34,769 research outputs found
The subgroup growth spectrum of virtually free groups
For a finitely generated group denote by the growth
coefficient of , that is, the infimum over all real numbers such
that . We show that the growth coefficient of a virtually
free group is always rational, and that every rational number occurs as growth
coefficient of some virtually free group. Moreover, we describe an algorithm to
compute
Extreme-value statistics from Lagrangian convex hull analysis for homogeneous turbulent Boussinesq convection and MHD convection
We investigate the utility of the convex hull of many Lagrangian tracers to
analyze transport properties of turbulent flows with different anisotropy. In
direct numerical simulations of statistically homogeneous and stationary
Navier-Stokes turbulence, neutral fluid Boussinesq convection, and MHD
Boussinesq convection a comparison with Lagrangian pair dispersion shows that
convex hull statistics capture the asymptotic dispersive behavior of a large
group of passive tracer particles. Moreover, convex hull analysis provides
additional information on the sub-ensemble of tracers that on average disperse
most efficiently in the form of extreme value statistics and flow anisotropy
via the geometric properties of the convex hulls. We use the convex hull
surface geometry to examine the anisotropy that occurs in turbulent convection.
Applying extreme value theory, we show that the maximal square extensions of
convex hull vertices are well described by a classic extreme value
distribution, the Gumbel distribution. During turbulent convection,
intermittent convective plumes grow and accelerate the dispersion of Lagrangian
tracers. Convex hull analysis yields information that supplements standard
Lagrangian analysis of coherent turbulent structures and their influence on the
global statistics of the flow.Comment: 18 pages, 10 figures, preprin
Testing Lorentz invariance by use of vacuum and matter filled cavity resonators
We consider tests of Lorentz invariance for the photon and fermion sector
that use vacuum and matter-filled cavities. Assumptions on the wave-function of
the electrons in crystals are eliminated from the underlying theory and
accurate sensitivity coefficients (including some exceptionally large ones) are
calculated for various materials. We derive the Lorentz-violating shift in the
index of refraction n, which leads to additional sensitivity for matter-filled
cavities ; and to birefringence in initially isotropic media. Using published
experimental data, we obtain improved bounds on Lorentz violation for photons
and electrons at levels of 10^-15 and below. We discuss implications for future
experiments and propose a new Michelson-Morley type experiment based on
birefringence in matter.Comment: 15 pages, 8 table
Lagrangian Statistics of Navier-Stokes- and MHD-Turbulence
We report on a comparison of high-resolution numerical simulations of
Lagrangian particles advected by incompressible turbulent hydro- and
magnetohydrodynamic (MHD) flows. Numerical simulations were performed with up
to collocation points and 10 million particles in the Navier-Stokes
case and collocation points and 1 million particles in the MHD case. In
the hydrodynamics case our findings compare with recent experiments from
Mordant et al. [1] and Xu et al. [2]. They differ from the simulations of
Biferale et al. [3] due to differences of the ranges choosen for evaluating the
structure functions. In Navier-Stokes turbulence intermittency is stronger than
predicted by a multifractal approach of [3] whereas in MHD turbulence the
predictions from the multifractal approach are more intermittent than observed
in our simulations. In addition, our simulations reveal that Lagrangian
Navier-Stokes turbulence is more intermittent than MHD turbulence, whereas the
situation is reversed in the Eulerian case. Those findings can not consistently
be described by the multifractal modeling. The crucial point is that the
geometry of the dissipative structures have different implications for
Lagrangian and Eulerian intermittency. Application of the multifractal approach
for the modeling of the acceleration PDFs works well for the Navier-Stokes case
but in the MHD case just the tails are well described.Comment: to appear in J. Plasma Phy
Rheology of gelling polymers in the Zimm model
In order to study rheological properties of gelling systems in dilute
solution, we investigate the viscosity and the normal stresses in the Zimm
model for randomly crosslinked monomers. The distribution of cluster topologies
and sizes is assumed to be given either by Erd\H os-R\'enyi random graphs or
three-dimensional bond percolation. Within this model the critical behaviour of
the viscosity and of the first normal stress coefficient is determined by the
power-law scaling of their averages over clusters of a given size with .
We investigate these Mark--Houwink like scaling relations numerically and
conclude that the scaling exponents are independent of the hydrodynamic
interaction strength. The numerically determined exponents agree well with
experimental data for branched polymers. However, we show that this traditional
model of polymer physics is not able to yield a critical divergence at the gel
point of the viscosity for a polydisperse dilute solution of gelation clusters.
A generally accepted scaling relation for the Zimm exponent of the viscosity is
thereby disproved.Comment: 9 pages, 2 figure
Collusion in Experimental Bertrand Duopolies with Convex Costs:The Role of Information and Cost Asymmetry
We report the results of a series of experimental Bertrand duopolies where firms have convex costs. Theoretically these duopolies are characterized by a multiplicity of Nash equilibria. Using a 2x2 design, we analyze price choices in symmetric and asymmetric markets under 2 information conditions: complete versus incomplete information about profits. We find that information has no effect in symmetric markets with respect to market prices and the time it takes for markets to stabilize. However, in asymmetric markets, complete information leads to higher average market prices and quicker convergence of price choices.
Invertible Dirac operators and handle attachments on manifolds with boundary
For spin manifolds with boundary we consider Riemannian metrics which are
product near the boundary and are such that the corresponding Dirac operator is
invertible when half-infinite cylinders are attached at the boundary. The main
result of this paper is that these properties of a metric can be preserved when
the metric is extended over a handle of codimension at least two attached at
the boundary. Applications of this result include the construction of
non-isotopic metrics with invertible Dirac operator, and a concordance
existence and classification theorem.Comment: Accepted for publication in Journal of Topology and Analysi
Faraday waves on a viscoelastic liquid
We investigate Faraday waves on a viscoelastic liquid. Onset measurements and
a nonlinear phase diagram for the selected patterns are presented. By virtue of
the elasticity of the material a surface resonance synchronous to the external
drive competes with the usual subharmonic Faraday instability. Close to the
bicriticality the nonlinear wave interaction gives rise to a variety of novel
surface states: Localised patches of hexagons, hexagonal superlattices,
coexistence of hexagons and lines. Theoretical stability calculations and
qualitative resonance arguments support the experimental observations.Comment: 4 pages, 4figure
- …