Scattering for the Zakharov system in 3 dimensions

We prove global existence and scattering for small localized solutions of the Cauchy problem for the Zakharov system in 3 space dimensions. The wave component is shown to decay pointwise at the optimal rate of t^{-1}, whereas the Schr\"odinger component decays almost at a rate of t^{-7/6}.Comment: Minor changes and referee's comments include

On the Logarithmic Asymptotics of the Sixth Painleve' Equation (Summer 2007)

We study the solutions of the sixth Painlev\'e equation with a logarithmic asymptotic behavior at a critical point. We compute the monodromy group associated to the solutions by the method of monodromy preserving deformations and we characterize the asymptotic behavior in terms of the monodromy itself.Comment: LaTeX with 8 figure

Possible solution to the 7^7Li problem by the long lived stau

Modification of standard big-bang nucleosynthesis is considered in the minimal supersymmetric standard model to resolve the excessive theoretical prediction of the abundance of primordial lithium 7. We focus on the stau as a next-lightest superparticle, which is long lived due to its small mass difference with the lightest superparticle. It provides a number of additional decay processes of $\mathrm{^{7}Li}$ and $\mathrm{^{7}Be}$. A particularly important process is the internal conversion in the stau-nucleus bound state, which destroys the $\mathrm{^{7}Li}$ and $\mathrm{^{7}Be}$ effectively. We show that the modification can lead to a prediction consistent with the observed abundance of $\mathrm{^{7}Li}$.Comment: 6 pages, 5 figure

Movable algebraic singularities of second-order ordinary differential equations

Any nonlinear equation of the form y''=\sum_{n=0}^N a_n(z)y^n has a (generally branched) solution with leading order behaviour proportional to (z-z_0)^{-2/(N-1)} about a point z_0, where the coefficients a_n are analytic at z_0 and a_N(z_0)\ne 0. We consider the subclass of equations for which each possible leading order term of this form corresponds to a one-parameter family of solutions represented near z_0 by a Laurent series in fractional powers of z-z_0. For this class of equations we show that the only movable singularities that can be reached by analytic continuation along finite-length curves are of the algebraic type just described. This work generalizes previous results of S. Shimomura. The only other possible kind of movable singularity that might occur is an accumulation point of algebraic singularities that can be reached by analytic continuation along infinitely long paths ending at a finite point in the complex plane. This behaviour cannot occur for constant coefficient equations in the class considered. However, an example of R. A. Smith shows that such singularities do occur in solutions of a simple autonomous second-order differential equation outside the class we consider here

Scattering and small data completeness for the critical nonlinear Schroediger equation

We prove Asymptotic Completeness of one dimensional NLS with long range nonlinearities. We also prove existence and expansion of asymptotic solutions with large data at infinity

Synthesis and characterization of mixed oxide nanowires for gas sensing

A healthy and long-lasting life is the utmost wish of any living being thus aging. The aging phenomenon cannot be stopped but may be controlled to some extent when we live in appropriate environments. Usually, the outdoor environment is polluted by two means natural events (windblown dust, volcano eruptions, etc.) and man-made ones (burning of facile fuels, factories, volatile organic compounds, etc.). Pollution due to harmful air such as sulfur oxides (SO2), nitrogen oxides (NOX), carbon monoxide (CO), ammonia (NH3), methane (CH4), and volatile organic compounds (VOCs) is one of the significant issues since it is more sensitive to compromising the natural ecosystem and environment. So, exposure to these compounds worsens the aging phenomena of the living being (headache, fainting, skin and eye irradiation, respiratory infections, heart disease, lung cancer, and even superficial death). Therefore, it is necessary the detection these compounds in the environment. Accordingly, metal oxides (MOXs) gas sensors have conventionally been employed to detect and quantify harmful gases in both indoor and outdoor environments. However, one of the major problems with these sensors is achieving selective detection. Herein, we propose a novel design with two metal oxides (ZnO and Co3O4) that provide very high gas response together with superior selectivity. The proposed structure is a one-dimensional (1D) metal oxide composite; Co3O4/ZnO nanowires. The composite was prepared by in-situ thermal oxidation of metallic Co thin layer (50 nm) and evaporation of ZnO powder at a temperature of 800 ᵒC at a pressure of 0.15 mbar. The pressure was maintained by a controlled mixture of O2 and Ar. The morphological, compositional, and structural analyses are evidence of the successful growth of the Co3O4/ZnO composite nanowire with the root of Co3O4 and the tip with Pt (catalyzer) and Co3O4. The gas sensing characterization shows exciting sensing functionality towards acetone (C3H6O) compared to that of tested gases (C2H5OH, H2S, NH3, CO, NO2, and H2). The reported highest response (ΔG/G; G is the conductance) was above the value of 5000 toward 50 ppm (parts per million) C3H6O at 40 RH% air when working at 250 °C with the potential of detecting sub ppb (parts per billion) concentration levels of C3H6O. The very high C3H6O sensing performance together with exceptionally high selectivity of the sensor ascribed to Pt nanoparticle and the Co3O4 section on the tip of the Co3O4/ZnO. Moreover, the formation of heterojunctions, synergistic gas sensing, and the catalytic activity of the proposed design enhances the response of the sensors. Accordingly, scanning electron microscopic (SEM), transmission electron microscope (TEM), energy-dispersive X-ray spectroscopy (EDS), X-ray photoelectron spectroscopy (XPS), X-ray diffraction (XRD) characterization, and the sensing mechanisms are comprehensively discussed at the conference

Performance of Dye-Sensitized Solar Cell Using Size-Controlled Synthesis of TiO2 Nanostructure

Titanium dioxide (TiO2) or titania shows a great interest in solar cell application due to its morphology and crystalline structure. Moreover, it is an affordable compound that could make solar cells more cost economical than traditional silicon solar cells. In this study, one-step hydrothermal method is demonstrated to synthesis rutile TiO2 nanorods and nanoflowers morphology in nanoscale dimension on different hydrothermal reaction times for Dye-sensitized solar cells application. Increasing the reaction time could influence in formation of higher crystalline rutile phase titania nanostructure before abruptly decreases as the prolong hydrothermal process carry out. The length of the nanorods produced shows increasing behaviour and the growth of nanoflowers are become denser obviously. Band gap estimation is 2.75 eV slightly lower than bulk rutile TiO2. It shows that the growth mechanism under different reaction times has great influences on the morphologies and alignment of the nanostructure. Further, the DSSCs fabricated using 15 hours reaction time exhibited the best photovoltaic performance with highest efficiency of 3.42% and highest short-circuit photocurrent of 0.7097V

Glass Transition in the Polaron Dynamics of CMR Manganites

Neutron scattering measurements on a bilayer manganite near optimal doping show that the short-range polarons correlations are completely dynamic at high T, but then freeze upon cooling to a temperature T* 310 K. This glass transition suggests that the paramagnetic/insulating state arises from an inherent orbital frustration that inhibits the formation of a long range orbital- and charge-ordered state. Upon further cooling into the ferromagnetic-metallic state (Tc=114 K), where the polarons melt, the diffuse scattering quickly develops into a propagating, transverse optic phonon.Comment: 4 pages, 4 figures. Physical Review Letters (in Press