Twin solutions to singular boundary value problems

In this paper we establish the existence of two nonnegative solutions to singular and singular focal boundary value problems. Our nonlinearity may be singular at , and/or .

     

Anisotropic vacuum-induced interference in decay channels

We demonstrate how the anisotropy of the vacuum of the electromagnetic field can lead to quantum interferences among the decay channels of close lying states. Our key result is that interferences are given by the scalar formed from the antinormally ordered electric field correlation tensor for the anisotropic vacuum and the dipole matrix elements for the two transitions. We present results for emission between two conducting plates as well as for a two photon process involving fluorescence produced under coherent cw excitation.     

Resonant tunneling of ultracold atoms through vacuum induced potentials

We demonstrate resonant tunneling of ultracold atoms through potentials produced by the interaction of atoms with the vacuum field of a system of cavities. We show the close connection of the transmission characteristics to the resonant states in vacuum induced potentials. Transmission of cold atoms, though sharing some features with tunneling in finite semiconductor superlattices, is strongly dependent on the coherent addition of amplitudes from various wells and barriers.     

Reconstruction of the Wigner transform of a rotationally symmetric two-dimensional beam from the Wigner transform of the beam's one-dimensional sample

A coherent rotationally symmetric two-dimensional beam is essentially one-dimensional in content: It is fully determined by the one-dimensional sample along a diagonal of the circularly symmetric field distribution in a transverse plane. The linear transform that reconstructs the four-dimensional Wigner distribution of the full two-dimensional beam from the two-dimensional Wigner distribution of the one-dimensional sample is presented.     

Trap elimination and reduction of size dispersion due to aging in CdS<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Se<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript> quantum dots

Quantum Dots of CdS _x Se_1−x embedded in borosilicate glass matrix have been grown using Double-Step annealing method. Optical characterization of the quantum dots has been done through the combinative analysis of optical absorption and photoluminescence spectroscopy at room temperature. Decreasing trend of photoluminescence intensity with aging has been observed and is attributed to trap elimination. The changes in particle size, size distribution, number of quantum dots, volume fraction, trap related phenomenon and Gibbs free energy of quantum dots, has been explained on the basis of the diffusion-controlled growth process, which continues with passage of time. For a typical case, it was found that after 24 months of aging, the average radii increased from 3.05 to 3.12 nm with the increase in number of quantum dots by 190% and the size-dispersion decreased from 10.8% to 9.9%. For this sample, the initial size range of the quantum dots was 2.85 to 3.18 nm. After that no significant change was found in these parameters for the next 12 months. This shows that the system attains almost a stable nature after 24 months of aging. It was also observed that the size-dispersion in quantum dots reduces with the increase in annealing duration, but at the cost of quantum confinement effect. Therefore, a trade off optimization has to be done between the size-dispersion and the quantum confinement.     

Steady-state self-focusing of Gaussian electromagnetic beams in an inhomogeneous nonlinear medium: Effect of absorption and initial curvature of the beam

The authors have investigated the effect of linear absorption and initial curvature of an electromagnetic Gaussian beam on focusing/defocusing in an inhomogeneous nonlinear medium. Numerical computations have been made for linear inhomogeneity and saturating nonlinearity, characteristic of dielectrics and collisional plasmas. The maximum and minimum of the beam width keep decreasing with increase in distance of propagation (or absorption), till the beam becomes very weak and diverges steeply; penetration in an overdense medium also decreases with increasing absorption. Converging beams initially converge and then go in: (i) the oscillatory divergence (ii) self-focusing or (iii) steady divergence mode, depending upon the initial values of beam width and axial irradiance. The maximum penetration in an overdense medium has the highest values for −0.7<(df/dξ)_ξ=0<0.4 and falls sharply, outside these limits.     

Low-velocity pneumatic conveying in horizontal pipe for coarse particles and fine powders

First,the characteristics of low-velocity conveying of particles having different hardness are experimentally investigated in a horizontal pipeline in terms of flow pattern and pressure drop to show that the slug flow can be classified into two types depending on the settling of particles along the pipeline,and the period is small for slug flow without the settled layer,which is called solitary slug flow.The pressure drop for soft particles is shown to be larger than that for hard particles.Then,experimental results are presented on horizontal fluidized-bed conveying of fine powders to show that air release from the top surface of the conveying channel is an important factor for high mass flow rate of particles.     

Optical properties of multilayered Period-Doubling and Rudin-Shapiro porous silicon dielectric heterostructures

To investigate the optical properties in quasi-regular porous-silicon-based dielectric Period-Doubling and Rudin-Shapiro multilayer systems, we study here the reflection of light from these structures. The Period-Doubling and Rudin-Shapiro structures are fabricated in such a way that the optical thickness of each layer is one quarter of 600 and 640 nm respectively. We find that porous silicon Period-Doubling dielectric multilayers could demonstrate the optical properties similar to the classical periodic Febry–Perot interference filters with one or multiple resonant peaks, but with an advantage of having total optical thickness much lesser than the periodic structures. Additionally, light propagation in porous silicon Rudin-Shapiro structures is investigated for the first time, both theoretically and experimentally. The reflectance spectra of the structures exhibit photonic band gaps centered at predetermined wavelengths. In both cases, numerical simulation of light transmission is performed using transfer matrix method.