The Regularity of Solutions to Mixed Boundary Value Problems of Second-Order Elliptic Equations with Small Angles

This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.

In-Situ Measuring the Particle Mean Size and Dust Concentration by Near-Forward Small Angle Light Scattering

This paper presents a method of measuring the particle mean size and dust concentration by small angle near forward light scattering optics and the extinction theory. Its theory is based on Fraunhofer diffraction theory which is the approximation of Mie scattering within the forward Fraunhofer diffraction lobe, and Rosin Rammler function is introduced to describe the particle size distribution in two phase flow in advance. Compared with the values by the sample weight method, the measurement results have a reasonable agreement. The present work has demonstrated that this method will be probably used to monitor the parameters of two phase flow.

Small Angle X-ray Scattering Study of Precipitation Kinetics in Al-Zn-Mg-Cu Alloys

The evolution of microstructure parameters （precipitate size and volume fraction） for two types of Al-Zn-Mg-Cu alloys （7075 and 7055） during aging has been studied by synchrotron-radiation small angle X-ray scattering （SAXS）.The results show that the precipitates are only a few nanorneters for both alloys ageing even at higher temperature of 160℃ for 72 h （4.44 and 5.82 nm, respectively）. The maximum of the precipitate volume fraction increases with in creasing Zn content and is about 0.023-0.028 and 0.052-0.054, respectively. The coarsening of precipitate is consistent with LSW （Lifshitz-Slyozov-Wagner） model even at the initial stage where volume fraction is still varying.The activation energy of coarsening regime has been determined to be about 1.22±0.02 eV and 1.25±0.02 eV for alloys 7075 and 7055, respectively.

Small-angle X-ray scattering investigation of aging behavior of Al-Cu-Mg-Ag alloys using synchrotron radiation

The aging behavior of Al-Cu-Mg-Ag alloys with high Cu/Mg was studied by transmission electron microscopy (TEM) and small-angle X-ray scattering (SAXS) using synchrotron radiation. TEM study reveals that the major strengthening phases of the alloy after aging at 160?C for 10 h are Ω and less θ′. SAXS study shows that the scattering patterns are composed of several concentric circles at the beginning of aging process, which is replaced by the butterfly-wings scattering patterns with the increase of aging time. The butterfly-wings scattering patterns are composed of several branches. The angles between the branches are roughly equal to that between the habit planes of precipitates. The evolution of Guinier radius with aging time indicates the good coarsening resistance of the precipitates. The evolution of integrated intensity is consistent with the classical two-step precipitation process.

Stability of the Dividing Distribution Function Method for ParticleSize Distribution Analysis in Small Angle X－Ray Scattering

The Dividing Distribution Function (DDF) method is one of the methods by which the particle size distribution of ultrafine powder can be evaluated from its small angle X-ray scattering data. In this paper, the stability of the solution obtained from DDF method has been investigated through optimizing the coefficient matrix, introducing a damping factor and a least square treatment. All calculations were accomplished with a microcomputer. It was shown that the average deviations of the size distribution obtained are not larger than the assigned random errors to the scattering intensities as long as the corresponding requirements are satisfied.

Growth Kinetics of Nanocrystals and Nanorods by Employing Small-angle X-ray Scattering (SAXS) and Other Techniques

In this article, we report the results of our detailed investigations of the growth kinetics of zero-dimensional nanocrystals as well as one-dimensional nanorods by the combined use of small angel X-ray scattering （SAXS）, transmission electron microscopy （TEM） along with other physical techniques. The study includes growth kinetics of gold nanocrystals formed by the reduction of HAuCl4 by tetrakis（hydroxymethyl） phosphonium chloride in aqueous solution, of CdSe nanocrystals formed by the reaction of cadmium stearate and selenium under solvothermal conditions, and of ZnO nanorods formed by the reaction of zinc acetate with sodium hydroxide under solvothermal conditions in the absence and presence of capping agents. The growth of gold nanocrystals does not follow the diffusion-limited Ostwald ripening, and instead follows a Sigmoidal rate curve. The heat change associated with the growth determined by isothermal titration calorimetry is about 10 kcal·mol^-1 per I nm increase in the diameter of the nanocrystals. In the case of CdSe nanocrystals also, the growth mechanism deviates from diffusion-limited growth and follows a combined model containing both diffusion and surface reaction terms. Our study of the growth kinetics of uncapped and poly（vinyl pyrollidone） （PVP）-capped ZnO nanorods has yielded interesting insights. We observe small nanocrystals next to the ZnO nanorods after a lapse of time in addition to periodic focusing and defocusing of the width of the length distribution. These observations lend support to the diffusion-limited growth model for the growth of uncapped ZnO nanorods. Accordingly, the time dependence on the length of uncapped nanorods follows the L3 law as required for diffusion-limited Ostwald ripening. The PVP-capped nanorods, however, show a time dependence, which is best described by a combination of diffusion （L^3） and surface reaction （L^2） terms.

