polyTEM.spatial.stats.bending_probability

polyTEM.spatial.stats.bending_probability(v1, v2, model='nematic', resolution=1, **kwargs)

Calculates the bending probability between aggregate segments v1 and v2 Segments are quantified as v = (x,y,alpha,a,b,c) where (a,b,c) is a unit vector of the nematic director (segment tangent), located at (x,y) (x,y) are in units of pixels

Models: 1) Single-chain WLC in Free Solution

p = exp(-1/2 * Lp * omega**2) Lp is the chain persistence length omega is the bending rate dtheta/dd (d is distance)

  1. WLC in thermotropic nematic field obtained from Frank-Oseen Theory

    p = exp(-bg) bg = Ks*(div(n))**2 + Kb*curl(div(n))**2 bg = 0.5*Ks*(s1 + s2)**2 + 0.5*Kb*(b1**2 + b2**2)

BUGS: RUNTIME WARNING for model=’single-chain’: invalid value encountered in arccos when calculating theta?

Parameters:

  • v1 – vector field of chain orientation segments

  • v2 – vector field of chain orientation segments

  • model – “single-chain”,”Frank-Oseen” or “nematic”

  • resolution – A/pixel resolution, needed for model=”single-chain”

  • Lp – units A, Persistence Length of polymer, default 3nm

  • Ks – units pixels

  • Kb – units pixels