13,882 research outputs found
On deformation and classification of V-systems
The V-systems are special finite sets of covectors which appeared in the
theory of the generalized Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations.
Several families of V-systems are known but their classification is an open
problem. We derive the relations describing the infinitesimal deformations of
V-systems and use them to study the classification problem for V-systems in
dimension 3. We discuss also possible matroidal structures of V-systems in
relation with projective geometry and give the catalogue of all known
irreducible rank 3 V-systems.Comment: Slightly revised version, one of the figures correcte
In search for a perfect shape of polyhedra: Buffon transformation
For an arbitrary polygon consider a new one by joining the centres of
consecutive edges. Iteration of this procedure leads to a shape which is affine
equivalent to a regular polygon. This regularisation effect is usually ascribed
to Count Buffon (1707-1788). We discuss a natural analogue of this procedure
for 3-dimensional polyhedra, which leads to a new notion of affine -regular
polyhedra. The main result is the proof of existence of star-shaped affine
-regular polyhedra with prescribed combinatorial structure, under partial
symmetry and simpliciality assumptions. The proof is based on deep results from
spectral graph theory due to Colin de Verdiere and Lovasz.Comment: Slightly revised version with added example of pentakis dodecahedro
Magnetic properties of the spin-1 two-dimensional Heisenberg model on a triangular lattice
Motivated by the recent experiment in NiGaS, the spin-1 Heisenberg
model on a triangular lattice with the ferromagnetic nearest- and
antiferromagnetic third-nearest-neighbor exchange interactions,
and , is studied in the range of the parameter . Mori's projection operator technique is used as a method, which retains the
rotation symmetry of spin components and does not anticipate any magnetic
ordering. For zero temperature several phase transitions are observed. At the ground state is transformed from the ferromagnetic order into
a disordered state, which in its turn is changed to an antiferromagnetic
long-range ordered state with the incommensurate ordering vector at . With growing the ordering vector moves along the line to the
commensurate point , which is reached at . The
final state with the antiferromagnetic long-range order can be conceived as
four interpenetrating sublattices with the spin structure on each of
them. Obtained results offer a satisfactory explanation for the experimental
data in NiGaS.Comment: 2 pages, 3 figure
Phase diagram of the three-dimensional Anderson model of localization with random hopping
We examine the localization properties of the three-dimensional (3D) Anderson
Hamiltonian with off-diagonal disorder using the transfer-matrix method (TMM)
and finite-size scaling (FSS). The nearest-neighbor hopping elements are chosen
randomly according to . We find that the
off-diagonal disorder is not strong enough to localize all states in the
spectrum in contradistinction to the usual case of diagonal disorder. Thus for
any off-diagonal disorder, there exist extended states and, consequently, the
TMM converges very slowly. From the TMM results we compute critical exponents
of the metal-insulator transitions (MIT), the mobility edge , and study
the energy-disorder phase diagram.Comment: 4 pages, 5 EPS figures, uses annalen.cls style [included]; presented
at Localization 1999, to appear in Annalen der Physik [supplement
Parallel-in-Time Multi-Level Integration of the Shallow-Water Equations on the Rotating Sphere
The modeling of atmospheric processes in the context of weather and climate
simulations is an important and computationally expensive challenge. The
temporal integration of the underlying PDEs requires a very large number of
time steps, even when the terms accounting for the propagation of fast
atmospheric waves are treated implicitly. Therefore, the use of
parallel-in-time integration schemes to reduce the time-to-solution is of
increasing interest, particularly in the numerical weather forecasting field.
We present a multi-level parallel-in-time integration method combining the
Parallel Full Approximation Scheme in Space and Time (PFASST) with a spatial
discretization based on Spherical Harmonics (SH). The iterative algorithm
computes multiple time steps concurrently by interweaving parallel high-order
fine corrections and serial corrections performed on a coarsened problem. To do
that, we design a methodology relying on the spectral basis of the SH to
coarsen and interpolate the problem in space. The methods are evaluated on the
shallow-water equations on the sphere using a set of tests commonly used in the
atmospheric flow community. We assess the convergence of PFASST-SH upon
refinement in time. We also investigate the impact of the coarsening strategy
on the accuracy of the scheme, and specifically on its ability to capture the
high-frequency modes accumulating in the solution. Finally, we study the
computational cost of PFASST-SH to demonstrate that our scheme resolves the
main features of the solution multiple times faster than the serial schemes
Phase diagram and binding energy of interacting Bose gases
From the many-body T-matrix the condition for a medium-dependent bound state
and its binding energy is derived for a homogeneous interacting Bose gas. This
condition provides the critical line in the phase diagram in terms of the
medium-dependent scattering length. Separating the Bose pole from the
distribution function the influence of a Bose condensate is discussed and a
thermal minimum of the critical scattering length is found
White dwarf masses in cataclysmic variables
The white dwarf (WD) mass distribution of cataclysmic variables (CVs) has
recently been found to dramatically disagree with the predictions of the
standard CV formation model. The high mean WD mass among CVs is not imprinted
in the currently observed sample of CV progenitors and cannot be attributed to
selection effects. Two possibilities have been put forward: either the WD grows
in mass during CV evolution, or in a significant fraction of cases, CV
formation is preceded by a (short) phase of thermal time-scale mass transfer
(TTMT) in which the WD gains a sufficient amount of mass. We investigate if
either of these two scenarios can bring theoretical predictions and
observations into agreement. We employed binary population synthesis models to
simulate the present intrinsic CV population. We incorporated aspects specific
to CV evolution such as an appropriate mass-radius relation of the donor star
and a more detailed prescription for the critical mass ratio for dynamically
unstable mass transfer. We also implemented a previously suggested wind from
the surface of the WD during TTMT and tested the idea of WD mass growth during
the CV phase by arbitrarily changing the accretion efficiency. We compare the
model predictions with the characteristics of CVs derived from observed
samples. We find that mass growth of the WDs in CVs fails to reproduce the
observed WD mass distribution. In the case of TTMT, we are able to produce a
large number of massive WDs if we assume significant mass loss from the surface
of the WD during the TTMT phase. However, the model still produces too many CVs
with helium WDs. Moreover, the donor stars are evolved in many of these
post-TTMT CVs, which contradicts the observations. We conclude that in our
current framework of CV evolution neither TTMT nor WD mass growth can fully
explain either the observed WD mass or the period distribution in CVs.Comment: 15 pages, 7 figures, 1 table, accepted for publication in A&A.
Replaced and added a reference, corrected typo
- …