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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 91 records · Page 5

Algorithm for Stabilizing a POD-Based Dynamical System

This algorithm provides a new way to improve the accuracy and asymptotic behavior of a low-dimensional system based on the proper orthogonal decomposition (POD). Given a data set representing the evolution of a system of partial differential equations (PDEs), such as the Navier-Stokes equations for incompressible flow, one may obtain a low-dimensional model in the form of ordinary differential equations (ODEs) that should model the dynamics of the flow. Temporal sampling of the direct numerical simulation of the PDEs produces a spatial time series. The POD extracts the temporal and spatial eigenfunctions of this data set. Truncated to retain only the most energetic modes followed by Galerkin projection of these modes onto the PDEs obtains a dynamical system of ordinary differential equations for the time-dependent behavior of the flow. In practice, the steps leading to this system of ODEs entail numerically computing first-order derivatives of the mean data field and the eigenfunctions, and the computation of many inner products. This is far from a perfect process, and often results in the lack of long-term stability of the system and incorrect asymptotic behavior of the model. This algorithm describes a new stabilization method that utilizes the temporal eigenfunctions to derive correction terms for the coefficients of the dynamical system to significantly reduce these errors.

Kalb, Virginia L.↗

Electrochemical Control of the Ultrafast Lattice Response of a Layered Semimetal

The unique layer-stacking in two-dimensional (2D) van der Waals materials facilitates the formation of nearly degenerate phases of matter and opens novel routes for the design of low-power, reconfigurable functional materials. Electrochemical ion intercalation between stacked layers offers a promising approach to stabilize bulk metastable phases and to explore the effects of extreme carrier doping and strain. However, in situ characterization methods to study the structural evolution and dynamical functional properties of these intercalated materials remains limited. Here a novel experimental platform is presented capable of simultaneously performing electrochemical lithium-ion intercalation and multimodal ultrafast characterization of the lattice using both electron diffraction and nonlinear optical techniques. Using the layered semimetal WTe 2 as a model system, the interlayer shear phonon mode that modulates stacking between 2Dlayers is probed, showing that small amounts of lithiation enhance the amplitude and lifetime of the phonon, contrary to expectations. This results from the dynamically fluctuating and anharmonic structure between nearly degenerate phases at room temperature, which can be stabilized by electronic carriers accompanying the inserted lithium ions. At high lithiation, the T d ’ structure emerges and quenches the phonon response. This work defines new approaches for using electrochemistry to engineer the dynamic structure of 2D materials.

36 MATERIALS SCIENCE↗

Unraveling Morphology and Chemistry Dynamics in Fluoroethylene Carbonate Generated Silicon Anode Solid Electrolyte Interphase Across Delithiated and Lithiated States: Relative Cycling Stability Enabled by an Elastomeric Polymer Matrix

The silicon solid electrolyte interphase (SEI) faces cyclical cracking and reconstruction due to the ∼350% volume expansion. Understanding the SEI dynamic morphology and chemistry evolution from delithiated to lithiated states is thereby paramount to engineering a stable Si anode. Fluoroethylene carbonate (FEC) is a preferred additive with widely demonstrated enhancement of the Si cycling. Thus, insights into the dynamics of the FEC-SEI may provide hints toward engineering the Si interface. Herein, complementary ATR-FTIR, AFM, tip IR, and XPS probing reveal the presence of an elastomeric polycarbonate-like matrix in the FEC-generated SEI which is absent from the FEC-free SEI. Adding FEC to the baseline 1 M LiPF 6 in EC:EMC (1:1) electrolyte promotes formation of a thinner and more conformal SEI, and subdues morphology and chemistry changes between consecutive half-cycles. From AFM, morphological stabilization of the FEC-SEI occurs earlier. Furthermore, conventional SEI biproducts such as Li 2 CO 3 and LiEDC appear in reduced quantities in the FEC-SEI implying a reduced quantity of Li-consuming species. The thin polymeric FEC-SEI enables deeper (de)lithiation of silicon. In conclusion, the enhanced mechanical compliance, chemical invariance, and reduced Li inventory consumption of the FEC-SEI are logically the key features underlying the Si cycling enhancement by FEC.

