500 research outputs found
Hamiltonian submanifolds of regular polytopes
We investigate polyhedral -manifolds as subcomplexes of the boundary
complex of a regular polytope. We call such a subcomplex {\it -Hamiltonian}
if it contains the full -skeleton of the polytope. Since the case of the
cube is well known and since the case of a simplex was also previously studied
(these are so-called {\it super-neighborly triangulations}) we focus on the
case of the cross polytope and the sporadic regular 4-polytopes. By our results
the existence of 1-Hamiltonian surfaces is now decided for all regular
polytopes.
Furthermore we investigate 2-Hamiltonian 4-manifolds in the -dimensional
cross polytope. These are the "regular cases" satisfying equality in Sparla's
inequality. In particular, we present a new example with 16 vertices which is
highly symmetric with an automorphism group of order 128. Topologically it is
homeomorphic to a connected sum of 7 copies of . By this
example all regular cases of vertices with or, equivalently, all
cases of regular -polytopes with are now decided.Comment: 26 pages, 4 figure
Partitioning the triangles of the cross polytope into surfaces
We present a constructive proof that there exists a decomposition of the
2-skeleton of the k-dimensional cross polytope into closed surfaces
of genus , each with a transitive automorphism group given by the
vertex transitive -action on . Furthermore we show
that for each the 2-skeleton of the (k-1)-simplex is a union
of highly symmetric tori and M\"obius strips.Comment: 13 pages, 1 figure. Minor update. Journal-ref: Beitr. Algebra Geom. /
Contributions to Algebra and Geometry, 53(2):473-486, 201
Combinatorial 3-manifolds with transitive cyclic symmetry
In this article we give combinatorial criteria to decide whether a transitive
cyclic combinatorial d-manifold can be generalized to an infinite family of
such complexes, together with an explicit construction in the case that such a
family exists. In addition, we substantially extend the classification of
combinatorial 3-manifolds with transitive cyclic symmetry up to 22 vertices.
Finally, a combination of these results is used to describe new infinite
families of transitive cyclic combinatorial manifolds and in particular a
family of neighborly combinatorial lens spaces of infinitely many distinct
topological types.Comment: 24 pages, 5 figures. Journal-ref: Discrete and Computational
Geometry, 51(2):394-426, 201
Perturbative behaviour of a vortex in a trapped Bose-Einstein condensate
We derive a set of equations that describe the shape and behaviour of a
single perturbed vortex line in a Bose-Einstein condensate. Through the use of
a matched asymptotic expansion and a unique coordinate transform a relation for
a vortex's velocity, anywhere along the line, is found in terms of the
trapping, rotation, and distortion of the line at that location. This relation
is then used to find a set of differential equations that give the line's
specific shape and motion. This work corrects a previous similar derivation by
Anatoly A. Svidzinsky and Alexander L. Fetter [Phys. Rev. A \textbf{62}, 063617
(2000)], and enables a comparison with recent numerical results.Comment: 12 pages with 3 figure
Coupled CFD-CAA approach for rotating systems
We present a recently developed computational scheme for the numerical simulation of flow induced sound for rotating systems. Thereby, the flow is fully resolved in time by utilizing a DES (Detached Eddy Simulation) turbulance model and using an arbitrary mesh interface scheme for connecting rotating and stationary domains. The acoustic field is modeled by a perturbation ansatz resulting in a convective wave equation based on the acoustic scalar potential and the substational time derivative of the incompressible flow pressure as a source term. We use the Finite-Element (FE) method for solving the convective wave equation and apply a Nitsche type mortaring at the interface between rotating and stationary domains. The whole scheme is applied to the numerical computation of a side channel blower
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Simulation of cyclotron resonant scattering features: The effect of bulk velocity
X-ray binary systems consisting of a mass donating optical star and a highly magnetized neutron star, under the right circumstances, show quantum mechanical absorption features in the observed spectra called cyclotron resonant scattering features (CRSFs). We have developed a simulation to model CRSFs using Monte Carlo methods. We calculate Green's tables which can be used to imprint CRSFs to arbitrary X-ray continua. Our simulation keeps track of scattering parameters of individual photons, extends the number of variable parameters of previous works, and allows for more flexible geometries. Here we focus on the influence of bulk velocity of the accreted matter on the CRSF line shapes and positions
