2,872 research outputs found
On the Leray-Hopf Extension Condition for the Steady-State Navier-Stokes Problem in Multiply-Connected Bounded Domains
Employing the approach of A. Takeshita [Pacific J. Math., Vol. 157 (1993),
151--158], we give an elementary proof of the invalidity of the Leray-Hopf
Extension Condition for certain multiply connected bounded domains of R^n,
n=2,3, whenever the flow through the different components of the boundary is
non-zero. Our proof is alternative to and, to an extent, more direct than the
recent one proposed by J.G. Heywood [J. Math. Fluid Mech. Vol. 13 (2011),
449--457]
Short-Pulsed Wavepacket Propagation in Ray-Chaotic Enclosures
Wave propagation in ray-chaotic scenarios, characterized by exponential
sensitivity to ray-launching conditions, is a topic of significant interest,
with deep phenomenological implications and important applications, ranging
from optical components and devices to time-reversal focusing/sensing schemes.
Against a background of available results that are largely focused on the
time-harmonic regime, we deal here with short-pulsed wavepacket propagation in
a ray-chaotic enclosure. For this regime, we propose a rigorous analytical
framework based on a short-pulsed random-plane-wave statistical representation,
and check its predictions against the results from
finite-difference-time-domain numerical simulations.Comment: 11 pages, 11 figures; minor modifications in the tex
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