We study molecular motor-induced microtubule self-organization in dilute and semi-dilutefilament solutions. In the dilute case, we use a probabilistic model of microtubuleinteraction via molecular motors to investigate microtubule bundle dynamics. Microtubulesare modeled as polar rods interacting through fully inelastic, binary collisions. Ourmodel indicates that initially disordered systems of interacting rods exhibit anorientational instability resulting in spontaneous ordering. We study the existence anddynamic interaction of microtubule bundles analytically and numerically. Our resultsreveal a long term attraction and coalescing of bundles indicating a clear coarsening inthe system; microtubule bundles concentrate into fewer orientations on a slow logarithmictime scale. In semi-dilute filament solutions, multiple motors can bind a filament toseveral others and, for a critical motor density, induce a transition to an ordered phasewith a nonzero mean orientation. Motors attach to a pair of filaments and walk along thepair bringing them into closer alignment. We develop a spatially homogenous, mean-fieldtheory that explicitly accounts for a force-dependent detachment rate of motors, which inturn affects the mean and the fluctuations of the net force acting on a filament. We showthat the transition to the oriented state can be both continuous and discontinuous whenthe force-dependent detachment of motors is important.

The effects of radiation transport on nonlocal electron heat flow in high Z laser-produced plasmas is studied. Using a Fokker-Planck model for the electron heat flow, which is coupled to a radiation transport model, it is found that radiation transport strongly modifies electron heat transport at the critical surface and in the overdense regions for an aluminum plasma. It is concluded that, without radiation transport effects, the plasma temperature, as computed from Fokker-Planck models, is overestimated in the critical region and underestimated in the overdense region, for high-Z plasmas.

Using anisotropic Fokker-Planck models, we calculate the evolution of mass and luminosity functions of the Galactic globular cluster system. Our models include two-body relaxation, binary heating, tidal shocks, dynamical friction, and stellar evolution. We perform Fokker-Planck simulations for a large number of virtual globular clusters and synthesize these results to study the relation between the initial and present GCMFs.

Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical energy. This suggests that, in nonequilibrium systems, fluctuations may be oriented or organized to do work. Here we seek to understand how this is manifested by quantitative mathematical portrayals of these systems.