Propagation and coherence properties of higher order partially coherent dark hollow beams in turbulence

We formulate and evaluate in terms of graphical outputs, source and receiver plane expressions, the complex degree of coherence, beam size variation and power in bucket performance for higher order partially coherent dark hollow beams propagating in turbulent atmosphere. Our formulation is able to cover square, rectangular, circular, elliptical geometries for dark hollow and flat-topped beams in one single expression. From the graphical outputs of the receiver plane, it is observed that higher order partially coherent dark hollow beams will initially develop an outer ring around a central lobe, but will eventually evolve towards a Gaussian shape as the propagation distance is extended. It is further observed that stronger turbulence levels and greater partial coherence have similar effects on beam profile. During propagation, modulus of complex degree of coherence of partially coherent dark hollow beams appears to rise above that of the source plane values, reaching as high as near unity. Beam size analysis shows that, among the types examined, (nearly) flat-topped beam experiences the least beam expansion. Power in bucket analysis indicates that lowest order square fully coherent dark beam offers the best power capturing.     

Propagation of modified Bessel-Gaussian beams in turbulence

We investigate the propagation characteristics of modified Bessel-Gaussian beams traveling in a turbulent atmosphere. The source beam formulation comprises a Gaussian exponential and the summation of modified Bessel functions. Based on an extended Huygens–Fresnel principle, the receiver plane intensity is formulated and solved down to a double integral stage. Source beam illustrations show that modified Bessel-Gaussian beams, except the lowest order case, will have well-like shapes. Modified Bessel-Gaussian beams with summations will experience lobe slicing and will display more or less the same profile regardless of order content. After propagating in turbulent atmosphere, it is observed that a modified Bessel-Gaussian beam will transform into a Bessel-Gaussian beam. Furthermore it is seen that modified Bessel-Gaussian beams with different Bessel function combinations, but possessing nearly the same profile, will differentiate during propagation. Increasing turbulence strength is found to accelerate the beam transformation toward the eventual Gaussian shape.     

Optimal control of a one-dimensional storage process

We consider the discounted and ergodic optimal control problems related to a one-dimensional storage process. The existence and uniqueness of the corresponding Bellman equation and the regularity of the optimal value is established. Using the Bellman equation an optimal feedback control is constructed. Finally we show that under this optimal control the origin is reachable.This work was supported by the National Science Foundation under Grant No. MCS 8121940.     

Generalized beams in ABCDGH systems

For a generalized beam at the source plane passing through co-located aperture and a propagation path consisting of an off-axis x-y asymmetric ABCDGH system, the receiver plane irradiance expression is derived using the Collins integral. A collection of source beam profiles that are obtainable from the generalized beam formulation are illustrated. Plots are given for viewing the progress of selected generalized beam types along the propagation axis, containing a single thin lens, co-centric and misaligned in the x-direction. The received power falling onto a finite aperture surface is calculated for various misalignment situations.     

Enantioselective Allylic Alkylation Catalyzed by Novel C2‐Symmetric Bisphosphinites

In this article, we present our results concerning new C₂‐symmetric bisphosphinites with a (1R,2R)‐1,2‐bis([1,1′: 3′,1″‐terphenyl]‐5′‐yl)ethane backbone. For the given chirality of the backbone, derivatives with aromatic and aliphatic substituents at the donor P‐atoms were synthesized with moderate yields in a straightforward manner. These compounds were evaluated in the Pd⁰‐catalyzed enantioselective allylic alkylations (up to 67% ee).     

Aromatization of triafulvene and its exocyclic Si,Ge, and Sn derivations by complexation with halogen atoms

The geometries of triafulvene (TF) and its exocyclic Si, Ge, and Sn analogues complexes with F, Cl, Br, and I halogen atoms (TF(X)···Y, X═C, Si, Ge, and Sn; Y═F, Cl, Br, and I) were studied. The complexes were optimized at DFT(B3LYP)/6–311+G(d,p) level of theory. To assess the aromaticity of the considered complexes the geometry-based (HOMA), magnetism-based (NICS), and recently introduced electronic-based (electric field gradient (EFG(0); Shannon aromaticity (SA)) aromaticity indices were employed. The increasing tendency of aromaticity in each complex species was noted as the series of TF(X)···F > TF(X)···Cl > TF(X)···Br > TF((X)···I. Then, the binding energies corrected by basis set super position error (BSSE) were calculated by single point energy calculations at M06-2X/6-311+G(d,p) level. Natural bond orbital (NBO) analysis confirmed that the charge transfer takes place from TF(X) to the halogen atoms. Some topological parameters, within the framework of the quantum theory of atoms in molecules (QTAIM), were also calculated to estimate the aromaticity of the complexes. It was seen that there are some important correlations between the topological parameters and aromaticity indices. In addition the most striking finding was that all the TF(X) molecules are connected with the halogen atoms through Y···C1═C2 (π) noncovalent interaction. This interaction was also investigated through noncovalent interaction (NCI) analysis.     

Bis(p‐nitrobenzoxasulfamato) Complexes of Cadmium(II) and Mercury(II) ‐ Synthesis,Spectra, and X‐Ray Crystal Structures

The reaction of sodium benzoxasulfamate (nbs) with cadmium(II) and mercury(II) sulfate in aqueous solution yield the novel complexes [Cd(nbs)₂(H₂O)₄] (1) and [Hg(nbs)₂(H₂O)₃] ( 2 ), respectively. The complexes were characterized by elemental analyses, IR spectroscopy and X‐ray crystallography. Complex 1 is monomeric and has an octahedral arrangement in which the N‐donor nbs ligands occupy the axial positions, while the water oxygen atoms form the equatorial plane. Complex 2 is polymeric and shows a pentagonal bipyramidal arrangement achieved by the bridging of the HgN₂O₃ units through the weak interaction of the O atoms of the nitro group. The nbs ligands also occupy the axial positions of the pentagonal bipyramid, whereas three water and two nitro oxygen atoms constitute the pentagonal plane. The crystal structure packing in both crystals is achieved by the intermolecular hydrogen bonds involving water hydrogen atoms, nitro and sulfonyl oxygen atoms.