Energy Amplification Research Articles

Separating, purifying and decoding elastic waves by mimicking a cochlea on a thin plate

A human cochlea is capable of continuously separating and amplifying sound of different frequencies to specific positions from 20 to 20,000 Hz, which makes it a high-resolution living sensor. The realization of cochlea-like structure for elastic waves in solids offers a highly desirable functionality on high throughput mechanical energy harvesting and sensing, but remains a challenging topic owing to narrow band and intricate configuration. Here we propose and demonstrate a generic framework of elastic cochlea on a thin plate, enabled by a pair of compact metafence layers. It is experimentally realized to harvest and separate flexural waves in quite a wide frequency range from 5.8 to 21.8 kHz, together with a continuous energy amplification exceeding one magnitude order. An enhanced mode, characterized by a near zero group velocity at a tailored cutoff width, is uncovered to illustrate the filtering and amplification physics. Moreover, complex information demultiplexing and undistorted decoding are further realized by harnessing the high-Q signal sensing and purification. The proposed prototype may stimulate substantial applications on information processing, non-destructive evaluation and other wave regulation scenarios.

Evaluation of the strain energy during the interaction between micro-crack and semi-infinite crack in a brittle material

The main goal of this research is to evaluate the strain energy in a brittle material during the interaction of the semi-infinite crack with a neighboring micro-crack. The problem is formulated by considering a cracked thin plate having a micro-crack that rotates around itself and around the semi-infinite crack whose the cracked plate is subjected to a uniform load under mode I. During the interaction between the semi-infinite crack and micro-crack, the strain energy and stress field can be generated at the crack tip of semi-infinite crack. The theoretical analysis of this interaction is treated mathematically by the complex potentials functions. It is shown that the positioning of the micro-crack relative to the semi-infinite crack leads to amplification, reduction and absorption of the strain energy at the crack-tip. The theoretical results agree with those found numerically.

Simultaneous low-frequency vibration isolation and energy harvesting via attachable metamaterials

In this study, we achieved energy localization and amplification of flexural vibrations by utilizing the defect mode of plate-attachable locally resonant metamaterials, thereby realizing compact and low-frequency vibration energy suppression and energy harvesting with enhanced output performance. We designed a cantilever-based metamaterial unit cell to induce local resonance inside a periodic supercell structure and form a bandgap within the targeted low-frequency range of 300–450 Hz. Subsequently, a defect area was created by removing some unit cells to break the periodicity inside the metamaterial, which led to the isolation and localization of the vibration energy. This localized vibration energy was simultaneously converted into electrical energy by a piezoelectric energy harvester coupled with a metamaterial inside the defect area. Consequently, a substantially enhanced energy harvesting output power was achieved at 360 Hz, which was 43-times higher than that of a bare plate without metamaterials. The proposed local resonant metamaterial offers a useful and multifunctional platform with the capability of vibration energy isolation and harvesting, while exhibiting easy handling via attachable designs that can be tailored in the low-frequency regime.

Regenerative Orr mechanism yielding large non-modal perturbation energy growth in a viscosity stratified plane shear flow

Transiently growing non-modal perturbations can play a crucial role in the transition of plane shear flows in modally stable regimes. In terms of the extent of transient amplification, three-dimensional perturbations are typically more prominent due to the lift-up effect. In contrast, two-dimensional (2D) spanwise-independent perturbations are often considered less important as they typically undergo modest levels of transient growth and are short-lived. The Orr mechanism is key to the amplification of energy for 2D perturbations. In this work, we discuss 2D non-modal perturbations of three-layer viscosity stratified flows with the mean shear rates of the outer layers being equal. Strikingly, a novel regenerative Orr mechanism is found that allows for significant amount of energy amplification despite the 2D nature of the perturbations. Moreover, these perturbations survive for considerably long times. The perturbation structure shows symmetry about the middle layer and evolves such that the Orr mechanism can repeatedly occur in a regenerative manner resulting in the perturbation energy evolving in a markedly non-monotonic fashion. When these same perturbations are introduced in a uniform plane shear flow, the corresponding non-modal transient amplifications are shown to be much smaller.

