Direct lactonization of α-amino γ,δ-unsaturated carboxylic acid esters via olefin activation: stereo- and regioselective production of homoserine lactone scaffolds having contiguous stereocenters

Triflic acid-mediated stereoselective direct lactonization of a variety of α-amino γ,δ-unsaturated carboxylic acid esters and the construction of new γ-butyrolactone structural motifs are reported. Several α-amino γ,δ-unsaturated carboxylic acid esters underwent stereo- and regioselective 1,5-cyclization and afforded a variety of highly substituted homoserine lactone scaffolds having contiguous stereocenters. The direct lactonization of the chiral α-amino γ,δ-unsaturated carboxylic acid esters with triflic acid led to the enantioselective synthesis of the novel homoserine lactones. A plausible mechanism for the direct lactonization of α-amino γ,δ-unsaturated carboxylic acid esters is presented. The stereochemistry of major isomers 3f, 7a, 7b, and 7d was unambiguously established from the X-ray structure analysis.     

Rayleigh two-point resolution by a semi-transparent and φ-phase annular optical system operating in partially coherent light

A theoretical study has been made to investigate the dependence of the two-point resolution by an aberration free, semi-transparent and φ-phase annular aperture, on the real part of the complex degree of coherence. Rayleigh's criterion in its modified version has been used for the partially coherent optical systems and a comparison between Rayleigh and Sparrow resolution has been made. In order to reveal important information concerning the characteristics of the image, the intensity distribution from two mutually partially coherent point sources has also been evaluated.     

Resolving power of phase annular and annulus apertures illuminated by partially coherent light

A more suitable criterion has been used in assessing the limit of resolution of phase annular and annulus apertures, operating in partially coherent light. In order to show the variation of the limit of resolution with the degree of coherence, the results of some specific examples have been presented graphically.     

Stretch-induced stress patterns and wrinkles in hyperelastic thin sheets

Wrinkles are commonly observed in stretched thin sheets and membranes. This paper presents a numerical study on stretch-induced wrinkling of hyperelastic thin sheets based on nonlinear finite element analyses. The model problem is set up for uniaxial stretching of a rectangular sheet with two clamped ends and two free edges. A two-dimensional stress analysis is performed first under the plane-stress condition to determine stretch-induced stress distribution patterns in the elastic sheets, assuming no wrinkles. As a prerequisite for wrinkling, development of compressive stresses in the transverse direction is found to depend on both the length-to-width aspect ratio of the sheet and the applied tensile strain in the longitudinal direction. A phase diagram is constructed with four different distribution patterns of the stretch-induced compressive stresses, spanning a wide range of aspect ratio and tensile strain. Next, an eigenvalue analysis is performed to find the potential buckling modes of the elastic sheet under the prescribed boundary conditions. Finally, a nonlinear post-buckling analysis is performed to show evolution of stretch-induced wrinkles. In addition to the aspect ratio and tensile strain, it is found that the critical condition for wrinkling and the post-buckling behavior both depend sensitively on the sheet thickness. In general, wrinkles form only when both the magnitude and the distribution area of the compressive stresses are sufficiently large. The wrinkle wavelength decreases with increasing strain, in good agreement with the prediction by a scaling analysis. However, as the tensile strain increases, the wrinkle amplitude first increases and then decreases, eventually flattened beyond a moderately large critical strain, in contrast to the scaling analysis.     

Propagation of partially coherent Gaussian laser beams in graded-index fibres

Using statistical approach the author has solved the equations for the mutual coherence function of partially coherent Gaussian laser beams in graded-index fibres. The expressions for the complex degree of coherence and the intensity distribution have also been shown that the self-focusing length inside the fibre depends upon the degree of coherence. The result have been discussed for both conical and cylindrical guides.     

Cross focusing of two coaxial spatial modes of a single frequency of a laser beam in a nonlinear dielectric

The cross-focusing of two co-axial transverse modes of a laser beam viz. TEM₀₀ and TEM₀₁ modes of the same frequency in a non-linear dielectric has been studied. When the TEM₀₀ mode is stronger than the TEM₀₁ mode, both modes focus on the axis. In the opposite case, defocusing occurs at the axis and energy concentrates in a ring.