Exploitation of Brownian motions for the optimal control of fiber orientation distributions

Abstract

An analogy of the charge distribution on Julia sets with the Brownian motion Comment on ''Photoselection in uniaxial liquid crystals: The effect of rotational Brownian motion on measurements of orientational distribution functions'' J. Chem. Phys. 73, 3021 (1980); 10.1063/1.440440 Photoselection in uniaxial liquid crystals: The effect of rotational Brownian motion on measurements of orientational distribution function J. Chem. Phys. 73, 3019 (1980); 10.1063/1.440439 Polarized fluorescent emission in uniaxial liquid crystals. The effect of intramolecular energy transfer and rotational Brownian motion on measurements of the orientational distribution functionThe dynamical behavior of suspensions of rod-like particles is explored in unsteady elementary flows characterized by the following special property: while there may be arbitrarily large excursions from an initial state by the carrier fluid, the fluid returns to the initial state at the end of the time interval. In such a closed flow, it is shown that the orientation distribution of a dilute non-Brownian suspension will also return to its initial state, after arbitrarily large excursions driven by the flow of the carrier fluid. In contrast, the orientation distribution in a Brownian suspension will not return to its initial state at the end of the interval in a closed flow. These effects are exploited in a constrained nonlinear optimal control problem for the orientation distribution of a Brownian suspension in an example closed flow. The result of the control problem is a family of protocols that are most effective at achieving various degrees of anisotropy of the suspension, within the class of flows under consideration.