Long-Term Outcome of Surgery for Grade 4 Gynecomastia: A Single-Center Experience

Abstract Background Gynecomastia results in a feminine appearance of the male chest, leading to social embarrassment and loss of self-esteem in the afflicted males. Grade 4 gynecomastia is expected to have less than perfect results with liposuction and gland excision alone. This study was done to assess the long-term outcome of this surgery for grade 4 gynecomastia. Materials and Methods From January 2021 to December 2022, 81 patients with grade 4 gynecomastia were treated by us. All the patients underwent vibration amplification of sound energy at resonance (VASER) and suction-assisted liposuction of the chest and side rolls with excision of the gland with crescentic lift in the cases with ptosis. A retrospective study was done to analyze the long-term surgical outcomes in these patients by review of clinical records. Results Symmetry was achieved in 37/39 patients with grade 4a gynecomastia but only in 33/42 patients with grade 4b gynecomastia. The inframammary fold disappeared in 35/39 patients with grade 4a gynecomastia but only in 25/42 of grade 4b gynecomastia patients. Ptosis was corrected in 35/42 grade 4b gynecomastia patients. The mean follow-up was 15 months (range: 12–24 months). Only seven patients desired a second stage to correct the remaining deformity. Conclusion Liposuction with gland removal alone in grade 4a gynecomastia and with liposuction with crescentic nipple–areola complex (NAC) lift in patients of grade 4b gynecomastia give satisfactory results in patients with massively enlarged breasts. While grade 4a gynecomastia has overall better results and lesser complications as compared with grade 4b gynecomastia, the latter also has acceptable outcomes. Realistic prognosis needs to be explained to the patient preoperatively.

Non-modal analysis of transient growth in a liquid annular jet surrounded by gas flow

Transient energy growth is a common mathematical concept in many fluid flow systems, and it has been widely investigated in recent years using non-modal analysis. Non-modal analysis can characterize the short-term energy amplification of perturbations, which is influenced by the Reynolds number, the Weber number, and the initial conditions such as the wavenumber. In gas–liquid coaxial nozzles, annular jets are often produced, and their breakup process is influenced by transient energy growth. However, research in this area has been limited so far. This paper for the first time investigates the transient energy growth of an annular liquid jet in static gas and validates it using a modified annular jet model. In the derivation process, the gas–liquid interfaces inside and outside the annular liquid film are taken into account. It has been found that there exists an optimal initial condition for a certain Reynolds number and a Weber number. The increase in the Reynolds number and ratio of inner and outer radius of the annular jet can maximize the transient growth under a specific initial wavenumber, while the increase in gas/liquid density ratio and the Weber number will minimize the transient growth. It is also found that transient energy growth is caused by the displacement of the free boundary.

Koopman-inspired data-driven quantification of fluid–structure energy transfers

The linear-time-invariance notion to the Koopman analysis is a recent advance in fluid mechanics [Li et al., “The linear-time-invariance notion to the Koopman analysis: The architecture, pedagogical rendering, and fluid–structure association,” Phys. Fluids 34(12), 125136 (2022c) and Li et al., “The linear-time-invariance notion of the Koopman analysis—Part 2. Dynamic Koopman modes, physics interpretations and phenomenological analysis of the prism wake,” J. Fluid Mech. 959, A15 (2023a)], targeting the long-standing issue of correlating nonlinear excitation and response phenomena in fluid–structure interactions (FSI), or, in the simplified case, flow over rigid obstacles. Continuing the serial research, this work presents a data-driven, Koopman-inspired methodology to decouple nonlinear FSI by establishing cause-and-effect correspondences between structure surface pressure and the flow field. Exploiting unique features of the Koopman operator, the new methodology renders dynamic visualizations of in-sync, fluid–structure-coupled Koopman modes possible, fostering phenomenological analysis and statistical quantifications of FSI energy transfers. Instantaneous contribution contours and densities offer new angles to evaluate pathways of energy amplification and diminution. The methodology enables better descriptions and interpretations of phenomena occurring in the flow and on the boundary (walls) of an FSI domain and readily applies to a broad spectrum of engineering problems given its data-driven nature.

