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We study the dynamics of topological defects in active nematic films with spatially varying activity and consider two set-ups: (i) a constant activity gradient and (ii) a sharp jump in activity. A constant gradient of extensile (contractile) activity endows the comet-like +1/2 defect with a finite vorticity that drives the defect to align its nose in the direction of decreasing (increasing) gradient. A constant gradient does not, however, affect the known self-propulsion of the +1/2 defect and has no effect on the −1/2 that remains a non-motile particle. A sharp jump in activity acts like a wall that traps the defects, affecting the translational and rotational motion of both charges. The +1/2 defect slows down as it approaches the interface and the net vorticity tends to reorient the defect polarization so that it becomes perpendicular to the interface. The −1/2 defect acquires a self-propulsion towards the activity interface, while the vorticity-induced active torque tends to align the defect to a preferred orientation. This effective attraction of the negative defects to the wall is consistent with the observation of an accumulation of negative topological charge at both active/passive interfaces and physical boundaries.
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The mechanism of electrical conduction in glassy semiconductors
We argue that the dominant charge carrier in glassy semiconducting alloys is a compound particle in the form of an electron or hole bound to an intimate pair of topological lattice defects; the particle is similar to the polaron solution of the Su–Schrieffer–Heeger Hamiltonian. The spatial component of the density of states for these special polarons is determined by the length scale of spatial modulation of electronegativity caused by a separate set of standalone topological defects. The latter length scale is fixed by the cooperativity size for structural relaxation; the size is largely independent of temperature in the glass but above melting, it decreases with temperature. Thus we predict that the temperature dependence of the electrical conductivity should exhibit a jump in the slope near the glass transition; the size of the jump is predicted to increase with the fragility of the melt. The predicted values of the jump and of the conductivity itself are consistent with experiment.
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- Award ID(s):
- 1956389
- PAR ID:
- 10575235
- Publisher / Repository:
- Proceedings of the National Academy of Sciences
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 122
- Issue:
- 10
- ISSN:
- 0027-8424
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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