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At least 397 records · Page 22

All sources NASA NTRS DOE OSTI

DOE OSTI2020

Validation of gyrokinetic simulations in NSTX and projections for high-k turbulence measurements in NSTX-U

An extensive validation effort performed for a modest-beta NSTX NBI-heated H-mode discharge predicts that electron thermal transport can be entirely explained by electron-scale turbulence fluctuations driven by the electron temperature gradient mode (ETG), both in conditions of strong and weak ETG turbulence drive. Thermal power-balance estimates computed by TRANSP as well as the shape of the high-k density fluctuation wavenumber spectrum and the fluctuation level ratio between strongly driven and weakly driven ETG-turbulence conditions can be matched by nonlinear gyrokinetic simulations and a synthetic diagnostic for high-k scattering. Linear gyrokinetic simulations suggest that the ion-scale instability in the weak ETG condition is close to the critical threshold for the kinetic ballooning mode instability, and nonlinear ion-scale gyrokinetic simulations show that turbulence might be in a state reminiscent of a Dimits' shift regime, opening speculation on the role that ion-scale turbulence might play for the weak ETG condition. A simulation that matched all experimental constraints is chosen to project high-k turbulence spectra in NSTX-U, revealing that the new high-k system [R. Barchfeld et al., Rev. Sci. Instrum. 89, 10C114 (2018)] should be sensitive to density fluctuations from radially elongated streamer structures. In this study, two schemes are designed to characterize the radial and poloidal wavenumber dependence of the density fluctuation wavenumber power spectrum around the streamer peak, suggesting future high-k fluctuation measurements could be sensitive to an asymmetry in the k r spectrum introduced due to the presence of strong background flow shear.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Reconstruction of the Density Power Spectrum from Quasar Spectra using Machine Learning

We describe a novel end-to-end approach using Machine Learning to reconstruct the power spectrum of cosmological density perturbations at high redshift from observed quasar spectra. State-of-the-art cosmological simulations of structure formation are used to generate a large synthetic dataset of line-of-sight absorption spectra paired with 1-dimensional fluid quantities along the same line-of-sight, such as the total density of matter and the density of neutral atomic hydrogen. With this dataset, we build a series of data-driven models to predict the power spectrum of total matter density. We are able to produce models which yield reconstruction to accuracy of about 1% for wavelengths $k \leq 2 h Mpc^{-1}$, while the error increases at larger $k$. We show the size of data sample required to reach a particular error rate, giving a sense of how much data is necessary to reach a desired accuracy. This work provides a foundation for developing methods to analyse very large upcoming datasets with the next-generation observational facilities.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

Quantum-Accurate Multiscale Modeling of Shock Hugoniots, Ramp Compression Paths, Structural and Magnetic Phase Transitions, and Transport Properties in Highly Compressed Metals

Fully characterizing high energy density (HED) phenomena using pulsed power facilities (Z machine) and coherent light sources is possible only with complementary numerical modeling for design, diagnostic development, and data interpretation. The exercise of creating numerical tests, that match experimental conditions, builds critical insight that is crucial for the development of a strong fundamental understanding of the physics behind HED phenomena and for the design of next generation pulsed power facilities. The persistence of electron correlation in HED materials arising from Coulomb interactions and the Pauli exclusion principle is one of the greatest challenges for accurate numerical modeling and has hitherto impeded our ability to model HED phenomena across multiple length and time scales at sufficient accuracy. An exemplar is a ferromagnetic material like iron, while familiar and widely used, we lack a simulation capability to characterize the interplay of structure and magnetic effects that govern material strength, kinetics of phase transitions and other transport properties. Herein we construct and demonstrate the Molecular-Spin Dynamics (MSD) simulation capability for iron from ambient to earth core conditions, all software advances are open source and presently available for broad usage. These methods are multi-scale in nature, direct comparisons between high fidelity density functional theory (DFT) and linear-scaling MSD simulations is done throughout this work, with advancements made to MSD allowing for electronic structure changes being reflected in classical dynamics. Main takeaways for the project include insight into the role of magnetic spins on mechanical properties and thermal conductivity, development of accurate interatomic potentials paired with spin Hamiltonians, and characterization of the high pressure melt boundary that is of critical importance to planetary modeling efforts.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Engineered current-density profile diode laser

