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Journal articles on the topic 'Bragg equation (Bragg Law)'

Author: Grafiati

Published: 24 April 2022

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1

Camacho de la Rosa, Angela, David Becerril, María Guadalupe Gómez-Farfán, and Raúl Esquivel-Sirvent. "Bragg Mirrors for Thermal Waves." Energies 14, no. 22 (November 9, 2021): 7452. http://dx.doi.org/10.3390/en14227452.

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We present a numerical calculation of the heat transport in a Bragg mirror configuration made of materials that do not obey Fourier’s law of heat conduction. The Bragg mirror is made of materials that are described by the Cattaneo-Vernotte equation. By analyzing the Cattaneo-Vernotte equation’s solutions, we define the thermal wave surface impedance to design highly reflective thermal Bragg mirrors. Even for mirrors with a few layers, very high reflectance is achieved (>90%). The Bragg mirror configuration is also a system that makes evident the wave-like nature of the solution of the Cattaneo-Vernotte equation by showing frequency pass-bands that are absent if the materials obey the usual Fourier’s law.

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2

Zayed, Elsayed M. E., Mohamed E. M. Alngar, Anjan Biswas, Mehmet Ekici, Padmaja Guggilla, Salam Khan, Hashim Mohammad Alshehri, and Milivoj R. Belic. "Optical Solutions in Fiber Bragg Gratings with Polynomial Law Nonlinearity and Cubic-Quartic Dispersive Reflectivity-=SUP=-*-=/SUP=-." Оптика и спектроскопия 129, no. 11 (2021): 1409. http://dx.doi.org/10.21883/os.2021.11.51648.1016-21.

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Optical solitons with ber Bragg gratings and polynomial law of nonlinear refractive index are addressed in the paper. The auxiliary equation approach together with an addendum to Kudryashov's method identify soliton solutions to the model. Singular periodic solutions emerge from these integration schemes as a byproduct. Keywords: solitons; cubic-quartic; Bragg gratings.

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3

Zayed, Elsayed M. E., Mohamed E. M. Alngar, Anjan Biswas, Mehmet Ekici, Abdullah Khamis Alzahrani, and Milivoj R. Belic. "Solitons in fiber Bragg gratings with cubic–quartic dispersive reflectivity having Kerr law of nonlinear refractive index." Journal of Nonlinear Optical Physics & Materials 29, no. 03n04 (September 2020): 2050011. http://dx.doi.org/10.1142/s0218863520500113.

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This paper retrieves soliton solutions to fiber Bragg ratings with dispersive reflectivity where cubic–quartic dispersive effects are considered as opposed to the usual chromatic dispersion. The auxiliary equation approach and an addendum to Kudryashov’s scheme display a complete spectrum of soliton forms to the model that is studied with Kerr effect.

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4

Tseng, I.-Fan, Chi-Shian You, and Chia-Cheng Tsai. "Bragg Reflections of Oblique Water Waves by Periodic Surface-Piercing and Submerged Breakwaters." Journal of Marine Science and Engineering 8, no. 7 (July 16, 2020): 522. http://dx.doi.org/10.3390/jmse8070522.

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The Bragg reflections of oblique water waves by periodic surface-piercing structures over periodic bottoms are investigated using the eigenfunction matching method (EMM). Based on the assumption of small wave amplitude, the linear wave theory is employed in the solution procedure. In the step approximation, the surface-piercing structures and the bottom profiles are sliced into shelves separated by abrupt steps. For each shelf, the solution is composed of eigenfunctions with unknown coefficients representing the wave amplitudes. Upon applying the conservations of mass and momentum, a system of linear equations is obtained and is then solved by a sparse-matrix solver. The proposed EMM is validated by several examples in the literature. Then, the method is applied to solve Bragg reflections of oblique water waves by various surface-piercing structures over periodic bottoms. From the numerical experiments, Bragg’s law of oblique waves was used to predict the occurrences of Bragg resonance.

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5

Smirnov, Yury G., Eugenii Yu Smol’kin, and Dmitry V. Valovik. "Nonlinear Double-Layer Bragg Waveguide: Analytical and Numerical Approaches to Investigate Waveguiding Problem." Advances in Numerical Analysis 2014 (January 22, 2014): 1–11. http://dx.doi.org/10.1155/2014/231498.

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The paper is concerned with propagation of surface TE waves in a circular nonhomogeneous two-layered dielectric waveguide filled with nonlinear medium. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of the Green function. The existence of propagating TE waves for chosen nonlinearity (the Kerr law) is proved using the contraction mapping method. Conditions under which k waves can propagate are obtained, and intervals of localization of the corresponding propagation constants are found. For numerical solution of the problem, a method based on solving an auxiliary Cauchy problem (the shooting method) is proposed. In numerical experiment, two types of nonlinearities are considered and compared: the Kerr nonlinearity and nonlinearity with saturation. New propagation regime is found.

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6

Ogilvie, Robert E. "Is there a “universal” MAC equation?" Proceedings, annual meeting, Electron Microscopy Society of America 48, no. 2 (August 12, 1990): 228–29. http://dx.doi.org/10.1017/s0424820100134740.

