Reflection Of Wave Packets Research Articles

Quantitative ultrasonic characterization of Ti-6Al-4V components with surface roughness

Ultrasonic immersion testing enables nondestructive characterization of material microstructure through quantitative linkages between wave propagation parameters and features of interest. However, accurate measurements of metrics such as wave speed and attenuation generally require smooth test samples to ensure the reflected wave packets are not distorted. Thus, rough surfaces are mechanically polished before ultrasonic testing, which compromises the nondestructive nature of the measurement, distorting the sample geometry and imparting local damage. This challenge is particularly salient with the advent of manufacturing processes, such as metal additive manufacturing, that result in rough samples that must be characterized for heterogeneities in their as-manufactured state. This work examines the influence of surface roughness on longitudinal wave speed and attenuation in wrought and additively manufactured Ti-6Al-4V specimens. Samples are measured in an ultrasonic immersion setup before and after mechanical polishing using varying transducer frequencies and focal profiles. The resulting data informs the error generated in ultrasonic measurements as a function of roughness parameters, thereby informing the sample preparation needed for desired precision levels. Lastly, new measurement protocols are explored to correct for the presence of surface irregularities in a point-by-point fashion. This work was supported by the Robert W. Young Award for Undergraduate Student Research.

Physics-informed deep filtering of ultrasonic guided waves for incipient defect inspection of large-scale square tube structures

For large-scale structure inspection, the traditional ultrasonic inspection methods are time-consuming and inefficient. Recently, many approaches based on ultrasonic guided waves have been developed. However, during the propagation of guided waves, as the propagation distance increases, the signal amplitude attenuates gradually, as a result, the reflected wave packets from the incipient defects are always seriously contaminated or even buried in noise, and the defect signatures cannot be effectively identified in this circumstance. To detect incipient defect as early as possible to ensure structure safety, it is very essential to suppress the background noise and enhance the reflected wave packet from defect. To address this issue, a physics-informed deep filtering method is proposed for ultrasonic guided waves enhancement. In the proposed method, a deep learning model is constructed and trained based on template signals of ultrasonic guided waves simulated by digital model with different parameters, and then generalized to enhancement of weak ultrasonic guided waves from practical cases. The simulation test and experimental results on large-scale square tube structures indicate that the proposed ultrasonic guided waves enhancement method is effective for early-stage defect inspection and outperforms the traditional guided waves enhancement approaches.

Non-invasive analysis of macro-crack on the characteristics of ultrasonic guided wave

The effects of macro-crack in plates on the characteristic of ultrasonic guided wave were studied. Using the Finite Element Model and numerical calculation method, the finite element mesh models of various macro-crack in aluminum plate were established. The single S0 or A0 mode Lamb wave was excited in plate by the wave structure loading method. The propagation time and amplitude of wave packet in the received signal were analyzed to study the phenomenon of mode transformation and the relationship between macro-crack size and signal amplitude. The simulation results show that there is mode conversion when the single mode Lamb wave interacts with an asymmetric macro-crack, and no mode conversion with a symmetric macro-crack. The energy of reflected wave increases with the increase of the depth and width of macro-crack, and the energy of transmitted wave decreases correspondingly. The size and inclined angle of macro-crack can be quantitatively estimated by the fitting function from the energies of reflected and transmitted waves. The variation of crack depth, width and angle is approximately linear with the amplitudes of reflected and transmitted wave packets. A fitting function is constructed by using the amplitude ratio of reflected wave packet or transmitted wave packet to total wave packet, which can be used to estimate the macro-crack depth, width and angle. This conclusion is helpful to the detection of macro-crack in the actual production and service of plate structures.

Propagation of wave packets along large-scale background waves

We study propagation of high-frequency wave packets along a large-scale background wave, which evolves according to dispersionless hydrodynamic equations for two variables (fluid density and flow velocity). Influence of the wave packet on evolution of the background wave is neglected, so the large-scale evolution can be found independently of the wave packet's motion. At the same time, propagation of the packet depends in an essential way on the background wave, and it can be considered in a framework of the geometric optics approximation with the use of Hamilton equations for the carrier wave number and the mean co-ordinate of the packet. We derive equations for the carrier wave number as a function of the parameters, which describe the background wave. When they are solved, the path of the packet can be found by simple integration of the Hamilton equation. The theory is illustrated by its application to the problem of propagation of wave packets along expanding a large-scale wave, in which evolution is described by the shallow water equations. In particular, they correspond to the dispersionless limit of the defocusing nonlinear Schrödinger equation, and then the expanding wave can be considered as an expanding cloud of the Bose–Einstein condensate. Reflection of wave packets from upstream flows and their propagation along stationary flows are also discussed. The analytical solutions found for these particular cases agree very well with an exact numerical solution of the nonlinear Schrödinger equation.

