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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 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Digitization and subduction of S U ( N ) gauge theories

The simulation of lattice gauge theories on quantum computers necessitates digitizing gauge fields. One approach involves substituting the continuous gauge group with a discrete subgroup, but the implications of this approximation still need to be clarified. To gain insights, we investigate the subduction of S U ( 2 ) and S U ( 3 ) to discrete crystal-like subgroups. Using classical lattice calculations, we show that subduction offers valuable information based on subduced direct sums, helping us identify additional terms to incorporate into the lattice action that can mitigate the effects of digitization. Furthermore, we compute the static potentials of all irreducible representations of Σ ( 360 × 3 ) at a fixed lattice spacing. Our results reveal a percent-level agreement with the Casimir scaling of S U ( 3 ) for irreducible representations that subduce to a single Σ ( 360 × 3 ) irreducible representation. This provides a diagnostic measure of approximation quality, as some irreducible representations closely match the expected results while others exhibit significant deviations. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Effects of Landau quantization on neutrino emission and absorption

Some neutron stars known as magnetars possess very strong magnetic fields, with surface fields as large as 10 15 G and internal fields that are possibly stronger. Recent observations of the radio pulsar GLEAM-X J1627 suggest it may have a surface field as strong as 10 16 G. In the presence of a strong magnetic field, Leinson and Perez showed and Baiko and Yakovlev confirmed that the energy levels of electrons and protons are quantized and the direct Urca process allows neutron stars to cool rapidly, even at low density. For the case of magnetic fields 𝐵 ≳ 10 16 G, we find features in the emissivity due to energy quantization that are not captured by the frequently employed quasiclassical approximation where energy levels are treated as nearly continuous. Resonances can result in amplification of the neutrino emissivity at specific densities compared to a calculation that neglects quantization, particularly at low temperature. These effects are not important for the thermal evolution of an entire neutron star, but may be relevant for phenomena that depend on behavior at specific densities. Here, we present a fully relativistic calculation of the direct Urca rate in a strong magnetic field using the standard V-A weak Lagrangian incorporating mean field nuclear effects and discuss approaches to the numerical challenge the modified wave functions present and a new semianalytic approximation. These tools are also applicable to calculating neutrino opacities in strong magnetic fields in the ejecta of binary neutron star mergers. We calculate the opacities for neutrinos capturing on free nucleons at subsaturation densities and temperatures exceeding an MeV. We find an enhancement to capture processes of the lowest energy neutrinos by an order of magnitude or more due to suppression of electron Pauli blocking in the case of capture on neutrons, and from the effect of the nucleon magnetic moments in the case of capture on protons.

astrophysical electromagnetic fields↗
DOE OSTI2025

Exploring entanglement and spectral split correlations in three-flavor collective neutrino oscillations

In environments with prodigious numbers of neutrinos, such as core-collapse supernovae, neutron star mergers, or the early Universe, neutrino-neutrino interactions are dynamically significant. They can dominate neutrino flavor evolution and force it to be nonlinear, causing collective neutrino oscillations. Such collective oscillations have been studied numerically, for systems with up to millions of neutrinos, using mean-field or one-particle effective approximations. However, such a system of interacting neutrinos is a quantum many-body system, wherein quantum correlations could play a significant role in the flavor evolution—thereby motivating the exploration of many-body treatments that follow the time evolution of these correlations. In many-body flavor evolution calculations with two neutrino flavors, the emergence of spectral splits in the neutrino energy distributions has been found to be correlated with the degree of quantum entanglement across the spectrum. In this work, for the first time, we investigate the emergence of spectral splits in the three-flavor many-body collective neutrino oscillations. We find that the emergence of spectral splits resembles the number and location found in the mean-field approximation but not in the width. Moreover, unlike in the two-flavor many-body calculations, we find that additional degrees of freedom make it more difficult to establish a correlation between the location of the spectral splits and the degree of quantum entanglement across the neutrino energy spectrum. The observation from the two-flavor case, that neutrinos nearest to the spectral split frequency exhibit the highest level of entanglement, is more difficult to ascertain in the three-flavor case because of the presence of multiple spectral splits across different pairwise combinations of flavor and/or mass states. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Searching for MeV-mass neutrinophilic dark matter with large scale dark matter detectors

