6,884 research outputs found
An absorbing boundary formulation for the stratified, linearized, ideal MHD equations based on an unsplit, convolutional perfectly matched layer
Perfectly matched layers are a very efficient and accurate way to absorb
waves in media. We present a stable convolutional unsplit perfectly matched
formulation designed for the linearized stratified Euler equations. However,
the technique as applied to the Magneto-hydrodynamic (MHD) equations requires
the use of a sponge, which, despite placing the perfectly matched status in
question, is still highly efficient at absorbing outgoing waves. We study
solutions of the equations in the backdrop of models of linearized wave
propagation in the Sun. We test the numerical stability of the schemes by
integrating the equations over a large number of wave periods.Comment: 8 pages, 7 figures, accepted, A &
Phase-field approach to heterogeneous nucleation
We consider the problem of heterogeneous nucleation and growth. The system is
described by a phase field model in which the temperature is included through
thermal noise. We show that this phase field approach is suitable to describe
homogeneous as well as heterogeneous nucleation starting from several general
hypotheses. Thus we can investigate the influence of grain boundaries,
localized impurities, or any general kind of imperfections in a systematic way.
We also put forward the applicability of our model to study other physical
situations such as island formation, amorphous crystallization, or
recrystallization.Comment: 8 pages including 7 figures. Accepted for publication in Physical
Review
Recalibrating -order trees and \mbox{Homeo}_+(S^1)-representations of link groups
In this paper we study the left-orderability of -manifold groups using an
enhancement, called recalibration, of Calegari and Dunfield's "flipping"
construction, used for modifying \mbox{Homeo}_+(S^1)-representations of the
fundamental groups of closed -manifolds. The added flexibility accorded by
recalibration allows us to produce \mbox{Homeo}_+(S^1)-representations of
hyperbolic link exteriors so that a chosen element in the peripheral subgroup
is sent to any given rational rotation. We apply these representations to show
that the branched covers of families of links associated to arbitrary
epimorphisms of the link group onto a finite cyclic group are left-orderable.
This applies, for instance, to fibered hyperbolic strongly quasipositive links.
Our result on the orderability of branched covers implies that the degeneracy
locus of any pseudo-Anosov flow on an alternating knot complement must be
meridional, which generalizes the known result that the fractional Dehn twist
coefficient of any hyperbolic fibered alternating knot is zero. Applications of
these representations to order-detection of slopes are also discussed in the
paper.Comment: 43 pages, 12 figure
JSJ decompositions of knot exteriors, Dehn surgery and the -space conjecture
In this article, we apply slope detection techniques to study properties of
toroidal -manifolds obtained by performing Dehn surgeries on satellite knots
in the context of the -space conjecture. We show that if is an -space
knot or admits an irreducible rational surgery with non-left-orderable
fundamental group, then the JSJ graph of its exterior is a rooted interval.
Consequently, any rational surgery on a composite knot has a left-orderable
fundamental group. This is the left-orderable counterpart of Krcatovich's
result on the primeness of -space knots, which we reprove using our methods.
Analogous results on the existence of co-orientable taut foliations are proved
when the knot has a fibred companion. Our results suggest a new approach to
establishing the counterpart of Krcatovich's result for surgeries with
co-orientable taut foliations, on which partial results have been achieved by
Delman and Roberts. Finally, we prove results on left-orderable -surgeries
on knots with small.Comment: 25 pages, 1 appendi
Slope detection and toroidal 3-manifolds
We investigate the -space conjecture for toroidal -manifolds using
various notions of slope detection. This leads to a proof that toroidal
-manifolds with small order first homology have left-orderable fundamental
groups and, under certain fibring conditions, admit co-oriented taut
foliations. It also allows us to show that cyclic branched covers of prime
satellite knots are not -spaces, have left-orderable fundamental groups and,
when they have fibred companion knots, admit co-oriented taut foliations. A
partial extension to prime toroidal links leads to a proof that prime
quasi-alternating links are either hyperbolic or -torus links. Our main
technical result gives sufficient conditions for certain slopes on the
boundaries of rational homology solid tori to be detected by left-orders,
foliations and Heegaard Floer homology.Comment: 60 pages, 26 figure
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