Interior regularity criteria in weak spaces for the Navier-Stokes equations

We study the interior regularity of weak solutions of the incompressible Navier-Stokes equations in ×(0,T), where and 0<T<. The local boundedness of a weak solution u is proved under the assumption that is sufficiently small for some (r,s) with and 3r<. Our result extends the well-known criteria of Serrin (1962), Struwe (1988) and Takahashi (1990) to the weak space-time spaces.Mathematics Subject Classification (2000): 35Q30, 76N10     

Metal-induced gap states at well defined alkali-halide/metal interfaces

In order to search for states specific to insulator/metal interfaces, we have studied epitaxially grown interfaces with element-selective near edge x-ray absorption fine structure. An extra peak is observed below the bulk edge onset for LiCl films on Cu and Ag substrates. The nature of chemical bonds as probed by x-ray photoemission spectroscopy and Auger electron spectroscopy remains unchanged, so we regard this as evidence for metal-induced gap states (MIGS) formed by the proximity to a metal, rather than local bonds at the interface. The dependence on the film thickness shows that the MIGS are as thin as one monolayer. An ab initio electronic structure calculation supports the existence of the MIGS that are strongly localized at the interface.     

Analysis of spurious bulk waves in ball surface wave device

We analyzed the acoustic waves propagating in a sphere to establish a useful guideline for the design of NDE apparatus and ball surface acoustic wave (SAW) device exploiting the diffraction-free propagation of SAW on a sphere. First, we calculated the laser-generated acoustic displacements both under ablation condition and under thermoelastic condition and verified experimentally the validity of the calculation. Next, the acoustic waves excited by out-of-plane stress and those excited by in-plane stress were compared. The results showed that when the out-of-plane stress was applied, the relative amplitudes of the bulk waves to that of the SAW were larger and the number of bulk waves was larger than that when the in-plane stress was applied, while the SAW had similar waveforms in each case. The ratio of the relative amplitude of the bulk waves for the out-of-plane stress and the in-plane stress was 3.1:1 at phi(1)=90 degrees and 1.67:1 at phi(1)=0 degrees. The large amplitude for the out-of-plane stress can be explained by wide directivities of bulk waves. Consequently, we found that it is necessary for ball SAW device to select a piezoelectric material and form of interdigital transducer so that the in-plane stress becomes dominant.     

Breakdown of a Mott insulator: a nonadiabatic tunneling mechanism

Time-dependent nonequilibrium properties of a strongly correlated electron system driven by large electric fields is obtained by means of solving the time-dependent Schr?dinger equation for the many-body wave function numerically in one dimension. While the insulator-to-metal transition depends on the electric field and the interaction, the metallization is found to be described in terms of a universal Landau-Zener quantum tunneling among the many-body levels. These processes induce current oscillation for small systems, while giving rise to finite resistivity through dissipation for larger systems/on longer time scales.     

Characterization and protonation behavior of bipyridine thiol self-assembled monolayer on Au(1 1 1) studied using X-ray photoelectron spectroscopy and scanning tunneling microscopy

The adsorption process, molecular arrangement and protonation behavior of self-assembled monolayers (SAMs) of bipyridine thiol on Au(1 1 1) were investigated using X-ray photoelectron spectroscopy (XPS) and scanning tunneling microscopy (STM), with a view towards constructing a molecular ion sensor. When the bipyridine SAMs were immersed in a strong CF₃SO₃H solution for protonation of the bipyridine group, additional N(1s) XPS peaks were generated at higher binding peak positions where the origin of the peak was considered to be the N-H species. We further investigated the relationship between the immersion time for the SAMs and the probability of protonation. We observed a decrease in the probability of protonation with a longer immersion time for the SAMs. We consider that both the bipyridine molecular arrangements and the molecular density on the Au surface are crucial for controlling the probability of protonation based on the STM and XPS data.     

Total synthesis of (+)-5α-dihydropregnenolone via acetylene-cation cyclization

The stereoselective total synthesis of (+)-5α-dihydropregnenolone $\text{7}$ via acetylene-cation cyclization of $\text{6}$, which was readily prepared from the optically active D-ring aromatic steroid $\text{1}$, is described.     

Superstructure and phase transitions in CsPbCl3

Superstructure of CsPbCl₃ is investigated by X-ray diffraction experiments. In the room temperature phase, three types of superlattice reflections are observed which correspond to the X, M and R points of the cubic Brillouin zone. On heating from room temperature, an integrated intensity of the X point reflection exhibits a discontinuous decrease at 37°C, while the R and M point reflections disappear at 42 and 47°C respectively. Explanations of these phase transitions in terms of condensation of soft-zone boundary phonon modes are presented.