The indirect detection of dark matter (DM) through its annihilation products is one of the primary strategies for DM detection. One of the least constrained classes of models is neutrinophilic DM, because the annihilation products, weakly interacting neutrinos, are challenging to observe. Here, we consider a scenario where MeV-mass DM exclusively annihilates to the third neutrino mass eigenstate, which is predominantly of tau and muon flavor. In such a scenario, the potential detection rate of the neutrinos originating from the DM annihilation in our Galaxy in the conventional detectors would be suppressed by up to approximately two orders of magnitude. This is because the best sensitivity of such detectors for neutrinos with energies below approximately 100 MeV is for electron neutrino flavor. In this work, we highlight the potential of large-scale DM detectors in uncovering such signals in the tens of MeV range of DM masses. In addition, we discuss how coincident signals in direct detection DM experiments and upcoming neutrino detectors such as DUNE, Hyper-Kamiokande, and JUNO could provide new perspectives on the DM problem. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Inverse bremsstrahlung absorption rate for super-Gaussian electron distribution functions including plasma screening

Here we provide analytic expressions for the effective Coulomb logarithm for inverse bremsstrahlung absorption which predict significant corrections to the Langdon effect and overall absorption rate compared to previous estimates. The calculation of the collisional absorption rate of laser energy in a plasma by the inverse bremsstrahlung mechanism usually makes the approximation of a constant Coulomb logarithm. We dispense with this approximation and instead take into account the velocity dependence of the Coulomb logarithm, leading to a more accurate expression for the absorption rate valid in both classical and quantum conditions. In contrast to previous work, the laser intensity enters into the Coulomb logarithm. In most laser-plasma interactions the electron distribution function is super-Gaussian [Langdon, Phys. Rev. Lett. 44, 575 (1980)], and we find the absorption rate under these conditions is increased by as much as ≈ 30% compared to previous estimates at low density. In many cases of interest the correction to Langdon's predicted reduction in absorption is large; for example at Z = 6 and Te = 400 eV the Langdon prediction for the absorption is in error by a factor of ≈ 2. However, we also account for the additional effect of plasma screening, which predicts a reduction in absorption by a similar amount (up to ≈ 30%). These two effects compete to determine the overall absorption, which may be increased or decreased, depending on the conditions. The corrections can be incorporated into radiation-hydrodynamics simulation codes by replacing the familiar Coulomb logarithm with an analytic expression which depends on the super-Gaussian order “M” and the screening length.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Adaptation of Wallace's approach to the specific heat of elemental solids with significant intrinsic anharmonicity, particularly the light actinide metals

The quasiharmonic approximation is the most common method for modeling the specific heat of solids; however, it fails to capture the effects of intrinsic anharmonicity. In this study, we introduce the “elastic softening approximation,” an alternative approach to modeling intrinsic anharmonic effects on thermodynamic quantities, which is grounded in Wallace's thermodynamic framework that tracks entropy changes resulting from the continuous change (e.g., softening) of phonons as a function of temperature. A key finding of our study is a correlation between Poisson's ratio and the differential rate of phonon softening at finite frequencies, compared to lower frequencies relevant to elastic moduli measurements. We observe that elemental solids such as α -Be, diamond, Al, Cu, In, W, Au, and Pb, which span a wide range of Poisson's ratios and exhibit varying degrees of intrinsic anharmonicity, consistently follow this trend. When applied to α -U, α -Pu, and δ -Pu, our method reveals unusually large anharmonic phonon contributions at elevated temperatures across all three light actinide metals. These findings are attributed to the unique combination of enhanced covalency and softer elastic moduli inherent in the actinides, potentially influenced by their 5 f -electron bonding. Published by the American Physical Society 2025

