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At least 289 records · Page 16

Experimental Investigation of Unsteady Shock Wave Turbulent Boundary Layer Interactions About a Blunt Fin

A series of experiments were performed to investigate the effects of Mach number variation on the characteristics of the unsteady shock wave/turbulent boundary layer interaction generated by a blunt fin. A single blunt fin hemicylindrical leading edge diameter size was used in all of the experiments which covered the Mach number range from 2.0 to 5.0. The measurements in this investigation included surface flow visualization, static and dynamic pressure measurements, both on centerline and off-centerline of the blunt fin axis. Surface flow visualization and static pressure measurements showed that the spatial extent of the shock wave/turbulent boundary layer interaction increased with increasing Mach number. The maximum static pressure, normalized by the incoming static pressure, measured at the peak location in the separated flow region ahead of the blunt fin was found to increase with increasing Mach number. The mean and standard deviations of the fluctuating pressure signals from the dynamic pressure transducers were found to collapse to self-similar distributions as a function of the distance perpendicular to the separation line. The standard deviation of the pressure signals showed initial peaked distribution, with the maximum standard deviation point corresponding to the location of the separation line at Mach number 3.0 to 5.0. At Mach 2.0 the maximum standard deviation point was found to occur significantly upstream of the separation line. The intermittency distributions of the separation shock wave motion were found to be self-similar profiles for all Mach numbers. The intermittent region length was found to increase with Mach number and decrease with interaction sweepback angle. For Mach numbers 3.0 to 5.0 the separation line was found to correspond to high intermittencies or equivalently to the downstream locus of the separation shock wave motion. The Mach 2.0 tests, however, showed that the intermittent region occurs significantly upstream of the separation line. Power spectral densities measured in the intermittent regions were found to have self-similar frequency distributions when compared as functions of a Strouhal number for all Mach numbers and interaction sweepback angles. The maximum zero-crossing frequencies were found to correspond with the peak frequencies in the power spectra measured in the intermittent region.

Barnhart, Paul J.↗

Role of Chemical Disorder in High Temperature Dislocation Glide in Refractory Multi-principal Element Alloys

Refractory multi-principal element alloys (RMPEAs) combine a chemically disordered lattice with a structurally ordered, single‐phase body‐centered cubic (bcc) crystal structure. Chemical fluctuations in these alloys give rise to significant energy barriers that impede dislocation motion. In this study, we use phase field dislocation dynamics to examine how spatial temperature fluctuations compete with randomness in energy barriers to affect the motion of long screw dislocations in three equi-atomic MoNbTa‐based RMPEAs: MoNbTa, MoNbTaW, and MoNbTaVW. Over a wide range of homologous temperatures (T h ≈ 0–0.6), we determined a screw dislocation ‘flow stress’ as the minimum applied stress to sustain continuous motion over a long excursion distance within a fixed timeframe. All three RMPEAs exhibit temperature dependent flow stress with three characteristic glide regimes: at low homologous temperatures, flow stress drops sharply, and screw glide remains planar and rectilinear; at intermediate homologous temperatures, the flow stress levels off as glide becomes planar but wavy; and at high homologous temperatures, flow stress plateaus as screws exhibit nonplanar, three‐dimensional motion. Glide kinetics and transition temperatures are controlled by the chemically induced fluctuations in the energy landscape. The rectilinear to wavy transition temperature is controlled by statistically weakest local barriers in the glide plane, whereas the wavy to 3D transition temperature is governed by statistically strongest local barriers. At low and intermediate homologous temperatures, the relative spread in energy barriers governs glide behavior by controlling the local kinetics of kink pair formation and kink pinning. At high homologous temperatures, the average barrier height governs the glide behavior by controlling the number of out-of-plane excursions during 3D glide. These findings reveal how random chemical fluctuations determine screw‐driven plasticity in RMPEAs, providing critical insight for the design of high temperature structural alloys.