25 ENERGY STORAGE↗

Thermally induced structural evolution and nanoscale interfacial dynamics in Bi-Sb-Te layered nanostructures

Layered chalcogenides, including Bi-Sb-Te ternary alloys and heterostructures, are renowned as thermoelectric and topological insulators and have recently been highlighted as plasmonic building blocks beyond noble metals. Here, we conduct joint in situ transmission electron microscopy and density functional theory calculations to investigate the temperature-dependent nanoscale dynamics and interfacial properties, identifying the role of native defects and edge configurations in the anisotropic sublimation of Bi 2 Te 3 -Sb 2 Te 3 heterostructures and Sb 2-x Bi x Te 3 alloys. We report structural dynamics, including edge evolution, layer-by-layer sublimation, and the formation and coalescence of thermally induced polygonal nanopores. These nanopores are initiated by preferential dissociation of tellurium, reducing thermal stability in heterostructures. Triangular and quasi-hexagonal configurations dominate nanopore structures in heterostructures. Our calculations reveal antisite defects (Te Sb and Te Bi ) as key players in defect-assisted sublimation. These findings enhance our understanding of nanoscale dynamics and assist in designing tunable low-dimensional chalcogenides.

Bi2Te3-Sb2Te3 heterostructure↗

Elucidating Interfacial Stability between Lithium Metal Anode and Li Phosphorus Oxynitride via In Situ Electron Microscopy

Li phosphorus oxynitride (LiPON) is one of a very few solid electrolytes that have demonstrated high stability against Li metal and extended cyclability with high Coulombic efficiency for all solid-state batteries (ASSBs). However, theoretical calculations show that LiPON reacts with Li metal. Here, we utilize in situ electron microscopy to observe the dynamic evolutions at the LiPON–Li interface upon contacting and under biasing. We reveal that a thin interface layer (~60 nm) develops at the LiPON–Li interface upon contact. This layer is composed of conductive binary compounds that show a unique spatial distribution that warrants an electrochemical stability of the interface, serving as an effective passivation layer. Our results explicate the excellent cyclability of LiPON and reconcile the existing debates regarding the stability of the LiPON–Li interface, demonstrating that, though glassy solid electrolytes may not have a perfect initial electrochemical window with Li metal, they may excel in future applications for ASSBs.

25 ENERGY STORAGE↗

The Importance of Nonequilibrium to Equilibrium Transition Pathways for the Efficiency and Stability of Organic Solar Cells

Controlled morphology of solution-processed thin films have realized impressive achievements for non-fullerene acceptor (NFA)–based organic solar cells (OSCs). Given the large set of donor–acceptor pairs, employing various processing conditions to realize optimal morphology for high efficiency and stable OSCs is a strenuous task. Therefore, comprehensive correlations between processing conditions and morphology evolution pathways have to be developed for efficient performance and stability of devices. Within the framework of the blend system, crystallization transitions of NFA molecules are tracked utilizing the first heating scan of differential scanning calorimeter (DSC) measurement correlating with respective morphology evolution of blend films. Real-time dynamics measurements and morphology characterizations are combined to provide optimal morphology transition pathways as NFA molecules are shown to be released from the mixed phase to form balanced ordered packing with variant processing conditions. Polymer:NFA films are fabricated using blade coating incorporating solvent additive or thermal annealing as processing conditions as a correlation is formulated between performance and stability of solar cells with morphology transition pathways. In conclusion, this work demonstrates the significance of processing condition-controlled transition pathways for the realization of optimal morphology leading to superior OSC devices.

14 SOLAR ENERGY↗

Material Changes in Electrocatalysis: An In Situ/Operando Focus on the Dynamics of Cobalt‐Based Oxygen Reduction and Evolution Catalysts

Abstract The shift towards cheaper, non‐platinum group metal electrocatalyst materials for clean energy technologies is coupled with challenges in maintaining long‐term performance. For practical purposes, electrocatalytic stability typically focuses on catalyst electrochemical performance over time. However, a deeper understanding of catalyst material property changes during operation is needed to enable material‐specific design strategies for long‐term stabilization. In the last several decades, improvements in material characterization techniques have made it possible to probe the composition, structure, and degradation products of catalysts in situ/operando. Herein we review the current understanding of in situ/operando material stability of Co‐based electrocatalysts for the oxygen evolution (OER) and reduction reactions (ORR) in acidic and alkaline environments. We focus on in situ/operando materials characterization of three categories of Co‐based OER/ORR catalysts: oxides and (oxy)hydroxides, mixed‐metal catalysts, and non‐oxide materials. This review aims to compile and compare the results from multiple studies and techniques to provide insight into the role that the starting material, pH, and applied potential have on the active surface and stability of Co‐based materials. We conclude by highlighting directions that have been underexplored with opportunities for continued research including improving in situ/operando characterization, methods to probe long‐term material changes, and the development of operando studies on full‐scale devices. Using Co‐based materials as a case study, this review shows the vital role that in situ/operando characterization must play in the future of improving electrocatalyst stability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Impact of tensor forces on quasifission product yield distributions

