decay problem for the dissipative wave equation in odd dimensions

Consider the Cauchy problem in odd dimensions for the dissipative wave equation: (□+∂_t)u=0 in with (u,∂_tu)|_t=0=(u₀,u₁). Because the L² estimates and the L^∞ estimates of the solution u(t) are well known, in this paper we pay attention to the L^p estimates with 1p<2 (in particular, p=1) of the solution u(t) for t0. In order to derive L^p estimates we first give the representation formulas of the solution u(t)=∂_tS(t)u₀+S(t)(u₀+u₁) and then we directly estimate the exact solution S(t)g and its derivative ∂_tS(t)g of the dissipative wave equation with the initial data (u₀,u₁)=(0,g). In particular, when p=1 and n1, we get the L¹ estimate: u(t)_L¹Ce^−t/4(u_0W^n,1+u_1W^n−1,1)+C(u_0L¹+u_1L¹) for t0.     

Phase structure and critical behavior of multi-Higgs U(1) lattice gauge theory in three dimensions

We study the three-dimensional (3D) compact U(1) lattice gauge theory coupled with N-flavor Higgs fields by means of the Monte Carlo simulations. This model is relevant to multi-component superconductors, antiferromagnetic spin systems in easy plane, inflational cosmology, etc. It is known that there is no phase transition in the N = 1 model. For N = 2, we found that the system has a second-order phase transition line in the c₂ (gauge coupling)-c₁ (Higgs coupling) plane, which separates the confinement phase and the Higgs phase. Numerical results suggest that the phase transition belongs to the universality class of the 3D XY model as the previous works by Babaev et al. and Smiseth et al. suggested. For N = 3, we found that there exists a critical line similar to that in the N = 2 model, but the critical line is separated into two parts; one for c₂<c_2tc=2.4±0.1 with first-order transitions, and the other for c_2tc<c₂ with second-order transitions, indicating the existence of a tricritical point. We verified that similar phase diagram appears for the N = 4 and N = 5 systems. We also studied the case of anistropic Higgs coupling in the N = 3 model and found that there appear two second-order phase transitions or a single second-order transition and a crossover depending on the values of the anisotropic Higgs couplings. This result indicates that an “enhancement” of phase transition occurs when multiple phase transitions coincide at a certain point in the parameter space.     

Effects of annealing on properties of ZnO thin films prepared by electrochemical deposition in chloride medium

The development of cost-effective and low-temperature synthesis techniques for the growth of high-quality zinc oxide thin films is paramount for fabrication of ZnO-based optoelectronic devices, especially ultraviolet (UV)-light-emitting diodes, lasers and detectors. We demonstrate that the properties, especially UV emission, observed at room temperature, of electrodeposited ZnO thin films from chloride medium (at 70 °C) on fluor-doped tin oxide (FTO) substrates is strongly influenced by the post-growth thermal annealing treatments. X-ray diffraction (XRD) measurements show that the films have preferably grown along (0 0 2) direction. Thermal annealing in the temperature range of 150-400 °C in air has been carried out for these ZnO thin films. The as-grown films contain chlorine which is partially removed after annealing at 400 °C. Morphological changes upon annealing are discussed in the light of compositional changes observed in the ZnO crystals that constitute the film. The optical quality of ZnO thin films was improved after post-deposition thermal treatment at 150 °C and 400 °C in our experiments due to the reducing of defects levels and of chlorine content. The transmission and absorption spectra become steeper and the optical bandgap red shifted to the single-crystal value. These findings demonstrate that electrodeposition have potential for the growth of high-quality ZnO thin films with reduced defects for device applications.     

Splittings in the variety of residuated lattices

It is shown that the only algebra that splits the lattice of subvarieties of the variety of residuated lattices is the two element boolean algebra. Received October 4, 1999; accepted in final form August 11, 2000.     

Photorefractive effect in the relaxor ferroelectric material 0.91Pb(Zn1/3Nb2/3)O3-0.09PbTiO3

The photorefractive effect in a nominally undoped 0.91Pb(Zn1/3Nb2/3)O3-0.09PbTiO3 single crystal is measured. We report what is, to our knowledge, the first observation of the photorefractive effect in Pb-based relaxor ferroelectric crystals. The crystal is grown by the flux solution method. Then it is cut into a 2 mm x 4 mm x 8 mm piece and electrically poled along the [111] direction. The coupling constant of the two-wave mixing is 17 cm(-1), and the normalized time constant under 1-W/cm(2) illumination is 12 s at a wave-length of 476 nm. The effective trap density is calculated as 5 x 10(16) cm(-3) from the Debye screening length under the assumption of Kukhtarev's band-transport model. The dominant carrier is identified to be holes from the direction of two-wave mixing energy transfer.     