Nonlinear Nonmodal Analysis of Hypersonic Flow over Blunt Cones

The linear amplification of modal disturbances that lead to boundary-layer transition in two-dimensional/axisymmetric hypersonic configurations is strongly reduced by the presence of a blunt nose tip, and the mechanisms underlying the low Mack’s second-mode N-factor values at the observed onset of transition over the cone frustum are currently unknown. Linear nonmodal analysis has shown that both planar and oblique traveling disturbances that peak within the entropy-layer experience appreciable energy amplification for moderate to large nose-tip bluntness. The present study extends the previous linear analysis by including the nonlinear effects. Specifically, the harmonic Navier–Stokes equations (HNSE) are solved with a fully implicit formulation and the Newton–Raphson method. The increased number of degrees of freedom for the nonlinear system presents difficulties for solution strategies based on direct solution of the linearized system. Such difficulties are overcome by using the generalized minimal residual method (GMRES) iterative method with a preconditioner corresponding to a simplified Jacobian without the cross-derivative terms. The HNSE solver is verified by comparing with nonlinear parabolized stability equation results for the nonlinear evolution of planar waves in an incompressible Blasius boundary layer and in a Mach 6 flow over a blunt cone. Finally, nonlinear nonmodal results are presented for planar traveling disturbances over a blunt cone configuration with reduced transition N factor as measured in wind-tunnel experiments. The nonmodal analysis demonstrates that entropy-layer disturbances generated close to the nose tip can seed the amplification of higher-frequency Mack’s second-mode instabilities farther downstream and hence can lead to a reduction in the transition N factor.

Nonmodal stability analysis of Poiseuille flow through a porous medium

We unravel the nonmodal stability of a three-dimensional nonstratified Poiseuille flow in a saturated hyperporous medium constrained by impermeable rigid parallel plates. The primary objective is to broaden the scope of previous studies that conducted modal stability analysis for two-dimensional disturbances. Here, we explore both temporal and spatial transient disturbance energy growths for three-dimensional disturbances when the Reynolds number and porosity of the material are high, based on evolution equations with respect to time and space, respectively. Modal stability analysis reveals that the critical Reynolds number for the onset of shear mode instability increases as porosity increases. Moreover, the Darcy viscous drag term stabilizes shear mode instability, resulting in a delay in the transition from laminar flow to turbulence. In addition, it demonstrates the suppression of three-dimensional shear mode instability as the spanwise wavenumber increases, thereby confirming the statement of Squire’s theorem. By contrast, nonmodal stability analysis discloses that both temporal and spatial transient disturbance energy growths curtail as the effect of the Darcy viscous drag force intensifies. But their maximum values behave like O(Re2) for a fixed porous material, where Re is the Reynolds number. However, for different porous materials, the scalings for both temporal and spatial transient disturbance energy growths are different. Furthermore, increasing porosity also suppresses both temporal and spatial disturbance energy growths. Finally, we observe that temporal transient disturbance energy growth becomes larger for a spanwise perturbation, while spatial transient disturbance energy growth becomes larger for a steady perturbation when angular frequency vanishes. The initial disturbance that excites the largest temporal energy amplification generates two sets of alternating high-speed and low-speed elongated streaks in the streamwise direction.

On the nonlinear energy interactions in vibro-impacting cantilever

The nonlinear energy interactions are an intriguing aspect of nonlinear oscillators, such as vibro-impacting cantilevers (VICs). Despite extensive research, the domain of energy interactions in nonlinear oscillators still requires further exploration. The motivation arises from the complex and captivating dynamics as well as the vast array of potential applications. This paper presents a comprehensive investigation of various energy interaction mechanisms within the resonance realms of the first and second mode resonance frequencies of harmonically base-excited VICs. These energy interactions are of paramount importance as they give rise to the captivating response of the VIC, characterized by multi- and quasi-periodicity, energy amplification, combination resonances, amplitude modulation, and other intriguing features. This paper introduces the phenomenon termed “Harmonic Resonance Energy Stimulation (HRES)” and extensively investigates its role in generating the secondary jump in the frequency response. Moreover, the present study discovers and reports the non-resonant energy interactions and resulting modulating, quasi-periodic response in the VIC. Various illustrative plots obtained from the theoretical investigation, relying on the mathematical model, have been utilized to facilitate a comprehensive investigation. The results hold immense significance as they contribute valuable knowledge to the nonlinear dynamics of VIC, which is of great importance in research advancements and practical applications.

