alma::analytic1D::MSD_calculator_Laplace Class Reference

Class for computing the exact analytical RTA solution for mean square thermal energy displacement. More...

#include <analytic1d.hpp>

Public Member Functions
	MSD_calculator_Laplace (const alma::Crystal_structure *poscar, const alma::Gamma_grid *grid, const Eigen::ArrayXXd *w, double T)
	Constructor: initialise internal variables.
void	setDirection (const Eigen::Vector3d unitvector)
	Function setting the thermal transport axis.
void	setLinGrid (double fmin, double fmax, int Nf)
	Construct a linear temporal frequency grid from fmin to fmax with Nf elements.
void	setLogGrid (double fmin, double fmax, int Nf)
	Construct a logarithmic temporal frequency grid from fmin to fmax with Nf elements.
void	setLaplaceGrid (const Eigen::Ref< const Eigen::VectorXcd > sgrid)
	Manually set a Laplace grid.
Eigen::VectorXd	getGrid ()
	Retrieve the temporal frequency grid.
Eigen::VectorXcd	getLaplaceGrid ()
Eigen::VectorXcd	getMSD ()
	Compute MSD and retrieve it.

Detailed Description

Class for computing the exact analytical RTA solution for mean square thermal energy displacement.

By definition, the MSD is the variance of the macroscopic energy density: MSD = Integral(x^2*P(x,s),x=-infinity..infinity). Results are valid across all regimes (from fully ballistic to fully diffusive transport). Calculations are performed fully analytically by using the moment generating properties of the energy density in spatial frequency domain: MSD = minus second derivative of P(xi,s) at xi = 0.

---

The documentation for this class was generated from the following files:

• analytic1d.hpp
• analytic1d.cpp