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At least 19 records

Mitigation of resistive drift wave and ion temperature gradient instabilities by velocity shear

The effects of velocity shear on the resistive drift wave instability in the non-adiabatic limit and the toroidal ion temperature gradient instability are investigated for a plasma of inhomogeneous density/ion temperature, respectively. For the resistive drift wave, we find that the instability growth rate decreases monotonically with increasing magnitude of shear, but we find that complete stabilization is impossible. For the ion temperature gradient instability, we find that the standard WKB approximation is insufficient to describe the full behavior of the instability, and that an analysis of the localized eigenmode problem reveals two separate unstable solutions, which the WKB approximation does not predict. The impact of flow shear on these two new unstable solutions is discussed. In both resistive drift wave and ion temperature gradient instabilities, the sheared flow causes a shifting, tilting, and sharpening of the electrostatic potential eddies.

Physics↗

Shear band velocity and activation volume during shear deformation by acoustic emission in a Zr-based bulk metallic glass

Here, an analysis is presented for the shear band velocity of plastic deformation and activation volume of the shear transformation zone (STZ) in a Zr 60 Cu 30 Al 10 bulk metallic glass (BMG). Compared to the values calculated by the stick-slip model, the values of shear band velocity calculated after optimization by the acoustic emission technique are much larger than those reported previously. Plastic flow in BMGs is found to be described by a power-law correlation between the maximum velocity of the shear band and the strain rates. Combining the free volume theory and the STZ theory, the relationship between the volume change in the STZ and the shear band velocity is derived as $Ω=A$(27–ln$v/l$). The value of A, which is a material dependent constant, is 5.43 × 10 –3 for the current BMG at room temperature.

36 MATERIALS SCIENCE↗

The Kelvin–Helmholtz Instability at the Boundary of Relativistic Magnetized Jets

We study the linear stability of a planar interface separating two fluids in relative motion, focusing on conditions appropriate for the boundaries of relativistic jets. The jet is magnetically dominated, whereas the ambient wind is gas-pressure-dominated. We derive the most general form of the dispersion relation and provide an analytical approximation of its solution for an ambient sound speed much smaller than the jet Alfvén speed v A , as appropriate for realistic systems. The stability properties are chiefly determined by the angle ψ between the wavevector and the jet magnetic field. For ψ = π/2, magnetic tension plays no role, and our solution resembles the one of a gas-pressure-dominated jet. Here, only sub-Alfvénic jets are unstable ($0\lt {M}_{e}\equiv (v/{v}_{{\rm{A}}})\cos \theta \lt 1$ , where v is the shear velocity and θ the angle between the velocity and the wavevector). For ψ = 0, the free energy in the velocity shear needs to overcome the magnetic tension, and only super-Alfvénic jets are unstable ($1\lt {M}_{e}\lt \sqrt{{(1+{{\rm{\Gamma }}}_{w}^{2})/[1+({v}_{{\rm{A}}}/c)}^{2}{{\rm{\Gamma }}}_{w}^{2}]}$, with Γ w the wind adiabatic index). Our results have important implications for the propagation and emission of relativistic magnetized jets.

79 ASTRONOMY AND ASTROPHYSICS↗

NETL Plastic Pipes Project (Final Report)