Ni thin films vacuum-evaporated on polyethylene naphthalate substrates with and without the application of magnetic field

We study the structural properties of the surface roughness, the surface mound size and the interfacial structure in Ni thin films vacuum-deposited on polyethylene naphthalate (PEN) organic substrates with and without the application of magnetic field and discuss its feasibility of fabricating quantum cross (QC) devices. For Ni/PEN evaporated without the magnetic field, the surface roughness decreases from 1.3 nm to 0.69 nm and the surface mound size increases from 32 nm to 80 nm with the thickness increased to 41 nm. In contrast, for Ni/PEN evaporated in the magnetic field of 360 Oe, the surface roughness tends to slightly decrease from 1.3 nm to 1.1 nm and the surface mound size shows the almost constant value of 28-30 nm with the thickness increased to 35 nm. It can be also confirmed for each sample that there is no diffusion of Ni into the PEN layer, resulting in clear Ni/PEN interface and smooth Ni surface. Therefore, these experimental results indicate that Ni/PEN films can be expected as metal/insulator hybrid materials in QC devices, leading to novel high-density memory devices.     

Smallness of fundamental groups for arithmetic schemes

The smallness is proved of étale fundamental groups for arithmetic schemes. This is a higher dimensional analogue of the Hermite-Minkowski theorem. We also refer to the case of varieties over finite fields. As an application, we prove certain finiteness results of representations of the fundamental groups over algebraically closed fields.     

Two Non-closure Properties on the Class of Subexponential Densities

Relations between subexponential densities and locally subexponential distributions are discussed. It is shown that the class of subexponential densities is neither closed under convolution roots nor closed under asymptotic equivalence. A remark is given on the closure under convolution roots for the class of convolution equivalent distributions.     

Incoherent quasielastic neutron scattering study on the polymorphism of tristearin: dynamical properties of hydrocarbon chains

Dynamical properties of acyl chains in the three polymorphic phases alpha, beta', and beta of tristearin [C(3)H(5)(OCOC(17)H(35))3] have been studied by means of incoherent quasielastic neutron scattering (IQNS) using selectively deuterated samples. The mean square displacement of hydrogen atoms, , was estimated from the scattering vector Q dependence of the elastic scattering component under the harmonic approximation. It was shown that the temperature dependence of was significantly different between the three phases. There was no marked difference in between these phases up to 193 K, and the value increased linearly with temperature. Although the beta phase remained linear up to 293 K, the alpha and beta' phases started to show a nonlinear increase around 200 K, suggesting an anharmonic nature of molecular motions. The alpha phase exhibited the most conspicuous temperature dependence. These characteristics were ascribable to the difference in the lateral packing of acyl chains. Compared with the beta phase which has a tightly packed T// subcell, the beta' and alpha phases have looser O perpendicular and H subcells, respectively. The molecular motion in the alpha phase was analyzed using the model of uniaxial rotational diffusion in a onefold cosine potential. It has been clarified that the rotational fluctuation about the chain axis in the alpha phase is rather restricted compared with that in the rotator phase of n-alkanes.     

Reversible Sodium Metal Electrodes: Is Fluorine an Essential Interphasial Component?

Alkaline metals are an ideal negative electrode for rechargeable batteries. Forming a fluorine‐rich interphase by a fluorinated electrolyte is recognized as key to utilizing lithium metal electrodes, and the same strategy is being applied to sodium metal electrodes. However, their reversible plating/stripping reactions have yet to be achieved. Herein, we report a contrary concept of fluorine‐free electrolytes for sodium metal batteries. A sodium tetraphenylborate/monoglyme electrolyte enables reversible sodium plating/stripping at an average Coulombic efficiency of 99.85 % over 300 cycles. Importantly, the interphase is composed mainly of carbon, oxygen, and sodium elements with a negligible presence of fluorine, but it has both high stability and extremely low resistance. This work suggests a new direction for stabilizing sodium metal electrodes via fluorine‐free interphases.