Hyers–Ulam stability of a first order partial differential equation

We prove that the existence of a global prime integral leads, in appropriate conditions, to the Hyers–Ulam stability of a linear partial differential equation of first order.     

High-efficiency longitudinally-pumped miniature Nd:YVO4 laser

We report on fundamental and intracavity frequency-doubled emission in a miniature Nd:YVO₄ (3×3×1 mm) laser. A maximum slope efficiency of η_s=58.6%, with optical efficiency of η₀=53.0% at 780 mW pump power was realized in a TEM₀₀ output beam. To obtain the optimum pump-beam focusing conditions we applied a new formalism in which the pump-beam propagation in the active medium was described by its M² factor. A good agreement between theoretical predictions and experimental results was observed. In second-harmonic regime, obtained by a KTP crystal, 230 mW green power that corresponds to 54% nonlinear conversion efficiency was reached.     

Direct deposition and assembly of gold colloidal particles using a nanofountain probe

We report the direct delivery and assembly of negatively charged gold colloidal particles atop positively charged amino-terminated silicon oxide surfaces using a nanofountain atomic force microscopy probe. The experimental results and fluid simulations indicate that the flow of nanoparticles is confined to the core tip region of the probe. This leads to the assembly of high-resolution submicron patterns (200 nm) on the substrate with feature sizes dependent on the tip-substrate contact time. A diffusion mechanism for the patterning is proposed and discussed.     

Comment on Q-Switched Tm：YAG Laser Intracavity-Pumped by a 1064 nm Laser

The paper published in Chin. Phys. Lett. 26 （2009） 124211 reported a Q-switched 2-tim Tm：YAG laser that is intracavity pumped by a Nd： YAG laser with emission at 1.06μm. However, analysis of the experimental setup concludes that only the Nd：YAG laser is Q-switched, and the Tm：YAG laser operates in the free-generation regime. Therefore, Q-switch operation for the 2μm emission wavelength is not realized.     

Structural investigations of ITO-ZnO films grown by the combinatorial pulsed laser deposition technique

Mixtures of transparent and conductive oxides such as ITO-ZnO have been grown by a combinatorial pulsed laser deposition technique from two targets that were located 15 mm apart. The films were deposited on (1 0 0)Si and quartz substrates that were heated at temperatures from 300 to 500 °C. Measurements of the In to Zn ratios along the transversal axis of the substrates, which passes through the maximum thickness points corresponding to each target position were performed using energy dispersive X-ray spectroscopy and spectroscopic ellipsometry. From simulations of the X-ray reflectivity spectra, collected with a 2 mm mask on different locations along the transversal axis of the samples, the density and thickness of the deposited films were calculated and then the In to Zn ratios. The crystalline structure and electrical properties of the deposited films were also investigated along the same axis. Changes in the ratio of In/Zn along this axis resulted in changes of the film lattice constant and texture.     

Hybrid MC/RISM technique for simulation of polymer solutions: Monte Carlo+ RISM integral equations

A new (hybrid) method is reported for modelling complex macromolecular systems. The approach combines the traditional atomistic Monte Carlo (MC) computer simulation of flexible polymer chains with the numerical solution of the site-site Ornstein-Zernike-like (RISM) integral equations. The method is used for calculating properties of a linear polymer in dilute solution. Since the condensed-phase environment of a flexible macromolecule affects the equilibrium configuration probability distribution of the macromolecule, the site-site intramolecular correlation function and the intramolecular potential field are treated in a self-consistent manner. Briefly, the MC method is applied to generate the configurations of a single chain molecule. Using the coordinates of chain beads, the averaged intrapolymer correlation function is obtained. Then, solving the coupled RISM equations for a given density of solvent particles, we find the polymer-solvent correlation functions. This yields the medium-induced intrapolymer potential and the corresponding effective intramolecular energies, which are used in the standard Metropolis MC procedure. The structural properties of the polymer chain are computed by averaging over the statistically representative set of configurations. As a result of many such iterations, the intramolecular structure is determined self-consistently. Using the hybrid MC/RISM method, extensive studies have been made of static properties of flexible polymer chains surrounded by LJ particles with purely repulsive interactions between the particles and chain beads. Also, direct molecular dynamics simulations have been carried out and have demonstrated that the hybrid MC/RISM approach gives a quite accurate prediction for condensed-phase effects.     

Interatomic potentials for the Na+—Rg complexes (Rg = He,Ne and Ar)

Interatomic potential energy curves are presented for the Na⁺—Rg (Rg = He, Ne and Ar) cationic complexes. The curves are calculated at the CCSD(T)/aug-cc-pVQZ level of theory, with correction for basis set superposition error being performed point-by-point. Ninety-six different bond lengths are used in the generation of the curves. From the curves rovibrational energy levels are calculated. These, in turn, are used to calculate the heat of formation of the cationic complexes, both by calculating partition functions under the assumption of a rigid rotor, harmonic oscillator, and also explicitly using the calculated rovibrational energy levels. The long range region of each of the curves is used to derive the D ₄ and D ₆ parameters, the former being used to derive the static polarizability a ₁ of each of the Rg atoms and the latter the first dispersion coefficients, C ₆(Na⁺—Rg).     

Hyers-Ulam stability of a general linear partial differential equation

Aequationes mathematicae - In this paper we will study Hyers-Ulam stability for a general linear partial differential equation of first order in a Banach space.     

Flow-invariant closed sets with respect to nonlinear semigroup flows

A general result on the flow-invariance of a closed subset with respect to a differential equation associated with a nonlinear semigroup generator on Banach spaces is given. Applications to the flow-invariance of controlled flux sets (including the Enstrophy and Helicity sets) with respect to semilinear parabolic equations and Navier-Stokes equations are given.