Plastic or composite pipelines have been the bane of the utility locating industry because they are neither conductive nor magnetic which are the properties traditionally used to locate buried utilities. Ground penetrating radar (GPR) is an effective geophysical tool for locating plastic/composite pipelines where resistive cover allows for adequate penetration of radar energy. However, GPR has limited applicability in areas where the soil cover is conductive due to significant clay and/or salt content. This study examines complementary near-surface geophysical methods that are potentially useful for locating buried plastic/composite pipelines, either singly or in combination. Specifically, this modeling study used computational numerical methods to forward model the response of GPR, resistivity, seismic, gravity gradiometry, and photoacoustic/thermoacoustic imaging methods to plastic/composite pipelines for various scenarios including: (1) pipe diameters ranging between 2 in. to 12 in.; (2) burial depths ranging between 3 ft. to 4 ft.; (3) various degrees in contrast in physical properties (i.e., electrical permittivity, elasticity, resistivity, density); and (4) various experimental acquisition choices (e.g., GPR radar and seismic source frequencies, electrode spacing). Numerical modeling performed herein reconfirmed that GPR is the preferred method for detecting/locating plastic pipelines. A caveat for GPR detection is that the material covering the plastic pipe (trench fill material and adjacent soil) must be sufficiently resistive to allow the two-way propagation to the required depth of investigation and back to the surface. GPR was the only method modeled in this study that can be used to directly detect plastic pipelines of 2-in.-diameter and larger when buried 3-ft-deep. GPR data processing and imaging also can determine pipe depth, pipe diameter, trench dimensions, and moisture conditions. Seismic modeling results suggest that direct detection of a 12-in.-diameter plastic pipe at 3-ft.-depth may be possible under favorable conditions; however, the associated signature would be weak (e.g., surface- to S-wave, backscattered surface-waves, and/or forward scattered surface-waves to S-wave). Direct pipe detection under field conditions with noise and strong lateral geologic heterogeneity is doubtful. Numerical modeling also suggests that plastic pipelines can be indirectly located by detecting the trench in which they are buried. GPR, direct current (DC) resistivity, and seismic methods have the potential to locate the pipeline trench if there is sufficient contrast between the trench-wall and trench-fill materials for the physical property being measured by each method (i.e., electrical permittivity for GPR; resistivity for DC resistivity; or density, compressional velocity, or shear velocity for seismic). Modeling also indicated that currently available (commercial) gravity gradiometers would be unable to directly detect/locate plastic pipelines ≤ 8-in.-diameter when buried 3-ft.-deep given the typical instrument noise floor for field surveying as well as the expected density variations due to geologic heterogeneity. The numerical modeling performed in this project did not identify a universal geophysical technology that can locate buried plastic pipelines in all parts of the United States (although GPR is suggested for all areas with resistive cover). However, the project results suggest that a towed land streamer simultaneously acquiring multiple geophysical data types including multi-offset GPR, multi-channel DC resistivity, seismic geophone- and/or distributed acoustic sensing (DAS), and potentially photoacoustic/thermoacoustic data would be an appropriate platform for locating buried plastic pipeline. Moreover, the complementary multiphysics data acquired by a towed land streamer would permit the use of joint and/or cooperative inversion frameworks for a more rigorous and consistent data interpretation.

42 ENGINEERING↗

Monitoring Seasonal Shear Wave Velocity Changes in the Top 6 m at Garner Valley in Southern California With Borehole Data

Abstract Subsurface structures play important roles in seismic ground motion, crustal hydrology, stability of the built environment, and more. Constraining temporal changes of subsurface shear wave velocity ( V S ) can provide useful information to all these topics and the growing field of hydrological monitoring with seismic velocity. Using borehole records at Garner Valley, CA, we estimate seasonal subsurface V S variations from impulse response functions (IRFs) of earthquake data (2005–2018) along with IRFs and cross‐correlation of cross‐hole experiment data (2015–2018). The inferred V S variations are up to ∼25% in the top 6 m and ∼10% at 2–5 m in depth. The V S variations correlate strongly with the water table depth changes, suggesting that the changes are mostly due to fluctuations of pore pressure in the shallow material. The shallow velocity changes alter the near‐surface conditions, can affect seismic hazard estimation, and may be improperly attributed to deeper processes without careful analysis.

58 GEOSCIENCES↗

Close-Out Project Description for Koepke's Dept of Energy grant DE-SC0021405

Objectives: To establish, for lab & space conditions, EM-IEDDI’s (electromagnetic shear-driven instability's) dispersion relation, unstable range, instability threshold, and mode characteristics, we need LAPD’s Alfven-wave-favorable electromagnetic-style conditions, including higher "beta" (0.001 < beta ≤ 0.3) and low-collisionality. Also, we attempted to intentionally launch or spontaneously destabilize compressional and shear Alfven waves in the strong, localized, perpendicular-velocity-shear region at the interface between coaxial plasmas (one plasma cylinder inside an outer, otherwise hollow, tube, each having a different, controllable, value of plasma electrostatic potential, i.e., “space” potential (not to be confused with the temperature-dependent “floating” potential of an object immersed in the plasma). Nonlinear wave-wave interactions between same-family (EM-IEDD or Alfven) and cross-family (EM-IEDD-with-Alfven) fluctuations were targeted for documentation over a range of spectral overlap. Although laboratory experiments were conducted, the following theoretical work was left unfinished: Analytical non-modal prediction Computational non-modal prediction Check to see if Mikhailenko’s theory formulation leads to his published graphs

