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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Jet wake from linearized hydrodynamics

We explore how to improve the hybrid model description of the particles originating from the wake that a jet produced in a heavy ion collision leaves in the droplet of quark-gluon plasma (QGP) through which it propagates, using linearized hydrodynamics on a background Bjorken flow. Jet energy and momentum loss described by the hybrid model become currents sourcing linearized hydrodynamics. By solving the linearized hydrodynamic equations numerically, we investigate the development of the wake in the dynamically evolving droplet of QGP, study the effect of viscosity, scrutinize energy-momentum conservation, and check the validity of the linear approximation. We find that linearized hydrodynamics works better in the viscous case because diffusive modes damp the energy-momentum perturbation produced by the jet. We calculate the distribution of particles produced from the jet wake by using the Cooper-Frye prescription and find that both the transverse momentum spectrum and the distribution of particles in azimuthal angle are similar in shape in linearized hydrodynamics and in the hybrid model. Their normalizations are different because the momentum-rapidity distribution in the linearized hydrodynamics analysis is more spread out, due to sound modes. Since the Bjorken flow has no transverse expansion, we explore the effect of transverse flow by using local boosts to add it into the Cooper-Frye formula. After including the effects of transverse flow in this way, the transverse momentum spectrum becomes harder: more particles with transverse momenta bigger than 2 GeV are produced than in the hybrid model. Although we defer implementing this analysis in a jet Monte Carlo, as would be needed to make quantitative comparisons to data, we gain a qualitative sense of how the jet wake may modify jet observables by computing proxies for two example observables: the lost energy recovered in a cone of varying open angle, and the fragmentation function. We find that linearized hydrodynamics with transverse flow effects added improves the description of the jet wake in the hybrid model in just the way that comparison to data indicates is needed. Our study illuminates a path to improving the description of the wake in the hybrid model, highlighting the need to take into account the effects of both transverse flow and the broadening of the energy-momentum perturbation in spacetime rapidity on particle production.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Investigating sol–gel matrix loading capacity toward producing surrogate nuclear explosive debris with realistic composition

Post detonation nuclear forensic materials which resemble the size, color, elemental composition, and radionuclide content of real nuclear debris would be valuable for developing and validating new nuclear forensic techniques. As nuclear fallout types vary significantly, the ability to tailor each of these parameters accurately is desired to produce materials capable of testing analytical methods under a wide array of forensic scenarios. Sol–gel synthesis techniques can provide tunability of size, shape and composition for producing a wide variety of solid nuclear forensics benchmarking materials. Further, the sol–gel process consists of forming a metal oxide material, often silica, through polymerization of a metal-alkoxy precursor. In this work, we characterize the ability to load sol–gel particles with secondary elemental components such as iron, aluminum, and calcium toward producing benchmarking materials approximating the elemental composition of historic nuclear debris from the Nevada National Security Site. We also demonstrate quantitative radionuclide encapsulation toward producing benchmarking materials with controllable radionuclide content. Finally, we employ these techniques to produce nuclear debris benchmarking materials with controllable elemental matrix composition and radionuclide content and compare these samples with the composition of a historic fallout sample previously reported from the Nevada National Security Site.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Near-Surface Layer Perforations as Precursors to Fracture in Accumulative Roll Bonding of a Multilayered Metal Composite

We use micro-computed tomography (µ-CT) to characterize the sizes, shapes, and locations of layer perforation (LP) defects in laminates of copper (Cu) and tantalum (Ta) processed by accumulative roll bonding (ARB). One—termed Cu/Ta—was processed from an initial stacking of seven alternating Cu and Ta sheets, with the exterior sheets being Cu. In the other—termed Ta/Cu—the exterior sheets are Ta. Cu/Ta remained intact during processing and exhibits an approximately uniform spatial distribution of LPs. By contrast, Ta/Cu fractured by longitudinal splitting. LPs in this latter sample are concentrated near the sample surfaces. Moreover, their density increases with decreasing distance to the fracture surface. Furthermore, these findings show that materials undergoing ARB may remain intact, despite profuse formation of LPs, provided that the LPs are uniformly distributed. However, a non-uniform distribution of LPs is correlated with longitudinal splitting.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Subcloud and Cloud-Base Latent Heat Fluxes during Shallow Cumulus Convection