Nonlinear scaling of fluctuation kinetic energy for shock–vorticity wave interaction

Turbulent kinetic energy (TKE) is a quantity of primary importance in shock–turbulence interaction (STI). Linear interaction analysis (LIA) serves as a theoretical method to predict the amplification of TKE in STI. LIA is constrained by low-amplitude fluctuations and neglects nonlinear effects. In this paper, we explore the nonlinear amplification of the kinetic energy of fluctuations in the interaction between a vorticity wave and a shock wave that serves as a building block flow for STI. A weakly nonlinear framework (WNLF) is introduced to analyze nonlinear effects in fluctuation kinetic energy (FKE) and identify the dominant physical mechanisms driving its amplification. The theoretical framework is validated through high-accuracy numerical simulations of shock–vorticity wave interactions. The simulation results are compared with the predictions derived from the WNLF for a range of intensities and inclinations of shock-upstream vorticity fluctuations at different Mach numbers, and WNLF is found to successfully scale the numerical data for FKE, thus confirming the validity and applicability of the framework. According to WNLF findings, at lower supersonic Mach numbers, the intermodal interaction between vorticity–vorticity modes is important, whereas the interaction between vorticity and acoustic modes becomes dominant at higher Mach numbers. Using the intermodal interactions, a model based on WNLF is proposed to predict TKE amplification in STI. In comparison to direct numerical simulation, the WNLF based model predicts the TKE amplification for moderate turbulent Mach number and lower supersonic flow Mach numbers. This is a significant improvement over the LIA results available in the literature.

A randomized intraindividual comparative study evaluating the effects of two ultrasound-assisted liposuction devices on the abdomen

BackgroundUltrasound-assisted liposuction (UAL) has become popular because of its favorable outcomes in terms of fat emulsification, blood loss reduction, and skin tightening. This study aimed to compare the effects of two UAL devices on the abdomen by assessing postsurgery skin biomechanical properties. MethodsThis single-blind, prospective study (2020-2022) involved 13 liposuction procedures performed on patients without chronic diseases. Each patient's abdomen was divided vertically from the xiphoid to the perineum. Vibration amplification of sound energy at resonance (VASER)-assisted liposuction (Solta Medical, Inc., Hayward, CA) was performed on one half, while the other half underwent liposuction with high-frequency ultrasound energy (HEUS)-assisted technology. Skin biomechanical measurements, including distensibility, net elasticity, biological elasticity, hydration, erythema, melanin, and skin firmness, were taken at 12 and 24 months postsurgery, focusing on the anterior abdomen, 8cm to the right and left of the umbilicus. ResultsAnalysis of the above skin biomechanical measurements revealed no significant differences between the HEUS and VASER devices, except for skin firmness, which showed a notable increase following HEUS surgery. Patient-perceived clinical differences were assessed via nonvalidated questionnaires, revealing no distinctions between devices. ConclusionBiomechanical skin results post-UAL surgery with these devices on the abdomen were not significantly different, although HEUS revealed increased skin firmness. This suggests that HEUS-assisted technology, akin to other devices, is a viable option for UAL procedures.

Transient growth of wavelet-based resolvent modes in the buffer layer of wall-bounded turbulence

In this work, we study the transient growth of the principal resolvent modes in the minimal flow unit using a reformulation of resolvent analysis in a time-localized wavelet basis. We target the most energetic spatial wavenumbers for the minimal flow unit and obtain modes that are constant in the streamwise direction and once-periodic in the spanwise direction. The forcing modes are in the shape of streamwise rolls, though pulse-like in time, and the response modes are in the form of transiently growing streaks. We inject the principal transient forcing mode at different intensities into a simulation of the minimal flow unit and compare the resulting nonlinear response to the linear one. The peak energy amplification scales quadratically with the intensity of the injected mode, and this peak occurs roughly at the same time for all forcing intensities. However, the larger energy amplification intensifies the magnitude of the nonlinear terms, which play an important role in damping the energy growth and accelerating energy decay of the principal resolvent mode. We also observe that the damping effect of the nonlinearities is less prominent close to the wall. Finally, we find that the principal resolvent forcing mode is more effective than other structures at amplifying the streak energy in the turbulent minimal-flow unit. In addition to lending support to the claim that linear mechanisms are important to near-wall turbulence, this work identifies time scales for the nonlinear breakdown of linearly-generated streaks.