Quantum shell effects are crucial for the stability and structure of atomic nuclei and play a key role in the discovery of superheavy elements. Furthermore, during nuclear collisions, the dynamical evolution of these shell effects disrupts the equilibration process necessary for forming a compound nucleus, leading to the breakup of the initial composite as a result of quasifission. As such, quasifission reactions hinder the formation of a superheavy element.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

MSASGCN : Multi-Head Self-Attention Spatiotemporal Graph Convolutional Network for Traffic Flow Forecasting

Traffic flow forecasting is an essential task of an intelligent transportation system (ITS), closely related to intelligent transportation management and resource scheduling. Dynamic spatial-temporal dependencies in traffic data make traffic flow forecasting to be a challenging task. Most existing research cannot model dynamic spatial and temporal correlations to achieve well-forecasting performance. The multi-head self-attention mechanism is a valuable method to capture dynamic spatial-temporal correlations, and combining it with graph convolutional networks is a promising solution. Therefore, we propose a multi-head self-attention spatiotemporal graph convolutional network (MSASGCN) model. It can effectively capture local correlations and potential global correlations of spatial structures, can handle dynamic evolution of the road network, and, in the time dimension, can effectively capture dynamic temporal correlations. Experiments on two real datasets verify the stability of our proposed model, obtaining a better prediction performance than the baseline algorithms. The correlation metrics get significantly reduced compared with traditional time series prediction methods and deep learning methods without using graph neural networks, according to MAE and RMSE results. Compared with advanced traffic flow forecasting methods, our model also has a performance improvement and a more stable prediction performance. We also discuss some problems and challenges in traffic forecasting.

Cao, Yang↗

Structure and Dynamics of Domains in Ferroelectric Nanostructures – Phase-Field Modeling (Final Technical Report)

Domain pattern formation is one of the most common phenomena in nature and is a topic of immense interest in many fields ranging from materials science and physics to chemistry and biology. This DOE sponsored research project explored the basic science concerning the thermodynamic stability of mesoscale polarization domain patterns and their temporal evolution mechanisms during formation and subsequent switching in ferroelectric nanostructures and heterostructures. The project employed the computational phase-field method in combination of microelasticity and electrostatic theories. The research was carried out in close collaboration with a number of experimental groups who used High Resolution Transmission Electron Microscopy (HRTEM), in situ TEM with Scanning Probe Microscopy (SPM), or Piezoresponse Force Microscopy (PFM) to characterize the domain structures and dynamics of ferroelectric thin films and heterostructures and who grow high-quality ferroelectric and multiferroic thin films using advanced growth techniques such as Molecular Beam Epitaxy (MBE), Pulsed Laser Deposition (PLLD), and sputtering. The research efforts of the project help establish the phase-field method as the most powerful method for understanding and predicting domain structures in ferroelectric thin films and nanostructures. The findings of the project led to the basic understanding of stability and switching mechanisms of ferroelectric domains under different mechanical boundary conditions and under either homogeneous capacitor configurations or local fields using metallic probes as electrodes and the emergence of charged domain walls during domain switching. The project predicted the spatial length scales, temperature ranges, and electromechanical conditions for different polar states in heterostructures and guided the discovery of both transient and stable novel polarization states containing vortex lattices in oxide superlattices. The project resulted in 134 journal publications and 6 PhD theses with all the PhD graduates currently working in either academia or industry within the United States. The basic understanding on the stability of mesoscale polar states and pattern evolution achieved by the project improved our ability to control and engineer properties of ferroelectric thin films and heterostructures for potential applications in nanoscale electronic devices.