Topological Modes in Dual Lattice Models
Lattice gauge theory with gauge group is reconsidered in four
dimensions on a simplicial complex . One finds that the dual theory,
formulated on the dual block complex , contains topological modes
which are in correspondence with the cohomology group ,
in addition to the usual dynamical link variables. This is a general phenomenon
in all models with single plaquette based actions; the action of the dual
theory becomes twisted with a field representing the above cohomology class. A
similar observation is made about the dual version of the three dimensional
Ising model. The importance of distinct topological sectors is confirmed
numerically in the two dimensional Ising model where they are parameterized by
.Comment: 10 pages, DIAS 94-3
From Golden Spirals to Constant Slope Surfaces
In this paper, we find all constant slope surfaces in the Euclidean 3-space,
namely those surfaces for which the position vector of a point of the surface
makes constant angle with the normal at the surface in that point. These
surfaces could be thought as the bi-dimensional analogue of the generalized
helices. Some pictures are drawn by using the parametric equations we found.Comment: 11 pages, 8 figure
A Closed Contour of Integration in Regge Calculus
The analytic structure of the Regge action on a cone in dimensions over a
boundary of arbitrary topology is determined in simplicial minisuperspace. The
minisuperspace is defined by the assignment of a single internal edge length to
all 1-simplices emanating from the cone vertex, and a single boundary edge
length to all 1-simplices lying on the boundary. The Regge action is analyzed
in the space of complex edge lengths, and it is shown that there are three
finite branch points in this complex plane. A closed contour of integration
encircling the branch points is shown to yield a convergent real wave function.
This closed contour can be deformed to a steepest descent contour for all sizes
of the bounding universe. In general, the contour yields an oscillating wave
function for universes of size greater than a critical value which depends on
the topology of the bounding universe. For values less than the critical value
the wave function exhibits exponential behaviour. It is shown that the critical
value is positive for spherical topology in arbitrary dimensions. In three
dimensions we compute the critical value for a boundary universe of arbitrary
genus, while in four and five dimensions we study examples of product manifolds
and connected sums.Comment: 16 pages, Latex, To appear in Gen. Rel. Gra
Formation of phase lags at the cyclotron energies in the pulse profiles of magnetized, accreting neutron stars
Context: Accretion-powered X-ray pulsars show highly energy-dependent and
complex pulse-profile morphologies. Significant deviations from the average
pulse profile can appear, in particular close to the cyclotron line energies.
These deviations can be described as energy-dependent phase lags, that is, as
energy-dependent shifts of main features in the pulse profile. Aims: Using a
numerical study we explore the effect of cyclotron resonant scattering on
observable, energy-resolved pulse profiles. Methods: We generated the
observable emission as a function of spin phase, using Monte Carlo simulations
for cyclotron resonant scattering and a numerical ray-tracing routine
accounting for general relativistic light-bending effects on the intrinsic
emission from the accretion columns. Results: We find strong changes in the
pulse profile coincident with the cyclotron line energies. Features in the
pulse profile vary strongly with respect to the average pulse profile with the
observing geometry and shift and smear out in energy additionally when assuming
a non-static plasma. Conclusions: We demonstrate how phase lags at the
cyclotron energies arise as a consequence of the effects of angular
redistribution of X-rays by cyclotron resonance scattering in a strong magnetic
field combined with relativistic effects. We also show that phase lags are
strongly dependent on the accretion geometry. These intrinsic effects will in
principle allow us to constrain a system's accretion geometry.Comment: 4 pages, 4 figures; updated reference lis
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