Longitudinal Field Research Articles

Superdiffusive to ballistic transport in nonintegrable Rydberg simulator

A common wisdom posits that transport of conserved quantities across clean nonintegrable quantum systems at high temperatures is diffusive when probed from the emergent hydrodynamic regime. We show that this empirical paradigm may alter if the strong interaction limit is taken. Using Krylov-typicality and purification matrix-product-state methods, we establish in short-to-intermediate time scales the following observations for the nonintegrable lattice model imitating the experimental Rydberg blockade simulator. Given the strict projection owing to the infinite density-density repulsion V, the Rydberg chain’s energy transport in the presence of a transverse field g is tentatively superdiffusive at infinite temperature featured by an anomalous scaling exponent 34\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{3}{4}$$\\end{document}, indicating the potential existence of a novel dynamical universality class. Imposing, in addition, a growing longitudinal field h causes a putative superdiffusion-to-ballistic transport transition at h ≈ g. Interestingly, all the above results persist for large but finite interactions and temperatures, provided that the strongly interacting condition g, h ≪ kBT ≪ V is fulfilled. Our predictions are testable by current Rydberg quantum simulation facilities.

Ultrasonic imaging of concrete-embedded corroded steel liners using linear and nonlinear evaluation

ABSTRACT This study explores the efficacy of horizontally polarised shear (SH) waves in ultrasonic inspection of concrete-embedded steel liner plates, focusing on corrosion detection. SH-waves are found to significantly improve the localisation and potential dimensional assessment of embedded plate-like structures compared to compressional (P) waves, as evidenced by SH C-scans. Anomalies corresponding to severe corrosion are discernible in SH C-scans, whereas they are minimally visible in P-wave scans. Nonlinear evaluation explores harmonic-based imaging, including second harmonic generation (SHG) and third harmonic generation. Nonlinear SH-wave evaluation accurately locates the most severely corroded embedded plate, whereas comparative P-wave evaluations fail. However, potential FFT sidelobe contamination in the results warrants consideration. These results suggest a promising use for nonlinear waveform distortion in SH-wave-based corrosion detection though conclusive evidence of the source of SHG is uncertain. Experiments utilised an automatic scanner system for consistent control. The concrete specimen investigated herein contained pre-corroded plates which hint at heightened nonlinear effects when corrosion occurs post-embedment due to corrosion-induced cracking. These findings encourage further investigation into SH-waves for nonlinear ultrasonic detection of concrete-embedded steel liner plates and the development of instrumentation tailored to such methods.

Characterization of Elastic Constants of Langatate Single Crystals with 32 Symmetry Using Ultrasonic Pulse‐Echo Technique

AbstractIn this study, the propagation of plane waves in the lanthanum gallium tantalate (langatate, LGT) single crystals is investigated. Moreover, the flight time of different waves in the LGT rectangular parallelepiped sample is measured using the ultrasonic pulse‐echo (UPE) technique, and the elastic constants of the LGT sample are determined. The experimental results clearly show echoes corresponding to the longitudinal and transverse waves along the x‐axis. The waves along the z‐axis have a similar property. However, the waves along the y‐axis are more complex than those along the x‐ and z‐axes. The echoes corresponding to the quasi‐longitudinal waves along the y‐axis are clear, but those corresponding to the transverse and quasi‐transverse waves along the y‐axis are not. The elastic constant can be accurately determined if the wave echoes corresponding to this constant propagate without distinct distortion and are clear; otherwise, it may be impossible to accurately determine the constant using UPE. All elastic constants except of the LGT single crystals can be determined using UPE from one sample. This study uses UPE to provide a reference for the characterization of elastic constants of piezoelectric crystals with 32 symmetry from one sample.