Defects↗

Correlated Lattice Fluctuations in CsPbBr 3 Quantum Dots Give Rise to Long-Lived Electronic Coherence

Electronic coherence is central to numerous areas of science, from quantum biology to quantum materials. In quantum materials, lead-halide perovskite (LHP) quantum dots (QDs) have been shown to support electronic coherence through observation of coherent single-photon emission and superfluorescence arising from spatial coherence at low temperatures. In contrast, direct measurement of temporal coherence between exciton states has been lacking. Here, we employ coherent multi-dimensional spectroscopy to observe an electronic coherence between exciton states in CsPbBr 3 QDs that is long-lived at room temperature, surviving nearly three times longer than the electronic dephasing time. This observation of a long-lived electronic coherence at room temperature points to nearly perfectly correlated lattice fluctuations for each excitonic state in the superposition. In conclusion, these experiments reveal that the properties of LHP QDs extend to lattice dynamics that give rise to correlated fluctuations in the basis exciton states, a process that may next be optimized by design.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Acoustic Tomography of the Atmosphere: A Large-Eddy Simulation Sensitivity Study

Accurate measurement of atmospheric turbulent fluctuations is critical for understanding environmental dynamics and improving models in applications such as wind energy. Advanced remote sensing technologies are essential for capturing instantaneous velocity and temperature fluctuations. Acoustic tomography (AT) offers a promising approach that utilizes sound travel times between an array of transducers to reconstruct turbulence fields. This study presents a systematic evaluation of the time-dependent stochastic inversion (TDSI) algorithm for AT using synthetic travel-time measurements derived from large-eddy simulation (LES) fields under both neutral and convective atmospheric boundary-layer conditions. Unlike prior work that relied on field observations or idealized fields, the LES framework provides a ground-truth atmospheric state, enabling quantitative assessment of TDSI retrieval reliability, sensitivity to travel-time measurement noise, and dependence on covariance model parameters and temporal data integration. A detailed sensitivity analysis was conducted to determine the best-fit model parameters, identify the tolerance thresholds for parameter mismatch, and establish a maximum spatial resolution. The TDSI algorithm successfully reconstructed large-scale velocity and temperature fluctuations with root mean square errors ( RMSE s) below 0.35 m/s and 0.12 K, respectively. Spectral analysis established a maximum spatial resolution of approximately 1.4 m, and reconstructions remained robust for travel-time measurement uncertainties up to 0.002 s. These findings provide critical insights into the operational limits of TDSI and inform future applications of AT for atmospheric turbulence characterization and system design.

17 WIND ENERGY↗

Revealing mechanisms of processing defect mitigation in laser powder bed fusion via shaped beams using high-speed X-ray imaging

The laser powder bed fusion (LPBF) process utilizing a focused Gaussian-shaped beam faces challenges, including pore formation, melt pool fluctuation and liquid spattering. While beam shaping technology has been explored as a potential approach for defect mitigation, the beam-matter interaction dynamics during melting with shaped beams remain unclear. Here, we report the direct observation of ring-shaped beam-matter interaction dynamics, including pore formation, melt pool fluctuation and liquid spattering, and unveil defect mitigation mechanisms in ring-shaped beam laser powder bed fusion process. Here, we find that, by spatially manipulating incident laser rays, the ring-shaped beam controls keyhole morphology, thereby managing the distribution of the reflected rays. This manipulation can effectively eliminate the formation of an unstable cavity at the keyhole tip, stabilizing the keyhole and mitigating keyhole pores. This enhanced keyhole stability effectively reduces the melt pool fluctuation, the formation of liquid breakup induced spatters and liquid droplet colliding induced large spatters in the laser powder bed fusion process. Additionally, the high-energy forefront of the ring-shaped beam effectively melts the powder bed, reducing agglomeration liquid spatter in the laser powder bed fusion process. The discovered defect mitigation mechanisms may guide the design of beam shaping strategies for simultaneously increasing the quality and productivity of metal additive manufacturing.