Doppler and Raman lidar observations of vertical velocity and water vapor mixing ratio are used to probe the physics and statistics of subcloud and cloud-base latent heat fluxes during cumulus convection at the ARM Southern Great Plains (SGP) site in Oklahoma, United States. The statistical results show that latent heat fluxes increase with height from the surface up to ~0.8 Z i (where Z i is the convective boundary layer depth) and then decrease to ~0 at Z i . Peak fluxes aloft exceeding 500 W m −2 are associated with periods of increased cumulus cloud cover and stronger jumps in the mean humidity profile. These entrainment fluxes are much larger than the surface fluxes, indicating substantial drying over the 0–0.8 Z i layer accompanied by moistening aloft as the CBL deepens over the diurnal cycle. We also show that the boundary layer humidity budget is approximately closed by computing the flux divergence across the 0–0.8 Z i layer. Composite subcloud velocity and water vapor anomalies show that clouds are linked to coherent updraft and moisture plumes. The moisture anomaly is Gaussian, most pronounced above 0.8 Z i and systematically wider than the velocity anomaly, which has a narrow central updraft flanked by downdrafts. This size and shape disparity results in downdrafts characterized by a high water vapor mixing ratio and thus a broad joint probability density function (JPDF) of velocity and mixing ratio in the upper CBL. We also show that cloud-base latent heat fluxes can be both positive and negative and that the instantaneous positive fluxes can be very large (~10 000 W m −2 ). However, since cloud fraction tends to be small, the net impact of these fluxes remains modest.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Transverse energy–energy correlations of jets in the electron–proton deep inelastic scattering at HERA

We study the event shape variables, transverse energy–energy correlation TEEC (cosφ) and its asymmetry ATEEC (cosφ) in deep inelastic scattering (DIS) at the electron–proton collider HERA, where φ is the angle between two jets defined using a transverse-momentum (k T ) jet algorithm. At HERA, jets are defined in the Breit frame, and the leading nontrivial transverse energy–energy correlations arise from the 3-jet configurations. With the help of the NLOJET++, these functions are calculated in the leading order (LO) and the next-to-leading order (NLO) approximations in QCD at the electron–proton center-of-mass energy $\sqrt{s}$ = 314 GeV. We restrict the angular region to -0.8 ≤ cosφ ≤ 0.8, as the forward- and backward-angular regions require resummed logarithmic corrections, which we have neglected in this work. Following experimental jet-analysis at HERA, we restrict the DIS-variables x, y = Q 2 /(xs), where Q 2 = -q 2 is the negative of the momentum transfer squared q 2 , to 0 ≤ x ≤ 1, 0.2 ≤ y ≤ 0.6, and the pseudo-rapidity variable in the laboratory frame (η lab ) to the range -1 ≤ η lab ≤ 2.5. The TEEC and ATEEC functions are worked out for two ranges in Q 2 , defined by 5.5GeV 2 ≤ Q 2 ≤ 80GeV 2 , called the low-Q 2 -range, and 150GeV 2 ≤ Q 2 ≤ 1000GeV 2 , called the high-Q 2 -range. We show the sensitivity of these functions on the parton distribution functions (PDFs), the factorization (μ F ) and renormalization (μ R ) scales, and on α s (M$^2_Z$). Of these the correlations are stable against varying the scale μ F and the PDFs, but they do depend on μ R . For the choice of the scale μ R =$\sqrt{\langle ET \rangle^2+Q^2}$, advocated in earlier jet analysis at HERA, the shape variables TEEC and ATEEC are found perturbatively robust. These studies are useful in the analysis of the HERA data, including the determination of α s (M$^2_Z$) from the shape variables.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Paclitaxel loading in cationic liposome vectors is enhanced by replacement of oleoyl with linoleoyl tails with distinct lipid shapes

