Computation
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Eigenvalue tracing
Problem, difficulties and algorithms
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Spectral representation of dissipation in spherical coordinates
Representation of the volumetric integral of squared curl of a vector field, in terms of the spectral coefficients of the vector field
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Converting sympy to gmpy2 functions
sympy printer class translating sympy expressions to gmpy2 functions
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Arbitrary precision Gauss-Jacobi nodes and weights
Calculating Gauss-Jacobi nodes (roots of Jacobi polynomials) and weights to arbitrary precision
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Eigenvalue problem with Physics-informed Neural Network
Solve eigenvalue-eigenfunction pair with PINNs
Maths
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How similar are random vectors in high dimensions?
Given two random vectors in high-dimensional space, how similar are they expected to be?
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Associated Legendre function to one-sided Jacobi polynomial
An interesting observation - associated Legendre functions are just one-sided Jacobi polynomials in disguise - with some prefactors
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Parity of spherical harmonics
z-parity of spherical harmonics and poloidal toroidal fields expressed in spherical harmonics
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Adjoint method 1 - Adjoint of operators
First tool for adjoint method - what is an adjoint?
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Vector representation on a sphere
Helmholtz representation, Mie representation, etc.
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Curvilinear coordinates
Differential forms in curvilinear coordinates, using exterior differentials and Christoffel symbol.
Physics
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Green's function for advection-wave equation
Green's function for wave equation with advection in 1D infinite domain
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Diffusion on poloidal and toroidal vector fields
Poloidal fields and toroidal fields are invariant function spaces under magnetic diffusion, even with radially varying diffusivity
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Alfvén waves
Alfvén waves, dispersion relations in ideal and diffusive medium; Hartmann boundary layer.
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Boundary conditions for magnetohydrodynamics
Electromagnetic and kinematic boundary conditions that is used in MHD.
Tools
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A compilation of reference books
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Converting standard markdown to kramdown markdown
Kramdown markdown seems to follow a different style from standard markdown. This leads to complications when publicating a standard markdown page quickly.