The efficiency of propulsion by a rotating flagellum

[At very low Reynolds number, the regime in which fluid dynamics is governed by Stokes equations, a helix that translates along its axis under an external force but without an external torque will necessarily rotate. By the linearity of the Stokes equations, the same helix that is caused to rotate due to an external torque will necessarily translate. This is the physics that underlies the mechanism of flagellar propulsion employed by many microorganisms. Here, I examine the linear relationships between forces and torques and translational and angular velocities of helical objects to understand the nature of flagellar propulsion.]

Molecular dynamics of a grid-mounted molecular dipolar rotor in a rotating electric field

Classical molecular dynamics is applied to the rotation of a dipolar molecular rotor mounted on a square grid and driven by rotating electric field E(ν) at T ≃ 150 K. The rotor is a complex of Re with two substituted o-phenanthrolines, one positively and one negatively charged, attached to an axial position of Rh\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{2}^{4+}}}\end{equation*}\end{document} in a [2]staffanedicarboxylate grid through 2-(3-cyanobicyclo[1.1.1]pent-1-yl)malonic dialdehyde. Four regimes are characterized by a, the average lag per turn: (i) synchronous (a < 1/e) at E(ν) = |E(ν)| > Ec(ν) [Ec(ν) is the critical field strength], (ii) asynchronous (1/e < a < 1) at Ec(ν) > E(ν) > Ebo(ν) > kT/μ, [Ebo(ν) is the break-off field strength], (iii) random driven (a ≃ 1) at Ebo(ν) > E(ν) > kT/μ, and (iv) random thermal (a ≃ 1) at kT/μ > E(ν). A fifth regime, (v) strongly hindered, W > kT, Eμ, (W is the rotational barrier), has not been examined. We find Ebo(ν)/kVcm−1 ≃ (kT/μ)/kVcm−1 + 0.13(ν/GHz)1.9 and Ec(ν)/kVcm−1 ≃ (2.3kT/μ)/kVcm−1 + 0.87(ν/GHz)1.6. For ν > 40 GHz, the rotor behaves as a macroscopic body with a friction constant proportional to frequency, η/eVps ≃ 1.14 ν/THz, and for ν < 20 GHz, it exhibits a uniquely molecular behavior.

Constraints on nebular dynamics and chemistry based on observations of annealed magnesium silicate grains in comets and in disks surrounding Herbig Ae/Be stars

Understanding dynamic conditions in the Solar Nebula is the key to prediction of the material to be found in comets. We suggest that a dynamic, large-scale circulation pattern brings processed dust and gas from the inner nebula back out into the region of cometesimal formation—extending possibly hundreds of astronomical units (AU) from the sun—and that the composition of comets is determined by a chemical reaction network closely coupled to the dynamic transport of dust and gas in the system. This scenario is supported by laboratory studies of Mg silicates and the astronomical data for comets and for protoplanetary disks associated with young stars, which demonstrate that annealing of nebular silicates must occur in conjunction with a large-scale circulation. Mass recycling of dust should have a significant effect on the chemical kinetics of the outer nebula by introducing reduced, gas-phase species produced in the higher temperature and pressure environment of the inner nebula, along with freshly processed grains with “clean” catalytic surfaces to the region of cometesimal formation. Because comets probably form throughout the lifetime of the Solar Nebula and processed (crystalline) grains are not immediately available for incorporation into the first generation of comets, an increasing fraction of dust incorporated into a growing comet should be crystalline olivine and this fraction can serve as a crude chronometer of the relative ages of comets. The formation and evolution of key organic and biogenic molecules in comets are potentially of great consequence to astrobiology.