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The search for an empirical absorption equation begins with the work of Siegbahn (1) in 1914. At that time Siegbahn showed that the value of (μ/ρ) for a given element could be expressed as a function of the wavelength (λ) of the x-ray photon by the following equationwhere C is a constant for a given material, which will have sudden jumps in value at critial absorption limits. Siegbahn found that n varied from 2.66 to 2.71 for various solids, and from 2.66 to 2.94 for various gases.Bragg and Pierce (2) , at this same time period, showed that their results on materials ranging from Al(13) to Au(79) could be represented by the followingwhere μa is the atomic absorption coefficient, Z the atomic number. Today equation (2) is known as the “Bragg-Pierce” Law. The exponent of 5/2(n) was questioned by many investigators, and that n should be closer to 3. The work of Wingardh (3) showed that the exponent of Z should be much lower, p = 2.95, however, this is much lower than that found by most investigators.

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7

Leonardi, Alberto. "Whole pair distribution function modeling: the bridging of Bragg and Debye scattering theories." IUCrJ 8, no. 2 (February 10, 2021): 257–69. http://dx.doi.org/10.1107/s2052252521000324.

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Microstructure-based design of materials requires an atomic level understanding of the mechanisms underlying structure-dependent properties. Methods for analyzing either the traditional diffraction profile or the pair distribution function (PDF) differ in how the information is accessed and in the approximations usually applied. Any variation of structural and microstructural features over the whole sample affects the Bragg peaks as well as any diffuse scattering. Accuracy of characterization relies, therefore, on the reliability of the analysis methods. Methods based on Bragg's law investigate the diffraction peaks in the intensity plot as distinct pieces of information. This approach reaches a limitation when dealing with disorder scenarios that do not conform to such a peak-by-peak basis. Methods based on the Debye scattering equation (DSE) are, otherwise, well suited to evaluate the scattering from a disordered phase but the structure information is averaged over short-range distances usually accessed by experiments. Moreover, statistical reliability is usually sacrificed to recover some of the computing-efficiency loss compared with traditional line-profile-analysis methods. Here, models based on Bragg's law are used to facilitate the computation of a whole PDF and then model powder-scattering data via the DSE. Models based on Bragg's law allow the efficient solution of the dispersion of a crystal's properties in a powder sample with statistical reliability, and the PDF provides the flexibility of the DSE. The whole PDF is decomposed into the independent directional components, and the number of atom pairs separated by a given distance is statistically estimated using the common-volume functions. This approach overcomes the need for an atomistic model of the material sample and the computation of billions of pair distances. The results of this combined method are in agreement with the explicit solution of the DSE although the computing efficiency is comparable with that of methods based on Bragg's law. Most importantly, the method exploits the strengths and different sensitivities of the Bragg and Debye theories.

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8

LINTON, C. M. "Water waves over arrays of horizontal cylinders: band gaps and Bragg resonance." Journal of Fluid Mechanics 670 (January 25, 2011): 504–26. http://dx.doi.org/10.1017/s0022112010005471.

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The existence of a band-gap structure associated with water waves propagating over infinite periodic arrays of submerged horizontal circular cylinders in deep water is established. Waves propagating at right angles to the cylinder axes and at an oblique angle are both considered. In each case an exact linear analysis is presented with numerical results obtained by solving truncated systems of equations. Calculations for large finite arrays are also presented, which show the effect of an incident wave having a frequency within a band gap – with the amount of energy transmitted across the array tending to zero as the size of the array is increased. The location of the band gaps is not as predicted by Bragg's law, but we show that an approximate determination of their position can be made very simply if the phase of the transmission coefficient for a single cylinder is known.

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9

Hackley, Vincent A., Peter K. Stoimenov, Derek L. Ho, Li Piin Sung, and Kenneth J. Klabunde. "Structure development in aerogel-processed nanocrystalline alkaline earth oxides as revealed by SANS." Journal of Applied Crystallography 38, no. 4 (July 13, 2005): 619–31. http://dx.doi.org/10.1107/s0021889805015244.

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Nanocrystalline MgO, CaO and SrO were prepared according to a modified aerogel process (AP). Small-angle neutron scattering (SANS) was used to probe the nanoscale structural features of these materials after each stage of the synthetic process, including hydrolysis, supercritical drying and calcining. SANS data were interpreted using a classical analysis involving power-law and Guinier regimes, and by application of the maximum entropy method. Results are compared with previously published structural data based on X-ray diffraction, electron microscopy and gas adsorption. It is found that the gel hydrolysis product suspended in methanol and toluene exhibits rod-like scattering at small length scales. This is consistent with a filiform morphology previously reported for air-dried Mg(OH)2alcogel, yet SANS data for air-dried alcogels tested in this study indicate no evidence for low-dimensional structure on any length scale. A previous assertion of mass fractal structure in the AP aerogels and oxides was not confirmed by the present data. Instead, surface fractal scattering was found to be the most dominant characteristic feature associated with the SANS data for all AP powders examined. Additionally, MgO and CaO exhibited a correlation peak that corresponds to liquid-like ordering at Bragg length scales of 5.9 nm and 20.3 nm, respectively. These values are roughly consistent with previous independent estimates of primary particle size, suggesting that local packing of primary crystallites is facilitated by the calcination/dehydration process. An alternative interpretation treats these features as Guinier scattering regions. Fitting of results using the unified Guinier/power-law equation yields sphere-equivalent radii for the primary particles that are nearly identical to the Bragg lengths calculated from the positions of the maxima. Air-dried alcogels produced very weak maxima that could be interpreted either as correlation peaks or as Guinier regions. No maxima were observed for aerogel samples. Maximum entropy analysis using a spherical shape factor produced interesting but complex results for the calculated volume size distributions of these materials. Overall, the observed trend shows an increase in structural feature size with increasing metal cation size.

