Substituents effect on thermal electrocyclic reaction of dihydroazulene–vinylheptafulvene photoswitch: a DFT study to improve the photoswitch

Thermal cyclization for a series of substituted vinylheptafulvenes (VHFs) to dihydroazulenes (DHAs) was studied at PBE0 method of density functional theory in the gas phase and in the acetonitrile solvent (through PCM). Judicious control of the thermal reaction through substituent is quite necessary to design thermally robust DHA–VHF photoswitches. For most of the substituents, DHA was predicted thermodynamically stable over VHF except for amino (in gas phase and solvent) and hydroxyl (in acetonitrile), where DHA isomers were calculated thermally unstable compared to VHF. Activation barriers for thermal electrocyclic reaction in both media showed positive correlation with Taft’s σ _R values at positions 7 and 5, however, a negative correlation was observed at position 4 and 6. The latter unprecedented behavior is proposed to arise from the delocalization of negative charges on the seven membered ring. Activation barriers for amino-substituted VHFs were generally lower than expected from Taft’s σ _R. A fluoro group at the position 7 was quite effective in imparting very high activation barrier (31.73 kcal mol^?1) for the thermal cyclization in the gas phase. However, in the acetonitrile solvent, the highest activation barriers were observed for electron withdrawing CHO (28.10 kcal mol^?1) and NO₂ (28.13 kcal mol^?1) groups at positions 7.     

A practical acoustical absorption analysis of coir fiber based on rigid frame modeling

An analytical study based on rigid frame model is demonstrated to evaluate the acoustic absorption of coir fiber. Effects of different conditions such as combination of air gap and perforated plate (PP) are studied in this work. Materials used here are treated as rigid rather than elastic, since the flow resistivity of coir fiber is very low. The well-known rigid frame Johnson-Allard equivalent-fluid model is applied to obtain the acoustic impedance of single layer coir fiber. Atalla and Sgard model is employed to estimate the surface impedance of PP. Acoustic transmission approach (ATA) is utilized for adding various consecutive layers in multilayer structure. Models are examined in different conditions such as single layer coir fiber, coir fiber backed with air gap, single layer PP in combination with coir fiber and air gap. Experiments are conducted in impedance tube on normal incidence sound absorption to validate the results. Results from the measurement are found to be in well agreement with the theoretical absorption coefficients. The performance of the rigid frame modeling method is checked more specifically in all conditions, by the mean prediction error rate of normal incidence sound absorption coefficients. Comparison between the measured absorption coefficients and predicted by rigid frame method shows discrepancy lower than 20 and 15% for most of the conditions in the frequency range of 0.2?C1.5 and 1.5?C5 kHz, respectively. Moreover, acoustic absorption of various single and multilayer structures is compared with the simpler empirical methods such as Delany-Bazley and Miki model; and complicated method such as Biot-Allard Model and Allard Transfer Function (TF) method. Comparisons show that the presented method offers a better accuracy of the results than the empirical models. Subsequently, it can provide almost same absorption plot with Biot-Allard model (single layer combination) and TF method (multilayer combination) proving it to be a comprehensively easy and general analytical tool. Therefore, the rigid frame model can be implemented relatively easier than other similar models to analyze the acoustic absorption of coir fiber in most of the conditions.     

Diffraction of an electromagnetic wave from an infinitely long slit in an infinite metallic sheet

The diffraction of anE-polarized and anH-polarized wave by an imperfectly conducting slit (on which impedance boundary conditions are imposed) in an infinite metallic plane is investigated. The two independent problems are solved by using integral transforms, the Wiener-Hopf technique and asymptotic approximations. It is found that the diffracted field consists of the sum of fields produced by the two edges of the planes formed by the slit and a field due to the interaction of the two edges.     

Series solution of hydromagnetic flow and heat transfer with Hall effect in a second grade fluid over a stretching sheet

We examine the problem of flow and heat transfer in a second grade fluid over a stretching sheet [K. Vajravelu, T. Roper, Int. J. Nonlinear Mech. 34, 1031 (1999)]. The equations considered by Vajravelu and Roper [K. Vajravelu, T. Roper, Int. J. Nonlinear Mech. 34, 1031 (1999)], are found to be incorrect in the literature. In this paper, we not only corrected the equation but found a useful analytic solution to this important problem. We also extended the problem for hydromagnetic flow and heat transfer with Hall effect. The explicit analytic homotopy solution for the velocity field and heat transfer are presented. Graphs for the velocity field, skin friction coefficient, and rate of heat transfer are presented. Tables for the skin friction coefficient and rate of heat transfer are also presented. The convergence of the solution is also properly checked and discussed.     

Diffraction of a plane wave by a soft-hard strip

In this paper we have studied the problem of diffraction of a plane wave by a finite soft-hard strip. By using the Fourier transform the boundary value problem is reduced to a matrix Wiener-Hopf equation. Using the matrix factorization of the kernel matrix, the problem is solved for two coupled equations using the Wiener-Hopf technique and the method of steepest descent. It is observed that the diffracted field is the sum of the fields produced by the two edges of the strip and an interaction field. Some graphs showing the effects of various parameters on the field produced by two edges of the strip are also plotted.     

Unsteady MHD flow due to noncoaxial rotations of micropolar fluid and an accelerated disk with partial slip condition

An analysis is carried out to study the magnetohydrodynamic (MHD) flow of an incompressible micropolar fluid. The flow is induced by the noncoaxial rotations of constantly accelerated porous disk and a micropolar fluid. The influence of partial slip on the flow has been taken into consideration. Numerical solution of the governing flow problem is given by means of Newto's method. The important finding in this communication is the effects of partial slip on the velocity and microrotation vector. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Dust-Lower-Hybrid Surface Waves in Classical and Degenerate Plasmas

The dispersion relation for general dust low frequency electrostatic surface waves propagating on an interface between a magnetized dusty plasma region and a vacuum is derived by using specular reflection boundary conditions both in classical and quantum regimes. The frequency limit ω«ω_ci«ω_ce is considered and the dispersion relation for the Dust-Lower-Hybrid Surface Waves (DLHSW's) is derived for both classical and quantum plasma half-space and analyzed numerically. It is shown that the wave behavior changes as the quantum nature of the problem is considered.     

Synchronization of circular restricted three body problem with lorenz hyper chaotic system using a robust adaptive sliding mode controller

In this computational study, we synchronize the Circular Restricted Three Body Problem (CRTBP) with Lorenz Hyper Chaotic System (LHCS) using a Robust Adaptive Sliding Mode Controller (RASMC) together with uncertainties, external disturbances and fully unknown parameters. A simple suitable sliding surface, which includes synchronization errors, is constructed and appropriate update laws are used to tackle the uncertainties, external disturbances and unknown parameters. All simulations to achieve the synchronization for the implemented technique for the two non‐identical systems under consideration are being done using Mathematica. © 2013 Wiley Periodicals, Inc. Complexity 18: 58‐64, 2013