12,078 research outputs found
Two-dimensional Stokes flow driven by elliptical paddles
A fast and accurate numerical technique is developed for solving the biharmonic equation in a multiply connected domain, in two dimensions. We apply the technique to the computation of slow viscous flow (Stokes flow) driven by multiple stirring rods. Previously, the technique has been
restricted to stirring rods of circular cross section; we show here how the prior method fails for noncircular rods and how it may be adapted to accommodate general rod cross sections, provided only that for each there exists a conformal mapping to a circle. Corresponding simulations of the flow are described, and their stirring properties and energy requirements are discussed briefly. In particular the method allows an accurate calculation of the flow when flat paddles are used to stir a fluid chaotically
The Responsible Corporate Officer, Criminal Liability, and Mens Rea: Limitations on the RCO Doctrine
The Responsible Corporate Officer, Criminal Liability, and Mens Rea: Limitations on the RCO Doctrine
Optimization of graded multilayer designs for astronomical x-ray telescopes
We developed a systematic method for optimizing the design of depth-graded multilayers for astronomical hard-x-ray and soft-γ-ray telescopes based on the instrument’s bandpass and the field of view. We apply these methods to the design of the conical-approximation Wolter I optics employed by the balloon-borne High Energy Focusing Telescope, using W/Si as the multilayer materials. In addition, we present optimized performance calculations of mirrors, using other material pairs that are capable of extending performance to photon energies above the W K-absorption edge (69.5 keV), including Pt/C, Ni/C, Cu/Si, and Mo/Si
Addendum to: Capillary floating and the billiard ball problem
We compare the results of our earlier paper on the floating in neutral
equilibrium at arbitrary orientation in the sense of Finn-Young with the
literature on its counterpart in the sense of Archimedes. We add a few remarks
of personal and social-historical character.Comment: This is an addendum to my article Capillary floating and the billiard
ball problem, Journal of Mathematical Fluid Mechanics 14 (2012), 363 -- 38
On recurrence and ergodicity for geodesic flows on noncompact periodic polygonal surfaces
We study the recurrence and ergodicity for the billiard on noncompact
polygonal surfaces with a free, cocompact action of or . In the
-periodic case, we establish criteria for recurrence. In the more difficult
-periodic case, we establish some general results. For a particular
family of -periodic polygonal surfaces, known in the physics literature
as the wind-tree model, assuming certain restrictions of geometric nature, we
obtain the ergodic decomposition of directional billiard dynamics for a dense,
countable set of directions. This is a consequence of our results on the
ergodicity of \ZZ-valued cocycles over irrational rotations.Comment: 48 pages, 12 figure
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