A new family of convex weakly compact valued random variables in Banach space and applications to laws of large numbers

We consider a new family of convex weakly compact valued integrable random sets which is called an adapted array of convex weakly compact valued integrable random variables of type p (1?p?2). By this concept, more general laws of large numbers will be established. Some illustrative examples are provided.     

Ultrashort pulse generation using fiber FM laser

Ultrashort optical pulse generation using a fiber FM laser is presented and analyzed in detail. Fiber FM laser operation is realized using a fiber ring with an internal phase modulator and an erbium-doped fiber amplifier. To compress FM laser pulses, an external dispersive single-mode fiber is employed. Furthermore, by external intensity modulation, the pulse background is removed. The background ratio of the generated ultrashort pulse is calculated and compared with the experimental results. The experimental results show an output optical pulse width of 1.77 ps and a spectral bandwidth of 0.5 THz.     

Adsorption of surface functionalized silica nanoparticles onto mineral surfaces and decane/water interface

The adsorption of silica nanoparticles onto representative mineral surfaces and at the decane/water interface was studied. The effects of particle size (the mean diameters from 5 to 75?nm), concentration and surface type on the adsorption were studied in detail. Silica nanoparticles with four different surfaces [unmodified, surface modified with anionic (sulfonate), cationic (quaternary ammonium (quat)) or nonionic (polyethylene glycol (PEG)) surfactant] were used. The zeta potential of these silica nanoparticles ranges from ?79.8 to 15.3?mV. The shape of silica particles examined by a Hitachi-S5500 scanning transmission electron microscope (STEM) is quite spherical. The adsorption of all the nanoparticles (unmodified or surface modified) on quartz and calcite surfaces was found to be insignificant. We used interfacial tension (IFT) measurements to investigate the adsorption of silica nanoparticles at the decane/water interface. Unmodified nanoparticles or surface modified ones with sulfonate or quat do not significantly affect the IFT of the decane/water interface. It also does not appear that the particle size or concentration influences the IFT. However, the presence of PEG as a surface modifying material significantly reduces the IFT. The PEG surface modifier alone in an aqueous solution, without the nanoparticles, yields the same IFT reduction for an equivalent PEG concentration as that used for modifying the surface of nanoparticles. Contact angle measurements of a decane droplet on quartz or calcite plate immersed in water (or aqueous nanoparticle dispersion) showed a slight change in the contact angle in the presence of the studied nanoparticles. The results of contact angle measurements are in good agreement with experiments of adsorption of nanoparticles on mineral surfaces or decane/water interface. This study brings new insights into the understanding and modeling of the adsorption of surface-modified silica nanoparticles onto mineral surfaces and water/decane interface.     

Improbability of void growth in aluminum via dislocation nucleation under typical laboratory conditions

The rate at which dislocations nucleate from spherical voids subjected to shear loading is predicted from atomistic simulation. By employing the latest version of the finite temperature string method, a variational transition state theory approach can be utilized, enabling atomistic predictions at ordinary laboratory time scales, loads, and temperatures. The simulation results, in conjunction with a continuum model, show that the deformation and growth of voids in Al are not likely to occur via dislocation nucleation under typical loadings regardless of void size.     

Optically gated resonant emission of single quantum dots

We report on the resonant emission in coherently driven single semiconductor quantum dots. We demonstrate that an ultraweak nonresonant laser acts as an optical gate for the quantum dot resonant response. We show that the gate laser suppresses Coulomb blockade at the origin of a resonant emission quenching, and that the optically gated quantum dots systematically behave as ideal two-level systems in both regimes of coherent and incoherent resonant emission.     

Ti-free optical waveguiding regions produced by LiNbO3 etching during the indiffusion of Ti

We report the observation, first to our knowledge, of optical waveguiding found beneath trenches etched in congruent lithium niobate using the recently reported etching during the indiffusion of Ti process. Observations of multi-mode and single-mode guiding at visible wavelengths and preliminary measurements of waveguide insertion losses are presented.     

Lower compactness estimates for scalar balance laws

In this paper, we study the compactness in L of the semigroup (St)_t≥0 of entropy weak solutions to strictly convex scalar conservation laws in one space dimension. The compactness of St for each t > 0 was established by P. D. Lax. Upper estimates for the Kolmogorov e‐entropy of the image of bounded sets in L¹ n L^∞ through S_t were given by C. De Lellis and F. Golse. Here we provide lower estimates on this e‐entropy of the same order as the one established by De Lellis and Golse, thus showing that such an e‐entropy is of size ≈ 1/ε. Moreover, we extend these estimates of compactness to the case of convex balance laws. © 2012 Wiley Periodicals, Inc.     

Multi-dimensional stability of planar Lax shocks in hyperbolic–elliptic coupled systems

We study nonlinear time-asymptotic stability of small-amplitude planar Lax shocks in a model consisting of a system of multi-dimensional conservation laws coupled with an elliptic system. Such a model can be found in context of dynamics of a gas in presence of radiation. Our main result asserts that the standard uniform Evans stability condition implies nonlinear stability. The main analysis is based on the earlier developments by Zumbrun for multi-dimensional viscous shock waves and by Lattanzio–Mascia–Nguyen–Plaza–Zumbrun for one-dimensional radiative shock profiles.