Journal articles: 'Volume scattering function'

1

Kruglov, Timofey. "Correlation function of the excluded volume." Journal of Applied Crystallography 38, no. 5 (September 15, 2005): 716–20. http://dx.doi.org/10.1107/s0021889805017000.

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2

Hong, S. S. "A Method for Deriving the Mean Volume Scattering Phase Function for Zodiacal Dust." International Astronomical Union Colloquium 85 (1985): 215–18. http://dx.doi.org/10.1017/s0252921100084657.

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AbstractA linear combination of 3 Henyey-Greenstein phase functions is substituted for the mean volume scattering phase function in the zodiacal light brightness integral. Results of the integral are then compared with the observed brightness to form residuals. Minimization of the residuals provides us with the best combination of Henyey-Greenstein functions for the scattering phase function of zodiacal dust particles.

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3

Zhang, Xiaodong, Marlon Lewis, Michael Lee, Bruce Johnson, and Gennady Korotaev. "The volume scattering function of natural bubble populations." Limnology and Oceanography 47, no. 5 (September 2002): 1273–82. http://dx.doi.org/10.4319/lo.2002.47.5.1273.

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4

Tan, Hiroyuki, Tomohiko Oishi, Akihiko Tanaka, Roland Doerffer, and Yasuhiro Tan. "Chlorophyll-a specific volume scattering function of phytoplankton." Optics Express 25, no. 12 (May 26, 2017): A564. http://dx.doi.org/10.1364/oe.25.00a564.

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5

Li, Xin, Changwoo Do, Yun Liu, Luis Sánchez-Diáz, Gregory Smith, and Wei-Ren Chen. "A scattering function of star polymers including excluded volume effects." Journal of Applied Crystallography 47, no. 6 (November 4, 2014): 1901–5. http://dx.doi.org/10.1107/s1600576714022249.

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This work presents a new model for the form factor of a star polymer consisting of self-avoiding branches. This new model incorporates excluded volume effects and is derived from the two-point correlation function for a star polymer. This model is compared with small-angle neutron scattering measurements from polystyrene stars immersed in a good solvent, tetrahydrofuran. It is shown that this model provides a good description of the scattering signature originating from the excluded volume effect, and it explicitly elucidates the connection between the global conformation of a star polymer and the local stiffness of its constituent branch.

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6

Tan, Hiroyuki, Roland Doerffer, Tomohiko Oishi, and Akihiko Tanaka. "A new approach to measure the volume scattering function." Optics Express 21, no. 16 (July 30, 2013): 18697. http://dx.doi.org/10.1364/oe.21.018697.

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7

Hirata, Takafumi. "Irradiance inversion theory to retrieve volume scattering function of seawater." Applied Optics 42, no. 9 (March 20, 2003): 1564. http://dx.doi.org/10.1364/ao.42.001564.

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8

Kirk, John T. O. "Volume scattering function, average cosines, and the underwater light field." Limnology and Oceanography 36, no. 3 (May 1991): 455–67. http://dx.doi.org/10.4319/lo.1991.36.3.0455.

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9

Chen, Shu-Wen, Feng Lu, and Yao Ma. "Fitting Green’s Function FFT Acceleration Applied to Anisotropic Dielectric Scattering Problems." International Journal of Antennas and Propagation 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/123739.

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A volume integral equation based fast algorithm using the Fast Fourier Transform of fitting Green’s function (FG-FFT) is proposed in this paper for analysis of electromagnetic scattering from 3D anisotropic dielectric objects. For the anisotropic VIE model, geometric discretization is still implemented by tetrahedron cells and the Schaubert-Wilton-Glisson (SWG) basis functions are also used to represent the electric flux density vectors. Compared with other Fast Fourier Transform based fast methods, using fitting Green’s function technique has higher accuracy and can be applied to a relatively coarse grid, so the Fast Fourier Transform of fitting Green’s function is selected to accelerate anisotropic dielectric model of volume integral equation for solving electromagnetic scattering problems. Besides, the near-field matrix elements in this method are used to construct preconditioner, which has been proved to be effective. At last, several representative numerical experiments proved the validity and efficiency of the proposed method.

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10

Chen Du, 陈都, 刘秉义 Liu Bingyi, 杨倩 Yang Qian, 唐军武 Tang Junwu, and 吴松华 Wu Songhua. "近180°水中悬浮颗粒物体积散射函数测量." Infrared and Laser Engineering 50, no. 6 (2021): 20211029. http://dx.doi.org/10.3788/irla20211029.

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11

Li, Xin, Chwen-Yang Shew, Lilin He, Flora Meilleur, Dean A. A. Myles, Emily Liu, Yang Zhang, et al. "Scattering functions of Platonic solids." Journal of Applied Crystallography 44, no. 3 (April 27, 2011): 545–57. http://dx.doi.org/10.1107/s0021889811011691.

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The single-particle small-angle scattering properties of five Platonic solids, including the tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron, are systematically investigated. For each given geometry, the Debye spatial autocorrelation function, pair distance distribution function and intraparticle structure factor (form factor) are calculated and compared with the corresponding scattering function of a spherical reference system. From the theoretical models, the empirical relationship between the dodecahedral and icosahedral structural characteristics and those of the equivalent spheres is found. Moreover, the single-particle scattering properties of icosahedral and spherical shells with identical volume are investigated, and the prospect of using different data analysis approaches to explore their structural differences is presented and discussed.

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12

Gommes, Cedric J. "Small-angle scattering and scale-dependent heterogeneity." Journal of Applied Crystallography 49, no. 4 (June 23, 2016): 1162–76. http://dx.doi.org/10.1107/s1600576716007810.

