On the hydrostatic approximation of the Navier-Stokes equations in a thin strip

In this paper, we first prove the global well-posedness of a scaled anisotropic Navier-Stokes system and the hydrostatic Navier-Stokes system in a 2-D striped domain with small analytic data in the tangential variable. Then we justify the limit from the anisotropic Navier-Stokes system to the hydrostatic Navier-Stokes system with analytic data

Stereoisomer libraries: Total synthesis of all 16 stereoisomers of the pine sawfly sex pheromone by a fluorous mixture-synthesis approach

All 16 stereoisomers of the sex pheromone of pine sawfly (3,7,11-trimethylundecanol propanoate ester) have been synthesized on a 10- to 20-mg scale by a split-parallel fluorous mixture-synthesis approach. Spectral data obtained for all 32 compounds (16 alcohols and the corresponding propionates) matched well with published data, thereby validating the fluorous-tag encoding of diastereoisomers. This fluorous-tag encoding method is recommended for the efficient synthesis of multiple stereoisomers for spectroscopic studies, biological tests, or other structure-function relationships

Observation of Terahertz Radiation via the Two-Color Laser Scheme with Uncommon Frequency Ratios

In the widely-studied two-color laser scheme for terahertz (THz) radiation from a gas, the frequency ratio of the two lasers is usually fixed at $\omega_2/\omega_1=$1:2. We investigate THz generation with uncommon frequency ratios. Our experiments show, for the first time, efficient THz generation with new ratios of $\omega_2/\omega_1=$1:4 and 2:3. We observe that the THz polarization can be adjusted by rotating the longer-wavelength laser polarization and the polarization adjustment becomes inefficient by rotating the other laser polarization; the THz energy shows similar scaling laws with different frequency ratios. These observations are inconsistent with multi-wave mixing theory, but support the gas-ionization model. This study pushes the development of the two-color scheme and provides a new dimension to explore the long-standing problem of the THz generation mechanism.Comment: 6 pages, 3 figure

Different steady states for spin currents in noncollinear multilayers

We find there are at least two different steady states for transport across noncollinear magnetic multilayers. In the conventional one there is a discontinuity in the spin current across the interfaces which has been identified as the source of current induced magnetic reversal; in the one advocated herein the spin torque arises from the spin accumulation transverse to the magnetization of a magnetic layer. These two states have quite different attributes which should be discerned by current experiments.Comment: 8 pages, no figure. Accepted for publication in Journal of Physics: Condensed Matte

Electromagnetic energy storage and power dissipation in nanostructures

The processes of storage and dissipation of electromagnetic energy in nanostructures depend on both the material properties and the geometry. In this paper, the distributions of local energy density and power dissipation in nanogratings are investigated using the rigorous coupled-wave analysis. It is demonstrated that the enhancement of absorption is accompanied by the enhancement of energy storage both for material at the resonance of its dielectric function described by the classical Lorentz oscillator and for nanostructures at the resonance induced by its geometric arrangement. The appearance of strong local electric field in nanogratings at the geometry-induced resonance is directly related to the maximum electric energy storage. Analysis of the local energy storage and dissipation can also help gain a better understanding of the global energy storage and dissipation in nanostructures for photovoltaic and heat transfer applications