Structure of paper for unsccm'09 procs

1x - triple, quadruple; 2x- triple, quadruple

delta(s) curves; delta_dot fields.

Standard notation summarized elsewhere, to mirror the proposal as closely as possible to avoid ambiguities.

Particular system: 2xtriple

Questions: Where shall we describe our indentation
Defect Structure(fig refs from proposal)
1) Saddle node scaling - deltaDot(depth)
--Fig 7 left
2) Rescaling of deltaDot wrt sqrt(delD)
--Fig 4 (left & right)
Story for 1 &2)
-> Usual saddle node square root criticality arising from (atleast) a 3rd order polynomial representing energy as it can form inflection/saddle points. Locus of minima is a diverging parabola.
-> Why we work at 0K: want to track the minima as closely as possible
-> Can demonstrate: evidence of the square root scaling, onset of scaling from as far as 1e-2 : should try to relate this to energy change in the crystal as this shall be a measure of barrier height?
-> Geometrical Instability: role of lowest mode(s) leads smoothly to point 4 (so switch 3 & 4?).

3) Small values of delta(s) @ criticality
--Fig 6 (all 3) + Picture of the velocity vector field without circles {in a grid of 2-by-2}
**Talk about the Pierels framework -- look harder at the proposal.

4) Lowest eigs wrt to deltaD (have this only for MD, do we need for energy minimization???)
--Standard 2 pictures (eigVals evolution + zoomed view) from the Chaos submission.
** Usual story from the Chaos submission. May have to modify if we decide to have energy minimization modes.

Mesoscale Resolver:
1) Min_eig (x,r,R;delD)
Have picture for 2xtriple.
--Fig 8 (left), maybe fig 8(centre) -- not sure as it doesn't present a clear picture.
--Festering Wound Picture from the blog (15 Oct, '09 post).
Have log scale plot but nothing to show dependence on delD.
-- Might be interesting to demonstrate pictorially the observation: 'as long as the mesoscale probing region intersects the defect core, we obtain the characteristic dislocating lowest mode'. What sort of picture shall one make here ? A 2-by-4 grid might do a good job ?? Just found the pictures, they look somewhat strange ...(in Mac in ~/Desktop/mesoModes/)

2) delta_dot(s) (x,r,R;delD)
--Will have to make picture, not entirely clear what we want. What does it mean to look at meso-scale velocity/displacement field?

___________________________________________

More to do on indentation:
-- Use previous displacement as an initial guess with decimation and see what happens.
-- Writing class smoothIndenter to abstract fix_indent. Main problem: efficiently (& cleanly) changing a single line in a text file.

Update: running the force-zeroing minimizer - bactracking, problems...

The energy minimizer (adapted from MR) tries to find force zeros. However when the minimizer tries to take a large step, we need to take a smaller step (backtrack). Two strategies are currently applied for backtracking: (i) Decimation - new step is 1/10 of previous step, (ii) AH - linearizes force and solves for the zero of the straight line.

Decimation is significantly slower than AH because it uses no information about the magnitude of the forces & hence tries a large number of moves whereas AH zeroes onto the correct move very quicky. Since decimation samples a large number of points of the search space, most of which are far from the starting point, the chance of it finding a minimum far away from the staring point is very high.

The latter case has been observed in indentation runs where decimation frequently shows a load drop before AH, especially when stepping by 1e-6 & sometimes when we step by 1e-5 too.

Problems/Observations with indentation runs:
(i) The biggest problem is that 4x-quadruple nucleates along 2 modes. Despite shifting the indenter horizontally, the problem persists. The best I was able to do was with AH, where upto steps of 1e-4, I was able to obtain nucleation along a single mode. However I still got a featureless velocity field.
ASIDE: An MD run, with fix viscous on, showed only one nucleation mode. The indeter depth was ~1 particle spacing lower than energy minimization.

(ii) I just observed that one gets a featureless velocity field in 2xquad if the state had been reached with decim but we try to define velocity with AH (or vice versa, can't recall). This is very peculiar and should be looked into.

(iii) All of the other systems gave defect-incipient velocity vector field that allowed computeCrossStrain.py to do its job 'fromScratch', although most velocity fields weren't 'clean' - especiallly those from 'decim' (probably because of its tendency to jump far).