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10

Zayed, Elsayed M. E., Mohamed E. M. Alngar, Mahmoud El-Horbaty, Anjan Biswas, Ali Saleh Alshomrani, Salam Khan, Mehmet Ekici, and Houria Triki. "Optical solitons in fiber Bragg gratings having Kerr law of refractive index with extended Kudryashov’s method and new extended auxiliary equation approach." Chinese Journal of Physics 66 (August 2020): 187–205. http://dx.doi.org/10.1016/j.cjph.2020.04.003.

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11

Eljarrat, Alberto, Lluís López-Conesa, César Magén, Žarko Gačević, Sergio Fernández-Garrido, Enrique Calleja, Sónia Estradé, and Francesca Peiró. "Insight into the Compositional and Structural Nano Features of AlN/GaN DBRs by EELS-HAADF." Microscopy and Microanalysis 19, no. 3 (May 9, 2013): 698–705. http://dx.doi.org/10.1017/s1431927613000512.

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AbstractIII-V nitride (AlGa)N distributed Bragg reflector devices are characterized by combined high-angle annular dark-field (HAADF) and electron energy loss spectroscopy (EELS) in the scanning transmission electron microscope. Besides the complete structural characterization of the AlN and GaN layers, the formation of AlGaN transient layers is revealed using Vegard law on profiles of the position of the bulk plasmon peak maximum. This result is confirmed by comparison of experimental and simulated HAADF intensities. In addition, we present an advantageous method for the characterization of nano-feature structures using low-loss EELS spectrum image (EEL-SI) analysis. Information from the materials in the sample is extracted from these EEL-SI at high spatial resolution.The log-ratio formula is used to calculate the relative thickness, related to the electron inelastic mean free path. Fitting of the bulk plasmon is performed using a damped plasmon model (DPM) equation. The maximum of this peak is related to the chemical composition variation using the previous Vegard law analysis. In addition, within the context of the DPM, information regarding the structural properties of the material can be obtained from the lifetime of the oscillation. Three anomalous segregation regions are characterized, revealing formation of metallic Al islands.

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12

Yamada, Y. "Preliminary Study on the Radar Vegetation Index (RVI) Application to Actual Paddy Fields by ALOS/PALSAR Full-polarimetry SAR Data." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XL-7/W3 (April 28, 2015): 129–31. http://dx.doi.org/10.5194/isprsarchives-xl-7-w3-129-2015.

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Kim and van Zyl (2001) proposed a kind of radar vegetation index (RVI). RVI = 4*min(λ1, λ2, λ3) / (λ1 + λ2 + λ3) They modified the equation as follows. (2009) RVI = 8 * σ<sup>0</sup>hv / (σ<sup>0</sup>hh + σ<sup>0</sup>vv +σ<sup>0</sup>hv ) by L-band full-polarimetric SAR data. They applied it into rice crop and soybean. (Y.Kim, T.Jackson et al., 2012) They compared RVI for L-, C- and X-bands to crop growth data, LAI and NDVI. They found L-band RVI was well correlated with Vegetation Water Content, LAI and NDVI. But the field data were collected by the multifrequency polarimetric scatterometer. The platform height was 4.16 meters from the ground. The author tried to apply the method to actual paddy fields near Tsukuba science city in Japan using ALOS/PALSAR, full-polarimetry L-band SAR data. The staple crop in Eastern Asia is rice and paddy fields are dominant land use. A rice-planting machine comes into wide use in this areas. The young rice plants were bedded regularly ridged line in the paddy fields by the machine. The space between two ridges of rice plants is about 30 cm and the wave length of PALSAR sensor is about 23 cm. Hence the Bragg scattering will appear depending upon the direction of the ridges of paddy fields. Once the Bragg scattering occurs, the backscattering values from the pixels should be very high comparing the surrounding region. Therefore the radar vegetation index (RVI) would be saturated. The RVI did not follow the increasing of vegetation anymore. Japan has launched ALOS-2 satellite and it has PALSAR-2, L-band SAR. Therefore RVI application product by PALSAR-2 will be watched with deep interest.

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13

Rana, Sohel, Harish Subbaraman, Austin Fleming, and Nirmala Kandadai. "Numerical Analysis of Radiation Effects on Fiber Optic Sensors." Sensors 21, no. 12 (June 15, 2021): 4111. http://dx.doi.org/10.3390/s21124111.

