Soliton solutions of the nonlinear Schr\"odinger equation with defect conditions

A recent development in the derivation of soliton solutions for initial-boundary value problems through Darboux transformations, motivated to reconsider solutions to the nonlinear Schr\"odinger (NLS) equation on two half-lines connected via integrable defect conditions. Thereby, the Darboux transformation to construct soliton solutions is applied, while preserving the spectral boundary constraint with a time-dependent defect matrix. In this particular model, $N$-soliton solutions vanishing at infinity are constructed. Further, it is proven that solitons are transmitted through the defect independently of one another.Comment: 35 pages, 6 figure

Anisotropic ferromagnetism in carbon doped zinc oxide from first-principles studies

A density functional theory study of substitutional carbon impurities in ZnO has been performed, using both the generalized gradient approximation (GGA) and a hybrid functional (HSE06) as exchange-correlation functional. It is found that the non-spinpolarized C$_\mathrm{Zn}$ impurity is under almost all conditions thermodynamically more stable than the C$_\mathrm{O}$ impurity which has a magnetic moment of $2\mu_{\mathrm{B}}$, with the exception of very O-poor and C-rich conditions. This explains the experimental difficulties in sample preparation in order to realize $d^{0}$-ferromagnetism in C-doped ZnO. From GGA calculations with large 96-atom supercells, we conclude that two C$_\mathrm{O}$-C$_\mathrm{O}$ impurities in ZnO interact ferromagnetically, but the interaction is found to be short-ranged and anisotropic, much stronger within the hexagonal $ab$-plane of wurtzite ZnO than along the c-axis. This layered ferromagnetism is attributed to the anisotropy of the dispersion of carbon impurity bands near the Fermi level for C$_{\mathrm{O}}$ impurities in ZnO. From the calculated results, we derive that a C$_{\mathrm{O}}$ concentration between 2% and 6% should be optimal to achieve $d^{0}$-ferromagnetism in C-doped ZnO.Comment: 9 pages, 7 figure

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Photography by Jeremy K. Gruner

Retrospection

Photography by Jeremy K. Gruner

Comparison of lens- and fiber-coupled CCD detectors for X-ray computed tomography

Lens- and fiber-coupled X-ray detectors with identical CCD chips were compared in their performance in high-resolution computed tomography experiments

Scaling Study and Thermodynamic Properties of the cubic Helimagnet FeGe

The critical behavior of the cubic helimagnet FeGe was obtained from isothermal magnetization data in very close vicinity of the ordering temperature. A thorough and consistent scaling analysis of these data revealed the critical exponents $\beta=0.368$, $\gamma=1.382$, and $\delta=4.787$. The anomaly in the specific heat associated with the magnetic ordering can be well described by the critical exponent $\alpha=-0.133$. The values of these exponents corroborate that the magnetic phase transition in FeGe belongs to the isotropic 3D-Heisenberg universality class. The specific heat data are well described by ab initio phonon calculations and confirm the localized character of the magnetic moments.Comment: 10 pages, 8 figure