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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,495 records · Page 83
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Scaling methodologies and similarity analysis for thermal hydraulics test facility development for water-cooled small modular reactor

Small modular reactors (SMRs) represent a promising option for providing clean and sustainable energy due to their potential for enhanced safety, reduced capital costs, and increased siting flexibility. However, new reactor systems require the development and operation of representative scaled-down test facilities to support the verification and validation of system computer codes and models. Here this study reviews the research on scaling methodologies and similarity principles pivotal in developing non-nuclear integral effects test and separate effects test facilities for water-cooled SMRs. The study focuses on a review of the scaling methods, similarity approaches, and possible challenges posed by the unique and compact design features of integral-pressurized water reactor-type SMRs, and their representative test facilities. This study also reviews previous research related to scaling and similarity methodologies and provides insights into design considerations for achieving prototypic conditions in test facilities. The findings and recommendations emphasize the broader impact of appropriate scaling and similarity principles to ensure meaningful and transferable results from non-nuclear test facilities to accelerate the safe and efficient deployment of next-generation water-cooled SMRs.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2014

Geometrical scaling and modal decay rates in periodic arrays of deeply subwavelength Terahertz resonators

It is well known that due to the high conductivity of noble metals at terahertz frequencies and scalability of macroscopic Maxwell equations, a geometrical downscaling of a terahertz resonator results in the linear upscaling of its resonance frequency. However, the scaling laws of modal decay rates, important for the resonator excitation efficiency, are much less known. Here, we investigate the extent to which the scale-invariance of decay rates is violated due to the finite conductivity of the metal. We find that the resonance quality factor or the excitation efficiency may be substantially affected by scaling and show that this happens as a result of the scale-dependence of the metal absorption rate, while the radiative decay and the dielectric cavity absorption rates are approximately scale-invariant. In particular, we find that by downscaling overcoupled resonators, their excitation efficiency increases, while the opposite happens with undercoupled resonators.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

DETAIL Component Scaling and Methodology Comparison

The purpose of this study was to develop a process to convert input signals from one facility into another by reflecting geometric and environmental settings. The Dynamic Energy Transport and Integration Laboratory (DETAIL) is a research facility in development. Its aim is to emulate the daily interactions among power production industry systems and receive real-time data from those systems as inputs. To convert signals and ensure that the temporal sequences and magnitudes reflect laboratory settings, the ability to scale and project data is essential. To demonstrate this ability, Dynamical System Scaling (DSS) and Hierarchical Two-Tiered Scaling (H2TS) (methodologies that enable systems to scale and project or extrapolate data sets to desired environments while conserving the observed behavior based on first principles) were applied to DETAIL’s thermocline thermal storage system in the Thermal Energy Distribution System (TEDS) facility and solid-oxide electrolysis cell in the High Temperature Hydrogen Electrolysis (HTHE) facility. Both thermocline and electrolysis cell systems were successfully scaled, and test cases were conducted to generate a doubly accelerated energy charge and discharge in reference to past experimental data from the facilities. The research results represented a case for the thermocline system that required signals to be accelerated without altering the stored energy. To enhance the quality of the accelerated data, error propagation analyses were conducted on DSS post-processing terms to determine the consequences of raw-data-associated errors.

08 HYDROGEN↗
DOE OSTI2018

Violation of Field Line Conservation and Associated Spatial Scales in Particle-in-Cell Simulations and MMS Data

For the first time, space flight technology exists to detect, in situ, violation of magnetic field line conservation. The violation of magnetic line conservation on scales smaller than the system size is a necessary and sufficient condition for finite magnetic field reconnection. We demonstrate that violation of line conservation produces a detectable, structured signature both in particle-in-cell simulations of reconnection and in data from the Magnetospheric Multi-Scale mission. In particle-in-cell simulations of asymmetric reconnection, the quantity—which we call M—that identifies this violation achieves significant values in electron skin depth-scale layers that extend away from the separator, with higher values emerging on the low-density, high-magnetic-field side of the current sheet. At the separator, M owes largely to perpendicular gradients in the parallel electric field, while it attains its highest values away from the separator in dispersed, layered structures associated with gradients in the perpendicular nonideal electric field and electron transport. Sub-ion scale bipolar forms of the quantity also appear further from the separator. In two MMS burst data intervals detecting the electron diffusion region, we find that M exceeds measurement uncertainties both at the separator and near the separatrices. One interval has highly sheared reconnecting fields and the other a stronger guide field. For one event, we determine the location and scale of M and the inner electron diffusion region relative to electron outflows and the magnetic separatrices. The measure can therefore serve as a potent diagnostic for magnetic reconnection in space measurements.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Novel Defense Mechanisms in the Armor of the Scales of the “Living Fossil” Coelacanth Fish

