Stable numerical schemes for a partly convolutional partial integro-differential equation

A model partial integro-differential operator (PIDO) that contains both local and nonlocal diffusion operators is considered in this article. This type of operators come in modeling various scientific and financial engineering problems. In most cases, people use finite difference schemes to generate solutions of such model problems. We compare and analyze stability and accuracy of two such finite difference schemes. We first present a discrete analogue of the PIDO and then approximate the semi-discrete time dependent problem using two different one step methods and show the stability conditions and the accuracy of the schemes. We use the Fourier transforms throughout our analysis.     

Shear deformation plate continua of large double layered space structures

A simple method is presented to model large rigid-jointed lattice structures as continuous elastic media with couple stresses using energy equivalence. In our analysis the transition from the discrete system to the continuous media is achieved by expanding the displacements and the rotations of the nodal points in a Taylor series about a suitable chosen origin. The strain energy of the continuous media with couple stresses is then specialized to obtain shear deformation plate continua. Equivalent continua for single layered grids, double layered grids and three-dimensional lattices are then obtained.     

Generation of femtosecond pulses at 1350 nm by Cerenkov radiation in higher-order-mode fiber

We demonstrate a method of generating short pulses at 1350 nm by exciting Cerenkov radiation in a higher-order-mode fiber with a 1064 nm femtosecond fiber laser. We measure a 106 fs, 0.66 nJ output pulse. Cerenkov radiation in fibers allows for energy transfer between a soliton and a dispersive wave, providing an effective and engineerable platform to shift the wavelength of a femtosecond source. With appropriate design of the higher-order-mode fiber, this method of generating short pulses at 1350 nm can be extended to other wavelengths and to higher pulse energies.     

Finite difference scheme for large-deflection analysis of non-prismatic cantilever beams subjected to different types of continuous and discontinuous loadings

An efficient scheme, called quasi-linearization finite differences, is developed for large-deflection analysis of prismatic and non-prismatic slender cantilever beams subjected to various types of continuous and discontinuous external variable distributed and concentrated loads in horizontal and vertical global directions. Simultaneous equations of highly nonlinear and linear terms are obtained when casting the derived exact highly nonlinear governing differential equation using central finite differences on the nodes along the beam. A quasi-linearization scheme is used to solve these equations based on successive corrections of the nonlinear terms in the simultaneous equations. The nonlinear terms in the simultaneous equations are assumed constant during each correction (iteration). Several representative numerical examples of prismatic and non-prismatic slender cantilever beams with different loading conditions are analyzed to illustrate the merits of the adopted numerical scheme as well as its validity, accuracy and efficiency. The results of the present scheme are checked using large-displacement finite element analysis by the MSC/NASTRAN program. A comparison between the present secheme, MSC/NASTRAN and available results from the literature reveals excellent agreement. The advantage of the new scheme is that the load can be applied in one step with few iterations (3–6 iterations).     

Action of Hydrazines on 2‐(2‐Oxindolin‐3‐ylidene)malononitrile, (E,Z)‐Ethyl 2‐cyano‐2‐(2‐oxindolin‐3‐ylidene)acetate and Isatin‐β‐thiosemicarbazone as a Source of Spiro Indoline‐pyrazole Systems

2‐(2‐Oxindolin‐3‐ylidene)malononitrile ( 1a ) or (E,Z)‐ethyl 2‐cyano‐2‐(2‐oxindolin‐3‐ylidene)acetate ( 1b ) or isatin‐β‐thiosemicarbazone ( 1c ) undergoes reactions with prototype hydrazine hydrate itself and some of its simple congeners to give hydrazone derivatives bearing indoline‐2‐one moiety ( 2 ). The hydrazone derivatives ( 2 ) when heated with acetyl acetone or ethyl acetoacetate in dry pyridine afforded the spiro indoline derivatives ( 3a , 3b ). Also, cinnoline derivative ( 9 ) is obtained by action of hydrazine hydrate on the N‐acetyl derivative of ( 6a ). The structures of the newly synthesized compounds were evaluated by IR, ¹H‐NMR spectroscopy, mass spectra and elemental analyses.