Beam shaping↗

Steady state and dynamical structure of a cosmic-ray-modified termination shock

A hydrodynamic model is developed for the structure of a cosmic-ray-modified termination shock. The model is based on the two-fluid equations of diffuse shock acceleration (Drury and Volk, 1981). Both the steady state structure of the shock and its interaction with outer heliospheric disturbances are considered. Under the assumption that the solar wind is decelerated by diffusing interstellar cosmic rates, it is shown that the natural state of the termination shock is a gradual deceleration and compression, followed by a discontinuous jump to a downstream state which is dominated by the pressure contribution of the cosmic rays. A representative model is calculated for the steady state which incorporates both interstellar cosmic ray mediation and diffusively accelerated anomalous ions through a proposed thermal leakage mechanism. The interaction of large-scale disturbances with the equilibrium termination shock model is shown to result in some unusual downstream structure, including transmitted shocks and cosmic-ray-modified contact discontinuities. The structure observed may be connected to the 2-kHz outer heliospheric radio emission (Cairns et al., 1992a, b). The time-dependent simulations also demonstrate that interaction with solar wind compressible turbulence (e.g., traveling interplanetary shocks, etc.) could induce the termination shock to continually fluctuate between cosmic-ray-dominated and gas-dynamic states. This fluctuation may represent a partial explanation of the galactic cosmic ray modulation effect and illustrates that the Pioneer and Voyager satellites will encounter an evolving shock whose structure and dynamic properties are strongly influence by the mediation of interstellar and anomalous cosmic rays.

Donohue, D. J.↗

Toward nonthermal control of excited quantum materials: framework and investigations by ultrafast electron scattering and imaging

Quantum material systems upon applying ultrashort laser pulses provide a rich platform to access excited material phases and their transformations that are not entirely like their equilibrium counterparts. The addressability and potential controls of metastable or long-trapped out-of-equilibrium phases have motivated interests both for the purposes of understanding the nonequilibrium physics and advancing the quantum technologies. Thus far, the dynamical spectroscopic probes eminently focus on microscopic electronic and phonon responses. For characterizing the long-range dynamics, such as order parameter fields and fluctuation effects, the ultrafast scattering probes offer direct sensitivity. Bridging the connections between the microscopic dynamics and macroscopic responses is central toward establishing the nonequilibrium physics behind the light-induced phases. Here, we present a path toward such understanding by cross-examining the structure factors associated with different dynamical states obtained from ultrafast electron scattering, imaging, and modeling. We give the basic theoretical framework on describing the non-equilibrium scattering problems and briefly describe how such framework relates to the out-of-equilibrium phenomena. We give effective models outlining the emergences of nonthermal critical points, hidden phases, and non-equilibrium relaxational responses from vacuum-suspended rare-earth tritellurides, tantalum disulfides thin films, and vanadium dioxide nanocrystalline materials upon light excitations.

79 ASTRONOMY AND ASTROPHYSICS↗

Quantifying the Energy Budget in the Solar Wind from 13.3 to 100 Solar Radii

A variety of energy sources, ranging from dynamic processes, such as magnetic reconnection and waves, to quasi steady terms, such as plasma pressure, may contribute to the acceleration of the solar wind. We utilize a combination of charged particle and magnetic field observations from the Parker Solar Probe (PSP) to attempt to quantify the steady-state contribution of the proton pressure, the electric potential, and the wave energy to the solar wind proton acceleration observed by PSP between 13.3 and ∼100 solar radii (R☉). The proton pressure provides a natural kinematic driver of the outflow. The ambipolar electric potential acts to couple the electron pressure to the protons, providing another definite proton acceleration term. Fluctuations and waves, while inherently dynamic, can act as an additional effective steady-state pressure term. To analyze the contributions of these terms, we utilize radial binning of single-point PSP measurements, as well as repeated crossings of the same stream at different distances on individual PSP orbits (i.e., fast radial scans). In agreement with previous work, we find that the electric potential contains sufficient energy to fully explain the acceleration of the slower wind streams. On the other hand, we find that the wave pressure plays an increasingly important role in the faster wind streams. The combination of these terms can explain the continuing acceleration of both slow and fast wind streams beyond 13.3 R☉.

J S Halekas↗

A high speed data acquisition system for the analysis of velocity, density, and total temperature fluctuations at transonic speeds

The use of a high-speed Dynamic Data Acquisition System (DDAS) to measure simultaneously velocity, density, and total temperature fluctuations is described. The DDAS is used to automate the acquisition of hot-wire calibration data. The data acquisition, data handling, and data reporting techiques used by DDAS are described. Sample data are used to compare results obtained with the DDAS with those obtained from the FM tape and post-test digitization method.

