3,531 research outputs found
Large time wellposdness to the 3-D Capillary-Gravity Waves in the long wave regime
In the regime of weakly transverse long waves, given long-wave initial data,
we prove that the nondimensionalized water wave system in an infinite strip
under influence of gravity and surface tension on the upper free interface has
a unique solution on [0,{T}/\eps] for some \eps independent of constant
We shall prove in the subsequent paper \cite{MZZ2} that on the same time
interval, these solutions can be accurately approximated by sums of solutions
of two decoupled Kadomtsev-Petviashvili (KP) equations.Comment: Split the original paper(The long wave approximation to the 3-D
capillary-gravity waves) into two parts, this is the first on
Geometric Phase: a Diagnostic Tool for Entanglement
Using a kinematic approach we show that the non-adiabatic, non-cyclic,
geometric phase corresponding to the radiation emitted by a three level cascade
system provides a sensitive diagnostic tool for determining the entanglement
properties of the two modes of radiation. The nonunitary, noncyclic path in the
state space may be realized through the same control parameters which control
the purity/mixedness and entanglement. We show analytically that the geometric
phase is related to concurrence in certain region of the parameter space. We
further show that the rate of change of the geometric phase reveals its
resilience to fluctuations only for pure Bell type states. Lastly, the
derivative of the geometric phase carries information on both purity/mixedness
and entanglement/separability.Comment: 13 pages 6 figure
Ni-Cr textured substrates with reduced ferromagnetism for coated conductor applications
A series of biaxially textured Ni(1-x)Cr(x) materials, with compositions x =
0, 7, 9, 11, and 13 at % Cr, have been studied for use as substrate materials
in coated conductor applications with high temperature superconductors. The
magnetic properties were investigated, including the hysteretic loss in a Ni-7
at % Cr sample that was controllably deformed; for comparison, the loss was
also measured in a similarly deformed pure Ni substrate. Complementary X-ray
diffraction studies show that thermo-mechanical processing produces nearly
complete {100} cube texturing, as desired for applications.Comment: PDF only; 19 pp., incl 10 figure
Ultrasonic Attenuation in Clean d-Wave Superconductors
We calculate the low temperature longitudinal ultrasonic attenuation rate
in clean d-wave superconductors. We consider the contribution of
previously ignored processes involving the excitation of a pair of quasi-holes
or quasi-particles. These processes, which are forbidden by energy conservation
in conventional s-wave superconductors, have a finite phase space in d-wave
superconductors due to the presence of nodes in the gap which give rise to soft
low-energy electronic excitations. We find the contribution to from
these processes to be proportional to in the regime ,(ultra-low temperature regime) and to be proportional to 1/T in
the region , (low temperature regime) where is the ultrasound wave-vector and is the maximum gap amplitude.
We explicitly evaluate these terms, for parameters appropriate to the cuprates,
for along the nodal and the antinodal directions and compare it with
the contribution from processes considered earlier(I.Vekhter et al {\it Phys.
Rev.}{\bf B59}, 7123(1999)). In the ultra-low temperature regime, the processes
considered by us make a contribution which is smaller by about a factor of 10
for along the nodal direction, while along the antinodal direction it
is larger by a factor of 100 or so. In the low temperature regime on the other
hand the contribution made by these terms is small. However taken together with
the original terms we describe a possible way to evaluate the parameter
.Comment: 9 pages, RevTex, accepted for publication in Physica
D-optimal designs via a cocktail algorithm
A fast new algorithm is proposed for numerical computation of (approximate)
D-optimal designs. This "cocktail algorithm" extends the well-known vertex
direction method (VDM; Fedorov 1972) and the multiplicative algorithm (Silvey,
Titterington and Torsney, 1978), and shares their simplicity and monotonic
convergence properties. Numerical examples show that the cocktail algorithm can
lead to dramatically improved speed, sometimes by orders of magnitude, relative
to either the multiplicative algorithm or the vertex exchange method (a variant
of VDM). Key to the improved speed is a new nearest neighbor exchange strategy,
which acts locally and complements the global effect of the multiplicative
algorithm. Possible extensions to related problems such as nonparametric
maximum likelihood estimation are mentioned.Comment: A number of changes after accounting for the referees' comments
including new examples in Section 4 and more detailed explanations throughou
Ultrasonic Attenuation in the Vortex State of d-wave Superconductors
We calculate the low temperature quasi-particle contribution to the
ultrasonic attenuation rate in the mixed state of d-wave superconductors. Our
calculation is performed within the semi-classical approximation using
quasi-particle energies that are Doppler shifted, with respect to their values
in the Meissner phase, by the supercurrent associated with the vortices. We
find that the attenuation at low temperatures and at fields has a temperature independent contribution which is proportional to
where is the applied magnetic field. We indicate how our result
in combination with the zero-field result for ultrasonic attenuation can be
used to calculate one of the parameters , or given the
values for any two of them.Comment: 10 pages, RevTeX, submitted to Physica
Low temperature superlattice in monoclinic PZT
TEM has shown that the strongly piezoelectric material Pb(Zr0.52Ti0.48)O3
separates into two phases at low temperatures. The majority phase is the
monoclinic phase previously found by x-ray diffraction. The minority phase,
with a nanoscale coherence length, is a slightly distorted variant of the first
resulting from the anti-phase rotation of the oxygen octahedra about [111].
This work clears up a recent controversy about the origin of superlattice peaks
in these materials, and supports recent theoretical results predicting the
coexistence of ferroelectric and rotational instabilities.Comment: REVTeX4, 4 eps figures embedded. JPG version of figs. 2&4 is also
include
Constructing 3D crystal templates for photonic band gap materials using holographic optical tweezers
A simple and robust method is presented for the construction of 3-dimensional crystals from silica and polystyrene microspheres. The crystals are suitable for use as templates in the production of three-dimensional photonic band gap (PBG) materials. Manipulation of the microspheres was achieved using a dynamic holographic assembler (DHA) consisting of computer controlled holographic optical tweezers. Attachment of the microspheres was achieved by adjusting their colloidal interactions during assembly. The method is demonstrated by constructing a variety of 3-dimensional crystals using spheres ranging in size from 3 µm down to 800 nm. A major advantage of the technique is that it may be used to build structures that cannot be made using self-assembly. This is illustrated through the construction of crystals in which line defects have been deliberately included, and by building simple cubic structures
Aharonov-Bohm Effect in Cyclotron and Synchrotron Radiations
We study the impact of Aharonov-Bohm solenoid on the radiation of a charged
particle moving in a constant uniform magnetic field. With this aim in view,
exact solutions of Klein-Gordon and Dirac equations are found in the
magnetic-solenoid field. Using such solutions, we calculate exactly all the
characteristics of one-photon spontaneous radiation both for spinless and
spinning particle. Considering non-relativistic and relativistic
approximations, we analyze cyclotron and synchrotron radiations in detail.
Radiation peculiarities caused by the presence of the solenoid may be
considered as a manifestation of Aharonov-Bohm effect in the radiation. In
particular, it is shown that new spectral lines appear in the radiation
spectrum. Due to angular distribution peculiarities of the radiation intensity,
these lines can in principle be isolated from basic cyclotron and synchrotron
radiation spectraComment: 38 pages, LaTex fil
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