A note on a class of singular integro-differential equations

A simplified analysis is employed to handle a class of singular integro-differential equations for their solutions

Integrated optics � technology and applications

The emergence of optoelectronics and photonics as viable alternatives to electronics in many key areas of engineering relevance is indeed significant. This paper presents a tutorial review of integrated optics � a technologically important development in photonics. Materials, processes, device technology and applications are highlighted.

Generation of novel materials for nonlinear optics: Analysis of hydrogen-bonded networks in haloaromatic and aliphatic amine-tartrate complexes

Five tartrate-amine complexes have been studied in terms of crystal packing and hydrogen bonding frameworks. The salts are 3-bromoanilinium-L-monohydrogen tartrate 1, 3-fluoroanilinium-D-dibenzoylmonohydrogen tartrate 2, 1-nonylium-D-dibenzoylmonohydrogen tartrate 3, 1 -decylium-D-dibenzoylmonohydrogen tartrate 4, and 1,4-diaminobutanium-D-dibenzoyl tartrate trihydrate 5. The results indicate that there are no halogen-halogen interactions in the haloaromatic-tartrate complexes. The anionic framework allows accomodation of ammonium ions that bear alkyl chain residues of variable lengths. The long chain amines in these structures remain disordered while the short chain amines form multidirectional hydrogen bonds on either side.

Systematic crystallographic investigation of hydrogen-bonded networks involving monohydrogen tartrate-amine complexes: Potential materials for nonlinear optics

Crystal structures of six binary salts involving aromatic amines as cations and hydrogen tartrates as anions are presented. The materials are 2,6-xylidinium-L-monohydrogen tartrate monohydrate, C12H18O6.5N, P22(1)2(1), a = 7.283(2) Angstrom, b = 17.030(2) Angstrom, c = 22.196(2) Angstrom, Z = 8; 2,6-xylidinium-D-dibenzoyl monohydrogen tartrate, C26H25O8N, P2(1), a = 7.906(1) Angstrom, b = 24.757(1) Angstrom, c = 13.166(1) Angstrom, beta = 105.01(1)degrees, Z = 4; 2,3-xylidinium-D-dibenzoyl monohydrogen tartrate monohydrate, C26H26O8.5N, P2(1), a = 7.837(1) Angstrom, b = 24.488(1) Angstrom, c = 13.763(1) Angstrom, beta = 105.69(1)degrees, Z = 4; 2-toluidinium-D-dibenzoyl monohydrogen tartrate, C25H23O8N, P2(1)2(1)2(1), a = 13.553(2) Angstrom, b = 15.869(3) Angstrom, c = 22.123(2) Angstrom, Z = 8; 3-toluidinium-D-dibenzoyl monohydrogen tartrate (1:1), C25H23O8N, P1, a = 7.916(3) Angstrom, b = 11.467(6) Angstrom, c = 14.203(8) Angstrom, alpha = 96.44(4)degrees, beta = 98.20(5)degrees, = 110.55(5)degrees, Z = 2; 3-toluidinium-D-dibenzoyl tartrate dihydrate (1:2), C32H36O10N, P1, a = 7.828(3) Angstrom, b = 8.233(1) Angstrom, c = 24.888(8) Angstrom, alpha = 93.98 degrees, beta = 94.58(3)degrees, = 89.99(2)degrees, Z = 2. An analysis of the hydrogen-bonding schemes in terms of crystal packing, stoichiometric variations, and substitutional variations in these materials provides insights to design hydrogen-bonded networks directed toward the engineering of crystalline nonlinear optical materials.

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.

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.

A near-singular, flexure jointed, moment sensitive Stewart platform based fore-torque sensor

A force-torque sensor capable of accurate measurement of the three components of externally applied forces and moments is required for force control in robotic applications involving assembly operations. The goal in this paper is to design a Stewart platform based force torque sensor at a near-singular configuration sensitive to externally applied moments. In such a configuration, we show an enhanced mechanical amplification of leg forces and thereby higher sensitivity for the applied external moments. In other directions, the sensitivity will be that of a normal load sensor determined by the sensitivity of the sensing element and the associated electronic amplification, and all the six components of the force and torque can be sensed. In a sensor application, the friction, backlash and other non-linearities at the passive spherical joints of the Stewart platform will affect the measurements in unpredictable ways. In this sensor, we use flexural hinges at the leg interfaces of the base and platform of the sensor. The design dimensions of the flexure joints in the sensor have been arrived at using FEA. The sensor has been fabricated, assembled and instrumented. It has been calibrated for low level loads and is found to show linearity and marked sensitivity to moments about the three orthogonal X, Y and Z axes. This sensor is compatible for usage as a wrist sensor for a robot under development at ISRO Satellite Centre.

