference term. Numerical examples illustrate the analysis for two viscous fluid circular cylindrical cross-sections immersed in a non-viscous fluid. Computations for the (non-dimensional) scattering, absorption, and extinction cross-section factors are performed with particular emphasis on varying the angle of incidence, the interparticle distance, and the sizes, and the physical properties of the particles. A symmetric behavior is observed for the dimensionless multiple scattering cross-section, while asymmetries arise for both the dimensionless absorption and extinction cross-sections with respect to the angle of incidence. The present analysis provides a complete analytical and computational method for the prediction of cross-section and energy efficiency factors in multiple acoustic scattering of plane waves of arbitrary incidence by a pair of scatterers. The results can be used as a priori information in the direct or inverse characterization of multiple scattering systems such as acoustically engineered fluid metamaterials with reconfigurable periodicities, cloaking devices, liquid crystals, and other applications.

Closed-loop multiple-scattering imaging with sparse seismic measurements

NASA Astrophysics Data System (ADS)

Berkhout, A. J. Guus

2018-03-01

In the theoretical situation of noise-free, complete data volumes (`perfect data'), seismic data matrices are fully filled and multiple-scattering operators have the minimum-phase property. Perfect data allow direct inversion methods to be successful in removing surface and internal multiple scattering. Moreover, under these perfect data conditions direct source wavefields realize complete illumination (no irrecoverable shadow zones) and, therefore, primary reflections (first-order response) can provide us with the complete seismic image. However, in practice seismic measurements always contain noise and we never have complete data volumes at our disposal. We actually deal with sparse data matrices that cannot be directly inverted. The message of this paper is that in practice multiple scattering (including source ghosting) must not be removed but must be utilized. It is explained that in the real world we badly need multiple scattering to fill the illumination gaps in the subsurface. It is also explained that the proposed multiple-scattering imaging algorithm gives us the opportunity to decompose both the image and the wavefields into order-based constituents, making the multiple scattering extension easy to apply. Last but not least, the algorithm allows us to use the minimum-phase property to validate and improve images in an objective way.

Efficient Solution of Three-Dimensional Problems of Acoustic and Electromagnetic Scattering by Open Surfaces

NASA Technical Reports Server (NTRS)

Turc, Catalin; Anand, Akash; Bruno, Oscar; Chaubell, Julian

2011-01-01

We present a computational methodology (a novel Nystrom approach based on use of a non-overlapping patch technique and Chebyshev discretizations) for efficient solution of problems of acoustic and electromagnetic scattering by open surfaces. Our integral equation formulations (1) Incorporate, as ansatz, the singular nature of open-surface integral-equation solutions, and (2) For the Electric Field Integral Equation (EFIE), use analytical regularizes that effectively reduce the number of iterations required by iterative linear-algebra solution based on Krylov-subspace iterative solvers.

Quantum mechanical generalized phase-shift approach to atom-surface scattering: a Feshbach projection approach to dealing with closed channel effects.

PubMed

Maji, Kaushik; Kouri, Donald J

2011-03-28

We have developed a new method for solving quantum dynamical scattering problems, using the time-independent Schrödinger equation (TISE), based on a novel method to generalize a "one-way" quantum mechanical wave equation, impose correct boundary conditions, and eliminate exponentially growing closed channel solutions. The approach is readily parallelized to achieve approximate N(2) scaling, where N is the number of coupled equations. The full two-way nature of the TISE is included while propagating the wave function in the scattering variable and the full S-matrix is obtained. The new algorithm is based on a "Modified Cayley" operator splitting approach, generalizing earlier work where the method was applied to the time-dependent Schrödinger equation. All scattering variable propagation approaches to solving the TISE involve solving a Helmholtz-type equation, and for more than one degree of freedom, these are notoriously ill-behaved, due to the unavoidable presence of exponentially growing contributions to the numerical solution. Traditionally, the method used to eliminate exponential growth has posed a major obstacle to the full parallelization of such propagation algorithms. We stabilize by using the Feshbach projection operator technique to remove all the nonphysical exponentially growing closed channels, while retaining all of the propagating open channel components, as well as exponentially decaying closed channel components.

Multiple scattering and the density distribution of a Cs MOT.

PubMed

Overstreet, K; Zabawa, P; Tallant, J; Schwettmann, A; Shaffer, J

2005-11-28

Multiple scattering is studied in a Cs magneto-optical trap (MOT). We use two Abel inversion algorithms to recover density distributions of the MOT from fluorescence images. Deviations of the density distribution from a Gaussian are attributed to multiple scattering.

Effects of multiple scattering on time- and depth-resolved signals in airborne lidar systems

NASA Technical Reports Server (NTRS)

Punjabi, A.; Venable, D. D.

1986-01-01

A semianalytic Monte Carlo radiative transfer model (SALMON) is employed to probe the effects of multiple-scattering events on the time- and depth-resolved lidar signals from homogeneous aqueous media. The effective total attenuation coefficients in the single-scattering approximation are determined as functions of dimensionless parameters characterizing the lidar system and the medium. Results show that single-scattering events dominate when these parameters are close to their lower bounds and that when their values exceed unity multiple-scattering events dominate.

Intermediate energy proton-deuteron elastic scattering

NASA Technical Reports Server (NTRS)

Wilson, J. W.

1973-01-01

A fully symmetrized multiple scattering series is considered for the description of proton-deuteron elastic scattering. An off-shell continuation of the experimentally known twobody amplitudes that retains the exchange symmeteries required for the calculation is presented. The one boson exchange terms of the two body amplitudes are evaluated exactly in this off-shell prescription. The first two terms of the multiple scattering series are calculated explicitly whereas multiple scattering effects are obtained as minimum variance estimates from the 146-MeV data of Postma and Wilson. The multiple scattering corrections indeed consist of low order partial waves as suggested by Sloan based on model studies with separable interactions. The Hamada-Johnston wave function is shown consistent with the data for internucleon distances greater than about 0.84 fm.

Effect of electron-electron scattering on the conductance of a quantum wire studied with the Boltzman transport equation

NASA Astrophysics Data System (ADS)

Lyo, S. K.; Huang, Danhong

2006-05-01

Electron-electron scattering conserves total momentum and does not dissipate momentum directly in a low-density system where the umklapp process is forbidden. However, it can still affect the conductance through the energy relaxation of the electrons. We show here that this effect can be studied with arbitrary accuracy in a multisublevel one-dimensional (1D) single quantum wire system in the presence of roughness and phonon scattering using a formally exact solution of the Boltzmann transport equation. The intrasubband electron-electron scattering is found to yield no net effect on the transport of electrons in 1D with only one sublevel occupied. For a system with a multilevel occupation, however, we find a significant effect of intersublevel electron-electron scattering on the temperature and density dependence of the resistance at low temperatures.

Systematic approach to thermal leptogenesis

NASA Astrophysics Data System (ADS)

Frossard, T.; Garny, M.; Hohenegger, A.; Kartavtsev, A.; Mitrouskas, D.

2013-04-01

In this work we study thermal leptogenesis using nonequilibrium quantum field theory. Starting from fundamental equations for correlators of the quantum fields we describe the steps necessary to obtain quantum-kinetic equations for quasiparticles. These can easily be compared to conventional results and overcome conceptional problems inherent in the canonical approach. Beyond CP-violating decays we include also those scattering processes which are tightly related to the decays in a consistent approximation of fourth order in the Yukawa couplings. It is demonstrated explicitly how the S-matrix elements for the scattering processes in the conventional approach are related to two- and three-loop contributions to the effective action. We derive effective decay and scattering amplitudes taking medium corrections and thermal masses into account. In this context we also investigate CP-violating Higgs decay within the same formalism. From the kinetic equations we derive rate equations for the lepton asymmetry improved in that they include quantum-statistical effects and medium corrections to the quasiparticle properties.

Efficient propagation-inside-layer expansion algorithm for solving the scattering from three-dimensional nested homogeneous dielectric bodies with arbitrary shape.

PubMed

Bellez, Sami; Bourlier, Christophe; Kubické, Gildas

2015-03-01

This paper deals with the evaluation of electromagnetic scattering from a three-dimensional structure consisting of two nested homogeneous dielectric bodies with arbitrary shape. The scattering problem is formulated in terms of a set of Poggio-Miller-Chang-Harrington-Wu integral equations that are afterwards converted into a system of linear equations (impedance matrix equation) by applying the Galerkin method of moments (MoM) with Rao-Wilton-Glisson basis functions. The MoM matrix equation is then solved by deploying the iterative propagation-inside-layer expansion (PILE) method in order to obtain the unknown surface current densities, which are thereafter used to handle the radar cross-section (RCS) patterns. Some numerical results for various structures including canonical geometries are presented and compared with those of the FEKO software in order to validate the PILE-based approach as well as to show its efficiency to analyze the full-polarized RCS patterns.

Improvements in simulation of multiple scattering effects in ATLAS fast simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Basalaev, A. E., E-mail: artem.basalaev@cern.ch

Fast ATLAS Tracking Simulation (Fatras) package was verified on single layer geometry with respect to full simulation with GEANT4. Fatras hadronic interactions and multiple scattering simulation were studied in comparison with GEANT4. Disagreement was found in multiple scattering distributions of primary charged particles (μ, π, e). A new model for multiple scattering simulation was implemented in Fatras. The model was based on R. Frühwirth’s mixture models. New model was tested on single layer geometry and a good agreement with GEANT4 was achieved. Also a comparison of reconstructed tracks’ parameters was performed for Inner Detector geometry, and Fatras with new multiplemore » scattering model proved to have better agreement with GEANT4. New model of multiple scattering was added as a part of Fatras package in the development release of ATLAS software—ATHENA.« less

The Radiated Field Generated by a Monopole Source in a Short, Rigid, Rectangular Duct. Degree awarded by George Washington Univ.

NASA Technical Reports Server (NTRS)

Lakota, Barbara Anne

1998-01-01

This thesis develops a method to model the acoustic field generated by a monopole source placed in a moving rectangular duct. The walls of the duct are assumed to be infinitesimally thin and the source is placed at the center of the duct. The total acoustic pressure is written in terms of the free-space pressure, or incident pressure, and the scattered pressure. The scattered pressure is the augmentation to the incident pressure due to the presence of the duct. It satisfies a homogeneous wave equation and is discontinuous across the duct walls. Utilizing an integral representation of the scattered pressure, a set of singular boundary integral equations governing the unknown jump in scattered pressure is derived. This equation is solved by the method of collocation after representing the jump in pressure as a double series of shape functions. The solution obtained is then substituted back into the integral representation to determine the scattered pressure, and the total acoustic pressure at any point in the field. A few examples are included to illustrate the influence of various geometric and kinematic parameters on the radiated sound field.

Microscopic theory of linear light scattering from mesoscopic media and in near-field optics.

PubMed

Keller, Ole

2005-08-01

On the basis of quantum mechanical response theory a microscopic propagator theory of linear light scattering from mesoscopic systems is presented. The central integral equation problem is transferred to a matrix equation problem by discretization in transitions between pairs of (many-body) energy eigenstates. The local-field calculation which appears from this approach is valid down to the microscopic region. Previous theories based on the (macroscopic) dielectric constant concept make use of spatial (geometrical) discretization and cannot in general be trusted on the mesoscopic length scale. The present theory can be applied to light scattering studies in near-field optics. After a brief discussion of the macroscopic integral equation problem a microscopic potential description of the scattering process is established. In combination with the use of microscopic electromagnetic propagators the formalism allows one to make contact to the macroscopic theory of light scattering and to the spatial photon localization problem. The quantum structure of the microscopic conductivity response tensor enables one to establish a clear physical picture of the origin of local-field phenomena in mesoscopic and near-field optics. The Huygens scalar propagator formalism is revisited and its generality in microscopic physics pointed out.

Equations for normal-mode statistics of sound scattering by a rough elastic boundary in an underwater waveguide, including backscattering.

PubMed

Morozov, Andrey K; Colosi, John A

2017-09-01

Underwater sound scattering by a rough sea surface, ice, or a rough elastic bottom is studied. The study includes both the scattering from the rough boundary and the elastic effects in the solid layer. A coupled mode matrix is approximated by a linear function of one random perturbation parameter such as the ice-thickness or a perturbation of the surface position. A full two-way coupled mode solution is used to derive the stochastic differential equation for the second order statistics in a Markov approximation.

X-ray Raman scattering from molecules and solids in the framework of the Mahan-Nozières-De Dominicis model

NASA Astrophysics Data System (ADS)

Privalov, Timofei; Gel'mukhanov, Faris; Ågren, Hans

2001-10-01

We have developed a formulation of resonant x-ray Raman scattering of molecules and solids based on the Mahan-Nozières-De Dominicis model. A key step in the formulation is given by a reduction of the Keldysh-Dyson equations for the Green's function to a set of linear algebraic equations. This gave way for a tractable scheme that can be used to analyze the resonant x-ray scattering in the whole time domain. The formalism is used to investigate the role of core-hole relaxation, interference, band filling, detuning, and size of the scattering target. Numerical applications are performed with a one-dimensional tight-binding model.

Pion-nucleon scattering: from chiral perturbation theory to Roy-Steiner equations

NASA Astrophysics Data System (ADS)

Kubis, Bastian; Hoferichter, Martin; de Elvira, Jacobo Ruiz; Meißner, Ulf-G.

2016-11-01

Ever since Weinberg's seminal predictions of the pion-nucleon scattering amplitudes at threshold, this process has been of central interest for the study of chiral dynamics involving nucleons. The scattering lengths or the pion-nucleon σ-term are fundamental quantities characterizing the explicit breaking of chiral symmetry by means of the light quark masses. On the other hand, pion-nucleon dynamics also strongly affects the long-range part of nucleon-nucleon potentials, and hence has a far-reaching impact on nuclear physics. We discuss the fruitful combination of dispersion-theoretical methods, in the form of Roy-Steiner equations, with chiral dynamics to determine pion-nucleon scattering amplitudes at low energies with high precision.*

Numerical time-domain electromagnetics based on finite-difference and convolution

NASA Astrophysics Data System (ADS)

Lin, Yuanqu

Time-domain methods posses a number of advantages over their frequency-domain counterparts for the solution of wideband, nonlinear, and time varying electromagnetic scattering and radiation phenomenon. Time domain integral equation (TDIE)-based methods, which incorporate the beneficial properties of integral equation method, are thus well suited for solving broadband scattering problems for homogeneous scatterers. Widespread adoption of TDIE solvers has been retarded relative to other techniques by their inefficiency, inaccuracy and instability. Moreover, two-dimensional (2D) problems are especially problematic, because 2D Green's functions have infinite temporal support, exacerbating these difficulties. This thesis proposes a finite difference delay modeling (FDDM) scheme for the solution of the integral equations of 2D transient electromagnetic scattering problems. The method discretizes the integral equations temporally using first- and second-order finite differences to map Laplace-domain equations into the Z domain before transforming to the discrete time domain. The resulting procedure is unconditionally stable because of the nature of the Laplace- to Z-domain mapping. The first FDDM method developed in this thesis uses second-order Lagrange basis functions with Galerkin's method for spatial discretization. The second application of the FDDM method discretizes the space using a locally-corrected Nystrom method, which accelerates the precomputation phase and achieves high order accuracy. The Fast Fourier Transform (FFT) is applied to accelerate the marching-on-time process in both methods. While FDDM methods demonstrate impressive accuracy and stability in solving wideband scattering problems for homogeneous scatterers, they still have limitations in analyzing interactions between several inhomogenous scatterers. Therefore, this thesis devises a multi-region finite-difference time-domain (MR-FDTD) scheme based on domain-optimal Green's functions for solving sparsely-populated problems. The scheme uses a discrete Green's function (DGF) on the FDTD lattice to truncate the local subregions, and thus reduces reflection error on the local boundary. A continuous Green's function (CGF) is implemented to pass the influence of external fields into each FDTD region which mitigates the numerical dispersion and anisotropy of standard FDTD. Numerical results will illustrate the accuracy and stability of the proposed techniques.

Time-varying phononic crystals

NASA Astrophysics Data System (ADS)

Wright, Derek Warren

The primary objective of this thesis was to gain a deeper understanding of acoustic wave propagation in phononic crystals, particularly those that include materials whose properties can be varied periodically in time. This research was accomplished in three ways. First, a 2D phononic crystal was designed, created, and characterized. Its properties closely matched those determined through simulation. The crystal demonstrated band gaps, dispersion, and negative refraction. It served as a means of elucidating the practicalities of phononic crystal design and construction and as a physical verification of their more interesting properties. Next, the transmission matrix method for analyzing 1D phononic crystals was extended to include the effects of time-varying material parameters. The method was then used to provide a closed-form solution for the case of periodically time-varying material parameters. Some intriguing results from the use of the extended method include dramatically altered transmission properties and parametric amplification. New insights can be gained from the governing equations and have helped to identify the conditions that lead to parametric amplification in these structures. Finally, 2D multiple scattering theory was modified to analyze scatterers with time-varying material parameters. It is shown to be highly compatible with existing multiple scattering theories. It allows the total scattered field from a 2D time-varying phononic crystal to be determined. It was shown that time-varying material parameters significantly affect the phononic crystal transmission spectrum, and this was used to switch an incident monochromatic wave. Parametric amplification can occur under certain circumstances, and this effect was investigated using the closed-form solutions provided by the new 1D method. The complexity of the extended methods grows logarithmically as opposed linearly with existing methods, resulting in superior computational complexity for large numbers of scatterers. Also, since both extended methods provide analytic solutions, they may give further insights into the factors that govern the behaviour of time-varying phononic crystals. These extended methods may now be used to design an active phononic crystal that could demonstrate new or enhanced properties.

Lidar inelastic multiple-scattering parameters of cirrus particle ensembles determined with geometrical-optics crystal phase functions.

PubMed

Reichardt, J; Hess, M; Macke, A

2000-04-20

Multiple-scattering correction factors for cirrus particle extinction coefficients measured with Raman and high spectral resolution lidars are calculated with a radiative-transfer model. Cirrus particle-ensemble phase functions are computed from single-crystal phase functions derived in a geometrical-optics approximation. Seven crystal types are considered. In cirrus clouds with height-independent particle extinction coefficients the general pattern of the multiple-scattering parameters has a steep onset at cloud base with values of 0.5-0.7 followed by a gradual and monotonic decrease to 0.1-0.2 at cloud top. The larger the scattering particles are, the more gradual is the rate of decrease. Multiple-scattering parameters of complex crystals and of imperfect hexagonal columns and plates can be well approximated by those of projected-area equivalent ice spheres, whereas perfect hexagonal crystals show values as much as 70% higher than those of spheres. The dependencies of the multiple-scattering parameters on cirrus particle spectrum, base height, and geometric depth and on the lidar parameters laser wavelength and receiver field of view, are discussed, and a set of multiple-scattering parameter profiles for the correction of extinction measurements in homogeneous cirrus is provided.

Asymmetrical flow field-flow fractionation coupled with multiple detections: A complementary approach in the characterization of egg yolk plasma.

PubMed

Dou, Haiyang; Li, Yueqiu; Choi, Jaeyeong; Huo, Shuying; Ding, Liang; Shen, Shigang; Lee, Seungho

2016-09-23

The capability of asymmetrical flow field-flow fractionation (AF4) coupled with UV/VIS, multiangle light scattering (MALS) and quasi-elastic light scattering (QELS) (AF4-UV-MALS-QELS) for separation and characterization of egg yolk plasma was evaluated. The accuracy of hydrodynamic radius (Rh) obtained from QELS and AF4 theory (using both simplified and full expression of AF4 retention equations) was discussed. The conformation of low density lipoprotein (LDL) and its aggregates in egg yolk plasma was discussed based on the ratio of radius of gyration (Rg) to Rh together with the results from bio-transmission electron microscopy (Bio-TEM). The results indicate that the full retention equation is more relevant than simplified version for the Rh determination at high cross flow rate. The Rh from online QELS is reliable only at a specific range of sample concentration. The effect of programmed cross flow rate (linear and exponential decay) on the analysis of egg yolk plasma was also investigated. It was found that the use of an exponentially decaying cross flow rate not only reduces the AF4 analysis time of the egg yolk plasma, but also provides better resolution than the use of either a constant or linearly decaying cross flow rate. A combination of an exponentially decaying cross flow AF4-UV-MALS-QELS and the utilization of full retention equation was proved to be a useful method for the separation and characterization of egg yolk plasma. Copyright © 2016 Elsevier B.V. All rights reserved.

Influence of Scattering on Ballistic Nanotransistor Design

NASA Technical Reports Server (NTRS)

Anantram, M. P.; Svizhenko, Alexei; Biegel, Bryan, A. (Technical Monitor)

2002-01-01

Importance of this work: (1) This is the first work to model electron-phonon scattering within a quantum mechanical approach to nanotransistors. The simulations use the non equilibrium Green's function method. (2) A simple equation which captures the importance of scattering as a function of the spatial location from source to drain is presented. This equation helps interpret the numerical simulations. (3) We show that the resistance per unit length in the source side is much larger than in the drain side. Thus making scattering in the source side of the device much more important than scattering in the drain side. Numerical estimates of ballisticity for 10nm channel length devices in the presence of of electron-phonon scattering are given. Based on these calculations, we propose that to achieve a larger on-current in nanotransistors, it is crucial to keep the highly doped source extension region extremely small, even if this is at the cost of making the highly doped drain extension region longer.

Modeling techniques for quantum cascade lasers

NASA Astrophysics Data System (ADS)

Jirauschek, Christian; Kubis, Tillmann

2014-03-01

Quantum cascade lasers are unipolar semiconductor lasers covering a wide range of the infrared and terahertz spectrum. Lasing action is achieved by using optical intersubband transitions between quantized states in specifically designed multiple-quantum-well heterostructures. A systematic improvement of quantum cascade lasers with respect to operating temperature, efficiency, and spectral range requires detailed modeling of the underlying physical processes in these structures. Moreover, the quantum cascade laser constitutes a versatile model device for the development and improvement of simulation techniques in nano- and optoelectronics. This review provides a comprehensive survey and discussion of the modeling techniques used for the simulation of quantum cascade lasers. The main focus is on the modeling of carrier transport in the nanostructured gain medium, while the simulation of the optical cavity is covered at a more basic level. Specifically, the transfer matrix and finite difference methods for solving the one-dimensional Schrödinger equation and Schrödinger-Poisson system are discussed, providing the quantized states in the multiple-quantum-well active region. The modeling of the optical cavity is covered with a focus on basic waveguide resonator structures. Furthermore, various carrier transport simulation methods are discussed, ranging from basic empirical approaches to advanced self-consistent techniques. The methods include empirical rate equation and related Maxwell-Bloch equation approaches, self-consistent rate equation and ensemble Monte Carlo methods, as well as quantum transport approaches, in particular the density matrix and non-equilibrium Green's function formalism. The derived scattering rates and self-energies are generally valid for n-type devices based on one-dimensional quantum confinement, such as quantum well structures.

Modeling techniques for quantum cascade lasers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jirauschek, Christian; Kubis, Tillmann

2014-03-15

Quantum cascade lasers are unipolar semiconductor lasers covering a wide range of the infrared and terahertz spectrum. Lasing action is achieved by using optical intersubband transitions between quantized states in specifically designed multiple-quantum-well heterostructures. A systematic improvement of quantum cascade lasers with respect to operating temperature, efficiency, and spectral range requires detailed modeling of the underlying physical processes in these structures. Moreover, the quantum cascade laser constitutes a versatile model device for the development and improvement of simulation techniques in nano- and optoelectronics. This review provides a comprehensive survey and discussion of the modeling techniques used for the simulation ofmore » quantum cascade lasers. The main focus is on the modeling of carrier transport in the nanostructured gain medium, while the simulation of the optical cavity is covered at a more basic level. Specifically, the transfer matrix and finite difference methods for solving the one-dimensional Schrödinger equation and Schrödinger-Poisson system are discussed, providing the quantized states in the multiple-quantum-well active region. The modeling of the optical cavity is covered with a focus on basic waveguide resonator structures. Furthermore, various carrier transport simulation methods are discussed, ranging from basic empirical approaches to advanced self-consistent techniques. The methods include empirical rate equation and related Maxwell-Bloch equation approaches, self-consistent rate equation and ensemble Monte Carlo methods, as well as quantum transport approaches, in particular the density matrix and non-equilibrium Green's function formalism. The derived scattering rates and self-energies are generally valid for n-type devices based on one-dimensional quantum confinement, such as quantum well structures.« less

A fast numerical solution of scattering by a cylinder: Spectral method for the boundary integral equations

NASA Technical Reports Server (NTRS)

Hu, Fang Q.

1994-01-01

It is known that the exact analytic solutions of wave scattering by a circular cylinder, when they exist, are not in a closed form but in infinite series which converges slowly for high frequency waves. In this paper, we present a fast number solution for the scattering problem in which the boundary integral equations, reformulated from the Helmholtz equation, are solved using a Fourier spectral method. It is shown that the special geometry considered here allows the implementation of the spectral method to be simple and very efficient. The present method differs from previous approaches in that the singularities of the integral kernels are removed and dealt with accurately. The proposed method preserves the spectral accuracy and is shown to have an exponential rate of convergence. Aspects of efficient implementation using FFT are discussed. Moreover, the boundary integral equations of combined single and double-layer representation are used in the present paper. This ensures the uniqueness of the numerical solution for the scattering problem at all frequencies. Although a strongly singular kernel is encountered for the Neumann boundary conditions, we show that the hypersingularity can be handled easily in the spectral method. Numerical examples that demonstrate the validity of the method are also presented.

Dynamical relationship between wind speed magnitude and meridional temperature contrast: Application to an interannual oscillation in Venusian middle atmosphere GCM

NASA Astrophysics Data System (ADS)

Yamamoto, Masaru; Takahashi, Masaaki

2018-03-01

We derive simple dynamical relationships between wind speed magnitude and meridional temperature contrast. The relationship explains scatter plot distributions of time series of three variables (maximum zonal wind speed UMAX, meridional wind speed VMAX, and equator-pole temperature contrast dTMAX), which are obtained from a Venus general circulation model with equatorial Kelvin-wave forcing. Along with VMAX and dTMAX, UMAX likely increases with the phase velocity and amplitude of a forced wave. In the scatter diagram of UMAX versus dTMAX, points are plotted along a linear equation obtained from a thermal-wind relationship in the cloud layer. In the scatter diagram of VMAX versus UMAX, the apparent slope is somewhat steep in the high UMAX regime, compared with the low UMAX regime. The scatter plot distributions are qualitatively consistent with a quadratic equation obtained from a diagnostic equation of the stream function above the cloud top. The plotted points in the scatter diagrams form a linear cluster for weak wave forcing, whereas they form a small cluster for strong wave forcing. An interannual oscillation of the general circulation forming the linear cluster in the scatter diagram is apparent in the experiment of weak 5.5-day wave forcing. Although a pair of equatorial Kelvin and high-latitude Rossby waves with a same period (Kelvin-Rossby wave) produces equatorward heat and momentum fluxes in the region below 60 km, the equatorial wave does not contribute to the long-period oscillation. The interannual fluctuation of the high-latitude jet core leading to the time variation of UMAX is produced by growth and decay of a polar mixed Rossby-gravity wave with a 14-day period.

Analysis on the electromagnetic scattering properties of crops at multi-band

NASA Astrophysics Data System (ADS)

Wu, Tao; Wu, Zhensen; Liu, Xiaoyi

2014-12-01

The vector radiative transfer (VRT) theory for active microwave remote sensing and Rayleigh-Gans approximation (GRG) are applied in the study, and an iterative algorithm is used to solve the RT equations, thus we obtain the zeroorder and first-order equation for numerical results. The Michigan Microwave Canopy Scattering (MIMICS) model is simplified to adapt to the crop model, by analyzing body-surface bistatic scattering and backscattering properties between a layer of soybean or wheat consisting of stems and leaves and different underlying soil surface at multi-band (i.e. P, L, S, X, Ku-band), we obtain microwave scattering mechanisms of crop components and the effect of underlying ground on total crop scattering. Stem and leaf are regard as a needle and a circular disk, respectively. The final results are compared with some literature data to verify our calculating method, numerical results show multi-band crop microwave scattering properties differ from scattering angle, azimuth angle and moisture of vegetation and soil, which offer the part needed information for the design of future bistatic radar systems for crop sensing applications.

Multiple scattering of waves in random media: Application to the study of the city-site effect in Mexico City area.

NASA Astrophysics Data System (ADS)

Ishizawa, O. A.; Clouteau, D.

2007-12-01

Long-duration, amplifications and spatial response's variability of the seismic records registered in Mexico City during the September 1985 earthquake cannot only be explained by the soil velocity model. We will try to explain these phenomena by studying the extent of the effect of buildings' diffracted wave fields during an earthquake. The main question is whether the presence of a large number of buildings can significantly modify the seismic wave field. We are interested in the interaction between the incident wave field propagating in a stratified half- space and a large number of structures at the free surface, i.e., the coupled city-site effect. We study and characterize the seismic wave propagation regimes in a city using the theory of wave propagation in random media. In the coupled city-site system, the buildings are modeled as resonant scatterers uniformly distributed at the surface of a deterministic, horizontally layered elastic half-space representing the soil. Based on the mean-field and the field correlation equations, we build a theoretical model which takes into account the multiple scattering of seismic waves and allows us to describe the coupled city-site system behavior in a simple and rapid way. The results obtained for the configurationally averaged field quantities are validated by means of 3D results for the seismic response of a deterministic model. The numerical simulations of this model are computed with MISS3D code based on classical Soil-Structure Interaction techniques and on a variational coupling between Boundary Integral Equations for a layered soil and a modal Finite Element approach for the buildings. This work proposes a detailed numerical and a theoretical analysis of the city-site interaction (CSI) in Mexico City area. The principal parameters in the study of the CSI are the buildings resonant frequency distribution, the soil characteristics of the site, the urban density and position of the buildings in the city, as well as the type of incident wave. The main results of the theoretical and numerical models allow us to characterize the seismic movement in urban areas.