36 MATERIALS SCIENCE↗
DOE OSTI2025

Fully thermal meta-GGA exchange correlation free-energy density functional

The application of density functional theory to materials in the warm dense matter regime has motivated the development of exchange-correlation functionals which incorporate proper, explicit temperature dependence. Previous work has yielded fully-thermal exchange-correlation free energy functionals at the local density approximation (LDA) and generalized gradient approximation (GGA) levels of refinement. Recently an additive thermal correction scheme was utilized to construct a meta-GGA exchange-correlation (XC) functional in which thermal effects are treated at the GGA level. Here, the f TSCAN free-energy XC functional presented here includes thermal effects through the meta-GGA level in the context of the SCAN (strongly constrained and appropriately normed) ground-state functional. The f TSCAN functional provides generality while achieving similar performance to a thermal GGA functional at high temperatures, e.g. pressures within 1% of path integral Monte Carlo simulations of warm dense hydrogen, and a significant improvement over ground-state functionals. At low temperatures, f TSCAN demonstrates improvements in accuracy relative to lower-level and deorbitalized functionals, indicating that calculations using f TSCAN may be expected to perform well across experimentally relevant densities and pressures.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Tunable Inductive Coupler for High-Fidelity Gates Between Fluxonium Qubits

The fluxonium qubit is a promising candidate for quantum computation due to its long coherence times and large anharmonicity. We present a tunable coupler that realizes strong inductive coupling between two heavy-fluxonium qubits, each with approximately 50-MHz frequencies and approximately 5-GHz anharmonicities. The coupler enables the qubits to have a large tuning range of 𝑋⁢𝑋 coupling strengths (−35 to 75 MHz). The 𝑍⁢𝑍 coupling strength is <3 kHz across the entire coupler bias range and <100 Hz at the coupler off position. These qualities lead to fast high-fidelity single- and two-qubit gates. By driving at the difference frequency of the two qubits, we realize a $\sqrt{i\textrm{SWAP}}$ gate in 258 ns with fidelity 99.72%, and by driving at the sum frequency of the two qubits, we achieve a $\sqrt{𝑏⁢\textrm{SWAP}}$ gate in 102 ns with fidelity 99.91%. This latter gate is only five qubit Larmor periods in length. We run cross-entropy benchmarking for over 20 consecutive hours and measure stable gate fidelities, with $\sqrt{𝑏⁢\textrm{SWAP}}$ drift (2⁢𝜎) <0.02% and $\sqrt{i\textrm{SWAP}}$ drift <0.08%.

Zhang, Helin↗
DOE OSTI2024

Superconducting Qubits above 20 GHz Operating over 200 mK

Current state-of-the-art superconducting microwave qubits are cooled to extremely low temperatures to avoid sources of decoherence. Higher qubit operating temperatures would significantly increase the cooling power available, which is desirable for scaling up the number of qubits in quantum computing architectures and integrating qubits in experiments requiring increased heat dissipation. To operate superconducting qubits at higher temperatures, it is necessary to address both quasiparticle decoherence (which becomes significant for aluminum junctions above 160 mK) and dephasing from thermal microwave photons (which are problematic above 50 mK). Using low-loss niobium-trilayer junctions, which have reduced sensitivity to quasiparticles due to the higher superconducting transition temperature of niobium, we fabricate transmons with higher frequencies than previously studied, up to 24 GHz. We measure decoherence and dephasing times of about 1 μs, corresponding to average qubit quality factors of approximately 10 5 , and find that decoherence is unaffected by quasiparticles up to 1 K. Without relaxation from quasiparticles, we are able to explore dephasing from purely thermal sources, finding that our qubits can operate up to approximately 250 mK while maintaining similar performance. The thermal resilience of these qubits creates new options for scaling up quantum processors, enables hybrid quantum experiments with high heat-dissipation budgets, and introduces a material platform for even-higher-frequency qubits.