The present technology can be used to control the current injection profile in the longitudinal direction of a high-power diode laser in order to optimize current densities as a function of position in the cavity to promote higher reliable output power and increase the electrical to optical conversion efficiency of the device beyond the level which can be achieved without application of this technique. This approach can be utilized, e.g., in the fabrication of semiconductor laser chips to improve the output power and wall plug efficiency for applications requiring improved performance operation.

Leisher, Paul O.↗

DOE OSTI2024

Engineered current-density profile diode laser

Leisher, Paul O.↗

DOE OSTI2021

Creation of an axially uniform plasma channel in a laser-assisted capillary discharge

Dissipative capillary discharges form plasma channels which allow for high power laser guiding, enabling efficient electron acceleration in a laser wakefield accelerator. However, at the low plasma densities required to produce high-energy electrons, in order to avoid capillary wall damage, high power lasers need a tighter transverse confinement that cannot be achieved by the capillary discharge powered by Ohmic heating alone. The introduction of an additional laser for heating of the plasma leads to deeper and narrower plasma channels. Here we investigate the formation of laser-heated axially uniform plasma channels. Here, we show that a high degree of longitudinal uniformity can be achieved despite significant evolution of the heater laser during its propagation through the channel.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

AGR-5/6/7 Final Release-to-Birth Ratio Data Analysis

AGR-5/6/7 is the last of a series of Advanced Gas Reactor (AGR) experiments conducted in the Advanced Test Reactor (ATR) at Idaho National Laboratory (INL) in support of development and qualification of tristructural isotropic (TRISO) low-enriched fuel for use in the high-temperature gas cooled reactor (HTGR). AGR configuration and irradiation conditions are based on prismatic HTGR technology that is distinguished primarily through the use of helium coolant, a low-power-density ceramic core capable of withstanding very high temperatures, and TRISO-coated particle fuel. The AGR tests provide valuable irradiation-performance data to support fuel process development, qualify fuel for normal operation and accident conditions, and support development and validation of fuel performance and fission-product (FP) transport models and codes. Each AGR test consists of multiple independently controlled and monitored capsules containing fuel compacts placed in a graphite cylinder shrouded by a steel shell. Release-to-birth ratios (R/B) for fission-gas isotopes released from each capsule are calculated from release rates, measured by germanium detectors in the Fission Product Monitoring System (FPMS) installed downstream from each capsule, and birth rates calculated using numerical models of FG generation. The R/Bs are a critical measure of the ability of the fuel kernel, the particle coating layers, and the compact matrix to retain fission-gas atoms, preventing their release into the sweep-gas flow, and the impact of initially defective particles and/or particle-coating failures that occur during irradiation. For fission-gas isotopes, particle failure is defined as failure of all coating layers, allowing gaseous fission atoms to escape from a particle. During the first five cycles (162B ? 165A), R/Bs were stable in the 10-8?10-6 range, and no in-pile particle failures were observed, based on the gross gamma counts. The maximum R/B value of around 2 ? 10-6 for Kr-85m resulted from the presence of as-fabricated exposed kernels (based on the high exposed kernel fraction), the dispersed uranium, and high fuel particle temperatures in Capsule 1. Comparison of capsule-measured R/Bs from these early cycles to predictions using the previously developed AGR R/B model demonstrated FG release from the AGR-5/6/7 TRISO fuel was comparable to that of previous experiments. In addition, the Kr-85m R/B per-exposed-kernel values are comparable to R/B values obtained in AGR-3/4 irradiation experiment and four irradiation experiments performed during 1980s: (1) HRB-17/18, (2) COMEDIE-BD1, (3) HFR B1, and (4) HRB-21. In contrast, all measured R/B values are lower than predictions by the commonly used Richards and German models, which are intentionally conservative. A large number of in-pile particle failures occurred in Capsule 1 by the end of Cycle 166A. During the final four cycles (166A ? 168A), apparent damage to the Capsule 1 gas line appeared to cause FG leakage from that capsule into the other four capsules, resulting in an increase in fission gas (FG) detected in the effluent for all capsules. Isolation of the Capsule 1 gas line during the last three cycles also prevented measurement of its FG release. Thus, R/Bs in all capsules after Cycle 166A are highly uncertain because of undefined amount of leakage from Capsule 1, especially for long-lived isotopes. A few hundred in-pile particle failures were estimated for Capsule 1 before the end of Cycle 166A, but the total number of failures is unknown due to the lack of FG release data in the later cycles. Based primarily on evidence from the gross gamma counts during Cycle 168A, approximately 15 particles failed in Capsule 3 and four particles failed in Capsule 2. In-pile failures in Capsule 3 were anticipated because this capsule was designed to operate beyond the HTGR normal operating temperature range. In contrast, no in-pile failures were identified in the top two capsules (4 and 5) based on the absence of the typical spikes in gross gamma counts and low failure estimates using the AGR model, developed in INL/EXT-14-32970, for R/B of the short-lived isotopes (Kr-89 and Xe-137) with minimal leakage from Capsule 1.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Ultrafast time-resolved 2D imaging of laser-driven fast electron transport in solid density matter using an x-ray free electron laser