Identification of the low resistivity-low contrast (LRLC) gas-bearing pay zones in Shaly sand reservoirs using acoustic data: a case study from the Messinian Abu Madi formation, onshore Nile Delta, Egypt

AbstractDetection of the low resistivity-low contrast (LRLC) reservoirs is among the main challenges in the oil industry. In this concern, the LRLC pay zones of the Upper Messinian Abu Madi clastic reservoirs in the onshore Nile Delta Gas fields became a main challenge for significant exploration. This type of reservoirs, including low resistivity-low contrast zones and thin-bedded intervals, are often overlooked using the conventional petrophysical evaluation techniques, especially in the wildcat exploratory wells or highly agitated shoreline depositional environments like the Nile Delta of Egypt. These hidden low contrast reservoirs are generally challenging due to the presence of many shale intercalations/laminations and/or due to increasing the shale volume represented in the form of dispersed distribution, and the dominance of conductive clay minerals. Therefore, in this study, the expected high resistivity values of the gas-bearing reservoir intervals of the Abu Madi Formation in the onshore Begonia gas Field, as a typical case study of the LRLC reservoirs, are masked due to the relatively high shale conductivity, particularly when the thickness of these intervals is less than the vertical resolution of the utilized conventional resistivity log. To verify the LRLC phenomena of the Begonia gas Field, the obtained data was compared to the South Abu El Naga gas Field as a normal case study with a relatively high resistivity gas-bearing pay zone. To overcome the impact of the conductive clay mineral content and identify these hidden low resistivity reservoir intervals, it is necessary to integrate the conventional logging data (gamma-ray, shallow and deep resistivity, density, and neutron) with the acoustic log data including shear and compressional sonic data. In this way, a useful relationship can be established enabling the detection of these hidden LRLC reservoir intervals. This integration is based on the principle that shear waves are not influenced by the fluids types, whereas the compressional sonic waves are influenced by the reservoir fluids. However, to effectively investigate these concealed LRLC reservoir intervals, which can boost production and increase the potential reserves, it is essential to have a low water cut value. The present study represents introduces an efficient workflow, which can be extended to other similar LRLC pay zones in the Nile Delta and northeast Africa. It is also extendible to the LRLC reservoirs in similar deltaic systems having conductive minerals-bearing reservoirs or thin beds.

Seismic shear wave noise suppression and application to well tie

Abstract Seismic shear waves have been employed in oil and gas exploration for decades. A 2D seismic shear wave inline was acquired in Sanhu area, located in the Qaidam Basin in western China. Although the acquired shear wave data exhibits high resolution and comparable bandwidth to the compressional wave, it is contaminated by various types of noise, including linear noise, single-frequency noise, and especially internal multiples. Internal multiples seriously compromise the primary reflections at both near-offset and far-offset and are difficult to be suppressed. This paper presents a case study of noise attenuation for the seismic shear wave. Firstly, single-frequency noise and linear noise are attenuated through filtering methods. Then, two methods (the Radon transform and the frequency-wavenumber (F-K) filtering) are evaluated for their effectiveness in multiple suppression and amplitude preservation. The results indicate that both methods successfully reduce long-period multiples at far-offset, enhancing the signal-to-noise ratio. We show that F-K filtering retains the characteristic ‘strong-weak-strong’ amplitude variation in the SV-SV wave data gather, making it preferable for subsequent AVO (amplitude variation with offset) analysis and inversion. Finally, a wave-equation-based MSI (multiple suppression inversion) method is used to suppress near-offset internal multiples. This involves iteratively predicting internal multiples and adaptively subtracting them from the original data. Stacked sections of different offsets are compared to demonstrate de-multiple result, and the result is also validated by the improvement of well calibration with the seismic shear wave data.

A search for mode coupling in magnetic bright points

Magnetic bright points (MBPs) are one of the smallest manifestations of the magnetic field in the solar atmosphere and are observed to extend from the photosphere up to the chromosphere. As such, they represent an excellent feature to use in searches for types of magnetohydrodynamic (MHD) waves and mode coupling in the solar atmosphere. In this work, we aim to study wave propagation in the lower solar atmosphere by comparing intensity oscillations in the photosphere with the chromosphere via a search for possible mode coupling, in order to establish the importance of these types of waves in the solar atmosphere, and their contribution to heating the chromosphere. These observations were conducted in July 2011 with the Rapid Oscillations of the Solar Atmosphere (ROSA) and the Hydrogen-Alpha Rapid Dynamics Camera (HARDCam) instruments at the Dunn Solar Telescope. Observations with good seeing were made in the G-band and Halpha wave bands. Speckle reconstruction and several post facto techniques were applied to return science-ready images. The spatial sampling of the images was 0.069arcsec /pixel (50 km/pixel). We used wavelet analysis to identify traveling MHD waves and derive frequencies in the different bandpasses. We isolated a large sample of MBPs using an automated tracking algorithm throughout our observations. Two dozen of the brightest MBPs were selected from the sample for further study. We find oscillations in the G-band MBPs, with frequencies between 1.5 and 3.6 mHz. Corresponding MBPs in the lower solar chromosphere observed in Halpha show a frequency range of 1.4 to 4.3 mHz. In about 38<!PCT!> of the MBPs, the ratio of Halpha to G-band frequencies was near two. Thus, these oscillations show a form of mode coupling where the transverse waves in the photosphere are converted into longitudinal waves in the chromosphere. The phases of the Halpha and G-band light curves show strong positive and negative correlations only 21<!PCT!> and 12<!PCT!> of the time, respectively. From simple estimates we find an energy flux of approx 45 $ $ W m$^ $ and show that the energy flowing through MBPs is enough to heat the chromosphere, although higher-resolution data are needed to explore this contribution further. Regardless, mode coupling is important in helping us understand the types of MHD waves in the lower solar atmosphere and the overall energy budget.