Transmission and Reflection of Upward-Propagating Rossby Waves in the Lowermost Stratosphere: Importance of the Tropopause Inversion Layer

Abstract Extreme stratospheric vortex states are often associated with extreme heat flux and upward wave propagation in the troposphere and lower stratosphere; however, the factors that dictate whether an upward-directed wave in the troposphere will reach the bottom of the vortex versus being reflected back to the troposphere are not fully understood. Following Charney and Drazin, an analytical quasigeostrophic planetary-scale model is used to examine the role of the tropopause inversion layer (TIL) in wave propagation and reflection. The model consists of three different layers: troposphere, TIL, and stratosphere. It is shown that a larger buoyancy frequency in the TIL leads to weaker upward transmission to the stratosphere and enhanced reflection back to the troposphere, and thus reflection of wave packets is sensitive not just to the zonal wind but also to the TIL’s buoyancy frequency. The vertical–zonal cross section of a wave packet for a more prominent TIL in the analytical model is similar to the corresponding wave packet for observational events in which the wave amplitude decays rapidly just above the tropopause. Similarly, a less prominent TIL both in the model and in reanalysis data is associated with enhanced wave transmission and a weak change in wave phase above the tropopause. These results imply that models with a poor representation of the TIL will suffer from a bias in both the strength and phase of waves that transit the tropopause region.

Defect localization in waveguide assemblies with curved joints via wave finite elements and time of flight analysis

A numerical approach is proposed to localize defects in elastic waveguides connected by curved elastic joints. 2D assemblies involving straight waveguides with a curved joint and a defect are specifically dealt with, where the joint is placed between the measurement point (output signals) and the defect. Such an analysis requires assessing wave conversion phenomena and times of flight for wave packets when they are transmitted through the joint and reflected by the defect. In this paper, the wave finite element (WFE) method is used to help understand these phenomena. An original strategy is proposed where the times of flight, for transmitted or reflected wave packets, are defined from the frequency derivatives of the arguments of the scattering matrices of the joint and the defect. The procedure to localize a defect follows from comparing the theoretical expressions of the times of flight with those recorded at the measurement point. Also, the proposed approach enables the identification of the types of waves which are truly transmitted through the joint and reflected by the defect. Numerical experiments are carried out which highlight the relevance, in terms of accuracy and robustness, of the proposed approach.

Ultrashort Pulse Reflectometry (USPR) diagnostic for EAST

Ultrashort Pulse Reflectometry (USPR) is a plasma diagnostic technique involving the propagation of ultrashort duration (∼few nsec) chirps which contain frequency components spanning large portions of the plasma density profile. Upon reflection, each frequency component reflects from a distinct density layer. The reflected wave packet is down-converted and passed through a multi-channel filter bank, with time-of-flight (TOF) measurements made on each of the filtered wave packets which are then used to reconstruct the electron density profile. Applied previously to the Sustained Spheromak Physics Experiment, UC Davis is updating this technique with higher power (>10X) sources, enhanced channel counts, and high speed customized TOF electronics. A 32 channel USPR system is being developed for the Experimental Advanced Superconducting Tokamak (EAST) device with frequencies spanning 52 to 92 GHz, reflecting from the right-hand plasma cut-off layer. The system will employ three monostatic transmit/receive horns each covering a different waveguide band. Each of the two higher frequency bands will have 8 distinct frequency channels, with the lowest frequency band, spanning 52 to 65 GHz, to have 16 receiver channels to better resolve the EAST scrape-off layer. With a pulse repetition rate of 1 MHz and simultaneous acquisition of all 32 TOF signals, electron density profiles may be obtained with time resolutions of as short as 3–6 µsec.