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Linear analysis of the Kelvin–Helmholtz instability in relativistic magnetized symmetric flows

ABSTRACT We study the linear stability of a planar interface separating two fluids in relative motion, focusing on the symmetric configuration where the two fluids have the same properties (density, temperature, magnetic field strength, and direction). We consider the most general case with arbitrary sound speed cs, Alfvén speed vA, and magnetic field orientation. For the instability associated with the fast mode, we find that the lower bound of unstable shear velocities is set by the requirement that the projection of the velocity on to the fluid-frame wavevector is larger than the projection of the Alfvén speed on to the same direction, i.e. shear should overcome the effect of magnetic tension. In the frame where the two fluids move in opposite directions with equal speed v, the upper bound of unstable velocities corresponds to an effective relativistic Mach number $M_{\rm re}\equiv v/v_{\rm {f}\perp }\sqrt{(1-v_{\rm {f}\perp }^2)/(1-v^2)} \cos \theta =\sqrt{2}$, where $v_{\rm {f}\perp }=[v_{\rm {A}}^2+c_{\rm s}^2(1-v_{\rm {A}}^2)]^{1/2}$ is the fast speed assuming a magnetic field perpendicular to the wavevector (here, all velocities are in units of the speed of light), and θ is the laboratory-frame angle between the flow velocity and the wavevector projection on to the shear interface. Our results have implications for shear flows in the magnetospheres of neutron stars and black holes – both for single objects and for merging binaries – where the Alfvén speed may approach the speed of light.

Astronomy & Astrophysics↗

The Impact of Alfvénic Shear Flow on Magnetic Reconnection and Turbulence

Magnetic reconnection is a fundamental and omnipresent energy conversion process in plasma physics. Novel observations of fields and particles from Parker Solar Probe (PSP) have shown the absence of reconnection in a large number of current sheets in the near-Sun solar wind. Using near-Sun observations from PSP encounters 4–11 (2020 January–2022 March), we investigate whether reconnection onset might be suppressed by velocity shear. We compare estimates of the tearing mode growth rate in the presence of shear flow for time periods identified as containing reconnecting current sheets versus nonreconnecting times, finding systematically larger growth rates for reconnection periods. Upon examination of the parameters associated with reconnection onset, we find that 85% of the reconnection events are embedded in slow, non-Alfvénic wind streams. We compare with fast, slow non-Alfvénic, and slow Alfvénic streams, finding that the growth rate is suppressed in highly Alfvénic fast and slow wind, and reconnection is not seen in these wind types, as would be expected from our theoretical expressions. These wind streams have strong Alfvénic flow shear, consistent with the idea of reconnection suppression by such flows. This could help explain the frequent absence of reconnection events in the highly Alfvénic, near-Sun solar wind observed by PSP. Finally, we find a steepening of both the trace and magnitude magnetic field spectra within reconnection periods in comparison to ambient wind. We tie this to the dynamics of relatively balanced turbulence within these reconnection periods and the potential generation of compressible fluctuations.

slow solar wind↗

Electron-scale Magnetic Holes Generation Driven by Whistler-to-Bernstein Mode Conversion in Fully Kinetic Plasma Turbulence

Magnetic holes (MHs) are coherent structures characterized by a strong and localized magnetic field amplitude dip, commonly observed in the heliosphere. These structures come in different sizes, from magnetohydrodynamic to kinetic scales. Subion-scale MHs are usually sustained by an electron current vortex and exhibit a strong electron temperature anisotropy, with higher temperatures perpendicular to the background magnetic field. Magnetospheric multiscale observations (MMSs) have revealed electron-scale MHs to be ubiquitous in the turbulent Earth’s magnetosheath and the solar wind, potentially playing an important role in the energy cascade and dissipation. Despite abundant observations, the origin of electron-scale MHs is still unclear and debated. In this work, we use fully kinetic simulations to investigate the role of plasma turbulence in generating electron-scale MHs. We find that the turbulence spontaneously produces electron-scale MHs via the following mechanism: first, large-scale turbulent velocity shears produce regions with high electron temperature anisotropy; these localized regions become unstable, generating oblique electron-scale whistler waves; as they propagate over the inhomogeneous turbulent background, whistler fluctuations develop an electrostatic component, turning into Bernstein-like modes; the strong electrostatic fluctuations produce current filaments that merge into an electron-scale current vortex; the resulting electron vortex locally reduces the magnetic field amplitude, finally evolving into an electron-scale MH. We show that MHs generated by this mechanism have properties consistent with MMSs and nontrivial kinetic features with a “mushroom”-shaped electron velocity distribution function. Our results have potential implications for understanding the formation and occurrence of electron-scale MHs in astrophysical turbulent and space environments, such as the Earth’s magnetosheath and the solar wind.

