Second-order boundary-layer effects for the unsteady laminar incompressible three-dimensional stagnation-point flow

All the second-order boundary-layer effects on the unsteady laminar incompressible flow at the stagnation-point of a three-dimensional body for both nodal and saddle point regions have been studied. It has been assumed that the free-stream velocity, wall temperature and mass transfer vary arbitrarily with time. The effect of the Prandtl number has been taken into account. The partial differential equations governing the flow have been derived for the first time and then solved numerically unsteady free-stream velocity distributions, the nature of the using an implicit finite-difference scheme. It is found that the stagnation point and the mass transfer strongly affect the skin friction and heat transfer whereas the effects of the Prandtl number and the variation of the wall temperature with time are only on the heat transfer. The skin friction due to the combined effects of first- and second-order boundary layers is less than the skin friction due to, the first-order boundary layers whereas the heat transfer has the opposite behaviour. Suction increases the skin friction and heat transfer but injection does the opposite

Nonlinear static and dynamic damped response of a composite rectangular plate resting on a two-parameter elastic foundation

Nonlinear static and dynamic response analyses of a clamped. rectangular composite plate resting on a two-parameter elastic foundation have been studied using von Karman's relations. Incorporating the material damping, the governing coupled, nonlinear partial differential equations are obtained for the plate under step pressure pulse load excitation. These equations have been solved by a one-term solution and by applying Galerkin's technique to the deflection equation. This yields an ordinary nonlinear differential equation in time. The nonlinear static solution is obtained by neglecting the time-dependent variables. Thc nonlinear dynamic damped response is obtained by applying the ultraspherical polynomial approximation (UPA) technique. The influences of foundation modulus, shear modulus, orthotropy, etc. upon the nonlinear static and dynamic responses have been presented.

Highly Efficient and Thermally Stable Second-Order Nonlinear Optical Chromophores and Electrooptic Polymers

Organic polymeric electro-optic (E-O) materials have attracted significant attention because of their potential use as fast and efficient components of integrated photonic devices (1,2). However, the practical application of these materials in optical devices is somewhat limited by the stringent material requirements imposed by the device design, fabrication processes and operating environments. Among the various material requirements, the most notable ones are large electro-optic coefficients (r(33)) and high thermal stability (3). The design of poled polymeric materials with high electro-optic activity (r(33)) involves the optimization of the percent incorporation of efficient (large beta mu) second order nonlinear optical (NLO) chromophores into the polymer matrices and the effective creation of poling-induced non-centrosymmetric structures. The factors that affect the material stability are a) the inherent thermal stability of the NLO chromophores, b) the chemical stability of the NLO chromophores during the polymer processing conditions, and c) the long-term dipolar alignment stability at high temperatures. Although considerable progress has been made in achieving these properties (4), organic polymeric materials suitable for practical E-O device applications are yet to be developed. This chapter highlights some of our approaches in the optimization of molecular and material nonlinear optical and thermal properties.

A new class of three dimensional D-pi-A trigonal cryptand derivatives for second-order nonlinear optics

Synthesis, crystal structures, linear and nonlinear optical properties of tris D-pi-A cryptand derivatives with C-3 symmetry are reported. Three fold symmetry inherent in the cryptand molecules has been utilized for designing these molecules. Molecular nonlinearities have been measured by hyper-Rayleigh scattering (HRS) experiments. Among the compounds studied, L-1 adopts non-centrosymmetric crystal structure. Compounds L-1, L-2, L-3 and L-4 show a measurable SHG powder signal. These molecules are more isotropic and have significantly higher melting points than the classical p-nitroaniline based dipolar NLO compounds, making them useful for further device applications. Besides, different acceptor groups can be attached to the cryptand molecules to modulate their NLO properties.

Aryl monosulphides and symmetrical disulphides based second order nonlinear optical chromophores with transparency in the visible

A series of aryl monosulphides and disulphides have been synthesized and characterized. Their molecular hyperpolarizability (beta) has been measured in solution with the hyper-Rayleigh Scattering technique and also calculated by semiempirical AMI method. The trend in the observed and calculated values of first hyperpolarizability of these compounds has been found to be in good agreement. These compounds show moderate P values and excellent transparency in the visible region.