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Although small-angle scattering is often discussed qualitatively in terms of material heterogeneity, when it comes to quantitative data analysis this notion becomes somehow hidden behind the concept of correlation function. In the present contribution, a quantitative measure of heterogeneity is defined, it is shown how it can be calculated from scattering data, and its structural significance for the purpose of material characterization is discussed. Conceptually, the procedure consists of using a finite probe volume to define a local average density at any point of the material; the heterogeneity is then quantitatively defined as the fluctuations of the local average density when the probe volume is moved systematically through the sample. Experimentally, it is shown that the so-defined heterogeneity can be estimated by projecting the small-angle scattering intensity onto the form factor of the chosen probe volume. Choosing probe volumes of various sizes and shapes enables one to comprehensively characterize the heterogeneity of a material over all its relevant length scales. General results are derived for asymptotically small and large probes in relation to the material surface area and integral range. It is also shown that the correlation function is equivalent to a heterogeneity calculated with a probe volume consisting of two points only. The interest of scale-dependent heterogeneity for practical data analysis is illustrated with experimental small-angle X-ray scattering patterns measured on a micro- and mesoporous material, on a gel, and on a semi-crystalline polyethylene sample. Using different types of probes to analyse a given scattering pattern enables one to focus on different structural characteristics of the material, which is particularly useful in the case of hierarchical structures.

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13

Zhang, X., Y. Huot, D. J. Gray, A. Weidemann, and W. J. Rhea. "Inversion of the volume scattering function and spectral absorption in coastal waters with biogeochemical implications." Biogeosciences Discussions 10, no. 6 (June 3, 2013): 9003–41. http://dx.doi.org/10.5194/bgd-10-9003-2013.

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Abstract. In the aquatic environment, particles can be broadly separated into phytoplankton (PHY), non-algal particle (NAP) and dissolved (or very small particle, VSP) fractions. Typically, absorption spectra are inverted to quantify these fractions, but volume scattering functions (VSFs) can also be used. Both absorption spectra and VSFs were used to calculate particle fractions for an experiment in Chesapeake Bay. A complete set of water inherent optical properties was measured using a suite of commercial instruments and a prototype Multispectral Volume Scattering Meter (MVSM); the chlorophyll concentration, [Chl] was determined using the HPLC method. The total scattering coefficient (measured by an ac-s) and the VSF (at a few backward angles, measured by a HydroScat 6 and an ECO-VSF) agreed with the LISST and MVSM data within 5%, thus indicating inter-instrument consistency. The size distribution and scattering parameters for PHY, NAP and VSP were inverted from measured VSFs. For the absorption inversion, the "dissolved" absorption spectra were measured for filtrate passing through a 0.2 μm filter, whereas [Chl] and NAP absorption spectra were inverted from the particulate fraction. Even though the total scattering coefficient showed no correlation with [Chl], estimates of [Chl] from the VSF-inversion agreed well with the HPLC measurements (r = 0.68, mean relative error s = −20%). The scattering associated with NAP and VSP both correlated well with the NAP and "dissolved" absorption coefficients, respectively. While NAP dominated forward, and hence total, scattering, our results also suggest that the scattering by VSP was far from negligible and dominated backscattering.

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14

He Hua, 何华. "Research on Volume Scattering Phase Function under Ultraviolet Non-Line-of-Sight Single Scattering Link." Laser & Optoelectronics Progress 52, no. 3 (2015): 030603. http://dx.doi.org/10.3788/lop52.030603.

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15

Brewster, Quinn. "Volume Scattering of Radiation in Packed Beds of Large, Opaque Spheres." Journal of Heat Transfer 126, no. 6 (December 1, 2004): 1048–50. http://dx.doi.org/10.1115/1.1795247.

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A simple model is proposed for radiative properties of close-packed large, opaque spheres that accounts for nonvanishing volume of the particles, i.e., volume scattering as opposed to point scattering. It is based on the mean-beam-length concept applied to an assembly of particles, as illustrated by Mills. The resulting particle-scattering properties differ from those of classical pseudocontinuum theory based on point scattering by the simple factor of void fraction, and reduce to the point-scattering expressions in the limit of small particle volume fraction. The volume-scattering model matches detailed Monte Carlo results for extinction obtained by Kaviany and Singh and by Coquard and Baillis, which explicitly accounted for particle volume. The present model also confirms the Monte Carlo finding that the effects of nonvanishing particle volume are felt primarily in the extinction coefficient; albedo and phase function are relatively unaffected. These findings pertain only to the geometric optics regime where dependent scattering (wave coherence effects) are negligible.

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16

Ciccariello, Salvino, Piero Riello, and Alvise Benedetti. "On physical scattering density fluctuations of amorphous samples." Journal of Applied Crystallography 51, no. 5 (September 13, 2018): 1404–20. http://dx.doi.org/10.1107/s1600576718011330.

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Using the rigorous results obtained by Wiener [Acta Math. (1930), 30, 118–242] on the Fourier integral of a bounded function and the condition that small-angle scattering intensities of amorphous samples are almost everywhere continuous, the conditions that must be obeyed by a function η(r) for this to be considered a physical scattering density fluctuation are obtained. These conditions can be recast in the following form: the V → ∞ limit of the modulus of the Fourier transform of η(r), evaluated over a cubic box of volume V and divided by V 1/2, exists and its square obeys the Porod invariant relation. Some examples of one-dimensional scattering density functions obeying the aforesaid condition are numerically illustrated.

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17

Guo Yilu, 郭乙陆, 陶邦一 Tao Bangyi, 黄海清 Huang Haiqing, 吴超钒 Wu Chaofan, 宋. 宏. Song Hong, and 冷建兴 Leng Jianxing. "Wide angle volume scattering function measurement methods for particles in water." Infrared and Laser Engineering 49, no. 2 (2020): 203011. http://dx.doi.org/10.3788/irla202049.0203011.