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Optical fiber sensors (OFS) are a potential candidate for monitoring physical parameters in nuclear environments. However, under an irradiation field the optical response of the OFS is modified via three primary mechanisms: (i) radiation-induced attenuation (RIA), (ii) radiation-induced emission (RIE), and (iii) radiation-induced compaction (RIC). For resonance-based sensors, RIC plays a significant role in modifying their performance characteristics. In this paper, we numerically investigate independently the effects of RIC and RIA on three types of OFS widely considered for radiation environments: fiber Bragg grating (FBG), long-period grating (LPG), and Fabry-Perot (F-P) sensors. In our RIC modeling, experimentally calculated refractive index (RI) changes due to low-dose radiation are extrapolated using a power law to calculate density changes at high doses. The changes in RI and length are subsequently calculated using the Lorentz–Lorenz relation and an established empirical equation, respectively. The effects of both the change in the RI and length contraction on OFS are modeled for both low and high doses using FIMMWAVE, a commercially available vectorial mode solver. An in-depth understanding of how radiation affects OFS may reveal various potential OFS applications in several types of radiation environments, such as nuclear reactors or in space.

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14

Pope, Christopher G. "X-Ray Diffraction and the Bragg Equation." Journal of Chemical Education 74, no. 1 (January 1997): 129. http://dx.doi.org/10.1021/ed074p129.

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15

Martijn de Sterke, C., and Benjamin J. Eggleton. "Bragg solitons and the nonlinear Schrödinger equation." Physical Review E 59, no. 1 (January 1, 1999): 1267–69. http://dx.doi.org/10.1103/physreve.59.1267.

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16

Deych, L. I., and A. A. Lisyansky. "Polariton dispersion law in periodic-Bragg and near-Bragg multiple quantum well structures." Physical Review B 62, no. 7 (August 15, 2000): 4242–44. http://dx.doi.org/10.1103/physrevb.62.4242.

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17

Keller, W. A., and D. S. de Vasconcelos. "Modified Bragg law for heterolayer structures." Acta Crystallographica Section A Foundations of Crystallography 49, s1 (August 21, 1993): c385. http://dx.doi.org/10.1107/s0108767378089205.

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18

Zuev, A. D. "Using the general equation of a conic for the calculation of the instrument function of a Bragg–Brentano diffractometer." Journal of Applied Crystallography 41, no. 1 (January 16, 2008): 115–23. http://dx.doi.org/10.1107/s002188980704976x.

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The general equation of the conic representing the intersection of the receiving-slit plane with the diffraction cone as well as with the reflection cone of a plane crystal monochromator are given for a diffractometer in Bragg–Brentano geometry. Apart from the fact that this equation can be easily used to calculate the total instrument function as well as specific instrument functions for diffractometers in Bragg–Brentano geometry, it also provides tools for elucidating different aberrations of the diffractometer in Bragg–Brentano geometry.

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19

Yi, Ting. "Some general solutions for linear Bragg–Hawthorne equation." Physics of Fluids 33, no. 7 (July 2021): 077113. http://dx.doi.org/10.1063/5.0055228.

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20

Chukhovskii, F. N., and M. Krisch. "The lens equation for Bragg diffraction optics. The general case of asymmetrical reflection." Journal of Applied Crystallography 25, no. 2 (April 1, 1992): 211–13. http://dx.doi.org/10.1107/s0021889891012074.

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The lens equation for Bragg diffraction of monochromatic X-rays and neutrons in the case of a cylindrically curved crystal is derived for the general Bragg- and Laue-case geometries. The resulting equation is identical to the formula for polychromatic focusing only in the limits of symmetrical reflection and/or in Rowland geometry.

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21

Belonenko, Mikhail B., Julia V. Nevzorova, and Elena N. Galkina. "Discrete solitons in Bragg environment with carbon nanotubes." Modern Physics Letters B 29, no. 11 (April 30, 2015): 1550041. http://dx.doi.org/10.1142/s0217984915500414.

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In this paper, we study the propagation of ultrashort optical pulses, which can be regarded as discrete solitons in this case, when the medium with carbon nanotubes (CNTs), has spatially modulated refractive index. As a result we were able to obtain the effective equation, which represents an analog of the classical sine-Gordon equation. A detailed analysis of the dependence on various parameters of the problem has been performed.

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22

Гинзбург, Н. С., А. С. Сергеев, Е. Р. Кочаровская, А. М. Малкин, and В. Ю. Заславский. "Повышение мощности и улучшение направленности излучения широкоапертурных гетеролазеров при оптимизации размеров брэгговской решетки." Физика и техника полупроводников 55, no. 8 (2021): 659. http://dx.doi.org/10.21883/ftp.2021.08.51132.08.

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We investigate the dynamics of heterolasers with finite-length planar Bragg structures. Based on the analysis of the dispersion equation describing the eigenwaves propagation in a Bragg structure, we present a physical interpretation of selection of modes with frequencies higher than the stopband. We demonstrate the improvement of stability by using the Bragg structures with transverse dimensions lower than the width of the active area of DFB heterolasers. As a result, the single-mode oscillation regime is sustained over a wider range of pump levels, and, correspondingly, of the output radiation power.

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23

Wijewardena Gamalath, K. A. I. L., and G. L. A. U. Jayawardena. "Diffraction of Light by Acoustic Waves in Liquids." International Letters of Chemistry, Physics and Astronomy 4 (September 2013): 39–57. http://dx.doi.org/10.18052/www.scipress.com/ilcpa.4.39.

