21,017 research outputs found

    Comment on "Anderson transition in disordered graphene"

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    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

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    We study characteristic Cauchy problems for the Korteweg-deVries (KdV) equation ut=uux+uxxxu_t=uu_x+u_{xxx}, and the Kadomtsev-Petviashvili (KP) equation uyy=(uxxx+uux+ut)xu_{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)=u0(x)u(0,x)=u_0(x), we show that there is no solution holomorphic in any neighbourhood of (t,x)=(0,0)(t,x)=(0,0) in C2{\mathbb C}^2 unless u0(x)=a0+a1xu_0(x)=a_0+a_1x. This also furnishes a nonexistence result for a class of yy-independent solutions of the KP equation. We extend this to yy-dependent cases by considering initial values given at y=0y=0, u(t,x,0)=u0(x,t)u(t,x,0)=u_0(x,t), uy(t,x,0)=u1(x,t)u_y(t,x,0)=u_1(x,t), where the Taylor coefficients of u0u_0 and u1u_1 around t=0t=0, x=0x=0 are assumed nonnegative. We prove that there is no holomorphic solution around the origin in C3{\mathbb C}^3 unless u0u_0 and u1u_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

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    We determine the frequency dependence of four independent CdWO4_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 AuA_u and BuB_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 CdWO4_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

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    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 Al0.72_{0.72}Ga0.28_{0.28}N alloys determined by mid-infrared optical Hall effect

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    The effective electron mass parameter in Si-doped Al0.72_{0.72}Ga0.28_{0.28}N is determined to be m=(0.336±0.020)m0m^\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=0.232m0m^\ast=0.232\,m_0 for GaN, an average effective electron mass of m=0.376m0m^\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 E1_1(TO) and one phonon mode behavior of the A1_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

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    We determine the frequency dependence of the four independent Cartesian tensor elements of the dielectric function for monoclinic symmetry Y2_2SiO5_5 using generalized spectroscopic ellipsometry from 40-1200 cm1^{-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 Au_{\mathrm{u}} and 22 Bu_{\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 Au_{\mathrm{u}} symmetry and 22 Bu_{\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

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    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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