Abstract Lipid carriers of hydrophobic paclitaxel (PTX) are used in clinical trials for cancer chemotherapy. Improving their loading capacity requires enhanced PTX solubilization. We compared the time-dependence of PTX membrane solubility as a function of PTX content in cationic liposomes (CLs) with lipid tails containing one (oleoyl; DOPC/DOTAP) or two (linoleoyl; DLinPC/newly synthesized DLinTAP) cis double bonds by using microscopy to generate kinetic phase diagrams. The DLin lipids displayed significantly increased PTX membrane solubility over DO lipids. Remarkably, 8 mol% PTX in DLinTAP/DLinPC CLs remained soluble for approximately as long as 3 mol% PTX (the solubility limit, which has been the focus of most previous studies and clinical trials) in DOTAP/DOPC CLs. The increase in solubility is likely caused by enhanced molecular affinity between lipid tails and PTX, rather than by the transition in membrane structure from bilayers to inverse cylindrical micelles observed with small-angle X-ray scattering. Importantly, the efficacy of PTX-loaded CLs against prostate cancer cells (their IC50 of PTX cytotoxicity) was unaffected by changing the lipid tails, and toxicity of the CL carrier was negligible. Moreover, efficacy was approximately doubled against melanoma cells for PTX-loaded DLinTAP/DLinPC over DOTAP/DOPC CLs. Our findings demonstrate the potential of chemical modifications of the lipid tails to increase the PTX membrane loading while maintaining (and in some cases even increasing) the efficacy of CLs. The increased PTX solubility will aid the development of liposomal PTX carriers that require significantly less lipid to deliver a given amount of PTX, reducing side effects and costs.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Direct Measurement of Helicoid Surface States in RhSi Using Nonlinear Optics

Despite the fundamental nature of the edge state in topological physics, direct measurement of electronic and optical properties of the Fermi arcs of topological semimetals has posed a significant experimental challenge, as their response is often overwhelmed by the metallic bulk. However, laser-driven currents carried by surface and bulk states can propagate in different directions in nonsymmorphic crystals, allowing for the two components to be easily separated. Motivated by a recent theoretical prediction G. Chang et al., Phys. Rev. Lett. 124, 166404 (2020), we have measured the linear and circular photogalvanic effect currents deriving from the Fermi arcs of the nonsymmorphic, chiral Weyl semimetal RhSi over the 0.45-1.1 eV incident photon energy range. Our data are in good agreement with the predicted spectral shape of the circular photogalvanic effect as a function of photon energy, although the direction of the surface photocurrent departed from the theoretical expectation over the energy range studied. In conclusion, surface currents arising from the linear photogalvanic effect were observed as well, with the unexpected result that only two of the six allowed tensor element were required to describe the measurements, suggesting an approximate emergent mirror symmetry inconsistent with the space group of the crystal.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Measurements of H Λ 3 and H Λ 4 Lifetimes and Yields in Au + Au Collisions in the High Baryon Density Region

We report precision measurements of hypernuclei $^3_ΛH$ and $^4_ΛH$ lifetimes obtained from Au + Au collisions at $\sqrt{sNN}$ = 3.0 GeV and 7.2 GeV collected by the STAR experiment at the Relativistic Heavy Ion Collider, and the first measurement of $^3_ΛH$ and $^4_ΛH$ midrapidity yields in Au + Au collisions at $\sqrt{sNN}$ = 3.0 GeV. $^3_ΛH$ and $^4_ΛH$, being the two simplest bound states composed of hyperons and nucleons, are cornerstones in the field of hypernuclear physics. Their lifetimes are measured to be 221 ± 15 (stat) ± 19 (syst) ps for $^3_ΛH$ and 218 ± 6 (stat) ± 13 (syst) ps for $^4_ΛH$. The p T -integrated yields of $^3_ΛH$ and $^4_ΛH$ are presented in different centrality and rapidity intervals. It is observed that the shape of the rapidity distribution of $4_ΛH$ is different for 0%–10% and 10%–50% centrality collisions. Thermal model calculations, using the canonical ensemble for strangeness, describes the $^3_ΛH$ yield well, while underestimating the $^4_ΛH$ yield. Transport models, combining baryonic mean-field and coalescence (jam) or utilizing dynamical cluster formation via baryonic interactions (phqmd) for light nuclei and hypernuclei production, approximately describe the measured $^3_ΛH$ and $^4_ΛH$ yields. Our measurements provide means to precisely assess our understanding of the fundamental baryonic interactions with strange quarks, which can impact our understanding of more complicated systems involving hyperons, such as the interior of neutron stars or exotic hypernuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Extracting doubly excited state lifetimes in helium directly in the time domain with attosecond noncollinear four-wave-mixing spectroscopy