Expansion of Tabulated Scattering Matrices in Generalized Spherical Functions

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Geogdzhayev, Igor V.; Yang, Ping

2016-01-01

An efficient way to solve the vector radiative transfer equation for plane-parallel turbid media is to Fourier-decompose it in azimuth. This methodology is typically based on the analytical computation of the Fourier components of the phase matrix and is predicated on the knowledge of the coefficients appearing in the expansion of the normalized scattering matrix in generalized spherical functions. Quite often the expansion coefficients have to be determined from tabulated values of the scattering matrix obtained from measurements or calculated by solving the Maxwell equations. In such cases one needs an efficient and accurate computer procedure converting a tabulated scattering matrix into the corresponding set of expansion coefficients. This short communication summarizes the theoretical basis of this procedure and serves as the user guide to a simple public-domain FORTRAN program.

An analytic solution of the radiative transfer equation for a gray scattering atmosphere in motion

NASA Astrophysics Data System (ADS)

Pistinner, Shlomi; Shaviv, Giora

1994-12-01

We provide a formal analytic solution of the radiative transfer equation for a gray moving atmosphere in a plane parallel geometry. A formal solution in the diffusion and the free-streaming limit is also provided in the case of a spherically extended atmosphere. The formal solutions are written explicitly for scattering atmospheres in which the density and the velocity fields are given by a power law. A self-consistent temperature profile accurate to O(Beta = v/c) is provided for the case in which the absorption or the scattering are temperature independent. The gray extinction temperature profile is considerably simplified in the case of a scattering atmosphere. Steady state flow and homologous expansion are special cases that are considered in detail.

An analytic solution of the radiative transfer equation for a gray scattering atmosphere in motion

NASA Technical Reports Server (NTRS)

Pistinner, Shlomi; Shaviv, Giora

1994-01-01

We provide a formal analytic solution of the radiative transfer equation for a gray moving atmosphere in a plane parallel geometry. A formal solution in the diffusion and the free-streaming limit is also provided in the case of a spherically extended atmosphere. The formal solutions are written explicitly for scattering atmospheres in which the density and the velocity fields are given by a power law. A self-consistent temperature profile accurate to O(Beta = v/c) is provided for the case in which the absorption or the scattering are temperature independent. The gray extinction temperature profile is considerably simplified in the case of a scattering atmosphere. Steady state flow and homologous expansion are special cases that are considered in detail.

Electromagnetic scattering of large structures in layered earths using integral equations

NASA Astrophysics Data System (ADS)

Xiong, Zonghou; Tripp, Alan C.

1995-07-01

An electromagnetic scattering algorithm for large conductivity structures in stratified media has been developed and is based on the method of system iteration and spatial symmetry reduction using volume electric integral equations. The method of system iteration divides a structure into many substructures and solves the resulting matrix equation using a block iterative method. The block submatrices usually need to be stored on disk in order to save computer core memory. However, this requires a large disk for large structures. If the body is discretized into equal-size cells it is possible to use the spatial symmetry relations of the Green's functions to regenerate the scattering impedance matrix in each iteration, thus avoiding expensive disk storage. Numerical tests show that the system iteration converges much faster than the conventional point-wise Gauss-Seidel iterative method. The numbers of cells do not significantly affect the rate of convergency. Thus the algorithm effectively reduces the solution of the scattering problem to an order of O(N2), instead of O(N3) as with direct solvers.

Relativistic theory of particles in a scattering flow I: basic equations, diffusion and drift.

NASA Astrophysics Data System (ADS)

Achterberg, A.; Norman, C. A.

2018-06-01

We reconsider the theory of particle transport in a scattering medium, allowing for relativistic flow velocities. The theory uses a mixed set of variables, with position and time measured in the Laboratory Frame, and particle energy and momentum measured in the Fluid Rest Frame, the reference frame where scattering is assumed to be elastic. We give a new derivation for the fictitious force terms in the equation of motion that are present if the Fluid Rest Frame is not an inertial frame. By using a 3+1 notation we discuss the physical interpretation of the different terms in the fictitious force. It is shown that different approaches to the problem of particle propagation in a magnetized medium due to Skilling (1975) and Kulsrud (1983) are largely equivalent. We extend known results for non-relativistic flows to include the effects of cross-field diffusion for cosmic rays in a magnetized plasma. We also carefully consider the correct form of the diffusion approximation for scattering, and show that the resulting equations can be cast in conservation form.

Thermal conductivity of III-V semiconductor superlattices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mei, S., E-mail: song.mei@wisc.edu; Knezevic, I., E-mail: irena.knezevic@wisc.edu

2015-11-07

This paper presents a semiclassical model for the anisotropic thermal transport in III-V semiconductor superlattices (SLs). An effective interface rms roughness is the only adjustable parameter. Thermal transport inside a layer is described by the Boltzmann transport equation in the relaxation time approximation and is affected by the relevant scattering mechanisms (three-phonon, mass-difference, and dopant and electron scattering of phonons), as well as by diffuse scattering from the interfaces captured via an effective interface scattering rate. The in-plane thermal conductivity is obtained from the layer conductivities connected in parallel. The cross-plane thermal conductivity is calculated from the layer thermal conductivitiesmore » in series with one another and with thermal boundary resistances (TBRs) associated with each interface; the TBRs dominate cross-plane transport. The TBR of each interface is calculated from the transmission coefficient obtained by interpolating between the acoustic mismatch model (AMM) and the diffuse mismatch model (DMM), where the weight of the AMM transmission coefficient is the same wavelength-dependent specularity parameter related to the effective interface rms roughness that is commonly used to describe diffuse interface scattering. The model is applied to multiple III-arsenide superlattices, and the results are in very good agreement with experimental findings. The method is both simple and accurate, easy to implement, and applicable to complicated SL systems, such as the active regions of quantum cascade lasers. It is also valid for other SL material systems with high-quality interfaces and predominantly incoherent phonon transport.« less

Radiative transport equation for the Mittag-Leffler path length distribution

NASA Astrophysics Data System (ADS)

Liemert, André; Kienle, Alwin

2017-05-01

In this paper, we consider the radiative transport equation for infinitely extended scattering media that are characterized by the Mittag-Leffler path length distribution p (ℓ ) =-∂ℓEα(-σtℓα ) , which is a generalization of the usually assumed Lambert-Beer law p (ℓ ) =σtexp(-σtℓ ) . In this context, we derive the infinite-space Green's function of the underlying fractional transport equation for the spherically symmetric medium as well as for the one-dimensional string. Moreover, simple analytical solutions are presented for the prediction of the radiation field in the single-scattering approximation. The resulting equations are compared with Monte Carlo simulations in the steady-state and time domain showing, within the stochastic nature of the simulations, an excellent agreement.

Lasing in strongly scattering dielectric microstructures

NASA Astrophysics Data System (ADS)

Florescu, Lucia

In the first part of this thesis, a detailed analysis of lasing in random multiple-light-scattering media with gain is presented. Random laser emission is analyzed using a time-dependent diffusion model for light propagating in the medium containing active atoms. We demonstrate the effects of scatterers to narrow the emission spectral linewidth and to shorten the emitted pulse duration at a specific threshold pump intensity. This threshold pump intensity decreases with scatterer density and excitation spot diameter, in excellent agreement with experimental results. The coherence properties of the random laser are studied using a generalized master equation. The random laser medium is treated as a collection of low quality-factor cavities, coupled by random photon diffusion. Laser-like coherence, on average, is demonstrated above a specific pumping threshold. We demonstrate that with stronger scattering, the pumping threshold for the transition from chaotic to isotropic coherent light emission decreases and enhanced optical coherence for the emitted light is achieved above threshold. The second part of this thesis presents a study of lasing in photonic crystals (PCs). The emission from an incoherently pumped atomic system in interaction with the electro-magnetic reservoir of a PC is analyzed using a set of generalized semiclassical Maxwell-Bloch equations. We demonstrate that the photonic band edge facilitates the enhancement of stimulated emission and the reduction of internal losses, leading to an important lowering of the laser threshold. In addition, an increase of the laser output at a photonic band edge is demonstrated. We next develop a detailed quantum theory of a coherently pumped two-level atom in a photonic band gap material, coupled to both a multi-mode wave-guide channel and a high-quality micro-cavity embedded within the PC. The cavity field characteristics are highly distinct from that of a corresponding high-Q cavity in ordinary vacuum. We demonstrate enhanced, inversionless, and nearly coherent light generation when the photon density of states (DOS) jump between the Mollow spectral components of atomic resonance fluorescence is large. In the case of a vanishing photon DOS on the lower Mollow sideband and no dipolar dephasing, the emitted photon statistics is Poissonian and the cavity field exhibits quadrature coherence.

Scattering from arbitrarily shaped microstrip patch antennas

NASA Technical Reports Server (NTRS)

Shively, David G.; Deshpande, Manohar D.; Cockrell, Capers R.

1992-01-01

The scattering properties of arbitrarily shaped microstrip patch antennas are examined. The electric field integral equation for a current element on a grounded dielectric slab is developed for a rectangular geometry based on Galerkin's technique with subdomain rooftop basis functions. A shape function is introduced that allows a rectangular grid approximation to the arbitrarily shaped patch. The incident field on the patch is expressed as a function of incidence angle theta(i), phi(i). The resulting system of equations is then solved for the unknown current modes on the patch, and the electromagnetic scattering is calculated for a given angle. Comparisons are made with other calculated results as well as with measurements.

Remote monitoring of environmental particulate pollution - A problem in inversion of first-kind integral equations

NASA Technical Reports Server (NTRS)

Fymat, A. L.

1975-01-01

The determination of the microstructure, chemical nature, and dynamical evolution of scattering particulates in the atmosphere is considered. A description is given of indirect sampling techniques which can circumvent most of the difficulties associated with direct sampling techniques, taking into account methods based on scattering, extinction, and diffraction of an incident light beam. Approaches for reconstructing the particulate size distribution from the direct and the scattered radiation are discussed. A new method is proposed for determining the chemical composition of the particulates and attention is given to the relevance of methods of solution involving first kind Fredholm integral equations.

Coupled NASTRAN/boundary element formulation for acoustic scattering

NASA Technical Reports Server (NTRS)

Everstine, Gordon C.; Henderson, Francis M.; Schuetz, Luise S.

1987-01-01

A coupled finite element/boundary element capability is described for calculating the sound pressure field scattered by an arbitrary submerged 3-D elastic structure. Structural and fluid impedances are calculated with no approximation other than discretization. The surface fluid pressures and normal velocities are first calculated by coupling a NASTRAN finite element model of the structure with a discretized form of the Helmholtz surface integral equation for the exterior field. Far field pressures are then evaluated from the surface solution using the Helmholtz exterior integral equation. The overall approach is illustrated and validated using a known analytic solution for scattering from submerged spherical shells.

The multiple Coulomb scattering of very heavy charged particles.

PubMed

Wong, M; Schimmerling, W; Phillips, M H; Ludewigt, B A; Landis, D A; Walton, J T; Curtis, S B

1990-01-01

An experiment was performed at the Lawrence Berkeley Laboratory BEVALAC to measure the multiple Coulomb scattering of 650-MeV/A uranium nuclei in 0.19 radiation lengths of a Cu target. Differential distributions in the projected multiple scattering angle were measured in the vertical and horizontal planes using silicon position-sensitive detectors to determine particle trajectories before and after target scattering. The results were compared with the multiple Coulomb scattering theories of Fermi and Molière, and with a modification of the Fermi theory, using a Monte Carlo simulation. These theories were in excellent agreement with experiment at the 2 sigma level. The best quantitative agreement is obtained with the Gaussian distribution predicted by the modified Fermi theory.

Born approximation, multiple scattering, and butterfly algorithm

NASA Astrophysics Data System (ADS)

Martinez, Alex; Qiao, Zhijun

2014-06-01

Many imaging algorithms have been designed assuming the absence of multiple scattering. In the 2013 SPIE proceeding, we discussed an algorithm for removing high order scattering components from collected data. In this paper, our goal is to continue this work. First, we survey the current state of multiple scattering in SAR. Then, we revise our method and test it. Given an estimate of our target reflectivity, we compute the multi scattering effects in our target region for various frequencies. Furthermore, we propagate this energy through free space towards our antenna, and remove it from the collected data.

SAR Polarimetry

NASA Technical Reports Server (NTRS)

vanZyl, Jakob J.

2012-01-01

Radar Scattering includes: Surface Characteristics, Geometric Properties, Dielectric Properties, Rough Surface Scattering, Geometrical Optics and Small Perturbation Method Solutions, Integral Equation Method, Magellan Image of Pancake Domes on Venus, Dickinson Impact Crater on Venus (Magellan), Lakes on Titan (Cassini Radar, Longitudinal Dunes on Titan (Cassini Radar), Rough Surface Scattering: Effect of Dielectric Constant, Vegetation Scattering, Effect of Soil Moisture. Polarimetric Radar includes: Principles of Polarimetry: Field Descriptions, Wave Polarizations: Geometrical Representations, Definition of Ellipse Orientation Angles, Scatter as Polarization Transformer, Scattering Matrix, Coordinate Systems, Scattering Matrix, Covariance Matrix, Pauli Basis and Coherency Matrix, Polarization Synthesis, Polarimeter Implementation.

An analytical theory of radio-wave scattering from meteoric ionization - I. Basic equation

NASA Astrophysics Data System (ADS)

Pecina, P.

2016-01-01

We have developed an analytical theory of radio-wave scattering from ionization of meteoric origin. It is based on an integro-differential equation for the polarization vector, P, inside the meteor trail, representing an analytical solution of the set of Maxwell equations, in combination with a generalized radar equation involving an integral of the trail volume electron density, Ne, and P represented by an auxiliary vector, Q, taken over the whole trail volume. During the derivation of the final formulae, the following assumptions were applied: transversal as well as longitudinal dimensions of the meteor trail are small compared with the distances of the relevant trail point to both the transmitter and receiver and the ratio of these distances to the wavelength of the wave emitted by the radar is very large, so that the stationary-phase method can be employed for evaluation of the relevant integrals. Further, it is shown that in the case of sufficiently low electron density, Ne, corresponding to the case of underdense trails, the classical McKinley's radar equation results as a special case of the general theory. The same also applies regarding the Fresnel characteristics. Our approach is also capable of yielding solutions to the problems of the formation of Fresnel characteristics on trails having any electron density, forward scattering and scattering on trails immersed in the magnetic field. However, we have also shown that the geomagnetic field can be removed from consideration, due to its low strength. The full solution of the above integro-differential equation, valid for any electron volume densities, has been left to subsequent works dealing with this particular problem, due to its complexity.

NLO evolution of 3-quark Wilson loop operator

DOE PAGES

Balitsky, I.; Grabovsky, A. V.

2015-01-07

It is well known that high-energy scattering of a meson from some hadronic target can be described by the interaction of that target with a color dipole formed by two Wilson lines corresponding to fast quark-antiquark pair. Moreover, the energy dependence of the scattering amplitude is governed by the evolution equation of this color dipole with respect to rapidity. Similarly, the energy dependence of scattering of a baryon can be described in terms of evolution of a three-Wilson-lines operator with respect to the rapidity of the Wilson lines. We calculate the evolution of the 3-quark Wilson loop operator in themore » next-to-leading order (NLO) and present a quasi-conformal evolution equation for a composite 3-Wilson-lines operator. Thus we also obtain the linearized version of that evolution equation describing the amplitude of the odderon exchange at high energies.« less

The Physics of Polarization

NASA Astrophysics Data System (ADS)

Landi Degl'Innocenti, Egidio

2015-10-01

The introductory lecture that has been delivered at this Symposium is a condensed version of an extended course held by the author at the XII Canary Island Winter School from November 13 to November 21, 2000. The full series of lectures can be found in Landi Degl'Innocenti (2002). The original reference is organized in 20 Sections that are here itemized: 1. Introduction, 2. Description of polarized radiation, 3. Polarization and optical devices: Jones calculus and Muller matrices, 4. The Fresnel equations, 5. Dichroism and anomalous dispersion, 6. Polarization in everyday life, 7. Polarization due to radiating charges, 8. The linear antenna, 9. Thomson scattering, 10. Rayleigh scattering, 11. A digression on Mie scattering, 12. Bremsstrahlung radiation, 13. Cyclotron radiation, 14. Synchrotron radiation, 15. Polarization in spectral lines, 16. Density matrix and atomic polarization, 17. Radiative transfer and statistical equilibrium equations, 18. The amplification condition in polarized radiative transfer, and 19. Coupling radiative transfer and statistical equilibrium equations.

Unified connected theory of few-body reaction mechanisms in N-body scattering theory

NASA Technical Reports Server (NTRS)

Polyzou, W. N.; Redish, E. F.

1978-01-01

A unified treatment of different reaction mechanisms in nonrelativistic N-body scattering is presented. The theory is based on connected kernel integral equations that are expected to become compact for reasonable constraints on the potentials. The operators T/sub +-//sup ab/(A) are approximate transition operators that describe the scattering proceeding through an arbitrary reaction mechanism A. These operators are uniquely determined by a connected kernel equation and satisfy an optical theorem consistent with the choice of reaction mechanism. Connected kernel equations relating T/sub +-//sup ab/(A) to the full T/sub +-//sup ab/ allow correction of the approximate solutions for any ignored process to any order. This theory gives a unified treatment of all few-body reaction mechanisms with the same dynamic simplicity of a model calculation, but can include complicated reaction mechanisms involving overlapping configurations where it is difficult to formulate models.

Collisional redistribution of radiation. II - The effects of degeneracy on the equations of motion for the density matrix. III - The equation of motion for the correlation function and the scattered spectrum

NASA Technical Reports Server (NTRS)

Burnett, K.; Cooper, J.

1980-01-01

The effect of correlations between an absorber atom and perturbers in the binary-collision approximation are applied to degenerate atomic systems. A generalized absorption profile which specifies the final state of the atom after an absorption event is related to the total intensities of Rayleigh scattering and fluorescence from the atom. It is suggested that additional dynamical information to that obtainable from ordinary absorption experiments is required in order to describe redistributed atomic radiation. The scattering of monochromatic radiation by a degenerate atom is computed in a binary-collision approximation; an equation of motion is derived for the correlation function which is valid outside the quantum-regression regime. Solutions are given for the weak-field conditions in terms of generalized absorption and emission profiles that depend on the indices of the atomic multipoles.

Stochastic analysis of pitch angle scattering of charged particles by transverse magnetic waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lemons, Don S.; Liu Kaijun; Winske, Dan

2009-11-15

This paper describes a theory of the velocity space scattering of charged particles in a static magnetic field composed of a uniform background field and a sum of transverse, circularly polarized, magnetic waves. When that sum has many terms the autocorrelation time required for particle orbits to become effectively randomized is small compared with the time required for the particle velocity distribution to change significantly. In this regime the deterministic equations of motion can be transformed into stochastic differential equations of motion. The resulting stochastic velocity space scattering is described, in part, by a pitch angle diffusion rate that ismore » a function of initial pitch angle and properties of the wave spectrum. Numerical solutions of the deterministic equations of motion agree with the theory at all pitch angles, for wave energy densities up to and above the energy density of the uniform field, and for different wave spectral shapes.« less

Modeling of Electromagnetic Scattering by Discrete and Discretely Heterogeneous Random Media by Using Numerically Exact Solutions of the Maxwell Equations

NASA Technical Reports Server (NTRS)

Dlugach, Janna M.; Mishchenko, Michael I.

2017-01-01

In this paper, we discuss some aspects of numerical modeling of electromagnetic scattering by discrete random medium by using numerically exact solutions of the macroscopic Maxwell equations. Typical examples of such media are clouds of interstellar dust, clouds of interplanetary dust in the Solar system, dusty atmospheres of comets, particulate planetary rings, clouds in planetary atmospheres, aerosol particles with numerous inclusions and so on. Our study is based on the results of extensive computations of different characteristics of electromagnetic scattering obtained by using the superposition T-matrix method which represents a direct computer solver of the macroscopic Maxwell equations for an arbitrary multisphere configuration. As a result, in particular, we clarify the range of applicability of the low-density theories of radiative transfer and coherent backscattering as well as of widely used effective-medium approximations.

Connection of Scattering Principles: A Visual and Mathematical Tour

ERIC Educational Resources Information Center

Broggini, Filippo; Snieder, Roel

2012-01-01

Inverse scattering, Green's function reconstruction, focusing, imaging and the optical theorem are subjects usually studied as separate problems in different research areas. We show a physical connection between the principles because the equations that rule these "scattering principles" have a similar functional form. We first lead the reader…

Bose-Einstein condensation of photons from the thermodynamic limit to small photon numbers

NASA Astrophysics Data System (ADS)

Nyman, Robert A.; Walker, Benjamin T.

2018-03-01

Photons can come to thermal equilibrium at room temperature by scattering multiple times from a fluorescent dye. By confining the light and dye in a microcavity, a minimum energy is set and the photons can then show Bose-Einstein condensation. We present here the physical principles underlying photon thermalization and condensation, and review the literature on the subject. We then explore the 'small' regime where very few photons are needed for condensation. We compare thermal equilibrium results to a rate-equation model of microlasers, which includes spontaneous emission into the cavity, and we note that small systems result in ambiguity in the definition of threshold.

Sound propagation in urban areas: a periodic disposition of buildings.

PubMed

Picaut, J; Hardy, J; Simon, L

1999-10-01

A numerical simulation of background noise propagation is performed for a network of hexagonal buildings. The obtained results suggest that the prediction of background noise in urban spaces is possible by means of a modified diffusion equation using two parameters: the diffusion coefficient that expresses the spreading out of noise resulting from diffuse scattering and multiple reflections by buildings, and an attenuation term accounting for the wall absorption, atmospheric attenuation, and absorption by the open top. The dependence of the diffusion coefficient with geometrical shapes and the diffusive nature of the buildings are investigated in the case of a periodic disposition of hexagonal buildings.

XaNSoNS: GPU-accelerated simulator of diffraction patterns of nanoparticles

NASA Astrophysics Data System (ADS)

Neverov, V. S.

XaNSoNS is an open source software with GPU support, which simulates X-ray and neutron 1D (or 2D) diffraction patterns and pair-distribution functions (PDF) for amorphous or crystalline nanoparticles (up to ∼107 atoms) of heterogeneous structural content. Among the multiple parameters of the structure the user may specify atomic displacements, site occupancies, molecular displacements and molecular rotations. The software uses general equations nonspecific to crystalline structures to calculate the scattering intensity. It supports four major standards of parallel computing: MPI, OpenMP, Nvidia CUDA and OpenCL, enabling it to run on various architectures, from CPU-based HPCs to consumer-level GPUs.

Nonlinear optical response in narrow graphene nanoribbons

NASA Astrophysics Data System (ADS)

Karimi, Farhad; Knezevic, Irena

We present an iterative method to calculate the nonlinear optical response of armchair graphene nanoribbons (aGNRs) and zigzag graphene nanoribbons (zGNRs) while including the effects of dissipation. In contrast to methods that calculate the nonlinear response in the ballistic (dissipation-free) regime, here we obtain the nonlinear response of an electronic system to an external electromagnetic field while interacting with a dissipative environment (to second order). We use a self-consistent-field approach within a Markovian master-equation formalism (SCF-MMEF) coupled with full-wave electromagnetic equations, and we solve the master equation iteratively to obtain the higher-order response functions. We employ the SCF-MMEF to calculate the nonlinear conductance and susceptibility, as well as to calculate the dependence of the plasmon dispersion and plasmon propagation length on the intensity of the electromagnetic field in GNRs. The electron scattering mechanisms included in this work are scattering with intrinsic phonons, ionized impurities, surface optical phonons, and line-edge roughness. Unlike in wide GNRs, where ionized-impurity scattering dominates dissipation, in ultra-narrow nanoribbons on polar substrates optical-phonon scattering and ionized-impurity scattering are equally prominent. Support by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0008712.

A Theoretical Understanding of Circular Polarization Memory in Random Media

NASA Astrophysics Data System (ADS)

Dark, Julia

Radiative transport theory describes the propagation of light in random media that absorb, scatter, and emit radiation. To describe the propagation of light, the full polarization state is quantified using the Stokes parameters. For the sake of mathematical convenience, the polarization state of light is often neglected leading to the scalar radiative transport equation for the intensity only. For scalar transport theory, there is a well-established body of literature on numerical and analytic approximations to the radiative transport equation. We extend the scalar theory to the vector radiative transport equation (vRTE). In particular, we are interested in the theoretical basis for a phenomena called circular polarization memory. Circular polarization memory is the physical phenomena whereby circular polarization retains its ellipticity and handedness when propagating in random media. This is in contrast to the propagation of linear polarization in random media, which depolarizes at a faster rate, and specular reflection of circular polarization, whereby the circular polarization handedness flips. We investigate two limits that are of known interest in the phenomena of circular polarization memory. The first limit we investigate is that of forward-peaked scattering, i.e. the limit where most scattering events occur in the forward or near-forward directions. The second limit we consider is that of strong scattering and weak absorption. In the forward-peaked scattering limit we approximate the vRTE by a system of partial differential equations motivated by the scalar Fokker-Planck approximation. We call the leading order approximation the vector Fokker-Planck approximation. The vector Fokker Planck approximation predicts that strongly forward-peaked media exhibit circular polarization memory where the strength of the effect can be calculated from the expansion of the scattering matrix in special functions. In addition, we find in this limit that total intensity, linear polarization, and circular polarization decouple. From this result we conclude, that in the Fokker-Planck limit the scalar approximation is an appropriate leading order approximation. In the strong scattering and weak absorbing limit the vector radiative transport equation can be analyzed using boundary layer theory. In this case, the problem of light scattering in an optically thick medium is reduced to a 1D vRTE near the boundary and a 3D diffusion equation in the interior. We develop and implement a numerical solver for the boundary layer problem by using a discrete ordinate solver in the boundary layer and a spectral method to solve the diffusion approximation in the interior. We implement the method in Fortran 95 with external dependencies on BLAS, LAPACK, and FFTW. By analyzing the spectrum of the discretized vRTE in the boundary layer, we are able to predict the presence of circular polarization memory in a given medium.

Application of a multiple scattering model to estimate optical depth, lidar ratio and ice crystal effective radius of cirrus clouds observed with lidar.

NASA Astrophysics Data System (ADS)

Gouveia, Diego; Baars, Holger; Seifert, Patric; Wandinger, Ulla; Barbosa, Henrique; Barja, Boris; Artaxo, Paulo; Lopes, Fabio; Landulfo, Eduardo; Ansmann, Albert

2018-04-01

Lidar measurements of cirrus clouds are highly influenced by multiple scattering (MS). We therefore developed an iterative approach to correct elastic backscatter lidar signals for multiple scattering to obtain best estimates of single-scattering cloud optical depth and lidar ratio as well as of the ice crystal effective radius. The approach is based on the exploration of the effect of MS on the molecular backscatter signal returned from above cloud top.

An iterative fullwave simulation approach to multiple scattering in media with randomly distributed microbubbles

NASA Astrophysics Data System (ADS)

Joshi, Aditya; Lindsey, Brooks D.; Dayton, Paul A.; Pinton, Gianmarco; Muller, Marie

2017-05-01

Ultrasound contrast agents (UCA), such as microbubbles, enhance the scattering properties of blood, which is otherwise hypoechoic. The multiple scattering interactions of the acoustic field with UCA are poorly understood due to the complexity of the multiple scattering theories and the nonlinear microbubble response. The majority of bubble models describe the behavior of UCA as single, isolated microbubbles suspended in infinite medium. Multiple scattering models such as the independent scattering approximation can approximate phase velocity and attenuation for low scatterer volume fractions. However, all current models and simulation approaches only describe multiple scattering and nonlinear bubble dynamics separately. Here we present an approach that combines two existing models: (1) a full-wave model that describes nonlinear propagation and scattering interactions in a heterogeneous attenuating medium and (2) a Paul-Sarkar model that describes the nonlinear interactions between an acoustic field and microbubbles. These two models were solved numerically and combined with an iterative approach. The convergence of this combined model was explored in silico for 0.5 × 106 microbubbles ml-1, 1% and 2% bubble concentration by volume. The backscattering predicted by our modeling approach was verified experimentally with water tank measurements performed with a 128-element linear array transducer. An excellent agreement in terms of the fundamental and harmonic acoustic fields is shown. Additionally, our model correctly predicts the phase velocity and attenuation measured using through transmission and predicted by the independent scattering approximation.

Second-order multiple-scattering theory associated with backscattering enhancement for a millimeter wavelength weather radar with a finite beam width

NASA Astrophysics Data System (ADS)

Kobayashi, Satoru; Tanelli, Simone; Im, Eastwood

2005-12-01

Effects of multiple scattering on reflectivity are studied for millimeter wavelength weather radars. A time-independent vector theory, including up to second-order scattering, is derived for a single layer of hydrometeors of a uniform density and a uniform diameter. In this theory, spherical waves with a Gaussian antenna pattern are used to calculate ladder and cross terms in the analytical scattering theory. The former terms represent the conventional multiple scattering, while the latter terms cause backscattering enhancement in both the copolarized and cross-polarized components. As the optical thickness of the hydrometeor layer increases, the differences from the conventional plane wave theory become more significant, and essentially, the reflectivity of multiple scattering depends on the ratio of mean free path to radar footprint radius. These results must be taken into account when analyzing radar reflectivity for use in remote sensing.

Focusing of light energy inside a scattering medium by controlling the time-gated multiple light scattering

NASA Astrophysics Data System (ADS)

Jeong, Seungwon; Lee, Ye-Ryoung; Choi, Wonjun; Kang, Sungsam; Hong, Jin Hee; Park, Jin-Sung; Lim, Yong-Sik; Park, Hong-Gyu; Choi, Wonshik

2018-05-01

The efficient delivery of light energy is a prerequisite for the non-invasive imaging and stimulating of target objects embedded deep within a scattering medium. However, the injected waves experience random diffusion by multiple light scattering, and only a small fraction reaches the target object. Here, we present a method to counteract wave diffusion and to focus multiple-scattered waves at the deeply embedded target. To realize this, we experimentally inject light into the reflection eigenchannels of a specific flight time to preferably enhance the intensity of those multiple-scattered waves that have interacted with the target object. For targets that are too deep to be visible by optical imaging, we demonstrate a more than tenfold enhancement in light energy delivery in comparison with ordinary wave diffusion cases. This work will lay a foundation to enhance the working depth of imaging, sensing and light stimulation.

Compton Scattering by Static and Moving Media. Part 1; The Transfer Equation and its Moments

NASA Technical Reports Server (NTRS)

Psaltis, Dimitrios; Lamb, Frederick K.