79 ASTRONOMY AND ASTROPHYSICS↗

Simulating High-Frequency Seismograms in Realistic Earth Models to Better Understand Source Discrimination Based on Differential Magnitudes ( M L− M c)

Discriminating low-yield underground nuclear explosions from small earthquakes is a key task in monitoring nuclear test ban treaties. P/S amplitude ratios have been an effective discriminant for moderate-sized events recorded at regional distances, but it is unclear if they are as effective in discriminating small seismic events recorded at local distances (<150 km). The difference between local magnitude (M L ) and coda duration magnitude (M c ) has been proposed as a new discriminant that may complement P/S amplitude ratios at local distances. Here, in this work, we calculate high-frequency (up to ∼4 Hz) synthetic seismograms at epicentral distances of 0–30 km in realistic models of the Salt Lake basin (Utah, United States) to better understand how variations in source type and depth affect M L −M c values. The Earth models incorporate simplified 1D and deterministic 3D structures, small-wavelength stochastic velocity perturbations, and surface topography. Coda waves are enhanced for the more complicated models compared to the base 1D model, but still underpredict observed durations by about a factor of two, which results in overprediction of amplitude to duration ratios (i.e., M L −M c values) for a near-surface explosion and a 7 km deep earthquake. For both source types, the predicted M L and M c values decrease as source depth increases, and M L −M c shows only minor variation with depth; however, M L −M c is on average ∼0.5 units smaller for explosions than earthquakes. This finding may imply that M L −M c has sensitivity to source type, in addition to being a depth discriminant, but more modeling is needed given the limitations of the current study. Future modeling should incorporate higher-frequency (≳5 Hz) simulations over a larger distance range (0–150 km), where M L and M c are commonly measured, while honoring low shear velocities (<300 m/s) near the surface and sampling a wider range of earthquake and explosion source mechanisms.

Hutchings, Sean J. [Univ. of Utah, Salt Lake City,↗

Transport Barriers in magnetized plasmas- general theory with dynamical constraints

Abstract A fundamental dynamical constraint—that fluctuation induced charge-weighted particle flux must vanish- can prevent instabilities from accessing the free energy in the strong gradients characteristic of Transport Barriers (TBs). Density gradients, when large enough, lead to a violation of the constraint and hence preclude unstable modes and turbulent transport. This mechanism, then, broadens the class of configurations (in magnetized plasmas) where these high confinement states can be formed and sustained. The need for velocity shear, the conventional agent for TB formation, is obviated. The most important ramifications of the constraint is to permit a charting out of the domains conducive to TB formation and hence to optimally confined fusion worthy states; the detailed investigation is conducted through new analytic methods and extensive gyrokinetic simulations.

Physics↗

TEAMER – Enhanced Flow Measurement for Aquantis Tidal Turbine Test

The AQ10 is a floating, two-bladed, passive yawing tidal turbine developed by Aquantis that has a 10-meterrotor diameter, 160 kW rating, and employs reliable off-the-shelf powertrain and power conversion hardware. Aquantis is planning on-water turbine power performance and loads (blade loading and thrust)testing, where the turbine will be pushed through still water up to 4 knots and placed in a ‘station keeping’ tow in a tidal race up to its rated speed. On-water testing will be conducted using vessels and floating platforms on the sea surface to improve ease of testing and reduce disturbance to the environment. In this TEAMER project, Pacific Northwest National Laboratory (PNNL) will conduct water velocity and turbulence measurements in front of the turbine during on-water testing using acoustic Doppler instrumentation. By measuring both the tidal current flowing past the turbine and the resulting electrical power output, test results will provide a power curve (power vs flow speed) for the turbine up to rated power. Measurements of turbulence and velocity shear in front of the rotor will also provide information to assess the structural response of the rotor blades. With this analysis, Aquantis can use the performance and loads data to validate Tidal Bladed and OpenFAST simulations of the measured operating conditions. Measuring the power performance of a prototype turbine is a valuable step to improving device development and conducting a complete power performance assessment to IEC/TS 62600-200 standards in the future.

