Academic literature on the topic 'Guinier approximation'
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Journal articles on the topic "Guinier approximation"
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Roig-Solvas, Biel, Dana Brooks, and Lee Makowski. "A direct approach to estimate the anisotropy of protein structures from small-angle X-ray scattering." Journal of Applied Crystallography 52, no. 2 (February 26, 2019): 274–83. http://dx.doi.org/10.1107/s1600576719000918.
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In the field of small-angle X-ray scattering (SAXS), the task of estimating the size of particles in solution is usually synonymous with the Guinier plot. The approximation behind this plot, developed by Guinier in 1939, provides a simple yet accurate characterization of the scattering behavior of particles at low scattering angle or momentum transfer q, together with a computationally efficient way of inferring their radii of gyration R G. Moreover, this approximation is valid beyond spherical scatterers, making its use ubiquitous in the SAXS world. However, when it is important to estimate further particle characteristics, such as the anisotropy of the scatterer's shape, no similar or extended approximations are available. Existing tools to characterize the shape of scatterers rely either on prior knowledge of the scatterers' geometry or on iterative procedures to infer the particle shape ab initio. In this work, a low-angle approximation of the scattering intensity I(q) for ellipsoids of revolution is developed and it is shown how the size and anisotropy information can be extracted from the parameters of that approximation. The goal of the approximation is not to estimate a particle's full structure in detail, and thus this approach will be less accurate than well known iterative and ab initio reconstruction tools available in the literature. However, it can be considered as an extension of the Guinier approximation and used to generate initial estimates for the aforementioned iterative techniques, which usually rely on R G and D max for initialization. This formulation also demonstrates that nonlinearity in the Guinier plot can arise from anisotropy in the scattering particles. Beyond ideal ellipsoids of revolution, it is shown that this approximation can be used to estimate the size and shape of molecules in solution, in both computational and experimental scenarios. The limits of the approach are discussed and the impact of a particle's anisotropy in the Guinier estimate of R G is assessed.
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Michels, Andreas, Artem Malyeyev, Ivan Titov, Dirk Honecker, Robert Cubitt, Elizabeth Blackburn, and Kiyonori Suzuki. "Magnetic Guinier law." IUCrJ 7, no. 1 (January 1, 2020): 136–42. http://dx.doi.org/10.1107/s2052252519016439.
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Small-angle scattering of X-rays and neutrons is a routine method for the determination of nanoparticle sizes. The so-called Guinier law represents the low-q approximation for the small-angle scattering curve from an assembly of particles. The Guinier law has originally been derived for nonmagnetic particle-matrix-type systems and it is successfully employed for the estimation of particle sizes in various scientific domains (e.g. soft-matter physics, biology, colloidal chemistry, materials science). An important prerequisite for it to apply is the presence of a discontinuous interface separating particles and matrix. Here, the Guinier law is introduced for the case of magnetic small-angle neutron scattering and its applicability is experimentally demonstrated for the example of nanocrystalline cobalt. It is well known that the magnetic microstructure of nanocrystalline ferromagnets is highly nonuniform on the nanometre length scale and characterized by a spectrum of continuously varying long-wavelength magnetization fluctuations, i.e. these systems do not manifest sharp interfaces in their magnetization profile. The magnetic Guinier radius depends on the applied magnetic field, on the magnetic interactions (exchange, magnetostatics) and on the magnetic anisotropy-field radius, which characterizes the size over which the magnetic anisotropy field is coherently aligned into the same direction. In contrast to the nonmagnetic conventional Guinier law, the magnetic version can be applied to fully dense random-anisotropy-type ferromagnets.
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Ko¨ylu¨, U¨ O¨, and G. M. Faeth. "Optical Properties of Soot in Buoyant Laminar Diffusion Flames." Journal of Heat Transfer 116, no. 4 (November 1, 1994): 971–79. http://dx.doi.org/10.1115/1.2911473.
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The structure and optical properties of soot were studied in the fuel-rich (underfire) region of buoyant laminar diffusion flames of ethylene and acetylene burning in coflowing air. The objective was to evaluate scattering predictions based on the Rayleigh–Debye–Gans (RDG) approximation for polydisperse fractal aggregates of spherical primary soot particles having constant diameters, for conditions where the Guinier (small angle) regime, and the transition between the Guinier and the power-law (large-angle) regimes, were dominant, in order to supplement earlier work for conditions where the power-law regime was dominant. Soot structure was measured using thermophoretic sampling and analysis by transmission electron microscopy (TEM) to yield primary particle diameters, distributions of the number of primary particles per aggregate, and the aggregate mass fractal dimensions. Soot optical property measurements included vv, hh, hv, and vh differential scattering cross sections, total scattering cross sections, and the albedo at 514.5 nm, as well as several soot structure parameters inferred from these measurements using the approximate theory. The approximate RDG theory generally provided an acceptable basis to treat the optical properties of the present soot aggregates over a range of conditions spanning the Guinier and power-law regimes. Other scattering approximations were less satisfactory with performance progressively becoming less satisfactory in the order: RDG polydisperse fractal aggregate scattering using a single mean squared radius of gyration (from the Guinier regime), Mie scattering for an equivalent sphere, and Rayleigh scattering—the last underestimating differential scattering levels by a factor of roughly 100 for the present test conditions.