Josephson junctions↗
DOE OSTI2025

Rapid Initial-State Preparation for the Quantum Simulation of Strongly Correlated Molecules

Studies on quantum algorithms for ground-state energy estimation often assume perfect ground-state preparation; however, in reality the initial state will have imperfect overlap with the true ground state. Here, we address that problem in two ways: by faster preparation of matrix-product-state (MPS) approximations and by more efficient filtering of the prepared state to find the ground-state energy. We show how to achieve unitary synthesis with a Toffoli complexity about 7 × lower than that in prior work and use that to derive a more efficient MPS-preparation method. For filtering, we present two different approaches: sampling and binary search. For both, we use the theory of window functions to avoid large phase errors and minimize the complexity. We find that the binary-search approach provides better scaling with the overlap at the cost of a larger constant factor, such that it will be preferred for overlaps less than about 0.003 . Finally, we estimate the total resources to perform ground-state energy estimation of Fe - S cluster systems, including the Fe Mo cofactor by estimating the overlap of different MPS initial states with potential ground states of the Fe Mo cofactor using an extrapolation procedure. With a modest MPS bond dimension of 4000 , our procedure produces an estimate of approximately 0.9 overlap squared with a candidate ground state of the Fe Mo cofactor, producing a total resource estimate of 7.3 × 10 10 Toffoli gates; neglecting the search over candidates and assuming the accuracy of the extrapolation, this validates prior estimates that have used perfect ground-state overlap. This presents an example of a practical path to prepare states of high overlap in a challenging-to-compute chemical system. Published by the American Physical Society 2025

Berry, Dominic W. (ORCID:0000000334461449)↗
DOE OSTI2025

Single-Shot Reconstruction of Electron Beam Longitudinal Phase Space in a Laser Wakefield Accelerator

We report on a single-shot longitudinal phase-space reconstruction diagnostic for electron beams in a laser wakefield accelerator via the experimental observation of distinct periodic modulations in the angularly resolved spectra. Such modulated angular spectra arise as a result of the direct interaction between the ultrarelativistic electron beam and the laser driver in the presence of the wakefield. A constrained theoretical model for the coupled oscillator, assisted by a genetic algorithm, can recreate the experimental electron spectra and, thus, fully reconstructs the longitudinal phase-space distribution of the electron beam with a temporal resolution of approximately 1.3 fs. In particular, it reveals the slice energy spread of the electron beam, which is important to measure for applications such as x-ray free electron lasers. In our experiment, the root-mean-square energy spread retrieved is bounded at 9.9 MeV, corresponding to a 0.9%–3.0% relative spread, despite the overall GeV energy beam having approximately 100% relative energy spread.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Magnetic correlations and pairing tendencies of the hybrid stacking nickelate superlattice La 7 Ni 5 O 17 (La 3 ⁢Ni 2 ⁢O 7 /La 4 Ni 3 ⁢O 10 ) under pressure

Motivated by the recent rapid progress in high-𝑇 𝑐 nickelate superconductors, we comprehensively study the physical properties of the alternating bilayer trilayer stacking nickelate La 7 ⁢Ni 5 ⁢O 17 . The high-symmetry phase of this material, without the tilting of oxygen octahedra, is not stable at ambient conditions but becomes stable under high pressure, where a small hole pocket 𝛾 0 , composed of the 𝑑 3⁢𝑧 2 −𝑟 2 states in the trilayer sublattice, appears. Here, this pocket was identified in our previous work for trilayer La 4 ⁢Ni 3 ⁢O 10 as important to develop superconductivity. Moreover, using random-phase approximation calculations, we find a leading 𝑠 ± pairing state for the high-symmetry phase under pressure with similar pairing strength as that obtained previously for the bilayer La 3⁢ Ni 2 ⁢O 7 compound, suggesting a similar or higher superconducting transition temperature 𝑇 𝑐 , at the random-phase approximation level. In addition, we find that the dominant magnetic fluctuations in the system driving this pairing state have antiferromagnetic structure both in-plane and between the planes of the top and bottom trilayer and bilayer sublattices, while the middle trilayer is magnetically decoupled.

Zhang, Yang [Univ. of Tennessee, Knoxville, TN (Un↗
DOE OSTI2026

Loop series expansions for tensor networks

Belief propagation (BP) can be a useful tool to approximately contract a tensor network, provided that the contributions from any closed loops in the network are sufficiently weak. In this article, we describe how a loop series expansion can be applied to systematically improve the accuracy of a BP approximation to a tensor network contraction, in principle converging arbitrarily close to the exact result. More generally, our result provides a framework for expanding a tensor network as a sum of component networks in a hierarchy of increasing complexity. We benchmark this proposal for the contraction of infinite projected entangled pair states, either representing the ground state of an Affleck-Kennedy-Lieb-Tasaki (AKLT) model or with randomly defined tensors, where it is shown to improve in accuracy over standard BP by several orders of magnitude while incurring only a minor increase in computational cost. These results indicate that the proposed series expansions could be a useful tool to accurately evaluate tensor networks in cases that otherwise exceed the limits of established contraction routines.