In this work, experiments and analysis revealing the unique defense mechanisms of the coelacanth, a lobe-finned fish termed a “living fossil”, are reported, as it was considered to be extinct until 1938, but extant for 400 million years. Additionally, this defense is provided by primitive elasmoid scales having a rare double-twisted Bouligand structure of lamellae which provides extraordinary resistance to deformation without failure. Distinct from other elasmoid scales, the collagen fibrils in the coelacanth fish scales form bundles which are embedded in a matrix comprising fibers arranged perpendicular to the layered (double-twisted Bouligand) structure that provide added rigidity and resistance to deformation. Using in situ synchrotron small-angle X-ray scattering during uniaxial tensile testing, the deformation mechanisms of the collagen are identified in terms of fibril stretching, reorientation, sliding, bending, and delamination. The unique structure of the coelacanth scales, distinct from modern elasmoid scales such as the carp, provides a variety of mechanisms to arrest cracking, making it an outstanding damage-tolerant material to resist predator attacks.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Large-scale reactive thermoset printing: Complex interactions between temperature evolution, viscosity, and cure shrinkage

Thermoset composites are strong candidates for large-scale material extrusion additive manufacturing (AM). However, uncured thermoset composites become unstable as print height increases. Here, chemical initiation of vinyl ester immediately before deposition was used to suppress collapse and enable large-scale thermoset printing. Structural stability was assessed by printing thin walls at various layer times and monitoring thermal gradients with an infrared camera. Stable printing was observed at a layer time of 4.50 min, approximately half the gel time of the material (8 min). Self-weight collapse occurred at short layer time (0.68 min), whereas warpage occurred at long layer time (6.50 min). Here, a new behavior was discovered at intermediate layer time (2.25 min) where the heat generated by the reaction causes new, un-gelled layers to flow. Forced convection eliminates this behavior, stabilizing the 2.25-min layer time print. These findings motivated development of a less exothermic material system, which was used to print a large-scale mold and demonstrate the value of this understanding. By presenting these challenges of large-scale reactive thermoset AM for the first time, this work motivates focused studies of the complex interplay between rheological, thermal, and chemical behaviors to improve the feasibility of large-scale thermoset AM. Tensile properties of the printed material were also measured. Longitudinal and transverse elastic moduli are 3.79 and 2.95 GPa, respectively, and corresponding tensile strengths are 36.11 and 18.83 MPa. The glass transition temperature is 93.13 °C.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Implications of Grain-Scale Mineralogical Heterogeneity for Radionuclide Transport in Fractured Media

The geological disposal of nuclear waste is based on the multi-barrier concept, comprising various engineered and natural barriers, to confine the radioactive waste and isolate it from the biosphere. Some of the planned repositories for high-level nuclear waste will be hosted in fractured crystalline rock formations. The potential of these formations to act as natural transport barriers is related to two coupled processes: diffusion into the rock matrix and sorption onto the mineral surfaces available in the rock matrix. Different in situ and laboratory experiments have pointed out the ubiquitous heterogeneous nature of the rock matrix: mineral surfaces and pore space are distributed in complex microstructures and their distribution is far from being homogeneous (as typically assumed by Darcy-scale coarse reactive transport models). We use a synthetically generated fracture–matrix system to assess the implications of grain-scale physical and mineralogical heterogeneity on cesium transport and retention. The resulting grain-scale reactive transport model is solved using high-performance computing technologies, and the results are compared with those derived from two alternative models, denoted as upscaled models, where mineral abundance is averaged over the matrix volume. In the grain-scale model, the penetration of cesium into the matrix is faster and the penetration front is uneven and finger-shaped. The analysis of the cesium breakthrough curves computed at two different points in the fracture shows that the upscaled models provide later first-arrival time estimates compared to the grain-scale model. The breakthrough curves computed with the three models converge at late times. These results suggest that spatially averaged upscaled parameters of sorption site distribution can be used to predict the late-time behavior of breakthrough curves but could be inadequate to simulate the early behavior.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2015