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Mohammed, Ahmed S. A., Agnese Carino, Andrea Testino, Mohammad Reza Andalibi, and Antonio Cervellino. "A dilute gold nanoparticle suspension as small-angle X-ray scattering standard for an absolute scale using an extended Guinier approximation." Journal of Applied Crystallography 52, no. 2 (March 26, 2019): 344–50. http://dx.doi.org/10.1107/s1600576719001109.
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In this article, a practical procedure for absolute intensity calibration for small-angle scattering (SAXS) studies on liquid microjets is established. A gold nanoparticle suspension is used as standard so that the intercept at Q = 0 of the SAXS scattering curve provides a scaling reference. In order to obtain the most precise extrapolation at Q = 0, an extension of the Guinier approximation has been used, with a second-order term in the fit that adapts to a larger Q range.
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Sperling, Z. "Specimen displacement error in focusing systems." Powder Diffraction 10, no. 4 (December 1995): 278–81. http://dx.doi.org/10.1017/s0885715600014974.
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The error is investigated which results from the employment of tangential approximation in the calculation of line shift caused by specimen displacement from the recording circle in focusing systems (Guinier, Seemann–Bohlin). After an exact expression has been deduced and compared with the approximate formula in a numerical example, it is concluded that the error caused by the approximate formula may be important only in exceptional cases. The deduced exact formula is also compared with that given by Rafaja and Valvoda [Powder Diffr. 6, 200–203 (1991)] with the conclusion that both formulas are mathematically equivalent and complementary with respect to the theoretical and measured values of the diffraction angle 2θ.
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Farias, T. L., M. G. Carvalho, U¨ O¨ Ko¨ylu¨, and G. M. Faeth. "Computational Evaluation of Approximate Rayleigh–Debye–Gans/Fractal-Aggregate Theory for the Absorption and Scattering Properties of Soot." Journal of Heat Transfer 117, no. 1 (February 1, 1995): 152–59. http://dx.doi.org/10.1115/1.2822296.
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A computational evaluation of an approximate theory for the optical properties of soot is described, emphasizing the small-angle (Guinier) regime. The approximate theory (denoted RDG-FA theory) is based on the Rayleigh–Debye–Gans scattering approximation while treating soot as mass-fractal aggregates of spherical primary particles that have constant diameters and refractive indices. The approximate theory was evaluated by more exact predictions from the solution of the volume integral equation formulation of the governing equations, using the method of moments, and based on the ICP algorithm of Iskander et al. (1989). Numerical simulations were used to construct statistically significant populations of soot aggregates having appropriate fractal properties and prescribed numbers of primary particles per aggregate. Optical properties considered included absorption, differential scattering, and total scattering cross sections for conditions typical of soot within flame environments at wavelengths in the visible and the infrared. Specific ranges of aggregate properties were as follows: primary particle optical size parameters up to 0.4, numbers of primary particles per aggregate up to 512, mean fractal dimensions of 1.75, mean fractal prefactors of 8.0, and refractive indices typical of soot. Over the range of the evaluation, ICP and RDG-FA predictions generally agreed within numerical uncertainties (ca. 10 percent) within the Guinier regime, complementing similar performance of RDG-FA theory in the power-law regime based on recent experiments. Thus, the use of approximate RDG-FA theory to estimate the optical properties of soot appears to be acceptable—particularly in view of the significant uncertainties about soot optical properties due to current uncertainties about soot refractive indices.
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Gommes, Cedric J., Raphael Chattot, and Jakub Drnec. "Stochastic models of dense or hollow nanoparticles and their scattering properties." Journal of Applied Crystallography 53, no. 3 (May 29, 2020): 811–23. http://dx.doi.org/10.1107/s1600576720005464.
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A family of stochastic models of disordered particles is proposed, obtained by clipping a Gaussian random field with a function that is space dependent. Depending on the shape of the clipping function, dense or hollow particles can be modelled. General expressions are derived for the form factor of the particles, for their average volume and surface area, and for their density and surface-area distributions against the distance to the particle centre. A general approximation for the form factor is also introduced, based on the density and surface-area distributions, which coincides with the Guinier and Porod expressions in the limits of low and high scattering vector magnitude q. The models are illustrated with the fitting of small-angle X-ray scattering (SAXS) data measured on Pt/Ni hollow nanoparticles. The SAXS analysis and modelling notably capture the collapse of the particles' porosity after being used as oxygen-reduction catalysts.