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18

Twardowski, Michael, and Alberto Tonizzo. "Ocean Color Analytical Model Explicitly Dependent on the Volume Scattering Function." Applied Sciences 8, no. 12 (December 19, 2018): 2684. http://dx.doi.org/10.3390/app8122684.

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An analytical radiative transfer (RT) model for remote sensing reflectance that includes the bidirectional reflectance distribution function (BRDF) is described. The model, called ZTT (Zaneveld-Twardowski-Tonizzo), is based on the restatement of the RT equation by Zaneveld (1995) in terms of light field shape factors. Besides remote sensing geometry considerations (solar zenith angle, viewing angle, and relative azimuth), the inputs are Inherent Optical Properties (IOPs) absorption a and backscattering bb coefficients, the shape of the particulate volume scattering function (VSF) in the backward direction, and the particulate backscattering ratio. Model performance (absolute error) is equivalent to full RT simulations for available high quality validation data sets, indicating almost all residual errors are inherent to the data sets themselves, i.e., from the measurements of IOPs and radiometry used as model input and in match up assessments, respectively. Best performance was observed when a constant backward phase function shape based on the findings of Sullivan and Twardowski (2009) was assumed in the model. Critically, using a constant phase function in the backward direction eliminates a key unknown, providing a path toward inversion to solve for a and bb. Performance degraded when using other phase function shapes. With available data sets, the model shows stronger performance than current state-of-the-art look-up table (LUT) based BRDF models used to normalize reflectance data, formulated on simpler first order RT approximations between rrs and bb/a or bb/(a + bb) (Morel et al., 2002; Lee et al., 2011). Stronger performance of ZTT relative to LUT-based models is attributed to using a more representative phase function shape, as well as the additional degrees of freedom achieved with several physically meaningful terms in the model. Since the model is fully described with analytical expressions, errors for terms can be individually assessed, and refinements can be readily made without carrying out the gamut of full RT computations required for LUT-based models. The ZTT model is invertible to solve for a and bb from remote sensing reflectance, and inversion approaches are being pursued in ongoing work. The focus here is with development and testing of the in-water forward model, but current ocean color remote sensing approaches to cope with an air-sea interface and atmospheric effects would appear to be transferable. In summary, this new analytical model shows good potential for future ocean color inversion with low bias, well-constrained uncertainties (including the VSF), and explicit terms that can be readily tuned. Emphasis is put on application to the future NASA Plankton, Aerosol, Cloud, and ocean Ecosystem (PACE) mission.

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19

Lee, Jungki, and Hogwan Jeong. "Parallel Volume Integral Equation Method for Two-Dimensional Elastodynamic Analysis." International Journal of Computational Methods 16, no. 06 (May 27, 2019): 1840025. http://dx.doi.org/10.1142/s021987621840025x.

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The parallel volume integral equation method (PVIEM) is applied for the analysis of two-dimensional elastic wave scattering problems in an unbounded isotropic solid containing various types of multiple multilayered anisotropic inclusions. It should be noted that the volume integral equation method (VIEM) does not require the use of the Green’s function for the anisotropic inclusion — only the Green’s function for the unbounded isotropic matrix is needed. A detailed analysis of the SH wave scattering problem is presented for various types of multiple multilayered orthotropic inclusions. Numerical results are presented for the elastic fields at the interfaces for square and hexagonal packing arrays of various types of multilayered orthotropic inclusions in a broad frequency range of practical interest. Standard parallel programming was used to speed up computation in the VIEM. The PVIEM enables us to investigate the effects of single/multiple scattering, fiber packing type, fiber volume fraction, single/multiple layer(s), multilayer’s shapes and geometry, isotropy/anisotropy, and softness/hardness of various types of multiple multilayered anisotropic inclusions on displacements and stresses at the interfaces of the inclusions and far-field scattering patterns. Also, powerful capabilities of the PVIEM for the analysis of general two-dimensional multiple scattering problems are investigated.

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20

Horvath, Helmuth, Lucas Alados Arboledas, and Francisco José Olmo Reyes. "Angular scattering of the Sahara dust aerosol." Atmospheric Chemistry and Physics 18, no. 23 (December 13, 2018): 17735–44. http://dx.doi.org/10.5194/acp-18-17735-2018.

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Abstract. Soil erosion aerosols can be transported considerable distances, the Sahara being one of the major sources in the world. In June 2016 the volume scattering function of the atmospheric aerosol was determined in the Sierra Nevada, Spain, at an altitude of 2500 m. Measurements were performed with a polar nephelometer permitting measurements between scattering angles of 5 to 175∘. The values at the missing angles could be estimated to a high accuracy, using the shape of the scattering function adjacent to the missing angles, and thus a complete volume scattering function was available. During the measuring period intrusions of long-range transported Sahara aerosol happened several times. The classification of the aerosol was done by back trajectories and by the Angström exponent of the wavelength-dependent scattering coefficient, which was determined by a three-wavelength Integrating Nephelometer. The phase function of the Sahara aerosol had a stronger forward scattering, and less backscattering compared to the non-Sahara aerosol, which is in agreement with other findings for irregular particles. The asymmetry parameter of the phase function is the best characteristic to distinguish Sahara aerosol from non-Sahara aerosol. In this study the asymmetry parameter for the Sahara aerosol was larger than 0.65, whereas the non-Sahara aerosol had an asymmetry parameter below 0.6. A comparison with measurements performed with long-range transported Gobi desert aerosols observed in Kyoto, Japan, showed very similar results.

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21

Takenaka, Mikihito, Shotaro Nishitsuji, Naoya Amino, Yasuhiro Ishikawa, Daisuke Yamaguchi, and Satoshi Koizumi. "STRUCTURE ANALYSES OF SWOLLEN RUBBER–CARBON BLACK SYSTEMS BY USING CONTRAST VARIATION SMALL-ANGLE NEUTRON SCATTERING." Rubber Chemistry and Technology 85, no. 2 (June 1, 2012): 157–64. http://dx.doi.org/10.5254/rct.12.89960.