Confinement of bright matter-wave solitons on top of a pedestal-shaped potential

Reflection of wave packets from downward potential steps and attractive potentials, known as a quantum reflection, has been explored for bright matter-wave solitons and breathers with the main emphasis on the possibility to trap them on top of a pedestal-shaped potential. In numerical simulations with particular parameter settings, we observed that moving solitons return from the borders of the potential and remain trapped for a sufficiently long time. The shuttle motion of the soliton is accompanied by shedding some amount of matter at each reflection from the borders of the trap, thus reducing its norm. The time-shift observed in a step-like decay of the moving soliton's norm in the two-soliton configuration is linked to the trajectory jump phenomenon. In the framework of the proposed model, several fundamental properties of solitons have been illustrated, such as a discontinuous jump of trajectories of colliding solitons, splitting of the breather, and the absence of matter exchange between interacting solitons. The obtained results can be of interest for the design of new soliton experiments with Bose-Einstein condensates.

Reflection of neutrons from a resonant potential structure oscillating in space

The work is devoted to the theoretical study of the interaction of a plane wave with a resonant potential structure oscillating in space. An approximate analytical solution to the non-stationary Schrödinger equation for this problem is given. A numerical quantum calculation of the problem of a wave packet reflection from such a structure has been performed. The results of three solution methods are compared in order to determine the degree of the reflection time influence on the spectrum of the reflected state. It was found that under resonance conditions, when the reflection time increases significantly, there is a strong suppression of scattering with energy transfer. It is shown that this effect is due to combination of the long interaction time with the spatial oscillation of the potential. Such effect is absent in the case of the reflection from the potential oscillating in magnitude and characterized by the same reflection time.

New energy-based decoherence correction approaches for trajectory surface hopping

Inspired by the branching corrected surface hopping (BCSH) method [J. Xu and L. Wang, J. Chem. Phys. 150, 164101 (2019)], we present two new decoherence time formulas for trajectory surface hopping. Both the proposed linear and exponential formulas characterize the decoherence time as functions of the energy difference between adiabatic states and correctly capture the decoherence effect due to wave packet reflection as predicted by BCSH. The relevant parameters are trained in a series of 200 diverse models with different initial nuclear momenta, and the exact quantum solutions are utilized as references. As demonstrated in the three standard Tully models, the two new approaches exhibit significantly higher reliability than the widely used counterpart algorithm while holding the appealing efficiency, thus promising for nonadiabatic dynamics simulations of general systems.

Reflection from the ionosphere and exit to the ground of whistler wave packets: A dynamical model

In the theory of wave propagation in near-Earth space, there is a long-standing but still unsolved problem — this is the problem of whistler exit to the ground after passing through the magnetospheric trajectory. Snell’s law forbids exit of a wave to the ground if the angle between the wave normal and the vertical is outside the penetration cone, which is almost always true, at least for middle and low latitudes. However, whistlers are often recorded at ground stations, where they were first discovered. Most of the previous theoretical works considered the exit of whistlers to the ground as a stationary problem, taking the wave field in the form E=Re[E0(h)exp(iκξ−iωt)] with a constant frequency ω and a constant wave number κ, where h and ξ are the vertical and horizontal coordinates, respectively. Taking the field in this form assumes that the parameters of the medium are time independent and change only in the vertical direction. However, those are necessary, but not sufficient conditions for using the above given form of the wave field. It is clear that the real problem is not stationary, and the wave packet incident on the ionosphere from above is limited both in vertical and horizontal directions. Investigation of the whistler wave packet reflection from the ionosphere and exit to the ground as a non-stationary two-dimensional problem is the subject of this work.