Rigid-foldable spiral origami with compression-torsion coupled motion mode

Rigid foldable origami enables smooth and precise folding without stretching or bending its constituent panels and is promising for applications such as reprogrammable matter, self-folding machines, reconfigurable antennas, and deployable spacecraft. The diverse range of potential applications necessitates the need for the design and detailed analysis of different rigid-foldable origami structures, especially those with intricate motion modes. In this paper, we introduce a rigid-foldable spiral origami design that features a compression-torsion coupled motion mode. This design exhibits rich static and dynamic properties. Under static conditions, the compression-torsion coupled motion mode creates multiple self-locking positions and allows for the development of mechanical static diodes. Under dynamic conditions, the compression-torsion coupling effect in the spiral origami facilitates precise control of wave modes within the origami chain when impacted by a ball with a moderate initial velocity. In the case of large initial velocities of the ball, the spiral origami can function as a wave generator, producing rarefaction solitary waves or compressive solitary waves. The proposed spiral origami design provides an opportunity to explore new applications of rigid-foldable origami with compression-torsion coupling effects.

Assessment of aging degradation in rubber using quasi-static components of ultrasonic longitudinal waves

Abstract Aging degradation is the main form of failure of rubber in service, leading to a decline in its physical and mechanical properties. This paper presents an efficient method for assessing the aging degradation of rubber using the quasi-static component (QSC) of ultrasonic longitudinal waves induced by acoustic radiation. The experiments quantitatively observe the response of the QSC pulse to different levels of ageing degradation. A pulse-echo ultrasonic transducer is employed to simultaneously capture the primary longitudinal wave (PLW) and QSC echoes, enabling the determination of the acoustic nonlinearity parameter of QSC with a single transducer excitation. The results suggest that, in comparison to traditional linear ultrasonic techniques based on attenuation coefficient and wave velocity measurements, the relative acoustic nonlinear parameter of QSC proves to be more sensitive to aging degradation in rubber. Particularly, the amplitude of the QSC pulse undergoes a significant change with increasing aging degradation, even when the PLW tone burst is completely attenuated. These findings confirm the effectiveness of QSC as a method for evaluating aging degradation in highly attenuative materials.

Investigation of rogue wave and dynamic solitary wave propagations of the $$\mathbf{M}$$-fractional (1 + 1)-dimensional longitudinal wave equation in a magnetic-electro-elastic circular rod

Investigation of rogue wave and dynamic solitary wave propagations of the $$\mathbf{M}$$-fractional (1 + 1)-dimensional longitudinal wave equation in a magnetic-electro-elastic circular rod

Measurement Method of Stress in High-Voltage Cable Accessories Based on Ultrasonic Longitudinal Wave Attenuation.

High-voltage cables are the main arteries of urban power supply. Cable accessories are connecting components between different sections of cables or between cables and other electrical equipment. The stress in the cold shrink tube of cable accessories is a key parameter to ensure the stable operation of the power system. This paper attempts to explore a method for measuring the stress in the cold shrink tube of high-voltage cable accessories based on ultrasonic longitudinal wave attenuation. Firstly, a pulse ultrasonic longitudinal wave testing system based on FPGA is designed, where the ultrasonic sensor operates in a single-transmit, single-receive mode with a frequency of 3 MHz, a repetition frequency of 50 Hz, and a data acquisition and transmission frequency of 40 MHz. Then, through experiments and theoretical calculations, the transmission and attenuation characteristics of ultrasonic longitudinal waves in multi-layer elastic media are studied, revealing an exponential relationship between ultrasonic wave attenuation and the thickness of the cold shrink tube. Finally, by establishing a theoretical model of the radial stress of the cold shrink tube, using the thickness of the cold shrink tube as an intermediate variable, an effective measurement of the stress of the cold shrink tube was achieved.

