Universal Analytical Scattering Form Factor for Sh

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A novel analytical and steady density distribution perform with a broadly variable form is reported and used to derive an analytical scattering type aspect that enables to universally describe the scattering from particles with all the radial density profile of homogeneous spheres, shells or core-shell-particles. Composed through the sum of two Fermi-Dirac distribution capabilities,Cheap Tiffany, the shape in the density profile may be altered constantly from step-like by means of Gaussian-like or parabolic to asymptotically hyperbolic by various a single rescaled “shape-parameter”, d (R being the particle radius). Using this density profile,Tiffany & Co, the scattering sort issue may be calculated numerically. An analytical sort element could be derived using an approximate expression for the original Fermi-Dirac distribution perform. This approximation is accurate for sufficiently small rescaled form parameters,US Patent # 7,931,258. Fluid-elastomeric damper as, d/R,Tiffany Sydney, up to values of d/R ≈ 0.1, and thus captures step-like,Authentic Pandora Beads, Gaussian-like and parabolic as well as asymptotically hyperbolic profile shapes. It is expected that this sort aspect is particularly useful in a model-dependent analysis of small angle scattering data, since the applied steady and analytical functionality for the particle density profile can be compared directly using the density profile extracted from the data by model-free approaches like the generalized inverse Fourier transform method.
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