1997-01-01

Compton scattering of photons by nonrelativistic particles is thought to play an important role in forming the radiation spectrum of many astrophysical systems. Here we derive the time-dependent photon kinetic equation that describes spontaneous and induced Compton scattering, as well as absorption and emission by static and moving media, the corresponding radiative transfer equation, and their zeroth and first angular moments, both in the system frame and in the frame comoving with the medium. We show that it is necessary to use the correct relativistic differential scattering cross section in order to obtain a photon kinetic equation that is correct to first order in Epsilon/m(sub e), T(sub e)/m(sub e), and V, where Epsilon is the photon energy, T(sub e) and m(sub e) are the electron temperature and rest mass, and V is the electron bulk velocity in units of the speed of light. We also demonstrate that the terms in the radiative transfer equation that are second order in V should usually be retained, because if the radiation energy density is sufficiently large, compared to the radiation flux, the effects of bulk Comptonization described by the terms that are second order in V can be as important as the effects described by the terms that are first order in V, even when V is small. The system- and fluid-frame equations that we derive are correct to first order in Epsilon/m(sub e). Our system-frame equations, which are correct to second order in V, may be used when V is not too large. Our fluid-frame equations, which are exact in V, may be used when V approaches 1. Both sets of equations are valid for systems of arbitrary optical depth and can therefore be used in both the free-streaming and diffusion regimes. We demonstrate that Comptonization by the electron bulk motion occurs whether or not the radiation field is isotropic or the bulk flow converges and that it is more important than thermal Comptonization if V(sup 2) is greater than 3T(sub e)/m(sub e).

Computer code for scattering from impedance bodies of revolution. Part 3: Surface impedance with s and phi variation. Analytical and numerical results

NASA Technical Reports Server (NTRS)

Uslenghi, Piergiorgio L. E.; Laxpati, Sharad R.; Kawalko, Stephen F.

1993-01-01

The third phase of the development of the computer codes for scattering by coated bodies that has been part of an ongoing effort in the Electromagnetics Laboratory of the Electrical Engineering and Computer Science Department at the University of Illinois at Chicago is described. The work reported discusses the analytical and numerical results for the scattering of an obliquely incident plane wave by impedance bodies of revolution with phi variation of the surface impedance. Integral equation formulation of the problem is considered. All three types of integral equations, electric field, magnetic field, and combined field, are considered. These equations are solved numerically via the method of moments with parametric elements. Both TE and TM polarization of the incident plane wave are considered. The surface impedance is allowed to vary along both the profile of the scatterer and in the phi direction. Computer code developed for this purpose determines the electric surface current as well as the bistatic radar cross section. The results obtained with this code were validated by comparing the results with available results for specific scatterers such as the perfectly conducting sphere. Results for the cone-sphere and cone-cylinder-sphere for the case of an axially incident plane were validated by comparing the results with the results with those obtained in the first phase of this project. Results for body of revolution scatterers with an abrupt change in the surface impedance along both the profile of the scatterer and the phi direction are presented.

Coupled radial Schrödinger equations written as Dirac-type equations: application to an amplitude-phase approach

NASA Astrophysics Data System (ADS)

Thylwe, Karl-Erik; McCabe, Patrick

2012-04-01

The classical amplitude-phase method due to Milne, Wilson, Young and Wheeler in the 1930s is known to be a powerful computational tool for determining phase shifts and energy eigenvalues in cases where a sufficiently slowly varying amplitude function can be found. The key for the efficient computations is that the original single-state radial Schrödinger equation is transformed to a nonlinear equation, the Milne equation. Such an equation has solutions that may or may not oscillate, depending on boundary conditions, which then requires a robust recipe for locating the (optimal) ‘almost constant’ solutions for its use in the method. For scattering problems the solutions of the amplitude equations always approach constants as the radial distance r tends to infinity, and there is no problem locating the ‘optimal’ amplitude functions from a low-order semiclassical approximation. In the present work, the amplitude-phase approach is generalized to two coupled Schrödinger equations similar to an earlier generalization to radial Dirac equations. The original scalar amplitude then becomes a vector quantity, and the original Milne equation is generalized accordingly. Numerical applications to resonant electron-atom scattering are illustrated.

The scattering variety

NASA Astrophysics Data System (ADS)

He, Yang-Hui; Matti, Cyril; Sun, Chuang

2014-10-01

The so-called Scattering Equations which govern the kinematics of the scattering of massless particles in arbitrary dimensions have recently been cast into a system of homogeneous polynomials. We study these as affine and projective geometries which we call Scattering Varieties by analyzing such properties as Hilbert series, Euler characteristic and singularities. Interestingly, we find structures such as affine Calabi-Yau threefolds as well as singular K3 and Fano varieties.

White-light parametric instabilities in plasmas.

PubMed

Santos, J E; Silva, L O; Bingham, R

2007-06-08

Parametric instabilities driven by partially coherent radiation in plasmas are described by a generalized statistical Wigner-Moyal set of equations, formally equivalent to the full wave equation, coupled to the plasma fluid equations. A generalized dispersion relation for stimulated Raman scattering driven by a partially coherent pump field is derived, revealing a growth rate dependence, with the coherence width sigma of the radiation field, scaling with 1/sigma for backscattering (three-wave process), and with 1/sigma1/2 for direct forward scattering (four-wave process). Our results demonstrate the possibility to control the growth rates of these instabilities by properly using broadband pump radiation fields.

Designing scattering-free isotropic index profiles using phase-amplitude equations

NASA Astrophysics Data System (ADS)

King, C. G.; Horsley, S. A. R.; Philbin, T. G.

2018-05-01

The Helmholtz equation can be written as coupled equations for the amplitude and phase. By considering spatial phase distributions corresponding to reflectionless wave propagation in the plane and solving for the amplitude in terms of this phase, we designed two-dimensional graded-index media which do not scatter light. We give two illustrative examples, the first of which is a periodic grating for which diffraction is completely suppressed at a single frequency at normal incidence to the periodicity. The second example is a medium which behaves as a "beam shifter" at a single frequency; acting to laterally shift a plane wave, or sufficiently wide beam, without reflection.

Biasing anisotropic scattering kernels for deep-penetration Monte Carlo calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carter, L.L.; Hendricks, J.S.

1983-01-01

The exponential transform is often used to improve the efficiency of deep-penetration Monte Carlo calculations. This technique is usually implemented by biasing the distance-to-collision kernel of the transport equation, but leaving the scattering kernel unchanged. Dwivedi obtained significant improvements in efficiency by biasing an isotropic scattering kernel as well as the distance-to-collision kernel. This idea is extended to anisotropic scattering, particularly the highly forward Klein-Nishina scattering of gamma rays.

Topics in electromagnetic, acoustic, and potential scattering theory

NASA Astrophysics Data System (ADS)

Nuntaplook, Umaporn

With recent renewed interest in the classical topics of both acoustic and electromagnetic aspects for nano-technology, transformation optics, fiber optics, metamaterials with negative refractive indices, cloaking and invisibility, the topic of time-independent scattering theory in quantum mechanics is becoming a useful field to re-examine in the above contexts. One of the key areas of electromagnetic theory scattering of plane electromagnetic waves --- is based on the properties of the refractive indices in the various media. It transpires that the refractive index of a medium and the potential in quantum scattering theory are intimately related. In many cases, understanding such scattering in radially symmetric media is sufficient to gain insight into scattering in more complex media. Meeting the challenge of variable refractive indices and possibly complicated boundary conditions therefore requires accurate and efficient numerical methods, and where possible, analytic solutions to the radial equations from the governing scalar and vector wave equations (in acoustics and electromagnetic theory, respectively). Until relatively recently, researchers assumed a constant refractive index throughout the medium of interest. However, the most interesting and increasingly useful cases are those with non-constant refractive index profiles. In the majority of this dissertation the focus is on media with piecewise constant refractive indices in radially symmetric media. The method discussed is based on the solution of Maxwell's equations for scattering of plane electromagnetic waves from a dielectric (or "transparent") sphere in terms of the related Helmholtz equation. The main body of the dissertation (Chapters 2 and 3) is concerned with scattering from (i) a uniform spherical inhomogeneity embedded in an external medium with different properties, and (ii) a piecewise-uniform central inhomogeneity in the external medium. The latter results contain a natural generalization of the former (previously known) results. The link with time-independent quantum mechanical scattering, via morphology-dependent resonances (MDRs), is discussed in Chapter 2. This requires a generalization of the classical problem for scattering of a plane wave from a uniform spherically-symmetric inhomogeneity (in which the velocity of propagation is a function only of the radial coordinate r. i.e.. c = c(r)) to a piecewise-uniform inhomogeneity. In Chapter 3 the Jost-function formulation of potential scattering theory is used to solve the radial differential equation for scattering which can be converted into an integral equation corresponding via the Jost boundary conditions. The first two iterations for the zero angular momentum case l = 0 are provided for both two-layer and three-layer models. It is found that the iterative technique is most useful for long wavelengths and sufficiently small ratios of interior and exterior wavenumbers. Exact solutions are also provided for these cases. In Chapter 4 the time-independent quantum mechanical 'connection' is exploited further by generalizing previous work on a spherical well potential to the case where a delta 'function' potential is appended to the exterior of the well (for l ≠ 0). This corresponds to an idealization of the former approach to the case of a 'coated sphere'. The poles of the associated 'S-matrix' are important in this regard, since they correspond directly with the morphology-dependent resonances discussed in Chapter 2. These poles (for the l = 0 case, to compare with Nussenzveig's analysis) are tracked in the complex wavenumber plane as the strength of the delta function potential changes. Finally, a set of 4 Appendices is provided to clarify some of the connections between (i) the scattering of acoustic/electromagnetic waves from a penetrable/dielectric sphere and (ii) time-independent potential scattering theory in quantum mechanics. This, it is hoped, will be the subject of future work.

Influence of multiple scattering on CloudSat measurements in snow: A model study

NASA Astrophysics Data System (ADS)

Matrosov, Sergey Y.; Battaglia, Alessandro

2009-06-01

The effects of multiple scattering on larger precipitating hydrometers have an influence on measurements of the spaceborne W-band (94 GHz) CloudSat radar. This study presents initial quantitative estimates of these effects in “dry” snow using radiative transfer calculations for appropriate snowfall models. It is shown that these effects become significant (i.e., greater than approximately 1 dB) when snowfall radar reflectivity factors are greater than about 10-15 dBZ. Reflectivity enhancement due to multiple scattering can reach 4-5 dB in heavier stratiform snowfalls. Multiple scattering effects counteract signal attenuation, so the observed CloudSat reflectivity factors in snowfall could be relatively close to the values that would be observed in the case of single scattering and the absence of attenuation.

A method for estimating the incident PAR on inclined surfaces

NASA Astrophysics Data System (ADS)

Xie, Xiaoping; Gao, Wei; Gao, Zhiqiang

2008-08-01

A new simple model has been developed that incorporates Digital Elevation Model (DEM) and Moderate Resolution Imaging Spectroradiometer (MODIS) products to produce incident photosynthetically active radiation (PAR) for tilted surface. The method is based on a simplification of the general radiative transfer equation, which considers five major processes of attenuation of solar radiation: 1) Rayleigh scattering, 2) absorption by ozone and water vapor, 3) aerosol scattering, 4) multiple reflectance between surface and atmosphere, and 5) three terrain factors: slope and aspect, isotropic sky view factor, and additional radiation by neighbor reflectance. A comparison of the model results with observational data from the Yucheng and Changbai Mountain sites of the Chinese Ecosystem Research Network (CERN) shows the correlation coefficient as 0.929 and 0.904, respectively. A comparison of the model results with the 2006 filed measured PAR in the Yucheng and Changbai sites shows the correlation coefficient as 0.929 and 0.904, respectively, and the average percent error as 10% and 15%, respectively.

Computing wave functions in multichannel collisions with non-local potentials using the R-matrix method

NASA Astrophysics Data System (ADS)

Bonitati, Joey; Slimmer, Ben; Li, Weichuan; Potel, Gregory; Nunes, Filomena

2017-09-01

The calculable form of the R-matrix method has been previously shown to be a useful tool in approximately solving the Schrodinger equation in nuclear scattering problems. We use this technique combined with the Gauss quadrature for the Lagrange-mesh method to efficiently solve for the wave functions of projectile nuclei in low energy collisions (1-100 MeV) involving an arbitrary number of channels. We include the local Woods-Saxon potential, the non-local potential of Perey and Buck, a Coulomb potential, and a coupling potential to computationally solve for the wave function of two nuclei at short distances. Object oriented programming is used to increase modularity, and parallel programming techniques are introduced to reduce computation time. We conclude that the R-matrix method is an effective method to predict the wave functions of nuclei in scattering problems involving both multiple channels and non-local potentials. Michigan State University iCER ACRES REU.

Multi-group Fokker-Planck proton transport in MCNP{trademark}

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adams, K.J.

1997-11-01

MCNP has been enhanced to perform proton transport using a multigroup Fokker Planck (MGFP) algorithm with primary emphasis on proton radiography simulations. The new method solves the Fokker Planck approximation to the Boltzmann transport equation for the small angle multiple scattering portion of proton transport. Energy loss is accounted for by applying a group averaged stopping power over each transport step. Large angle scatter and non-inelastic events are treated as extinction. Comparisons with the more rigorous LAHET code show agreement to a few per cent for the total transmitted currents. The angular distributions through copper and low Z compounds showmore » good agreement between LAHET and MGFP with the MGFP method being slightly less forward peaked and without the large angle tails apparent in the LAHET simulation. Suitability of this method for proton radiography simulations is shown for a simple problem of a hole in a copper slab. LAHET and MGFP calculations of position, angle and energy through more complex objects are presented.« less

Modeling Radar Scattering by Planetary Regoliths for Varying Angles of Incidence

NASA Astrophysics Data System (ADS)

Prem, P.; Patterson, G. W.; Zimmerman, M. I.

2017-12-01

Bistatic radar observations can play an important role in characterizing the texture and composition of planetary regoliths. Multiple scattering within a closely-packed particulate medium, such as a regolith, can lead to a response referred to as the Coherent Backscatter Opposition Effect (CBOE), associated with an increase in the intensity of backscattered radiation and an increase in Circular Polarization Ratio (CPR) at small bistatic angles. The nature of the CBOE is thought to depend not only on regolith properties, but also on the angle of incidence (Mishchenko, 1992). The latter factor is of particular interest in light of recent radar observations of the Moon over a range of bistatic and incidence angles by the Mini-RF instrument (on board the Lunar Reconnaissance Orbiter), operating in bistatic mode with a ground-based transmitter at the Arecibo Observatory. These observations have led to some intriguing results that are not yet well-understood ­- for instance, the lunar South Polar crater Cabeus shows an elevated CPR at only some combinations of incidence angle/bistatic angle, a potential clue to the depth distribution of water ice at the lunar poles (Patterson et al., 2017). Our objective in this work is to develop a model for radar scattering by planetary regoliths that can assist in the interpretation of Mini-RF observations. We approach the problem by coupling the Multiple Sphere T-Matrix (MSTM) code of Mackowski and Mishchenko (2011) to a Monte Carlo radiative transfer model. The MSTM code is based on the solution of Maxwell's equations for the propagation of electromagnetic waves in the presence of a cluster of scattering/absorbing spheres, and can be used to model the scattering of radar waves by an aggregation of nominal regolith particles. The scattering properties thus obtained serve as input to the Monte Carlo model, which is used to simulate radar scattering at larger spatial scales. The Monte Carlo approach has the advantage of being able to readily accommodate varying incidence angles, as well as heterogeneities in regolith composition and properties - factors that may be of interest in both lunar and other contexts. We will report on the development and validation of the coupled MSTM-Monte Carlo model, and discuss its application to problems of interest.

Integrability: mathematical methods for studying solitary waves theory

NASA Astrophysics Data System (ADS)

Wazwaz, Abdul-Majid

2014-03-01

In recent decades, substantial experimental research efforts have been devoted to linear and nonlinear physical phenomena. In particular, studies of integrable nonlinear equations in solitary waves theory have attracted intensive interest from mathematicians, with the principal goal of fostering the development of new methods, and physicists, who are seeking solutions that represent physical phenomena and to form a bridge between mathematical results and scientific structures. The aim for both groups is to build up our current understanding and facilitate future developments, develop more creative results and create new trends in the rapidly developing field of solitary waves. The notion of the integrability of certain partial differential equations occupies an important role in current and future trends, but a unified rigorous definition of the integrability of differential equations still does not exist. For example, an integrable model in the Painlevé sense may not be integrable in the Lax sense. The Painlevé sense indicates that the solution can be represented as a Laurent series in powers of some function that vanishes on an arbitrary surface with the possibility of truncating the Laurent series at finite powers of this function. The concept of Lax pairs introduces another meaning of the notion of integrability. The Lax pair formulates the integrability of nonlinear equation as the compatibility condition of two linear equations. However, it was shown by many researchers that the necessary integrability conditions are the existence of an infinite series of generalized symmetries or conservation laws for the given equation. The existence of multiple soliton solutions often indicates the integrability of the equation but other tests, such as the Painlevé test or the Lax pair, are necessary to confirm the integrability for any equation. In the context of completely integrable equations, studies are flourishing because these equations are able to describe the real features in a variety of vital areas in science, technology and engineering. In recognition of the importance of solitary waves theory and the underlying concept of integrable equations, a variety of powerful methods have been developed to carry out the required analysis. Examples of such methods which have been advanced are the inverse scattering method, the Hirota bilinear method, the simplified Hirota method, the Bäcklund transformation method, the Darboux transformation, the Pfaffian technique, the Painlevé analysis, the generalized symmetry method, the subsidiary ordinary differential equation method, the coupled amplitude-phase formulation, the sine-cosine method, the sech-tanh method, the mapping and deformation approach and many new other methods. The inverse scattering method, viewed as a nonlinear analogue of the Fourier transform method, is a powerful approach that demonstrates the existence of soliton solutions through intensive computations. At the center of the theory of integrable equations lies the bilinear forms and Hirota's direct method, which can be used to obtain soliton solutions by using exponentials. The Bäcklund transformation method is a useful invariant transformation that transforms one solution into another of a differential equation. The Darboux transformation method is a well known tool in the theory of integrable systems. It is believed that there is a connection between the Bäcklund transformation and the Darboux transformation, but it is as yet not known. Archetypes of integrable equations are the Korteweg-de Vries (KdV) equation, the modified KdV equation, the sine-Gordon equation, the Schrödinger equation, the Vakhnenko equation, the KdV6 equation, the Burgers equation, the fifth-order Lax equation and many others. These equations yield soliton solutions, multiple soliton solutions, breather solutions, quasi-periodic solutions, kink solutions, homo-clinic solutions and other solutions as well. The couplings of linear and nonlinear equations were recently discovered and subsequently received considerable attention. The concept of couplings forms a new direction for developing innovative construction methods. The recently obtained results in solitary waves theory highlight new approaches for additional creative ideas, promising further achievements and increased progress in this field. We are grateful to all of the authors who accepted our invitation to contribute to this comment section.

Multiple Scattering Effects on Pulse Propagation in Optically Turbid Media.

NASA Astrophysics Data System (ADS)

Joelson, Bradley David

The effects of multiple scattering in a optically turbid media is examined for an impulse solution to the radiative transfer equation for a variety of geometries and phase functions. In regions where the complexities of the phase function proved too cumbersome for analytic methods Monte Carlo techniques were developed to describe the entire scalar radiance distribution. The determination of a general spread function is strongly dependent on geometry and particular regions where limits can be placed on the variables of the problem. Hence, the general spread function is first simplified by considering optical regions which reduce the complexity of the variable dependence. First, in the small-angle limit we calculate some contracted spread functions along with their moments and then use Monte Carlo techniques to establish the limitations imposed by the small-angle approximation in planar geometry. The point spread function (PSF) for a spherical geometry is calculated for the full angular spread in the forward direction of ocean waters using Monte Carlo methods in the optically thin and moderate depths and analytic methods in the diffusion domain. The angular dependence of the PSF for various ocean waters is examined for a range of optical parameters. The analytic method used in the diffusion calculation is justified by examining the angular dependence of the radiance of a impulse solution in a planar geometry for a prolongated Henyey-Greenstein phase function of asymmetry factor approximately equal to that of the ocean phase functions. The Legendre moments of the radiance are examined in order to examine the viability of the diffusion approximation which assumes a linearly anisotropic angular distribution for the radiance. A realistic lidar calculation is performed for a variety of ocean waters to determine the effects of multiple scattering on the determination of the speed of sound by using the range gated frequency spectrum of the lidar signal. It is shown that the optical properties of the ocean help to ensure single scatter form for the frequency spectra of the lidar signal. This spectra can then be used to compute the speed of sound and backscatter probability.

A Fast Vector Radiative Transfer Model for Atmospheric and Oceanic Remote Sensing

NASA Astrophysics Data System (ADS)

Ding, J.; Yang, P.; King, M. D.; Platnick, S. E.; Meyer, K.

2017-12-01

A fast vector radiative transfer model is developed in support of atmospheric and oceanic remote sensing. This model is capable of simulating the Stokes vector observed at the top of the atmosphere (TOA) and the terrestrial surface by considering absorption, scattering, and emission. The gas absorption is parameterized in terms of atmospheric gas concentrations, temperature, and pressure. The parameterization scheme combines a regression method and the correlated-K distribution method, and can easily integrate with multiple scattering computations. The approach is more than four orders of magnitude faster than a line-by-line radiative transfer model with errors less than 0.5% in terms of transmissivity. A two-component approach is utilized to solve the vector radiative transfer equation (VRTE). The VRTE solver separates the phase matrices of aerosol and cloud into forward and diffuse parts and thus the solution is also separated. The forward solution can be expressed by a semi-analytical equation based on the small-angle approximation, and serves as the source of the diffuse part. The diffuse part is solved by the adding-doubling method. The adding-doubling implementation is computationally efficient because the diffuse component needs much fewer spherical function expansion terms. The simulated Stokes vector at both the TOA and the surface have comparable accuracy compared with the counterparts based on numerically rigorous methods.

Extended resolvent and inverse scattering with an application to KPI

NASA Astrophysics Data System (ADS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Prinari, B.

2003-08-01

We present in detail an extended resolvent approach for investigating linear problems associated to 2+1 dimensional integrable equations. Our presentation is based as an example on the nonstationary Schrödinger equation with potential being a perturbation of the one-soliton potential by means of a decaying two-dimensional function. Modification of the inverse scattering theory as well as properties of the Jost solutions and spectral data as follows from the resolvent approach are given.

Modeling of Graphene Planar Grating in the THz Range by the Method of Singular Integral Equations

NASA Astrophysics Data System (ADS)

Kaliberda, Mstislav E.; Lytvynenko, Leonid M.; Pogarsky, Sergey A.

2018-04-01

Diffraction of the H-polarized electromagnetic wave by the planar graphene grating in the THz range is considered. The scattering and absorption characteristics are studied. The scattered field is represented in the spectral domain via unknown spectral function. The mathematical model is based on the graphene surface impedance and the method of singular integral equations. The numerical solution is obtained by the Nystrom-type method of discrete singularities.

Solution to the Boltzmann equation for layered systems for current perpendicular to the planes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Butler, W. H.; Zhang, X.-G.; MacLaren, J. M.

2000-05-01

Present theories of giant magnetoresistance (GMR) for current perpendicular to the planes (CPP) are based on an extremely restricted solution to the Boltzmann equation that assumes a single free electron band structure for all layers and all spin channels. Within this model only the scattering rate changes from one layer to the next. This model leads to the remarkable result that the resistance of a layered material is simply the sum of the resistances of each layer. We present a solution to the Boltzmann equation for CPP for the case in which the electronic structure can be different for differentmore » layers. The problem of matching boundary conditions between layers is much more complicated than in the current in the planes (CIP) geometry because it is necessary to include the scattering-in term of the Boltzmann equation even for the case of isotropic scattering. This term couples different values of the momentum parallel to the planes. When the electronic structure is different in different layers there is an interface resistance even in the absence of intermixing of the layers. The size of this interface resistance is affected by the electronic structure, scattering rates, and thicknesses of nearby layers. For Co-Cu, the calculated interface resistance and its spin asymmetry is comparable to that measured at low temperature in sputtered samples. (c) 2000 American Institute of Physics.« less

Roy-Steiner equations for pion-nucleon scattering

NASA Astrophysics Data System (ADS)

Ditsche, C.; Hoferichter, M.; Kubis, B.; Meißner, U.-G.

2012-06-01

Starting from hyperbolic dispersion relations, we derive a closed system of Roy-Steiner equations for pion-nucleon scattering that respects analyticity, unitarity, and crossing symmetry. We work out analytically all kernel functions and unitarity relations required for the lowest partial waves. In order to suppress the dependence on the high energy regime we also consider once- and twice-subtracted versions of the equations, where we identify the subtraction constants with subthreshold parameters. Assuming Mandelstam analyticity we determine the maximal range of validity of these equations. As a first step towards the solution of the full system we cast the equations for the π π to overline N N partial waves into the form of a Muskhelishvili-Omnès problem with finite matching point, which we solve numerically in the single-channel approximation. We investigate in detail the role of individual contributions to our solutions and discuss some consequences for the spectral functions of the nucleon electromagnetic form factors.

Scattering of Lamb waves by cracks in a composite graphite fiber-reinforced epoxy plate

NASA Technical Reports Server (NTRS)

Bratton, Robert; Datta, Subhendu K.; Shah, Arvind

1990-01-01

Recent investigations of space construction techniques have explored the used of composite materials in the construction of space stations and platforms. These composites offer superior strength to weight ratio and are thermally stable. For example, a composite material being considered is laminates of graphite fibers in an epoxy matrix. The overall effective elastic constants of such a medium can be calculated from fiber and matrix properties by using an effective modulus theory as shown in Datta, el. al. The investigation of propagation and scattering of elastic waves in composite materials is necessary in order to develop an ability to characterize cracks and predict the reliability of composite structures. The objective of this investigation is the characterization of a surface breaking crack by ultrasonic techniques. In particular, the use of Lamb waves for this purpose is studied here. The Lamb waves travel through the plate, encountering a crack, and scatter. Of interest is the modeling of the scattered wave in terms of the Lamb wave modes. The direct problem of propagation and scattering of Lamb waves by a surface breaking crack has been analyzed. This would permit an experimentalist to characterize the crack by comparing the measured response to the analytical model. The plate is assumed to be infinite in the x and y directions with a constant thickness in the z direction. The top and bottom surfaces are traction free. Solving the governing wave equations and using the stress-free boundary conditions results in the dispersion equation. This equation yields the guided modes in the homogeneous plate. The theoretical model is a hybrid method that combines analytical and finite elements techniques to describe the scattered displacements. A finite region containing the defects is discretized by finite elements. Outside the local region, the far field solution is expressed as a Fourier summation of the guided modes obtained from the dispersion equation. Continuity of tractions and displacements at the boundaries of the two regions provides the necessary equations to determine the expansion coefficients and the nodal displacements. In the hybrid method used here these defects can be of arbitrary shapes as well as inclusions of different materials.

Prediction of submarine scattered noise by the acoustic analogy

NASA Astrophysics Data System (ADS)

Testa, C.; Greco, L.

2018-07-01

The prediction of the noise scattered by a submarine subject to the propeller tonal noise is here addressed through a non-standard frequency-domain formulation that extends the use of the acoustic analogy to scattering problems. A boundary element method yields the scattered pressure upon the hull surface by the solution of a boundary integral equation, whereas the noise radiated in the fluid domain is evaluated by the corresponding boundary integral representation. Propeller-induced incident pressure field on the scatterer is detected by combining an unsteady three-dimensional panel method with the Bernoulli equation. For each frequency of interest, numerical results concern with sound pressure levels upon the hull and in the flowfield. The validity of the results is established by a comparison with a time-marching hydrodynamic panel method that solves propeller and hull jointly. Within the framework of potential-flow hydrodynamics, it is found out that the scattering formulation herein proposed is appropriate to successfully capture noise magnitude and directivity both on the hull surface and in the flowfield, yielding a computationally efficient solution procedure that may be useful in preliminary design/multidisciplinary optimization applications.

Spin-scattering rates in metallic thin films measured by ferromagnetic resonance damping enhanced by spin-pumping

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boone, C. T.; Shaw, J. M.; Nembach, H. T.

2015-06-14

We determined the spin-transport properties of Pd and Pt thin films by measuring the increase in ferromagnetic resonance damping due to spin-pumping in ferromagnetic (FM)-nonferromagnetic metal (NM) multilayers with varying NM thicknesses. The increase in damping with NM thickness depends strongly on both the spin- and charge-transport properties of the NM, as modeled by diffusion equations that include both momentum- and spin-scattering parameters. We use the analytical solution to the spin-diffusion equations to obtain spin-diffusion lengths for Pt and Pd. By measuring the dependence of conductivity on NM thickness, we correlate the charge- and spin-transport parameters, and validate the applicabilitymore » of various models for momentum-scattering and spin-scattering rates in these systems: constant, inverse-proportional (Dyakanov-Perel), and linear-proportional (Elliot-Yafet). We confirm previous reports that the spin-scattering time appears to be shorter than the momentum scattering time in Pt, and the Dyakanov-Perel-like model is the best fit to the data.« less

Optimal control penalty finite elements - Applications to integrodifferential equations

NASA Astrophysics Data System (ADS)

Chung, T. J.

The application of the optimal-control/penalty finite-element method to the solution of integrodifferential equations in radiative-heat-transfer problems (Chung et al.; Chung and Kim, 1982) is discussed and illustrated. The nonself-adjointness of the convective terms in the governing equations is treated by utilizing optimal-control cost functions and employing penalty functions to constrain auxiliary equations which permit the reduction of second-order derivatives to first order. The OCPFE method is applied to combined-mode heat transfer by conduction, convection, and radiation, both without and with scattering and viscous dissipation; the results are presented graphically and compared to those obtained by other methods. The OCPFE method is shown to give good results in cases where standard Galerkin FE fail, and to facilitate the investigation of scattering and dissipation effects.

