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.]

The parsec-scale jet in M87.

We briefly review the observed structure and evolution of the M87 jet on scales less, similar1 parsec (pc; 1 pc = 3.09 x 10(16) m). Filamentary features, limb-brightening, and side-to-side oscillation are common characteristics of the pc-scale, and kpc-scale jets. The most prominent emission features on both the pc and subpc scales appear stationary (v/c < 0.1). Nonetheless, based on the jet's flux evolution, the presence of kpc-scale superluminal motion, and the absence of a visible counter-jet, we argue for the presence of an underlying relativistic flow, consistent with unified models. The initial jet collimation appears to occur on scales <0.1 pc, thus favoring electromagnetic processes associated with a black hole and accretion disk.

The nuclear jet and counterjet region of the radio galaxy Cygnus A.

Very-long-baseline interferometry images of the nuclear region of the radio galaxy Cygnus A reveal a pronounced "core" and a knotty jet and counterjet. The knots are moving away from the core at apparent speeds which are subluminal for h = 1 [h = H0/100 km.s-1.Mpc-1;1 parsec (pc) = 3.09 x 10(16)m] and about c for h = 0.5. The jet is aligned with the outer, kiloparsec-scale jet to within 2 degrees. The counterjet has a total flux density at 5 GHz of about one-fifth of that of the jet. In the context of the twin relativistic jet model for active galactic nuclei, the jet in Cygnus A is oriented at an angle to our line of sight of 35-80 degrees and 55-85 degrees, and the intrinsic velocity of the jet fluid is 0.4-0.6c and 0.6-1c for h = 1 and h = 0.5, respectively.