16 TIDAL AND WAVE POWER↗

Identification of Kelvin-Helmholtz generated vortices in magnetised fluids

The Kelvin-Helmholtz Instability (KHI), arising from velocity shear across the magnetopause, plays a significant role in the viscous-like transfer of mass, momentum, and energy from the shocked solar wind into the magnetosphere. While the KHI leads to growth of surface waves and vortices, suitable detection methods for these applicable to magnetohydrodynamics (MHD) are currently lacking. A novel method is derived based on the well-established λ-family of hydrodynamic vortex identification techniques, which define a vortex as a local minimum in an adapted pressure field. The J × B Lorentz force is incorporated into this method by using an effective total pressure in MHD, including both magnetic pressure and a pressure-like part of the magnetic tension derived from a Helmholtz decomposition. The λ MHD method is shown to comprise of four physical effects: vortical momentum, density gradients, fluid compressibility, and the rotational part of the magnetic tension. A local three-dimensional MHD simulation representative of near-flank magnetopause conditions (plasma β’s 0.5 – 5 and convective Mach numbers M f ∼ 0.4) under northward interplanetary magnetic field (IMF) is used to validate λ MHD . Analysis shows it correlates well with hydrodynamic vortex definitions, though the level of correlation decreases with vortex evolution. Overall, vortical momentum dominates λ MHD at all times. During the linear growth phase, density gradients act to oppose vortex formation. By the highly nonlinear stage, the formation of small-scale structures leads to a rising importance of the magnetic tension. Compressibility was found to be insignificant throughout. Finally, a demonstration of this method adapted to tetrahedral spacecraft observations is performed.

79 ASTRONOMY AND ASTROPHYSICS↗

3D seismic imaging of a fracture damage zone controlling reservoir compartmentalization at the Raft River EGS using multi-azimuth walkaway VSP

Accurate imaging of steeply dipping fracture zones in crystalline enhanced geothermal systems (EGS) is critical for constraining permeability architecture and guiding stimulation design. However, such structures remain poorly resolved by conventional surface seismic methods. We present a fully three-dimensional (3D) elastic-waveform inversion-migration workflow applied to multi-azimuth walkaway vertical seismic profiling (VSP) data acquired in a deviated borehole at the Raft River EGS. The workflow integrates first-arrival traveltime tomography, multi-scale elastic waveform inversion (EWI), and elastic least-squares reverse-time migration (ELSRTM) to recover high-resolution compressional-and shear-wave velocity models and to image structural discontinuities in the crystalline basement. The results reveal a laterally continuous low-velocity anomaly, with shear-wave velocity reductions of 25-30%, consistent with fractureinduced mechanical weakening. Two steeply dipping discontinuities bound a 50-80 m wide fracture damage zone. Independent constraints from microseismic clustering and geochemical compartmentalization corroborate the geometry and structural significance of this feature. Synthetic modeling further confirms that structures of this scale are resolvable (~30 m). These findings indicate that the Narrows structure is a distributed fracture damage zone rather than a discrete fault plane. By resolving fracture-zone geometry at the tens-of-meters scale using a single borehole, this workflow provides a practical and transferable approach for improving structural characterization, reducing uncertainty in permeability architecture, and supporting reservoir modeling and stimulation design in fractured crystalline EGS reservoirs.

58 GEOSCIENCES↗

The Influence of Shallow Subsurface Properties on Particle Motion in Acoustic-Seismic Coupling

Atmospheric acoustic waves transmit energy into the solid Earth through air-to-ground coupling. These waves are recorded by seismic sensors and provide insight into both atmospheric phenomena and subsurface properties. Interpreting these signals is often challenging because they are modulated by subsurface structure and the incidence angle of the acoustic wave. This study examines acoustic--seismic coupling generated by the 2012 Camp Minden Explosion, which was recorded by hundreds of seismoacoustic stations. We apply a novel technique to quantify the seismic particle motion, model coupled waves with a propagator matrix approach, and apply a Bayesian inversion to infer properties of the shallow subsurface. Our analysis reveals that prograde motion is widespread and focused in low shear-wave velocity regions, such as the Mississippi Embayment, and retrograde motion is more common in higher shear-velocity areas. Inversion results at some stations produce plausible subsurface models with strong waveform fits, while inversions at other sites are less successful. These results indicate prograde particle motion in air-to-ground coupled waves is more prevalent than previously recognized and may serve as a diagnostic for shallow velocity structure. Our comprehensive modeling and inversion framework provides a potential method to extract layered near-surface properties from acoustic-seismic coupling observations.