RETRACTED: Identification and delineation of potash deposits in Saskatchewan, Canada using pulsed radar technology

Editorial notice: This article has been retracted. See the associated retraction notice here . Saskatchewan, Canada, contains almost half of the world’s known potash deposits, within the Middle Devonian Prairie Evaporite Formation. As the global demand for potash increases, so does the need for faster, greener and cheaper methods of potash identification and extraction. The primary methods for exploration and development of potash include traditional 2D and 3D seismic methods, along with exploration drilling, downhole geophysical logging, coring, and assays for geological interpretation. One challenge with existing seismic geophysical methods in potash exploration is the difficulty in differentiating the responses and interpretation between the evaporite (sylvinite and halite (NaCl)) beds which are intermittently deposited within the Prairie Evaporite Formation. We field tested a new pulsed radar method for subsurface geophysical measurements at the Vanguard Area, Saskatchewan, to demonstrate whether subsurface evaporties could be directly identified non-invasively from ground level. In the Vanguard Area, the Prairie Evaporite Formation occurs at a depth of approximately 1500 m below ground surface (BGS). Achieving deep penetration of the transmitted pulsed radar wave packets, whilst discerning the materials from which the reflected wave packets (containing difference frequency and energy levels) bounced back from, was another scientific challenge. Following robust testing and due diligence on the method, we have been able to confirm that the pulsed radar method is capable of identifying broad lithological zones, differentiating halite units from sylvinite units (the potash-bearing members) within the Prairie Evaporite Formation, and also differentiating individual sub-members within each major potash member. A high-level identification of potash grade (%KCl) of the potash sub-members was also assessed. Based on this preliminary work, the results presented provide significant evidence and resulting confidence in the promise of utilizing the pulsed radar technology for successful identification and delineation of potash deposits

Branching corrected surface hopping: Resetting wavefunction coefficients based on judgement of wave packet reflection

We present a new interpretation of the decoherence correction in surface hopping by examining the inconsistency of the traditional time-dependent Schrödinger equation and propose an elegant decoherence correction algorithm to deal with wave packet branching. In contrast to the widely used approaches based on decoherence rates, our branching corrected surface hopping (BCSH) resets the wavefunction directly after wave packet branching is identified through prediction of trajectory reflection. The appealing simplicity and reliability of BCSH are demonstrated in a series of widely studied one-dimensional and two-dimensional scattering models using exact quantum solutions and existing surface hopping approaches as references. The BCSH approach exhibits a high performance in all investigated systems, showing good potential for applications in general nonadiabatic dynamics simulations.

Transmission and Reflection of Wave Packets by Asymmetric Semi-Harmonic Potential Barriers

We study the scattering of a particle by a square barrier potential that has a parabolic hole in between. The barrier is parameterized in such a form that the hole can be partially or completely removed. This can be also chosen to be symmetric or asymmetric with respect to the hole. Some expressions for the phase time are given and the time spent by the particle in the interaction zone of the barrier is calculated. It is shown that the related time delay depends on the symmetry operations that one can do on the potential.

Suppression of quantum-mechanical reflection by environmental decoherence

In quantum mechanics an incoming particle wave packet with sufficient energy will undergo both transmission and reflection when encountering a barrier of lower energy, but in classical mechanics there is no reflection, only transmission. In this paper we seek to explain the disappearance of quantum-mechanical reflection in the quasiclassical limit, using the standard machinery of decoherence through environmental interaction. We consider two models. In the first, the incoming particle is classicalized by coupling to an environment and modeled using a standard master equation of Lindblad form with Lindblad operator proportional to position (the simplest version of quantum Brownian motion). We find, however, that suppression of reflection is achieved only for environmental interaction so strong that large fluctuations in momentum are generated, which blurs the distinction between incoming and reflected wave packets. This negative conclusion also holds for a complex potential which has similar implications for attempts to understand the suppression of the Zeno effect using the same mechanism (discussed in more detail elsewhere). A different master equation with Lindblad operator proportional to momentum is shown to be successful in suppressing reflection without large fluctuations but such a master equation is unphysical. We consider a second model in which the barrier is modeled quantum mechanically by a massive target particle coupled to an environment to maintain it in a quasiclassical state. This avoids the fluctuations problem since the incoming particle is not coupled to the environment directly. We find that reflection is significantly suppressed as long as the decoherence time scale of the target particle is much smaller than certain characteristic scattering time scales of the incoming particle, or equivalently, as long as the velocity fluctuations in the target are larger than the velocity of the incoming particle.

Optical field modulation on the group delay of chiral tunneling in graphene

The influences of optical fields on the group delay of chiral tunneling in graphene are investigated in real time using the finite-difference time-domain method. The group delay of tunneling electrons irradiated by an optical field is significantly different from that observed in traditional quantum tunneling. We found that when the barrier width increases, the group delay becomes constant for the reflected wave packet, but increases linearly for the transmitted wave packet. This peculiar tunneling effect can be attributed to current leakage in a time-dependent barrier generated via the optical Stark effect.