Wave attenuation and transformation across a highly turbid muddy tidal flat-salt marsh system

Understanding wave processes within the coastal system is crucial for the appropriate design of coastal prevention engineering and offshore structures. To address the limitations of field observations and traditional methods, an array of pressure sensors and optical instruments were deployed across a shoreward intertidal flat consisting of the fluid muddy seabed, bare flat, and salt marsh in a highly turbid coastal area. We found that the Spartina alterniflora salt marsh has the strongest wave dissipation capacity. Although bare flats have the weakest wave dissipation capacity, they are the most extensive within the intertidal zone, resulting in substantial total wave energy dissipation. A noteworthy positive feedback between fluid mud and wave dissipation is observed. Additionally, the incident waves undergo complex transitions during propagation, which are strongly modulated by tidal influences. In particular, when the wave propagation direction is opposite to the tidal current, there is an amplification of wave energy within the tidal flat. This amplification is attributed to the "jacking effect" of the tidal current, hindering the transformation of the wind waves into the low-energy capillary waves. It is important to note that the high-energy infragravity waves are gradually released and steadily increase as the incident waves propagate shoreward. This implies their potentially significant role in nearshore processes, especially during extreme dynamic events or along extensive coastlines.

Beyond optimal disturbances: a statistical framework for transient growth

The theory of transient growth describes how linear mechanisms can cause temporary amplification of disturbances even when the linearized system is asymptotically stable as defined by its eigenvalues. This growth is traditionally quantified by finding the initial disturbance that generates the maximum response at the peak time of its evolution. However, this can vastly overstate the growth of a real disturbance. In this paper, we introduce a statistical perspective on transient growth that models statistics of the energy amplification of the disturbances. We derive a formula for the mean energy amplification and spatial correlation of the growing disturbance in terms of the spatial correlation of the initial disturbance. The eigendecomposition of the correlation provides the most prevalent structures, which are the statistical analogue of the standard left singular vectors of the evolution operator. We also derive accurate confidence bounds on the growth by approximating the probability density function of the energy. Applying our analysis to Poiseuille flow yields a number of observations. First, the mean energy amplification is often drastically smaller than the maximum. In these cases, it is exceedingly unlikely to achieve near-optimal growth due to the exponential behaviour observed in the probability density function. Second, the characteristic length scale of the initial disturbances has a significant impact on the expected growth, with large-scale initial disturbances growing orders of magnitude more than small-scale ones. Finally, while the optimal growth scales quadratically with Reynolds number, the mean energy amplification scales only linearly for certain reasonable choices of the initial correlation.

Dual analysis of stability in plane Poiseuille channel flow with uniform vertical crossflow

In this paper, we investigate the effect of uniform vertical crossflow on the plane Poiseuille channel flow. The derivation and linearization of the Navier–Stokes equations are performed to enable numerical solution through the fourth-order Orr–Sommerfeld equation. The Chebyshev collocation method is employed for this purpose. A dual approach is employed to examine the basic velocity profile, involving both reference velocity analysis (z = 0) and maximum streamwise velocity analysis (z = zmax). The two approaches provide distinct perspectives on the flow and may yield different stability predictions, depending on the values of the parameters used. Modal analysis is conducted to comprehend the asymptotic behavior of the system, achieved through the plotting of eigenspectrum, neutral stability curves, and growth rate curves for disturbances. Accurate values of critical triplets are obtained, aligning with the existing literature. The non-modal analysis is performed to understand the short-term behavior of the system, aided by pseudospectra, evolutionary patterns of energy amplification of the disturbances G(t) over time, and delineation of regions, indicating stability, potential instability, and instability. The collective results from both analyses reveal that the crossflow serves as a dual agent, contributing to both the stabilization and destabilization of the system.

Post-dynamical inspiral phase of common envelope evolution

During common envelope evolution, an initially weak magnetic field may undergo amplification by interacting with spiral density waves and turbulence generated in the stellar envelope by the inspiralling companion. Using 3D magnetohydrodynamical simulations on adaptively refined spherical grids with excised central regions, we studied the amplification of magnetic fields and their effect on the envelope structure, dynamics, and the orbital evolution of the binary during the post-dynamical inspiral phase. About 95% of magnetic energy amplification arises from magnetic field stretching, folding, and winding due to differential rotation and turbulence while compression against magnetic pressure accounts for the remaining ∼5%. Magnetic energy production peaks at a scale of 3ab, where ab is the semimajor axis of the central binary’s orbit. Because the magnetic energy production declines at large radial scales, the conditions are not favorable for the formation of magnetically collimated bipolar jet-like outflows unless they are generated on small scales near the individual cores, which we did not resolve. Magnetic fields have a negligible impact on binary orbit evolution, mean kinetic energy, and the disk-like morphology of angular momentum transport, but turbulent Maxwell stress can dominate Reynolds stress when accretion onto the central binary is allowed, leading to an α-disk parameter of ≃0.034. Finally, we discovered accretion streams arising from the stabilizing effect of the magnetic tension from the toroidal field about the orbital plane, which prevents overdensities from being destroyed by turbulence and enables them to accumulate mass and eventually migrate toward the binary.