58 GEOSCIENCES↗

Elasticity of davemaoite as a primary contributor to lower-mantle heterogeneities

Geophysical detection of subducted mid–ocean ridge basalt (MORB) in the lower mantle is hindered by uncertainties in the elasticity of Fe,Al,Mg,Ti–bearing davemaoite, a key MORB component. Using Brillouin spectroscopy and x-ray diffraction, we determined the elasticity of a Ca 0.906(1) Fe 2+ 0.027(1) Fe 3+ 0.042(1) Mg 0.033(1) Al 0.072(1) Ti 0.020(1) Si 0.912(1) O 3 davemaoite up to 113 gigapascals and 2294 K. Here, we found that it exhibited a shear wave velocity 10 to 20% slower than end-member davemaoite, making it the slowest phase among major lower-mantle minerals. Our models show that MORB, containing 20 to 25 volume percent davemaoite, potentially contributes to large low-shear-velocity provinces (LLSVPs), whereas a cumulate layer enriched in davemaoite crystallized from basal magma ocean may comprise ultralow-velocity zones (ULVZs). Davemaoite’s ability to host incompatible and heat-producing elements possibly links LLSVPs and ULVZs to mantle plume initiation and geochemical signatures of ocean island basalts.

Zhou, Wen-Yi [Texas A & M Univ., College Station, ↗

Investigation of Site Amplifications Using Ambient-Noise-Derived Shallow Velocity Structures Under a Dense Array in Oklahoma

The shear-wave velocity (V S ) structure plays an important role in characterizing site amplification. The Large-n Seismic Survey in Oklahoma (LASSO; 1820 stations) revealed large vertical ground-motion variability in a 25 km × 32 km area in northern Oklahoma. The LASSO array has a relatively simple and flat topography, typical in a sedimentary basin environment in the central United States. In this study, we use the dense array to investigate the velocity structure under the LASSO array and how vertical ground motions relate to the shallow-to-deep structures. We extract the fundamental-mode Rayleigh wave by cross-correlating one month of ambient noise (0.7–5 Hz). We use double-beamforming to measure the group and phase velocities and anisotropy. By jointly inverting the group and phase velocities, we obtain the V S structure. Here, we observe correlations between V S at depths of 0.1–1.5 km and vertical ground motions using sites on the stiffer Permian formations. The shallow Quaternary alluvium and terrace deposits can amplify vertical ground motions by a factor of 2–4.5 between 2 and 25 Hz and attenuate signals above 25 Hz. We use 1D V S profiles to simulate the SV-wave transfer functions. An average V S of 250 m/s in the upper 20–40 m may cause the observed amplification between 2 and 40 Hz. V S estimated by topographic slopes cannot predict the relative amplification. Our results highlight the large variability of site-dependent ground motion in a small local region and the importance of characterizing shallow structures to estimate seismic hazards. Small thickness variations of the shallow formation can significantly change the resonance amplitude and frequency, which likely reduces the coherency of the Rayleigh waves extracted from ambient noise.

Chang, Hilary [Massachusetts Inst. of Technology (↗

Sound Speeds of Solids from Ultrasonic Pulse Receiver Measurements

A common method of determining elastic material properties is utilizing an ultrasonic pulse receiver. This is a non-destructive test (NDT) causing no plastic deformation of the material. It requires a pulse generator, oscilloscope, and two transducers to measure the sound velocity of a material. Both longitudinal and shear sound velocities may be obtained by utilizing the appropriate transducer. Acoustic nondestructive testing methods are often used in manufacturing certification processes and for material defect detection in industry. These methods can also be utilized to directly measure the elastic moduli of a material without damaging the material. Overall, it is a low-cost experiment with minimal preparation, and is easy to use.

36 MATERIALS SCIENCE↗