Zone Diagrams in Euclidean Spaces and in Other Normed Spaces

Zone diagram is a variation on the classical concept of a Voronoi diagram. Given n sites in a metric space that compete for territory, the zone diagram is an equilibrium state in the competition. Formally it is defined as a fixed point of a certain "dominance" map. Asano, Matousek, and Tokuyama proved the existence and uniqueness of a zone diagram for point sites in Euclidean plane, and Reem and Reich showed existence for two arbitrary sites in an arbitrary metric space. We establish existence and uniqueness for n disjoint compact sites in a Euclidean space of arbitrary (finite) dimension, and more generally, in a finite-dimensional normed space with a smooth and rotund norm. The proof is considerably simpler than that of Asano et al. We also provide an example of non-uniqueness for a norm that is rotund but not smooth. Finally, we prove existence and uniqueness for two point sites in the plane with a smooth (but not necessarily rotund) norm.Comment: Title page + 16 pages, 20 figure

Tenth-order lepton g-2: Contribution from diagrams containing a sixth-order light-by-light-scattering subdiagram internally

This paper reports the result of our evaluation of the tenth-order QED correction to the lepton g-2 from Feynman diagrams which have sixth-order light-by-light-scattering subdiagrams, none of whose vertices couple to the external magnetic field. The gauge-invariant set of these diagrams, called Set II(e), consists of 180 vertex diagrams. In the case of the electron g-2 (a_e), where the light-by-light subdiagram consists of the electron loop, the contribution to a_e is found to be - 1.344 9 (10) (\alpha /\pi)^5. The contribution of the muon loop to a_e is - 0.000 465 (4) (\alpha /\pi)^5. The contribution of the tau-lepton loop is about two orders of magnitudes smaller than that of the muon loop and hence negligible. The sum of all of these contributions to a_e is - 1.345 (1) (\alpha /\pi)^5. We have also evaluated the contribution of Set II(e) to the muon g-2 (a_\mu). The contribution to a_\mu from the electron loop is 3.265 (12) (\alpha /\pi)^5, while the contribution of the tau-lepton loop is -0.038 06 (13) (\alpha /\pi)^5. The total contribution to a_\mu, which is the sum of these two contributions and the mass-independent part of a_e, is 1.882 (13) (\alpha /\pi)^5.Comment: 18 pages, 3 figures, REVTeX4, axodraw.sty used, changed title, corrected uncertainty of a_mu, added a referenc

Influence of magnetic impurities on charge transport in diffusive-normal-metal / superconductor junctions

Charge transport in the diffusive normal metal (DN) / insulator / $s$- and $d$-wave superconductor junctions is studied in the presence of magnetic impurities in DN in the framework of the quasiclassical Usadel equations with the generalized boundary conditions. The cases of $s$- and d-wave superconducting electrodes are considered. The junction conductance is calculated as a function of a bias voltage for various parameters of the DN metal: resistivity, Thouless energy, the magnetic impurity scattering rate and the transparency of the insulating barrier between DN and a superconductor. It is shown that the proximity effect is suppressed by magnetic impurity scattering in DN for any value of the barrier transparency. In low-transparent s-wave junctions this leads to the suppression of the normalized zero-bias conductance. In contrast to that, in high transparent junctions zero-bias conductance is enhanced by magnetic impurity scattering. The physical origin of this effect is discussed. For the d-wave junctions, the dependence on the misorientation angle $\alpha$ between the interface normal and the crystal axis of a superconductor is studied. The zero-bias conductance peak is suppressed by the magnetic impurity scattering only for low transparent junctions with $\alpha \sim 0$. In other cases the conductance of the d-wave junctions does not depend on the magnetic impurity scattering due to strong suppression of the proximity effect by the midgap Andreev resonant states.Comment: 11 pages, 13 figures;d-wave case adde

Protein-crystal growth experiment (planned)

To evaluate the effectiveness of a microgravity environment on protein crystal growth, a system was developed using 5 cubic feet Get Away Special payload canister. In the experiment, protein (myoglobin) will be simultaneously crystallized from an aqueous solution in 16 crystallization units using three types of crystallization methods, i.e., batch, vapor diffusion, and free interface diffusion. Each unit has two compartments: one for the protein solution and the other for the ammonium sulfate solution. Compartments are separated by thick acrylic or thin stainless steel plates. Crystallization will be started by sliding out the plates, then will be periodically recorded up to 120 hours by a still camera. The temperature will be passively controlled by a phase transition thermal storage component and recorded in IC memory throughout the experiment. Microgravity environment can then be evaluated for protein crystal growth by comparing crystallization in space with that on Earth

Spin-dependent observables in surrogate reactions

Observables emitted from various spin states in compound U nuclei are investigated to validate usefulness of the surrogate reaction method. It was found that energy spectrum of cascading $\gamma$-rays and their multiplicities, spectrum of evaporated neutrons, and mass-distribution of fission fragments show clear dependence on the spin of decaying nuclei. The present results indicate that they can be used to infer populated spin distributions which significantly affect the decay branching ratio of the compound system produced by the surrogate reactions

Reflectance measurement of two-dimensional photonic crystal nanocavities with embedded quantum dots

The spectra of two-dimensional photonic crystal slab nanocavities with embedded InAs quantum dots are measured by photoluminescence and reflectance. In comparing the spectra taken by these two different methods, consistency with the nanocavities' resonant wavelengths is found. Furthermore, it is shown that the reflectance method can measure both active and passive cavities. Q-factors of nanocavities, whose resonant wavelengths range from 1280 to 1620 nm, are measured by the reflectance method in cross polarization. Experimentally, Q-factors decrease for longer wavelengths and the intensity, reflected by the nanocavities on resonance, becomes minimal around 1370 nm. The trend of the Q-factors is explained by the change of the slab thickness relative to the resonant wavelength, showing a good agreement between theory and experiment. The trend of reflected intensity by the nanocavities on resonance can be understood as effects that originate from the PC slab and the underlying air cladding thickness. In addition to three dimensional finite-difference time-domain calculations, an analytical model is introduced that is able to reproduce the wavelength dependence of the reflected intensity observed in the experiment.Comment: 24 pages, 7 figures, corrected+full versio