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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
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
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Five Approaches to Literacy in Correctional Education
This article introduces literacy from a few âbig pictureâ perspectives, and then reviews five paradigms that have shaped the teaching and learning of literacy in residential confinement institutions for juveniles and adults. The paradigms are specific to correctional education, but they will be familiar to all alternative teachers and advocates of literacy instruction
Static magnetic correlations near the insulating-superconducting phase boundary in LaSrCuO
An elastic neutron scattering study has been performed on several single
crystals of LaSrCuO for {\it x} near the lower critical
concentration {\it x} for superconductivity. % In the insulating
spin-glass phase ({\it x} = 0.04 and 0.053), the previously reported
one-dimensional spin modulation along the orthorhombic {\it b}-axis is
confirmed. % Just inside the superconducting phase ({\it x} = 0.06), however,
two pairs of incommensurate magnetic peaks are additionally observed
corresponding to the spin modulation parallel to the tetragonal axes. % These
two types of spin modulations with similar incommensurabilities coexist near
the boundary. % The peak-width along spin-modulation direction
exhibits an anomalous maximum in the superconducting phase near {\it x},
where the incommensurability monotonically increases upon doping
across the phase boundary. % These results are discussed in connection with the
doping-induced superconducting phase transition.Comment: 9pages, 9figure
Collars and partitions of hyperbolic cone-surfaces
For compact Riemann surfaces, the collar theorem and Bers' partition theorem
are major tools for working with simple closed geodesics. The main goal of this
paper is to prove similar theorems for hyperbolic cone-surfaces. Hyperbolic
two-dimensional orbifolds are a particular case of such surfaces. We consider
all cone angles to be strictly less than to be able to consider
partitions.Comment: 11 pages, 9 figures; v2: minor changes, to appear in Geometriae
Dedicat
Magnetism of Superconducting UPt3
The phase diagram of superconducting in pressure-temperature
plane, together with the neutron scattering data is studied within a two
component superconducting order parameter scenario. In order to give a
qualitative explanation to the experimental data a set of two linearly
independent antiferromagnetic moments which emerge appropriately at the
temperature \mbox{} and \mbox{} and
couple to superconductivity is proposed. Several constraints on the fourth
order coefficients in the Ginzburg-Landau free energy are obtained.Comment: 17 pages, figures available on request to
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Equivalence between Poly\'a-Szeg\H{o} and relative capacity inequalities under rearrangement
The transformations of functions acting on sublevel sets that satisfy a
P\'olya-Szeg\H{o} inequality are characterized as those being induced by
transformations of sets that do not increase the associated capacity.Comment: 9 page
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