Nonlinear ion acoustic waves scattered by vortexes

NASA Astrophysics Data System (ADS)

Ohno, Yuji; Yoshida, Zensho

2016-09-01

The Kadomtsev-Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold (leaf) embedded in a larger phase space of more general ion acoustic waves (low-frequency electrostatic perturbations). The KP hierarchy is characterized not only by small amplitudes but also by irrotational (zero-vorticity) velocity fields. In fact, the KP equation is derived by eliminating vorticity at every order of the reductive perturbation. Here, we modify the scaling of the velocity field so as to introduce a vortex term. The newly derived system of equations consists of a generalized three-dimensional KP equation and a two-dimensional vortex equation. The former describes 'scattering' of vortex-free waves by ambient vortexes that are determined by the latter. We say that the vortexes are 'ambient' because they do not receive reciprocal reactions from the waves (i.e., the vortex equation is independent of the wave fields). This model describes a minimal departure from the integrable KP system. By the Painlevé test, we delineate how the vorticity term violates integrability, bringing about an essential three-dimensionality to the solutions. By numerical simulation, we show how the solitons are scattered by vortexes and become chaotic.

A single-sided representation for the homogeneous Green's function of a unified scalar wave equation.

PubMed

Wapenaar, Kees

2017-06-01

A unified scalar wave equation is formulated, which covers three-dimensional (3D) acoustic waves, 2D horizontally-polarised shear waves, 2D transverse-electric EM waves, 2D transverse-magnetic EM waves, 3D quantum-mechanical waves and 2D flexural waves. The homogeneous Green's function of this wave equation is a combination of the causal Green's function and its time-reversal, such that their singularities at the source position cancel each other. A classical representation expresses this homogeneous Green's function as a closed boundary integral. This representation finds applications in holographic imaging, time-reversed wave propagation and Green's function retrieval by cross correlation. The main drawback of the classical representation in those applications is that it requires access to a closed boundary around the medium of interest, whereas in many practical situations the medium can be accessed from one side only. Therefore, a single-sided representation is derived for the homogeneous Green's function of the unified scalar wave equation. Like the classical representation, this single-sided representation fully accounts for multiple scattering. The single-sided representation has the same applications as the classical representation, but unlike the classical representation it is applicable in situations where the medium of interest is accessible from one side only.

Nonlinear Wave Propagation

DTIC Science & Technology

1989-05-22

multidimensional systems of physi- cal significance. Prototypes are the Kadomtsev - Petviashvili and Davey-Stewartson equations . The nature of the boundary value...Ono equation bears many similarities to multidimensional problems, specifically the Kadomtsev - Petviashvili equation . In some sense the nonlocality...Inverse scattering and Direct Linearizing Transforms for the Kadomtsev - Petviashvili Equations , A.S. Fokas, and M.J. Ablowitz, Phys. Lett. Vol., 94A, No. 2

FAST TRACK COMMUNICATION Time-dependent exact solutions of the nonlinear Kompaneets equation

NASA Astrophysics Data System (ADS)

Ibragimov, N. H.

2010-12-01

Time-dependent exact solutions of the Kompaneets photon diffusion equation are obtained for several approximations of this equation. One of the approximations describes the case when the induced scattering is dominant. In this case, the Kompaneets equation has an additional symmetry which is used for constructing some exact solutions as group invariant solutions.

Method for measuring multiple scattering corrections between liquid scintillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Verbeke, J. M.; Glenn, A. M.; Keefer, G. J.

2016-04-11

In this study, a time-of-flight method is proposed to experimentally quantify the fractions of neutrons scattering between scintillators. An array of scintillators is characterized in terms of crosstalk with this method by measuring a californium source, for different neutron energy thresholds. The spectral information recorded by the scintillators can be used to estimate the fractions of neutrons multiple scattering. With the help of a correction to Feynman's point model theory to account for multiple scattering, these fractions can in turn improve the mass reconstruction of fissile materials under investigation.

Huygens-Fresnel picture for electron-molecule elastic scattering★

NASA Astrophysics Data System (ADS)

Baltenkov, Arkadiy S.; Msezane, Alfred Z.

2017-11-01

The elastic scattering cross sections for a slow electron by C2 and H2 molecules have been calculated within the framework of the non-overlapping atomic potential model. For the amplitudes of the multiple electron scattering by a target the wave function of the molecular continuum is represented as a combination of a plane wave and two spherical waves generated by the centers of atomic spheres. This wave function obeys the Huygens-Fresnel principle according to which the electron wave scattering by a system of two centers is accompanied by generation of two spherical waves; their interaction creates a diffraction pattern far from the target. Each of the Huygens waves, in turn, is a superposition of the partial spherical waves with different orbital angular momenta l and their projections m. The amplitudes of these partial waves are defined by the corresponding phases of electron elastic scattering by an isolated atomic potential. In numerical calculations the s- and p-phase shifts are taken into account. So the number of interfering electron waves is equal to eight: two of which are the s-type waves and the remaining six waves are of the p-type with different m values. The calculation of the scattering amplitudes in closed form (rather than in the form of S-matrix expansion) is reduced to solving a system of eight inhomogeneous algebraic equations. The differential and total cross sections of electron scattering by fixed-in-space molecules and randomly oriented ones have been calculated as well. We conclude by discussing the special features of the S-matrix method for the case of arbitrary non-spherical potentials. Contribution to the Topical Issue "Low energy positron and electron interactions", edited by James Sullivan, Ron White, Michael Bromley, Ilya Fabrikant, and David Cassidy.

CSDP: The seismology of continental thermal regimes

NASA Astrophysics Data System (ADS)

Aki, K.

1991-05-01

The past year continued to be extremely productive following up two major breakthroughs made in the preceding year. One of the breakthroughs was the derivation of an integral equation for time-dependent power spectra, which unified all the existing theories on seismic scattering including the radiative transfer theory for total energy and single-multiple scattering theories based on the ray approach. We successfully applied the method to the data from the United States Geological Survey (USGS) regional seismic arrays in central California, Long Valley and Island of Hawaii, and obtained convincing results on the scattering Q(sup -1) and intrinsic Q(sup -1) in these areas for the frequency range from 1 Hz to 20 Hz. The frequency dependence of scattering Q(sup -1) is, then, interpreted in terms of random medium with continuous or discrete scatterers. The other breakthrough was the application of T-matrix formulation to the seismic scattering problem. We are currently working on two dimensional inclusions with high and low velocity contrast with the surrounding medium. In addition to the above two main lines of research, we were able to use so-called 'T-phase' observed on the Island of Hawaii to map the Q value with a good spatial resolution. The T-phase is seismic waves converted from acoustic waves propagated through the sofar channel of the ocean. We found that we can eliminate remarkably well the frequency dependent recording site effect from the T-phase amplitude using the amplification factor for coda waves, further confirming the fundamental separability of source, path and site effects for coda waves, and proving the effectiveness of stochastic modeling of high-frequency seismic waves.

Trajectory-based understanding of the quantum-classical transition for barrier scattering

NASA Astrophysics Data System (ADS)

Chou, Chia-Chun

2018-06-01

The quantum-classical transition of wave packet barrier scattering is investigated using a hydrodynamic description in the framework of a nonlinear Schrödinger equation. The nonlinear equation provides a continuous description for the quantum-classical transition of physical systems by introducing a degree of quantumness. Based on the transition equation, the transition trajectory formalism is developed to establish the connection between classical and quantum trajectories. The quantum-classical transition is then analyzed for the scattering of a Gaussian wave packet from an Eckart barrier and the decay of a metastable state. Computational results for the evolution of the wave packet and the transmission probabilities indicate that classical results are recovered when the degree of quantumness tends to zero. Classical trajectories are in excellent agreement with the transition trajectories in the classical limit, except in some regions where transition trajectories cannot cross because of the single-valuedness of the transition wave function. As the computational results demonstrate, the process that the Planck constant tends to zero is equivalent to the gradual removal of quantum effects originating from the quantum potential. This study provides an insightful trajectory interpretation for the quantum-classical transition of wave packet barrier scattering.

SFDBSI_GLS v. 1.0

DOE Office of Scientific and Technical Information (OSTI.GOV)

Poppeliers, Christian

Matlab code for inversion of frequency domain, electrostatic geophysical data in terms of scalar scattering amplitudes in the subsurface. The data is assumed to be the difference between two measurements: electric field measurements prior to the injection of an electrically conductive proppant, and the electric field measurements after proppant injection. The proppant is injected into the subsurface via a well, and its purpose is to prop open fractures created by hydraulic fracturing. In both cases the illuminating electric field is assumed to be a vertically incident plane wave. The inversion strategy is to solve a set of linear system ofmore » equations, where each equation defines the amplitude of a candidate scattering volume. The model space is defined by M potential scattering locations and the frequency domain (of which there are k frequencies) data are recorded on N receivers. The solution thus solves a kN x M system of linear equations for M scalar amplitudes within the user-defined solution space. Practical Application: Oilfield environments where observed electrostatic geophysical data can reasonably be assumed to be scattered by subsurface proppant volumes. No field validation examples have so far been provided.« less

Volume integral equation for electromagnetic scattering: Rigorous derivation and analysis for a set of multilayered particles with piecewise-smooth boundaries in a passive host medium

NASA Astrophysics Data System (ADS)

Yurkin, Maxim A.; Mishchenko, Michael I.

2018-04-01

We present a general derivation of the frequency-domain volume integral equation (VIE) for the electric field inside a nonmagnetic scattering object from the differential Maxwell equations, transmission boundary conditions, radiation condition at infinity, and locally-finite-energy condition. The derivation applies to an arbitrary spatially finite group of particles made of isotropic materials and embedded in a passive host medium, including those with edges, corners, and intersecting internal interfaces. This is a substantially more general type of scatterer than in all previous derivations. We explicitly treat the strong singularity of the integral kernel, but keep the entire discussion accessible to the applied scattering community. We also consider the known results on the existence and uniqueness of VIE solution and conjecture a general sufficient condition for that. Finally, we discuss an alternative way of deriving the VIE for an arbitrary object by means of a continuous transformation of the everywhere smooth refractive-index function into a discontinuous one. Overall, the paper examines and pushes forward the state-of-the-art understanding of various analytical aspects of the VIE.

Mixed Quantum/Classical Theory for Molecule-Molecule Inelastic Scattering: Derivations of Equations and Application to N2 + H2 System.

PubMed

Semenov, Alexander; Babikov, Dmitri

2015-12-17

The mixed quantum classical theory, MQCT, for inelastic scattering of two molecules is developed, in which the internal (rotational, vibrational) motion of both collision partners is treated with quantum mechanics, and the molecule-molecule scattering (translational motion) is described by classical trajectories. The resultant MQCT formalism includes a system of coupled differential equations for quantum probability amplitudes, and the classical equations of motion in the mean-field potential. Numerical tests of this theory are carried out for several most important rotational state-to-state transitions in the N2 + H2 system, in a broad range of collision energies. Besides scattering resonances (at low collision energies) excellent agreement with full-quantum results is obtained, including the excitation thresholds, the maxima of cross sections, and even some smaller features, such as slight oscillations of energy dependencies. Most importantly, at higher energies the results of MQCT are nearly identical to the full quantum results, which makes this approach a good alternative to the full-quantum calculations that become computationally expensive at higher collision energies and for heavier collision partners. Extensions of this theory to include vibrational transitions or general asymmetric-top rotor (polyatomic) molecules are relatively straightforward.

Volterra integral equation-factorisation method and nucleus-nucleus elastic scattering

NASA Astrophysics Data System (ADS)

Laha, U.; Majumder, M.; Bhoi, J.

2018-04-01

An approximate solution for the nuclear Hulthén plus atomic Hulthén potentials is constructed by solving the associated Volterra integral equation by series substitution method. Within the framework of supersymmetry-inspired factorisation method, this solution is exploited to construct higher partial wave interactions. The merit of our approach is examined by computing elastic scattering phases of the α {-}α system by the judicious use of phase function method. Reasonable agreements in phase shifts are obtained with standard data.

Simultaneous inversion of intrinsic and scattering attenuation parameters incorporating multiple scattering effect

NASA Astrophysics Data System (ADS)

Ogiso, M.

2017-12-01

Heterogeneous attenuation structure is important for not only understanding the earth structure and seismotectonics, but also ground motion prediction. Attenuation of ground motion in high frequency range is often characterized by the distribution of intrinsic and scattering attenuation parameters (intrinsic Q and scattering coefficient). From the viewpoint of ground motion prediction, both intrinsic and scattering attenuation affect the maximum amplitude of ground motion while scattering attenuation also affect the duration time of ground motion. Hence, estimation of both attenuation parameters will lead to sophisticate the ground motion prediction. In this study, we try to estimate both parameters in southwestern Japan in a tomographic manner. We will conduct envelope fitting of seismic coda since coda has sensitivity to both intrinsic attenuation and scattering coefficients. Recently, Takeuchi (2016) successfully calculated differential envelope when these parameters have fluctuations. We adopted his equations to calculate partial derivatives of these parameters since we did not need to assume homogeneous velocity structure. Matrix for inversion of structural parameters would become too huge to solve in a straightforward manner. Hence, we adopted ART-type Bayesian Reconstruction Method (Hirahara, 1998) to project the difference of envelopes to structural parameters iteratively. We conducted checkerboard reconstruction test. We assumed checkerboard pattern of 0.4 degree interval in horizontal direction and 20 km in depth direction. Reconstructed structures well reproduced the assumed pattern in shallower part while not in deeper part. Since the inversion kernel has large sensitivity around source and stations, resolution in deeper part would be limited due to the sparse distribution of earthquakes. To apply the inversion method which described above to actual waveforms, we have to correct the effects of source and site amplification term. We consider these issues to estimate the actual intrinsic and scattering structures of the target region.Acknowledgment We used the waveforms of Hi-net, NIED. This study was supported by the Earthquake Research Institute of the University of Tokyo cooperative research program.

Electrical transport, electrothermal transport, and effective electron mass in single-crystalline In2O3 films

NASA Astrophysics Data System (ADS)

Preissler, Natalie; Bierwagen, Oliver; Ramu, Ashok T.; Speck, James S.

2013-08-01

A comprehensive study of the room-temperature electrical and electrothermal transport of single-crystalline indium oxide (In2O3) and indium tin oxide (ITO) films over a wide range of electron concentrations is reported. We measured the room-temperature Hall mobility μH and Seebeck coefficient S of unintentionally doped and Sn-doped high-quality, plasma-assisted molecular-beam-epitaxy-grown In2O3 for volume Hall electron concentrations nH from 7×1016 cm-3 (unintentionally doped) to 1×1021 cm-3 (highly Sn-doped, ITO). The resulting empirical S(nH) relation can be directly used in other In2O3 samples to estimate the volume electron concentration from simple Seebeck coefficient measurements. The mobility and Seebeck coefficient were modeled by a numerical solution of the Boltzmann transport equation. Ionized impurity scattering and polar optical phonon scattering were found to be the dominant scattering mechanisms. Acoustic phonon scattering was found to be negligible. Fitting the temperature-dependent mobility above room temperature of an In2O3 film with high mobility allowed us to find the effective Debye temperature (ΘD=700 K) and number of phonon modes (NOPML=1.33) that best describe the polar optical phonon scattering. The modeling also yielded the Hall scattering factor rH as a function of electron concentration, which is not negligible (rH≈1.4) at nondegenerate electron concentrations. Fitting the Hall-scattering-factor corrected concentration-dependent Seebeck coefficient S(n) for nondegenerate samples to the numerical solution of the Boltzmann transport equation and to widely used, simplified equations allowed us to extract an effective electron mass of m*=(0.30±0.03)me (with free electron mass me). The modeled mobility and Seebeck coefficient based on polar optical phonon and ionized impurity scattering describes the experimental results very accurately up to electron concentrations of 1019 cm-3, and qualitatively explains a mobility plateau or local maximum around 1020 cm-3. Ionized impurity scattering with doubly charged donors best describes the mobility in our unintentionally doped films, consistent with oxygen vacancies as unintentional shallow donors, whereas singly charged donors best describe our Sn-doped films. Our modeling yields a (phonon-limited) maximum theoretical drift mobility and Hall mobility of μ=190 cm2/Vs and μH=270 cm2/Vs, respectively. Simplified equations for the Seebeck coefficient describe the measured values in the nondegenerate regime using a Seebeck scattering parameter of r=-0.55 (which is consistent with the determined Debye temperature), and provide an estimate of the Seebeck coefficient to lower electron concentrations. The simplified equations fail to describe the Seebeck coefficient around the Mott transition (nMott=5.5×1018 cm-3) from nondegenerate to degenerate electron concentrations, whereas the numerical modeling accurately describes this region.

Book Review: Book review

NASA Astrophysics Data System (ADS)

Mishchenko, Michael I.

2017-01-01

The second - revised and enlarged - edition of this popular monograph is co-authored by Michael Kahnert and is published as Volume 145 of the Springer Series in Optical Sciences. As in the first edition, the main emphasis is on the mathematics of electromagnetic scattering and on numerically exact computer solutions of the frequency-domain macroscopic Maxwell equations for particles with complex shapes. The book is largely centered on Green-function solution of relevant boundary value problems and the T-matrix methodology, although other techniques (the method of lines, integral equation methods, and Lippmann-Schwinger equations) are also covered. The first four chapters serve as a thorough overview of key theoretical aspects of electromagnetic scattering intelligible to readers with undergraduate training in mathematics. A separate chapter provides an instructive analysis of the Rayleigh hypothesis which is still viewed by many as a highly controversial aspect of electromagnetic scattering by nonspherical objects. Another dedicated chapter introduces basic quantities serving as optical observables in practical applications. A welcome extension of the first edition is the new chapter on group theoretical aspects of electromagnetic scattering by particles with discrete symmetries. An essential part of the book is the penultimate chapter describing in detail popular public-domain computer programs mieschka and Tsym which can be applied to a wide range of particle shapes. The final chapter provides a general overview of available literature on electromagnetic scattering by particles and gives useful reading advice.

Simple analysis of scattering data with the Ornstein-Zernike equation

NASA Astrophysics Data System (ADS)

Kats, E. I.; Muratov, A. R.

2018-01-01

In this paper we propose and explore a method of analysis of the scattering experimental data for uniform liquidlike systems. In our pragmatic approach we are not trying to introduce by hands an artificial small parameter to work out a perturbation theory with respect to the known results, e.g., for hard spheres or sticky hard spheres (all the more that in the agreement with the notorious Landau statement, there is no physical small parameter for liquids). Instead of it being guided by the experimental data we are solving the Ornstein-Zernike equation with a trial (variational) form of the interparticle interaction potential. To find all needed correlation functions this variational input is iterated numerically to satisfy the Ornstein-Zernike equation supplemented by a closure relation. Our method is developed for spherically symmetric scattering objects, and our numeric code is written for such a case. However, it can be extended (at the expense of more involved computations and a larger amount of required experimental input information) for nonspherical particles. What is important for our approach is that it is sufficient to know experimental data in a relatively narrow range of the scattering wave vectors (q ) to compute the static structure factor in a much broader range of q . We illustrate by a few model and real experimental examples of the x-ray and neutron scattering data how the approach works.

A Backscattering Enhanced Microwave Canopy Scattering Model Based On MIMICS

NASA Astrophysics Data System (ADS)

Shen, X.; Hong, Y.; Qin, Q.; Chen, S.; Grout, T.

2010-12-01

For modeling microwave scattering of vegetated areas, several microwave canopy scattering models, based on the vectorized radiative transfer equation (VRT) that use different solving techniques, have been proposed in the past three decades. As an iterative solution of VRT at low orders, the Michigan Microwave Canopy Scattering Model (MIMICS) gives an analytical expression for calculating scattering as long as the volume scattering is not too strong. The most important usage of such models is to predict scattering in the backscattering direction. Unfortunately, the simplified assumption of MIMICS is that the scattering between the ground and trunk layers only includes the specular reflection. As a result, MIMICS includes a dominant coherent term which vanishes in the backscattering direction because this term contains a delta function factor of zero in this direction. This assumption needs reconsideration for accurately calculating the backscattering. In the framework of MIMICS, any incoherent terms that involve surface scattering factors must at least undergo surface scattering twice and volume scattering once. Therefore, these incoherent terms are usually very weak. On the other hand, due to the phenomenon of backscattering enhancement, the surface scattering in the backscattering direction is very strong compared to most other directions. Considering the facts discussed above, it is reasonable to add a surface backscattering term to the last equation of the boundary conditions of MIMICS. More terms appear in the final result including a backscattering coherent term which enhances the backscattering. The modified model is compared with the original MIMICS (version 1.0) using JPL/AIRSAR data from NASA Campaign Soil Moisture Experimental 2003 (SMEX03) and Washita92. Significant improvement is observed.

Diffuse reflectance relations based on diffusion dipole theory for large absorption and reduced scattering

NASA Astrophysics Data System (ADS)

Bremmer, Rolf H.; van Gemert, Martin J. C.; Faber, Dirk J.; van Leeuwen, Ton G.; Aalders, Maurice C. G.

2013-08-01

Diffuse reflectance spectra are used to determine the optical properties of biological samples. In medicine and forensic science, the turbid objects under study often possess large absorption and/or scattering properties. However, data analysis is frequently based on the diffusion approximation to the radiative transfer equation, implying that it is limited to tissues where the reduced scattering coefficient dominates over the absorption coefficient. Nevertheless, up to absorption coefficients of 20 m at reduced scattering coefficients of 1 and 11.5 mm-1, we observed excellent agreement (r2=0.994) between reflectance measurements of phantoms and the diffuse reflectance equation proposed by Zonios et al. [Appl. Opt. 38, 6628-6637 (1999)], derived as an approximation to one of the diffusion dipole equations of Farrell et al. [Med. Phys. 19, 879-888 (1992)]. However, two parameters were fitted to all phantom experiments, including strongly absorbing samples, implying that the reflectance equation differs from diffusion theory. Yet, the exact diffusion dipole approximation at high reduced scattering and absorption also showed agreement with the phantom measurements. The mathematical structure of the diffuse reflectance relation used, derived by Zonios et al. [Appl. Opt. 38, 6628-6637 (1999)], explains this observation. In conclusion, diffuse reflectance relations derived as an approximation to the diffusion dipole theory of Farrell et al. can analyze reflectance ratios accurately, even for much larger absorption than reduced scattering coefficients. This allows calibration of fiber-probe set-ups so that the object's diffuse reflectance can be related to its absorption even when large. These findings will greatly expand the application of diffuse reflection spectroscopy. In medicine, it may allow the use of blue/green wavelengths and measurements on whole blood, and in forensic science, it may allow inclusion of objects such as blood stains and cloth at crime scenes.

Relativistic optical model on the basis of the Moscow potential and lower phase shifts for nucleon-nucleon scattering at laboratory energies of up to 3 GeV

DOE Office of Scientific and Technical Information (OSTI.GOV)

Knyr, V. A.; Neudatchin, V. G.; Khokhlov, N. A.

Data of a partial-wave analysis of nucleon-nucleon scattering at energies of up to E{sub lab} = 3 GeV (lower partial waves) and the properties of the deuteron are described within the relativistic optical model based on deep attractive quasipotentials involving forbidden states (as exemplified by the Moscow potential). Partial-wave potentials are derived by the inverse-scattering-problem method based on the Marchenko equation by using present-day data from the partial-wave analysis of nucleon-nucleon scattering at energies of up to 3 GeV. Channel coupling is taken into account. The imaginary parts of the potentials are deduced from the phase equation of the variable-phasemore » approach. The general situation around the manifestation of quark effects in nucleon-nucleon interaction is discussed.« less

Effect of the scattering delay on time-dependent photon migration in turbid media.

PubMed

Yaroslavsky, I V; Yaroslavsky, A N; Tuchin, V V; Schwarzmaier, H J

1997-09-01

We modified the diffusion approximation of the time-dependent radiative transfer equation to account for a finite scattering delay time. Under the usual assumptions of the diffusion approximation, the effect of the scattering delay leads to a simple renormalization of the light velocity that appears in the diffusion equation. Accuracy of the model was evaluated by comparison with Monte Carlo simulations in the frequency domain for a semi-infinite geometry. A good agreement is demonstrated for both matched and mismatched boundary conditions when the distance from the source is sufficiently large. The modified diffusion model predicts that the neglect of the scattering delay when the optical properties of the turbid material are derived from normalized frequency- or time-domain measurements should result in an underestimation of the absorption coefficient and an overestimation of the transport coefficient. These observations are consistent with the published experimental data.

The loss rates of O+ in the inner magnetosphere caused by both magnetic field line curvature scattering and charge exchange reactions

NASA Astrophysics Data System (ADS)

Ji, Y.; Shen, C.

2014-03-01

With consideration of magnetic field line curvature (FLC) pitch angle scattering and charge exchange reactions, the O+ (>300 keV) in the inner magnetosphere loss rates are investigated by using an eigenfunction analysis. The FLC scattering provides a mechanism for the ring current O+ to enter the loss cone and influence the loss rates caused by charge exchange reactions. Assuming that the pitch angle change is small for each scattering event, the diffusion equation including a charge exchange term is constructed and solved; the eigenvalues of the equation are identified. The resultant loss rates of O+ are approximately equal to the linear superposition of the loss rate without considering the charge exchange reactions and the loss rate associated with charge exchange reactions alone. The loss time is consistent with the observations from the early recovery phases of magnetic storms.

A simple quantum mechanical treatment of scattering in nanoscale transistors

NASA Astrophysics Data System (ADS)

Venugopal, R.; Paulsson, M.; Goasguen, S.; Datta, S.; Lundstrom, M. S.

2003-05-01

We present a computationally efficient, two-dimensional quantum mechanical simulation scheme for modeling dissipative electron transport in thin body, fully depleted, n-channel, silicon-on-insulator transistors. The simulation scheme, which solves the nonequilibrium Green's function equations self consistently with Poisson's equation, treats the effect of scattering using a simple approximation inspired by the "Büttiker probes," often used in mesoscopic physics. It is based on an expansion of the active device Hamiltonian in decoupled mode space. Simulation results are used to highlight quantum effects, discuss the physics of scattering and to relate the quantum mechanical quantities used in our model to experimentally measured low field mobilities. Additionally, quantum boundary conditions are rigorously derived and the effects of strong off-equilibrium transport are examined. This paper shows that our approximate treatment of scattering, is an efficient and useful simulation method for modeling electron transport in nanoscale, silicon-on-insulator transistors.

Finite element solution of transient fluid-structure interaction problems

NASA Technical Reports Server (NTRS)

Everstine, Gordon C.; Cheng, Raymond S.; Hambric, Stephen A.

1991-01-01

A finite element approach using NASTRAN is developed for solving time-dependent fluid-structure interaction problems, with emphasis on the transient scattering of acoustic waves from submerged elastic structures. Finite elements are used for modeling both structure and fluid domains to facilitate the graphical display of the wave motion through both media. For the liquid, the use of velocity potential as the fundamental unknown results in a symmetric matrix equation. The approach is illustrated for the problem of transient scattering from a submerged elastic spherical shell subjected to an incident tone burst. The use of an analogy between the equations of elasticity and the wave equation of acoustics, a necessary ingredient to the procedure, is summarized.

Numerical heat transfer study in a scattering, absorbing and emitting semi-transparent porous medium in a cylindrical enclosure

NASA Astrophysics Data System (ADS)

Timoumi, M.; Chérif, B.; Sifaoui, M. S.

2005-12-01

In this paper, heat transfer problem through a semi-transparent porous medium in a cylindrical enclosure is investigated. The governing equations for this problem and the boundary conditions are non-linear differential equations depending on the dimensionless radial coordinate, Planck number N, scattering albedo ω, walls emissivity and thermal conductivity ratio kr. The set of differential equations are solved by a numerical technique taken from the IMSL MATH/LIBRARY. Various results are obtained for the dimensionless temperature profiles in the solid and fluid phases and the radiative heat flux. The effects of some radiative properties of the medium on the heat transfer rate are examined.

Direct time integration of Maxwell's equations in linear dispersive media with absorption for scattering and propagation of femtosecond electromagnetic pulses

NASA Technical Reports Server (NTRS)

Joseph, Rose M.; Hagness, Susan C.; Taflove, Allen

1991-01-01

The initial results for femtosecond pulse propagation and scattering interactions for a Lorentz medium obtained by a direct time integration of Maxwell's equations are reported. The computational approach provides reflection coefficients accurate to better than 6 parts in 10,000 over the frequency range of dc to 3 x 10 to the 16th Hz for a single 0.2-fs Gaussian pulse incident upon a Lorentz-medium half-space. New results for Sommerfeld and Brillouin precursors are shown and compared with previous analyses. The present approach is robust and permits 2D and 3D electromagnetic pulse propagation directly from the full-vector Maxwell's equations.

Multiple-Fiber-Optic Probe For Light-Scattering Measurements

NASA Technical Reports Server (NTRS)

Dhadwal, Harbans Singh; Ansari, Rafat R.

1996-01-01

Multiple-fiber-optical probe developed for use in measuring light scattered at various angles from specimens of materials. Designed for both static and dynamic light-scattering measurements of colloidal dispersions. Probe compact, rugged unit containing no moving parts and remains stationary during operation. Not restricted to operation in controlled, research-laboratory environment. Positioned inside or outside light-scattering chamber. Provides simultaneous measurements at small angular intervals over range of angles, made to include small scattering angles by orienting probe in appropriate direction.

A momentum-space formulation without partial wave decomposition for scattering of two spin-half particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fachruddin, Imam, E-mail: imam.fachruddin@sci.ui.ac.id; Salam, Agus

2016-03-11

A new momentum-space formulation for scattering of two spin-half particles, both either identical or unidentical, is formulated. As basis states the free linear-momentum states are not expanded into the angular-momentum states, the system’s spin states are described by the product of the spin states of the two particles, and the system’s isospin states by the total isospin states of the two particles. We evaluate the Lippmann-Schwinger equations for the T-matrix elements in these basis states. The azimuthal behavior of the potential and of the T-matrix elements leads to a set of coupled integral equations for the T-matrix elements in twomore » variables only, which are the magnitude of the relative momentum and the scattering angle. Some symmetry relations for the potential and the T-matrix elements reduce the number of the integral equations to be solved. A set of six spin operators to express any interaction of two spin-half particles is introduced. We show the spin-averaged differential cross section as being calculated in terms of the solution of the set of the integral equations.« less

Stimulated scattering of electromagnetic waves carrying orbital angular momentum in quantum plasmas.