Lateral shift effect on the spatial interference of light wave propagating in the single-layered dielectric film

Under the oblique incidence condition, the multiple reflection of wave packets in a layered film structure will have a lateral shift increasing with the film thickness. In the analysis of the spatial interference with consideration of the lateral shift effect, a set of new analytic formulae to normalize the intensity of the s-and p-polarized wave packet was obtained to reduce the error of the ellipsometry parameters significantly as the optical path difference delta is close to mpi. The principle and method developed in this work also can be applied to other film structures in more general applications.

Impact of traveling phonon wave packets on the optical response of quantum dots

AbstractThe influence of phonon wave packets created by the optical excitation of a quantum dot (QD) structure on four‐wave‐mixing (FWM) signals is analyzed theoretically. Two different structures are compared: a single QD in a half‐space geometry located close to the surface, where the emitted phonon wave packet after reflection at the surface reenters the QD and a pair of QDs in an infinite medium, where the phonon wave packet created in one QD travels across the other QD. Although the strain fields are very similar pronounced differences in the FWM polarizations are found.In the single QD system we observe clear signatures of the reflected wave packet in the FWM signal at positive delay times, which can also be observed in the time‐integrated FWM signal from an inhomogeneously broadened ensemble of such QDs. In the two QD case no signatures of the traveling wave packet are seen in the signal at positive delays and, consequently, in the ensemble signal. However, they are clearly seen in the FWM signal at negative delay times. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Computational investigation of wave packet barrier scattering in the complex plane: Examination of the complex quantum potential utilizing numerical analytic continuation techniques

In this study, we utilize numerical analytic continuation (NAC) to compute the complex quantum potential from the complex-extension of wave packets computed on the real-axis. The Cauchy method is utilized due to its robustness and flexibility. The Bohm and complex quantum potentials are compared; both potentials display complicated (but dissimilar) structure on the real-axis. We focus on generating numerically accurate maps of the evolving complex quantum potential for the Eckart barrier scattering problem. Although the complex quantum potential is initially constant, it later develops structures for the reflected wave packet that make it just as complicated as Bohm’s quantum potential, at least on the real-axis.

Propagation and reflection of gravity waves in a meridionally sheared wind field

Although the properties of gravity waves propagating in a vertically sheared flow have been extensively studied, the effects of a horizontally sheared wind on gravity wave propagations were seldom reported. In this paper, according to the linear theory, the characteristics of gravity wave reflection in a meridionally sheared zonal background wind field are discussed, which are evidently different from those of wave reflected by a vertically sheared flow. By numerical simulations, we present the whole process of a gravity wave packet reflection in a meridionally sheared wind. When the wave reaches the reflecting level, the zonal disturbance velocity in the evanescent region shows an evanescent wave configuration, which is consistent with the Airy function form predicted by the linear theory; while the meridional disturbance velocity exhibits rather different wave structures. The wave number spectra of zonal and meridional disturbance velocities also show different characteristics in the reflection process. The energy center of the wave packet is reflected in a position nearer than the reflecting level predicted by the linear theory. While the wave propagates along (against) the meridionally sheared wind, the meridional perturbation kinetic energy and total wave energy decrease (increase), whereas, the zonal perturbation kinetic energy increases (decreases); and an energy exchange between the wave potential and wave kinetic energies can be observed. Earth rotation has a slight influence on the energy transfer between the wave and the background flow. If the wind shear beyond the reflecting level isn't strong enough, part components of the incident wave may steadily penetrate across the reflecting level, and yields a transmission wave. A large amplitude gravity wave propagating in a meridionally sheared wind can obviously induce a mean flow, which strengthens slightly the wave reflection, indicating that the transmission rate slightly decreases with the increasing amplitude of the incident wave. This differs from the reflection of waves in a vertical sheared wind field, in which the mean flow induced by the large amplitude wave significantly enhances the wave transmission effect. In the meridionally sheared flow, the transmission rate seems to mainly depend on the sheared wind and the parameters and spectral components of the incident waves.