36 MATERIALS SCIENCE↗

Establishing defect-property relationships for 2D-nanomaterials (Final technical report)

Studies of new families of two-dimensional nanomaterials (2DNMs) have established that they possess unique properties that diverge from those of their bulk counterparts. This project aimed to determine how tolerant 2DNMs are to extreme photon and particle fluxes and to identify the mechanisms governing their radiation response. Early work indicated that graphene is not as representative of other 2DNMs as previously assumed; however, the origin of this difference remained unclear. To address these knowledge gaps, this project investigated the physical processes occurring at multiple length scales in transition metal dichalcogenides (TMDs) and quantified their structural stability and property evolution under far-from-equilibrium conditions. In-situ and ex-situ ion and electron irradiations were performed to directly control and monitor defect formation in TMDs. Complementary density functional theory (DFT) and molecular dynamics (MD) simulations were employed to elucidate the mechanisms of defect generation and evolution. The outcomes of this work established mechanistic understanding of irradiation-induced defect formation in 2DNMs, quantified the radiation tolerance of TMDs, and built a fundamental knowledge base for correlating defect structures with material properties. Collectively, these results provide new insights into the stability of low-dimensional materials in extreme environments and enable the predictive design of radiation-tolerant 2DNMs.

2D materials↗

Chemical and Structural Evolution of AgCu Catalysts in Electrochemical CO 2 Reduction

Silver–copper (AgCu) bimetallic catalysts hold great potential for electrochemical carbon dioxide reduction reaction (CO 2 RR), which is a promising way to realize the goal of carbon neutrality. Although a wide variety of AgCu catalysts have been developed so far, it is relatively less explored how these AgCu catalysts evolve during CO 2 RR. The absence of insights into their stability makes the dynamic catalytic sites elusive and hampers the design of AgCu catalysts in a rational manner. Here, in this study, we synthesized intermixed and phase-separated AgCu nanoparticles on carbon paper electrodes and investigated their evolution behavior in CO 2 RR. Our time-sequential electron microscopy and elemental mapping studies show that Cu possesses high mobility in AgCu under CO 2 RR conditions, which can leach out from the catalysts by migrating to the bimetallic catalyst surface, detaching from the catalysts, and agglomerating as new particles. Besides, Ag and Cu manifest a trend to phase-separate into Cu-rich and Ag-rich grains, regardless of the starting catalyst structure. The composition of the Cu-rich and Ag-rich grains diverges during the reaction and eventually approaches thermodynamic values, i.e., Ag 0.88 Cu 0.12 and Ag 0.05 Cu 0.95 . The separation between Ag and Cu has been observed in the bulk and on the surface of the catalysts, highlighting the importance of AgCu phase boundaries for CO 2 RR. In addition, an operando high-energy-resolution X-ray absorption spectroscopy study confirms the metallic state of Cu in AgCu as the catalytically active sites during CO 2 RR. Taken together, this work provides a comprehensive understanding of the chemical and structural evolution behavior of AgCu catalysts in CO 2 RR.

Chen, Peng-Cheng↗

One-Step Synthesis and Operando Electrochemical Impedance Spectroscopic Characterization of Heterostructured MoP–Mo 2 N Electrocatalysts for Stable Hydrogen Evolution Reaction

Here this study presents a novel synthesis of self-standing MoP and Mo 2 N heterostructured electrocatalysts with enhanced stability and catalytic performance. Facilitated by the controlled phase and interfacial microstructure, the seamless structures of these catalysts minimize internal resistivity and prevent local corrosion, contributing to increased stability. The chemical synthesis proceeds with etching step to activate the surface, followed by phosphor-nitriding in a chemical vapor deposition chamber to produce MoP-Mo 2 N@Mo heterostructured electrocatalysts. X-ray diffraction analyses confirm the presence of MoP, Mo 2 N, and Mo phases in the electrocatalyst. Morphology studies using scanning electron microscopy characterizes the hierarchical growth of structures, indicating successful formation of the heterostructure. X-ray photoelectron spectroscopy (XPS) analyses of the as-synthesized and post-catalytic activity samples reveal the chemical shift in terms of binding energy (BE) of Mo 3d XPS peak, especially after catalytic activity. The XPS BE shifts attributed to changes in oxidation state, electron transfer, and surface reconstruction during catalysis. Electrochemical evaluation of the catalysts demonstrates the superior performance of the MoP-Mo 2 N@Mo heterostructured catalyst in hydrogen evolution reactions (HER), with lower overpotentials and enhanced Tafel slopes. Stability tests reveal changes in double layer capacitance over time, suggesting surface reconstruction and increased active surface area during catalysis. Operando electrochemical impedance spectroscopy (EIS) further elucidates the dynamic changes in resistance and charge transfer during HER. Overall, comprehensive understanding of the synthesis, characterization, and electrochemical behavior of the developed MoP-Mo 2 N@Mo heterostructured electrocatalyst as presented in this paper highlights their potential utilization in sustainable energy applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Fully Coupled Aeroelastic Stability Analysis of Adaptive Shape Memory Alloy Structural Technologies for Airframe Noise Reduction