PubMed

Shukla, P K; Eliasson, B; Stenflo, L

2012-07-01

We investigate stimulated scattering instabilities of coherent circularly polarized electromagnetic (CPEM) waves carrying orbital angular momentum (OAM) in dense quantum plasmas with degenerate electrons and nondegenerate ions. For this purpose, we employ the coupled equations for the CPEM wave vector potential and the driven (by the ponderomotive force of the CPEM waves) equations for the electron and ion plasma oscillations. The electrons are significantly affected by the quantum forces (viz., the quantum statistical pressure, the quantum Bohm potential, as well as the electron exchange and electron correlations due to electron spin), which are included in the framework of the quantum hydrodynamical description of the electrons. Furthermore, our investigation of the stimulated Brillouin instability of coherent CPEM waves uses the generalized ion momentum equation that includes strong ion coupling effects. The nonlinear equations for the coupled CPEM and quantum plasma waves are then analyzed to obtain nonlinear dispersion relations which exhibit stimulated Raman, stimulated Brillouin, and modulational instabilities of CPEM waves carrying OAM. The present results are useful for understanding the origin of scattered light off low-frequency density fluctuations in high-energy density plasmas where quantum effects are eminent.

Two-Flux Method for Transient Radiative Transfer in a Semitransparent Layer

NASA Technical Reports Server (NTRS)

Siegel, Robert

1996-01-01

The two-flux method was used to obtain transient solutions for a plane layer including internal reflections and scattering. The layer was initially at uniform temperature, and was heated or cooled by external radiation and convection. The two-flux equations were examined as a means for evaluating the radiative flux gradient in the transient energy equation. Comparisons of transient temperature distributions using the two-flux method were made with results where the radiative flux gradient was evaluated from the exact radiative transfer equations. Good agreement was obtained for optical thicknesses from 0.5 to 5 and for refractive indices of 1 and 2. Illustrative results obtained with the two-flux method demonstrate the effect of isotropic scattering coupled with changing the refractive index. For small absorption with large scattering the maximum layer temperature is increased when the refractive index is increased. For larger absorption the effect is opposite, and the maximum temperature decreases with increased refractive index .

In vivo diagnosis of skin cancer using polarized and multiple scattered light spectroscopy

NASA Astrophysics Data System (ADS)

Bartlett, Matthew Allen

This thesis research presents the development of a non-invasive diagnostic technique for distinguishing between skin cancer, moles, and normal skin using polarized and multiple scattered light spectroscopy. Polarized light incident on the skin is single scattered by the epidermal layer and multiple scattered by the dermal layer. The epidermal light maintains its initial polarization while the light from the dermal layer becomes randomized and multiple scattered. Mie theory was used to model the epidermal light as the scattering from the intercellular organelles. The dermal signal was modeled as the diffusion of light through a localized semi-homogeneous volume. These models were confirmed using skin phantom experiments, studied with in vitro cell cultures, and applied to human skin for in vivo testing. A CCD-based spectroscopy system was developed to perform all these experiments. The probe and the theory were tested on skin phantoms of latex spheres on top of a solid phantom. We next extended our phantom study to include in vitro cells on top of the solid phantom. Optical fluorescent microscope images revealed at least four distinct scatterers including mitochondria, nucleoli, nuclei, and cell membranes. Single scattering measurements on the mammalian cells consistently produced PSD's in the size range of the mitochondria. The clinical portion of the study consisted of in vivo measurements on cancer, mole, and normal skin spots. The clinical study combined the single scattering model from the phantom and in vitro cell studies with the diffusion model for multiple scattered light. When parameters from both layers were combined, we found that a sensitivity of 100% and 77% can be obtained for detecting cancers and moles, respectively, given the number of lesions examined.

Equations for Estimating the Strength of TV Signals Scattered by Wind Turbines

NASA Technical Reports Server (NTRS)

Spera, David A.; Sengupta, Dipak L.

1994-01-01

During the late 1970's and early 1980's, concerns about the potential interference of wind turbine generators with electromagnetic communication signals led to a series of research studies, both in the laboratory and in the field, conducted by the staff of the University of Michigan Radiation Laboratory. These studies were sponsored by organizations such as the U.S. Department of Energy, the Solar Energy Research Institute, and private developers of wind power stations. Research objectives were to identify the mechanisms by which wind turbines might adversely affect communication signals, estimate the severity of these effects for different types of signals (e.g. television, radio, microwave, and navigation), and formulate mathematical models with which to predict the sizes of potential interference zones around wind turbines and wind power plants. This work formed the basis for preliminary standards on assessing electromagnetic interference (EMI) by wind turbines. With the current renewal of interest in wind energy projects, it is appropriate that the many experimental and analytical aspects of this pioneering work be reviewed and correlated. The purpose of this study is to combine test data and theory from previously published and unpublished research reports into a unified and consistent set of equations which are useful for estimating potential levels of television interference from wind turbines. To be comprehensive, these equations will include both horizontal-axis and vertical-axis wind turbines (HAWT's and VAWT's), blade configuration parameters (e.g. number, size, material, twist, and coning), signal frequency and power, and directional characteristics of the receiving antenna. The approach that is followed in this report is as follows. First, some basic equations that describe electromagnetic signals with interference are presented without detailed derivations, since the latter are available in the references. Minor changes in terminology are made for purposes of consistency. Next, the concept of a signal scatter ratio is introduced, which defines the fraction of the signal impinging on a wind turbine that is scattered by its blades onto a nearby receiver. Equations from references are modified for the calculation of experimental scatter ratios (from measured signals containing interference) and idealized scatter ratios (from rotor characteristics and relative locations of the transmitter, the turbine, and the receiver). Experimental and idealized scatter ratios are then calculated and compared for 75 cases from the literature, in which TVI measurements were made around a variety of wind turbines. An empirical equation is then defined for estimating the probability that an actual scatter ratio will differ from an idealized ratio by a given amount. Finally a sample calculation of the size of a potential TV interference zone around a hypothetical wind power station is presented.

Effects of absorption on multiple scattering by random particulate media: exact results.

PubMed

Mishchenko, Michael I; Liu, Li; Hovenier, Joop W

2007-10-01

We employ the numerically exact superposition T-matrix method to perform extensive computations of elec nottromagnetic scattering by a volume of discrete random medium densely filled with increasingly absorbing as well as non-absorbing particles. Our numerical data demonstrate that increasing absorption diminishes and nearly extinguishes certain optical effects such as depolarization and coherent backscattering and increases the angular width of coherent backscattering patterns. This result corroborates the multiple-scattering origin of such effects and further demonstrates the heuristic value of the concept of multiple scattering even in application to densely packed particulate media.

Microscopic modeling of gas-surface scattering. I. A combined molecular dynamics-rate equation approach

NASA Astrophysics Data System (ADS)

Filinov, A.; Bonitz, M.; Loffhagen, D.

2018-06-01

A combination of first principle molecular dynamics (MD) simulations with a rate equation model (MD-RE approach) is presented to study the trapping and the scattering of rare gas atoms from metal surfaces. The temporal evolution of the atom fractions that are either adsorbed or scattered into the continuum is investigated in detail. We demonstrate that for this description one has to consider trapped, quasi-trapped and scattering states, and present an energetic definition of these states. The rate equations contain the transition probabilities between the states. We demonstrate how these rate equations can be derived from kinetic theory. Moreover, we present a rigorous way to determine the transition probabilities from a microscopic analysis of the particle trajectories generated by MD simulations. Once the system reaches quasi-equilibrium, the rates converge to stationary values, and the subsequent thermal adsorption/desorption dynamics is completely described by the rate equations without the need to perform further time-consuming MD simulations. As a proof of concept of our approach, MD simulations for argon atoms interacting with a platinum (111) surface are presented. A detailed deterministic trajectory analysis is performed, and the transition rates are constructed. The dependence of the rates on the incidence conditions and the lattice temperature is analyzed. Based on this example, we analyze the time scale of the gas-surface system to approach the quasi-stationary state. The MD-RE model has great relevance for the plasma-surface modeling as it makes an extension of accurate simulations to long, experimentally relevant time scales possible. Its application to the computation of atomic sticking probabilities is given in the second part (paper II).

An Improved Green's Function for Ion Beam Transport

NASA Technical Reports Server (NTRS)

Tweed, J.; Wilson, J. W.; Tripathi, R. K.

2003-01-01

Ion beam transport theory allows testing of material transmission properties in the laboratory environment generated by particle accelerators. This is a necessary step in materials development and evaluation for space use. The approximations used in solving the Boltzmann transport equation for the space setting are often not sufficient for laboratory work and those issues are the main emphasis of the present work. In consequence, an analytic solution of the linear Boltzmann equation is pursued in the form of a Green's function allowing flexibility in application to a broad range of boundary value problems. It has been established that simple solutions can be found for the high charge and energy (HZE) by ignoring nuclear energy downshifts and dispersion. Such solutions were found to be supported by experimental evidence with HZE ion beams when multiple scattering was added. Lacking from the prior solutions were range and energy straggling and energy downshift with dispersion associated with nuclear events. Recently, we have found global solutions including these effects providing a broader class of HZE ion solutions.

Roy-Steiner-equation analysis of pion-nucleon scattering

NASA Astrophysics Data System (ADS)

Meißner, U.-G.; Ruiz de Elvira, J.; Hoferichter, M.; Kubis, B.

2017-03-01

Low-energy pion-nucleon scattering is relevant for many areas in nuclear and hadronic physics, ranging from the scalar couplings of the nucleon to the long-range part of two-pion-exchange potentials and three-nucleon forces in Chiral Effective Field Theory. In this talk, we show how the fruitful combination of dispersion-theoretical methods, in particular in the form of Roy-Steiner equations, with modern high-precision data on hadronic atoms allows one to determine the pion-nucleon scattering amplitudes at low energies with unprecedented accuracy. Special attention will be paid to the extraction of the pion-nucleon σ-term, and we discuss in detail the current tension with recent lattice results, as well as the determination of the low-energy constants of chiral perturbation theory.

Particle Transport through Scattering Regions with Clear Layers and Inclusions

NASA Astrophysics Data System (ADS)

Bal, Guillaume

2002-08-01

This paper introduces generalized diffusion models for the transport of particles in scattering media with nonscattering inclusions. Classical diffusion is known as a good approximation of transport only in scattering media. Based on asymptotic expansions and the coupling of transport and diffusion models, generalized diffusion equations with nonlocal interface conditions are proposed which offer a computationally cheap, yet accurate, alternative to solving the full phase-space transport equations. The paper shows which computational model should be used depending on the size and shape of the nonscattering inclusions in the simplified setting of two space dimensions. An important application is the treatment of clear layers in near-infrared (NIR) spectroscopy, an imaging technique based on the propagation of NIR photons in human tissues.

Non-LTE line formation in a magnetic field. I. Noncoherent scattering and true absorption

DOE Office of Scientific and Technical Information (OSTI.GOV)

Domke, H.; Staude, J.

1973-08-01

The formation of a Zeeman-multiplet by noncoherent scattering and true absorption in a Milne-- Eddington atmosphere is considered assuming a homogeneous magnetic field and complete depolarization of the atomic line levels. The transfer equation for the Stokes parameters is transformed into a scalar integral equation of the Wiener-- Hopf type which is solved by Sobolev's method in closed form. The influence of the magnetic field on the mean scattering number in an infinite medium is discussed. The solution of the line formation problem is obtained for a Planckian source fruction. This solution may be simplified by making the ''finite fieldmore » approximation'', which should be sufficiently accurate for practical purposes. (auth)« less

Quasiparticle Interactions in Neutron Matter for Applications in Neutron Stars

NASA Technical Reports Server (NTRS)

Wambach, J; Ainsworth, T. L.; Pines, D.

1993-01-01

A microscopic model for the quasiparticle interaction in neutron matter is presented. Both-particle (pp) and particle-hole (ph) correlations are included. The pp correlations are treated in semi-empirical way, while ph correlations are incorporated by solving coupled two-body equations for particle-hole interaction and the scattering amplitude of the Fermi sphere. The resulting integral equations self-consistently sum the ph reducible diagrams. Antisymmetry is kept at all stages and hence the forward-scattering sum rules for the scattering amplitude are obeyed. Results for Landau parameters and transport coefficients in a density regime representing the crust of a neutron star are presented. We also estimate the (1)S(sub 0) gap parameter for neutron superfluidity and comment briefly on neutron-star implications.

Analysis of scattering by a linear chain of spherical inclusions in an optical fiber

NASA Astrophysics Data System (ADS)

Chremmos, Ioannis D.; Uzunoglu, Nikolaos K.

2006-12-01

The scattering by a linear chain of spherical dielectric inclusions, embedded along the axis of an optical fiber, is analyzed using a rigorous integral equation formulation, based on the dyadic Green's function theory. The coupled electric field integral equations are solved by applying the Galerkin technique with Mie-type expansion of the field inside the spheres in terms of spherical waves. The analysis extends the previously studied case of a single spherical inhomogeneity inside a fiber to the multisphere-scattering case, by utilizing the classic translational addition theorems for spherical waves in order to analytically extract the direct-intersphere-coupling coefficients. Results for the transmitted and reflected power, on incidence of the fundamental HE11 mode, are presented for several cases.

Angular width of the Cherenkov radiation with inclusion of multiple scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zheng, Jian, E-mail: jzheng@ustc.edu.cn

2016-06-15

Visible Cherenkov radiation can offer a method of the measurement of the velocity of charged particles. The angular width of the radiation is important since it determines the resolution of the velocity measurement. In this article, the angular width of Cherenkov radiation with inclusion of multiple scattering is calculated through the path-integral method, and the analytical expressions are presented. The condition that multiple scattering processes dominate the angular distribution is obtained.

A forward-adjoint operator pair based on the elastic wave equation for use in transcranial photoacoustic computed tomography

PubMed Central

Mitsuhashi, Kenji; Poudel, Joemini; Matthews, Thomas P.; Garcia-Uribe, Alejandro; Wang, Lihong V.; Anastasio, Mark A.

2017-01-01

Photoacoustic computed tomography (PACT) is an emerging imaging modality that exploits optical contrast and ultrasonic detection principles to form images of the photoacoustically induced initial pressure distribution within tissue. The PACT reconstruction problem corresponds to an inverse source problem in which the initial pressure distribution is recovered from measurements of the radiated wavefield. A major challenge in transcranial PACT brain imaging is compensation for aberrations in the measured data due to the presence of the skull. Ultrasonic waves undergo absorption, scattering and longitudinal-to-shear wave mode conversion as they propagate through the skull. To properly account for these effects, a wave-equation-based inversion method should be employed that can model the heterogeneous elastic properties of the skull. In this work, a forward model based on a finite-difference time-domain discretization of the three-dimensional elastic wave equation is established and a procedure for computing the corresponding adjoint of the forward operator is presented. Massively parallel implementations of these operators employing multiple graphics processing units (GPUs) are also developed. The developed numerical framework is validated and investigated in computer19 simulation and experimental phantom studies whose designs are motivated by transcranial PACT applications. PMID:29387291

High pressure and temperature equation of state and spectroscopic study of CeO 2

DOE PAGES

Jacobsen, Matthew K.; Velisavljevic, Nenad; Dattelbaum, Dana Mcgraw; ...

2016-03-17

One of the most widely used x-ray standards and a highly applied component of catalysis systems, CeO 2 has been studied for the purpose of better understanding its equation of state and electronic properties. Diamond anvil cells have been used to extend the equation of state for this material to 130 GPa and explore the electronic behavior with applied load. From the x-ray diffraction studies, it has been determined that the high pressure phase transition extends from approximately 35–75 GPa at ambient temperature. Elevation of temperature is found to decrease the initiation pressure for this transition, with multiple distinct temperaturemore » regions which indicate structural related anomalies. In addition, hydrostatic and non-hydrostatic effects are compared and exhibit a drastic difference in bulk moduli. Furthermore, the electronic results indicate a change in the scattering environment of the cerium atom, associated with the high pressure phase transition. Overall, these results present the first megabar pressure study and the first high pressure and temperature study of ceria. Additionally, this shows the first combined study of the K and L III edges of this material to 33 GPa.« less

Acoustic and elastic multiple scattering and radiation from cylindrical structures

NASA Astrophysics Data System (ADS)

Amirkulova, Feruza Abdukadirovna

Multiple scattering (MS) and radiation of waves by a system of scatterers is of great theoretical and practical importance and is required in a wide variety of physical contexts such as the implementation of "invisibility" cloaks, the effective parameter characterization, and the fabrication of dynamically tunable structures, etc. The dissertation develops fast, rapidly convergent iterative techniques to expedite the solution of MS problems. The formulation of MS problems reduces to a system of linear algebraic equations using Graf's theorem and separation of variables. The iterative techniques are developed using Neumann expansion and Block Toeplitz structure of the linear system; they are very general, and suitable for parallel computations and a large number of MS problems, i.e. acoustic, elastic, electromagnetic, etc., and used for the first time to solve MS problems. The theory is implemented in Matlab and FORTRAN, and the theoretical predictions are compared to computations obtained by COMSOL. To formulate the MS problem, the transition matrix is obtained by analyzing an acoustic and an elastic single scattering of incident waves by elastic isotropic and anisotropic solids. The mathematical model of wave scattering from multilayered cylindrical and spherical structures is developed by means of an exact solution of dynamic 3D elasticity theory. The recursive impedance matrix algorithm is derived for radially heterogeneous anisotropic solids. An explicit method for finding the impedance in piecewise uniform, transverse-isotropic material is proposed; the solution is compared to elasticity theory solutions involving Buchwald potentials. Furthermore, active exterior cloaking devices are modeled for acoustic and elastic media using multipole sources. A cloaking device can render an object invisible to some incident waves as seen by some external observer. The active cloak is generated by a discrete set of multipole sources that destructively interfere with an incident wave to produce zero total field over a finite spatial region. The approach precisely determines the necessary source amplitudes and enables a cloaked region to be determined using Graf's theorem. To apply the approach, the infinite series of multipole expansions are truncated, and the accuracy of cloaking is studied by modifying the truncation parameter.

Correlation between Satellite-Derived Aerosol Characteristics and Oceanic Dimethylsulfide (DMS)

DTIC Science & Technology

1988-12-01

intensity gained by multiple scattering into the beam from all directions and the beam addition term accounting for single scattering events. The physical...the extinction and scattering coefficients are the integracion over radius of the product of the cross sectional area of aerosol particles, the...the same photon more than once is small. Therefore, the multiple interaction term can be neglected and a single scattering approximation is made. The

Imaging hydraulic fractures at Median Tectonic Line, Japan using multiply generated and scattered tube waves in a shallow VSP experiment

NASA Astrophysics Data System (ADS)

Minato, Shohei; Ghose, Ranajit; Tsuji, Takeshi; Ikeda, Michiharu; Onishi, Kozo

2016-04-01

Tube waves are low frequency guided waves that propagate along a fluid-filled borehole. The analysis of tube waves is a promising approach to image and characterize hydraulic fractures intersecting a borehole. It exploits tube waves generated by an external seismic wavefield which compresses fractures and injects fluid into the borehole. It also utilizes the attenuation of tube waves due to fluid exchange between the fracture and the borehole, which creates scattered waves (reflection and transmission). Conventional approaches consider tube waves due to a single fracture. However, when the spacing between multiple fractures is short relative to the wavelength of the tube waves, the generated and scattered tube waves interfere with each other, making it difficult to isolate the effect of a single fracture. The analysis of closely spaced fractures is important in highly fractured areas, such as a fault zone. In this study, we explore the possibility of prediction and utilization of generated and scattered tube waves due to multiple fractures. We derive a new integral equation of the full tube wavefield using 1D wavefield representation theory incorporating nonwelded interfaces. We adapt the recent developments in modeling tube wave generation/scattering at a fracture. In these models, a fracture is represented as a parallel wall or a thin poloelastic layer. This allowed us to consider the effects of a dynamic fracture aperture with fracture compliances and the permeability. The representation also leads to a new imaging method for the hydraulic fractures, using multiply-generated and scattered tube waves. This is achieved by applying an inverse operator to the observed tube waves, which focuses the tube waves to the depth where they are generated and/or scattered. The inverse operator is constructed by a tube wave Green's function with a known propagation velocity. The Median Tectonic Line (MTL) is the most significant fault in Japan, extending NE-SW for over 1000 km across the Japanese Islands. We observed multiple tube waves in a P-wave VSP experiment in a 250 m deep, vertical borehole located on the MTL at Shikoku, Japan. The borehole televiewer and the core studies show that below 40 m depth, the Sambagawa metamorphic rocks contain highly fractured zones which consist of more than 100 open fractures and more than 30 cataclasites. We predict the full tube wavefield using the values of fracture depth and thickness known from the borehole televiewer. We model the open fractures as parallel-wall fractures and the cataclasites as thin poroelastic layers. Furthermore, we estimate the depth of the hydraulic fractures by applying the inverse operator. The results show that the tube waves could be generated and scattered at these permeable structures. Our preliminary results also indicate the possibility that the effect of the open fractures is more dominant in the generation and scattering of tube waves than that of the cataclasites in this field. The formulation and the results presented in this study and the following discussion will be useful in analysis of tube waves in highly fractured zones, in order to localize and characterize hydraulic fractures.

Scattering from Marine Sediments in a Very Shallow Water Environment

DTIC Science & Technology

2015-12-28

taking into account only large-scale changes of the environment. Keywords: Reciprocity , integral equations, volume and roughness scattering...for Public Release, Distribution Unlimited A. Ivakin: Scattering in range-dependent waveguides 5 II. VOLUME PERTURBATIONS: RECIPROCITY THEOREM...6], i.e. with the same υ , and therefore same Q , which, along with following discussion of reciprocity , explains the choice of this parameter

SS-HORSE method for studying resonances

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blokhintsev, L. D.; Mazur, A. I.; Mazur, I. A., E-mail: 008043@pnu.edu.ru

A new method for analyzing resonance states based on the Harmonic-Oscillator Representation of Scattering Equations (HORSE) formalism and analytic properties of partial-wave scattering amplitudes is proposed. The method is tested by applying it to the model problem of neutral-particle scattering and can be used to study resonance states on the basis of microscopic calculations performed within various versions of the shell model.

Scattering of elastic waves by a spheroidal inclusion

NASA Astrophysics Data System (ADS)

Johnson, Lane R.

2018-03-01

An analytical solution is presented for scattering of elastic waves by prolate and oblate spheroidal inclusions. The problem is solved in the frequency domain where separation of variables leads to a solution involving spheroidal wave functions of the angular and radial kind. Unlike the spherical problem, the boundary equations remain coupled with respect to one of the separation indices. Expanding the angular spheroidal wave functions in terms of associated Legendre functions and using their orthogonality properties leads to a set of linear equations that can be solved to simultaneously obtain solutions for all coupled modes of both scattered and interior fields. To illustrate some of the properties of the spheroidal solution, total scattering cross-sections for P, SV and SH plane waves incident at an oblique angle on a prolate spheroid, an oblate spheroid and a sphere are compared. The waveforms of the scattered field exterior to the inclusion are calculated for these same incident waves. The waveforms scattered by a spheroid are strongly dependent upon the angle of incidence, are different for incident SV and SH waves and are asymmetrical about the centre of the spheroid with the asymmetry different for prolate and oblate spheroids.

Testing the Perey effect

DOE PAGES

Titus, L. J.; Nunes, Filomena M.

2014-03-12

Here, the effects of non-local potentials have historically been approximately included by applying a correction factor to the solution of the corresponding equation for the local equivalent interaction. This is usually referred to as the Perey correction factor. In this work we investigate the validity of the Perey correction factor for single-channel bound and scattering states, as well as in transfer (p, d) cross sections. Method: We solve the scattering and bound state equations for non-local interactions of the Perey-Buck type, through an iterative method. Using the distorted wave Born approximation, we construct the T-matrix for (p,d) on 17O, 41Ca,more » 49Ca, 127Sn, 133Sn, and 209Pb at 20 and 50 MeV. As a result, we found that for bound states, the Perey corrected wave function resulting from the local equation agreed well with that from the non-local equation in the interior region, but discrepancies were found in the surface and peripheral regions. Overall, the Perey correction factor was adequate for scattering states, with the exception of a few partial waves corresponding to the grazing impact parameters. These differences proved to be important for transfer reactions. In conclusion, the Perey correction factor does offer an improvement over taking a direct local equivalent solution. However, if the desired accuracy is to be better than 10%, the exact solution of the non-local equation should be pursued.« less

Direct Calculation of the Scattering Amplitude Without Partial Wave Decomposition. III; Inclusion of Correlation Effects

NASA Technical Reports Server (NTRS)

Shertzer, Janine; Temkin, Aaron

2007-01-01

In the first two papers in this series, we developed a method for studying electron-hydrogen scattering that does not use partial wave analysis. We constructed an ansatz for the wave function in both the static and static exchange approximations and calculated the full scattering amplitude. Here we go beyond the static exchange approximation, and include correlation in the wave function via a modified polarized orbital. This correlation function provides a significant improvement over the static exchange approximation: the resultant elastic scattering amplitudes are in very good agreement with fully converged partial wave calculations for electron-hydrogen scattering. A fully variational modification of this approach is discussed in the conclusion of the article Popular summary of Direct calculation of the scattering amplitude without partial wave expansion. III ....." by J. Shertzer and A. Temkin. In this paper we continue the development of In this paper we continue the development of a new approach to the way in which researchers have traditionally used to calculate the scattering cross section of (low-energy) electrons from atoms. The basic mathematical problem is to solve the Schroedinger Equation (SE) corresponding the above physical process. Traditionally it was always the case that the SE was reduced to a sequence of one-dimensional (ordinary) differential equations - called partial waves which were solved and from the solutions "phase shifts" were extracted, from which the scattering cross section was calculated.

Simple aerosol correction technique based on the spectral relationships of the aerosol multiple-scattering reflectances for atmospheric correction over the oceans.

PubMed

Ahn, Jae-Hyun; Park, Young-Je; Kim, Wonkook; Lee, Boram

2016-12-26

An estimation of the aerosol multiple-scattering reflectance is an important part of the atmospheric correction procedure in satellite ocean color data processing. Most commonly, the utilization of two near-infrared (NIR) bands to estimate the aerosol optical properties has been adopted for the estimation of the effects of aerosols. Previously, the operational Geostationary Color Ocean Imager (GOCI) atmospheric correction scheme relies on a single-scattering reflectance ratio (SSE), which was developed for the processing of the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) data to determine the appropriate aerosol models and their aerosol optical thicknesses. The scheme computes reflectance contributions (weighting factor) of candidate aerosol models in a single scattering domain then spectrally extrapolates the single-scattering aerosol reflectance from NIR to visible (VIS) bands using the SSE. However, it directly applies the weight value to all wavelengths in a multiple-scattering domain although the multiple-scattering aerosol reflectance has a non-linear relationship with the single-scattering reflectance and inter-band relationship of multiple scattering aerosol reflectances is non-linear. To avoid these issues, we propose an alternative scheme for estimating the aerosol reflectance that uses the spectral relationships in the aerosol multiple-scattering reflectance between different wavelengths (called SRAMS). The process directly calculates the multiple-scattering reflectance contributions in NIR with no residual errors for selected aerosol models. Then it spectrally extrapolates the reflectance contribution from NIR to visible bands for each selected model using the SRAMS. To assess the performance of the algorithm regarding the errors in the water reflectance at the surface or remote-sensing reflectance retrieval, we compared the SRAMS atmospheric correction results with the SSE atmospheric correction using both simulations and in situ match-ups with the GOCI data. From simulations, the mean errors for bands from 412 to 555 nm were 5.2% for the SRAMS scheme and 11.5% for SSE scheme in case-I waters. From in situ match-ups, 16.5% for the SRAMS scheme and 17.6% scheme for the SSE scheme in both case-I and case-II waters. Although we applied the SRAMS algorithm to the GOCI, it can be applied to other ocean color sensors which have two NIR wavelengths.

Analysis of dense-medium light scattering with applications to corneal tissue: experiments and Monte Carlo simulations.

PubMed

Kim, K B; Shanyfelt, L M; Hahn, D W

2006-01-01

Dense-medium scattering is explored in the context of providing a quantitative measurement of turbidity, with specific application to corneal haze. A multiple-wavelength scattering technique is proposed to make use of two-color scattering response ratios, thereby providing a means for data normalization. A combination of measurements and simulations are reported to assess this technique, including light-scattering experiments for a range of polystyrene suspensions. Monte Carlo (MC) simulations were performed using a multiple-scattering algorithm based on full Mie scattering theory. The simulations were in excellent agreement with the polystyrene suspension experiments, thereby validating the MC model. The MC model was then used to simulate multiwavelength scattering in a corneal tissue model. Overall, the proposed multiwavelength scattering technique appears to be a feasible approach to quantify dense-medium scattering such as the manifestation of corneal haze, although more complex modeling of keratocyte scattering, and animal studies, are necessary.

Multiple scattering contribution to the diffuse light of a night sky: A model which embraces all orders of scattering

NASA Astrophysics Data System (ADS)

Kocifaj, Miroslav

2018-02-01

The mechanism in which multiple scattering influences the radiance of a night sky has been poorly quantified until recently, or even completely unknown from the theoretical point of view. In this paper, the relative contribution of higher-scattering radiances to the total sky radiance is treated analytically for all orders of scattering, showing that a fast and accurate numerical solution to the problem exists. Unlike a class of ray tracing codes in which CPU requirements increase tremendously with each new scattering mode, the solution developed here requires the same processor time for each scattering mode. This allows for rapid estimation of higher-scattering radiances and residual error that is otherwise unknown if these radiances remain undetermined. Such convergence testing is necessary to guarantee accuracy and the stability of the numerical predictions. The performance of the method developed here is demonstrated in a set of numerical experiments aiming to uncover the relative importance of higher-scattering radiances at different distances from a light source. We have shown, that multiple scattering effects are generally low if distance to the light source is below 30 km. At large distances the multiple scattering can become important at the dark sky elements situated opposite to the light source. However, the brightness at this part of sky is several orders of magnitude smaller than that of a glowing dome of light over a city, so we do not expect that a partial increase or even doubling the radiance of otherwise dark sky elements can noticeably affect astronomical observations or living organisms (including humans). Single scattering is an appropriate approximation to the sky radiance of a night sky in the vast majority of cases.

