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.     

One-neutron stripping reactions of <Superscript>11</Superscript>Be and <Superscript>19</Superscript>C on light target

We have calculated the one-neutron absorption cross-section and the longitudinal momentum distribution of the core fragment coming out from the breakup of ¹¹Be and ¹⁹C on ⁹Be target at 63 MeV/A and 88 MeV/A beam energies respectively. The reaction mechanism is treated within the framework of the eikonal approximation. The effective range of the nuclear interaction between the core and the valence neutron within the projectile has been determined by comparing the predicted stripping cross-section with the recently measured one. The effective range for ¹⁹C has been found to be smaller than that for ¹¹Be. It qualitatively indicates that ¹⁹C is slightly more halo than ¹¹Be. The smaller width, predicted as well as measured, of the LMD of ¹⁸C than ¹⁰Be also strengthens this fact. The experimental data concerning the LMD of core fragments have been well represented.      

Effects of E2 and El-E2 Interference on Coulomb Dissociation of 19C

We investigate the effects of higher order multipole transitions, in particular electric quadrupole （E2） and El-E2 interference, on the Coulomb dissociation of 19 C within the framework of the first order eikonal approximation. The sensitivity of the total Coulomb breakup cross section and the longitudinal momentum distribution of the core fragment to these effects are checked. The breakup occurs predominately through the dipole transition and the contribution of E2 transition to the total cross section is found to be within the range from 1 to 3% of that of El. It is further observed that the El-E2 interference term contributes nothing to the integrated cross section. On the other hand, the longitudinal momentum distribution is observed to be insensitive to the E2 transition while the El-E2 interference introduces a small asymmetry in its shape.     

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.