This final report documents work performed by ATA Engineering, Inc., (ATA) to develop computational models and analyze the coupled fluid-structure response of two types of noise treatments applied to the leading-edge-slat component of a high-lift system typical of modern transport aircraft. The first treatment is a slat-gap filler (SGF), which closes the gap between the suction surfaces of a deployed slat and an aircraft main wing, and the second treatment is a slat-cove filler (SCF), which replaces the recirculating flow on the slat cove with a surface that promotes flow attachment. The representative airframe chosen for this work was NASA’s High-Lift Common Research Model (CRM-HL) in a baseline high-lift configuration. Superelastic shape memory alloys (SMAs) have been identified as enabling materials for these structural treatments. Since the technology elements rely upon having a highly reconfigurable structure, designs were assessed for their static aeroelastic deflection as well as their dynamic aeroelastic stability using coupled computational fluid dynamics (CFD) and nonlinear computational structural dynamics (NL-CSD) tools. Specifically, fluid-structure interaction (FSI) problems were solved computationally using the CFD solver Loci/CHEM and the NL-CSD solver Abaqus. As a part of the overall project, a similar capability was implemented using the CFD solver FUN3D coupled to Abaqus, although that work is documented in a separate report and that FSI framework was not used to analyze any of NASA’s SGF and SCF configurations. The technical approach consisted of solving for the flow field around the entire vehicle using a global CFD model, followed by extraction of relevant local subdomain data for CFD and NL-CSD co-simulations. The SGF design was analyzed using both 2D and 3D co-simulations to predict quasi-static aeroelastic deformations and to assess dynamic aeroelastic stability, whereas the SCF was analyzed in 2D only. SGF static aeroelastic response predictions focused on characterizing the deformed shape, with maximum displacements predicted to be on the order of magnitude of the technology element panel thickness. SGF dynamic aeroelastic response predictions used Partial Floquet analysis of the temporal evolution of selected nodal displacements to quantify the sign and magnitude of aeroelastic damping. Results suggest that the CRM-HL operating conditions would result in a dynamically stable response. The simulated dynamic pressure was also increased up to a factor of about four, and resulting responses suggest that predicted dynamic stability would be achieved with some margin.

Fluid Structure Interaction↗

Thermal energy evolution and mechanical deformation of monocrystalline yttria-stabilized zirconia nanoparticles in aerosol deposition processes

Aerosol deposition (AD) is a coating process wherein aerosol particles are impacted on a target substrate. There are fundamental differences between the AD process (cold impact), where particle translational kinetic energy is high and thermal energy is low, and thermal spray deposition (thermal impact), where translational energy is lower but thermal energy is high. To better compare cold and thermal impact effects on particles, we carried out molecular dynamics simulations using yttria-stabilized zirconia (YSZ) nanoparticles on YSZ substrates as a model system. We performed cold impact simulations at 300 K with variable impact velocity in the 500 ms –1 –1500 ms –1 range to understand how increasing translational kinetic energy affects thermal energy and mechanical evolution. We then performed thermal impact simulations at variable temperature and impact velocity, but where the total kinetic energy of the nanoparticle was equivalent to that of a 300 K, 1000 impact. In cold impact, the temperature increases in YSZ nanoparticles at a rate of 10 13 – 10 14 K s –1 , and large temperature gradients result. Conversely, in thermal impact, nanoparticle temperatures remain uniform. Furthermore, the temperature gradients during cold impact coincide with plastic deformation in nanoparticles, while with larger thermal energies, plastic deformation is reduced.

