Spectral approach for the soliton and periodic solutions of the nonlinear wave equation

A spectral method that obtains the soliton and periodic solutions to the nonlinear wave equation is presented. The results show that the nonlinear group velocity is a function of the frequency shift as well as of the soliton power. When the frequency shift is a function of time, a solution in terms of the Jacobian elliptic function is obtained. This solution is periodic in nature, and, to generate such an optical pulse train, one must simultaneously amplitude- and frequency-modulate the optical carrier. Finally, we extend the method to include the effect of self-steepening.

Accelerated gradient based diffuse optical tomographic image reconstruction

Purpose: Fast reconstruction of interior optical parameter distribution using a new approach called Broyden-based model iterative image reconstruction (BMOBIIR) and adjoint Broyden-based MOBIIR (ABMOBIIR) of a tissue and a tissue mimicking phantom from boundary measurement data in diffuse optical tomography (DOT). Methods: DOT is a nonlinear and ill-posed inverse problem. Newton-based MOBIIR algorithm, which is generally used, requires repeated evaluation of the Jacobian which consumes bulk of the computation time for reconstruction. In this study, we propose a Broyden approach-based accelerated scheme for Jacobian computation and it is combined with conjugate gradient scheme (CGS) for fast reconstruction. The method makes explicit use of secant and adjoint information that can be obtained from forward solution of the diffusion equation. This approach reduces the computational time many fold by approximating the system Jacobian successively through low-rank updates. Results: Simulation studies have been carried out with single as well as multiple inhomogeneities. Algorithms are validated using an experimental study carried out on a pork tissue with fat acting as an inhomogeneity. The results obtained through the proposed BMOBIIR and ABMOBIIR approaches are compared with those of Newton-based MOBIIR algorithm. The mean squared error and execution time are used as metrics for comparing the results of reconstruction. Conclusions: We have shown through experimental and simulation studies that Broyden-based MOBIIR and adjoint Broyden-based methods are capable of reconstructing single as well as multiple inhomogeneities in tissue and a tissue-mimicking phantom. Broyden MOBIIR and adjoint Broyden MOBIIR methods are computationally simple and they result in much faster implementations because they avoid direct evaluation of Jacobian. The image reconstructions have been carried out with different initial values using Newton, Broyden, and adjoint Broyden approaches. These algorithms work well when the initial guess is close to the true solution. However, when initial guess is far away from true solution, Newton-based MOBIIR gives better reconstructed images. The proposed methods are found to be stable with noisy measurement data. (C) 2011 American Association of Physicists in Medicine. DOI: 10.1118/1.3531572]

Optical and electrical properties of SnS semiconductor crystals grown by physical vapor deposition technique

Tin sulfide (SnS) is a material of interest for use as an absorber in low cost solar cells. Single crystals of SnS were grown by the physical vapor deposition technique. The grown crystals were characterized to evaluate the composition, structure, morphology, electrical and optical properties using appropriate techniques. The composition analysis indicated that the crystals were nearly stoichiometric with Sn-to-S atomic percent ratio of 1.02. Study of their morphology revealed the layered type growth mechanism with low surface roughness. The grown crystals had orthorhombic structure with (0 4 0) orientation. They exhibited an indirect optical band gap of 1.06 eV and direct band gap of 1.21 eV with high absorption coefficient (up to 10(3) cm(-1)) above the fundamental absorption edge. The grown crystals were of p-type with an electrical resistivity of 120 Omega cm and carrier concentration 1.52 x 10(15) cm(-3). Analysis of optical absorption and diffuse reflectance spectra showed the presence of a wide absorption band in the wavelength range 300-1200 nm, which closely matches with a significant part of solar radiation spectrum. The obtained results were discussed to assess the suitability of the SnS crystal for the fabrication of optoelectronic devices. (C) 2011 Elsevier B.V. All rights reserved.

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.