The helium atom, with one nucleus and two electrons, is a prototypical system to study quantum many-body dynamics. Doubly excited states, or quantum states in which both electrons are excited by one photon, showcase electronic-correlation mediated effects. In this paper, the natural lifetimes of the doubly excited 1 P o 2 s n p Rydberg series and the 1 S e 2 p 2 dark state in helium in the 60–65 eV region are measured directly in the time domain with extreme-ultraviolet/near-infrared noncollinear attosecond four-wave-mixing (FWM) spectroscopy. The measured lifetimes agree with lifetimes deduced from spectral linewidths and theoretical predictions, and the roles of specific decay mechanisms are considered. While complex spectral line shapes in the form of Fano resonances are common in absorption spectroscopy of autoionizing states, the background-free and thus homodyned character of noncollinear FWM results exclusively in Lorentzian spectral features in the absence of strong-field effects. The onset of strong-field effects that would affect the extraction of accurate natural lifetimes in helium by FWM is determined to be approximately 0.3 Rabi cycles. This study provides a systematic understanding of the FWM parameters necessary to enable accurate lifetime extractions, which can be utilized in more complex quantum systems in the future. Published by the American Physical Society 2024

Rupprecht, Patrick (ORCID:000000026491793X)↗
DOE OSTI2024

DEM simulation of the compression of crushable sand: does the initial particle shape matter?

Advances in DEM modeling, combined with high-resolution X-ray tomography, opened the way for computer models based on virtual replicas of the particles which preserve nearly all facets of their geometry. This leads to simulation advantages, but also high computational costs. Here we tackle a question stemming from this trend: how accurate should particle models be to ensure accuracy? We address this question for the case of the compression of crushable sand. LS-DEM was used to generate three models of Ottawa sand (exact replicas, ellipsoids, and spheres) from digital images of its grains. Compression-induced crushing was simulated for all sets by tracking evolving size and shape distribution. The results confirm that exact replicas provide the closest match of the measurements. However, intermediate degrees of rendering (e.g. ellipsoids preserving volume and aspect ratio of the real grains) led to satisfactory results only marginally different from those of exact replicas. In conclusion, these findings provide an example of the protocols that may be followed to identify the optimal degree of particle approximation which should be regarded as mandatory to achieve a conscious, sustainable use of computational resources.

58 GEOSCIENCES↗
DOE OSTI2020

On the quantitative characterization of weld microstructures

Here, a new technique to quantify grain shape and grain boundary curvature in the fusion zone (FZ) and the heat-effected zone (HAZ) of refractory metals and alloys has been developed. The application of this technique to quantify the effect of welding speed on these microstructural characteristics in simulated molybdenum welds is highlighted in this study. A 50% increase in weld speed more than doubles the fraction of grain segments in the fusion zone with orientations between 00 to 300 to the normal to the welding direction, with a corresponding 50% decrease in the fraction of grain segments oriented along the welding direction. This increase in weld speed also results in a reduction in grain size from approximately 120 µm to 84 µm along the WD at the FZ centerline. Grain boundary curvature is negative near the weld centerline and the edge of the fusion zone, indicating that with increasing distance from the weld centerline, the grain segments progressively rotate towards a direction normal to the welding direction at both locations. Presence of regions with relatively straight grain segments indicated by curvatures close to zero were identified in between the weld centerline and the edge of the FZ at all weld speeds.

36 MATERIALS SCIENCE↗
DOE OSTI2025

On finite-dimensional smoothed-particle Hamiltonian reductions of the Vlasov equation

The inclusion of spatial smoothing in finite-dimensional particle-based Hamiltonian reductions of the Vlasov equation and related models is considered. Here, this work investigates the underlying Hamiltonian structure of such smoothed particle-based methods for Hamiltonian systems and the small-scale regularization such methods implicitly make in approximating the continuum theory. In the context of the Vlasov–Poisson equation and other mean-field Lie–Poisson systems, of which Vlasov–Poisson is a special case, smoothing amounts to a convolutive regularization of the Hamiltonian. This regularization may be interpreted as a change of the inner product structure used to identify the dual space in the Lie–Poisson Hamiltonian formulation. In particular, the shape function used for spatial smoothing may be identified as the kernel function of a reproducing kernel Hilbert space whose inner product is used to define the Lie–Poisson Hamiltonian structure. It is likewise possible to introduce smoothing in the Vlasov–Maxwell system, but in this case the Poisson bracket must be modified rather than the Hamiltonian. The smoothing applied to the Vlasov–Maxwell system is incorporated by inserting smoothing in the map from canonical to kinematic coordinates. In the filtered system, the Lorentz force law and the current, the two terms coupling the Vlasov equation with Maxwell’s equations, are spatially smoothed.