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Abstract In a previous study [Takenaka et al., Macromolecules 42, 308 (2009)], we have investigated the polymer layers absorbed on silica (Si) particles in rubber–Si systems with the contrast variation small-angle neutron scattering (SANS) method. We have investigated the polymer layers absorbed on carbon black (CB) particles in rubber–CB systems with contrast variation SANS method. The scattering intensities of specimens swollen by the solvents having various scattering length densities were measured. The contrast variation SANS for the specimens yielded partial scattering functions: the scattering function for polymer–polymer correlation SPP(q), the scattering function for CB–CB correlation SCC(q), and the scattering function for polymer–CB correlation SPC(q). The analyses of SCC(q) explored the structures of the aggregates formed by CB particles. The analyses of SPC(q) and SCC(q) clarified the existence of dense polymer layers around CB aggregates. Several characteristic parameters are estimated from the analyses, such as the size of aggregates, the thickness of layers, and the volume fractions of polymer layers and matrix. We found that the adsorption layer around CB aggregates is thicker than that around Si aggregates in rubber–Si systems.

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22

Sasaki, Kenji, Sinya Aoki, Takumi Doi, Shinya Gongyo, Tetsuo Hatsuda, Yoichi Ikeda, Takashi Inoue, Takumi Iritani, Noriyoshi Ishii, and Takaya Miyamoto. "Lattice QCD studies on baryon interactions in the strangeness -2 sector with physical quark masses." EPJ Web of Conferences 175 (2018): 05010. http://dx.doi.org/10.1051/epjconf/201817505010.

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We investigate baryon-baryon (BB) interactions in the strangeness S = −2 sector via the coupled-channel HAL QCD method which enables us to extract the scattering observables from Nambu-Bethe-Salpeter (NBS) wave function on the lattice. The simulations are performed with (almost) physical quark masses (mπ = 146MeV) and a huge lattice volume of La = 8.1fm. We discuss the fate of H-dibaryon state through the ΛΛ and NΞ coupled-channel scatterings

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23

Wang Wanyan, 王万研, 杨克成 Yang Kecheng, 罗曼 Luo Man, 郭文平 Guo Wenping, 夏珉 Xia Min, and 李微 Li Wei. "Measurement of Three-Dimensional Volume Scattering Function of Suspended Particles in Water." Acta Optica Sinica 38, no. 3 (2018): 0329001. http://dx.doi.org/10.3788/aos201838.0329001.

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24

Slade, Wayne H., and Emmanuel S. Boss. "Calibrated near-forward volume scattering function obtained from the LISST particle sizer." Optics Express 14, no. 8 (2006): 3602. http://dx.doi.org/10.1364/oe.14.003602.

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25

Jonasz, Miroslaw. "Volume scattering function measurement error: effect of angular resolution of the nephelometer." Applied Optics 29, no. 1 (January 1, 1990): 64. http://dx.doi.org/10.1364/ao.29.000064.

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26

Zhou, Yudi, Dong Liu, Peituo Xu, Chong Liu, Jian Bai, Liming Yang, Zhongtao Cheng, Peijun Tang, Yupeng Zhang, and Lin Su. "Retrieving the seawater volume scattering function at the 180° scattering angle with a high-spectral-resolution lidar." Optics Express 25, no. 10 (May 10, 2017): 11813. http://dx.doi.org/10.1364/oe.25.011813.

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27

Chami, Malik, David McKee, Edouard Leymarie, and Gueorgui Khomenko. "Influence of the angular shape of the volume-scattering function and multiple scattering on remote sensing reflectance." Applied Optics 45, no. 36 (December 20, 2006): 9210. http://dx.doi.org/10.1364/ao.45.009210.

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28

Zhang, X., Y. Huot, D. J. Gray, A. Weidemann, and W. J. Rhea. "Biogeochemical origins of particles obtained from the inversion of the volume scattering function and spectral absorption in coastal waters." Biogeosciences 10, no. 9 (September 13, 2013): 6029–43. http://dx.doi.org/10.5194/bg-10-6029-2013.

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Abstract. In the aquatic environment, particles can be broadly separated into phytoplankton (PHY), non-algal particle (NAP) and dissolved (or very small particle, VSP) fractions. Typically, absorption spectra are inverted to quantify these fractions, but volume scattering functions (VSFs) can also be used. Both absorption spectra and VSFs were used to estimate particle fractions for an experiment in the Chesapeake Bay. A complete set of water inherent optical properties was measured using a suite of commercial instruments and a prototype Multispectral Volume Scattering Meter (MVSM); the chlorophyll concentration, [Chl] was determined using the HPLC method. The total scattering coefficient measured by an ac-s and the VSF at a few backward angles measured by a HydroScat-6 and an ECO-VSF agreed with the LISST and MVSM data within 5%, thus indicating inter-instrument consistency. The size distribution and scattering parameters for PHY, NAP and VSP were inverted from measured VSFs. For the absorption inversion, the "dissolved" absorption spectra were measured for filtrate passing through a 0.2 μm filter, whereas [Chl] and NAP absorption spectra were inverted from the particulate fraction. Even though the total scattering coefficient showed no correlation with [Chl], estimates of [Chl] from the VSF-inversion agreed well with the HPLC measurements (r = 0.68, mean relative errors = −20%). The scattering associated with NAP and VSP both correlated well with the NAP and "dissolved" absorption coefficients, respectively. While NAP dominated forward, and hence total, scattering, our results also suggest that the scattering by VSP was far from negligible and dominated backscattering. Since the sizes of VSP range from 0.02 to 0.2 μm, covering (a portion of) the operationally defined "dissolved" matter, the typical assumption that colored dissolved organic matter (i.e., CDOM) does not scatter may not hold, particularly in a coastal or estuarine environment.