42 ENGINEERING↗

Dynamical Instabilities in Systems of Multiple Short-period Planets Are Likely Driven by Secular Chaos: A Case Study of Kepler-102

We investigated the dynamical stability of high-multiplicity Kepler and K2 planetary systems. Our numerical simulations find instabilities in ∼20% of the cases on a wide range of timescales (up to 5 × 10{sup 9} orbits) and over an unexpectedly wide range of initial dynamical spacings. To identify the triggers of long-term instability in multiplanet systems, we investigated in detail the five-planet Kepler-102 system. Despite having several near-resonant period ratios, we find that mean-motion resonances are unlikely to directly cause instability for plausible planet masses in this system. Instead, we find strong evidence that slow inward transfer of angular momentum deficit (AMD) via secular chaos excites the eccentricity of the innermost planet, Kepler-102 b, eventually leading to planet–planet collisions in ∼80% of Kepler-102 simulations. Kepler-102 b likely needs a mass ≳0.1 M {sub ⊕}, hence a bulk density exceeding about half Earth’s, in order to avoid dynamical instability. To investigate the role of secular chaos in our wider set of simulations, we characterize each planetary system’s AMD evolution with a “spectral fraction” calculated from the power spectrum of short integrations (∼5 × 10{sup 6} orbits). We find that small spectral fractions (≲0.01) are strongly associated with dynamical stability on long timescales (5 × 10{sup 9} orbits) and that the median time to instability decreases with increasing spectral fraction. Our results support the hypothesis that secular chaos is the driver of instabilities in many nonresonant multiplanet systems and also demonstrate that the spectral analysis method is an efficient numerical tool to diagnose long-term (in)stability of multiplanet systems from short simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

Single Iridium Atom Doped Ni 2 P Catalyst for Optimal Oxygen Evolution

Single-atom catalysts (SACs) with 100% active sites have excellent prospects for application in the oxygen evolution reaction (OER). However, further enhancement of the catalytic activity for OER is quite challenging, particularly for the development of stable SACs with overpotentials <180 mV. Here, we report an iridium single atom on Ni 2 P catalyst (Ir SA -Ni 2 P) with a record low overpotential of 149 mV at a current density of 10 mA·cm –2 in 1.0 M KOH. The Ir SA -Ni 2 P catalyst delivers a current density up to ∼28-fold higher than that of the widely used IrO 2 at 1.53 V vs RHE. Both the experimental results and computational simulations indicate that Ir single atoms preferentially occupy Ni sites on the top surface. The reconstructed Ir–O–P/Ni–O–P bonding environment plays a vital role for optimal adsorption and desorption of the OER intermediate species, which leads to marked enhancement of the OER activity. Additionally, the dynamic “top-down” evolution of the specific structure of the Ni@Ir particles is responsible for the robust single-atom structure and, thus, the stability property. In conclusion, this Ir SA -Ni 2 P catalyst offers novel prospects for simplifying decoration strategies and further enhancing OER performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Entanglement and correlations in fast collective neutrino flavor oscillations

Collective neutrino oscillations play a crucial role in transporting lepton flavor in astrophysical settings like supernovae and neutron star binary merger remnants, which are characterized by large neutrino densities. In these settings, simulations in the mean-field approximation show that neutrino-neutrino interactions can overtake vacuum oscillations and give rise to fast collective flavor evolution on time-scales t ∝ μ –1 , with μ proportional to the local neutrino density. In this work, we study the full out-of-equilibrium flavor dynamics in simple multi-angle geometries displaying fast oscillations in the mean field linear stability analysis. Focusing on simple initial conditions, we analyze the production of pair correlations and entanglement in the complete many-body-dynamics as a function of the number N of neutrinos in the system, for up to thousands of neutrinos. Similarly to simpler geometries with only two neutrino beams, we identify three regimes: stable configurations with vanishing flavor oscillations, marginally unstable configurations with evolution occurring on long time scales τ ≈ µ –1 $\sqrt{N}$, and unstable configurations showing flavor evolution on short time scales τ ≈ μ –1 log(N). Here, we present evidence that these fast collective modes are generated by the same dynamical phase transition which leads to the slow bipolar oscillations, establishing a connection between these two phenomena and explaining the difference in their time scales. We conclude by discussing a semi-classical approximation which reproduces the entanglement entropy at short to medium time scales and can be potentially useful in situations with more complicated geometries where classical simulation methods starts to become inefficient.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