56,044 research outputs found
A blowup criterion for ideal viscoelastic flow
We establish an analog of the Beale-Kato-Majda criterion for singularities of
smooth solutions of the system of PDE arising in the Oldroyd model for ideal
viscoelastic flow
Short Gamma-Ray Bursts with Extended Emission Observed with Swift/BAT and Fermi/GBM
Some short GRBs are followed by longer extended emission, lasting anywhere
from ~10 to ~100 s. These short GRBs with extended emission (EE) can possess
observational characteristics of both short and long GRBs (as represented by
GRB 060614), and the traditional classification based on the observed duration
places some of them in the long GRB class. While GRBs with EE pose a challenge
to the compact binary merger scenario, they may therefore provide an important
link between short and long duration events. To identify the population of GRBs
with EE regardless of their initial classifications, we performed a systematic
search of short GRBs with EE using all available data (up to February 2013) of
both Swift/BAT and Fermi/GBM. The search identified 16 BAT and 14 GBM detected
GRBs with EE, several of which are common events observed with both detectors.
We investigated their spectral and temporal properties for both the spikes and
the EE, and examined correlations among these parameters. Here we present the
results of the systematic search as well as the properties of the identified
events. Finally, their properties are also compared with short GRBs with EE
observed with BATSE, identified through our previous search effort. We found
several strong correlations among parameters, especially when all of the
samples were combined. Based on our results, a possible progenitor scenario of
two-component jet is discussed.Comment: Published in MNRAS; matched to the published versio
The Two Dimensional Liquid Crystal Droplet Problem with Tangential Boundary Condition
This paper studies a shape optimization problem which reduces to a nonlocal free boundary problem involving perimeter. It is motivated by a study of liquid crystal droplets with a tangential anchoring boundary condition and a volume constraint. We establish in 2D the existence of an optimal shape that has two cusps on the boundary. We also prove the boundary of the droplet is a chord-arc curve with its normal vector field in the VMO space, and its arc-length parametrization belongs to the Sobolev space . In fact, the boundary curves of such droplets closely resemble the so-called Weil-Petersson class of planar curves. In addition, the asymptotic behavior of the optimal shape when the volume becomes extremely large or small is also studied
On 2D Viscoelasticity with Small Strain
An exact two-dimensional rotation-strain model describing the motion of
Hookean incompressible viscoelastic materials is constructed by the polar
decomposition of the deformation tensor. The global existence of classical
solutions is proved under the smallness assumptions only on the size of initial
strain tensor. The proof of global existence utilizes the weak dissipative
mechanism of motion, which is revealed by passing the partial dissipation to
the whole system.Comment: Different contributions of strain and rotation of the deformation are
studied for viscoelastic fluids of Oldroyd-B type in 2
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