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For the acusto-optic interactions in liquids, an equation for the diffraction light intensity was obtained in terms of Klein Cook parameter Q. With optimized parameters for Q, incident light wave length of λ = 633 nm, sound wave length of Λ = 0.1 mm, acusto-optic interaction length L=0.1 m, and refractive index of the liquid in the range of 1 to 2, the existence of ideal Raman-Nath and Bragg diffractions were investigated in terms of phase delay and incident angle. The ideal Raman-Nath diffraction slightly deviated when the Klein Cook parameter was increased from 0 to 1 for low phase delay values and for large phase delay, the characteristics of the Bessel function disappeared. Higher value of Klein Cook parameter gave Bragg diffraction and ideal Bragg diffraction was obtained for Q ~100. A slight variation of the incident angle from Bragg angle had a considerable effect on Bragg diffraction pattern. Klein Cook parameter with the change of acoustic wave frequency was investigated for liquids with refractive index in the range1.3-1.7 and their diffraction patterns were compared with practically applicable acusto-optic crystals. For acusto-optic diffractions in liquids, sound velocity plays an important role in Bragg regime with Q increasing with increasing acoustic frequency. As acoustic wave frequency exceeded 10 MHz most of the liquids reached Bragg regime before these crystals.

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24

Brower, D. T., R. E. Revay, and T. C. Huang. "A study of X-ray reflectivity data analysis methods for thin film thickness determination." Powder Diffraction 11, no. 2 (June 1996): 114–16. http://dx.doi.org/10.1017/s0885715600009076.

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The determination of thin film thickness by four X-ray reflectivity methods (namely, the peak separation, the Fourier transform, the modified Bragg equation, and the curve-fitting methods) has been studied. An analysis of SrS and BaF2 thin films showed thickness values determined by the methods agreed to within 4%. The curve-fitting method had the highest accuracy but was time-consuming. The peak separation, the Fourier transform, and the modified Bragg equation methods are considerably faster and, on average, gave 2.8%, 0.9%, and 0.2% larger thicknesses than those of the curve-fitting method.

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25

Chen, S. J., D. G. Howitt, and A. B. Harker. "A dynamical bragg equation for high-order laue zone reflections." Scanning 22, no. 3 (December 6, 2006): 156–60. http://dx.doi.org/10.1002/sca.4950220302.

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26

Darwish, Adel, Emad Abo El-Dahab, Hamdy Ahmed, Ahmed H. Arnous, Manar S. Ahmed, Anjan Biswas, Padmaja Guggilla, Yakup Yıldırım, Fouad Mallawi, and Milivoj R. Belic. "Optical solitons in fiber Bragg gratings via modified simple equation." Optik 203 (February 2020): 163886. http://dx.doi.org/10.1016/j.ijleo.2019.163886.

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27

Isaacs, Neil. "A history of experimental phasing in macromolecular crystallography." Acta Crystallographica Section D Structural Biology 72, no. 3 (March 1, 2016): 293–95. http://dx.doi.org/10.1107/s205979831501476x.

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It was just over a century ago that W. L. Bragg published a paper describing the first crystal structures to be determined using X-ray diffraction data. These structures were obtained from considerations of X-ray diffraction (Bragg equation), crystallography (crystal lattices and symmetry) and the scattering power of different atoms. Although W. H. Bragg proposed soon afterwards, in 1915, that the periodic electron density in crystals could be analysed using Fourier transforms, it took some decades before experimental phasing methods were developed. Many scientists contributed to this development and this paper presents the author's own perspective on this history. There will be other perspectives, so what follows isahistory, rather thanthehistory, of experimental phasing.

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28

Wen, Chih-Chung, Tsung-Lin Lee, Chien-Lin Chen, and Yong-Jun Lin. "The Feasibility and Effectiveness of using Bragg Breakwaters in the Shoreline Wave Climate for East Taiwan Ocean Energy." Open Civil Engineering Journal 7, no. 1 (August 7, 2013): 101–8. http://dx.doi.org/10.2174/1874149520130612003.

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The purpose of this paper is to test the feasibility and affectivity of Bragg breakwaters on increasing wave energy by using wave conditions. The Bragg reflection phenomena will depend on the wavelength of surface waves and the spacing of the submerged breakwater. The spacing of the submerged breakwater is the most important parameter for designing a series of submerged breakwaters. In this paper, the Hybrid Mild-Slope Equation model (HMSE) was applied to calculate the phenomena of Bragg reflection and the feasibility and affectivity of ocean power. The data comprising wave records from three harbors in Taiwan during 1999 to 2004 were used to illustrate performance of this model. The effect and feasibility of Bragg breakwaters were also assessed in the practical cases. From the calculated results, the average of the ocean power comes to be 2.54 times more than the original condition in Keelung Harbor, 2.5 times in Su-Ao Harbor and 2.4 times in Hualien Harbor.

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29

Batstone, David, and Billy Bragg. "An Interview with Billy Bragg." Monthly Review 42, no. 9 (February 2, 1991): 20. http://dx.doi.org/10.14452/mr-042-09-1991-02_2.

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30

Zheng, Yu, Jiangtao Yue, Pan Zhang, and Ji'an Duan. "Analysis of parameter influence law of waveguide Bragg grating." Optics & Laser Technology 146 (February 2022): 107576. http://dx.doi.org/10.1016/j.optlastec.2021.107576.