Finite element approximation of the radiative transport equation in a medium with piece-wise constant refractive index

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lehtikangas, O., E-mail: Ossi.Lehtikangas@uef.fi; Tarvainen, T.; Department of Computer Science, University College London, Gower Street, London WC1E 6BT

2015-02-01

The radiative transport equation can be used as a light transport model in a medium with scattering particles, such as biological tissues. In the radiative transport equation, the refractive index is assumed to be constant within the medium. However, in biomedical media, changes in the refractive index can occur between different tissue types. In this work, light propagation in a medium with piece-wise constant refractive index is considered. Light propagation in each sub-domain with a constant refractive index is modeled using the radiative transport equation and the equations are coupled using boundary conditions describing Fresnel reflection and refraction phenomena onmore » the interfaces between the sub-domains. The resulting coupled system of radiative transport equations is numerically solved using a finite element method. The approach is tested with simulations. The results show that this coupled system describes light propagation accurately through comparison with the Monte Carlo method. It is also shown that neglecting the internal changes of the refractive index can lead to erroneous boundary measurements of scattered light.« less

The Coupling of Finite Element and Integral Equation Representations for Efficient Three-Dimensional Modeling of Electromagnetic Scattering and Radiation

NASA Technical Reports Server (NTRS)

Cwik, Tom; Zuffada, Cinzia; Jamnejad, Vahraz

1996-01-01

Finite element modeling has proven useful for accurtely simulating scattered or radiated fields from complex three-dimensional objects whose geometry varies on the scale of a fraction of a wavelength.

The use of lidar for stratospheric measurements

NASA Technical Reports Server (NTRS)

Mccormick, M. P.

1977-01-01

Stratospheric measurements possible with ground-based, airborne, and satellite-borne lidar systems are reviewed. The instruments, basic equations, and formats normally used for various scattering and absorption phenomena measurements are presented including a discussion of elastic, resonance, Raman, and fluorescence scattering techniques.

Imaging complex objects using learning tomography

NASA Astrophysics Data System (ADS)

Lim, JooWon; Goy, Alexandre; Shoreh, Morteza Hasani; Unser, Michael; Psaltis, Demetri

2018-02-01

Optical diffraction tomography (ODT) can be described using the scattering process through an inhomogeneous media. An inherent nonlinearity exists relating the scattering medium and the scattered field due to multiple scattering. Multiple scattering is often assumed to be negligible in weakly scattering media. This assumption becomes invalid as the sample gets more complex resulting in distorted image reconstructions. This issue becomes very critical when we image a complex sample. Multiple scattering can be simulated using the beam propagation method (BPM) as the forward model of ODT combined with an iterative reconstruction scheme. The iterative error reduction scheme and the multi-layer structure of BPM are similar to neural networks. Therefore we refer to our imaging method as learning tomography (LT). To fairly assess the performance of LT in imaging complex samples, we compared LT with the conventional iterative linear scheme using Mie theory which provides the ground truth. We also demonstrate the capacity of LT to image complex samples using experimental data of a biological cell.

Coherent Multiple Light Scattering in Ultracold Atomic Rb

NASA Astrophysics Data System (ADS)

Kulatunga, Pasad; Sukenik, C. I.; Balik, Salim; Havey, M. D.; Kupriyanov, D. V.; Sokolov, I. M.

2003-05-01

Wave transport in mesoscopic systems can be strongly influenced by coherent multiple scattering,which can lead to novel magneto-optic, transmission, and backscattering effects of light in atomic vapors. Although related to traditional studies of radiation trapping, in ultracold vapors negligible frequency or phase redistribution takes place in the scattering, and high-order coherent light scattering occurs. Among other things, this leads to enhancement of the influence of otherwise small non-resonant terms in the scattering amplitudes. We report investigation of multiple coherent light scattering from ultracold Rb atoms confined in a magneto-optic trap (MOT). In experimental studies, measurements are made of the angular, spectral, and polarization-dependent coherent backscattering profile of a low-intensity probe beam tuned near the F = 3 - F' = 4 hyperfine transition. The influence of higher probe beam intensity is also studied. In a theoretical study of angular intensity enhancement of backscattered light, we consider scattering orders up to 10 and a realistic and asymmetric Gaussian atom distribution in the MOT. Supported by NSF, NATO, and RFBR.

The generalized scattering coefficient method for plane wave scattering in layered structures

NASA Astrophysics Data System (ADS)

Liu, Yu; Li, Chao; Wang, Huai-Yu; Zhou, Yun-Song

2017-02-01

The generalized scattering coefficient (GSC) method is pedagogically derived and employed to study the scattering of plane waves in homogeneous and inhomogeneous layered structures. The numerical stabilities and accuracies of this method and other commonly used numerical methods are discussed and compared. For homogeneous layered structures, concise scattering formulas with clear physical interpretations and strong numerical stability are obtained by introducing the GSCs. For inhomogeneous layered structures, three numerical methods are employed: the staircase approximation method, the power series expansion method, and the differential equation based on the GSCs. We investigate the accuracies and convergence behaviors of these methods by comparing their predictions to the exact results. The conclusions are as follows. The staircase approximation method has a slow convergence in spite of its simple and intuitive implementation, and a fine stratification within the inhomogeneous layer is required for obtaining accurate results. The expansion method results are sensitive to the expansion order, and the treatment becomes very complicated for relatively complex configurations, which restricts its applicability. By contrast, the GSC-based differential equation possesses a simple implementation while providing fast and accurate results.

An empirical correction for moderate multiple scattering in super-heterodyne light scattering.

PubMed

Botin, Denis; Mapa, Ludmila Marotta; Schweinfurth, Holger; Sieber, Bastian; Wittenberg, Christopher; Palberg, Thomas

2017-05-28

Frequency domain super-heterodyne laser light scattering is utilized in a low angle integral measurement configuration to determine flow and diffusion in charged sphere suspensions showing moderate to strong multiple scattering. We introduce an empirical correction to subtract the multiple scattering background and isolate the singly scattered light. We demonstrate the excellent feasibility of this simple approach for turbid suspensions of transmittance T ≥ 0.4. We study the particle concentration dependence of the electro-kinetic mobility in low salt aqueous suspension over an extended concentration regime and observe a maximum at intermediate concentrations. We further use our scheme for measurements of the self-diffusion coefficients in the fluid samples in the absence or presence of shear, as well as in polycrystalline samples during crystallization and coarsening. We discuss the scope and limits of our approach as well as possible future applications.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alam, Aftab; Khan, Suffian N.; Smirnov, A. V.

Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an ecient sitecentered, electronic-structure technique for addressing an assembly of N scatterers. Wave-functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number L max = (l,m) max, while scattering matrices, which determine spectral properties, are truncated at L tr = (l,m) tr where phase shifts δl>l tr are negligible. Historically, L max is set equal to L tr, which is correct for large enough L max but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for L maxmore » > L tr with δl>l tr set to zero [Zhang and Butler, Phys. Rev. B 46, 7433]. We present a numerically ecient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R 3 process with rank N(l tr + 1) 2] and includes higher-L contributions via linear algebra [R 2 process with rank N(l max +1) 2]. Augmented-KKR approach yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe and L1 0 CoPt, and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus L max for a given L tr.« less

Relativistic proton-nucleus scattering and one-boson-exchange models

NASA Technical Reports Server (NTRS)

Maung, Khin Maung; Gross, Franz; Tjon, J. A.; Townsend, L. W.; Wallace, S. J.

1993-01-01

Relativistic p-(Ca-40) elastic scattering observables are calculated using four sets of relativistic NN amplitudes obtained from different one-boson-exchange (OBE) models. The first two sets are based upon a relativistic equation in which one particle is on mass shell and the other two sets are obtained from a quasipotential reduction of the Bethe-Salpeter equation. Results at 200, 300, and 500 MeV are presented for these amplitudes. Differences between the predictions of these models provide a study of the uncertainty in constructing Dirac optical potentials from OBE-based NN amplitudes.

Scattering of Dirac waves off Kerr black holes

NASA Astrophysics Data System (ADS)

Chakrabarti, Sandip K.; Mukhopadhyay, Banibrata

2000-10-01

Chandrasekhar separated the Dirac equation for spinning and massive particles in Kerr geometry into radial and angular parts. Here we solve the complete wave equation and find out how the Dirac wave scatters off Kerr black holes. The eigenfunctions, eigenvalues and reflection and transmission co-efficients are computed. We compare the solutions with several parameters to show how a spinning black hole recognizes the mass and energy of incoming waves. Very close to the horizon the solutions become independent of the particle parameters, indicating the universality of the behaviour.

Coherent transmission of an ultrasonic shock wave through a multiple scattering medium.

PubMed

Viard, Nicolas; Giammarinaro, Bruno; Derode, Arnaud; Barrière, Christophe

2013-08-01

We report measurements of the transmitted coherent (ensemble-averaged) wave resulting from the interaction of an ultrasonic shock wave with a two-dimensional random medium. Despite multiple scattering, the coherent waveform clearly shows the steepening that is typical of nonlinear harmonic generation. This is taken advantage of to measure the elastic mean free path and group velocity over a broad frequency range (2-15 MHz) in only one experiment. Experimental results are found to be in good agreement with a linear theoretical model taking into account spatial correlations between scatterers. These results show that nonlinearity and multiple scattering are both present, yet uncoupled.

High-order upwind schemes for the wave equation on overlapping grids: Maxwell's equations in second-order form

DOE Office of Scientific and Technical Information (OSTI.GOV)

Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.

High-order accurate upwind approximations for the wave equation in second-order form on overlapping grids are developed. Although upwind schemes are well established for first-order hyperbolic systems, it was only recently shown by Banks and Henshaw how upwinding could be incorporated into the second-order form of the wave equation. This new upwind approach is extended here to solve the time-domain Maxwell's equations in second-order form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor time-stepping is used to develop single-step space-time schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemannmore » problem into the discretization. Second-order and fourth-order accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwind-scheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional non-dissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materials in two and three space dimensions. Finally, the upwind scheme is shown to be robust and provide high-order accuracy.« less

High-order upwind schemes for the wave equation on overlapping grids: Maxwell's equations in second-order form

DOE PAGES

Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.

2017-09-28

High-order accurate upwind approximations for the wave equation in second-order form on overlapping grids are developed. Although upwind schemes are well established for first-order hyperbolic systems, it was only recently shown by Banks and Henshaw how upwinding could be incorporated into the second-order form of the wave equation. This new upwind approach is extended here to solve the time-domain Maxwell's equations in second-order form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor time-stepping is used to develop single-step space-time schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemannmore » problem into the discretization. Second-order and fourth-order accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwind-scheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional non-dissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materials in two and three space dimensions. Finally, the upwind scheme is shown to be robust and provide high-order accuracy.« less

High-order upwind schemes for the wave equation on overlapping grids: Maxwell's equations in second-order form

NASA Astrophysics Data System (ADS)

Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.

2018-01-01

High-order accurate upwind approximations for the wave equation in second-order form on overlapping grids are developed. Although upwind schemes are well established for first-order hyperbolic systems, it was only recently shown by Banks and Henshaw [1] how upwinding could be incorporated into the second-order form of the wave equation. This new upwind approach is extended here to solve the time-domain Maxwell's equations in second-order form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor time-stepping is used to develop single-step space-time schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemann problem into the discretization. Second-order and fourth-order accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwind-scheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional non-dissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materials in two and three space dimensions. The upwind scheme is shown to be robust and provide high-order accuracy.

Exact simulation of polarized light reflectance by particle deposits

NASA Astrophysics Data System (ADS)

Ramezan Pour, B.; Mackowski, D. W.

2015-12-01

The use of polarimetric light reflection measurements as a means of identifying the physical and chemical characteristics of particulate materials obviously relies on an accurate model of predicting the effects of particle size, shape, concentration, and refractive index on polarized reflection. The research examines two methods for prediction of reflection from plane parallel layers of wavelength—sized particles. The first method is based on an exact superposition solution to Maxwell's time harmonic wave equations for a deposit of spherical particles that are exposed to a plane incident wave. We use a FORTRAN-90 implementation of this solution (the Multiple Sphere T Matrix (MSTM) code), coupled with parallel computational platforms, to directly simulate the reflection from particle layers. The second method examined is based upon the vector radiative transport equation (RTE). Mie theory is used in our RTE model to predict the extinction coefficient, albedo, and scattering phase function of the particles, and the solution of the RTE is obtained from adding—doubling method applied to a plane—parallel configuration. Our results show that the MSTM and RTE predictions of the Mueller matrix elements converge when particle volume fraction in the particle layer decreases below around five percent. At higher volume fractions the RTE can yield results that, depending on the particle size and refractive index, significantly depart from the exact predictions. The particle regimes which lead to dependent scattering effects, and the application of methods to correct the vector RTE for particle interaction, will be discussed.

Relationship between the Amplitude and Phase of a Signal Scattered by a Point-Like Acoustic Inhomogeneity

NASA Astrophysics Data System (ADS)

Burov, V. A.; Morozov, S. A.

2001-11-01

Wave scattering by a point-like inhomogeneity, i.e., a strong inhomogeneity with infinitesimal dimensions, is described. This type of inhomogeneity model is used in investigating the point-spread functions of different algorithms and systems. Two approaches are used to derive the rigorous relationship between the amplitude and phase of a signal scattered by a point-like acoustic inhomogeneity. The first approach is based on a Marchenko-type equation. The second approach uses the scattering by a scatterer whose size decreases simultaneously with an increase in its contrast. It is shown that the retarded and advanced waves are scattered differently despite the relationship between the phases of the corresponding scattered waves.

Three-body unitarity with isobars revisited

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mai, M.; Hu, B.; Döring, M.

The particle exchange model of hadron interactions can be used to describe three-body scattering under the isobar assumption. Here, we start from the 3->3 scattering amplitude for spinless particles, which contains an isobar-spectator scattering amplitude. Using a Bethe-Salpeter Ansatz for the latter, we derive a relativistic three-dimensional scattering equation that manifestly fulfills three-body unitarity and two-body unitarity for the sub-amplitudes. Furthermore, this property holds for energies above breakup and also in the presence of resonances in the sub-amplitudes.

Three-body unitarity with isobars revisited

DOE PAGES

Mai, M.; Hu, B.; Döring, M.; ...

2017-09-08

The particle exchange model of hadron interactions can be used to describe three-body scattering under the isobar assumption. Here, we start from the 3->3 scattering amplitude for spinless particles, which contains an isobar-spectator scattering amplitude. Using a Bethe-Salpeter Ansatz for the latter, we derive a relativistic three-dimensional scattering equation that manifestly fulfills three-body unitarity and two-body unitarity for the sub-amplitudes. Furthermore, this property holds for energies above breakup and also in the presence of resonances in the sub-amplitudes.

Scattering of Lamb waves in a composite plate

NASA Technical Reports Server (NTRS)

Bratton, Robert; Datta, Subhendu; Shah, Arvind

1991-01-01

A combined analytical and finite element technique is developed to gain a better understanding of the scattering of elastic waves by defects. This hybrid method is capable of predicting scattered displacements from arbitrary shaped defects as well as inclusions of different material. The continuity of traction and displacements at the boundaries of the two areas provided the necessary equations to find the nodal displacements and expansion coefficients. Results clearly illustrate the influence of increasing crack depth on the scattered signal.

Riemann–Hilbert problem approach for two-dimensional flow inverse scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Agaltsov, A. D., E-mail: agalets@gmail.com; Novikov, R. G., E-mail: novikov@cmap.polytechnique.fr; IEPT RAS, 117997 Moscow

2014-10-15

We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.

The zig-zag walk with scattering and absorption on the real half line and in a lattice model

NASA Astrophysics Data System (ADS)

Wuttke, Joachim

2014-05-01

The Darwin-Hamilton equations, describing one-dimensional transport with scattering and absorption, are expanded into a recursion. The solution involves ballot numbers. The recurrence probability as function of scattering order is given by Catalan numbers. To reproduce this analytical result in a lattice model, a novel relation between Narayana and Catalan numbers is derived.

Single scattering solution for radiative transfer through Rayleigh and aerosol atmosphere

NASA Technical Reports Server (NTRS)

Otterman, J.

1977-01-01

A solution is presented to the radiative transfer of the solar irradiation through a turbid atmosphere, based on the single-scattering approximation, i.e., an assumption that a photon that underwent scattering either leaves the top of the atmosphere or strikes the surface. The solution depends on a special idealization of the scattering phase function of the aerosols. The equations developed are subsequently applied to analyze quantitatively the enhancement of the surface irradiation and the enhancement of the scattered radiant emittance as seen from above the atmosphere, caused by the surface reflectance and atmospheric back scattering. An order of magnitude error analysis is presented.

The application of the principles of invariance to the radiative transfer equation in plant canopies

NASA Technical Reports Server (NTRS)

Ganapol, B. D.; Myneni, R. B.

1992-01-01

Solutions of the radiative transfer equation describing photon interactions with vegetation canopies are important in remote sensing since they provide the canopy reflectance distribution required in the interpretation of satellite acquired information. The general one-dimensional two-angle transport problem for a finite copy of arbitrary leaf angle distribution is considered. Analytical solutions are obtained in terms of generalized Chandrasekhar's X- and Y-functions by invoking the principles of invariance. A critical step in the formulation involves the decomposition of the integral of the scattering phase function into a product of known functions of the incident and scattered photon directions. Several simplified cases previously considered in the literature are derived from the generalized solution. Various symmetries obeyed by the scattering operator and reciprocity relations are formally proved.

Peter J. W. Debye - a whole life devoted to science.

PubMed

Dalba, Giuseppe

2016-11-01

In 1915 P. Debye, one of the most prominent scientists in the field of condensed-matter physics and physical chemistry, published an X-ray scattering equation for randomly oriented scattering sites. This formula, since then used for describing the structure of powders, liquids and gases, has become a model for material analysis at the nanoscale. This paper re-examines briefly Debye's works on the origin and evolution of the scattering equation and its first uses. The career of the great scientist and some of his other numerous and diverse contributions to science are also reviewed. Additionally the paper addresses aspects of his life as a teacher, as a science manager and as a man, including the recent controversy about his conduct during the Third Reich regime.

Measurement and Modeling of Ultrasonic Pitch/catch Grain Noise

NASA Astrophysics Data System (ADS)

Margetan, F. J.; Gray, T. A.; Thompson, R. B.

2008-02-01

Ultrasonic grain noise arises from the scattering of sound waves by microstructural boundaries, and can limit the detection of weakly-reflecting internal defects in metals. In some cases of practical interest, such as focused-transducer inspections of aircraft engine components, so-called "single scattering" or "independent scatterer" models have proven to be reasonably accurate in predicting grain noise characteristics. In pulse/echo inspections it is difficult to experimentally assess the relative contributions of single scattering and multiple scattering, because both can generally contribute to the backscattered noise seen at any given observation time. For pitch/catch inspections, however, it is relatively easy to construct inspection geometries for which single-scattered noise should be insignificant, and hence any observed noise is presumably due to multiple scattering. This concept is demonstrated using pitch/catch shear-wave measurements performed on a well-characterized stainless-steel specimen. The inspection geometry allows us to control the overlap volume of the intersecting radiation fields of the two transducers. As we proceed from maximally overlapping fields to zero overlap, the single-scattering contribution to the observed grain noise is expected to decrease. Measurements are compared to the predictions of a single-scatterer model, and the relative contributions of single and multiple scattering to the observed grain noise are estimated.

A Unified Treatment of the Acoustic and Elastic Scattered Waves from Fluid-Elastic Media

NASA Astrophysics Data System (ADS)

Denis, Max Fernand

In this thesis, contributions are made to the numerical modeling of the scattering fields from fluid-filled poroelastic materials. Of particular interest are highly porous materials that demonstrate strong contrast to the saturating fluid. A Biot's analysis of porous medium serves as the starting point of the elastic-solid and pore-fluid governing equations of motion. The longitudinal scattering waves of the elastic-solid mode and the pore-fluid mode are modeled by the Kirchhoff-Helmholtz integral equation. The integral equation is evaluated using a series approximation, describing the successive perturbation of the material contrasts. To extended the series' validity into larger domains, rational fraction extrapolation methods are employed. The local Pade□ approximant procedure is a technique that allows one to extrapolate from a scattered field of small contrast into larger values, using Pade□ approximants. To ensure the accuracy of the numerical model, comparisons are made with the exact solution of scattering from a fluid sphere. Mean absolute error analyses, yield convergent and accurate results. In addition, the numerical model correctly predicts the Bragg peaks for a periodic lattice of fluid spheres. In the case of trabecular bones, the far-field scattering pressure attenuation is a superposition of the elastic-solid mode and the pore-fluid mode generated waves from the surrounding fluid and poroelastic boundaries. The attenuation is linearly dependent with frequency between 0.2 and 0.6MHz. The slope of the attenuation is nonlinear with porosity, and does not reflect the mechanical properties of the trabecular bone. The attenuation shows the anisotropic effects of the trabeculae structure. Thus, ultrasound can possibly be employed to non-invasively predict the principal structural orientation of trabecular bones.

Quasi-elastic nuclear scattering at high energies

NASA Technical Reports Server (NTRS)

Cucinotta, Francis A.; Townsend, Lawrence W.; Wilson, John W.

1992-01-01

The quasi-elastic scattering of two nuclei is considered in the high-energy optical model. Energy loss and momentum transfer spectra for projectile ions are evaluated in terms of an inelastic multiple-scattering series corresponding to multiple knockout of target nucleons. The leading-order correction to the coherent projectile approximation is evaluated. Calculations are compared with experiments.

Nonlinear Wave Propagation

DTIC Science & Technology

1983-12-30

Transform for the Kadomtsev - Petviashvili Equation , M.J. Ablowitz , D. Bar Yaacov and A.S. Fokas, to appear in Stud. in Appl. Math. I.N.S. #21 preprint...Benjamin-Ono equation bears many similariti to the multidimensional problem, especially the Kadomtsev - Petviashvili equation . We discuss many of these...appear in Stud. in Appl. Math. I.N.S. #22 preprint, 1982. 67. On the Inverse Scattering Transform for the Kadomtsev - Petviashvili Equation , M.J. Ablowitz

Extended Thermodynamics: a Theory of Symmetric Hyperbolic Field Equations

NASA Astrophysics Data System (ADS)

Müller, Ingo

2008-12-01

Extended thermodynamics is based on a set of equations of balance which are supplemented by local and instantaneous constitutive equations so that the field equations are quasi-linear first order differential equations. If the constitutive functions are subject to the requirements of the entropy principle, one may write them in symmetric hyperbolic form by a suitable choice of fields. The kinetic theory of gases, or the moment theories based on the Boltzmann equation provide an explicit example for extended thermodynamics. The theory proves its usefulness and practicality in the successful treatment of light scattering in rarefied gases. This presentation is based upon the book [1] of which the author of this paper is a co-author. For more details about the motivation and exploitation of the basic principles the interested reader is referred to that reference. It would seem that extended thermodynamics is worthy of the attention of mathematicians. It may offer them a non-trivial field of study concerning hyperbolic equations, if ever they get tired of the Burgers equation. Physicists may prefer to appreciate the success of extended thermodynamics in light scattering and to work on the open problems concerning the modification of the Navier-Stokes-Fourier theory in rarefied gases as predicted by extended thermodynamics of 13, 14, and more moments.

Nonlinear Wave Propagation

DTIC Science & Technology

2000-03-17

scattering problem has intrinsic interest in its own right. A new class of lump type solutions of the multidimensional Kadomtsev - Petviashvili (KP) equation ...solutions associated with the Kadomtsev - Petviashvili equation have more com- plicated interaction properties than the previously known lump...B-3. New Solutions of the Nonstationary Schrödinger and Kadomtsev - Petviashvili Equations , M.J. Ablowitz and J. Villarroel, in Symmetries and

Collins-Soper equation for the energy evolution of transverse-momentum and spin dependent parton distributions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Idilbi, Ahmad; Ji Xiangdong; Yuan Feng

The hadron-energy evolution (Collins and Soper) equation for all the leading-twist transverse-momentum and spin dependent parton distributions is derived in the impact parameter space. Based on this equation, we present a resummation formulas for the spin dependent structure functions of the semi-inclusive deep-inelastic scattering.

Heuristic Green's function of the time dependent radiative transfer equation for a semi-infinite medium.

PubMed

Martelli, Fabrizio; Sassaroli, Angelo; Pifferi, Antonio; Torricelli, Alessandro; Spinelli, Lorenzo; Zaccanti, Giovanni

2007-12-24

The Green's function of the time dependent radiative transfer equation for the semi-infinite medium is derived for the first time by a heuristic approach based on the extrapolated boundary condition and on an almost exact solution for the infinite medium. Monte Carlo simulations performed both in the simple case of isotropic scattering and of an isotropic point-like source, and in the more realistic case of anisotropic scattering and pencil beam source, are used to validate the heuristic Green's function. Except for the very early times, the proposed solution has an excellent accuracy (> 98 % for the isotropic case, and > 97 % for the anisotropic case) significantly better than the diffusion equation. The use of this solution could be extremely useful in the biomedical optics field where it can be directly employed in conditions where the use of the diffusion equation is limited, e.g. small volume samples, high absorption and/or low scattering media, short source-receiver distances and early times. Also it represents a first step to derive tools for other geometries (e.g. slab and slab with inhomogeneities inside) of practical interest for noninvasive spectroscopy and diffuse optical imaging. Moreover the proposed solution can be useful to several research fields where the study of a transport process is fundamental.

An integral-equation solution for TE radiation and scattering from conducting cylinders

NASA Technical Reports Server (NTRS)

Richmond, J. H.

1973-01-01

The piecewise-sinusoidal reaction technique is applied to low frequency radiation and scattering from noncircular cylinders with perfect or imperfect conductivity. This report presents the theory, computer programs and numerical results for these two-dimensional problems with the TE polarization.

Two-dimensional simulations of stimulated Brillouin scattering in laser produced plasmas

NASA Astrophysics Data System (ADS)

Amin, M. R.; Capjack, C. E.; Frycz, P.; Rozmus, W.; Tikhonchuk, V. T.

1993-07-01

A system of electromagnetic and ion acoustic wave equations coupled via the ponderomotive force are solved numerically in a two-dimensional planar geometry. The competition between forward, side, and backward Brillouin scattering of the finite size laser beam is studied for the first time without the standard paraxial optics approximation. Simulations reveal a strong dependence of the scattered light characteristics on the geometry of the interaction region, the shape of the pump beam, and the ion acoustic wave damping. The main effects include side and forward scattering enhancement and a stimulation of collimated backward scattered radiation.

Far-Field Lorenz-Mie Scattering in an Absorbing Host Medium: Theoretical Formalism and FORTRAN Program

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Yang, Ping

2018-01-01

In this paper we make practical use of the recently developed first-principles approach to electromagnetic scattering by particles immersed in an unbounded absorbing host medium. Specifically, we introduce an actual computational tool for the calculation of pertinent far-field optical observables in the context of the classical Lorenzâ€"Mie theory. The paper summarizes the relevant theoretical formalism, explains various aspects of the corresponding numerical algorithm, specifies the input and output parameters of a FORTRAN program available at https://www.giss.nasa.gov/staff/mmishchenko/Lorenz-Mie.html, and tabulates benchmark results useful for testing purposes. This public-domain FORTRAN program enables one to solve the following two important problems: (i) simulate theoretically the reading of a remote well-collimated radiometer measuring electromagnetic scattering by an individual spherical particle or a small random group of spherical particles; and (ii) compute the single-scattering parameters that enter the vector radiative transfer equation derived directly from the Maxwell equations.

Scattering theory for the radial H˙1/2-critical wave equation with a cubic convolution

NASA Astrophysics Data System (ADS)

Miao, Changxing; Zhang, Junyong; Zheng, Jiqiang

2015-12-01

In this paper, we study the global well-posedness and scattering for the wave equation with a cubic convolution ∂t2u - Δu = ± (| x | - 3 *| u | 2) u in dimensions d ≥ 4. We prove that if the radial solution u with life-span I obeys (u ,ut) ∈ Lt∞ (I H˙x 1 / 2 (Rd) × H˙x-1/2 (Rd)), then u is global and scatters. By the strategy derived from concentration compactness, we show that the proof of the global well-posedness and scattering is reduced to disprove the existence of two scenarios: soliton-like solution and high to low frequency cascade. Making use of the No-waste Duhamel formula and double Duhamel trick, we deduce that these two scenarios enjoy the additional regularity by the bootstrap argument of [7]. This together with virial analysis implies the energy of such two scenarios is zero and so we get a contradiction.

Far-field Lorenz-Mie scattering in an absorbing host medium: Theoretical formalism and FORTRAN program

NASA Astrophysics Data System (ADS)

Mishchenko, Michael I.; Yang, Ping

2018-01-01

In this paper we make practical use of the recently developed first-principles approach to electromagnetic scattering by particles immersed in an unbounded absorbing host medium. Specifically, we introduce an actual computational tool for the calculation of pertinent far-field optical observables in the context of the classical Lorenz-Mie theory. The paper summarizes the relevant theoretical formalism, explains various aspects of the corresponding numerical algorithm, specifies the input and output parameters of a FORTRAN program available at https://www.giss.nasa.gov/staff/mmishchenko/Lorenz-Mie.html, and tabulates benchmark results useful for testing purposes. This public-domain FORTRAN program enables one to solve the following two important problems: (i) simulate theoretically the reading of a remote well-collimated radiometer measuring electromagnetic scattering by an individual spherical particle or a small random group of spherical particles; and (ii) compute the single-scattering parameters that enter the vector radiative transfer equation derived directly from the Maxwell equations.

