15,800 research outputs found
Nonexistence results for the Korteweg-deVries and Kadomtsev-Petviashvili equations
We study characteristic Cauchy problems for the Korteweg-deVries (KdV)
equation , and the Kadomtsev-Petviashvili (KP) equation
with holomorphic initial data
possessing nonnegative Taylor coefficients around the origin. For the KdV
equation with initial value , we show that there is no solution
holomorphic in any neighbourhood of in unless
. This also furnishes a nonexistence result for a class of
-independent solutions of the KP equation. We extend this to -dependent
cases by considering initial values given at , ,
, where the Taylor coefficients of and around
, are assumed nonnegative. We prove that there is no holomorphic
solution around the origin in unless and are
polynomials of degree 2 or lower.Comment: 17 pages in LaTeX2e, to appear in Stud. Appl. Mat
Anisotropy, phonon modes, and lattice anharmonicity from dielectric function tensor analysis of monoclinic cadmium tungstate
We determine the frequency dependence of four independent CdWO Cartesian
dielectric function tensor elements by generalized spectroscopic ellipsometry
within mid-infrared and far-infrared spectral regions. Single crystal surfaces
cut under different angles from a bulk crystal, (010) and (001), are
investigated. From the spectral dependencies of the dielectric function tensor
and its inverse we determine all long wavelength active transverse and
longitudinal optic phonon modes with and symmetry as well as their
eigenvectors within the monoclinic lattice. We thereby demonstrate that such
information can be obtained completely without physical model line shape
analysis in materials with monoclinic symmetry. We then augment the effect of
lattice anharmonicity onto our recently described dielectric function tensor
model approach for materials with monoclinic and triclinic crystal symmetries
[Phys. Rev. B, 125209 (2016)], and we obtain excellent match between all
measured and modeled dielectric function tensor elements. All phonon mode
frequency and broadening parameters are determined in our model approach. We
also perform density functional theory phonon mode calculations, and we compare
our results obtained from theory, from direct dielectric function tensor
analysis, and from model lineshape analysis, and we find excellent agreement
between all approaches. We also discuss and present static and above
reststrahlen spectral range dielectric constants. Our data for CdWO are in
excellent agreement with a recently proposed generalization of the
Lyddane-Sachs-Teller relation for materials with low crystal symmetry [Phys.
Rev. Lett. 117, 215502 (2016)].Comment: arXiv admin note: text overlap with arXiv:1512.0859
Anisotropy and phonon modes from analysis of the dielectric function tensor and inverse dielectric function tensor of monoclinic yttrium orthosilicate
We determine the frequency dependence of the four independent Cartesian
tensor elements of the dielectric function for monoclinic symmetry YSiO
using generalized spectroscopic ellipsometry from 40-1200 cm. Three
different crystal cuts, each perpendicular to a principle axis, are
investigated. We apply our recently described augmentation of lattice
anharmonicity onto the eigendielectric displacement vector summation approach
[A. Mock et al., Phys. Rev. B 95, 165202 (2017)], and we present and
demonstrate the application of an eigendielectric displacement loss vector
summation approach with anharmonic broadening. We obtain excellent match
between all measured and model calculated dielectric function tensor elements
and all dielectric loss function tensor elements. We obtain 23 A
and 22 B symmetry long wavelength active transverse and
longitudinal optical mode parameters including their eigenvector orientation
within the monoclinic lattice. We perform density functional theory
calculations and obtain 23 A symmetry and 22 B
transverse and longitudinal optical mode parameters and their orientation
within the monoclincic lattice. We compare our results from ellipsometry and
density functional theory and find excellent agreement. We also determine the
static and above reststrahlen spectral range dielectric tensor values and find
a recently derived generalization of the Lyddane-Sachs-Teller relation for
polar phonons in monoclinic symmetry materials satisfied [M. Schubert, Phys.
Rev. Lett. 117, 215502 (2016)]
Light effective hole mass in undoped Ge/SiGe quantum wells
We report density-dependent effective hole mass measurements in undoped
germanium quantum wells. We are able to span a large range of densities
( cm) in top-gated field effect transistors by
positioning the strained buried Ge channel at different depths of 12 and 44 nm
from the surface. From the thermal damping of the amplitude of Shubnikov-de
Haas oscillations, we measure a light mass of at a density of
cm. We confirm the theoretically predicted dependence
of increasing mass with density and by extrapolation we find an effective mass
of at zero density, the lightest effective mass for a planar
platform that demonstrated spin qubits in quantum dots
Electron effective mass in AlGaN alloys determined by mid-infrared optical Hall effect
The effective electron mass parameter in Si-doped AlGaN is
determined to be from mid-infrared optical Hall
effect measurements. No significant anisotropy of the effective electron mass
parameter is found supporting theoretical predictions. Assuming a linear change
of the effective electron mass with the Al content in AlGaN alloys and
for GaN, an average effective electron mass of
can be extrapolated for AlN. The analysis of mid-infrared
spectroscopic ellipsometry measurements further confirms the two phonon mode
behavior of the E(TO) and one phonon mode behavior of the A(LO) phonon
mode in high-Al-content AlGaN alloys as seen in previous Raman scattering
studies
Integration of the electrochemical depolorized CO2 concentrator with the Bosch CO2 reduction subsystem
Regenerative processes for the revitalization of spacecraft atmospheres require an Oxygen Reclamation System (ORS) for the collection of carbon dioxide and water vapor and the recovery of oxygen from these metabolic products. Three life support subsystems uniquely qualified to form such an ORS are an Electrochemical CO2 Depolarized Concentrator (EDC), a CO2 Reduction Subsystem (BRS) and a Water Electrolysis Subsystem (WES). A program to develop and test the interface hardware and control concepts necessary for integrated operation of a four man capacity EDC with a four man capacity BRS was successfully completed. The control concept implemented proved successful in operating the EDC with the BRS for both constant CO2 loading as well as variable CO2 loading, based on a repetitive mission profile of the Space Station Prototype (SSP)
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