3,265 research outputs found
A Generalized Axis Theorem for Cube Complexes
We consider a finitely generated virtually abelian group acting properly
and without inversions on a CAT(0) cube complex . We prove that
stabilizes a finite dimensional CAT(0) subcomplex that is
isometrically embedded in the combinatorial metric. Moreover, we show that
is a product of finitely many quasilines. The result represents a higher
dimensional generalization of Haglund's axis theorem.Comment: 14 pages Corrected proof of Corollary 1.4. Various other corrections
made following referee report and comments made by thesis examiner. Appendix
added giving a proof of a theorem by Gerasimo
Classifying Finite Dimensional Cubulations of Tubular Groups
A tubular group is a group that acts on a tree with vertex
stabilizers and edge stabilizers. This paper develops further a
criterion of Wise and determines when a tubular group acts freely on a finite
dimensional CAT(0) cube complex. As a consequence we offer a unified
explanation of the failure of separability by revisiting the non-separable
3-manifold group of Burns, Karrass and Solitar and relating it to the work of
Rubinstein and Wang. We also prove that if an immersed wall yields an infinite
dimensional cubulation then the corresponding subgroup is quadratically
distorted.Comment: 24 pages, 11 figures. Minor corrections and clarifications. Some
figures are redrawn. The proof of Theorem 6.1 is rewritten for clarity and to
correct error
Hyperbolic groups that are not commensurably coHopfian
Sela proved every torsion-free one-ended hyperbolic group is coHopfian. We
prove that there exist torsion-free one-ended hyperbolic groups that are not
commensurably coHopfian. In particular, we show that the fundamental group of
every simple surface amalgam is not commensurably coHopfian.Comment: v3: 14 pages, 4 figures; minor changes. To appear in International
Mathematics Research Notice
Charge structure in volcanic plumes: a comparison of plume properties predicted by an integral plume model to observations of volcanic lightning during the 2010 eruption of Eyjafjallajökull, Iceland
Observations of volcanic lightning made using a lightning mapping array during the 2010 eruption of Eyjafjallajökull allow the trajectory and growth of the volcanic plume to be determined. The lightning observations are compared with predictions of an integral model of volcanic plumes that includes descriptions of the interaction with wind and the effects of moisture. We show that the trajectory predicted by the integral model closely matches the observational data and the model well describes the growth of the plume downwind of the vent. Analysis of the lightning signals reveals information on the dominant charge structure within the volcanic plume. During the Eyjafjallajökull eruption both monopole and dipole charge structures were observed in the plume. By using the integral plume model, we propose the varying charge structure is connected to the availability of condensed water and low temperatures at high altitudes in the plume, suggesting ice formation may have contributed to the generation of a dipole charge structure via thunderstorm-style ice-based charging mechanisms, though overall this charging mechanism is believed to have had only a weak influence on the production of lightning
A Cubical Flat Torus Theorem and the Bounded Packing Property
We prove the bounded packing property for any abelian subgroup of a group
acting properly and cocompactly on a CAT(0) cube complex. A main ingredient of
the proof is a cubical flat torus theorem. This ingredient is also used to show
that central HNN extensions of maximal free-abelian subgroups of compact
special groups are virtually special, and to produce various examples of groups
that are not cocompactly cubulated.Comment: 14 pages, 2 figures, submitted May 2015 Minor corrections and swapped
sections 2 and 3 Corrected an unfortunate typo in Theorem 2.1 - the
hypothesis that the cube complex be finite dimensional has now been adde
Unsteady turbulent buoyant plumes
We model the unsteady evolution of turbulent buoyant plumes following
temporal changes to the source conditions. The integral model is derived from
radial integration of the governing equations expressing the conservation of
mass, axial momentum and buoyancy. The non-uniform radial profiles of the axial
velocity and density deficit in the plume are explicitly described by shape
factors in the integral equations; the commonly-assumed top-hat profiles lead
to shape factors equal to unity. The resultant model is hyperbolic when the
momentum shape factor, determined from the radial profile of the mean axial
velocity, differs from unity. The solutions of the model when source conditions
are maintained at constant values retain the form of the well-established
steady plume solutions. We demonstrate that the inclusion of a momentum shape
factor that differs from unity leads to a well-posed integral model. Therefore,
our model does not exhibit the mathematical pathologies that appear in
previously proposed unsteady integral models of turbulent plumes. A stability
threshold for the value of the shape factor is identified, resulting in a range
of its values where the amplitude of small perturbations to the steady
solutions decay with distance from the source. The hyperbolic character of the
system allows the formation of discontinuities in the fields describing the
plume properties during the unsteady evolution. We compute numerical solutions
to illustrate the transient development following an abrupt change in the
source conditions. The adjustment to the new source conditions occurs through
the propagation of a pulse of fluid through the plume. The dynamics of this
pulse are described by a similarity solution and, by constructing this new
similarity solution, we identify three regimes in which the evolution of the
transient pulse following adjustment of the source qualitatively differ.Comment: 41 pages, 16 figures, under consideration for publication in Journal
of Fluid Mechanic
Geometric Prequantization of the Moduli Space of the Vortex equations on a Riemann surface
The moduli space of solutions to the vortex equations on a Riemann surface
are well known to have a symplectic (in fact K\"{a}hler) structure. We show
this symplectic structure explictly and proceed to show a family of symplectic
(in fact, K\"{a}hler) structures on the moduli space,
parametrised by , a section of a line bundle on the Riemann surface.
Next we show that corresponding to these there is a family of prequantum line
bundles on the moduli space whose curvature is
proportional to the symplectic forms .Comment: 8 page
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