Characterization of Compton-scatter imaging with an analytical simulation method

PubMed Central

Jones, Kevin C; Redler, Gage; Templeton, Alistair; Bernard, Damian; Turian, Julius V; Chu, James C H

2018-01-01

By collimating the photons scattered when a megavoltage therapy beam interacts with the patient, a Compton-scatter image may be formed without the delivery of an extra dose. To characterize and assess the potential of the technique, an analytical model for simulating scatter images was developed and validated against Monte Carlo (MC). For three phantoms, the scatter images collected during irradiation with a 6 MV flattening-filter-free therapy beam were simulated. Images, profiles, and spectra were compared for different phantoms and different irradiation angles. The proposed analytical method simulates accurate scatter images up to 1000 times faster than MC. Minor differences between MC and analytical simulated images are attributed to limitations in the isotropic superposition/convolution algorithm used to analytically model multiple-order scattering. For a detector placed at 90° relative to the treatment beam, the simulated scattered photon energy spectrum peaks at 140–220 keV, and 40–50% of the photons are the result of multiple scattering. The high energy photons originate at the beam entrance. Increasing the angle between source and detector increases the average energy of the collected photons and decreases the relative contribution of multiple scattered photons. Multiple scattered photons cause blurring in the image. For an ideal 5 mm diameter pinhole collimator placed 18.5 cm from the isocenter, 10 cGy of deposited dose (2 Hz imaging rate for 1200 MU min−1 treatment delivery) is expected to generate an average 1000 photons per mm2 at the detector. For the considered lung tumor CT phantom, the contrast is high enough to clearly identify the lung tumor in the scatter image. Increasing the treatment beam size perpendicular to the detector plane decreases the contrast, although the scatter subject contrast is expected to be greater than the megavoltage transmission image contrast. With the analytical method, real-time tumor tracking may be possible through comparison of simulated and acquired patient images. PMID:29243663

Characterization of Compton-scatter imaging with an analytical simulation method

NASA Astrophysics Data System (ADS)

Jones, Kevin C.; Redler, Gage; Templeton, Alistair; Bernard, Damian; Turian, Julius V.; Chu, James C. H.

2018-01-01

By collimating the photons scattered when a megavoltage therapy beam interacts with the patient, a Compton-scatter image may be formed without the delivery of an extra dose. To characterize and assess the potential of the technique, an analytical model for simulating scatter images was developed and validated against Monte Carlo (MC). For three phantoms, the scatter images collected during irradiation with a 6 MV flattening-filter-free therapy beam were simulated. Images, profiles, and spectra were compared for different phantoms and different irradiation angles. The proposed analytical method simulates accurate scatter images up to 1000 times faster than MC. Minor differences between MC and analytical simulated images are attributed to limitations in the isotropic superposition/convolution algorithm used to analytically model multiple-order scattering. For a detector placed at 90° relative to the treatment beam, the simulated scattered photon energy spectrum peaks at 140-220 keV, and 40-50% of the photons are the result of multiple scattering. The high energy photons originate at the beam entrance. Increasing the angle between source and detector increases the average energy of the collected photons and decreases the relative contribution of multiple scattered photons. Multiple scattered photons cause blurring in the image. For an ideal 5 mm diameter pinhole collimator placed 18.5 cm from the isocenter, 10 cGy of deposited dose (2 Hz imaging rate for 1200 MU min-1 treatment delivery) is expected to generate an average 1000 photons per mm2 at the detector. For the considered lung tumor CT phantom, the contrast is high enough to clearly identify the lung tumor in the scatter image. Increasing the treatment beam size perpendicular to the detector plane decreases the contrast, although the scatter subject contrast is expected to be greater than the megavoltage transmission image contrast. With the analytical method, real-time tumor tracking may be possible through comparison of simulated and acquired patient images.

Time-reversal optical tomography: detecting and locating extended targets in a turbid medium

NASA Astrophysics Data System (ADS)

Wu, Binlin; Cai, W.; Xu, M.; Gayen, S. K.

2012-03-01

Time Reversal Optical Tomography (TROT) is developed to locate extended target(s) in a highly scattering turbid medium, and estimate their optical strength and size. The approach uses Diffusion Approximation of Radiative Transfer Equation for light propagation along with Time Reversal (TR) Multiple Signal Classification (MUSIC) scheme for signal and noise subspaces for assessment of target location. A MUSIC pseudo spectrum is calculated using the eigenvectors of the TR matrix T, whose poles provide target locations. Based on the pseudo spectrum contours, retrieval of target size is modeled as an optimization problem, using a "local contour" method. The eigenvalues of T are related to optical strengths of targets. The efficacy of TROT to obtain location, size, and optical strength of one absorptive target, one scattering target, and two absorptive targets, all for different noise levels was tested using simulated data. Target locations were always accurately determined. Error in optical strength estimates was small even at 20% noise level. Target size and shape were more sensitive to noise. Results from simulated data demonstrate high potential for application of TROT in practical biomedical imaging applications.

Vibrational properties of nanocrystals from the Debye Scattering Equation

DOE PAGES

Scardi, P.; Gelisio, L.

2016-02-26

One hundred years after the original formulation by Petrus J.W. Debije (aka Peter Debye), the Debye Scattering Equation (DSE) is still the most accurate expression to model the diffraction pattern from nanoparticle systems. A major limitation in the original form of the DSE is that it refers to a static domain, so that including thermal disorder usually requires rescaling the equation by a Debye-Waller thermal factor. The last is taken from the traditional diffraction theory developed in Reciprocal Space (RS), which is opposed to the atomistic paradigm of the DSE, usually referred to as Direct Space (DS) approach. Besides beingmore » a hybrid of DS and RS expressions, rescaling the DSE by the Debye-Waller factor is an approximation which completely misses the contribution of Temperature Diffuse Scattering (TDS). The present work proposes a solution to include thermal effects coherently with the atomistic approach of the DSE. Here, a deeper insight into the vibrational dynamics of nanostructured materials can be obtained with few changes with respect to the standard formulation of the DSE, providing information on the correlated displacement of vibrating atoms.« less

A boundary integral equation method using auxiliary interior surface approach for acoustic radiation and scattering in two dimensions.

PubMed

Yang, S A

2002-10-01

This paper presents an effective solution method for predicting acoustic radiation and scattering fields in two dimensions. The difficulty of the fictitious characteristic frequency is overcome by incorporating an auxiliary interior surface that satisfies certain boundary condition into the body surface. This process gives rise to a set of uniquely solvable boundary integral equations. Distributing monopoles with unknown strengths over the body and interior surfaces yields the simple source formulation. The modified boundary integral equations are further transformed to ordinary ones that contain nonsingular kernels only. This implementation allows direct application of standard quadrature formulas over the entire integration domain; that is, the collocation points are exactly the positions at which the integration points are located. Selecting the interior surface is an easy task. Moreover, only a few corresponding interior nodal points are sufficient for the computation. Numerical calculations consist of the acoustic radiation and scattering by acoustically hard elliptic and rectangular cylinders. Comparisons with analytical solutions are made. Numerical results demonstrate the efficiency and accuracy of the current solution method.

Stability analysis of implicit time discretizations for the Compton-scattering Fokker-Planck equation

NASA Astrophysics Data System (ADS)

Densmore, Jeffery D.; Warsa, James S.; Lowrie, Robert B.; Morel, Jim E.

2009-09-01

The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.

Scattering theory for the defocusing fourth-order Schrödinger equation

NASA Astrophysics Data System (ADS)

Miao, Changxing; Zheng, Jiqiang

2016-02-01

In this paper, we study the global well-posedness and scattering theory for the defocusing fourth-order nonlinear Schrödinger equation (FNLS) \\text{i}{{u}t}+{{Δ }2}u +\\mid u{{\\mid}p}u=0 in dimensions d≥slant 8 . We prove that if the solution u is apriorily bounded in the critical Sobolev space, that is, u\\in Lt∞≤ft(I;\\overset{\\centerdot}{\\mathop{H}} x{{sc}}≤ft({{{R}}d}\\right)\\right) with all {{s}c}:=\\frac{d}{2}-\\frac{4}{p}≥slant 1 if p is an even integer or {{s}c}\\in ≤ft[1,2+p\\right) otherwise, then u is global and scatters. We will give a uniform way to treat the energy-subcritical, energy-critical and energy-supercritical FNLS by making use of the strategy derived from concentration compactness ideas, and we are able to overcome the logarithmic blowup in the double Duhamel trick in dimension eight by exploiting the refined dispersive estimate which is in sharp contrast to the Schrödinger equation.

The eight tetrahedron equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hietarinta, J.; Nijhoff, F.

1997-07-01

In this paper we derive from arguments of string scattering a set of eight tetrahedron equations, with different index orderings. It is argued that this system of equations is the proper system that represents integrable structures in three dimensions generalizing the Yang{endash}Baxter equation. Under additional restrictions this system reduces to the usual tetrahedron equation in the vertex form. Most known solutions fall under this class, but it is by no means necessary. Comparison is made with the work on braided monoidal 2-categories also leading to eight tetrahedron equations. {copyright} {ital 1997 American Institute of Physics.}

New nonlinear evolution equations from surface theory

NASA Astrophysics Data System (ADS)

Gürses, Metin; Nutku, Yavuz

1981-07-01

We point out that the connection between surfaces in three-dimensional flat space and the inverse scattering problem provides a systematic way for constructing new nonlinear evolution equations. In particular we study the imbedding for Guichard surfaces which gives rise to the Calapso-Guichard equations generalizing the sine-Gordon (SG) equation. Further, we investigate the geometry of surfaces and their imbedding which results in the Korteweg-deVries (KdV) equation. Then by constructing a family of applicable surfaces we obtain a generalization of the KdV equation to a compressible fluid.

Analytical study of the effects of clouds on the light produced by lightning

NASA Technical Reports Server (NTRS)

Phanord, Dieudonne D.

1990-01-01

Researchers consider the scattering of visible and infrared light due to lightning by cubic, cylindrical and spherical clouds. The researchers extend to cloud physics the work by Twersky for single and multiple scattering of electromagnetic waves. They solve the interior problem separately to obtain the bulk parameters for the scatterer equivalent to the ensemble of spherical droplets. With the interior solution or the equivalent medium approach, the multiple scattering problem is reduced to that of a single scatterer in isolation. Hence, the computing methods of Wiscombe or Bohren specialized to Mie scattering with the possibility for absorption were used to generate numerical results in short computer time.

An analytical theory of a scattering of radio waves on meteoric ionization - II. Solution of the integro-differential equation in case of backscatter

NASA Astrophysics Data System (ADS)

Pecina, P.

2016-12-01

The integro-differential equation for the polarization vector P inside the meteor trail, representing the analytical solution of the set of Maxwell equations, is solved for the case of backscattering of radio waves on meteoric ionization. The transversal and longitudinal dimensions of a typical meteor trail are small in comparison to the distances to both transmitter and receiver and so the phase factor appearing in the kernel of the integral equation is large and rapidly changing. This allows us to use the method of stationary phase to obtain an approximate solution of the integral equation for the scattered field and for the corresponding generalized radar equation. The final solution is obtained by expanding it into the complete set of Bessel functions, which results in solving a system of linear algebraic equations for the coefficients of the expansion. The time behaviour of the meteor echoes is then obtained using the generalized radar equation. Examples are given for values of the electron density spanning a range from underdense meteor echoes to overdense meteor echoes. We show that the time behaviour of overdense meteor echoes using this method is very different from the one obtained using purely numerical solutions of the Maxwell equations. Our results are in much better agreement with the observations performed e.g. by the Ondřejov radar.

Development and application of discontinuous Galerkin method for the solution of two-dimensional Maxwell equations

NASA Astrophysics Data System (ADS)

Wong, See-Cheuk

We inhabit an environment of electromagnetic (EM) waves. The waves within the EM spectrum---whether light, radio, or microwaves---all obey the same physical laws. A band in the spectrum is designated to the microwave frequencies (30MHz--300GHz), at which radar systems operate. The precise modeling of the scattered EM-ields about a target, as well as the numerical prediction of the radar return is the crux of the computational electromagnetics (CEM) problems. The signature or return from a target observed by radar is commonly provided in the form of radar cross section (RCS). Incidentally, the efforts in the reduction of such return forms the basis of stealth aircraft design. The object of this dissertation is to extend Discontinuous Galerkin (DG) method to solve numerically the Maxwell equations for scatterings from perfect electric conductor (PEC) objects. The governing equations are derived by writing the Maxwell equations in conservation-law form for scattered field quantities. The transverse magnetic (TM) and the transverse electric (TE) waveforms of the Maxwell equations are considered. A finite-element scheme is developed with proper representations for the electric and magnetic fluxes at a cell interface to account for variations in properties, in both space and time. A characteristic sub-path integration process, known as the "Riemann solver" is involved. An explicit Runge-Kutta Discontinuous Galerkin (RKDG) upwind scheme, which is fourth-order accurate in time and second-order in space, is employed to solve the TM and TE equations. Arbitrary cross-sectioned bodies are modeled, around which computational grids using random triangulation are generated. The RKDG method, in its development stage, was constructed and studied for solving hyperbolic conservation equations numerically. It was later extended to multidimensional nonlinear systems of conservation laws. The algorithms are described, including the formulations and treatments to the numerical fluxes, degrees of freedom, boundary conditions, and other implementation issues. The computational solution amounts to a near-field solution in form of contour plot and one extending from the scatterer to a far-field boundary located a few wavelengths away. Near-field to far-field transformation utilizing the Green's function is performed to obtain the bistatic radar cross section information. Results are presented for scatterings from a series of two-dimensional objects, including circular and square cylinders, ogive and NACA airfoils. Also, scatterings from more complex geometries such as cylindrical and rectangular cavitations are simulated. Exact solutions for selected cases are compared to the computational results and demonstrate excellent accuracy and efficiency in the RKDG calculations. In the whole, its ease and flexibility to incorporate the characteristic-based schemes for the flux integrals between cell interfaces, and the compact formulation allowing direct application to the boundary elements without modification are some of the admired features of the DG method.

Investigation of spin-zero bosons in q-deformed relativistic quantum mechanics

NASA Astrophysics Data System (ADS)

Sobhani, H.; Chung, W. S.; Hassanabadi, H.

2018-04-01

In this article, Scattering states of Klein-Gordon equation for three scatter potentials of single and double Dirac delta and a potential well in the q-deformed formalism of relativistic quantum mechanics have been derived. At first, we discussed how q-deformed formalism can be constructed and used. Postulates of this q-deformed quantum mechanics are noted. Then scattering problems for spin-zero bosons are studied.

Study of scattering cross section of a plasma column using Green's function volume integral equation method

NASA Astrophysics Data System (ADS)

Soltanmoradi, Elmira; Shokri, Babak

2017-05-01

In this article, the electromagnetic wave scattering from plasma columns with inhomogeneous electron density distribution is studied by the Green's function volume integral equation method. Due to the ready production of such plasmas in the laboratories and their practical application in various technological fields, this study tries to find the effects of plasma parameters such as the electron density, radius, and pressure on the scattering cross-section of a plasma column. Moreover, the incident wave frequency influence of the scattering pattern is demonstrated. Furthermore, the scattering cross-section of a plasma column with an inhomogeneous collision frequency profile is calculated and the effect of this inhomogeneity is discussed first in this article. These results are especially used to determine the appropriate conditions for radar cross-section reduction purposes. It is shown that the radar cross-section of a plasma column reduces more for a larger collision frequency, for a relatively lower plasma frequency, and also for a smaller radius. Furthermore, it is found that the effect of the electron density on the scattering cross-section is more obvious in comparison with the effect of other plasma parameters. Also, the plasma column with homogenous collision frequency can be used as a better shielding in contrast to its inhomogeneous counterpart.

Theoretical study of interactions of BSA protein in a NaCl aqueous solution

NASA Astrophysics Data System (ADS)

Pellicane, Giuseppe; Cavero, Miguel

2013-03-01

Bovine Serum Albumine (BSA) aqueous solutions in the presence of NaCl are investigated for different protein concentrations and low to intermediate ionic strengths. Protein interactions are modeled via a charge-screened colloidal model, in which the range of the potential is determined by the Debye-Hückel constant. We use Monte Carlo computer simulations to calculate the structure factor, and assume an oblate ellipsoidal form factor for BSA. The theoretical scattered intensities are found in good agreement with the experimental small angle X-ray scattering intensities available in the literature. The performance of well-known integral equation closures to the Ornstein-Zernike equation, namely the mean spherical approximation, the Percus-Yevick, and the hypernetted chain equations, is also assessed with respect to computer simulation.

Formation of quasiparallel Alfven solitons

NASA Technical Reports Server (NTRS)

Hamilton, R. L.; Kennel, C. F.; Mjolhus, E.

1992-01-01

The formation of quasi-parallel Alfven solitons is investigated through the inverse scattering transformation (IST) for the derivative nonlinear Schroedinger (DNLS) equation. The DNLS has a rich complement of soliton solutions consisting of a two-parameter soliton family and a one-parameter bright/dark soliton family. In this paper, the physical roles and origins of these soliton families are inferred through an analytic study of the scattering data generated by the IST for a set of initial profiles. The DNLS equation has as limiting forms the nonlinear Schroedinger (NLS), Korteweg-de-Vries (KdV) and modified Korteweg-de-Vries (MKdV) equations. Each of these limits is briefly reviewed in the physical context of quasi-parallel Alfven waves. The existence of these limiting forms serves as a natural framework for discussing the formation of Alfven solitons.

A study of the radiative transfer equation using a spherical harmonics-nodal collocation method

NASA Astrophysics Data System (ADS)

Capilla, M. T.; Talavera, C. F.; Ginestar, D.; Verdú, G.

2017-03-01

Optical tomography has found many medical applications that need to know how the photons interact with the different tissues. The majority of the photon transport simulations are done using the diffusion approximation, but this approximation has a limited validity when optical properties of the different tissues present large gradients, when structures near the photons source are studied or when anisotropic scattering has to be taken into account. As an alternative to the diffusion model, the PL equations for the radiative transfer problem are studied. These equations are discretized in a rectangular mesh using a nodal collocation method. The performance of this model is studied by solving different 1D and 2D benchmark problems of light propagation in tissue having media with isotropic and anisotropic scattering.

Physical processes in the strong magnetic fields of accreting neutron stars

NASA Technical Reports Server (NTRS)

Meszaros, P.

1984-01-01

Analytical formulae are fitted to observational data on physical processes occurring in strong magnetic fields surrounding accreting neutron stars. The propagation of normal modes in the presence of a quantizing magnetic field is discussed in terms of a wave equation in Fourier space, quantum electrodynamic effects, polarization and mode ellipticity. The results are applied to calculating the Thomson scattering, bremsstrahlung and Compton scattering cross-sections, which are a function of the frequency, angle and polarization of the magnetic field. Numerical procedures are explored for solving the radiative transfer equations. When applied to modeling X ray pulsars, a problem arises in the necessity to couple the magnetic angle and frequency dependence of the cross-sections with the hydrodynamic equations. The use of time-dependent averaging and approximation techniques is indicated.

Stark problem in terms of the Stokes multipliers for the triconfluent Heun equation

NASA Astrophysics Data System (ADS)

Osherov, V. I.; Ushakov, V. G.

2013-11-01

The solution of the Stark problem is obtained in terms of the Stokes multipliers for the triconfluent Heun equation (the quartic oscillator equation). The Stokes multipliers are found in an analytical form at positive energies. For negative energies, the Stokes parameters are calculated in frames of a consistent asymptotic approach. The scattering phase, positions, and widths of the Stark resonances are determined as solutions of an implicit equation.

Simulation of RF-fields in a fusion device

DOE Office of Scientific and Technical Information (OSTI.GOV)

De Witte, Dieter; Bogaert, Ignace; De Zutter, Daniel

2009-11-26

In this paper the problem of scattering off a fusion plasma is approached from the point of view of integral equations. Using the volume equivalence principle an integral equation is derived which describes the electromagnetic fields in a plasma. The equation is discretized with MoM using conforming basis functions. This reduces the problem to solving a dense matrix equation. This can be done iteratively. Each iteration can be sped up using FFTs.

On the theory and simulation of multiple Coulomb scattering of heavy-charged particles.

PubMed

Striganov, S I

2005-01-01

The Moliere theory of multiple Coulomb scattering is modified to take into account the difference between processes of scattering off atomic nuclei and electrons. A simple analytical expression for angular distribution of charged particles passing through a thick absorber is found. It does not assume any special form for a differential scattering cross section and has a wider range of applicability than a gaussian approximation. A well-known method to simulate multiple Coulomb scatterings is based on treating 'soft' and 'hard' collisions differently. An angular deflection in a large number of 'soft' collisions is sampled using the proposed distribution function, a small number of 'hard' collision are simulated directly. A boundary between 'hard' and 'soft' collisions is defined, providing a precise sampling of a scattering angle (1% level) and a small number of 'hard' collisions. A corresponding simulating module takes into account projectile and nucleus charged distributions and exact kinematics of a projectile-electron interaction.

The Cauchy problem for the Pavlov equation

NASA Astrophysics Data System (ADS)

Grinevich, P. G.; Santini, P. M.; Wu, D.

2015-10-01

Commutation of multidimensional vector fields leads to integrable nonlinear dispersionless PDEs that arise in various problems of mathematical physics and have been intensively studied in recent literature. This report aims to solve the scattering and inverse scattering problem for integrable dispersionless PDEs, recently introduced just at a formal level, concentrating on the prototypical example of the Pavlov equation, and to justify an existence theorem for global bounded solutions of the associated Cauchy problem with small data. An essential part of this work was made during the visit of the three authors to the Centro Internacional de Ciencias in Cuernavaca, Mexico in November-December 2012.

Modeling boundary measurements of scattered light using the corrected diffusion approximation

PubMed Central

Lehtikangas, Ossi; Tarvainen, Tanja; Kim, Arnold D.

2012-01-01

We study the modeling and simulation of steady-state measurements of light scattered by a turbid medium taken at the boundary. In particular, we implement the recently introduced corrected diffusion approximation in two spatial dimensions to model these boundary measurements. This implementation uses expansions in plane wave solutions to compute boundary conditions and the additive boundary layer correction, and a finite element method to solve the diffusion equation. We show that this corrected diffusion approximation models boundary measurements substantially better than the standard diffusion approximation in comparison to numerical solutions of the radiative transport equation. PMID:22435102

On the use of co-ordinate stretching in the numeral computation of high frequency scattering. [of jet engine noise by fuselage

NASA Technical Reports Server (NTRS)

Bayliss, A.

1978-01-01

The scattering of the sound of a jet engine by an airplane fuselage is modeled by solving the axially symmetric Helmholtz equation exterior to a long thin ellipsoid. The integral equation method based on the single layer potential formulation is used. A family of coordinate systems on the body is introduced and an algorithm is presented to determine the optimal coordinate system. Numerical results verify that the optimal choice enables the solution to be computed with a grid that is coarse relative to the wavelength.

Light-Scattering Characteristics of Optical Surfaces

DTIC Science & Technology

1975-01-01

6RSTR--O _____4. TITLE (ad . TYPE OF REPORT & PERIOD COVERED 4 Light-Scattering Characteristics of tica: / __ , o -, Sufcs 6 . PERFORMING ORG. REPORT...UO(-90 JJf A0(ct,B;O) e 2r( 6 +Pdd (2) A (cc, 8;A) - JJ U(.t,9;2) e~i2w(+O) dtdg (3) = fJ A(ao;) e i21r(a+00dade. ( 4 ) -c Equations (2) and ( 4 ...Eq. ( 4 ) and requiring the individual plane wave components to satisfy the Helmholtz equation, we find A(ca,;A) - Ao(Ca,;0) e 2wy ( 6 ) where • r. The

How the Klein–Nishina formula was derived: Based on the Sangokan Nishina Source Materials

PubMed Central

YAZAKI, Yuji

2017-01-01

In 1928, Klein and Nishina investigated Compton scattering based on the Dirac equation just proposed in the same year, and derived the Klein–Nishina formula for the scattering cross section of a photon. At that time the Dirac equation had the following unsettled conceptual questions: the negative energy states, its four-component wave functions, and the spin states of an electron. Hence, during their investigation struggles, they encountered various difficulties. In this article, we describe their struggles to derive the formula using the “Sangokan Nishina Source Materials” retained in the the Nishina Memorial Foundation. PMID:28603211

A numerical study of electromagnetic scattering from ocean like surfaces

NASA Technical Reports Server (NTRS)

Lentz, R. R.

1972-01-01

The integral equations describing electromagnetic scattering from one dimensional conducting surfaces are formulated and numerical results are presented. The results are compared with those obtained using approximate methods such as physical optics, geometrical optics, and perturbation theory. The integral equation solutions show that the surface radius of curvature must be greater than 2.5 wavelengths for either the physical optics or geometric optics to give satisfactory results. It has also been shown that perturbation theory agrees with the exact fields as long as the root mean square surface roughness is less than one-tenth of a wavelength.

Laplace-transform-based method to calculate back-reflected radiance from an isotropically scattering half-space

NASA Astrophysics Data System (ADS)

Rinzema, K.; Hoenders, B. J.; Ferwerda, H. A.

1997-07-01

We present a method to determine the back-reflected radiance from an isotropically scattering half-space with matched boundary. This method has the advantage that it leads very quickly to the relevant equations, the numerical solution of which is also quite easy. Essentially, the method is derived from a mathematical criterion that effectively forbids the existence of solutions to the transport equation which grow exponentially as one moves away from the surface and deeper into the medium. Preliminary calculations for infinitely wide beams yield results which agree very well with what is found in the literature.

Low frequency acoustic and electromagnetic scattering

NASA Technical Reports Server (NTRS)

Hariharan, S. I.; Maccamy, R. C.

1986-01-01

This paper deals with two classes of problems arising from acoustics and electromagnetics scattering in the low frequency stations. The first class of problem is solving Helmholtz equation with Dirichlet boundary conditions on an arbitrary two dimensional body while the second one is an interior-exterior interface problem with Helmholtz equation in the exterior. Low frequency analysis show that there are two intermediate problems which solve the above problems accurate to 0(k/2/ log k) where k is the frequency. These solutions greatly differ from the zero frequency approximations. For the Dirichlet problem numerical examples are shown to verify the theoretical estimates.

On increasing stability in the two dimensional inverse source scattering problem with many frequencies

NASA Astrophysics Data System (ADS)

Entekhabi, Mozhgan Nora; Isakov, Victor

2018-05-01

In this paper, we will study the increasing stability in the inverse source problem for the Helmholtz equation in the plane when the source term is assumed to be compactly supported in a bounded domain Ω with a sufficiently smooth boundary. Using the Fourier transform in the frequency domain, bounds for the Hankel functions and for scattering solutions in the complex plane, improving bounds for the analytic continuation, and the exact observability for the wave equation led us to our goals which are a sharp uniqueness and increasing stability estimate when the wave number interval is growing.

Accurate expansion of cylindrical paraxial waves for its straightforward implementation in electromagnetic scattering

NASA Astrophysics Data System (ADS)

Naserpour, Mahin; Zapata-Rodríguez, Carlos J.

2018-01-01

The evaluation of vector wave fields can be accurately performed by means of diffraction integrals, differential equations and also series expansions. In this paper, a Bessel series expansion which basis relies on the exact solution of the Helmholtz equation in cylindrical coordinates is theoretically developed for the straightforward yet accurate description of low-numerical-aperture focal waves. The validity of this approach is confirmed by explicit application to Gaussian beams and apertured focused fields in the paraxial regime. Finally we discuss how our procedure can be favorably implemented in scattering problems.

Scattering and Diffraction of Electromagnetic Radiation: An Effective Probe to Material Structure

NASA Technical Reports Server (NTRS)

Xu, Yu-Lin

2016-01-01

Scattered electromagnetic waves from material bodies of different forms contain, in an intricate way, precise information on the intrinsic, geometrical and physical properties of the objects. Scattering theories, ever deepening, aim to provide dependable interpretation and prediction to the complicated interaction of electromagnetic radiation with matter. There are well-established multiple-scattering formulations based on classical electromagnetic theories. An example is the Generalized Multi-particle Mie-solution (GMM), which has recently been extended to a special version ? the GMM-PA approach, applicable to finite periodic arrays consisting of a huge number (e.g., >>106) of identical scattering centers [1]. The framework of the GMM-PA is nearly complete. When the size of the constituent unit scatterers becomes considerably small in comparison with incident wavelength, an appropriate array of such small element volumes may well be a satisfactory representation of a material entity having an arbitrary structure. X-ray diffraction is a powerful characterization tool used in a variety of scientific and technical fields, including material science. A diffraction pattern is nothing more than the spatial distribution of scattered intensity, determined by the distribution of scattering matter by way of its Fourier transform [1]. Since all linear dimensions entered into Maxwell's equations are normalized by wavelength, an analogy exists between optical and X-ray diffraction patterns. A large set of optical diffraction patterns experimentally obtained can be found in the literature [e.g., 2,3]. Theoretical results from the GMM-PA have been scrutinized using a large collection of publically accessible, experimentally obtained Fraunhofer diffraction patterns. As far as characteristic structures of the patterns are concerned, theoretical and experimental results are in uniform agreement; no exception has been found so far. Closely connected with the spatial distribution of scattered intensities are cross sections, such as for extinction, scattering, absorption, and radiation pressure, as a critical type of key quantity addressed in most theoretical and experimental studies of radiative scattering. Cross sections predicted from different scattering theories are supposed to be in general agreement. For objects of irregular shape, the GMM-PA solutions can be compared with the highly flexible Discrete Dipole Approximation (DDA) [4,5] when dividing a target to no more than 106 unit cells. Also, there are different ways to calculate the cross sections in the GMM-PA, providing an additional means to examine the accuracy of the numerical solutions and to unveil potential issues concerning the theoretical formulations and numerical aspects. To solve multiple scattering by an assembly of material volumes through classical theories such as the GMM-PA, the radiative properties of the component scatterers, the complex refractive index in particular, must be provided as input parameters. When using a PA to characterize a material body, this involves the use of an adequate theoretical tool, an effective medium theory, to connect Maxwell's phenomenogical theory with the atomistic theory of matter. In the atomic theory, one regards matter as composed of interacting particles (atoms and molecules) embedded in the vacuum [6]. However, the radiative properties of atomic-scaled particles are known to be substantially different from bulk materials. Intensive research efforts in the fields of cluster science and nanoscience attempt to bridge the gap between bulk and atom and to understand the transition from classical to quantum physics. The GMM-PA calculations, which place virtually no restriction on the component-particle size, might help to gain certain insight into the transition.

Scattering of massless fermions by Schwarzschild and Reissner-Nordström black holes

NASA Astrophysics Data System (ADS)

Sporea, Ciprian A.