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Hjelm, R. P. "The small-angle approximation of X-ray and neutron scatter from rigid rods of non-uniform cross section of finite length." Journal of Applied Crystallography 18, no. 6 (December 1, 1985): 452–60. http://dx.doi.org/10.1107/s0021889885010706.
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The theory of small-angle neutron or X-ray scattering from a solution consisting of rods that are uncorrelated in position and orientation and its use in determining the mass per unit length and cross-sectional radius of gyration is extended to rods of finite length and non-uniform cross-sectional structure. The case of a rod made up of identical motifs spaced in a regularly repeating axial structure is considered first. Analysis of the small-angle scatter by a modified Guinier plot gives the mean mass per unit length of the motifs. The apparent squared cross-sectional radius of gyration is the weight average. These results are then generalized to the case where variable randomly distributed structural elements are present including variable spacing between the motifs making up the rod. In this way expressions are obtained that describe the scatter from rods with structural contributions from random thermal fluctuations, bound ligands and intrinsic structural heterogeneity. It is shown that, in general, systematic errors are introduced in the analysis of rods of finite length having variable structural components. However, if all the motifs have the same mass, and if the variance in their spacing is small, such errors are not important provided that the rods are of sufficient length.
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Ko¨ylu¨, U¨ O¨, and G. M. Faeth. "Optical Properties of Overfire Soot in Buoyant Turbulent Diffusion Flames at Long Residence Times." Journal of Heat Transfer 116, no. 1 (February 1, 1994): 152–59. http://dx.doi.org/10.1115/1.2910849.
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The optical properties of soot were studied for the fuel-lean (overfire) region of buoyant turbulent diffusion flames in still air. Results were limited to the long residence time regime where soot structure is independent of position in the overfire region and residence time for a particular fuel. Measurements included scattering, absorption, and extinction cross sections at 514.5 nm and extinction cross sections at 632.8 and 1152 nm for flames fueled with acetylene, propylene, ethylene, and propane. The measurements were used to evaluate scattering predictions based on the Rayleigh-Debye-Gans (RDG) approximation for randomly oriented poly disperse fractal aggregates of spherical primary soot particles having constant diameters. The present soot aggregates exhibited significant departures from Rayleigh-scattering behavior at 514.5 nm, with forward scattering roughly 100 times larger than wide-angle scattering and ratios of scattering to absorption cross sections in the range 0.22–0.41, increasing with increasing propensity of the fuel to soot. The approximate RDG theory generally provided an acceptable basis to treat the optical properties of the present overfire soot aggregates, although additional measurements in the Guinier (small angle) regime are needed for a definitive evaluation of model performance.
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François, O., L. Mohamed Abdallahi, J. Horikawa, I. Taniguchi, and T. Hervé. "Statistical Procedures for Spatiotemporal Neuronal Data with Applications to Optical Recording of the Auditory Cortex." Neural Computation 12, no. 8 (August 1, 2000): 1821–38. http://dx.doi.org/10.1162/089976600300015150.
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This article presents new procedures for multisite spatiotemporal neuronal data analysis. A new statistical model—the diffusion model—is considered, whose parameters can be estimated from experimental data thanks to mean-field approximations. This work has been applied to optical recording of the guinea pig's auditory cortex (layers II—III). The rates of innovation and internal diffusion inside the stimulated area have been estimated. The results suggest that the activity of the layer balances between the alternate predominance of its innovation process and its internal process.
Dissertations / Theses on the topic "Guinier approximation"
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(8775689), Luis Palacio. "SMALL ANGLE SCATTERING OF LARGE PROTEIN UNITS UNDER OSMOTIC STRESS." Thesis, 2020.