Structural and optical properties of RF sputtered Bi2VO5.5 thin films

Thin films of Bismuth Vanadate Bi2VO5.5 (BiV) have been deposited on amorphous quartz and polycrystalline silicon substrates by r.f. sputtering technique and characterised for their structural and optical properties. The os-deposited films at room temperature are found to be amorphous and transparent over the spectral range of 0.55 mu m to 12 mu m. Post-deposition annealing at 400 degrees C in air shows the formation of the BiV crystalline phase. The optical constants namely refractive index. extinction coefficient and optical bandgap of both amorphous and crystalline films have been determined. The refractive index of the as-deposited film is around 2.4 at 0.7 mu m and drops to 2.26 at 1.56 mu m. The optical bandgap of the material has been determined from the computed values of the absorption coefficients.

Estimation of low-velocity impact damage in laminated composite circular plates using nonlinear finite element analysis

Nonlinear finite element analysis is used for the estimation of damage due to low-velocity impact loading of laminated composite circular plates. The impact loading is treated as an equivalent static loading by assuming the impactor to be spherical and the contact to obey Hertzian law. The stresses in the laminate are calculated using a 48 d.o.f. laminated composite sector element. Subsequently, the Tsai-Wu criterion is used to detect the zones of failure and the maximum stress criterion is used to identify the mode of failure. Then the material properties of the laminate are degraded in the failed regions. The stress analysis is performed again using the degraded properties of the plies. The iterative process is repeated until no more failure is detected in the laminate. The problem of a typical T300/N5208 composite [45 degrees/0 degrees/-45 degrees/90 degrees](s) circular plate being impacted by a spherical impactor is solved and the results are compared with experimental and analytical results available in the literature. The method proposed and the computer code developed can handle symmetric, as well as unsymmetric, laminates. It can be easily extended to cover the impact of composite rectangular plates, shell panels and shells.

The physics and technology of gallium antimonide: An emerging optoelectronic material

Recent advances in nonsilica fiber technology have prompted the development of suitable materials for devices operating beyond 1.55 mu m. The III-V ternaries and quaternaries (AlGaIn)(AsSb) lattice matched to GaSb seem to be the obvious choice and have turned out to be promising candidates for high speed electronic and long wavelength photonic devices. Consequently, there has been tremendous upthrust in research activities of GaSb-based systems. As a matter of fact, this compound has proved to be an interesting material for both basic and applied research. At present, GaSb technology is in its infancy and considerable research has to be carried out before it can be employed for large scale device fabrication. This article presents an up to date comprehensive account of research carried out hitherto. It explores in detail the material aspects of GaSb starting from crystal growth in bulk and epitaxial form, post growth material processing to device feasibility. An overview of the lattice, electronic, transport, optical and device related properties is presented. Some of the current areas of research and development have been critically reviewed and their significance for both understanding the basic physics as well as for device applications are addressed. These include the role of defects and impurities on the structural, optical and electrical properties of the material, various techniques employed for surface and bulk defect passivation and their effect on the device characteristics, development of novel device structures, etc. Several avenues where further work is required in order to upgrade this III-V compound for optoelectronic devices are listed. It is concluded that the present day knowledge in this material system is sufficient to understand the basic properties and what should be more vigorously pursued is their implementation for device fabrication. (C) 1997 American Institute of Physics.

Nonlinear analysis of adhesively bonded lap joints considering viscoplasticity in adhesives

This paper presents nonlinear finite element analysis of adhesively bonded joints considering the elastoviscoplastic constitutive model of the adhesive material and the finite rotation of the joint. Though the adherends have been assumed to be linearly elastic, the yielding of the adhesive is represented by a pressure sensitive modified von Mises yield function. The stress-strain relation of the adhesive is represented by the Ramberg-Osgood relation. Geometric nonlinearity due to finite rotation in the joint is accounted for using the Green-Lagrange strain tensor and the second Piola-Kirchhoff stress tensor in a total Lagrangian formulation. Critical time steps have been calculated based on the eigenvalues of the transition matrices of the viscoplastic model of the adhesive. Stability of the viscoplastic solution and time dependent behaviour of the joints are examined. A parametric study has been carried out with particular reference to peel and shear stress along the interface. Critical zones for failure of joints have been identified. The study is of significance in the design of lap joints as well as on the characterization of adhesive strength. (C) 1999 Elsevier Science Ltd. All rights reserved.