Evaluation of 3D printed 316L stainless steel microstructure and mechanical property by laser ultrasonics

ABSTRACT In this paper, the laser ultrasonic non-destructive testing technology was used to detect the microstructure and mechanical properties of selective laser melting (SLM) 316 L stainless steel after post-treatment. The microstructure and mechanical properties of additively manufactured 316 L stainless steel were measured by Scanning electron microscopy (SEM), Electron backscatter diffraction (EBSD), tensile testing, etc. The laser ultrasonic longitudinal wave signal characteristic values were coupled with the microstructure and mechanical properties of SLM 316 L stainless steel. The results show that: The yield strength has a good correlation with wave speed and attenuation. With the increase of holding temperature and holding time, the grain size increases, the low angle grain boundary decreases, the yield strength gradually decreases from 409 MPa to 359 MPa, the wave velocity increases from 5579 m/s to 5700 m/s, and the frequency domain attenuation coefficient increases from 0.13 dB/mm to 0.16 dB/mm, the central frequency domain is about 10 MHz. The ultimate tensile strength is related to the frequency domain attenuation. The ultimate tensile strength decreases with the increase of the frequency domain attenuation coefficient. It can provide a reference for the evaluation of mechanical properties by laser ultrasonic testing.

Optical atompilz: Propagation-invariant strongly longitudinally polarized toroidal pulses

Recent advancements in optical, terahertz, and microwave systems have unveiled non-transverse optical toroidal pulses characterized by skyrmionic topologies, fractal-like singularities, space-time nonseparability, and anapole-exciting ability. Despite this, the longitudinally polarized fields of canonical toroidal pulses notably lag behind their transverse counterparts in magnitude. Interestingly, although mushroom-cloud-like toroidal vortices with strong longitudinal fields are common in nature, they remain unexplored in the realm of electromagnetics. Here, we present strongly longitudinally polarized toroidal pulses (SLPTPs), which boast a longitudinal component amplitude exceeding that of the transverse component by over tenfold. This unique polarization property endows SLPTPs with robust propagation characteristics, showcasing nondiffracting behavior. The propagation-invariant strongly longitudinally polarized field holds promise for pioneering light–matter interactions, far-field superresolution microscopy, and high-capacity wireless communication utilizing three polarizations.

The coupled band gap of longitudinal wave in metamaterial-based double-rod containing resonators

This study investigates the coupled band gap and vibration propagation characteristics of elastic waves in a metamaterial elastic double-rod system with attached periodic resonators. We derive the band gap structure and vibration attenuation equations of double-rod structure using the spectral element method, Bloch’s theorem, and the transfer matrix method. The validity of the coupled band gap is confirmed through forced vibration response analysis. Furthermore, we examine the effects of various parameters on the double-rod system, revealing that coupled band gaps exist with the average vibration attenuation rates of −50.23 dB for rod one and −47.87 dB for rod two, respectively. Remarkably, by adjusting the double-rod parameters, both the band gap frequency range and vibration attenuation ability of the coupled band gap can be adjusted to meet specific engineering requirements in low-frequency regions. This research contributes to developing continuous mechanical structures featuring coupled band gaps.

