Update: smooth indenter & analytical calculation of velocity & hessian

Smooth Indenter: Wrote a new class in smoothIndenter.py which encapsulates all information about the smooth indenter. This class produces the correct LAMMPS script needed on "moving" the indenter. The file minimizeWithIndenter.py was suitably modified for this type of indenter.
On running the indenter I found that, x-quadruple gives the expected nucleation pattern BUT x-triple nucleates 2 dislocations even after moving the indenter (horizontally) some 5-6 times.


Analytical Velocity: This has the advantage that the indenter needn't be given a small perturbation to measure the velocity field. The equation used is in another post. In order to make solution of the linear system seamless and not involve any MATLAB use, I have decided to adopt the scipy sparse.dok_matrix format for all matrices and vectors. The newTheoHessian.py file has all the changes but is yet to be tested. More results on this will be posted here when available.
Fig1: 'Crystal response forces' are the analytically calculated forces in the crystal due to an infinitesimal downward motion of the indenter. The displacement field is computed from 2 configurations 1e-6 apart in indenter depth. Numerical velocity is computed by moving the indenter by 1e-7 and calculating the resulting crystal displacement.


Analytical Hessian: is finally working for LJ smooth (& LJ cut) potential. In fig 2. (below) are the lowest mode of x-triple. Also quoted below are the 4 lowest eigenvalues (calculate from full hessians using Lanczos). There is very close agreement between the analytical and numerical results.

4 lowest Eigenvalues of full hessian of x-triple :-
Numerical : -0.0058792, -0.24143, -0.59427, -0.77723
Analytical: 0.0058764, 0.24143, 0.59427, 0.77723


Fig 2: Lowest eigenmodes of x-triple.