Optimum design of a helicopter rotor for low vibration using aeroelastic analysis and response surface methods

An aeroelastic analysis based on finite elements in space and time is used to model the helicopter rotor in forward flight. The rotor blade is represented as an elastic cantilever beam undergoing flap and lag bending, elastic torsion and axial deformations. The objective of the improved design is to reduce vibratory loads at the rotor hub that are the main source of helicopter vibration. Constraints are imposed on aeroelastic stability, and move limits are imposed on the blade elastic stiffness design variables. Using the aeroelastic analysis, response surface approximations are constructed for the objective function (vibratory hub loads). It is found that second order polynomial response surfaces constructed using the central composite design of the theory of design of experiments adequately represents the aeroelastic model in the vicinity of the baseline design. Optimization results show a reduction in the objective function of about 30 per cent. A key accomplishment of this paper is the decoupling of the analysis problem and the optimization problems using response surface methods, which should encourage the use of optimization methods by the helicopter industry. (C) 2002 Elsevier Science Ltd. All rights reserved.

Synthesis and characterization of mono- and bis-D-pi-A cryptand derivatives for second-order nonlinear optics and its modulation with different metal ion inputs

Two new classes of mono- and bis-D-pi-A cryptand derivatives with a flexible and a rigid cryptand core have been synthesized. The linear and nonlinear optical properties of these molecules are probed. The three dimensional cavity of the cryptand moiety has been utilized to modulate the SHG intensity to different extents in solution with metal ion inputs such as Ni-II,Cu-II,Zn-II, and Cd-II. We also report that decomplexation events can be used to reversibly modulate their NLO responses.

Unsymmetrical aryl disulfides with excellent transparency in the visible region for second order nonlinear optics

Several unsymmetrically substituted aromatic donor acceptor disulfides have been synthesized and analysed for their second order nonlinear optical properties. These molecules exhibit moderately high first hyperpolarizability (beta) with excellent transparency in the visible region. Most of the unsymmetrical disulfides have a cut-off wavelength below 420 nm. Calculations show that the molecules have an asymmetric charge distribution around the disulfide bond which is responsible for their high beta values. These results provide motivation for the design and synthesis of nonlinear optical chromophores with multiple disulfide bonds for large second order nonlinearity and excellent visible transparency.

The x¿n-x Plane for Analysis of Certain Second-Order Nonlinear Systems

Analysis of certain second-order nonlinear systems, not easily amenable to the phase-plane methods, and described by either of the following differential equations xÿn-2ÿ+ f(x)xÿ2n+g(x)xÿn+h(x)=0 ÿ+f(x)xÿn+h(x)=0 n≫0 can be effected easily by drawing the entire portrait of trajectories on a new plane; that is, on one of the xÿnÿx planes. Simple equations are given to evaluate time from a trajectory on any of these n planes. Poincaré's fundamental phase plane xÿÿx is conceived of as the simplest case of the general xÿnÿx plane.

Second order transport from anomalies

We study parity odd transport at second order in derivative expansion for a non-conformal charged fluid. We see that there are 27 parity odd transport coefficients, of which 12 are non-vanishing in equilibrium. We use the equilibrium partition function method to express 7 of these in terms of the anomaly, shear viscosity, charge diffusivity and thermodynamic functions. The remaining 5 are constrained by 3 relations which also involve the anomaly. We derive Kubo formulae for 2 of the transport coefficients and show these agree with that derived from the equilibrium partition function.

Transitory second-order reciprocal connection for two surfaces in point contact

This paper investigates the instantaneous spatial higher pair to lower pair substitute-connection which is kinematically equivalent up to acceleration analysis for two smooth surfaces in point contact. The existing first-order equivalent substitute-connection consisting of a Hooke's joint (U-joint) and a spherical joint (S-joint) connected by an additional link is extended up to second-order. A two step procedure is chalked out for achieving this equivalence. First, the existing method is employed for velocity equivalence. In the second step, the two centers of substitution are obtained as a conjugate relationship involving the principal normal curvatures of the surfaces at the contact point and the screw coordinates of the instantaneous screw axis (ISA) of the first-order relative motion. Unlike the classical planar replacement, this particular substitution cannot be done by merely examining the profiles of the contacting surfaces. An illustrative example of a three-link direct-contact mechanism is presented. (C) 2014 Elsevier Ltd. All rights reserved.