Importance of proper renormalization scale-setting for QCD testing at colliders

A primary problem affecting perturbative quantum chromodynamic (pQCD) analyses is the lack of a method for setting the QCD running-coupling renormalization scale such that maximally precise fixed-order predictions for physical observables are obtained. The Principle of Maximum Conformality (PMC) eliminates the ambiguities associated with the conventional renormalization scale-setting procedure, yielding predictions that are independent of the choice of renormalization scheme. The QCD coupling scales and the effective number of quark flavors are set order-by-order in the pQCD series. The PMC has a solid theoretical foundation, satisfying the standard renormalization group invariance condition and all of the self-consistency conditions derived from the renormalization group. The PMC scales at each order are obtained by shifting the arguments of the strong force coupling constant αs to eliminate all non-conformal {βi} terms in the pQCD series. The {βi} terms are determined from renormalization group equations without ambiguity. The correct behavior of the running coupling at each order and at each phase-space point can then be obtained. The PMC reduces in the N C → 0 Abelian limit to the Gell-Mann-Low method. In this brief report, we summarize the results of our recent application of the PMC to a number of collider processes, emphasizing the generality and applicability of this approach. A discussion of hadronic Z decays shows that, by applying the PMC, one can achieve accurate predictions for the total and separate decay widths at each order without scale ambiguities. We also show that, if one employs the PMC to determine the top-quark pair forward-backward asymmetry at the next-to-next-to-leading order level, one obtains a comprehensive, self-consistent pQCD explanation for the Tevatron measurements of the asymmetry. This accounts for the “increasing-decreasing” behavior observed by the D0 collaboration for increasing tt¯ invariant mass. At lower energies, the angular distributions of heavy quarks can be used to obtain a direct determination of the heavy quark potential. A discussion of the angular distributions of massive quarks and leptons is also presented, including the fermionic component of the two-loop corrections to the electromagnetic form factors. Furthermore, these results demonstrate that the application of the PMC systematically eliminates a major theoretical uncertainty for pQCD predictions, thus increasing collider sensitivity to possible new physics beyond the Standard Model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Assessing the Effectiveness of Large-Scale Environmental Restoration: Challenges and Opportunities

A recent National Academies consensus report addresses monitoring and assessment of cumulative effects of large-scale and multiple restoration projects within the context of long-term environmental change. Fines and penalties from the Deepwater Horizon oil spill in the Gulf of Mexico (GoM) have supported hundreds of restoration projects at spatial scales not often possible in the past. Here, in this paper, the report committee members and staff provide personal reflections from our time working on the study. We found that gaps in data collection, issues with data accessibility, and a lack of synthesis and analysis are hindering the ability to answer a basic question: What are the impacts of these many restoration efforts on improving ecosystem health and productivity in the GoM at the regional and Gulf wide scale? Restoration efforts are occurring in environments where many trends are changing and exhibiting higher variability than in the past, suggesting that previously successful restoration practices may no longer be adequate to compensate for the effects of environmental changes and variability. Our proposed approach to these challenges includes employing emerging monitoring technologies; using conceptual models; devising an adaptive management framework; rethinking restoration outcome goals; assessing cumulative effects; and undertaking rigorous synthesis and analysis of existing information on long-term environmental trends and restoration efforts. Restoration scientists and practitioners working in the GoM have an unprecedented opportunity to demonstrate large-scale environmental recovery if advances in monitoring, synthesis, assessment, and action are taken quickly. We are cautiously optimistic that, with mid-course adjustments, continued progress toward large-scale environmental recovery is possible.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

