Nonlinear Differential Games-Based Impact-Angle-Constrained Guidance Law

The problem of intercepting a maneuvering target at a prespecified impact angle is posed in nonlinear zero-sum differential games framework. A feedback form solution is proposed by extending state-dependent Riccati equation method to nonlinear zero-sum differential games. An analytic solution is obtained for the state-dependent Riccati equation corresponding to the impact-angle-constrained guidance problem. The impact-angle-constrained guidance law is derived using the states line-of-sight rate and projected terminal impact angle error. Local asymptotic stability conditions for the closed-loop system corresponding to these states are studied. Time-to-go estimation is not explicitly required to derive and implement the proposed guidance law. Performance of the proposed guidance law is validated using two-dimensional simulation of the relative nonlinear kinematics as well as a thrust-driven realistic interceptor model.

Comparison of a priori and a posteriori meshes for singularly perturbed nonlinear parameterized problems

This paper deals with the adaptive mesh generation for singularly perturbed nonlinear parameterized problems with a comparative research study on them. We propose an a posteriori error estimate for singularly perturbed parameterized problems by moving mesh methods with fixed number of mesh points. The well known a priori meshes are compared with the proposed one. The comparison results show that the proposed numerical method is highly effective for the generation of layer adapted a posteriori meshes. A numerical experiment of the error behavior on different meshes is carried out to highlight the comparison of the approximated solutions. (C) 2015 Elsevier B.V. All rights reserved.

Nonlinear control of an air-breathing engine including its validation with vehicle guidance

An implementable nonlinear control design approach is presented for a supersonic air-breathing ramjet engine. The primary objective is to ensure that the thrust generated by the engine tracks the commanded thrust without violating the operational constraints. An important constraint is to manage the shock wave location in the intake so that it neither gets detached nor gets too much inside the intake. Both the objectives are achieved by regulating the fuel flow to the combustion chamber and by varying the throat area of the nozzle simultaneously. The design approach accounts for the nonlinear cross-coupling effects and nullifies those. Also, an extended Kalman filter has been used to filter out the sensor and process noises as well as to make the states available for feedback. Furthermore, independent control design has been carried out for the actuators. To test the performance of the engine for a realistic flight trajectory, a representative trajectory is generated through a trajectory optimization process, which is augmented with a newly-developed finite-time state dependent Riccati equation technique for nullifying the perturbations online. Satisfactory overall performance has been obtained during both climb and cruise phases. (C) 2015 Elsevier Masson SAS. All rights reserved.

Demodulation of Narrowband Speech Spectrograms Using the Riesz Transform

We propose a two-dimensional (2-D) multicomponent amplitude-modulation, frequency-modulation (AM-FM) model for a spectrogram patch corresponding to voiced speech, and develop a new demodulation algorithm to effectively separate the AM, which is related to the vocal tract response, and the carrier, which is related to the excitation. The demodulation algorithm is based on the Riesz transform and is developed along the lines of Hilbert-transform-based demodulation for 1-D AM-FM signals. We compare the performance of the Riesz transform technique with that of the sinusoidal demodulation technique on real speech data. Experimental results show that the Riesz-transform-based demodulation technique represents spectrogram patches accurately. The spectrograms reconstructed from the demodulated AM and carrier are inverted and the corresponding speech signal is synthesized. The signal-to-noise ratio (SNR) of the reconstructed speech signal, with respect to clean speech, was found to be 2 to 4 dB higher in case of the Riesz transform technique than the sinusoidal demodulation technique.

Lower-Bound Axisymmetric Formulation for Geomechanics Problems Using Nonlinear Optimization

A lower-bound limit analysis formulation, by using two-dimensional finite elements, the three-dimensional Mohr-Coulomb yield criterion, and nonlinear optimization, has been given to deal with an axisymmetric geomechanics stability problem. The optimization was performed using an interior point method based on the logarithmic barrier function. The yield surface was smoothened (1) by removing the tip singularity at the apex of the pyramid in the meridian plane and (2) by eliminating the stress discontinuities at the corners of the yield hexagon in the pi-plane. The circumferential stress (sigma(theta)) need not be assumed. With the proposed methodology, for a circular footing, the bearing-capacity factors N-c, N-q, and N-gamma for different values of phi have been computed. For phi = 0, the variation of N-c with changes in the factor m, which accounts for a linear increase of cohesion with depth, has been evaluated. Failure patterns for a few cases have also been drawn. The results from the formulation provide a good match with the solutions available from the literature. (C) 2014 American Society of Civil Engineers.

Nonlinear mode coupling and internal resonances in MoS2 nanoelectromechanical system

Atomically thin two dimensional (2D) layered materials have emerged as a new class of material for nanoelectromechanical systems (NEMS) due to their extraordinary mechanical properties and ultralow mass density. Among them, graphene has been the material of choice for nanomechanical resonator. However, recent interest in 2D chalcogenide compounds has also spurred research in using materials such as MoS2 for the NEMS applications. As the dimensions of devices fabricated using these materials shrink down to atomically thin membrane, strain and nonlinear effects have become important. A clear understanding of the nonlinear effects and the ability to manipulate them is essential for next generation sensors. Here, we report on all electrical actuation and detection of few-layer MoS2 resonator. The ability to electrically detect multiple modes and actuate the modes deep into the nonlinear regime enables us to probe the nonlinear coupling between various vibrational modes. The modal coupling in our device is strong enough to detect three distinct internal resonances. (C) 2015 AIP Publishing LLC.