Evenbly, Glen [AWS Center for Quantum Computing, P↗
DOE OSTI2025

Trends in spatial correlations, two-phase coexistence, and criticality in a class of type-2 Schloegl models for autocatalysis

A class of type-2 Schloegl models is considered for particles on a square lattice with variable-range cooperativity. These models involve: (i) spontaneous particle annihilation at rate p; (ii) autocatalytic particle creation at unoccupied sites (i, j) with n ⩾ 2 particles within a specified neighborhood, Ω 𝑁 (i, j), of sites at rate $k_n$ = $\frac{^{(^n_2)}}{_{(^N_2)}}$ = $\frac{n{(n-1)}}{_{N(N-1)}}$; and (iii) possible spontaneous particle creation at unoccupied sites at “small” rate ɛ ⩾ 0. In some cases, Ω 𝑁 just includes all symmetry-equivalent sites at a single specific distance 𝑑 (in units of lattice constants) from the unoccupied site, e.g., 𝑑 = 1 (nearest-neighbor sites) where 𝑁 = 4, or 𝑑 = √5 (or √13 or…) where 𝑁 = 8. In other cases, Ω 𝑁 includes sites multiple distances from the unoccupied site, e.g., 𝑑 = {1,√2}, where 𝑁 = 8. Kinetic Monte Carlo (KMC) simulation reveals that these models exhibit a nonequilibrium discontinuous phase transition between high- and low-density states below a critical point, ɛ < ɛ c , with generic two-phase coexistence (2PC) at least for smaller 𝑁. With some exceptions, there is an approach toward mean-field behavior with increasing 𝑁 (so the regime of generic 2PC shrinks, and ɛ c approaches the mean-field value of 1/27). Additional insight into trends is provided by analysis of the exact master equations for the models via hierarchical truncation. These truncations utilize suitably tailored pair approximations which reflect the dominant nonequilibrium spatial correlations. These correlations in turn are shown to reflect the details of the autocatalytic particle creation process. For spatially heterogeneous states, the truncations produce coupled sets of lattice differential equations (LDE) which can describe orientation-dependent propagation of an interface between high- and low-density steady states for ɛ < ɛ c . Pair approximation values of 𝑝 = 𝑝 eq where the interface is stationary, and its orientation-dependence, are in semiquantitative agreement with KMC results. In conclusion, this comparison accounts for propagation failure in the LDE which complicates interpretation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Predicting interface structure using the minima hopping method

Here, we adapt the minima hopping method (MHM) to the problem of interfacial structure prediction and apply it to study a canonical problem, the tilt grain boundaries in SrTiO 3 . Our method employs a hybrid approach by first exploring the potential energy surface (PES) of different grain boundary samplings with an empirical force field, among which the fifteen candidates with lower energies are then refined using ab initio density functional theory (DFT) calculations. During the exploratory stage, we bias the search using a local order parameter to primarily sample various reconstructions in the vicinity of the interface, while preserving the crystallinity of the bulk regions. We further enhance the search by incorporating initial structures with rigid body displacements to account for translational variations between bulk phases, enabling the MHM to effectively generate both stoichiometric and nonstoichiometric SrTiO 3 Σ⁢3(111)[110] and Σ⁢3(112)[110] grain boundaries. From an algorithmic standpoint, MHM outperforms earlier studies based on genetic algorithms (GA) by identifying more stable interfacial structures of several SrTiO 3 grain boundaries. The performance of the present implementation of the MHM approach is primarily limited by exploring an approximate description of the PES with a rather simple Buckingham potential. This limitation leads to variations in performance when compared to approaches utilizing more advanced surrogate PES models, such as direct DFT-PES sampling or GA with the embedded atom method (EAM). Despite the present limitations, the MHM approach is able to yield interfacial structures with comparable or lower interfacial energies in specific cases, such as Σ⁢3(111)[110] Γ=1, ±0.5 and Σ⁢3(112)[110] Γ= ±1, −2, underscoring the robustness of the MHM approach even with a simple approximation of the DFT PES. The MHM interfacial structure prediction method thus offers an efficient approach to understanding the grain boundaries and heterointerfaces at the atomic scale, providing an important prerequisite for effective materials design.