From plot to scale: ex-ante assessment of conservation agriculture in Zambia

This study combined bottom-up and top-down approaches to assess the ex-ante effects of conservation agriculture (CA)-based systems in Zambia considering both biophysical and economic factors and prevailing farm systems characteristics. For continuous maize cropping we compared a CA-based system of no-tillage with crop residue retention to a control system of conventional tillage with crop residue removal. First, we simulated yield effects that were calibrated and evaluated against multiple datasets, including on-farm agronomic trials from two seasons and six sites. Next, we extrapolated our simulations to all maize-growing areas in Zambia using gridded climate and soil datasets. Then simulated yields (in kg ha( -1 )) were combined with economic data from a nationally-representative household survey to construct economic indicators including benefit-cost ratios (based on gross benefits and variable costs both in $ ha( -1 )) that captured the implicit value of crop residues and labor demands. The field scale (per ha) indicators were scaled out using harvested areas as an expansion factor. All indicators were calculated over 3-, 10-, and 20-year simulation periods using an interpolated sequence of historical climate data. Finally, we conducted a spatial farm typology analysis to help understand the spatial variation in our field-scale indicators and provide insights into trade-offs and the suitability of CA-based systems for farmers. Average changes in yield from using CA-based systems (compared with the control) at the district scale ranged from -37% to 70% (average 33%), with a similar range of changes in benefit-cost ratios once economic factors were included, in addition to intra-district yield variability. Combining the changes in benefit cost ratios with maize harvested area resulted in an average annual change in district-scale net benefit ranging from US $ - 3.9 to US $9.9 million (with an average of US $1.1 million). The heterogeneity in biophysical and economic factors gave a ranking of provinces different according to biophysical or economic indicators, reinforcing the importance of coupling biophysical and economic approaches. The spatial farm typology analysis highlighted the specific contexts of farmers relevant to the suitability of CA, such as their mineral fertilizer applications rates, ownership of livestock, and prevailing soil texture and rainfall.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Film condensation with high heat fluxes and scaled experiments using pure steam for reactor containment cooling

Condensation tests were performed using a newly developed test facility for scaling the passive containment cooling system (PCCS) to a small modular reactor (SMR). The PCCS of the SMR plays a pivotal role in ensuring greater safety, reliability, and compactness than what is afforded by traditional reactors. Therefore, a well-designed PCCS is essential to SMRs. However, previous studies and test data were unsuitable for scaling, due to high variation in the test geometry and operating conditions. This study intends to close this research gap by using a novel designed scaled test facility consisting of vertical condensing test sections featuring 1-, 2-, and 4-inch-diameter condensing tubes with annular water cooling, and by applying superheated and saturated steam with different steam mass flow ranges of 5–25 g/s. Further, the primary test data, including axial temperatures, mass flow rates, and pressures, were used in conjunction with a standard data reduction method to estimate critical parameters such as heat fluxes, heat transfer coefficients, and condensation rates. These scaled test data would support improving empirical correlations and validating condensation models to identify scaling distortion for SMR PCCSs.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Scale-up of microwave-assisted, continuous flow, liquid phase reactors: Application to 5-Hydroxymethylfurfural production

Microwave (MW) technology can be powerful for the electrification and intensification of chemical manufacturing. However, very few examples of scaled MW processes exist. In this work, we build a scaled, MW-assisted, continuous flow reactor for the processing of liquid phase chemistries with specific application to 5-hydroxymethylfurfural (HMF) production. Here, we demonstrate a corresponding computational fluid dynamics model to simulate the reactor’s temperature profile and performance, both of which are in good agreement with experiments. We construct a surrogate model to relate operating parameters to performance for guiding experiments, without demanding simulations, via active learning. Heat recirculation is demonstrated in this scaled reactor, further extending its scale and reducing the energy demand. An HMF yield of ~55 % and a productivity of 0.1 kg/hr, 8x higher than any other reactor, at a flowrate >20x than prior work, are demonstrated while maintaining energy efficiency of >98 %. A basic economic analysis estimates a $1.85/kg cost of HMF from fructose and >60 % reduction in CO 2 emissions than a conventional system without considering the impact of green electricity. We demonstrate that MW technology is well-applied to systems larger than the laboratory scale, and strategies to further reduction in cost and CO 2 are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Three-dimensional realizations of flood flow in large-scale rivers using the neural fuzzy-based machine-learning algorithms

