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Excel's storage of numbers in binary format also affects its accuracy. [3] To illustrate, the lower figure tabulates the simple addition 1 + x − 1 for several values of x. All the values of x begin at the 15 th decimal, so Excel must take them into account. Before calculating the sum 1 + x, Excel first approximates x as a binary number
Multi-Angle light scattering describes a technique for measuring the light scattered by a sample into a plurality of angles. It is used for determining both the absolute molar mass and the average size of molecules in solution , by detecting how they scatter light .
Maxwell's equations are the basis of theoretical and computational methods describing light scattering, but since exact solutions to Maxwell's equations are only known for selected particle geometries (such as spherical), light scattering by particles is a branch of computational electromagnetics dealing with electromagnetic radiation ...
This makes small-angle measurements in neutrons and X-rays a bit more tedious, as very small angles are needed, and the data in those angles is often "overpowered" by the = spot emerging in usual scattering experiments. The problem is mitigated by conducting longer experiments with more exposure time, which allows the required data to "intensify".
At the edges of the dataset, when one is missing some of the surrounding points, the missing points can be approximated by a number of methods. A simple and common method is to assume that the slope from the existing point to the target point continues without further change, and using this to calculate a hypothetical value for the missing point.
Current usage of the term "Mie solution" indicates a series approximation to a solution of Maxwell's equations. There are several known objects that allow such a solution: spheres, concentric spheres, infinite cylinders, clusters of spheres and clusters of cylinders. There are also known series solutions for scattering by ellipsoidal particles.
The collision causes the photon wavelength to increase by somewhere between 0 (for a scattering angle of 0°) and twice the Compton wavelength (for a scattering angle of 180°). [32] Thomson scattering is the classical elastic quantitative interpretation of the scattering process, [26] and this can be seen to happen with lower, mid-energy, photons.
The differential angular range of the scattered particle at angle θ is the solid angle element dΩ = sin θ dθ dφ. The differential cross section is the quotient of these quantities, dσ / dΩ . It is a function of the scattering angle (and therefore also the impact parameter), plus other observables such as the momentum of the ...