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29

Räisänen, P., A. Kokhanovsky, G. Guyot, O. Jourdan, and T. Nousiainen. "Parameterization of single-scattering properties of snow." Cryosphere 9, no. 3 (June 23, 2015): 1277–301. http://dx.doi.org/10.5194/tc-9-1277-2015.

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Abstract. Snow consists of non-spherical grains of various shapes and sizes. Still, in many radiative transfer applications, single-scattering properties of snow have been based on the assumption of spherical grains. More recently, second-generation Koch fractals have been employed. While they produce a relatively flat phase function typical of deformed non-spherical particles, this is still a rather ad hoc choice. Here, angular scattering measurements for blowing snow conducted during the CLimate IMpacts of Short-Lived pollutants In the Polar region (CLIMSLIP) campaign at Ny Ålesund, Svalbard, are used to construct a reference phase function for snow. Based on this phase function, an optimized habit combination (OHC) consisting of severely rough (SR) droxtals, aggregates of SR plates and strongly distorted Koch fractals is selected. The single-scattering properties of snow are then computed for the OHC as a function of wavelength λ and snow grain volume-to-projected area equivalent radius rvp. Parameterization equations are developed for λ = 0.199–2.7 μm and rvp = 10–2000 μm, which express the single-scattering co-albedo β, the asymmetry parameter g and the phase function P11 as functions of the size parameter and the real and imaginary parts of the refractive index. The parameterizations are analytic and simple to use in radiative transfer models. Compared to the reference values computed for the OHC, the accuracy of the parameterization is very high for β and g. This is also true for the phase function parameterization, except for strongly absorbing cases (β > 0.3). Finally, we consider snow albedo and reflected radiances for the suggested snow optics parameterization, making comparisons to spheres and distorted Koch fractals.

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30

Räisänen, P., A. Kokhanovsky, G. Guyot, O. Jourdan, and T. Nousiainen. "Parameterization of single-scattering properties of snow." Cryosphere Discussions 9, no. 1 (February 13, 2015): 873–926. http://dx.doi.org/10.5194/tcd-9-873-2015.

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Abstract. Snow consists of non-spherical grains of various shapes and sizes. Still, in many radiative transfer applications, single-scattering properties of snow have been based on the assumption of spherical grains. More recently, second-generation Koch fractals have been employed. While they produce a relatively flat phase function typical of deformed non-spherical particles, this is still a rather ad-hoc choice. Here, angular scattering measurements for blowing snow conducted during the CLimate IMpacts of Short-Lived pollutants In the Polar region (CLIMSLIP) campaign at Ny Ålesund, Svalbard, are used to construct a reference phase function for snow. Based on this phase function, an optimized habit combination (OHC) consisting of severely rough (SR) droxtals, aggregates of SR plates and strongly distorted Koch fractals is selected. The single-scattering properties of snow are then computed for the OHC as a function of wavelength λ and snow grain volume-to-projected area equivalent radius rvp. Parameterization equations are developed for λ = 0.199–2.7 μm and rvp = 10–2000 μm, which express the single-scattering co-albedo β, the asymmetry parameter g and the phase function P11 as functions of the size parameter and the real and imaginary parts of the refractive index. The parameterizations are analytic and simple to use in radiative transfer models. Compared to the reference values computed for the OHC, the accuracy of the parameterization is very high for β and g. This is also true for the phase function parameterization, except for strongly absorbing cases (β > 0.3). Finally, we consider snow albedo and reflected radiances for the suggested snow optics parameterization, making comparisons to spheres and distorted Koch fractals.

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31

Babin, Marcel, Dariusz Stramski, Rick A. Reynolds, Vanessa M. Wright, and Edouard Leymarie. "Determination of the volume scattering function of aqueous particle suspensions with a laboratory multi-angle light scattering instrument." Applied Optics 51, no. 17 (June 8, 2012): 3853. http://dx.doi.org/10.1364/ao.51.003853.

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32

Germer, Thomas A. "Bidirectional scattering distribution function measurements from volume diffusers: correction factors and associated uncertainties." Applied Optics 55, no. 25 (August 26, 2016): 6978. http://dx.doi.org/10.1364/ao.55.006978.

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33

Sullivan, James M., and Michael S. Twardowski. "Angular shape of the oceanic particulate volume scattering function in the backward direction." Applied Optics 48, no. 35 (December 4, 2009): 6811. http://dx.doi.org/10.1364/ao.48.006811.

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34

Sokolov, A., M. Chami, E. Dmitriev, and G. Khomenko. "Parameterization of volume scattering function of coastal waters based on the statistical approach." Optics Express 18, no. 5 (February 22, 2010): 4615. http://dx.doi.org/10.1364/oe.18.004615.

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35

Zhang, Xiaodong, Michael Twardowski, and Marlon Lewis. "Retrieving composition and sizes of oceanic particle subpopulations from the volume scattering function." Applied Optics 50, no. 9 (March 15, 2011): 1240. http://dx.doi.org/10.1364/ao.50.001240.

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36

Holoubek, Jaroslav, and Josef Baldrian. "Speckle patterns in small angle light scattering: The spatial autocorrelation function." Collection of Czechoslovak Chemical Communications 50, no. 12 (1985): 2873–83. http://dx.doi.org/10.1135/cccc19852873.