Machine learning methods have been extensively used to study the dynamics of complex fluid flows. One such algorithm, known as adaptive neural fuzzy inference system (ANFIS), can generate data-driven predictions for flow fields, but has not been applied to natural geophysical flows in large-scale rivers. Herein, we demonstrate the potential of ANFIS to produce three-dimensional (3D) realizations of the instantaneous flood flow field in several large-scale, virtual meandering rivers. The 3D dynamics of flood flow in large-scale rivers were obtained using large-eddy simulation (LES). The LES results, i.e., the 3D velocity components, were employed to train the learnable coefficients of an ANFIS. Further, the trained ANFIS, along with a few time-steps of LES results (precursor data) were then used to produce 3D realizations of flood flow fields in large-scale rivers with geometries other than the one the ANFIS was trained with. We also used the trained ANFIS to generate 3D realizations of river flow at a discharge other than that the ANFIS was trained with. The flow field results obtained from ANFIS were validated using separate LES runs to assess the accuracy of the 3D instantaneous realizations of the machine learning algorithm. An error analysis was conducted to quantify the discrepancies among the ANFIS and LES results for various flood flow predictions in large-scale rivers.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Comparative analysis of various pretreatments to mitigate fouling and scaling in membrane distillation

Membrane distillation (MD) has shown strong promise for treating hypersaline produced water (PW) streams. Scaling and fouling on the membrane surface, however, have been identified as major challenges for commercialization and widespread application. The focus of this study was to first identify the nature of foulants and scalants on the membrane surface and then investigate the pretreatment strategies that mitigate the extent of fouling and scaling on the membrane surface. Vacuum MD (VMD) was selected for this study because of its higher flux at more moderate feed temperatures that eventually leads better assessment of fouling and scaling on the membrane surface. VMD flux tests were carried out with three different real PW samples at total dissolved solids concentrations in the range of 120-160 g/L. It was found that an efficient pretreatment prior to MD is required to mitigate the fouling potential of the organic matter, mostly suspended constituents, in PW samples. Suspended organics fouled and quickly wetted the MD membrane. Major conventional treatments, including filtration, oxidation, coagulation, air floatation, and aeration were investigated to pretreat the PW before VMD tests. A comprehensive comparative analysis is presented showing that the ultrafiltration and coagulation pretreatments displayed the best performance in mitigating the fouling and scaling, while oxidative pretreatment was found to be effective in reducing the iron concentration to less than 5 ppm. The surface of scaled membranes was carefully characterized to further evaluate the performance of each pretreatment. The components that had the highest tendency to precipitate on the membrane surface were identified as strontium sulfate, calcium carbonate, sodium chloride, iron oxide, and silica. In closing, these findings are supported by thermodynamic estimation of the saturation index.

42 ENGINEERING↗
DOE OSTI2023

Pore-scale simulation of multiphase flow and reactive transport processes involved in geologic carbon sequestration

Multiphase flow and reactive transport are two essential physicochemical processes that govern the effectiveness of geological carbon sequestration (GCS). The interaction and feedback among different phases and components during intricate physicochemical processes hold great significance in understanding CO 2 sequestration. Pore-scale simulations can account for multiphase flow and reactive transport processes in porous media and obtain spatial distributions of parameters (density, velocity, concentration, etc.) in the pore space as well as their temporal evolutions. This proves especially valuable considering that experiments can be hindered by constraints in spatial and temporal resolution. The comprehensive insights garnered from pore-scale research can be leveraged for continuum modeling using the representative elementary volume (REV) concept. In this contribution, four sequential mechanisms of CO 2 -brine-rock interaction in three zones delineated by CO 2 saturation are elaborated to elucidate complicated physicochemical processes involved in GCS, which are followed by general descriptions of mathematical equations and pore-scale numerical methods. In addition, as interested and commonly encountered processes, leakage risks during GCS and CO 2 -enhanced oil recovery (CO 2 -EOR) processes are presented. The existing challenges and future directions are discussed for both the performance of the pore-scale models and the current gaps in the field of GCS. Importantly, we expect that this review will prove beneficial for researchers interested in pore-scale simulations, GCS, and related disciplines.