Potassium titanyl phosphate and its isomorphs: Growth, properties, and applications

Potassium titanyl phosphate (KTP) and its isomorphs have received enormous attention in the last 2 decades. In particular, KTP assumes importance due to its large nonlinear optic and electrooptic coefficients together with the broad thermal and angular acceptance for second harmonic generation. This article provides an overview of the material aspects, structural, physical, and chemical properties and device feasibility of the KTP family of crystals. Some of the current areas of research and development along with their significance in understanding the physical properties as well as device applications are addressed. Optical waveguide fabrication processes and characteristics with their relevance to the present-day technology are highlighted. Studies performed so far have enabled us to understand the fundamental aspects of these materials and what needs to be pursued vigorously is the exploitation of their device applications to the maximum extent.

Artifact-free reconstruction from off-axis digital holograms through nonlinear filtering

We present experimental investigation of a new reconstruction method for off-axis digital holographic microscopy (DHM). This method effectively suppresses the object auto-correlation, commonly called the zero-order term, from holographic measurements, thereby suppressing the artifacts generated by the intensities of the two beams employed for interference from complex wavefield reconstruction. The algorithm is based on non-linear filtering, and can be applied to standard DHM setups, with realistic recording conditions. We study the applicability of the technique under different experimental configurations, such as topographic images of microscopic specimens or speckle holograms.

A nonlinear spectral finite element model for analysis of wave propagation in solid with internal friction and dissipation

A geometrically non-linear Spectral Finite Flement Model (SFEM) including hysteresis, internal friction and viscous dissipation in the material is developed and is used to study non-linear dissipative wave propagation in elementary rod under high amplitude pulse loading. The solution to non-linear dispersive dissipative equation constitutes one of the most difficult problems in contemporary mathematical physics. Although intensive research towards analytical developments are on, a general purpose cumputational discretization technique for complex applications, such as finite element, but with all the features of travelling wave (TW) solutions is not available. The present effort is aimed towards development of such computational framework. Fast Fourier Transform (FFT) is used for transformation between temporal and frequency domain. SFEM for the associated linear system is used as initial state for vector iteration. General purpose procedure involving matrix computation and frequency domain convolution operators are used and implemented in a finite element code. Convergnence of the spectral residual force vector ensures the solution accuracy. Important conclusions are drawn from the numerical simulations. Future course of developments are highlighted.

Electrical and magneto-resistance of Co/CNT/epoxy thin film for strain and magnetic field sensing

Cobalt and iron nanoparticles are doped in carbon nanotube (CNT)/polymer matrix composites and studied for strain and magnetic field sensing properties. Characterization of these samples is done for various volume fractions of each constituent (Co and Fe nanoparticles and CNTs) and also for cases when only either of the metallic components is present. The relation between the magnetic field and polarization-induced strain are exploited. The electronic bandgap change in the CNTs is obtained by a simplified tight-binding formulation in terms of strain and magnetic field. A nonlinear constitutive model of glassy polymer is employed to account for (1) electric bias field dependent softening/hardening (2) CNT orientations as a statistical ensemble and (3) CNT volume fraction. An effective medium theory is then employed where the CNTs and nanoparticles are treated as inclusions. The intensity of the applied magnetic field is read indirectly as the change in resistance of the sample. Very small magnetic fields can be detected using this technique since the resistance is highly sensitive to strain. Its sensitivity due to the CNT volume fraction is also discussed. The advantage of this sensor lies in the fact that it can be molded into desirable shape and can be used in fabrication of embedded sensors where the material can detect external magnetic fields on its own. Besides, the stress-controlled hysteresis of the sample can be used in designing memory devices. These composites have potential for use in magnetic encoders, which are made of a magnetic field sensor and a barcode.