Small Angle X-ray Scattering Study of PS Conformation in Tetrahydrofuran Solvent with Gas Anti-solvent

Small angle X-ray scattering (SAXS) was used to study the effect of dissolved CO2 on the conformation of polystyrene (PS) in PS/tetrahydrofuran(THF) solution at 308.15 K and at pressures up to 3 MPa. The cloud pressure and the expansion curve of the solution were also determined. The dependence of the conformation on pressure was discussed.

Small angle X-ray scattering beamline at SSRF

Beamline BL16B1 at Shanghai Synchrotron Radiation Facility(SSRF) is dedicated to studying the microstructure and dynamic processes of polymers, nanomaterials, mesoporous materials, colloids, liquid crystals,metal materials, etc. At present, SAXS, wide angle X-ray scattering(WAXS), simultaneous SAXS/WAXS,grazing incident SAXS, and anomalous SAXS techniques are available for end user to conduct diverse experiments at this beamline. The sample-to-detector distance is adjustable from 0.2 m to 5 m. The practicable q-range is 0.03–3.6 nm-1at incident X-ray of 10 ke V for conventional SAXS whilst a continuous q-region of0.06–33 nm-1can be achieved in simultaneous SAXS/WAXS mode. Time-resolved SAXS measurements in sub-second level was achieved by the beamline upgrating in 2013. This paper gives detailed descriptions about the status, performance and applications of the SAXS beamline.

A new package:MySAS for small angle scattering data analysis

In this paper,A MySAS package,which is verified on Windows XP,can easily convert two-dimensional data in small angle neutron and X-ray scattering analysis,operate individually and execute one particular operation as numerical data reduction or analysis,and graphical visualization.This MySAS package can implement the input and output routines via scanning certain properties,thus recalling completely sets of repetition input and selecting the input files.On starting from the two-dimensional files,the MySAS package can correct the anisotropic or isotropic data for physical interpretation and select the relevant pixels.Over 50 model functions are fitted by the POWELL code using x^2 as the figure of merit function.

Quantitative evaluation of equatorial small-angle X-ray scattering for cylindrical fibers

Elongated microvoids, internal fibrillar structure, and edge scattering from both surface refraction cause an equatorial streak in small angle X-ray scattering. A model for analyzing the edge scattering of fibers is proposed. Simulation results indicate that the intensity of edge scattering from surface refraction of a cylindrical fiber is strong and makes an important contribution to the equatorial streak. Two factors influence edge scattering intensity. One is the sample-to-detector distance （D）; edge scattering intensity increases with increasing D. The equatorial streak becomes weak when D is shortened. The other factor is the refraction index. Edge scattering intensity increases as the real component of the refraction index decreases. In experiment, weak or even no equatorial streaks were found for samples measured in a roughly index-matching fluid. Edge scattering can be eliminated or weakened, and it can be calculated by comparing the intensities of a cylindrical fiber when it is measured in air and in index-matching fluid. The simulation data are basically in agreement with the experimental data.

Small-angle X-ray analysis of the effect of grain size on the thermal damage of octahydro-1, 3, 5, 7-tetranitro-1, 3, 5, 7 tetrazocine-based plastic-bounded expolsives

The microstmcture evolution of plastic-bonded explosives （PBXs） after thermal stimulus plays a key role in PBX performance. In this paper, the nanoscale pores of thermal-treated octahydro-1,3,5,7-tetranitro-1,3,5,7 tetrazocine （HMX）- based PBXs with different HMX particle sizes [approximately 40 （FLIP） and 100 μm （LHP）] were measured using small- angle X-ray scattering （SAXS）. No obvious pore variations were found in the LHP samples heated at 160 ℃ for 6 h, whereas the amount of pores of FHP decreased when subjected to 160 ℃ for 6 h. At 180 ℃, the average pore radii of FHP and LHP decreased from approximately 45 nm to 25 nm, and the total pore volume increased distinctively because of phase transformation. The LHP sample reached a high level of pore content after being held at 180 ℃ for 1 h, whereas FHP required 3 h. Both FHP and LHP had relatively high pore volumes when subjected to 200 ℃ for 1 and 3 h.

Scanning Microfocus Small Angle X-ray Scattering Study of the Avian Eggshell

Synchrotron microfocus small angle X-ray scattering was used to investigate the nanostructure and microscopic variation of eggshells. It uses a microbeam allowing the ability to probe interactions between the organic and inorganic components at nanometer level and is ideal for mapping over small areas to obtain a detailed analysis of structural variations. Thin sections of eggshells were scanned from the shell membrane （inner） to the cuticle （outer） surface. The data collected was used to produce two-dimensional maps showing microscopic changes within the different layers of the eggshell. The structural alterations ap- parently could have implications at the macroscopic level of the resulting eggshell. As the organic matrix is embedded within the eggshell this may contribute to the variations observed in calcite crystal form and texture, Structural information obtained about a biomaterial at different length scales is important in relating the structure to its functional properties. This knowledge and the principles behind the formation of biomaterials could be used in the attempt of bioengineering new systems.

