Polyorder research notebook
Notes on polymer field theory, numerical methods, and scientific software.
Perform cubic Hermite spline interpolation in Julia
This is a tutorial on how to use the Julia package CubicHermiteSpline.jl, which performs a cubic Hermite spline interpolation on an array of data points, $(x_i, y_i)$, given that their associated gradients, $k_i=(dy/dx)_i$, are known in advance.New v0.3.0 can now perform bivariate cubic Hermite...
Form factor of a homogeneous sphere
In this post we will first coin the term form factor for arbitrary particles by generalizing the idea of the atomic form factor. We then derive an analytical expression for the form factor of a homogeneous sphere. The functionality is implemented in two submodules:...
Fundamentals of X-Ray Scattering
In this post we will present a concise review of the fundamental theory of X-ray scattering, including electromagnetic waves, flux and intensity, scattering cross section and scattering length, scattering by an electron, interference, and atomic form factor. Although the specific properties of X-rays are...
A Jupyter notebook like blog post for demonstration
Numerical experiments are carried out to demonstrate the usage as well as serving as a test for the rotation.jl submodule. This is an appendix to the previous post. The format of this post mimics the Jupyter notebook. The output of a code block after...
Rotations and their representations
In this post we implement submodules rotation.jl of Scattering.jl to rotate a vector in the reference coordinate system to the internal coordinate system of the scatterer. Three representations of a rotaion operation are discussed and implemented. The conversion among and math operations on these...