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31

Mase, Hajime, Ken Takeba, Tetsuo Sakai, and Wataru Kioka. "Wave Equation Over Porous Rippled Bed and Analysis of Bragg Scattering." Doboku Gakkai Ronbunshu, no. 485 (1994): 95–102. http://dx.doi.org/10.2208/jscej.1994.485_95.

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32

Xiao, Hong Fei. "Analysis of Output Characteristic for Fiber Bragg Gratings Laser." Advanced Materials Research 216 (March 2011): 143–47. http://dx.doi.org/10.4028/www.scientific.net/amr.216.143.

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A spread equation of erbium-doped optical fiber laser was derived from the basic theory of laser. Then, the hypothesis of erbium-doped optical fiber ring laser was proposed. The special computation procedure and the theoretical arithmetic emulation of output characteristic for this laser were conducted by discussing the effect of the configuration. Moreover, this article further investigated the influence of the relationship between pumping and laser output, cavity distribution of gas gain, slope efficiency and the influence that the output coupling rate parameters having on the laser output of optical fiber laser.

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33

Ye, Wen, Bin Gu, and Yun Wang. "Airborne Distributed Position and Orientation System Transfer Alignment Method Based on Fiber Bragg Grating." Sensors 20, no. 7 (April 9, 2020): 2120. http://dx.doi.org/10.3390/s20072120.

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With the demand for high resolution remote sensing, load array technology has gradually become an effective measure to improve imaging resolution. However, the external flow and internal engine vibration disturbance may lead to the flexible deformation of wings. The traditional rigid baseline error compensation method cannot solve the problem of serious coupling movement error caused by flexible deformation. To address the problem, a transfer alignment model based on fiber Bragg grating for distributed position and orientation system is proposed in this paper. Firstly, based on the multidimensional requirements of flexible deformation information, the layout scheme of fiber Bragg grating was designed, then the continuous strain in the wing surface was obtained after the quadratic fitting of strain measured by fiber Bragg gratings, and the deformation displacement and angle are calculated. Thirdly, flexible deformation compensation for distributed position and orientation system based on fiber Bragg grating was studied. The state equation including position error, velocity error, misalignment angle, and inertial device error was established. The position and attitude information compensated by the flexible lever arm was used as the quantitative measurement. The filtering estimation improved the measurement accuracy of the slave inertial navigation systems. At last, the experiment was carried out and showed that the accuracy of the transfer alignment has been improved significantly.

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Yang, Q., and L. R. Zhao. "Characterization of nano-layered multilayer coatings using modified Bragg law." Materials Characterization 59, no. 9 (September 2008): 1285–91. http://dx.doi.org/10.1016/j.matchar.2007.11.001.

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Kaszkur, Zbigniew. "Nanopowder diffraction analysis beyond the Bragg law applied to palladium." Journal of Applied Crystallography 33, no. 1 (February 1, 2000): 87–94. http://dx.doi.org/10.1107/s002188989901290x.

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A method of powder diffraction analysis is proposed that is applicable to transition metal nanoparticles and which has been applied to palladium. From results of simulations it is shown that: (a) the overall average lattice constant of small transition metal clusters decreases with decreasing size of the cluster as a result of surface contraction; (b) the shift of a diffraction peak position driven by chemisorption increases monotonically with the decrease of cluster size and can be used for the estimation of cluster size; (c) the peak broadening of small clusters may be larger than that resulting from their size; the additional contribution originates from a high density of defects; (d) the extent of the microstrain may be evaluated from the peak broadening and the rate of attenuation of peak intensity; (e) the intensity scattered by small palladium clusters indicates significant surface disorder that may vary during a change of gas atmosphere and during chemisorption of oxygen at the surface.

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Kaszkur, Zbigniew. "Powder diffraction beyond the Bragg law: study of palladium nanocrystals." Journal of Applied Crystallography 33, no. 5 (October 1, 2000): 1262–70. http://dx.doi.org/10.1107/s0021889800009869.

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An experimental method of measurement of the subtle changes of structure of metal nanocrystals occurring on chemisorption of oxygen, interaction with inert gas and hydrogen,etc., is proposed. The measured patterns and their evolution are interpretedviaatomistic simulations. Described are quantitative observations of the changes in peak position, intensity and half width of the 111 diffraction peak of a palladium catalyst caused by modifying the gaseous environment. The results of the measurements are in line with an atomistic model proposed earlier and prove that the measured average lattice constant of palladium clusters evolves according to their surface relaxation. The evolution of the measured peak intensity suggests surface ordering effects and was used to propose a detailed structural model of nanocrystalline metal particles. The transition of palladium into β-Pd-H in hydrogen under normal conditions was used as a structure probe and provided evidence for the presence of icosahedral clusters in a highly dispersed catalyst. The icosahedral phase is not significantly modified under hydrogen atmosphere and does not transform into the β hydride.

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Kryzhanovsky, B. V., and L. B. Litinskii. "Generalized Bragg-Williams equation for systems with an arbitrary long-range interaction." Doklady Mathematics 90, no. 3 (November 2014): 784–87. http://dx.doi.org/10.1134/s1064562414070357.