Quantifying the impact of stiffness distributions on the dynamic behaviour of railway transition zones

Railway transition zones (RTZs) are regions where abrupt track stiffness changes occur that may lead to dynamic amplifications and subsequent track deterioration. The design challenges for these zones arise due to variations in material properties in both the depth (trackbed layers composed of different materials) and longitudinal directions of the track, as well as temporal variations in mechanical properties of materials due to several external factors over the operational period. This research aims to investigate the effects of these variations in material properties (i.e., of the resulting stiffness distributions in vertical and longitudinal directions) on the behaviour of RTZs, assess from this perspective the performance of a novel transition structure called the SHIELD, and establish a methodology for designing a robust solution to mitigate the dynamic amplifications in these zones. Results indicate that stiffness variations in both vertical and longitudinal directions significantly influence the dynamic behaviour of the RTZs. The study also suggests a permissible range of stiffness ratios to control the amplification of strain energy in the most critical components of RTZs, both in the initial state as well as during the operational phase (where material properties may vary over time). Moreover, the proposed methodology offers a valuable tool for the design and evaluation of RTZs and is applicable to various transition types and a broad spectrum of material properties.

Simulating Compressive Stream Interaction Regions during Parker Solar Probe’s First Perihelion Using Stream-aligned Magnetohydrodynamics

We used the stream-aligned magnetohydrodynamics (SA-MHD) model to simulate Carrington rotation 2210, which contains Parker Solar Probe’s (PSP) first perihelion at 36.5 R ⊙ on 2018 November 6, to provide context to the in situ PSP observations by FIELDS and SWEAP. The SA-MHD model aligns the magnetic field with the velocity vector at each point, thereby allowing for clear connectivity between the spacecraft and the source regions on the Sun, without unphysical magnetic field structures. During this Carrington rotation, two stream interaction regions (SIRs) form, due to the deep solar minimum. We include the energy partitioning of the parallel and perpendicular ions and the isotropic electrons to investigate the temperature anisotropy through the compression regions to better understand the wave energy amplification and proton thermal energy partitioning in a global context. Overall, we found good agreement in all in situ plasma parameters between the SA-MHD results and the observations at PSP, STEREO-A, and Earth, including at PSP’s perihelion and through the compression region of the SIRs. In the typical solar wind, the parallel proton temperature is preferentially heated, except in the SIR, where there is an enhancement in the perpendicular proton temperature. This is further showcased in the ion cyclotron relaxation time, which shows a distinct decrease through the SIR compression regions. This work demonstrates the success of the Alfvén wave turbulence theory for predicting interplanetary magnetic turbulence levels, while self-consistently reproducing solar wind speeds, densities, and overall temperatures, including at small heliocentric distances and through SIR compression regions.

Photon Acceleration by Superluminal Ionization Fronts

This paper explores the use of superluminal ionization fronts to accelerate and amplify electromagnetic radiation. These fronts are defined as optical boundaries between two regions of a gas, the neutral region and the plasma region, characterized by two different values of the refractive index. For that reason, the front velocity is not necessarily related to the motion of material particles, such as neutral atoms, ions and electrons, which can stay at rest. The fronts can therefore become superluminal without violating causality. In recent years, different experimental configurations, such as the flying focus, showed that it is possible to create superluminal fronts in the laboratory. These fronts can easily be described theoretically in a special reference frame, called the time frame, which is used here. In this frame, superluminal fronts reduce to time refraction, a process that is symmetrical to the well-known optical refraction. It is shown that propagation through such fronts can lead to considerable frequency shifts and energy amplification of probe laser beams. This could eventually be used to develop new sources of tunable radiation.