SMALL ANGLE NEUTRON SCATTERING INVESTIGATION OF Ni_(50)Mo(50)ALLOY AND ITS FRACTAL PROPERTIES

Small angle neutron scattering(SANS) technique has been used to investigate the Ni_(50)Mo_(50) system prepared by mechanical alloying(MA). Significant changes of the scattering intensity have been observed among the samples with different milling time.Interesting fractal-like behavior of the sample system have been found and attempts have been made to determine the fractal dimensions. It is expected that the fractal dimension can be related to the different stages of MA to some extent.

Characteristics of AOT Microemulsion Structure: a Small Angle X-ray Scattering Study

The method of synchrotron radiation small-angle X-ray scattering (SR-SAXS) has been used to obtain structural information on the system of bis (2-ethylhexyl) sulfosuccinate (AOT)/H2O/isooctane. By using the Guinier plot (Ln I (q) versus q(2)) on the data sets in a defined small q range (0.03-0.06 Angstrom (-1)), the gyration radius at different water/surfactant molar ratio, W-0, was obtained. With the increase of W-0, the gyration radius (R-g) increased at the range of 23.2 similar to 52.7 Angstrom.

SMALL ANGLE LIGHT SCATTERING MEASUREMENT OF THE ISOTROPIC TO NEMATIC TRANSITION OF A SIDE CHAIN NEMATIC POLYMETHACRYLATE

The kinetics of I-->N transition of a side chain nematic polymethacrylate has been studied by small angle depolarized light scattering intensity measurements using a charge coupled device linear image sensor. The polymer shows the transition temperatures K52N79I in degreesC, The H-v scattering intensity T(q,t) during the transition I (at 80.2degreesC)-->N (at 75.8degreesC) shows that T(q) is independent of q for all t, and during the initial stage (in 6 s) T(t) increases exponentially with t. In the later stage of the transition T(t) approaches a saturation value in 2 min. This experimental result indicates that the I-->N transition of a liquid crystalline polymer is a spinodal type of phase transition mediated by orientation fluctuation.

Control for Underactuated Reentry Aircraft in Small Angle of Attack

The control problem for under-actuated reentry vehicle like HTV-2 is considered with small angle of attack.The control strategy for an aircraft with positive lateral control departure parameter relies on strong lateral stability,which declines with the decrease of the angle of attack.Thus,to control the lateral-directional motion in a stable state is hard and even impossible in some scenarios where the under-actuated reentry vehicle,like HTV-2,flies in a low angle of attack.To address this problem,the lateral-directional open-loop motion characteristics are analyzed.The results show that in an uncontrolled state,the lateral-directional motion can automatically converge to stabilization thanks to the aerodynamic damping effect.Therefore,a method of turning-off the lateral-directional control and inviting aerodynamic damping to control can achieve stability.The six-degree-of-freedom simulation show that the lateral-directional motion can be stabilized by the aerodynamic damping,and the lateral position error caused by the bank angle deviation is limited near the zero-rise angle of attack.The control strategy is effective.

Small-angle neutron scattering study on the stability of oxide nanoparticles in long-term thermally aged 9Cr-oxide dispersion strengthened steel

A 9 Cr-oxide dispersion strengthened(ODS)steel was thermally aged at 873 K for up to 5000 h.The size distribution and chemical composition of the dispersed oxide nanoparticles were analyzed by small-angle neutron scattering under a magnetic field.Combined with transmission electron microscopy,Vickers micro-hardness tests and electron backscattered diffraction measurements,all the results showed that the thermal treatment had little or no effect on the size distributions and volume fractions of the oxide nanoparticles in the ferromagnetic matrix,which suggested excellent thermal stability of the 9 Cr-ODS steel.

Probing Nanoscale Morphology of PS/PMMA/CdS &PS/PVC/CdS Polymeric Nanocomposites through Small Angle X-Ray Scattering Analysis

Polymeric nanocomposites of PS/PMMA/CdS and PS/PVC/CdS samples have been synthesized through dispersion solution casting technique. The nanoparrticles of CdS were prepared by simple chemical method using CdCl2 and H2S gas produced from thiourea. The nanoscale morphology of the prepared polymeric nanocomposite samples is probed through small angle X-ray scattering (SAXS). The SAXS study reveals that CdS nanoparticles take place at voids position in the respective plymer blend matrix and exhibit their nano nature with very little tendency to agglomerates.

Studies on microdomain structure in segmented polyether polyurethaneureas by positron annihilation lifetime and small-angle X-ray scattering

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Correlating Rheological Experiments, TEVP Models, and Microstructure with Small Angle Light Scattering

The existence of an evolving microstructure in a 2.9 vol% fumed silica in paraffin oil and polyisobutylene is demonstrated experimentally and via rheological modeling during steady state and large amplitude oscillatory shear flow. The continuously evolving, rebuilding, and breaking down of the microstructure is shown, and correlated through the rheology experiments, thixo-elastovisco-plastic modeling, and small angle light scattering (SALS). All elements are then connected via a global, stochastic optimization algorithm that will provide parameter estimation with a “best-fit” of the steady state and transient data using the well-known Modified Delaware Thixotropic Model, allowing for the comparison of SALS results with experimental values.