4,978 research outputs found
Varying speed of light cosmology from a stringy short distance cutoff
It is shown that varying speed of light cosmology follows from a
string-inspired minimal length uncertainty relation. Due to the reduction of
the available phase space volume per quantum mode at short wavelengths, the
equation of state of ultrarelativistic particles stiffens at very high
densities. This causes a stronger than usual deceleration of the scale factor
which competes with a higher than usual propagation speed of the particles.
Various measures for the effective propagation speed are analyzed: the group
and phase velocity in the high energy tail, the thermal average of the group
and phase velocity, and the speed of sound. Of these three groups, only the
first provides a possible solution to the cosmological horizon problem.Comment: 5 pages, 2 figure
Finding involutions with small support
We show that the proportion of permutations in or such that
has even order and is an involution with support of cardinality
at most is at least a constant multiple of
. Using this result, we obtain the same conclusion for elements in
a classical group of natural dimension in odd characteristic that have even
order and power up to an involution with -eigenspace of dimension at most
for a linear or unitary group, or for a symplectic or orthogonal group
Thermonuclear supernova simulations with stochastic ignition
We apply an ad hoc model for dynamical ignition in three-dimensional
numerical simulations of thermonuclear supernovae assuming pure deflagrations.
The model makes use of the statistical description of temperature fluctuations
in the pre-supernova core proposed by Wunsch & Woosley (2004). Randomness in
time is implemented by means of a Poisson process. We are able to vary the
explosion energy and nucleosynthesis depending on the free parameter of the
model which controls the rapidity of the ignition process. However, beyond a
certain threshold, the strength of the explosion saturates and the outcome
appears to be robust with respect to number of ignitions. In the most energetic
explosions, we find about 0.75 solar masses of iron group elements. Other than
in simulations with simultaneous multi-spot ignition, the amount of unburned
carbon and oxygen at radial velocities of a few 1000 km/s tends to be reduced
for an ever increasing number of ignition events and, accordingly, more
pronounced layering results.Comment: 7 pages, 6 figures, accepted for publication in Astron. Astrophys.;
PDF version with full resolution figures available from
http://www.astro.uni-wuerzburg.de/~schmidt/Paper/StochIgnt_AA.pd
Finding involutions with small support
We show that the proportion of permutations in or such that
has even order and is an involution with support of cardinality
at most is at least a constant multiple of
. Using this result, we obtain the same conclusion for elements in
a classical group of natural dimension in odd characteristic that have even
order and power up to an involution with -eigenspace of dimension at most
for a linear or unitary group, or for a symplectic or orthogonal group
Elements in finite classical groups whose powers have large 1-Eigenspaces
We estimate the proportion of several classes of elements in finite classical
groups which are readily recognised algorithmically, and for which some power
has a large fixed point subspace and acts irreducibly on a complement of it.
The estimates are used in complexity analyses of new recognition algorithms for
finite classical groups in arbitrary characteristic
- …