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.

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.

Fuel-optimal G-MPSP Guidance for Powered Descent Phase of Soft Lunar Landing

A fuel optimal nonlinear sub-optimal guidance scheme is presented in this paper for soft landing of a lunar craft during the powered descent phase. The recently developed Generalized Model Predictive Static Programming (G-MPSP) is used to compute the required magnitude and angle of the thrust vector. Both terminal position and velocity vector are imposed as hard constraints, which ensures high position accuracy and facilitates initiation of vertical descent at the end of the powered descent phase. A key feature of the G-MPSP algorithm is that it converts the nonlinear dynamic programming problem into a low-dimensional static optimization problem (of the same dimension as the output vector). The control history update is done in closed form after computing a time-varying weighting matrix through a backward integration process. This feature makes the algorithm computationally efficient, which makes it suitable for on-board applications. The effectiveness of the proposed guidance algorithm is demonstrated through promising simulation results.

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.

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.

Fabrication and Nonlinear Thermomechanical Analysis of SU8 Thermal Actuator

SU8-based micromechanical structures are widely used as thermal actuators in the development of compliant micromanipulation tools. This paper reports the design, nonlinear thermomechanical analysis, fabrication, and thermal actuation of SU8 actuators. The thermomechanical analysis of the actuator incorporates nonlinear temperature-dependent properties of SU8 polymer to accurately model its thermal response during actuation. The designed SU8 thermal actuators are fabricated using surface micromachining techniques and the electrical interconnects are made to them using flip-chip bonding. The issues due to thermal stress during fabrication are discussed and a novel strategy is proposed to release the thermal stress in the fabricated actuators. Subsequent characterization of the actuator using an optical profilometer reveals excellent thermal response, good repeatability, and low hysteresis. The average deflection is similar to 8.5 mu m for an actuation current of similar to 5 mA. The experimentally obtained deflection profile and the tip deflection at different currents are both shown to be in good agreement with the predictions of the nonlinear thermomechanical model. This underscores the need to consider nonlinearities when modeling the response of SU8 thermal actuators. 2015-0087]

A Nonlinear Guidance Law for Impact Time Control

This paper discusses the problem of impact time control of an interceptor against a stationary target. A nonlinear guidance law is proposed with the interceptor heading angle variation as a function of the range to target. Closed-form expressions for the design parameters are derived for an exact analysis of the impact time. A feedback form of the guidance law is presented for addressing realistic implementation in the presence of autopilot lag. Using the closed-form expressions of the impact time, a cooperative guidance scheme is presented for simultaneous impact in a salvo attack. Extensive simulation studies are presented validating the analytic findings.

An Ensemble Kushner-Stratonovich-Poisson Filter for Recursive Estimation in Nonlinear Dynamical Systems

We propose a Monte Carlo filter for recursive estimation of diffusive processes that modulate the instantaneous rates of Poisson measurements. A key aspect is the additive update, through a gain-like correction term, empirically approximated from the innovation integral in the time-discretized Kushner-Stratonovich equation. The additive filter-update scheme eliminates the problem of particle collapse encountered in many conventional particle filters. Through a few numerical demonstrations, the versatility of the proposed filter is brought forth.