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The study deals with the determination of the spatial autocorrelation function of speckle patterns caused by the small-angle light scattering from polymer films. The autocorrelation function determines the shape, size and anisometry of the speckle. The effect of the inner structure and orientation of samples (polypropylene foil, poly(decamethylene terephthalate) and a sample of polypropylene filaments) is discussed; it is shown that under the usual experimental conditions the spatial autocorrelation function of speckle patterns can be determined on the basis of the van Cittert-Zernike theorem of the classical coherence theory. The good agreement between the theoretical and experimental dependences of anisometry, the angular dependence of speckle size and the dependence of speckle size on the sample thickness confirm the suitability of a uniform description based on the classical theory of coherence. From the standpoint of the theory of speckle effect, the results presented in this study allow us to infer that in the light scattering from polymer films under usual conditions the assumptions of the application of the central limit theorem are fulfilled: in the scattering volume there is a sufficient number of scattering units, and path fluctuations due to the scattering foil exceed the wavelength of light.

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Avdeev, Mikhail V. "Contrast variation in small-angle scattering experiments on polydisperse and superparamagnetic systems: basic functions approach." Journal of Applied Crystallography 40, no. 1 (January 12, 2007): 56–70. http://dx.doi.org/10.1107/s0021889806049491.

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The development of the basic functions approach [Stuhrmann (1995).Modern Aspects of Small-Angle Scattering, edited by H. Brumberger, pp. 221–254. Dordrecht: Kluwer Academic Publishers] for the contrast variation technique in small-angle scattering from systems of polydisperse and superparamagnetic non-interacting particles is presented. For polydisperse systems the modified contrast is introduced as the difference between the effective mean scattering length density (corresponding to the minimum of the scattering intensity as the function of the scattering length density of the solvent) and the density of the solvent. Then, the general expression for the scattering intensity is written in the classical way through the modified basic functions. It is shown that the shape scattering from the particle volume can be reliably obtained. Modifications of classical expressions describing changes in integral parameters of the scattering (intensity at zero angle, radius of gyration, Porod integral) with the contrast are analyzed. In comparison with the monodisperse case, the residual scattering in the minimum of intensity as a function of contrast (effective match point) in polydisperse systems makes it possible to treat the Guinier region of scattering curves around the effective match point quite precisely from the statistical viewpoint. However, limitations of such treatment exist, which are emphasized in the paper. In addition, the effect of magnetic scattering in small-angle neutron scattering from superparamagnetic nanoparticles is considered in the context of the basic functions approach. Conceptually, modifications of the integral parameters of the scattering in this case are similar to those obtained for polydisperse multicomponent particles. Various cases are considered, including monodisperse non-homogeneous and homogeneous magnetic particles, and polydisperse non-homogeneous and homogeneous magnetic particles. The developed approach is verified for two models representing the main types of magnetic fluids – systems of polydisperse superparamagnetic particles located in liquid carriers.

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Barabanenkov, M. Y., Y. N. Barabanenkov, and S. A. Nikitov. "Virtual Singular Scattering of Electromagnetic Waves in Transformation Media Concept." Advanced Electromagnetics 1, no. 1 (July 5, 2012): 38. http://dx.doi.org/10.7716/aem.v1i1.34.

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If a scatterer and an observation point (receive) both approach the so-called near field zone of a source of electromagnetic waves, the scattering process becomes singular one which is mathematically attributed to the spatial singularity of the free space Green function at the origin. Starting from less well known property of left-handed material slab to transfer the singularity of the free space Green function by implementing coordinate transformation, we present a phenomenon of virtual singular scattering of electromagnetic wave on an inhomogeneity located in the volume of left – handed material slab. Virtual singular scattering means that a scatterer is situated only virtually in the near field zone of a source, being, in fact, positioned in the far field zone. Such a situation is realized if a scatterer is embedded into a flat Veselago’s lens and approaches the lens’s inner focus because a slab of Veselago medium produces virtual sources inside and behind the slab and virtual scatterer (as a source of secondary waves) from both slab sides. Considering a line-like dielectric scatterer we demonstrate that the scattering efficiency is proportional to product of singular quasistatic parts of two empty space Green functions that means a multiplicative quasistatic singularity of the Green function for a slab of inhomogeneous Veselago medium. We calculate a resonance value of the scattering amplitude in the regime similar to the known Mie resonance scattering.

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Michels-Clark, T. M., V. E. Lynch, C. M. Hoffmann, J. Hauser, T. Weber, R. Harrison, and H. B. Bürgi. "Analyzing diffuse scattering with supercomputers." Journal of Applied Crystallography 46, no. 6 (November 7, 2013): 1616–25. http://dx.doi.org/10.1107/s0021889813025399.

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Two new approaches to quantitatively analyze diffuse diffraction intensities from faulted layer stacking are reported. The parameters of a probability-based growth model are determined with two iterative global optimization methods: a genetic algorithm (GA) and particle swarm optimization (PSO). The results are compared with those from a third global optimization method, a differential evolution (DE) algorithm [Storn & Price (1997).J. Global Optim.11, 341–359]. The algorithm efficiencies in the early and late stages of iteration are compared. The accuracy of the optimized parameters improves with increasing size of the simulated crystal volume. The wall clock time for computing quite large crystal volumes can be kept within reasonable limits by the parallel calculation of many crystals (clones) generated for each model parameter set on a super- or grid computer. The faulted layer stacking in single crystals of trigonal three-pointed-star-shaped tris(bicylco[2.1.1]hexeno)benzene molecules serves as an example for the numerical computations. Based on numerical values of seven model parameters (reference parameters), nearly noise-free reference intensities of 14 diffuse streaks were simulated from 1280 clones, each consisting of 96 000 layers (reference crystal). The parameters derived from the reference intensities with GA, PSO and DE were compared with the original reference parameters as a function of the simulated total crystal volume. The statistical distribution of structural motifs in the simulated crystals is in good agreement with that in the reference crystal. The results found with the growth model for layer stacking disorder are applicable to other disorder types and modeling techniques, Monte Carlo in particular.

