4,741 research outputs found
On the Margulis constant for Kleinian groups, I curvature
The Margulis constant for Kleinian groups is the smallest constant such
that for each discrete group and each point in the upper half space
, the group generated by the elements in which move less
than distance c is elementary. We take a first step towards determining this
constant by proving that if is nonelementary and discrete
with parabolic or elliptic of order , then every point in
is moved at least distance by or where
. This bound is sharp
Investigation of the reaction of the lunar surface to the impact of a lunar probe final report
Flash phenomena associated with hypervelocity impact for estimating flash from impact of lunar prob
Neutron Diffuse Scattering from Polar Nanoregions in the Relaxor Pb(Mg1/3Nb2/3)O3
We have studied the neutron diffuse scattering in the relaxor PMN. The
diffuse scattering appears around the Burns temperature (~620K), indicating its
origin from the polar nanoregions (PNR). While the relative diffuse intensities
are consistent with previous reports, they are entirely different from those of
the lowest-energy TO phonon. Because of that, it has been considered that this
TO mode could not be the ferroelectric soft mode. Recently, a neutron
scattering study has unambiguously shown that the TO mode does soften on
cooling. If the diffuse scattering in PMN originates from the soft mode
condensation, then the atomic displacements must satisfy the center of mass
condition. But, the atomic displacements determined from diffuse scattering
intensities do not fulfill this condition. To resolve this contradiction, we
propose a simple model in which the total atomic displacement consists of two
components: is created by the soft mode condensation, satisfying
the center of mass condition, and, represents a uniform
displacement of the PNR along their polar direction relative to the surrounding
(unpolarized) cubic matrix. Within this framework, we can successfully describe
the neutron diffuse scattering intensities observed in PMN.Comment: 7 pages, 7 figures (Revised: 11-16-2001
New Perspectives on Eye Development and the Evolution of Eyes and Photoreceptors
Recent experiments on the genetic control of eye development have opened up a completely new perspective on eye evolution. The demonstration that targeted expression of one and the same master control gene, that is, Pax6 can induce the formation of ectopic eyes in both insects and vertebrates, necessitates a reconsideration of the dogma of a polyphyletic origin of the various eye types in all the animal phyla. The involvement of Pax6 and six1 and six3 genes, which encode highly conserved transcription factors, in the genetic control of eye development in organisms ranging from planarians to humans argues strongly for a monophyletic origin of the eye. Because transcription factors can control the expression of any target gene provided it contains the appropriate gene regulatory elements, the conservation of the genetic control of eye development by Pax6 among all bilaterian animals is not due to functional constraints but a consequence of its evolutionary history. The prototypic eyes postulated by Darwin to consist of two cells only, a photoreceptor and a pigment cell, were accidentally controlled by Pax6 and the subsequent evolution of the various eye types occurred by building onto this original genetic program. A hypothesis of intercalary evolution is proposed that assumes that the eye morphogenetic pathway is progressively modified by intercalation of genes between the master control genes on the top of the hierarchy and the structural genes like rhodopsin at the bottom. The recruitment of novel genes into the eye morphogenetic pathway can be due to at least two different genetic mechanisms, gene duplication and enhancer fusion. In tracing back the evolution of eyes beyond bilaterians, we find highly developed eyes in some box-jellyfish as well as in some Hydrozoans. In Hydrozoans the same orthologous six genes (six1 and six3) are required for eye regeneration as in planarians, and in the box jellyfish Tripedalia a pax B gene, which may be a precursor of Pax6, was found to be expressed in the eyes. In contrast to the adults, which have highly evolved eyes, the Planula larva of Tripedalia has single- celled photoreceptors similar to some unicellular protists. For the origin of photoreceptor cells in metazoa, I propose two hypotheses, one based on cellular differentiation and a more speculative one based on symbiosis. The former assumes that photoreceptor cells originated from a colonial protist in which all the cells were photosensitive and subsequent cellular differentiation to give rise to photoreceptor cells. The symbiont hypothesis, which I call the Russian doll model, assumes that photosensitivity arose first in photosynthetic cyanobacteria that were subsequently taken up into red algae as primary chloroplasts. The red algae in turn were taken up by dinoflagellates as secondary chloroplasts and in some species evolved into the most sophisticated eye organelles, as found, for example, in some dinoflagellates like Erythropsis and Warnovia, which lack chloroplasts. Because dinoflagellates are commonly found as symbionts in cnidarians, the dinoflagellates may have transferred their photoreceptor genes to cnidarians. In cnidarians such as Tripedalia the step from photoreceptor organelles to multicellular eyes has occurred. These two hypotheses, the cellular differentiation and the symbiont hypothesis, are not mutually exclusive and are the subject of further investigation
Soft Mode Dynamics Above and Below the Burns Temperature in the Relaxor Pb(Mg_1/3Nb_2/3)O_3
We report neutron inelastic scattering measurements of the lowest-energy
transverse optic (TO) phonon branch in the relaxor Pb(Mg_1/3Nb_2/3)O_3 from 400
to 1100 K. Far above the Burns temperature T_d ~ 620 K we observe well-defined
propagating TO modes at all wave vectors q, and a zone center TO mode that
softens in a manner consistent with that of a ferroelectric soft mode. Below
T_d the zone center TO mode is overdamped. This damping extends up to, but not
above, the waterfall wave vector q_wf, which is a measure of the average size
of the PNR.Comment: 4 pages, 4 figures; modified discussion of Fig. 3, shortened
captions, added reference, corrected typos, accepted by Phys. Rev. Let
Theory of magnetism with temporal disorder applied to magnetically doped ZnO
A dynamic model of the asymmetric Ising glass is presented: an Ising model
with antiferromagnet bonds with probabilities q arranged at random in a
ferromagnetic matrix. The dynamics is introduced by changing the arrangement of
the antiferromagnetic bonds after n Monte Carlo steps but keeping the same
value of q and spin configuration. In the region where there is a second order
transition between the ferromagnetic and paramagnetic states the dynamic
behaviour follows that expected for motional narrowing and reverts to the
static behaviour only for large n. There is a different dynamic behaviour where
there is a first order transition between the ferromagnetic and spin glass
states where it shows no effects of motional narrowing. The implications of
this are discussed. This model is devised to explain the properties of doped
ZnO where the magnetisation is reduced when the exchange interactions change
with time.Comment: Paper was presented at MMM 2008 and is accepted for publication in
J.A.
Density matrix renormalisation group study of the correlation function of the bilinear-biquadratic spin-1 chain
Using the recently developed density matrix renormalization group approach,
we study the correlation function of the spin-1 chain with quadratic and
biquadratic interactions. This allows us to define and calculate the
periodicity of the ground state which differs markedly from that in the
classical analogue. Combining our results with other studies, we predict three
phases in the region where the quadratic and biquadratic terms are both
positive.Comment: 13 pages, Standard Latex File + 5 PostScript figures in separate (New
version with SUBSTANTIAL REVISIONS to appear in J Phys A
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