21,017 research outputs found

### Comment on "Anderson transition in disordered graphene"

We comment on a recent letter by Amini et al. (EPL 87, 37002 (2009))
concerning the existence of a mobility edge in disordered graphene.Comment: 3 pages, 3 figure

### Nonexistence results for the Korteweg-deVries and Kadomtsev-Petviashvili equations

We study characteristic Cauchy problems for the Korteweg-deVries (KdV)
equation $u_t=uu_x+u_{xxx}$, and the Kadomtsev-Petviashvili (KP) equation
$u_{yy}=\bigl(u_{xxx}+uu_x+u_t\bigr)_x$ with holomorphic initial data
possessing nonnegative Taylor coefficients around the origin. For the KdV
equation with initial value $u(0,x)=u_0(x)$, we show that there is no solution
holomorphic in any neighbourhood of $(t,x)=(0,0)$ in ${\mathbb C}^2$ unless
$u_0(x)=a_0+a_1x$. This also furnishes a nonexistence result for a class of
$y$-independent solutions of the KP equation. We extend this to $y$-dependent
cases by considering initial values given at $y=0$, $u(t,x,0)=u_0(x,t)$,
$u_y(t,x,0)=u_1(x,t)$, where the Taylor coefficients of $u_0$ and $u_1$ around
$t=0$, $x=0$ are assumed nonnegative. We prove that there is no holomorphic
solution around the origin in ${\mathbb C}^3$ unless $u_0$ and $u_1$ 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$_4$ 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 $A_u$ and $B_u$ 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$_4$ 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

### Involutions of knots that fix unknotting tunnels

Let K be a knot that has an unknotting tunnel tau. We prove that K admits a
strong involution that fixes tau pointwise if and only if K is a two-bridge
knot and tau its upper or lower tunnel.Comment: 9 pages, 3 figure

### Electron effective mass in Al$_{0.72}$Ga$_{0.28}$N alloys determined by mid-infrared optical Hall effect

The effective electron mass parameter in Si-doped Al$_{0.72}$Ga$_{0.28}$N is
determined to be $m^\ast=(0.336\pm0.020)\,m_0$ 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
$m^\ast=0.232\,m_0$ for GaN, an average effective electron mass of
$m^\ast=0.376\,m_0$ can be extrapolated for AlN. The analysis of mid-infrared
spectroscopic ellipsometry measurements further confirms the two phonon mode
behavior of the E$_1$(TO) and one phonon mode behavior of the A$_1$(LO) phonon
mode in high-Al-content AlGaN alloys as seen in previous Raman scattering
studies

### 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 Y$_2$SiO$_5$
using generalized spectroscopic ellipsometry from 40-1200 cm$^{-1}$. 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$_{\mathrm{u}}$
and 22 B$_{\mathrm{u}}$ 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$_{\mathrm{u}}$ symmetry and 22 B$_{\mathrm{u}}$
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)]

### Enhancement of in vitro Guayule propagation

A method for stimulating in vitro propagation of Guayule from a nutrient medium containing Guayule tissue by adding a substituted trialkyl amine bioinducing agent to the nutrient medium is described. Selective or differentiated propagation of shoots or callus is obtained by varying the amounts of substituted trialky amine present in the nutrient medium. The luxuriant growth provided may be processed for its poly isoprene content or may be transferred to a rooting medium for production of whole plants as identical clones of the original tissue. The method also provides for the production of large numbers of Guayule plants having identical desirable properties such as high polyisoprene levels

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