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Combet, Patrick P., and Philippe L. Lamy. "Laboratory Measurements of Light Scattering by Dust Particles." International Astronomical Union Colloquium 150 (1996): 409–13. http://dx.doi.org/10.1017/s0252921100501948.

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AbstractWe have set up an experimental device to optically study the scattering properties of dust particles. Measurements over the 8 — 174° interval of scattering angles are performed on a continuously flowing dust loaded jet illuminated by a polarized red HeNe laser beam. The scattering is averaged over the population of the dust particles in the jet, which can be determined independently, and give the “volume scattering function” for the two directions of polarization directly. While results for spherical particles are in good agreement with Mie theory, those for arbitrary particles show conspicuous deviations.

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Badger, John. "A new algorithm for the reconstruction of protein molecular envelopes from X-ray solution scattering data." Journal of Applied Crystallography 52, no. 5 (August 14, 2019): 937–44. http://dx.doi.org/10.1107/s1600576719009774.

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At sufficiently low resolution, the scattering density within the volume occupied by a well folded protein molecule appears relatively flat. By enforcing this condition, three-dimensional protein molecular envelopes may be reconstructed using information obtained from X-ray solution scattering profiles. A practical approach for solving the low-resolution structures of protein molecules from solution scattering data involves modelling the protein shape using a set of volume-filling points (`beads') and transforming the scattering data to a more convenient target, the pair distance distribution function, P(r). Using algorithms described here, the beads interact via a modified Lennard–Jones potential and their positions are adjusted and confined until they fit the expected protein volume and agreement with P(r) is obtained. This methodology allows the protein volume to be modelled by an arbitrary, user-defined number of beads, enabling the rapid reconstruction of protein structures of widely varying sizes. Tests carried out with a variety of synthetic and experimental data sets show that this approach gives efficient and reliable determinations of protein molecular envelopes.

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Hansen, Steen. "The structure factor in small-angle scattering and the effect of deviation from spherical symmetry." Journal of Applied Crystallography 44, no. 2 (February 2, 2011): 265–71. http://dx.doi.org/10.1107/s0021889811001075.

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The effect of deviation from spherical symmetry is studied for the structure factor. This is done by combining the analytical expression for the excluded volume of an ellipsoid of revolution with the expression for the excluded volume correlation function for a sphere. This approach makes it possible to estimate the effect of small deviations from spherical symmetry as a function of axial ratio and volume fraction for relatively low volume fractions. The calculations are relevant for the case of short-range potentials where the Percus–Yevick formula is frequently applied, and indicate that even minor deviations from spherical symmetry may lead to significant effects on the structure factor at low scattering angles.

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Bernhoeft, N. "Geometrical effects in diffraction analysis." Acta Crystallographica Section A Foundations of Crystallography 55, no. 2 (March 1, 1999): 274–88. http://dx.doi.org/10.1107/s0108767398008149.

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The use of X-ray and neutron scattering as a tool to study phase transitions is well established. As techniques improve and experiments are made under successively higher resolution, the need to consider the role of both the distribution of diffracting length scales and the incident-beam coherence volume is emphasized. The interplay of diffracting length scales and the beam coherence volume no longer permits calculation of diffraction profiles in terms of the sample intensity response convolved with an instrumental resolution function. Rather, the probe and sample now enter the calculation on an equal footing at the level of the scattering amplitudes. Under these conditions, it is found that the summation of coherent scattering amplitudes leads to characteristic profiles in wave-vector and, in the case of resonant X-ray scattering, energy space. In this latter case, in the vicinity of strong absorption edges, as used for example in resonant magnetic X-ray diffraction, the energy dependence of diffraction profiles may uniquely allow spatial localization of the scattering volume below the sample surface. This observation may considerably augment the range and power of resonant X-ray scattering.

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Chami, Malik, Eugeny B. Shybanov, Gueorgui A. Khomenko, Michael E. G. Lee, Oleg V. Martynov, and Gennady K. Korotaev. "Spectral variation of the volume scattering function measured over the full range of scattering angles in a coastal environment." Applied Optics 45, no. 15 (May 20, 2006): 3605. http://dx.doi.org/10.1364/ao.45.003605.

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Ugulen, Håvard S., Håkon Sandven, Børge Hamre, Arne S. Kristoffersen, and Camilla Sætre. "Analysis of multiple scattering errors in LISST-VSF volume scattering function measurements using Monte Carlo simulations and experimental data." Optics Express 29, no. 8 (April 7, 2021): 12413. http://dx.doi.org/10.1364/oe.419116.

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Lee, Jungki, Hyechang Lee, and Hogwan Jeong. "Multiple Scattering Using Parallel Volume Integral Equation Method: Interaction of SH Waves with Multiple Multilayered Anisotropic Elliptical Inclusions." Mathematical Problems in Engineering 2015 (2015): 1–48. http://dx.doi.org/10.1155/2015/809320.

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The parallel volume integral equation method (PVIEM) is applied for the analysis of elastic wave scattering problems in an unbounded isotropic solid containing multiple multilayered anisotropic elliptical inclusions. This recently developed numerical method does not require the use of Green’s function for the multilayered anisotropic inclusions; only Green’s function for the unbounded isotropic matrix is needed. This method can also be applied to solve general two- and three-dimensional elastodynamic problems involving inhomogeneous and/or multilayered anisotropic inclusions whose shape and number are arbitrary. A detailed analysis of the SH wave scattering is presented for multiple triple-layered orthotropic elliptical inclusions. Numerical results are presented for the displacement fields at the interfaces for square and hexagonal packing arrays of triple-layered elliptical inclusions in a broad frequency range of practical interest. It is necessary to use standard parallel programming, such as MPI (message passing interface), to speed up computation in the volume integral equation method (VIEM). Parallel volume integral equation method as a pioneer of numerical analysis enables us to investigate the effects of single/multiple scattering, fiber packing type, fiber volume fraction, single/multiple layer(s), multilayer’s shape and geometry, isotropy/anisotropy, and softness/hardness of the multiple multilayered anisotropic elliptical inclusions on displacements at the interfaces of the inclusions.