2017-12-01

We study the scattering of massless Dirac fermions by Schwarzschild and Reissner-Nordström black holes. This is done by applying partial wave analysis to the scattering modes obtained after solving the massless Dirac equation in the asymptotic regions of the two black hole geometries. We successfully obtain analytic phase shifts, with the help of which the scattering cross section is computed. The glory and spiral scattering phenomena are shown to be present, as in the case of massive fermion scattering by black holes. Supported by a grant of the Ministry of National Education and Scientific Research, RDI Programme for Space Technology and Advanced Research - STAR, project number 181/20.07.2017

Polarimetric scattering from layered media with multiple species of scatterers

NASA Technical Reports Server (NTRS)

Nghiem, S. V.; Kwok, R.; Yueh, S. H.; Kong, J. A.; Hsu, C. C.; Tassoudji, M. A.; Shin, R. T.

1995-01-01

Geophysical media are usually heterogeneous and contain multiple species of scatterers. In this paper a model is presented to calculate effective permittivities and polarimetric backscattering coefficients of multispecies-layered media. The same physical description is consistently used in the derivation of both permittivities and scattering coefficients. The strong permittivity fluctuation theory is extended to account for the multiple species of scatterers with a general ellipsoidal shape whose orientations are randomly distributed. Under the distorted Born approximation, polarimetric scattering coefficients are obtained. These calculations are applicable to the special cases of spheroidal and spherical scatterers. The model is used to study effects of scatterer shapes and multispecies mixtures on polarimetric signatures of heterogeneous media. The multispecies model accounts for moisture content in scattering media such as snowpack in an ice sheet. The results indicate a high sensitivity of backscatter to moisture with a stronger dependence for drier snow and ice grain size is important to the backscatter. For frost-covered saline ice, model results for bare ice are compared with measured data at C band and then the frost flower formation is simulated with a layer of fanlike ice crystals including brine infiltration over a rough interface. The results with the frost cover suggest a significant increase in scattering coefficients and a polarimetric signature closer to isotropic characteristics compared to the thin saline ice case.

Acoustic properties and density of polyurea at pressure up to 13.5 GPa through Brillouin scattering spectroscopy

NASA Astrophysics Data System (ADS)

Ransom, T. C.; Ahart, Muhtar; Hemley, Russell J.; Roland, C. M.

2018-05-01

Brillouin scattering was performed on an elastomeric polyurea, an important technological polymer. Being widely used for impact modification, of particular interest is its response to extreme pressure conditions. We applied pressures up to 13.5 GPa using a diamond anvil cell and measured the longitudinal and transverse sound velocities via Brillouin light scattering. From these data, the equation of state, the elastic moduli, and Poisson's ratio were obtained. By comparison with previous dilatometry measurements up to 1 GPa, we show how viscoelastic effects can be accounted for in order to obtain an accurate equation of state. Because of the extreme strain-rate hardening of vitrifying polyurea, the property changes associated with its solidification are more subtle in the high frequency Brillouin data than observed in conventional mechanical testing and dilatometry.

Wave-packet continuum-discretization approach to ion-atom collisions including rearrangement: Application to differential ionization in proton-hydrogen scattering

NASA Astrophysics Data System (ADS)

Abdurakhmanov, I. B.; Bailey, J. J.; Kadyrov, A. S.; Bray, I.

2018-03-01

In this work, we develop a wave-packet continuum-discretization approach to ion-atom collisions that includes rearrangement processes. The total scattering wave function is expanded using a two-center basis built from wave-packet pseudostates. The exact three-body Schrödinger equation is converted into coupled-channel differential equations for time-dependent expansion coefficients. In the asymptotic region these time-dependent coefficients represent transition amplitudes for all processes including elastic scattering, excitation, ionization, and electron capture. The wave-packet continuum-discretization approach is ideal for differential ionization studies as it allows one to generate pseudostates with arbitrary energies and distribution. The approach is used to calculate the double differential cross section for ionization in proton collisions with atomic hydrogen. Overall good agreement with experiment is obtained for all considered cases.

A spectral geometric model for Compton single scatter in PET based on the single scatter simulation approximation

NASA Astrophysics Data System (ADS)

Kazantsev, I. G.; Olsen, U. L.; Poulsen, H. F.; Hansen, P. C.

2018-02-01

We investigate the idealized mathematical model of single scatter in PET for a detector system possessing excellent energy resolution. The model has the form of integral transforms estimating the distribution of photons undergoing a single Compton scattering with a certain angle. The total single scatter is interpreted as the volume integral over scatter points that constitute a rotation body with a football shape, while single scattering with a certain angle is evaluated as the surface integral over the boundary of the rotation body. The equations for total and sample single scatter calculations are derived using a single scatter simulation approximation. We show that the three-dimensional slice-by-slice filtered backprojection algorithm is applicable for scatter data inversion provided that the attenuation map is assumed to be constant. The results of the numerical experiments are presented.

Quantum hydrodynamics: capturing a reactive scattering resonance.

PubMed

Derrickson, Sean W; Bittner, Eric R; Kendrick, Brian K

2005-08-01

The hydrodynamic equations of motion associated with the de Broglie-Bohm formulation of quantum mechanics are solved using a meshless method based upon a moving least-squares approach. An arbitrary Lagrangian-Eulerian frame of reference and a regridding algorithm which adds and deletes computational points are used to maintain a uniform and nearly constant interparticle spacing. The methodology also uses averaged fields to maintain unitary time evolution. The numerical instabilities associated with the formation of nodes in the reflected portion of the wave packet are avoided by adding artificial viscosity to the equations of motion. A new and more robust artificial viscosity algorithm is presented which gives accurate scattering results and is capable of capturing quantum resonances. The methodology is applied to a one-dimensional model chemical reaction that is known to exhibit a quantum resonance. The correlation function approach is used to compute the reactive scattering matrix, reaction probability, and time delay as a function of energy. Excellent agreement is obtained between the scattering results based upon the quantum hydrodynamic approach and those based upon standard quantum mechanics. This is the first clear demonstration of the ability of moving grid approaches to accurately and robustly reproduce resonance structures in a scattering system.

Low-energy electron scattering from CO. 2: Ab-initio study using the frame-transformation theory

NASA Technical Reports Server (NTRS)

Chandra, N.

1976-01-01

The Wigner-Eisenbud R matrix method has been combined with the frame transformation theory to study electron scattering from molecular systems. The R matrix, calculated at the boundary point of the molecular core radius, has been transformed to the space frame in order to continue the solution of the scattering equations in the outer region where rotational motion of the nuclei is taken into account. This procedure has been applied to a model calculation of thermal energy electron scattering from CO.

The role of CP violating scatterings in baryogenesis—case study of the neutron portal

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baldes, Iason; Bell, Nicole F.; Millar, Alexander

Many baryogenesis scenarios invoke the charge parity (CP) violating out-of-equilibrium decay of a heavy particle in order to explain the baryon asymmetry. Such scenarios will in general also allow CP violating scatterings. We study the effect of these CP violating scatterings on the final asymmetry in a neutron portal scenario. We solve the Boltzmann equations governing the evolution of the baryon number numerically and show that the CP violating scatterings play a dominant role in a significant portion of the parameter space.

A fixed energy fixed angle inverse scattering in interior transmission problem

NASA Astrophysics Data System (ADS)

Chen, Lung-Hui

2017-06-01

We study the inverse acoustic scattering problem in mathematical physics. The problem is to recover the index of refraction in an inhomogeneous medium by measuring the scattered wave fields in the far field. We transform the problem to the interior transmission problem in the study of the Helmholtz equation. We find an inverse uniqueness on the scatterer with a knowledge of a fixed interior transmission eigenvalue. By examining the solution in a series of spherical harmonics in the far field, we can determine uniquely the perturbation source for the radially symmetric perturbations.

Energy-loss cross sections for inclusive charge-exchange reactions at intermediate energies

NASA Technical Reports Server (NTRS)

Cucinotta, Francis A.; Townsend, Lawrence W.; Dubey, Rajendra R.

1993-01-01

Charge-exchange reactions for scattering to the continuum are considered in a high-energy multiple scattering model. Calculations for (p,n) and (He-3,H-3) reactions are made and compared with experimental results for C-12, O-16, and Al-27 targets. Coherent effects are shown to lead to an important role for inelastic multiple scattering terms when light projectiles are considered.

Remote Sensing of Marine Life and Submerged Target Motions with Ocean Waveguide Acoustics

NASA Astrophysics Data System (ADS)

Gong, Zheng

Many species of fish that inhabit the continental shelf waters can cause significant acoustic scattering at low- to mid-frequencies due to the large impedance contrast between their air-filled swimbladders and the surrounding water. In this thesis, we investigate the acoustic resonance scattering response from distributed fish groups both experimentally and theoretically including the effects of multiple scattering, attenuation, and dispersion in a random range-dependent ocean waveguide using an instantaneous wide-area imaging system. In navy sonar operations, the biological organisms can cause high false alarm rates or missed target detections since the biological scattering can be confused with or camouflage the returns from other discrete and distributed objects, such as underwater vehicles and geologic features. From an ecological perspective, the ability to instantaneously survey fish populations distributed over wide areas is important for fisheries management. The low-frequency target strength of shoaling Atlantic herring ( Clupea harengus) in the Gulf of Maine during their Autumn 2006 spawning season is estimated from experimental data acquired simultaneously at multiple frequencies in the 300 to 1200 Hz range using (1) a low-frequency ocean acoustic waveguide remote sensing (OAWRS) system, (2) areal population density calibration with several conventional fish finding sonar (CFFS) systems, and (3) low-frequency transmission loss measurements. The OAWRS system's instantaneous imaging diameter of 100 km and regular updating enabled unaliased monitoring of fish populations over ecosystem scales including shoals of Atlantic herring containing as many as 200 million individuals, as estimated based on single scattering assumption and confirmed by concurrent trawl and CFFS sampling. The mean scattering cross-section of an individual shoaling herring is found to consistently exhibit a strong, roughly 20 dB/octave roll-off with decreasing frequency over all days of the roughly 2-week experiment, consistent with the steep roll-offs expected for sub-resonance scattering from fish with air-filled swimbladders. A numerical Monte-Carlo model is developed to determine the statistical moments of the broadband matched filtered scattered returns from fish groups spanning over multiple range and cross-range resolution cells of a waveguide remote sensing system. It uses the parabolic equation to simulate acoustic field propagation in a random range-dependent ocean waveguide. The effects of (1) multiple scattering, (2) attenuation due to scattering, and (3) fish group 3D spatial configuration on fish population density imaging are examined. The model is applied to investigate (a) population density imaging of shoaling Atlantic herring during the 2006 Gulf of Maine Experiment (GOME06) and (b) examine the wide-area imaging of sparse aggregation of ground fish species, such as Atlantic Cod, in Ipswich Bay continental shelf environment using the waveguide remote sensing system. Incoherent intensities are shown to dominate the total scattered returns from distributed fish groups making single scattering assumption valid for inferring fish areal population densities from their matched filtered scattered intensities. Multiple scattering, attenuation, fish group 3D spatial configuration, and coherent effects, such as resonance shift, sub- and super-local-maxima are found to be negligible at the imaging frequencies employed and for the herring densities observed. Similar results are obtained for the sparsely aggregated cod, but coherent effects such as the double-peak in school resonance can be prominent at much lower fish densities. Attenuation due to scattering can be significant when the fish flesh viscosity is high, especially true for cod. We also investigate approaches for instantaneous long-range passive source localization and tracking with a towed horizontal line-array in a random range-dependent ocean waveguide using passive waveguide acoustics. This is very important for many sonar applications, such as localizing and tracking underwater vehicles and vocalizing marine mammal populations. Instantaneous passive source localization applying the (1) synthetic aperture tracking, (2) array invariant, (3) bearings-only target motion analysis in modified polar coordinates via the extended Kalman filter, and (4) bearings-migration minimum mean-square error methods using measurements made on a single towed horizontal receiver array in a random range-dependent ocean waveguide are examined. These methods are employed to localize and track a vertical source array deployed in the far-field of a towed horizontal receiver array during the Gulf of Maine 2006 Experiment. The source transmitted intermittent broadband pulses in the 300--1200 Hz frequency range. All four methods are found to be comparable with average errors of between 9% to 13% in estimating the mean source positions in a wide variety of source-receiver geometries and range separations up to 20 km. In the case of a relatively stationary source, the synthetic aperture tracking outperformed the other three methods by a factor of two with only 4% error. For a moving source, the Kalman filter method yielded the best performance with 8% error. The array invariant was the best approach for localizing sources within the endfire beam of the receiver array with less than 10% error.

Analysis of electromagnetic scattering characteristics of plasma sheath surrounding a hypersonic aerocraft based on high-order auxiliary differential equation finite-difference time-domain

NASA Astrophysics Data System (ADS)

Sun, Hao-yu; Cui, Zhiwei; Wang, Jiajie; Han, Yiping; Sun, Peng; Shi, Xiaowei

2018-06-01

A numerical analysis of electromagnetic (EM) scattering characteristics of a hypersonic aerocraft enveloped by a plasma sheath is presented. The flow field parameters around a hypersonic aerocraft are derived by numerically solving the Navier-Stokes equations. Through multiphysics coupling of flow field and electromagnetic field, distributions of plasma frequency and collision frequency in plasma sheaths are obtained. A high-order auxiliary differential equation finite-difference time-domain algorithm is employed to investigate the EM wave scattering properties of the aerocraft covered by a plasma sheath. The backward radar cross sections (RCSs) of a blunt cone in the hypersonic flows at different velocities and altitudes with frequencies from 0.1 GHz to 18 GHz are studied. Numerical results show that, for the cases of altitude ranging from 50 km to 55 km and velocity ranging from 18 Ma to 20 Ma, the plasma sheath enhances the backscattering of the blunt cone when frequencies are below 1.5 GHz, and it reduces the backward RCSs of the blunt cone as frequency ranges from 1.5 GHz to 13.5 GHz. The plasma sheath has a larger attenuation effect for frequency lying in the range of 2 GHz to 6 GHz, but it has little influence on the backward electromagnetic scattering characteristics when frequencies are above 14 GHz.

Multiple scattering modeling pipeline for spectroscopy and photometry of airless Solar System objects

NASA Astrophysics Data System (ADS)

Penttilä, Antti; Väisänen, Timo; Markkanen, Johannes; Martikainen, Julia; Gritsevich, Maria; Muinonen, Karri

2017-10-01

We combine numerical tools to analyze the reflectance spectra of granular materials. Our motivation comes from the lack of tools when it comes to intimate mixing of materials and modeling space-weathering effects with nano- or micron-sized inclusions. The current practice is to apply a semi-physical models such as the Hapke models (e.g., Icarus 195, 2008). These are expressed in a closed form so that they are fast to apply. The problem is that the validity of the model is not guaranteed, and the derived properties related to particle scattering can be unrealistic (JQSRT 113, 2012).Our pipeline consists of individual scattering simulation codes and a main program that chains them together. The chain for analyzing a macroscopic target with space-weathered mineral would go as: (1) Scattering properties of small inclusions inside a host matrix are derived using exact Maxwell equation solvers. From the scattering properties, we use the so-called incoherent fields and Mueller matrices as input for the next step; (2) Scattering by a regolith grain is solved using a geometrical optics method with surface reflections, internal absorption, and internal diffuse scattering; (3) The radiative transfer simulation is executed inputting the regolith grains from the previous step as the scatterers in a macroscopic planar volume element.For the most realistic asteroid reflectance model, the chain would produce the properties of a planar surface element. Then, a shadowing simulation over the surface elements would be considered, and finally the asteroid phase function would be solved by integrating the bidirectional reflectance distribution function of the planar element over the object's realistic shape model.The tools in the proposed chain already exist, and practical task for us is to tie these together into an easy-to-use public pipeline. We plan to open the pipeline as a web-based open service a dedicated server, using Django application server and Python environment for the main functionality. The individual programs to be ran under the chain can still be programmed with Fortran, C, or other.We acknowledge the ERC AdG No. 320773 ‘SAEMPL’ and the computational resources provided by CSC — IT Center for Science Ltd., Finland.

Electron kinetic effects in atmosphere breakdown by an intense electromagnetic pulse.

PubMed

Solovyev, A A; Terekhin, V A; Tikhonchuk, V T; Altgilbers, L L

1999-12-01

A physical model is proposed for description of electron kinetics driven by a powerful electromagnetic pulse in the Earth's atmosphere. The model is based on a numerical solution to the Boltzmann kinetic equation for two groups of electrons. Slow electrons (with energies below a few keV) are described in a two-term approximation assuming a weak anisotropy of the electron distribution function. Fast electrons (with energies above a few keV) are described by a modified macroparticle method, taking into account the electron acceleration in the electric field, energy losses in the continuous deceleration approximation, and the multiple pitch angle scattering. The model is applied to a problem of the electric discharge in a nitrogen, which is preionized by an external gamma-ray source. It is shown that the runaway electrons have an important effect on the energy distribution of free electrons, and on the avalanche ionization rate. This mechanism might explain the observation of multiple lightning discharges observed in the Ivy-Mike thermonuclear test in the early 1950's.

Investigations of electromagnetic scattering by columnar ice crystals

NASA Technical Reports Server (NTRS)

Weil, H.; Senior, T. B. A.

1976-01-01

An integral equation approach was developed to determine the scattering and absorption of electromagnetic radiation by thin walled cylinders of arbitrary cross-section and refractive index. Based on this method, extensive numerical data was presented at infrared wavelengths for hollow hexagonal cross section cylinders which simulate columnar sheath ice crystals.

Colorimetry and magnitudes of asteroids

NASA Technical Reports Server (NTRS)

Bowell, E.; Lumme, K.

1979-01-01

In the present paper, 1500 UBV observations are analyzed by a new rather general multiple scattering theory which provided clear insight into previously poorly-recognized optical nature of asteroid surfaces. Thus, phase curves are shown to consist of a surface-texture controlled component, due to singly scattered light, and a component due to multiple scattering. Phase curve shapes can be characterized by a single parameter, the multiple scattering factor, Q. As Q increases, the relative importance of the opposition effect diminishes. Asteroid surfaces are particulate and strikingly similar to texture, being moderately porous and moderately rough on a scale greater than the wavelength of light. In concequence, Q (and also the phase coefficient) correlate well with geometric albedo, and there exists a purely photometric means of determining albedos and diameters.

On the evaluation of air mass factors for atmospheric near-ultraviolet and visible absorption spectroscopy

NASA Technical Reports Server (NTRS)

Perliski, Lori M.; Solomon, Susan

1993-01-01

The interpretation of UV-visible twilight absorption measurements of atmospheric chemical constituents is dependent on how well the optical path, or air mass factor, of light collected by the spectrometer is understood. A simple single scattering model and a Monte Carlo radiative transfer scheme have been developed to study the effects of multiple scattering, aerosol scattering, surface albedo and refraction on air mass factors for scattered light observations. At fairly short visible wavelengths (less than about 450 nm), stratospheric air mass factors are found to be relatively insensitive to multiple scattering, surface albedo and refraction, as well as aerosol scattering by background aerosols. Longer wavelengths display greater sensitivity to refraction and aerosol scattering. Tropospheric air mass factors are found to be highly dependent on aerosol scattering, surface albedo and, at long visible wavelengths (about 650 nm), refraction. Absorption measurements of NO2 and O4 are shown to support these conclusions.

Effect of Multiple Scattering on the Compton Recoil Current Generated in an EMP, Revisited

DOE PAGES

Farmer, William A.; Friedman, Alex

2015-06-18

Multiple scattering has historically been treated in EMP modeling through the obliquity factor. The validity of this approach is examined here. A simplified model problem, which correctly captures cyclotron motion, Doppler shifting due to the electron motion, and multiple scattering is first considered. The simplified problem is solved three ways: the obliquity factor, Monte-Carlo, and Fokker-Planck finite-difference. Because of the Doppler effect, skewness occurs in the distribution. It is demonstrated that the obliquity factor does not correctly capture this skewness, but the Monte-Carlo and Fokker-Planck finite-difference approaches do. Here, the obliquity factor and Fokker-Planck finite-difference approaches are then compared inmore » a fuller treatment, which includes the initial Klein-Nishina distribution of the electrons, and the momentum dependence of both drag and scattering. It is found that, in general, the obliquity factor is adequate for most situations. However, as the gamma energy increases and the Klein-Nishina becomes more peaked in the forward direction, skewness in the distribution causes greater disagreement between the obliquity factor and a more accurate model of multiple scattering.« less

Eikonal solutions to optical model coupled-channel equations

NASA Technical Reports Server (NTRS)

Cucinotta, Francis A.; Khandelwal, Govind S.; Maung, Khin M.; Townsend, Lawrence W.; Wilson, John W.

1988-01-01

Methods of solution are presented for the Eikonal form of the nucleus-nucleus coupled-channel scattering amplitudes. Analytic solutions are obtained for the second-order optical potential for elastic scattering. A numerical comparison is made between the first and second order optical model solutions for elastic and inelastic scattering of H-1 and He-4 on C-12. The effects of bound-state excitations on total and reaction cross sections are also estimated.

Fokker-Planck-Based Acceleration for SN Equations with Highly Forward Peaked Scattering in Slab Geometry

NASA Astrophysics Data System (ADS)

Patel, Japan

Short mean free paths are characteristic of charged particles. High energy charged particles often have highly forward peaked scattering cross sections. Transport problems involving such charged particles are also highly optically thick. When problems simultaneously have forward peaked scattering and high optical thickness, their solution, using standard iterative methods, becomes very inefficient. In this dissertation, we explore Fokker-Planck-based acceleration for solving such problems.

ADE-FDTD Scattered-Field Formulation for Dispersive Materials

PubMed Central

Kong, Soon-Cheol; Simpson, Jamesina J.; Backman, Vadim

2009-01-01

This Letter presents a scattered-field formulation for modeling dispersive media using the finite-difference time-domain (FDTD) method. Specifically, the auxiliary differential equation method is applied to Drude and Lorentz media for a scattered field FDTD model. The present technique can also be applied in a straightforward manner to Debye media. Excellent agreement is achieved between the FDTD-calculated and exact theoretical results for the reflection coefficient in half-space problems. PMID:19844602

ADE-FDTD Scattered-Field Formulation for Dispersive Materials.

PubMed

Kong, Soon-Cheol; Simpson, Jamesina J; Backman, Vadim

2008-01-01

This Letter presents a scattered-field formulation for modeling dispersive media using the finite-difference time-domain (FDTD) method. Specifically, the auxiliary differential equation method is applied to Drude and Lorentz media for a scattered field FDTD model. The present technique can also be applied in a straightforward manner to Debye media. Excellent agreement is achieved between the FDTD-calculated and exact theoretical results for the reflection coefficient in half-space problems.

Fatigue and damage tolerance scatter models

NASA Astrophysics Data System (ADS)

Raikher, Veniamin L.

1994-09-01

Effective Total Fatigue Life and Crack Growth Scatter Models are proposed. The first of them is based on the power form of the Wohler curve, fatigue scatter dependence on mean life value, cycle stress ratio influence on fatigue scatter, and validated description of the mean stress influence on the mean fatigue life. The second uses in addition are fracture mechanics approach, assumption of initial damage existence, and Paris equation. Simple formulas are derived for configurations of models. A preliminary identification of the parameters of the models is fulfilled on the basis of experimental data. Some new and important results for fatigue and crack growth scatter characteristics are obtained.

Scattering models for some vegetation samples

NASA Technical Reports Server (NTRS)

Karam, M. A.; Fung, A. K.; Antar, Y. M. M.

1987-01-01

The Helmholtz integral equation is presently derived for a scatterer of arbitrary shape, and reduced in order to obtain the far zone-scattered field in terms of the field within the scatterer. Attention is given to the effect of different approaches to field estimation within the scatterer on the backscattering cross section, as illustrated numerically by the cases of a circular disk, a needle, and a finite-length cylinder. A comparison is made of the results obtained by modeling a leaf by means of a circular disk within the Shifrin approximation, and a tree branch by means of a finite-length cylinder, with measurements from a single leaf and a single branch.

Light scattering by tenuous particles - A generalization of the Rayleigh-Gans-Rocard approach

NASA Technical Reports Server (NTRS)

Acquista, C.

1976-01-01

We consider scattering by arbitrarily shaped particles that satisfy two conditions: (1) that the polarizability of the particle relative to the ambient medium be small compared to 1 and (2) that the phase shift introduced by the particle be less than 2. We solve the integro-differential equation proposed by Shifrin by using the method of successive iterations and then applying a Fourier transform. For the second iteration, results are presented that accurately describe scattering by a broad class of particles. The phase function and other elements of the scattering matrix are shown to be in excellent agreement with Mie theory for spherical scatterers.

Virtual Excitation and Multiple Scattering Correction Terms to the Neutron Index of Refraction for Hydrogen.

PubMed

Schoen, K; Snow, W M; Kaiser, H; Werner, S A

2005-01-01

The neutron index of refraction is generally derived theoretically in the Fermi approximation. However, the Fermi approximation neglects the effects of the binding of the nuclei of a material as well as multiple scattering. Calculations by Nowak introduced correction terms to the neutron index of refraction that are quadratic in the scattering length and of order 10(-3) fm for hydrogen and deuterium. These correction terms produce a small shift in the final value for the coherent scattering length of H2 in a recent neutron interferometry experiment.

Multiple Coulomb scattering in thin silicon

NASA Astrophysics Data System (ADS)

Berger, N.; Buniatyan, A.; Eckert, P.; Förster, F.; Gredig, R.; Kovalenko, O.; Kiehn, M.; Philipp, R.; Schöning, A.; Wiedner, D.

2014-07-01

We present a measurement of multiple Coulomb scattering of 1 to 6 GeV/c electrons in thin (50-140 μm) silicon targets. The data were obtained with the EUDET telescope Aconite at DESY and are compared to parametrisations as used in the Geant4 software package. We find good agreement between data and simulation in the scattering distribution width but large deviations in the shape of the distribution. In order to achieve a better description of the shape, a new scattering model based on a Student's t distribution is developed and compared to the data.

Strong scattering of short-period seismic waves by the core-mantle boundary and the P-diffracted wave

NASA Astrophysics Data System (ADS)

Bataille, Klaus; Lund, Fernando

We interpret the long-tail-in-time (up to 3 minutes) decay of short-period Pdiff as being due to multiple scattering within D″, which, for this purpose, is assumed to be an heterogeneous region with a low velocity zone just next to the core-mantle boundary. A simple multiple scattering theory, generalized for a two-dimensional spherical geometry, provides good agreement with observations for values of the scattering and attenuation coefficients (η) of about 10-3 km-1.

Topographical scattering of gravity waves

NASA Astrophysics Data System (ADS)

Miles, J. W.; Chamberlain, P. G.

1998-04-01

A systematic hierarchy of partial differential equations for linear gravity waves in water of variable depth is developed through the expansion of the average Lagrangian in powers of [mid R:][nabla del, Hamilton operator][mid R:] (h=depth, [nabla del, Hamilton operator]h=slope). The first and second members of this hierarchy, the Helmholtz and conventional mild-slope equations, are second order. The third member is fourth order but may be approximated by Chamberlain & Porter's (1995) ‘modified mild-slope’ equation, which is second order and comprises terms in [nabla del, Hamilton operator]2h and ([nabla del, Hamilton operator]h)2 that are absent from the mild-slope equation. Approximate solutions of the mild-slope and modified mild-slope equations for topographical scattering are determined through an iterative sequence, starting from a geometrical-optics approximation (which neglects reflection), then a quasi-geometrical-optics approximation, and on to higher-order results. The resulting reflection coefficient for a ramp of uniform slope is compared with the results of numerical integrations of each of the mild-slope equation (Booij 1983), the modified mild-slope equation (Porter & Staziker 1995), and the full linear equations (Booij 1983). Also considered is a sequence of sinusoidal sandbars, for which Bragg resonance may yield rather strong reflection and for which the modified mild-slope approximation is in close agreement with Mei's (1985) asymptotic approximation.

Sum rules and other properties involving resonance projection operators. [for optical potential description of electron scattering from atoms and ions

NASA Technical Reports Server (NTRS)

Berk, A.; Temkin, A.

1985-01-01

A sum rule is derived for the auxiliary eigenvalues of an equation whose eigenspectrum pertains to projection operators which describe electron scattering from multielectron atoms and ions. The sum rule's right-hand side depends on an integral involving the target system eigenfunctions. The sum rule is checked for several approximations of the two-electron target. It is shown that target functions which have a unit eigenvalue in their auxiliary eigenspectrum do not give rise to well-defined projection operators except through a limiting process. For Hylleraas target approximations, the auxiliary equations are shown to contain an infinite spectrum. However, using a Rayleigh-Ritz variational principle, it is shown that a comparatively simple aproximation can exhaust the sum rule to better than five significant figures. The auxiliary Hylleraas equation is greatly simplified by conversion to a square root equation containing the same eigenfunction spectrum and from which the required eigenvalues are trivially recovered by squaring.

Radiative transfer modeling through terrestrial atmosphere and ocean accounting for inelastic processes: Software package SCIATRAN

NASA Astrophysics Data System (ADS)

Rozanov, V. V.; Dinter, T.; Rozanov, A. V.; Wolanin, A.; Bracher, A.; Burrows, J. P.

2017-06-01

SCIATRAN is a comprehensive software package which is designed to model radiative transfer processes in the terrestrial atmosphere and ocean in the spectral range from the ultraviolet to the thermal infrared (0.18-40 μm). It accounts for multiple scattering processes, polarization, thermal emission and ocean-atmosphere coupling. The main goal of this paper is to present a recently developed version of SCIATRAN which takes into account accurately inelastic radiative processes in both the atmosphere and the ocean. In the scalar version of the coupled ocean-atmosphere radiative transfer solver presented by Rozanov et al. [61] we have implemented the simulation of the rotational Raman scattering, vibrational Raman scattering, chlorophyll and colored dissolved organic matter fluorescence. In this paper we discuss and explain the numerical methods used in SCIATRAN to solve the scalar radiative transfer equation including trans-spectral processes, and demonstrate how some selected radiative transfer problems are solved using the SCIATRAN package. In addition we present selected comparisons of SCIATRAN simulations with those published benchmark results, independent radiative transfer models, and various measurements from satellite, ground-based, and ship-borne instruments. The extended SCIATRAN software package along with a detailed User's Guide is made available for scientists and students, who are undertaking their own research typically at universities, via the web page of the Institute of Environmental Physics (IUP), University of Bremen: http://www.iup.physik.uni-bremen.de.