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38

Manceau, Alain, Matthew A. Marcus, S. Grangeon, M. Lanson, B. Lanson, A. C. Gaillot, S. Skanthakumar, and L. Soderholm. "Short-range and long-range order of phyllomanganate nanoparticles determined using high-energy X-ray scattering." Journal of Applied Crystallography 46, no. 1 (January 17, 2013): 193–209. http://dx.doi.org/10.1107/s0021889812047917.

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High-energy X-ray scattering (HEXS) is used to explore the pH-dependent structure of randomly stacked manganese oxide nanosheets of nominal formula δ-MnO2. Data are simulated in real space by pair distribution function (PDF) analysis and in reciprocal space by both the Bragg-rod method and the Debye equation in order to maximize the information gained from the total scattering measurements. The essential new features of this triple-analysis approach are (1) the use of a two-dimensional supercell in PDF modeling to describe local distortions around Mn layer vacancies, (2) the implementation in Bragg-rod calculations of a lognormal crystal size distribution in the layer plane and an empirical function for the effect of strain, and (3) the incorporation into the model used with the Debye equation of an explicit elastic deformation of the two-dimensional nanocrystals. The PDF analysis reveals steady migration at acidic pH of the Mn atoms from layer to interlayer sites, either above or below the Mn layer vacancies, and important displacement of the remaining in-layer Mn atoms toward vacancies. The increased density of the vacancy–interlayer Mn pairs at low pH causes their mutual repulsion and results in short-range ordering. The layer microstructure, responsible for the long-range lateral disorder, is modeled with spherically and cylindrically bent crystallites having volume-averaged radii of 20–40 Å. Thebunit-cell parameter from the hexagonal layer has different values in PDF, Bragg-rod and Debye equation modeling, because of the use of different weighting contributions from long-range and short-range distances in each method. The PDFbparameter is in effect a measure of the average inlayer Mn...Mn distance and consistently deviates from the average structure value determined by the Bragg-rod method by 0.02 Å at low pH, as a result of the local relaxation induced by vacancies. The layer curvature increases the Bragg-rod value by 0.01–0.02 Å with the cylindrical model and as much as 0.04–0.05 Å with the spherical model. Therefore, in principle, the diffraction alone can unambiguously determine with good accuracy only a volume-averaged apparent layer dimension of the manganese oxide nanosheets. Thebparameter is model dependent and has no single straightforward interpretation, so comparison ofbbetween different samples only makes sense if done in the context of a single specified model.

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Zhang, Gui Hua. "Study of the Second Order Sensitivity of the Fiber Bragg Gratings." Applied Mechanics and Materials 63-64 (June 2011): 732–35. http://dx.doi.org/10.4028/www.scientific.net/amm.63-64.732.

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According to the Bragging equation, the general mathematical formulas of the temperature change error and the strain error are got under the consideration of the second-order temperature sensitivity and the second-order strain sensitivity. The two error curves are given in the conditions of T = 20°C and e = 1000me.

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Buchholz, Daniel, Luciana Gomes Chagas, Christoph Vaalma, Liming Wu, and Stefano Passerini. "Water sensitivity of layered P2/P3-NaxNi0.22Co0.11Mn0.66O2 cathode material." J. Mater. Chem. A 2, no. 33 (2014): 13415–21. http://dx.doi.org/10.1039/c4ta02627f.

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The interlayer distance calculated with the Bragg equation identifies the sodium content below which the spontaneous hydration of P2/P3-Na_xNi_0.22Co_0.11Mn_0.66O₂ occurs.

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41

Wang, Zheng, Ping Yu Zhu, Hong Qiang Liang, and Wei Peng. "Study on the Transmission Spectrum of Fiber Bragg Grating as Temperature Sensor." Advanced Materials Research 819 (September 2013): 197–201. http://dx.doi.org/10.4028/www.scientific.net/amr.819.197.

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The temperature sensing characteristic of Fiber Bragg Grating (FBG) has been studied. The temperature sensing equation of FBG is revised. The accurate analysis results are obtained. The center wavelength drifts of the tested FBG are displayed in the screen of Optical Spectrum Analyzer (OSA).The experimental results show that the center wavelength of FBG is thermally red-shift with the rise of the temperature and blue-shift with the decrease of the temperature. The results are agree with the revised temperature sensing equation. It is noticed that the transmission spectrum width (SPEC-WD) of FBG fluctuates with the change of temperature. Nevertheless, the trend of the fluctuation is demonstrably towards increase, which perhaps is some potential auxiliary sensing function in future.

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Wang, Xiao Xia, and Win Lin Wang. "The Influence and Research of the Metal-Coated FBG on Temperature Sensitivity." Advanced Materials Research 146-147 (October 2010): 1894–97. http://dx.doi.org/10.4028/www.scientific.net/amr.146-147.1894.

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The Fiber Bragg Grating (FBG) sensor’s temperature sensitivity which is influenced by the metal-coated material and thickness was presented. The accurate equation was gotten according to the elasticity and fiber sensor theory. As indicated by the experiment, the changeable curve of the temperature sensitivity between theory equation and experiment is identical. And the FBGs sensitivities can be improved to 3~20 times.