A modified approach to numerical solution of Fredholm integral equations of the second kind

A modified approach to obtain approximate numerical solutions of Fredholin integral equations of the second kind is presented. The error bound is explained by the aid of several illustrative examples. In each example, the approximate solution is compared with the exact solution, wherever possible, and an excellent agreement is observed. In addition, the error bound in each example is compared with the one obtained by the Nystrom method. It is found that the error bound of the present method is smaller than the ones obtained by the Nystrom method. Further, the present method is successfully applied to derive the solution of an integral equation arising in a special Dirichlet problem. (C) 2015 Elsevier Inc. All rights reserved.

Wave propagation in a 2D nonlinear structural acoustic waveguide using asymptotic expansions of wavenumbers

Nonlinear acoustic wave propagation in an infinite rectangular waveguide is investigated. The upper boundary of this waveguide is a nonlinear elastic plate, whereas the lower boundary is rigid. The fluid is assumed to be inviscid with zero mean flow. The focus is restricted to non-planar modes having finite amplitudes. The approximate solution to the acoustic velocity potential of an amplitude modulated pulse is found using the method of multiple scales (MMS) involving both space and time. The calculations are presented up to the third order of the small parameter. It is found that at some frequencies the amplitude modulation is governed by the Nonlinear Schrodinger equation (NLSE). The first objective here is to study the nonlinear term in the NLSE. The sign of the nonlinear term in the NLSE plays a role in determining the stability of the amplitude modulation. Secondly, at other frequencies, the primary pulse interacts with its higher harmonics, as do two or more primary pulses with their resultant higher harmonics. This happens when the phase speeds of the waves match and the objective is to identify the frequencies of such interactions. For both the objectives, asymptotic coupled wavenumber expansions for the linear dispersion relation are required for an intermediate fluid loading. The novelty of this work lies in obtaining the asymptotic expansions and using them for predicting the sign change of the nonlinear term at various frequencies. It is found that when the coupled wavenumbers approach the uncoupled pressure-release wavenumbers, the amplitude modulation is stable. On the other hand, near the rigid-duct wavenumbers, the amplitude modulation is unstable. Also, as a further contribution, these wavenumber expansions are used to identify the frequencies of the higher harmonic interactions. And lastly, the solution for the amplitude modulation derived through the MMS is validated using these asymptotic expansions. (C) 2015 Elsevier Ltd. All rights reserved.

Spectral solutions to the Korteweg-de-Vries and nonlinear Schrodinger equations

In this paper, we present the solutions of 1-D and 2-D non-linear partial differential equations with initial conditions. We approach the solutions in time domain using two methods. We first solve the equations using Fourier spectral approximation in the spatial domain and secondly we compare the results with the approximation in the spatial domain using orthogonal functions such as Legendre or Chebyshev polynomials as their basis functions. The advantages and the applicability of the two different methods for different types of problems are brought out by considering 1-D and 2-D nonlinear partial differential equations namely the Korteweg-de-Vries and nonlinear Schrodinger equation with different potential function. (C) 2015 Elsevier Ltd. All rights reserved.

Weakly nonlinear acoustic wave propagation in a nonlinear orthotropic circular cylindrical waveguide

Nonlinear acoustic wave propagation is considered in an infinite orthotropic thin circular cylindrical waveguide. The modes are non-planar having small but finite amplitude. The fluid is assumed to be ideal and inviscid with no mean flow. The cylindrical waveguide is modeled using the Donnell's nonlinear theory for thin cylindrical shells. The approximate solutions for the acoustic velocity potential are found using the method of multiple scales (MMS) in space and time. The calculations are presented up to the third order of the small parameter. It is found that at some frequencies the amplitude modulation is governed by the Nonlinear Schrodinger Equation (NLSE). The first objective is to study the nonlinear term in the NLSE, as the sign of the nonlinear term determines the stability of the amplitude modulation. On the other hand, at other specific frequencies, interactions occur between the primary wave and its higher harmonics. Here, the objective is to identify the frequencies of the higher harmonic interactions. Lastly, the linear terms in the NLSE obtained using the MMS calculations are validated. All three objectives are met using an asymptotic analysis of the dispersion equation. (C) 2015 Acoustical Society of America.