Fracture analysis of concrete using singular fractal functions with lattice beam network and confirmation with acoustic emission study

In the present study singular fractal functions (SFF) were used to generate stress-strain plots for quasibrittle material like concrete and cement mortar and subsequently stress-strain plot of cement mortar obtained using SFF was used for modeling fracture process in concrete. The fracture surface of concrete is rough and irregular. The fracture surface of concrete is affected by the concrete's microstructure that is influenced by water cement ratio, grade of cement and type of aggregate 11-41. Also the macrostructural properties such as the size and shape of the specimen, the initial notch length and the rate of loading contribute to the shape of the fracture surface of concrete. It is known that concrete is a heterogeneous and quasi-brittle material containing micro-defects and its mechanical properties strongly relate to the presence of micro-pores and micro-cracks in concrete 11-41. The damage in concrete is believed to be mainly due to initiation and development of micro-defects with irregularity and fractal characteristics. However, repeated observations at various magnifications also reveal a variety of additional structures that fall between the `micro' and the `macro' and have not yet been described satisfactorily in a systematic manner [1-11,15-17]. The concept of singular fractal functions by Mosolov was used to generate stress-strain plot of cement concrete, cement mortar and subsequently the stress-strain plot of cement mortar was used in two-dimensional lattice model [28]. A two-dimensional lattice model was used to study concrete fracture by considering softening of matrix (cement mortar). The results obtained from simulations with lattice model show softening behavior of concrete and fairly agrees with the experimental results. The number of fractured elements are compared with the acoustic emission (AE) hits. The trend in the cumulative fractured beam elements in the lattice fracture simulation reasonably reflected the trend in the recorded AE measurements. In other words, the pattern in which AE hits were distributed around the notch has the same trend as that of the fractured elements around the notch which is in support of lattice model. (C) 2011 Elsevier Ltd. All rights reserved.

Time-dependent transitions with time-space noncommutativity and its implications in quantum optics

We study the time-dependent transitions of a quantum-forced harmonic oscillator in noncommutative R(1,1) perturbatively to linear order in the noncommutativity theta. We show that the Poisson distribution gets modified, and that the vacuum state evolves into a `squeezed' state rather than a coherent state. The time evolutions of uncertainties in position and momentum in vacuum are also studied and imply interesting consequences for modeling nonlinear phenomena in quantum optics.

An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order

This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded linear triangular (T3) elements and a special layer of five-noded singular triangular elements (sT5) connected to the singular-point of the stress field. The sT5 element has an additional node on each of the two edges connected to the singular-point. It allows us to represent simple and efficient enrichment with desired terms for the displacement field near the singular-point with the satisfaction of partition-of-unity property. The stiffness matrix of the discretized system is then obtained using the assumed displacement values (not the derivatives) over smoothing domains associated with the edges of elements. An adaptive procedure for the sES-FEM is proposed to enhance the quality of the solution with minimized number of nodes. Several numerical examples are provided to validate the reliability of the present sES-FEM method. (C) 2012 Elsevier B.V. All rights reserved.

Design of S bend waveguides for delay line applications in integrated optics

A novel scheme for generation of phase using optical delay lines is proposed. The design of the optical components in the circuit which includes the S bend waveguides and straight waveguide couplers are very important for integrated optics. Beam propagation Method and MatLab is employed for the design.

Joint data detection and dominant singular mode estimation in time varying reciprocal MIMO systems

This paper proposes an algorithm for joint data detection and tracking of the dominant singular mode of a time varying channel at the transmitter and receiver of a time division duplex multiple input multiple output beamforming system. The method proposed is a modified expectation maximization algorithm which utilizes an initial estimate to track the dominant modes of the channel at the transmitter and the receiver blindly; and simultaneously detects the un known data. Furthermore, the estimates are constrained to be within a confidence interval of the previous estimate in order to improve the tracking performance and mitigate the effect of error propagation. Monte-Carlo simulation results of the symbol error rate and the mean square inner product between the estimated and the true singular vector are plotted to show the performance benefits offered by the proposed method compared to existing techniques.