density functional theory↗
DOE OSTI2025

Flexible PCB Windings Size Optimization for Winding AC Resistance Minimization Under the Sinusoidal Voltage Regime

In this paper, optimization of the winding AC resistance of the flexible printed circuit board (FPCB) wire windings is performed. A one-dimensional model of the FPCB winding is introduced and an equation for the FPCB winding AC resistance and its low and medium frequency approximation are derived. The approximate FPCB winding AC resistance equation is used to derive optimum thickness of the FPCB winding conductor thickness at which minimum of winding AC resistance (global optimum) is achieved. The Finite Element Method analysis and experimental verification of derived equations (winding resistance, impedance, power loss, and temperature measurements) is performed in order validate derived model and winding resistance equation.

42 ENGINEERING↗
DOE OSTI2024

Efficient Unitary Designs from Random Sums and Permutations

A unitary k-design is an ensemble of unitaries that matches the first k moments of the Haar measure. In this work, we provide two efficient constructions of k-designs on n-qubits using new random matrix theory techniques. Our first construction is based on exponentiating sums of random i.i.d. Hermitian matrices and uses O(k2n2)-many gates. In the spirit of central limit theorems, we show that this random sum approximates the Gaussian Unitary Ensemble (GUE). We then show that the product of just two exponentiated GUE matrices is already approximately Haar random. Our second construction is based on products of exponentiated sums of random permutations and uses Õ(k poly (n)) many gates. The k dependence is optimal (up to polylogarithmic factors) and is inherited from the efficiency of existing k-wise independent permutations. Furthermore, replacing random permutations with quantum-secure pseudorandom permutations (PRPs), we also obtain a pseudorandom unitary (PRU) ensemble that is secure under nonadaptive queries. A central feature of both proofs is a new connection between the polynomial method in quantum query complexity and the large-dimension (N) expansion in random matrix theory. In particular, the first construction uses the polynomial method to control high moments of certain random matrix ensembles without requiring delicate Weingarten calculations. In doing so, we define and solve a moment problem on the unit circle, asking whether a finite number of equally weighted points can reproduce a given set of moments. In our second construction, the key step is to exhibit an orthonormal basis for irreducible representations of the partition algebra that has a low-degree large-N expansion. This allows us to show that the distinguishing probability is a low-degree rational polynomial of the dimension N.

algebra↗
DOE OSTI2025

Digital Filter Design for Point-on-Wave Sensors: Highlighting Frequency Response Limitations and Enhancing Grid Simulation Accuracy

Data is proving to be the backbone of today's and, more importantly, tomorrow's grid. As the system changes and introduces fast-acting devices like power electronics, overall observability tends to decrease from the utility point-of-view. This can be mitigated by adding more high-fidelity sensors onto the grid, although this incurs a cost. These sensors are never ideal, and each have unique frequency responses that may influence the data produced. This may, in turn, impact the protection and control of the power grid. This paper presents a methodology of representing these point-on-wave sensors digitally by estimating digital-filter representations of them, thereby introducing means of improving the sensor models used in electromagnetic-transient (EMT) simulations. This may help with identifying potential high-frequency, sensor-induced distortions, and system resonance compensation. Three commercial-grade medium-voltage point-on-wave sensors are utilized in a lab environment to obtain experimental frequency responses with a frequency sweep, and it is shown that both Infinite Impulse Response (IIR) and Finite Impulse Response (FIR) filter representations may approximate these responses with varying degrees of accuracy, though each has their own strengths and weaknesses. It is found that, in general, FIR estimation better approximates these sensors than IIR estimation does.

Wilson, Aaron [ORNL] (ORCID:0000000327331697)↗