Geometrically Nonlinear Dynamics of Composite Four-Bar Mechanisms

This work intends to demonstrate the importance of geometrically nonlinear crosssectional analysis of certain composite beam-based four-bar mechanisms in predicting system dynamic characteristics. All component bars of the mechanism are made of fiber reinforced laminates and have thin rectangular cross-sections. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. We restrict ourselves to linear materials with small strains within each elastic body (beam). Each component of the mechanism is modeled as a beam based on geometrically nonlinear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and nonlinear 1-D analyses along the four beam reference curves. For thin rectangular cross-sections considered here, the 2-D cross-sectional nonlinearity is overwhelming. This can be perceived from the fact that such sections constitute a limiting case between thin-walled open and closed sections, thus inviting the nonlinear phenomena observed in both. The strong elastic couplings of anisotropic composite laminates complicate the model further. However, a powerful mathematical tool called the Variational Asymptotic Method (VAM) not only enables such a dimensional reduction, but also provides asymptotically correct analytical solutions to the nonlinear cross-sectional analysis. Such closed-form solutions are used here in conjunction with numerical techniques for the rest of the problem to predict multi-body dynamic responses, more quickly and accurately than would otherwise be possible. The analysis methodology can be viewed as a three-step procedure: First, the cross-sectional properties of each bar of the mechanism is determined analytically based on an asymptotic procedure, starting from Classical Laminated Shell Theory (CLST) and taking advantage of its thin strip geometry. Second, the dynamic response of the nonlinear, flexible fourbar mechanism is simulated by treating each bar as a 1-D beam, discretized using finite elements, and employing energy-preserving and -decaying time integration schemes for unconditional stability. Finally, local 3-D deformations and stresses in the entire system are recovered, based on the 1-D responses predicted in the previous step. With the model, tools and procedure in place, we shall attempt to identify and investigate a few problems where the cross-sectional nonlinearities are significant. This will be carried out by varying stacking sequences and material properties, and speculating on the dominating diagonal and coupling terms in the closed-form nonlinear beam stiffness matrix. Numerical examples will be presented and results from this analysis will be compared with those available in the literature, for linear cross-sectional analysis and isotropic materials as special cases.

Optical and structural properties of TiO2 films deposited by Sol-Gel technique

TiO2 thin films were prepared by sol gel method. The structural investigations performed by means of X- ray diffraction (XRD) technique, Scanning electronic microscopy (SEM) showed the shape structure at T=600°C. The optical constants of the deposited film were obtained from the analysis of the experimental recorded transmittance spectral data over the wavelengths range 200-3000 nm. The values of some important parameters (refractive index n, dielectric constant ε ∞ and thickness d), and the third order optical nonlinear susceptibility χ(3) of TiO2 film are determined from these spectra. It has been found that the dispersion data obey the single oscillator relation of the Wemple-DiDomenico model, from which the dispersion parameters and high – frequency dielectric constant were determined. The estimation of the corresponding band gap Eg , χ (3) and ε ∞ are 2.57 eV, 0.021 × 10-10 esu and 5.20,respectively.

Ultrasound modulated optical tomography: Young's modulus of the insonified region from measurement of natural frequency of vibration

We demonstrate a method to recover the Young's modulus (E) of a tissue-mimicking phantom from measurements of ultrasound modulated optical tomography (UMOT). The object is insonified by a dualbeam, confocal ultrasound transducer (US) oscillating at frequencies f(0) and f(0) + Delta f and the variation of modulation depth (M) in the autocorrelation of light traversed through the focal region of the US transducer against Delta f is measured. From the dominant peaks observed in the above variation, the natural frequencies of the insonified region associated with the vibration along the US transducer axis are deduced. A consequence of the above resonance is that the speckle fluctuation at the resonance frequency has a higher signal-to-noise to ratio (SNR). From these natural frequencies and the associated eigenspectrum of the oscillating object, Young's modulus (E) of the material in the focal region is recovered. The working of this method is confirmed by recovering E in the case of three tissue-mimicking phantoms of different elastic modulus values. (C) 2011 Optical Society of America