10,470 research outputs found
Finite Lorentz Transformations, Automorphisms, and Division Algebras
We give an explicit algebraic description of finite Lorentz transformations
of vectors in 10-dimensional Minkowski space by means of a parameterization in
terms of the octonions. The possible utility of these results for superstring
theory is mentioned. Along the way we describe automorphisms of the two highest
dimensional normed division algebras, namely the quaternions and the octonions,
in terms of conjugation maps. We use similar techniques to define and
via conjugation, via symmetric multiplication, and via
both symmetric multiplication and one-sided multiplication. The
non-commutativity and non-associativity of these division algebras plays a
crucial role in our constructions.Comment: 24 pages, Plain TeX, 2 figures on 1 page submitted separately as
uuencoded compressed tar fil
Relation between shear parameter and Reynolds number in statistically stationary turbulent shear flows
Studies of the relation between the shear parameter S^* and the Reynolds
number Re are presented for a nearly homogeneous and statistically stationary
turbulent shear flow. The parametric investigations are in line with a
generalized perspective on the return to local isotropy in shear flows that was
outlined recently [Schumacher, Sreenivasan and Yeung, Phys. Fluids, vol.15, 84
(2003)]. Therefore, two parameters, the constant shear rate S and the level of
initial turbulent fluctuations as prescribed by an energy injection rate
epsilon_{in}, are varied systematically. The investigations suggest that the
shear parameter levels off for larger Reynolds numbers which is supported by
dimensional arguments. It is found that the skewness of the transverse
derivative shows a different decay behavior with respect to Reynolds number
when the sequence of simulation runs follows different pathways across the
two-parameter plane. The study can shed new light on different interpretations
of the decay of odd order moments in high-Reynolds number experiments.Comment: 9 pages, 9 Postscript figure
Rothberger gaps in fragmented ideals
The~\emph{Rothberger number} of a definable
ideal on is the least cardinal such that there
exists a Rothberger gap of type in the quotient algebra
. We investigate for a subclass of the ideals, the fragmented ideals,
and prove that for some of these ideals, like the linear growth ideal, the
Rothberger number is while for others, like the polynomial growth
ideal, it is above the additivity of measure. We also show that it is
consistent that there are infinitely many (even continuum many) different
Rothberger numbers associated with fragmented ideals.Comment: 28 page
Sequential Tunneling through Molecular Spin Rings
We consider electrical transport through molecules with Heisenberg-coupled
spins arranged in a ring structure in the presence of an easy-axis anisotropy.
The molecules are coupled to two metallic leads and a gate. In the charged
state of the ring, a Zener double-exchange mechanism links transport properties
to the underlying spin structure. This leads to a remarkable contact-site
dependence of the current, which for an antiferromagnetic coupling of the spins
can lead to a total suppression of the zero-bias conductance when the molecule
is contacted at adjacent sites.Comment: 4 pages, 3 figure
Transfer of optical spectral weight in magnetically ordered superconductors
We show that, in antiferromagnetic superconductors, the optical spectral
weight transferred to low frequencies below the superconducting transition
temperature originates from energies that can be much larger than twice the
superconducting gap . This contrasts to non-magnetic superconductors,
where the optical spectrum is suppressed only for frequencies below .
In particular, we demonstrate that the superfluid condensate of the
magnetically ordered superconductor is not only due to states of the
magnetically reconstructed Fermi surface, but is enhanced by transfer of
spectral weight from the mid infrared peak generated by the spin density wave
gap. We apply our results to the iron arsenide superconductors, addressing the
decrease of the zero-temperature superfluid density in the doping regime where
magnetism coexists with unconventional superconductivity.Comment: 5 figures, 10 pages; revised versio
Strong Coordination over Noisy Channels: Is Separation Sufficient?
We study the problem of strong coordination of actions of two agents and
that communicate over a noisy communication channel such that the actions
follow a given joint probability distribution. We propose two novel schemes for
this noisy strong coordination problem, and derive inner bounds for the
underlying strong coordination capacity region. The first scheme is a joint
coordination-channel coding scheme that utilizes the randomness provided by the
communication channel to reduce the local randomness required in generating the
action sequence at agent . The second scheme exploits separate coordination
and channel coding where local randomness is extracted from the channel after
decoding. Finally, we present an example in which the joint scheme is able to
outperform the separate scheme in terms of coordination rate.Comment: 9 pages, 4 figures. An extended version of a paper accepted for the
IEEE International Symposium on Information Theory (ISIT), 201
Strong Coordination over Noisy Channels: Is Separation Sufficient?
We study the problem of strong coordination of actions of two agents and
that communicate over a noisy communication channel such that the actions
follow a given joint probability distribution. We propose two novel schemes for
this noisy strong coordination problem, and derive inner bounds for the
underlying strong coordination capacity region. The first scheme is a joint
coordination-channel coding scheme that utilizes the randomness provided by the
communication channel to reduce the local randomness required in generating the
action sequence at agent . The second scheme exploits separate coordination
and channel coding where local randomness is extracted from the channel after
decoding. Finally, we present an example in which the joint scheme is able to
outperform the separate scheme in terms of coordination rate.Comment: 9 pages, 4 figures. An extended version of a paper accepted for the
IEEE International Symposium on Information Theory (ISIT), 201
- …