Find full textAbstract:
Large protein molecules are abundant in biological cells but are very difficult to study in physiological conditions due to molecular disorder. For large proteins, most structural information is obtained in crystalline states which can be achieved in certain conditions at very low temperature. X-ray and neutron crystallography methods can then be used for determination of crystalline structures at atomic level. However, in solution at room or physiological temperatures such highly resolved descriptions cannot be obtained except in very few cases. Scattering methods that can be used to study this type of structures at room temperature include small-angle x-ray and neutron scattering. These methods are used here to study two distinct proteins that are both classified as glycoproteins, which are a large class of proteins with diverse biological functions. In this study, two specific plasma glycoproteins were used: Fibrinogen (340 kDa) and Alpha 1-Antitrypsin or A1AT (52 kDa). These proteins have been chosen based on the fact that they have a propensity to form very large molecular aggregates due to their tendency to polymerize. One goal of this project is to show that for such complex structures, a combination of scattering methods that include SAXS, SANS, and DLS can address important structural and interaction questions despite the fact that atomic resolution cannot be obtained as in crystallography. A1AT protein has been shown to have protective roles of lung cells against emphysema, while fibrinogen is a major factor in the blood clotting process. A systematic approach to study these proteins interactions with lipid membranes and other proteins, using contrast-matching small-angle neutron scattering (SANS), small angle x-ray scattering (SAXS) and dynamic light scattering (DLS), is presented here. A series of structural reference points for each protein in solution were determined by performing measurements under osmotic stress controlled by the addition of polyethylene glycol-1,500 MW (PEG 1500) in the samples. Osmotic pressure changes the free energy of the molecular mixture and has consequences on the structure and the interaction of molecular aggregates. In particular, the measured radius of gyration (Rg) for A1AT shows a sharp structural transition when the concentration of PEG 1500 is between 33 wt\% and 36 wt\%. Similarly, a significant structural change was observed for fibrinogen when the concentration of PEG 1500 was above 40 wt\%. This analysis is applied to a study of A1AT interacting with lipid membranes and to a study of fibrinogen polymerization in the presence of the enzyme thrombin, which catalyzes the formation of blood clots. The experimental approach presented here and the applications to specific questions show that an appropriate combination of scattering methods can produce useful information on the behavior and the interactions of large protein systems in physiological conditions despite the lower resolution compared to crystallography.
Book chapters on the topic "Guinier approximation"
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Corlett, Richard T. "Vegetation." In The Physical Geography of Southeast Asia. Oxford University Press, 2005. http://dx.doi.org/10.1093/oso/9780199248025.003.0017.
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Southeast Asia is not a natural biogeographical unit: it extends well north out of the tropics in Myanmar, while the eastern boundary bisects the island of New Guinea. It is also divided in two by one of the sharpest zoogeographical boundaries in the world, Wallace’s line (Figure 7.1; Whitmore 1987). There is, however, one important unifying feature that distinguishes it from most other regions of the tropics: Southeast Asia is a region of forest climates. Only on the highest mountains in Papua and northern Myanmar is the climate too cold for forest and, with the possible exception of some small rain-shadow areas, it is nowhere too dry. Elsewhere the only permanent non-forest vegetation in the region before the human impacts of the last few millennia was on coastal cliffs and beaches, seasonally flooded river plains, active volcanoes, and perhaps some small inland areas on soils too poor to support forest. Today, however, as a result of human impacts, forest occupies less than half of the region, with various anthropogenic vegetation types occupying the rest. The recognition of Southeast Asia, as defined here, as a separate political and geographic entity is very recent, so it is not surprising that there has been no previous account of the vegetation of the whole region. Van Steenis (1957) gave a general account of the vegetation of Indonesia, while Whitmore (1984) concentrated on the tropical evergreen forests of the region, with only a brief description of the vegetation of drier climates. Champion (1936) described the principal forest types of Myanmar, while Vidal (1997) covered the vegetation of Thailand, Cambodia, and Lao PDR. Numerous other publications describe smaller areas or specific vegetation types. To a first approximation, the potential natural vegetation of the region (Plate 1) up to about 20°N is controlled by two main environmental gradients: a horizontal gradient of water availability and a vertical, altitudinal gradient. Water availability is determined largely by the amount and distribution of rainfall, with the length of the dry season the most important factor, although the water storage capacity of the soil becomes increasingly significant at the drier end of the gradient.
Conference papers on the topic "Guinier approximation"
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Hanspal, Navraj S., Keigi Fujiwara, and Michael R. King. "Finite Element Modelling of Blood Flow in Artery Stenosis." In ASME 4th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2006. http://dx.doi.org/10.1115/icnmm2006-96231.
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Recent work by our laboratories suggest that the endothelial cells that line blood vessels respond dramatically to shear stress gradients over millimeter and micrometer length scales, contributing to the progression of the atherosclerosis disease state. In this paper, we present a CFD model for the prediction and quantitative analyses of the hemodynamic behavior of blood flow in stenosed arteries of a guinea pig, comprised of a nearly axisymmetric vessel constriction. The blood is considered to be incompressible and the flow model is described by the Navier-Stokes and the continuity equations. A standard Galerkin finite element technique has been applied for the solution of the flow equations within a 2-D axisymmetric framework. Elemental discretization is based on the use of C0- continuous Taylor-Hood type isoparametric finite elements that are used for the approximation of the unknown field variables. An implicit-theta time-stepping scheme has been chosen for the temporal discretization of the flow equations. The rheological behaviour of blood is incorporated within the main flow model through the use of different non-Newtonian constitutive equations. Relationships of the stenosis severity and flow data such as flow rate and flow pressure are obtained from the numerical simulations. The results are presented in the form of velocity vectors and pressure surface plots and are examined for stability, convergence and theoretical consistency.