Numerical simulation and experimental study on nonlinear ultrasonic characterization of graphite size in nodular cast iron

Graphite morphology has a significant influence on mechanical properties such as tensile strength and hardness in nodular cast iron (NCI). Compared to the detection of graphite nodularity, there is relatively less ultrasonic simulation and detection experiment research on the graphite size. Therefore, it is of great importance to study rapid nondestructive testing methods for the internal graphite size of NCI. This study establishes a simulation model of nonlinear ultrasonic penetration longitudinal wave detection for graphite size. The acoustic nonlinearity parameter (ANP) is used to characterize the graphite size. Nonlinear ultrasonic detection experiments on the internal graphite size are conducted to verify the reliability of the nonlinear ultrasonic simulation model. The simulation and experimental results show that the ANP of penetrating longitudinal waves decreases with the increase of average graphite diameter. The relationship between ANP and internal graphite size is established. Moreover, the experimental results verified the accuracy of the numerical model. The decrease in ANP may be related to the decrease in the number of grain boundaries. Therefore, the nonlinear ultrasonic technique is an effective method for characterizing the internal graphite size. The establishment of a nonlinear ultrasonic simulation model for graphite size in NCI lays the research foundation for nonlinear ultrasonic microstructure characterization experiments.

Reflection, transmission, and AVO response of inhomogeneous plane waves in thermoporoelastic media with two-temperature equations of heat conduction

We develop a modified fluid-saturated thermoporoelastic model by introducing two temperature equations to account for the temperature differences between the solid skeleton and the pore filling. The modified two-temperature generalized thermoporoelastic (TTG) equation is an extension of the classical single-temperature Lord-Shulman (LS), Green-Lindsay, and generalized LS theories. It predicts four compressional waves and one shear wave based on the analysis of inhomogeneous plane waves. We study the exact reflection and transmission (R/T) coefficients at the interface separating two thermoporoelastic half-spaces and develop an amplitude-variation-with-offset (AVO) approximation. Comparison with the Biot poroelastic case of the water/oil contact shows that the TTG model reproduces the exact R/T results. The AVO response of oil, gas, and real CO2 geosequestration reservoirs illustrates the practical applicability of our model and provides the theoretical basis for the exploration of high-temperature resources.

Dual-Wave ZnO Film Ultrasonic Transducers for Temperature and Stress Measurements.

ZnO film ultrasonic transducers for temperature and stress measurements with dual-mode wave excitation (longitudinal and shear) were deposited using the reactive RF magnetron sputtering technique on Si and stainless steel substrates and construction steel bolts. It was found that the position in the substrate plane had a significant effect on the structure and ultrasonic performance of the transducers. The transducers deposited at the center of the deposition zone demonstrated a straight columnar structure with a c-axis parallel to the substrate normal and the generation of longitudinal waves. The transducers deposited at the edge of the deposition zone demonstrated inclined columnar structures and the generation of dominant shear or longitudinal shear waves. Transducers deposited on the bolts with dual-wave excitation were used to study the effects of high temperatures in the range from 25 to 525 °C and tensile stress in the range from 0 to 268 MPa on ultrasonic response. Dependencies between changes in the relative time of flight and temperature or axial stress were obtained. The dependencies can be described by second-order functions of temperature and stress. An analysis of the contributions of thermal expansion, strain, and the speed of sound to changes in the time of flight was performed. At high temperatures, a decrease in the signal amplitude was observed due to the decreasing resistivity of the transducer. The ZnO ultrasonic transducers can be used up to temperatures of ~500 °C.

High‐Pressure Melting Experiments of Fe3C and a Thermodynamic Model of Fe‐C Liquids for the Earth's Core

AbstractMelting experiments of Fe3C were conducted to 85 GPa in laser‐heated diamond anvil cells with in situ X‐ray diffraction and post‐experiment textural observation. From the determined pressure‐temperature conditions of the melting curve for Fe3C, together with literature data on the melting point of diamond and eutectic point of the system Fe‐Fe3C/Fe7C3 under high pressures, we established a self‐consistent thermodynamic model for high‐pressure melting of the system Fe‐C including the mixing parameters for liquids. The results show that mixing of Fe and C liquids is negatively nonideal from 1 bar to the pressure at the center of the Earth. The departure from ideal mixing becomes progressively larger with increasing pressure, which leads to greatly stabilized liquids under core pressures. The modeled carbon content in eutectic melts under core pressures is 3.3–4.4 wt%. From the Gibbs free energy, we derived an internally consistent parameters for Fe‐C outer cores which included the crystallizing points at their bottoms, isentropic thermal profiles, and densities and longitudinal seismic wave speeds (Vp). While the addition of carbon in excess of the eutectic melt composition effectively reduces the density of iron liquid, the Vp of iron liquid is not greatly changed. Therefore, the low density and high Vp of PREM relative to pure iron cannot be reconciled by an Fe‐C liquid. Therefore, the Earth's core cannot be approximated by the system Fe‐C and should include another light element.