Clukey, Steven J.↗

Semi-Classical Models for Virtual Antiparticle Pairs

Virtual particle-antiparticle pairs of massive elementary particle& are predicted in Quantum Field Theory (QFT) to appear from the vacuum and annihilate each other again within their Heisenberg lifetimes h/4mc(exp 2). In this work, semiclassical models of this process - for the cases of massive leptons, quarks, and the massive weak bosons W and Z - are constructed. It is shown that the dynamical lifetime of the particle- antiparticle system in each case equals the Heisenberg lifetime to good approximation, and obeys appropriate quantization conditions on the field fluctuation action. In other words, the dynamical lifetime of the semiclassical model agrees with QED and QCD to good approximation. But the formula for the dynamical lifetime in each model includes the force strength coupling constant (e in the lepton case, alpha(sup s) (q(exp 2)) in the quark cases), while the Heisenberg lifetime formula does not. Observing the agreement of the Heisenberg and dynamical lifetimes, we may derive the QED and QCD coupling constants in terms of h, c, and numerical factors only.

Batchelor, David↗

Zinc dynamics regulate early ovarian follicle development

Zinc fluctuations regulate key steps in late oocyte and pre-implantation embryo development; however, roles for zinc in preceding stages in early ovarian follicle development, when cooperative interactions exist between the oocyte and somatic cells, are unknown. To understand the roles of zinc during early follicle development, we applied single cell X-ray fluorescence microscopy, a radioactive zinc tracer, and a labile zinc probe to measure zinc in individual mouse oocytes and associated somatic cells within early follicles. Here, we report a significant stage-specific increase and compartmental redistribution in oocyte zinc content upon the initiation of early follicle growth. The increase in zinc correlates with the increased expression of specific zinc transporters, including two that are essential in oocyte maturation. While oocytes in follicles exhibit high tolerance to pronounced changes in zinc availability, somatic survival and proliferation are significantly more sensitive to zinc chelation or supplementation. Finally, transcriptomic, proteomic, and zinc loading analyses reveal enrichment of zinc targets in the ubiquitination pathway. Overall, these results demonstrate that distinct cell type- specific zinc regulations are required for follicle growth and indicate that physiological fluctuation in the localization and availability of this inorganic cofactor has fundamental functions in early gamete development.

59 BASIC BIOLOGICAL SCIENCES↗

Response of Subsurface Nitrogen-Cycling Microbial Communities to Environmental Fluctuations (Final Technical Report)

Riparian floodplains are dynamic ecosystems linking terrestrial and riverine systems. These floodplains experience hydrological shifts such as changes in water table height, flooding, and drought and can be ‘hotspots’ of biogeochemical cycling due to shifting sediment moisture (and saturation) and subsurface exchanges of water, nutrients, and other compounds across different sediment layers. Subsurface microbial communities are the primary drivers of biogeochemical processes in floodplains, and thus their structure and function can directly influence both surface and groundwater quality. The microbial nitrogen (N) cycle is particularly important in floodplains as it affects nutrient availability and removal. Two functional guilds of chemoautotrophic (i.e. CO2-fixing) microorganisms are responsible for the first oxidative step of the N cycle, nitrification: ammonia-oxidizing archaea (AOA) and bacteria (AOB) catalyze the oxidation of ammonia to nitrite, while nitrite-oxidizing bacteria (NOB) oxidize nitrite to nitrate. Despite the critical role nitrification plays in N-cycling in both terrestrial and aquatic ecosystems, our understanding of the diversity, ecophysiology, and activity of nitrifying organisms in subsurface floodplain soils/sediments is extremely limited. To help address this critical knowledge gap, the overarching goal of this project was to determine how shifts in key environmental parameters and gradients impact microbial N-cycling communities/processes, with particular emphasis on nitrification, within hydrologically-variable floodplain sediments in the Wind River Basin near Riverton, Wyoming. The three specific objectives of this project were to: (1) to associate in situ environmental drivers of N cycling with distinct functional guilds; (2) determine the guild response to variation in key ecosystem drivers; and (3) develop a dynamic ecosystem model of the microbial N cycle with the Riverton subsurface using community genomic and biogeochemical data collected in the first two objectives. Over the course of this project, we employed both 16S rRNA gene amplicon sequencing and genome-resolved metagenomics to examine the phylogenetic diversity and metabolic potential of subsurface nitrifier communities within 68 samples collected across multiple sites, depths, and time points within the Riverton floodplain, allowing for both spatial and temporal investigations at different scales. This project benefitted tremendously from recent advances in high-throughput sequencing technologies coupled with dramatic improvements in the computational tools and algorithms available for analyzing such large, complex genomic datasets. By pairing these cutting-edge genomic approaches with depth-resolved sampling and detailed geochemical analyses of the Riverton floodplain, we have gained novel insights into the structure and function of subsurface nitrifier communities in relation to both hydrology and biogeochemistry. This project resulted in the most detailed and comprehensive characterization of N-cycling floodplain microbial communities to date and will hopefully inspire and pave the way for future studies using similar approaches in other floodplains. Indeed, such information is critical for understanding subsurface biogeochemical cycling and how elemental stores are altered from perturbations initiated by the water cycle within floodplains. Finally, because of the terrestrial-aquatic nature of the Riverton floodplain, results from this project are also of relevance to disciplines such as soil science, estuarine science, limnology & oceanography, biogeochemistry, geobiology, environmental engineering, as well as genomics and data science.