Micro-satellite angular rate estimation using second-order sliding mode observer

Development of computationally efficient and accurate attitude rate estimation algorithm using low-cost commercially available star sensor arrays and processing unit for micro-satellite mission is presented. Our design reduces the computational load of least square (LS)-based rate estimation method while maintaining the same accuracy compared to other rate estimation approaches. Furthermore, rate estimation accuracy is improved by using recently developed fast and accurate second-order sliding mode observer (SOSMO) scheme. It also gives robust estimation in the presence of modeling uncertainties, unknown disturbances, and measurement noise. Simulation study shows that rate estimation accuracy achieved by our LS-based method is comparable with other methods for a typical commercially available star sensor array. The robustness analysis of SOSMO with respect to measurement noise is also presented in this paper. Simulation test bench for a practical scenario of satellite rate estimation uses moment-of-inertia variation and environmental disturbances affecting a typical micro-satellite at 500km circular orbit. Comparison studies of SOSMO with 1-SMO and pseudo-linear Kalman filter show that satisfactory estimation accuracy is achieved by SOSMO.

Studies in Nonlinear Optical Materials: Structure of Methyl 2-(4-Ethyl-5-methyl- 2-thioxo-2,3-dihydro-l,3-thiazol- 3-yl) propionate

CIoH15NO282, Mr=245"0, orthorhombic, P21212 ~, a = 6.639 (2), b = 8.205 (2), c = 22.528(6)A, V= I227.2(6)A 3, z=4, Dm= 1.315, Dx= 1.326gem -3, MoKa, 2=0.7107A, 12= 3.63 cm -1, F(000) = 520, T= 293 K, R = 0.037 for 1115 significant reflections. The second-harmonicgeneration (SHG) efficiency of this compound is only 1/10th of the urea standard. The observed low second-order nonlinear response may be attributed to the unfavourable packing of the molecules in the crystal lattice.

Studies in nonlinear optical materials: structure of di-2-menthyl 2-(N,N'-dimethyl-2-imidazolidinylidene)malonate monohydrate

C28H48N2Oa.H2 O, Mr=494.7, orthorhombic,P2~2~2~, a = 7.634 (2), b = 11.370 (2), c=34. 167 (4) A, V = 2966 (2) A 3, Z = 4, D m = 1.095,D x -- 1. 108 g cm -3, Mo Kct, 2 -- 0.7107 ,/k, ~ =0.43 cm -~, F(000) = 1088.0, T= 293 K, R = 0.061 for 1578 significant reflections. The second-harmonicgeneration (SHG) efficiency of this compound is negligible (1/100th of the urea standard). The observed low second-order nonlinear response has been attributed to the unfavourable packing of the molecules in the crystal lattice.

Robust design of multiple trailing edge flaps for helicopter vibration reduction: A multi-objective bat algorithm approach

The objective of this study is to determine an optimal trailing edge flap configuration and flap location to achieve minimum hub vibration levels and flap actuation power simultaneously. An aeroelastic analysis of a soft in-plane four-bladed rotor is performed in conjunction with optimal control. A second-order polynomial response surface based on an orthogonal array (OA) with 3-level design describes both the objectives adequately. Two new orthogonal arrays called MGB2P-OA and MGB4P-OA are proposed to generate nonlinear response surfaces with all interaction terms for two and four parameters, respectively. A multi-objective bat algorithm (MOBA) approach is used to obtain the optimal design point for the mutually conflicting objectives. MOBA is a recently developed nature-inspired metaheuristic optimization algorithm that is based on the echolocation behaviour of bats. It is found that MOBA inspired Pareto optimal trailing edge flap design reduces vibration levels by 73% and flap actuation power by 27% in comparison with the baseline design.