Stokes efficiency of molecular motors with inertia

AbstractA molecular motor utilizes chemical free energy to generate a unidirectional motion in a viscous media. The stochastic motion of a motor is governed by a Langevin equation coupled to the chemical occupancy state. The change of chemical occupancy state is governed by a discrete Markov process. The Stokes efficiency was introduced to measure how “efficiently” the motor uses chemical free energy to drive through the surrounding fluid. For the overdamping case where the effect of inertia is ignored, it was proved that the Stokes efficiency is bounded by 100% [H. Wang, G. Oster, The Stokes efficiency for molecular motors and its applications, Europhysics Letters 57 (2002) 134–140]. Here we present a proof for the general case

Laser Polishing of Silica Rods

Lasers have been widely used in surface modification. In this research a CO2 continuous wave laser has been used to polish the slot surface of the silica rods. The strong absorption of the lO.6 um C02 radiation by the silica surface promotes the softening of a very thin layer of material that flows under the action of surface tension. As a result, a mirror smooth glassy surface has been formed which decreases the surface roughness without any substantial change in the surface geometries. The effect of laser to surface inclination angle on the requisite power requirement was assessed experimentally and theoretically. With laser beam scanning controlled by a computer aided design (CAD) database without specific tooling or human intervention, reliability and reproducibility of this process have been greatly improved compared to conventional fire polishing. The potential use of laser polishing as a post-processing step for freeform-fabricated parts is very promising.Mechanical Engineerin

NONPARALLEL SOLUTIONS OF EXTENDED NEMATIC POLYMERS UNDER AN EXTERNAL FIELD

Abstract. We continue the study on equilibria of the Smoluchowski equation for dilute solutions of rigid extended (dipolar) nematics and dispersions under an imposed electric or magnetic field [25]. We first provide an alternative proof for the theorem that all equilibria are dipolar with the polarity vector parallel to the external field direction if the strength of the permanent dipole (µ) is larger than or equal to the product of the external field (E) and the anisotropy parameter (α0) (i.e. µ ≥ |α0|E). Then, we show that when µ < |α0|E, there is a critical value α ∗ ≥ 1 for the intermolecular dipole-dipole interaction strength (α) such that all equilibria are either isotropic or parallel to the external field if α ≤ α ∗ ; but nonparallel dipolar equilibria emerge when α> α ∗. The nonparallel equilibria are analyzed and the asymptotic behavior of α ∗ is studied. Finally, the asymptotic results are validated by direct numerical simulations. 1. Introduction. Extende