Towards an exact factorization of the molecular wave function

An exact single-product factorisation of the molecular wave function for the timedependent Schrodinger equation is investigated by using an ansatz involving a phasefactor. By using the Frenkel variational method, we obtain the Schrodinger equations for the electronic and nuclear wave functions. The concept of a potential energy surface (PES) is retained by introducing a modified Hamiltonian as suggested earlier by Cederbaum. The parameter in the phase factor is chosen such that the equations of motion retain the physically appealing Born- Oppenheimer-like form, and is therefore unique.

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.

Ultrasonic Guided Wave Sensor Network Optimization for Monitoring Rivet Line

Guided waves using piezo-electric wafer active sensors (PWAS) is one of the useful techniques of damage detection. Sensor network optimization with minimal network hardware footprint and maximal area of coverage remains a challenging problem. PWAS sensors are placed at discrete locations in order to inspect damages in plates and the idea has the potential to be extended to assembled structures. Various actuator-sensor configurations are possible within the network in order to identify and locate damages. In this paper we present a correlation based approach to monitor cracks emanating from rivet line using a simulated guided wave signal whose sensor is operating in pulse echo mode. Discussions regarding the identification of phase change due to reflections from the crack are also discussed in this paper.

Uncertainty Quantification in Ultrasonic Wave Based Detection of Delamination in Composite Structures

In this paper we consider the problem of guided wave scattering from delamination in laminated composite and further the problem of estimating delamination size and layer-wise location from the guided wave measurement. Damage location and region/size can be estimated from time of flight and wave packet spread, whereas depth information can be obtained from wavenumber modulation in the carrier packet. The key challenge is that these information are highly sensitive to various uncertainties. Variation in reflected and transmitted wave amplitude in a bar due to boundary/interface uncertainty is studied to illustrate such effect. Effect of uncertainty in material parameters on the time of flight are estimated for longitudinal wave propagation. To evaluate the effect of uncertainty in delamination detection, we employ a time domain spectral finite element (tSFEM) scheme where wave propagation is modeled using higher-order interpolation with shape function have spectral convergence properties. A laminated composite beam with layer-wise placement of delamination is considered in the simulation. Scattering due to the presence of delamination is analyzed. For a single delamination, two identical waveforms are created at the two fronts of the delamination, whereas waves in the two sub-laminates create two independent waveforms with different wavelengths. Scattering due to multiple delaminations in composite beam is studied.

Ultrasonic Guided Wave Based Damage Detection Using Low-dimensional Data from Laser Doppler Scan

In the current state of the art, it remains an open problem to detect damage with partial ultrasonic scan data and with measurements at coarser spatial scale when the location of damage is not known. In the present paper, a recent development of finite element based model reduction scheme in frequency domain that employs master degrees of freedom covering the surface scan region of interests is reported in context of non-contact ultrasonic guided wave based inspection. The surface scan region of interest is grouped into master and slave degrees of freedom. A finite element wise damage factor is derived which represents damage state over distributed areas or sharp condition of inter-element boundaries (for crack). Laser Doppler Vibrometer (LDV) scan data obtained from plate type structure with inaccessible surface line crack are considered along with the developed reduced order damage model to analyze the extent of scan data dimensional reduction. The proposed technique has useful application in problems where non-contact monitoring of complex structural parts are extremely important and at the same time LDV scan has to be done on accessible surfaces only.

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.

High frequency millimetre wave absorbers derived from polymeric nanocomposites

The world has dominated by automation, wireless communication and various electronic equipments, which has led to the most undesirable offshoots like electromagnetic (EM) pollution. The rationale is environmental concern and the necessity to develop EM absorbing materials. This paper reviews the state of the art of designing polymer based nanocomposites containing nanoscopic particles with high electrical conductivity and complex microwave properties for enhanced EM attenuation. Given the brevity of this review article, herein we have summarized the high frequency millimetre wave absorbing properties of polymer nanocomposites consisting of various nanoparticles that either reflect or absorb microwave radiation like electrically conducting carbon nanotubes (CNTs) and graphene nanosheets (GNs), high dielectric constant ceramic nanoparticles that show relaxation loss in the microwave frequency and magnetic metal and ferrite nanoparticles that absorb microwave radiation through natural resonance, eddy current and hysteresis losses. Furthermore, we have stressed the necessity and impact of hybrid nanoparticles consisting of magnetic and dielectric nanoparticles along with conducting inclusions like CNT and GNs in this review. Electromagnetic interference (EMI) theory and necessary criterion for attenuation has been briefly discussed. The emphasis is made on various mechanisms towards EM attenuation controlled by these nanoparticles. Various structures developed using polymer nanocomposites like bulk, foam and layered structures and their effect on EM attenuation has been elaborately discussed. In addition, various covalent/non-covalent modifications on nanoparticles have been juxtaposed in context to EM attenuation. In addition, we have highlighted important facets and direction for enhancing the microwave attenuation. (C) 2016 Elsevier Ltd. All rights reserved.

EXACT INTERNAL CONTROLLABILITY FOR THE WAVE EQUATION IN A DOMAIN WITH OSCILLATING BOUNDARY WITH NEUMANN BOUNDARY CONDITION

In this paper, we study the exact controllability of a second order linear evolution equation in a domain with highly oscillating boundary with homogeneous Neumann boundary condition on the oscillating part of boundary. Our aim is to obtain the exact controllability for the homogenized equation. The limit problem with Neumann condition on the oscillating boundary is different and hence we need to study the exact controllability of this new type of problem. In the process of homogenization, we also study the asymptotic analysis of evolution equation in two setups, namely solution by standard weak formulation and solution by transposition method.