Hamiltonian mechanics↗
DOE OSTI2021

Charge radii in covariant density functional theory: A global view

A systematic global investigation of differential charge radii has been performed within the CDFT framework for the first time. Theoretical results obtained with conventional covariant energy density functionals and the separable pairing interaction of Tian et al. [Phys. Lett. B 676, 44 (2009)] are compared with experimental differential charge radii in the regions of the nuclear chart in which available experimental data crosses the neutron shell closures at N=28,50,82, and 126. The analysis of absolute differential radii of different isotopic chains and their relative properties indicate clearly that such properties are reasonably well described in model calculations in the cases when the mean-field approximation is justified. However, while the observed clusterization of differential charge radii of different isotopic chains is well described above the N=50 and N=126 shell closures, it is more difficult to reproduce it above the N=28 and N=82 shell closures because of possible deficiencies in the underlying single-particle structure. The impact of the latter has been evaluated for spherical shapes and it was shown that the relative energies of the single-particle states and the patterns of their occupation with increasing neutron number have an appreciable impact on the evolution of the δ$\langle$r2$\rangle$N,N' values. These factors also limit the predictive power of model calculations in the regions of high densities of the single-particle states of different origin. It is shown that the kinks in the charge radii at neutron shell closures are due to the underlying single-particle structure and due to weakening or collapse of pairing at these closures. The regions of the nuclear chart in which the correlations beyond mean field are expected to have an impact on charge radii are indicated; the analysis shows that the assignment of a calculated excited prolate minimum to the experimental ground state allows us to understand the trends of the evolution of differential charge radii with neutron number in many cases of shape coexistence even at the mean-field level. It is usually assumed that pairing is a dominant contributor to odd-even staggering (OES) in charge radii. Our analysis paints a more complicated picture. It suggests a new mechanism in which the fragmentation of the single-particle content of the ground state in odd-mass nuclei due to particle-vibration coupling provides a significant contribution to OES in charge radii.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Response of a CMS HGCAL silicon-pad electromagnetic calorimeter prototype to 20–300 GeV positrons

The Compact Muon Solenoid collaboration is designing a new high-granularity endcap calorimeter, HGCAL, to be installed later this decade. As part of this development work, a prototype system was built, with an electromagnetic section consisting of 14 double-sided structures, providing 28 sampling layers. Each sampling layer has an hexagonal module, where a multipad large-area silicon sensor is glued between an electronics circuit board and a metal baseplate. The sensor pads of approximately 1.1 cm$^{2}$ are wire-bonded to the circuit board and are readout by custom integrated circuits. The prototype was extensively tested with beams at CERN's Super Proton Synchrotron in 2018. Based on the data collected with beams of positrons, with energies ranging from 20 to 300 GeV, measurements of the energy resolution and linearity, the position and angular resolutions, and the shower shapes are presented and compared to a detailed Geant4 simulation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Photo-response of the $N=Z$ nucleus $^{24}$Mg

The electric E1 and magnetic M1 dipole responses of the N = Z nucleus 24 Mg were investigated in an inelastic photon scattering experiment. The 13.0 MeV electrons, which were used to produce the unpolarised bremsstrahlung in the entrance channel of the 24 Mg(γ,γ') reaction, were delivered by the ELBE accelerator of the Helmholtz-Zentrum Dresden-Rossendorf. The collimated bremsstrahlung photons excited one J π = 1 – , four J π = 1 + , and six J π = 2 + states in 24 Mg. De-excitation γ rays were detected using the four high-purity germanium detectors of the γELBE setup, which is dedicated to nuclear resonance fluorescence experiments. In the energy region up to 13.0 MeV a total B(M1)↑ = 2.7(3) $μ$$^{2}_{N}$ is observed, but this N = Z nucleus exhibits only marginal E1 strength of less than ΣB(E1)↑≤ 0.61 × 10 –3 e 2 fm 2 . The B(Π1, $1$$^{π}_{i}$ → $2$$^{+}_{1}$)/B(Π1,$1$$^{π}_{i}$ → $0$$^{+}_{gs}$) branching ratios in combination with the expected results from the Alaga rules demonstrate that K is a good approximative quantum number for 24 Mg. The use of the known ρ 2 (E0, $0$$^{+}_{2}$ → $0$$^{+}_{gs}$) strength and the measured B(M1,1 + → $0$$^{+}_{2}$)/B(M1,1 + → $0$$^{+}_{gs}$) branching ratio of the 10.712 MeV 1 + level allows, in a two-state mixing model, an extraction of the difference Δ$β$$^{2}_{2}$ between the prolate ground-state structure and shape-coexisting superdeformed structure built upon the 6432-keV $0$$^{+}_{2}$ level.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Temporal reflection of an optical pulse from a short soliton: impact of Raman scattering