54 ENVIRONMENTAL SCIENCES↗

Flight Measurement of Wall-Pressure Fluctuations and Boundary-Layer Turbulence

The results are presented for a flight test program using a fighter type jet aircraft flying at pressure altitudes of 10,000, 20,000, and 30,000 feet at Mach numbers from 0.3 to 0.8. Specially designed apparatus was used to measure and record the output of microphones and hot-wire anemometers mounted on the forward-fuselage section and wing of the airplane. Mean-velocity profiles in the boundary layers were obtained from total-pressure measurements. The ratio of the root-mean-square fluctuating wall pressure to the free-stream dynamic pressure is presented as a function of Reynolds number and Mach number. The longitudinal component of the turbulent-velocity fluctuations was measured, and the turbulence-intensity profiles are presented for the wing and forward-fuselage section. In general, the results are in agreement with wind-tunnel measurements which have been-reported in the literature. For example, the variation the square root of p(sup 2)/q times the square root of p(sup 2) is the root mean square of the wall-pressure fluctuation, and q is the free-stream dynamic pressure) with Reynolds number was found to be essentially constant for the forward-fuselage-section boundary layer, while variations at the wing station were probably unduly affected by the microphone diameter (5/8 in.), which was large compared with the boundary-layer thickness.

Mull, Harold R.↗

Accurate and efficient predictions of keyhole dynamics in laser materials processing using machine learning-aided simulations

The keyhole phenomenon has been widely observed in laser materials processing, including laser welding, remelting, cladding, drilling, and additive manufacturing. Keyhole-induced defects, primarily pores, dramatically affect the performance of final products, impeding the broad use of these laser-based technologies. The formation of these pores is typically associated with the dynamic behavior of the keyhole. So far, the accurate characterization and prediction of keyhole features, particularly keyhole depth, as a function of time, has been a challenging task. In situ characterization of keyhole dynamic behavior using the synchrotron X-ray technique is informative but complicated and expensive. Current simulations are generally hindered by their poor accuracy and generalization abilities in predicting keyhole depths due to the lack of accurate laser absorptance data. In this study, we develop a machine learning-aided simulation method that accurately predicts keyhole dynamics, especially in keyhole depth fluctuations, over a wide range of processing parameters. In two case studies involving titanium and aluminum alloys, we achieve keyhole depth prediction with a mean absolute percentage error of 10 %, surpassing those simulated using the ray-tracing method with an error margin of 30 %, while also reducing computational time. This exceptional fidelity and efficiency empower our model to serve as a cost-effective alternative to synchrotron experiments. Our machine learning-aided simulation method is affordable and readily deployable for a large variety of materials, opening new doors to eliminate or reduce defects for a wide range of laser materials processing techniques.