Weakly corrected numerical solutions to stochastically driven nonlinear dynamical systems

A method to weakly correct the solutions of stochastically driven nonlinear dynamical systems, herein numerically approximated through the Eule-Maruyama (EM) time-marching map, is proposed. An essential feature of the method is a change of measures that aims at rendering the EM-approximated solution measurable with respect to the filtration generated by an appropriately defined error process. Using Ito's formula and adopting a Monte Carlo (MC) setup, it is shown that the correction term may be additively applied to the realizations of the numerically integrated trajectories. Numerical evidence, presently gathered via applications of the proposed method to a few nonlinear mechanical oscillators and a semi-discrete form of a 1-D Burger's equation, lends credence to the remarkably improved numerical accuracy of the corrected solutions even with relatively large time step sizes. (C) 2015 Elsevier Inc. All rights reserved.

Molecular profiling of sepsis in mice using Fourier Transform Infrared Microspectroscopy

Sepsis is a life threatening condition resulting from a high burden of infection. It is a major health care problem and associated with inflammation, organ dysfunction and significant mortality. However, proper understanding and delineating the changes that occur during this complex condition remains a challenge. A comparative study involving intra-peritoneal injection of BALB/c mice with Salmonella Typhimurium (infection), lipopolysaccharide (endotoxic shock) or thioglycollate (sterile peritonitis) was performed. The changes in organs and sera were profiled using immunological assays and Fourier Transform Infrared (FTIR) micro-spectroscopy. There is a rapid rise in inflammatory cytokines accompanied with lowering of temperature, respiratory rate and glucose amounts in mice injected with S. Typhimurium or lipopolysaccharide. FTIR identifies distinct changes in liver and sera: decrease in glycogen and protein/lipid ratio and increase in DNA and cholesteryl esters. These changes were distinct from the pattern observed in mice treated with thioglycollate and the differences in the data obtained between the three models are discussed. The combination of FTIR spectroscopy and other biomarkers will be valuable in monitoring molecular changes during sepsis. GRAPHICS] Intra-peritoneal infection with high dose of Salmonella Typhimurium leads to rapid increase in inflammatory cytokines, e.g. Tnf alpha (A). FTIR analysis of liver (B) and sera (C) identifies several metabolic changes: glycogen, protein/lipid, cholesteryl esters and DNA.

Nonlinear Dynamics of a Rotating Flexible Link

This paper deals with the study of the nonlinear dynamics of a rotating flexible link modeled as a one dimensional beam, undergoing large deformation and with geometric nonlinearities. The partial differential equation of motion is discretized using a finite element approach to yield four nonlinear, nonautonomous and coupled ordinary differential equations (ODEs). The equations are nondimensionalized using two characteristic velocities-the speed of sound in the material and a velocity associated with the transverse bending vibration of the beam. The method of multiple scales is used to perform a detailed study of the system. A set of four autonomous equations of the first-order are derived considering primary resonances of the external excitation and one-to-one internal resonances between the natural frequencies of the equations. Numerical simulations show that for certain ranges of values of these characteristic velocities, the slow flow equations can exhibit chaotic motions. The numerical simulations and the results are related to a rotating wind turbine blade and the approach can be used for the study of the nonlinear dynamics of a single link flexible manipulator.

Enhanced nonlinear optical properties of graphene oxide-silver nanocomposites measured by Z-scan technique

Nonlinear optical properties (NLO) of a graphene oxide-silver (GO-Ag) nanocomposite have been investigated by the Z-scan setup at Q-switched Nd:YAG laser second harmonic radiation i.e., at 532 nm excitation in a nanosecond regime. A noteworthy enhancement in the NLO properties in the GO-Ag nanocomposite has been reported in comparison with those of the synthesized GO nanosheet. The extracted value of third order nonlinear susceptibility (chi(3)), at a peak intensity of I-0 = 0.2 GW cm(-2), for GO-Ag has been found to be 2.8 times larger than that of GO. The enhancement in NLO properties in the GO-Ag nanocomposite may be attributed to the complex energy band structures formed during the synthesis which promote resonant transition to the conduction band via surface plasmon resonance (SPR) at low laser intensities and excited state transition (ESA) to the conduction band of GO at higher intensities. Along with this photogenerated charge carriers in the conduction band of silver or the increase in defect states during the formation of the GO-Ag nanocomposite may contribute to ESA. Open aperture Z-scan measurement indicates reverse saturable absorption (RSA) behavior of the synthesized nanocomposite which is a clear indication of the optical limiting (OL) ability of the nanocomposite.

The time finite element as a robust general scheme for solving nonlinear dynamic equations including chaotic systems

Schemes that can be proven to be unconditionally stable in the linear context can yield unstable solutions when used to solve nonlinear dynamical problems. Hence, the formulation of numerical strategies for nonlinear dynamical problems can be particularly challenging. In this work, we show that time finite element methods because of their inherent energy momentum conserving property (in the case of linear and nonlinear elastodynamics), provide a robust time-stepping method for nonlinear dynamic equations (including chaotic systems). We also show that most of the existing schemes that are known to be robust for parabolic or hyperbolic problems can be derived within the time finite element framework; thus, the time finite element provides a unification of time-stepping schemes used in diverse disciplines. We demonstrate the robust performance of the time finite element method on several challenging examples from the literature where the solution behavior is known to be chaotic. (C) 2015 Elsevier Inc. All rights reserved.