58 GEOSCIENCES↗
DOE OSTI2017

Lamellae spatial distribution modulates fracture behavior and toughness of african pangolin scales

Pangolin scales form a durable armor whose hierarchical structure offers an avenue towards high performance bio-inspired materials design. In this paper, the fracture resistance of African pangolin scales is examined using single edge crack three-point bend fracture testing in order to understand toughening mechanisms arising from the structures of natural mammalian armors. In these mechanical tests, the influence of material orientation and hydration level are examined. The fracture experiments reveal an exceptional fracture resistance due to crack deflection induced by the internal spatial orientation of lamellae. An order of magnitude increase in the measured fracture resistance due to scale hydration, reaching up to ~ 25 kJ/m 2 was measured. Post-mortem analysis of the fracture samples was performed using a combination of optical and electron microscopy, and X-ray computerized tomography. Interestingly, the crack profile morphologies are observed to follow paths outlined by the keratinous lamellae structure of the pangolin scale. Most notably, the inherent structure of pangolin scales offers a pathway for crack deflection and fracture toughening. Finally, the results of this study are expected to be useful as design principles for high performance biomimetic applications.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

A three-dimensional pore-scale model for redox flow battery electrode design analysis

A three-dimensional (3-D) pore-scale model has been developed to construct multiscale fibrous electrodes for redox flow batteries (RFB). New designs, such as biporous electrodes modify electrode structures by creating secondary pores on single carbon fiber to reduce internal battery resistance. Existing pore-scale models only resolve electrodes to the single carbon fiber scale and cannot incorporate recent multiscale electrode designs into numerical models. Our new model aims to bridge this gap and provide a tool to rapidly screen new electrode configurations. Two multiscale electrodes, laser-perforated and biporous electrodes, were investigated at varying operation conditions with the proposed 3-D pore-scale models. The laser-perforated electrode exhibits a reduced pressure drop, but follows the same permeability correlation compared to the corresponding pristine electrode. For the biporous electrode, the added specific surface area and faster reaction kinetics from the secondary pores are the most influential factors leading to improved battery efficiency. However, operating the biporous electrode in limiting current density conditions should be avoided due to the decreased mass transfer efficiency and a more significant voltage loss. Finally, we believe that our 3-D pore-scale model can accelerate the flow battery electrode design process and provide new insights into electrode geometry optimizations.

25 ENERGY STORAGE↗
DOE OSTI2025

Scalable phononic metamaterials: Tunable bandgap design and multi-scale experimental validation

Phononic metamaterials offer unprecedented control over wave propagation, making them essential for applications such as vibration isolation, waveguiding, and acoustic filtering. However, achieving scalable and precisely tunable bandgap properties across different length scales remains challenging. This study presents a user-friendly design framework for phononic metamaterials, enabling ultra-wide bandgap tunability (B/ω c ratios up to 172 %) across multiple frequency ranges and scales. Using finite element simulations of a Yablonovite-inspired unit cell, we establish a comprehensive parametric design space that illustrates how geometric parameters, such as sphere size and beam diameter, controls bandgap width and frequency. The scalability and robustness of the framework are validated through experimental testing on additively manufactured structures at both macro (10 mm) and micro (80 µm) scales, fabricated using Stereolithography and Two-Photon Polymerization. Transmission loss measurements, conducted with piezoelectric transducers and laser vibrometry, closely match simulations in the kHz and MHz frequency ranges, confirming the reliability and consistency of the bandgap behavior across scales. This work bridges theory and experiments at multiple scales, offering a practical methodology for the rapid design of phononic metamaterials and expanding their potential for diverse applications across a broad range of frequencies.

36 MATERIALS SCIENCE↗