16,828 research outputs found
Nonlinear lattice model of viscoelastic Mode III fracture
We study the effect of general nonlinear force laws in viscoelastic lattice
models of fracture, focusing on the existence and stability of steady-state
Mode III cracks. We show that the hysteretic behavior at small driving is very
sensitive to the smoothness of the force law. At large driving, we find a Hopf
bifurcation to a straight crack whose velocity is periodic in time. The
frequency of the unstable bifurcating mode depends on the smoothness of the
potential, but is very close to an exact period-doubling instability. Slightly
above the onset of the instability, the system settles into a exactly
period-doubled state, presumably connected to the aforementioned bifurcation
structure. We explicitly solve for this new state and map out its
velocity-driving relation
Taylor dispersion of gyrotactic swimming micro-organisms in a linear flow
The theory of generalized Taylor dispersion for suspensions of Brownian particles is developed to study the dispersion of gyrotactic swimming micro-organisms in a linear shear flow. Such creatures are bottom-heavy and experience a gravitational torque which acts to right them when they are tipped away from the vertical. They also suffer a net viscous torque in the presence of a local vorticity field. The orientation of the cells is intrinsically random but the balance of the two torques results in a bias toward a preferred swimming direction. The micro-organisms are sufficiently large that Brownian motion is negligible but their random swimming across streamlines results in a mean velocity together with diffusion. As an example, we consider the case of vertical shear flow and calculate the diffusion coefficients for a suspension of the alga <i>Chlamydomonas nivalis</i>. This rational derivation is compared with earlier approximations for the diffusivity
The Universal Gaussian in Soliton Tails
We show that in a large class of equations, solitons formed from generic
initial conditions do not have infinitely long exponential tails, but are
truncated by a region of Gaussian decay. This phenomenon makes it possible to
treat solitons as localized, individual objects. For the case of the KdV
equation, we show how the Gaussian decay emerges in the inverse scattering
formalism.Comment: 4 pages, 2 figures, revtex with eps
Microscopic Selection of Fluid Fingering Pattern
We study the issue of the selection of viscous fingering patterns in the
limit of small surface tension. Through detailed simulations of anisotropic
fingering, we demonstrate conclusively that no selection independent of the
small-scale cutoff (macroscopic selection) occurs in this system. Rather, the
small-scale cutoff completely controls the pattern, even on short time scales,
in accord with the theory of microscopic solvability. We demonstrate that
ordered patterns are dynamically selected only for not too small surface
tensions. For extremely small surface tensions, the system exhibits chaotic
behavior and no regular pattern is realized.Comment: 6 pages, 5 figure
Perforation of Bowel Associated with Blunt Abdominal Trauma in Children
Motor vehicle accidents remain the commonest cause of abdominal trauma in children, but there are many situations that expose the child more particularly to blunt abdominal trauma. In order to avoid unnecessary delay in diagnosis, a plan of management is proposed, based on our experience with 4 cases of abdominal trauma. The need for early diagnosis is emphasised
BEAMS: separating the wheat from the chaff in supernova analysis
We introduce Bayesian Estimation Applied to Multiple Species (BEAMS), an
algorithm designed to deal with parameter estimation when using contaminated
data. We present the algorithm and demonstrate how it works with the help of a
Gaussian simulation. We then apply it to supernova data from the Sloan Digital
Sky Survey (SDSS), showing how the resulting confidence contours of the
cosmological parameters shrink significantly.Comment: 23 pages, 9 figures. Chapter 4 in "Astrostatistical Challenges for
the New Astronomy" (Joseph M. Hilbe, ed., Springer, New York, forthcoming in
2012), the inaugural volume for the Springer Series in Astrostatistic
Phase-Field Model of Mode III Dynamic Fracture
We introduce a phenomenological continuum model for mode III dynamic fracture
that is based on the phase-field methodology used extensively to model
interfacial pattern formation. We couple a scalar field, which distinguishes
between ``broken'' and ``unbroken'' states of the system, to the displacement
field in a way that consistently includes both macroscopic elasticity and a
simple rotationally invariant short scale description of breaking. We report
two-dimensional simulations that yield steady-state crack motion in a strip
geometry above the Griffith threshold.Comment: submitted to PR
Solution of an infection model near threshold
We study the Susceptible-Infected-Recovered model of epidemics in the
vicinity of the threshold infectivity. We derive the distribution of total
outbreak size in the limit of large population size . This is accomplished
by mapping the problem to the first passage time of a random walker subject to
a drift that increases linearly with time. We recover the scaling results of
Ben-Naim and Krapivsky that the effective maximal size of the outbreak scales
as , with the average scaling as , with an explicit form for
the scaling function
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