On a new class of dynamic Hardy-type inequalities and some related generalizations

Aequationes mathematicae - In this paper, we establish a new class of dynamic inequalities of Hardy’s type which generalize and improve some recent results given in the literature. More...     

Close‐Packed Two‐Dimensional Silver Nanoparticle Arrays: Quadrupolar and Dipolar Surface Plasmon Resonance Coupling

Silver nanoparticles (NPs) ranging in size from 40 to 100 nm were prepared in high yield by using an improved seed‐mediated method. The homogeneous Ag NPs were used as building blocks for 2D assembled Ag NP arrays by using an oil/water interface. A close‐packed 2D array of Ag NPs was fabricated by using packing molecules (3‐mercaptopropyltrimethoxysilane) to control the interparticle spacing. The homogeneous 2D Ag NP array exhibited a strong quadrupolar cooperative plasmon mode resonance and a dipolar red‐shift relative to individual Ag NPs suspended in solution. A well‐arranged 2D Ag NP array was embedded in polydimethylsiloxane film and, with biaxial stretching to control the interparticle distance, concomitant variations of the quadrupolar and dipolar couplings were observed. As the interparticle distance increased, the intensity of the quadrupolar cooperative plasmon mode resonance decreased and dipolar coupling completely disappeared. The local electric field of the 2D Ag NP array was calculated by using finite difference time domain simulation and qualitatively showed agreement with the experimental measurements.     

Geometrical method for determining the surface damage threshold for femtosecond laser pulses

A new geometrical method to determine the surface damage threshold for ultrashort pulses is presented. It consists in the formation of a surface damage profile by a movement of the sample across the laser beam focus. A single measurement of the maximum transversal dimension of this damage profile, which depends solely on the laser beam power, is used to calculate the local damage threshold intensity. It is also theoretically shown that the damage in the transverse dimension can be controlled under the diffraction-limited spot.     

Hydrogen peroxide promoted hydroxylation of haloarenes and heteroarenes

Addition of aqueous hydrogen peroxide significantly accelerates the substitution reactions of hydroxide salts with haloarenes bearing electron withdrawing substituents. A similar effect is observed in the reactions of hydroxide salts with halogenated heteroarenes. Reactions are carried out in water or water-THF at ambient temperature or at 50-60 °C.     

A search technique for global optimization in a chaotic environment

We describe a new algorithm which uses the trajectories of a discrete dynamical system to sample the domain of an unconstrained objective function in search of global minima. The algorithm is unusually adept at avoiding nonoptimal local minima and successfully converging to a global minimum. Trajectories generated by the algorithm for objective functions with many local minima exhibit chaotic behavior, in the sense that they are extremely sensitive to changes in initial conditions and system parameters. In this context, chaos seems to have a beneficial effect: failure to converge to a global minimum from a given initial point can often be rectified by making arbitrarily small changes in the system parameters.     

Monte Carlo study of interfacial silicon suboxide layers and oxidation kinetics

A simple simulation scheme that simultaneously describes the growth kinetics of SiO₂ films at the nanometer scale and the SiO_x/Si interface dynamics (its extent, and spatial/temporal evolution) is presented. The simulation successfully applies to experimental data in the region above and below 10 nm, reproduces the Deal and Grove linear-parabolic law and the oxide growth rate enhancement in the very thin film regime (the so-called anomalous region). According to the simulation, the oxidation is governed mainly by two processes: (a) the formation of a transition suboxide layer and (b) its subsequent drift towards the silicon bulk. We found that it is the superposition of these two processes that produces the crossover from the anomalous oxidation region behavior to the linear-parabolic law.     

Metastability in the Potts model on the Cayley tree

Metastability in the ferromagneticp-state Potts model defined on the Cayley tree is discussed. It is shown that the sign of the boundary fieldH _s determines the order of the transition as well as the stability of the low-temperature phase. Lowering the temperature withH _s >0, a system withp<2 (p>2) will display a second (first)-order transition to a metastable (stable) phase. ForH _s >0 a second (first)-order transition to a metastable (stable) phase occurs ifp>2 (p<2). In this case the system also has a residual entropy which is negative forp<2.     

Exciton energy broadening due to interface fluctuations in ZnSe/ZnSxSe1−x strained quantum wells

The excitonic properties of a ZnSe/ZnS_xSe_1−x strained quantum well (QW) are calculated taking into account interface effects. Numerical results obtained with ZnS_0.18Se_0.82/ZnSe QWs show that graded interfaces can be responsible for a strong broadening of excitonic spectra.     

The symmetric eigenvalue complementarity problem

In this paper the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed. It is shown that the symmetric (EiCP) is equivalent to finding an equilibrium solution of a differentiable optimization problem in a compact set. A necessary and sufficient condition for solvability is obtained which, when verified, gives a convenient starting point for any gradient-ascent local optimization method to converge to a solution of the (EiCP). It is further shown that similar results apply to the Symmetric Generalized Eigenvalue Complementarity Problem (GEiCP). Computational tests show that these reformulations improve the speed and robustness of the solution methods.