Computational fluid dynamics↗

Impact of Alloy-Disorder-Induced Localization on Hole Diffusion in Highly Excited c -Plane and m -Plane (In, Ga) N Quantum Wells

The diffusion coefficient of holes can provide knowledge about carrier localization in (In, Ga)N, where the carrier dynamics are altered by randomly fluctuating potential landscape. In group-III nitrides, the diffusivity of holes is difficult to measure by electrical methods but it can be studied using optical techniques. Here, we investigate the dependence of the hole diffusion coefficient on direction and carrier density in c-plane and m-plane (In, Ga)N structures by employing the light-induced transient-grating technique. We show that the hole diffusion coefficient is anisotropic in the m-plane structure, where it is several times larger along the a crystallographic direction than along the c direction. Such anisotropy is observed within the broad range of carrier densities from 10 18 to 10 20 cm –3 . The diffusivity changes nonmonotonously with increasing photoexcitation, this dependence being different in thick and thin layers. We argue that an unexpectedly high diffusion coefficient at low carrier densities in thick quantum wells can be a signature of efficient hole transport via percolative paths occurring due to compositional disorder. In turn, a decrease of diffusivity with the excitation can reflect the effect of Coulomb blockade of these paths. Lastly, we demonstrate that disorder impacts carrier diffusivity even at carrier densities above 10 19 cm –3 , where the overflow of localized states must be included to explain the observed increase of the diffusion coefficient with the carrier density.

36 MATERIALS SCIENCE↗

Dynamic embedding of effective harmonic normal mode vibrations in all-atomistic energy gap fluctuations: Case study of light harvesting 2 complex

Environmental effects in excitation energy transfer have mostly been modeled by baths of harmonic oscillators, but to what extent such modeling provides a reliable description of actual interactions between molecular systems and environments remains an open issue. Here, we address this issue by investigating fluctuations in the excitation energies of the light harvesting 2 complex using a realistic all-atomistic simulation of the potential energy surface. Our analyses reveal that molecular motions exhibit significant anharmonic features, even for underdamped intramolecular vibrations. In particular, we find that the anharmonicity contributes to the broadening of spectral densities and substantial overlaps between neighboring peaks, which complicates the meaning of mode frequencies constituting a bath model. Thus, we develop a strategy to construct a minimally underdamped harmonic bath that has a clear connection to all-atomistic dynamics by utilizing actual normal modes of molecules but optimizing their frequencies such that the resulting bath model can best reproduce the all-atomistic simulation results. By subtracting the underdamped contribution from the entire fluctuations, we also show that identifying a residual spectral density representing all other contributions with overdamped behavior is possible. We find that this can be fitted well with a well-established analytic form of a spectral density function or, alternatively, modeled as explicit time dependent fluctuations with muti-exponential or power law type correlation functions. We provide an assessment and the implications of these possibilities. The approach presented here can also serve as a general strategy to construct a simplified bath model that can effectively represent the underlying all-atomistic bath dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Mean Flow Augmented Acoustics in Rocket Systems

Combustion instability in solid rocket motors and liquid engines is a complication that continues to plague designers and engineers. Many rocket systems experience violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process and gas dynamics. During sever cases of combustion instability fluctuation amplitudes can reach values equal to or greater than the average chamber pressure. Large amplitude oscillations lead to damaged injectors, loss of rocket performance, damaged payloads, and in some cases breach of case/loss of mission. Historic difficulties in modeling and predicting combustion instability has reduced most rocket systems experiencing instability into a costly fix through testing paradigm or to scrap the system entirely.

Fischbach, Sean R.↗

Intermittent Defect Fluctuations in Oxide Heterostructures

Abstract The heterogeneous nature, local presence, and dynamic evolution of defects typically govern the ionic and electronic properties of a wide variety of functional materials. While the last 50 years have seen considerable efforts into development of new methods to identify the nature of defects in complex materials, such as the perovskite oxides, very little is known about defect dynamics and their influence on the functionality of a material. Here, the discovery of the intermittent behavior of point defects (oxygen vacancies) in oxide heterostructures employing X‐ray photon correlation spectroscopy is reported. Local fluctuations between two ordered phases in strained SrCoO x with different degrees of stability of the oxygen vacancies are observed. Ab‐initio‐informed phase‐field modeling reveals that fluctuations between the competing ordered phases are modulated by the oxygen ion/vacancy interaction energy and epitaxial strain. The results demonstrate how defect dynamics, evidenced by measurement and modeling of their temporal fluctuations, give rise to stochastic properties that now can be fully characterized using coherent X‐rays, coupled for the first time to multiscale modeling in functional complex oxide heterostructures. The study and its findings open new avenues for engineering the dynamical response of functional materials used in neuromorphic and electrochemical applications.

36 MATERIALS SCIENCE↗