Nonlinear Jeans instability analysis of gravitating astrofluids in Eddington-inspired Born-Infeld gravity framework

The nonlinear Jeans instability dynamics in viscoelastic astrofluids within the Eddington-inspired Born-Infeld (EiBI) gravitational framework excitable in star-forming interstellar cloud fluids is semi-analytically investigated. Application of multiple scaling techniques here results in a unique form of the Korteweg-de Vries (KdV) equation moderated with a peculiar set of distinctive fluid polyparametric coefficients. A numerical illustrative platform portrays the excitation of diversified compressive solitary-chain wave patterns. The evolutionary existence of such structural patterns is further confirmed geometrically with the help of illustrative phase-plane analyses. The various parametric stabilizers and destabilizers, alongside accelerating and decelerating factors on the clouds, are illustratively analysed. It is seen that the composite cloud stability is significantly influenced by the strength polarity of the gravitational EiBI-parameter (χ). The dependency of the obtained solitary wave patterns on the EiBI-polarity is further confirmed in a numerical simulation platform illustratively. Our analysis also highlights that the influence of material density on the system stability is dependent on the EiBI-polarity. The nonlinear spatiotemporal evolution of the instability reveals a unique type of soliton fission phenomenon, indicative of inherently produced additional disturbances within the astrofluid. Our obtained results could be widely helpful in application to the EiBI-centric diverse astrocosmic phenomena, such as bounded structure formation and evolution in diverse complex astroenvirons.

Coherence of Compressional Pc3‐4 Pulsation Driven by Upstream Waves in Topside Ionosphere Observed by the Swarm Constellation

AbstractIn this study, we presented a detailed analysis of ultralow frequency compressional waves with frequencies ranging from 16 to 100 mHz by using magnetic measurements of Swarm A and B, when the two spacecraft were flying in a counter‐rotating configuration. These waves are assumed to be driven by processes in the fore‐shock region and subsequently termed as upstream waves (UWs). An automatic detection algorithm for identifying UW events has been developed and applied to the Swarm magnetic measurements. Different to previous studies we take advantage of the counter‐rotating Swarm constellation to investigate the large‐scale homogeneous wavefield. Only B‐field oscillations from both Swarm A and B satellites satisfy the following criteria are accepted for UWs analysis: (a) highly correlated with normalized correlation coefficient (Cc) larger than 0.9; (b) shifted by less than 3 s between observations; (c) separated up to 90° in latitude and/or longitude. By this procedure we have identified from the years 2018–2023 in total 577 orbits containing UWs in the magnetic recordings of both spacecraft. In the first step, we checked phase shifts between UW detections at large latitudinal separation. The two counter‐rotating spacecraft allowed to make use of the Doppler effect to check the possible propagation of UWs at ionospheric altitude. Although individual events show signs of north‐south wave propagation, on average no systematic motion could be found. Similarly, possible wave motions toward or away from noon hours have been checked. By analyzing the simultaneous observations at larger longitudinal separation, also hardly any phase differences are identified in the east‐west direction. Further by evaluating the statistical results, a mean tiny local time effect seems to emerge, indicating on average an earlier arrival of the waves in the morning and later in the evening hours.

Analytical and numerical models to predict the shape of incident pulse in split-Hopkinson bar experiments

In typical split-Hopkinson pressure bar experiments (SHPB), the striker bar impacts the incident bar via discs made from soft materials such as copper. These discs, also called pulse shapers, are used (i) to eliminate the high frequency components of the incident pulse, (ii) to obtain a finite rise time of the incident pulse and (iii) to obtain a constant strain rate. Although these pulse shapers have been used for over decades in SHPB experiments, no analytical solutions or simple models are available that can predict the incident pulse as a function of the striker velocity, pulse shaper geometry and material parameters. Assuming that the pulse shaper is a rigid-linearly hardening material, we derive the analytical solution for the incident pulse when the rise time of the incident pulse is less than twice the time taken for a longitudinal wave to travel along the length of the striker. For larger rise times, we additionally assume that the striker is rigid to obtain a simple numerical model to predict the incident pulse in the presence of a pulse shaper. Both these models are validated against numerical simulations and experiments to demonstrate their accuracy.