We study temporal reflection of an optical pulse from the refractive-index barrier created by a short pump soliton inside a nonlinear dispersive medium such as an optical fiber. One feature is that the soliton’s speed changes continuously as its spectrum redshifts because of intrapulse Raman scattering. We use the generalized nonlinear Schrödinger equation to find the shape and spectrum of the reflected pulse. Both are affected considerably by the soliton’s trajectory. The reflected pulse can become considerably narrower compared to the incident pulse under conditions that involve a type of temporal focusing. This phenomenon is explained through space–time duality by showing that the temporal situation is analogous to an optical beam incident obliquely on a parabolic mirror. We obtain an approximate analytic expression for the reflected pulse’s spectrum and use it to derive the temporal version of the transformation law for the

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Hexagonal Distributed Embedded Energy Converters (HexDEECs)

Distributed Embedded Energy Converter Technologies (DEEC-Tec) is a new domain for marine renewable energy research that utilizes a conglomeration of small distributed embedded energy converters (DEECs) that, in aggregate, form larger metamaterial frameworks. These resulting DEEC-Tec metamaterials can then, in turn, be used to construct flexible ocean wave energy converters called flexWECs. DEEC-Tec enables flexWECs: (i) to be inherently broad-banded ocean wave frequency energy converters and (ii) to have an inherent lack of highly loaded rigid bodies. The DEEC-Tec domain also benefits the marine renewable energy domain by inherently availing ways that marine energy can be harvested and converted that heretofore has not yet been considered possible: real-time execution of transforming topologies (e.g., actively changing a flexWEC's shape and form) and morphologies (e.g., actively changing a flexWEC's stiffness and damping throughout its entire structure). Presented, is one specific type of DEEC, a HexDEEC, that shows promise in aiding the adoption and further development of the DEEC-Tec domain - it is a small energy transducer being developed by the United States National Renewable Energy Laboratory. The HexDEEC is a small (characteristic length approximating a centimeter) energy transducer that converts the dynamic deformations of an elastomer into electricity through a charging-discharging cycle of a capacitor whose capacitance is varied by those elastic deformations. The HexDEEC is composed of a hyperelastic hexagonal housing (nominally silicon rubber) with six electrodes on its inner faces. The upper three electrodes share the same charge while the lower three electrodes oppose the upper electrode charges. Externally, the HexDEEC has two arms extending away from the middle vertices of the hexagon. Via principles governing the relationship between electrical capacitance and electrical potential (voltage and charge), electricity is generated when the HexDEEC's arms are dynamically pulled or released under tensile loading as doing so causes the distance between the upper and lower sets of electrodes to change - varying the energy converter's overall capacitance. Analytical and numerical modeling have already been used to estimate the electrical energy produced by a HexDEEC. The cursory models approximate the HexDEEC as a parallel plate variable capacitor - simplifying from six to two opposing plates with a constant dielectric volume between those two plates. To account for the elastic HexDEEC material properties, software such as SolidWorks and STAR-CCM+ have been used to generate hyperelastic models; notably, Mooney-Rivlin based models. Individual HexDEECs have been fabricated by drawing uncured liquid silicon rubber into molds via vacuum pressure. To simplify manufacturing, HexDEEC sub-components - e.g., electrodes, wires - can be placed within those molds such that they are directly embedded into the hexagonal housing during the curing process. Furthermore, DEEC-Tec metamaterials can be created by interweaving or sequentially layering multiple HexDEEC strands together. The HexDEEC based metamaterial could then generate electricity through its gross deformations. Ultimately, HexDEECs represent a specific type of energy transducer that can be leveraged, by the DEEC-Tec domain, to create metamaterials used to construct novel flexWECs.

DEEC-Tec↗