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MYARA, M., P. SIGNORET, J. P. TOURRENC, B. ORSAL, and J. JACQUET. "1/f NOISE IN DBR TUNABLE LASERS." Fluctuation and Noise Letters 06, no. 01 (March 2006): L35—L43. http://dx.doi.org/10.1142/s0219477506003124.

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Tunable Lasers are key-components for Wavelength Division Multiplexing optical communication applications at 1.55μm. In this paper, we compare a rate equation model with measurements performed in order to study the Bragg section contribution in the 1/f-optical-beam noise power spectral density.

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Lee, Andrew, Michael J. Withford, and Judith M. Dawes. "Investigation into the power-law dependence of fibre Bragg grating growth." Optics Communications 257, no. 2 (January 2006): 261–69. http://dx.doi.org/10.1016/j.optcom.2005.07.040.

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45

Ochiai, Tetsuyuki, and Kazuaki Sakoda. "Scaling law of enhanced second harmonic generation in finite Bragg stacks." Optics Express 13, no. 22 (2005): 9094. http://dx.doi.org/10.1364/opex.13.009094.

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46

Otero, Jorge, Ivan Felis, Miguel Ardid, Alicia Herrero, and José A. Merchán. "Acoustic Bragg Peak Localization in Proton Therapy Treatment: Simulation Studies." Proceedings 42, no. 1 (November 14, 2019): 71. http://dx.doi.org/10.3390/ecsa-6-06533.

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A full chain simulation of the acoustic hadron therapy monitoring for brain tumors is presented in this work. For the study, a proton beam of 100 MeV was considered. In the first stage, Geant4 was used to simulate the energy deposition and to study the behavior of the Bragg peak. The energy deposition in the medium produced local heating that can be considered instantaneous with respect to the hydrodynamic time scale producing a sound pressure wave. The resulting thermoacoustic signal was subsequently obtained by solving the thermoacoustic equation. The acoustic propagation was simulated by the Finite Element Method (FEM) in the brain and the skull, where a set of piezoelectric sensors were placed. Lastly, the final received signals in the sensors were processed in order to reconstruct the position of the thermal source and, thus, to determine the feasibility and accuracy of acoustic beam monitoring in hadron therapy.

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47

Otero, Jorge, Ivan Felis, Alicia Herrero, José A. Merchán, and Miguel Ardid. "Bragg Peak Localization with Piezoelectric Sensors for Proton Therapy Treatment." Sensors 20, no. 10 (May 25, 2020): 2987. http://dx.doi.org/10.3390/s20102987.

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A full chain simulation of the acoustic hadrontherapy monitoring for brain tumours is presented in this work. For the study, a proton beam of 100 MeV is considered. In the first stage, Geant4 is used to simulate the energy deposition and to study the behaviour of the Bragg peak. The energy deposition in the medium produces local heating that can be considered instantaneous with respect to the hydrodynamic time scale producing a sound pressure wave. The resulting thermoacoustic signal has been subsequently obtained by solving the thermoacoustic equation. The acoustic propagation has been simulated by FEM methods in the brain and the skull, where a set of piezoelectric sensors are placed. Last, the final received signals in the sensors have been processed in order to reconstruct the position of the thermal source and, thus, to determine the feasibility and accuracy of acoustic beam monitoring in hadrontherapy.

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48

Prajapati, Y., J. P. Saini, D. S. Chauhan, and Vivek Singh. "Analytical solution of the scalar wave equation for slightly deformed optical Bragg waveguide." Journal of Russian Laser Research 34, no. 2 (March 2013): 139–45. http://dx.doi.org/10.1007/s10946-013-9334-y.

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49

Prajapati, Y., Vivek Singh, and J. P. Saini. "Computing Eigen value equation and modal dispersion characteristics of an elliptical Bragg waveguide." Optik 125, no. 19 (October 2014): 5461–66. http://dx.doi.org/10.1016/j.ijleo.2014.06.075.

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50

Cui, L., and D. S. Jeng. "Numerical Study for Soil Response Around Submerged Breakwaters with Bragg Reflection." International Journal of Ocean and Coastal Engineering 01, no. 04 (December 2018): 1850005. http://dx.doi.org/10.1142/s2529807018500057.

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A better understanding of soil behavior in a seabed foundation around submerged breakwaters under combined wave and current loadings has become crucial regarding the design and maintenance for such breakwaters. Bragg effect is considered in this study, which is one of the important factors that influence the flow field and soil response in the vicinity of multiple breakwaters. The wave-current induced dynamic soil response (effective stresses, pore pressures and displacements) and its resultant residual liquefaction in a loosely deposited seabed foundation around multiple breakwaters are investigated. In this study, the wave motion is governed by VARANS equation and the Biot’s [Formula: see text]–[Formula: see text] approximation is used to govern soil-fluid interactions in porous medium. The elasto-plastic constitutive model (PZIII) is used to reproduce the plastic soil behavior in seabed foundation under long-term cyclic ocean loading. Numerical results show that the flow motion can be largely changed due to Bragg effects. The construction of breakwaters significantly change the stress field in seabed foundation. Parametric study shows that, under the strongest Bragg effect, the presence of currents, soil properties and wave characteristics have great impact on the liquefaction potential.

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