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Hansen, Steen. "Simultaneous estimation of the form factor and structure factor for globular particles in small-angle scattering." Journal of Applied Crystallography 41, no. 2 (March 8, 2008): 436–45. http://dx.doi.org/10.1107/s0021889808004937.

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Small-angle scattering data from non-dilute solutions of particles are often analysed by indirect Fourier transformation using a specific model structure factor to obtain an estimate of the distance distribution function that is free from concentration effects. A new approach is suggested here, whereby the concentration effects are expressed solely through real space functions without the use of an explicit structure factor. This is done by dividing the total distance distribution function for the scattering into three different contributions, as suggested by Kruglov [(2005).J. Appl. Cryst.38, 716–720]: (i) the single particle distribution which is due to intraparticle effects, (ii) the excluded volume distribution from excluded volume effects which is only dependent upon the geometry of the particles, and (iii) a structure distribution which is due to the remaining interaction between the particles. Only the single particle distribution and the structure distribution are allowed to vary freely (within the restrictions of a smoothness constraint). These two distributions may be separated mainly because they differ in their regions of support in real space. From the estimated distributions the structure factor can be calculated. For deviations of particles from spherical symmetry, the excluded volume distribution may be approximated by that of an ellipsoid of revolution. Excluded volume distributions have been calculated for ellipsoids of revolution of axial ratios between 0.1 and 10 and implemented in the programIFTc, which is described in the appendix. The validity of the approach is demonstrated for globular particles.

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Koestner, Daniel, Dariusz Stramski, and Rick Reynolds. "Measurements of the Volume Scattering Function and the Degree of Linear Polarization of Light Scattered by Contrasting Natural Assemblages of Marine Particles." Applied Sciences 8, no. 12 (December 19, 2018): 2690. http://dx.doi.org/10.3390/app8122690.

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The light scattering properties of seawater play important roles in radiative transfer in the ocean and optically-based methods for characterizing marine suspended particles from in situ and remote sensing measurements. The recently commercialized LISST-VSF instrument is capable of providing in situ or laboratory measurements of the volume scattering function, β p ( ψ ) , and the degree of linear polarization, DoLP p ( ψ ) , associated with particle scattering. These optical quantities of natural particle assemblages have not been measured routinely in past studies. To fully realize the potential of LISST-VSF measurements, we evaluated instrument performance, and developed calibration correction functions from laboratory measurements and Mie scattering calculations for standard polystyrene beads suspended in water. The correction functions were validated with independent measurements. The improved LISST-VSF protocol was applied to measurements of β p ( ψ ) and DoLP p ( ψ ) taken on 17 natural seawater samples from coastal and offshore marine environments characterized by contrasting assemblages of suspended particles. Both β p ( ψ ) and DoLP p ( ψ ) exhibited significant variations related to a broad range of composition and size distribution of particulate assemblages. For example, negative relational trends were observed between the particulate backscattering ratio derived from β p ( ψ ) and increasing proportions of organic particles or phytoplankton in the particulate assemblage. Our results also suggest a potential trend between the maximum values of DoLP p ( ψ ) and particle size metrics, such that a decrease in the maximum DoLP p ( ψ ) tends to be associated with particulate assemblages exhibiting a higher proportion of large-sized particles. Such results have the potential to advance optically-based applications that rely on an understanding of relationships between light scattering and particle properties of natural particulate assemblages.

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Lee, Jungki, and Hogwan Jeong. "Near and far field scattering of SH waves by multiple multilayered anisotropic circular inclusions using parallel volume integral equation method." Engineering Computations 35, no. 1 (March 5, 2018): 432–76. http://dx.doi.org/10.1108/ec-05-2016-0164.

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Purpose The purpose of this paper is to calculate near field and far field scattering of SH waves by multiple multilayered anisotropic circular inclusions using parallel volume integral equation method (PVIEM) quantitatively. Design/methodology/approach The PVIEM is applied for the analysis of elastic wave scattering problems in an unbounded solid containing multiple multilayered anisotropic circular inclusions. It should be noted that this numerical method does not require the use of the Green’s function for the inclusion – only the Green’s function for the unbounded isotropic matrix is needed. This method can also be applied to solve general elastodynamic problems involving inhomogeneous and/or anisotropic inclusions whose shape and number are arbitrary. Findings A detailed analysis of the SH wave scattering problem is presented for multiple multilayered orthotropic circular inclusions. Numerical results are presented for the displacement fields at the interfaces and the far field scattering patterns for square and hexagonal packing arrays of multilayered circular inclusions in a broad frequency range of practical interest. Originality/value To the best of the authors’ knowledge, the solution for scattering of SH waves by multiple multilayered anisotropic circular inclusions in an unbounded isotropic matrix is not currently available in the literature. However, in this paper, calculation of displacements on interfaces and far field scattering patterns of multiple multilayered anisotropic circular inclusions using PVIEM as a pioneer of numerical modeling enables us to investigate the effects of single/multiple scattering, fiber packing type, fiber volume fraction, single/multiple layer(s), the multilayer’s geometry, isotropy/anisotropy and softness/hardness.

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Berthon, Jean-François, Eugeny Shybanov, Michael E. G. Lee, and Giuseppe Zibordi. "Measurements and modeling of the volume scattering function in the coastal northern Adriatic Sea." Applied Optics 46, no. 22 (July 9, 2007): 5189. http://dx.doi.org/10.1364/ao.46.005189.

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Journal articles on the topic 'Volume scattering function'

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