High-power, short-pulse laser-driven fast electrons can rapidly heat and ionize a high-density target before it hydrodynamically expands. The transport of such electrons within a solid target has been studied using two-dimensional (2D) imaging of electron-induced Kα radiation. However, it is currently limited to no or picosecond scale temporal resolutions. Here, we demonstrate femtosecond time-resolved 2D imaging of fast electron transport in a solid copper foil using the SACLA x-ray free electron laser (XFEL). An unfocused collimated x-ray beam produced transmission images with sub-micron and ~10 fs resolutions. The XFEL beam, tuned to its photon energy slightly above the Cu K-edge, enabled 2D imaging of transmission changes induced by electron isochoric heating. Time-resolved measurements obtained by varying the time delay between the x-ray probe and the optical laser show that the signature of the electron-heated region expands at ~25% of the speed of light in a picosecond duration. Time-integrated Cu Kα images support the electron energy and propagation distance observed with the transmission imaging. The x-ray near-edge transmission imaging with a tunable XFEL beam could be broadly applicable for imaging isochorically heated targets by laser-driven relativistic electrons, energetic protons, or an intense x-ray beam.

47 OTHER INSTRUMENTATION↗

DOE OSTI2022

Wet chemical synthesis and properties of argyrodite sulfide solid electrolytes for solid state lithium batteries

The commercialization of the lithium-ion battery (LIB) in 1991 was responsible for the explosion in portable electronic technologies that has been seen over the past 30 years. With the advent of electric vehicles and other high-powered technologies, there is tremendous demand for LIBs with higher energy density and high safety. To achieve this, new electrode materials must be explored. The obvious choice of anode material would be pure metal lithium, which has a theoretical specific capacity of 3860 mAh g-1 . Unfortunately, metal lithium anodes have not been widely commercialized due to their tendency to react violently with the flammable liquid electrolytes used in today’s batteries. Battery safety can best be achieved by adopting solid electrolytes in place of liquid electrolytes. Solid electrolytes are nonvolatile and nonflammable, safely allowing for the combination of high-capacity cathode materials with a Li metal anode. Argyrodite sulfide solid electrolytes such as halogen-doped Li6PS5X (X = Cl, Br, I) are noted for their high ionic conductivity. But before sulfides can be commercially adopted, they possess several disadvantages which must be addressed, including time- and energy-consuming synthesis processes, poor electrochemical stability, and intrinsically poor air stability. This dissertation seeks to address each of these challenges through materials design an synthesis strategies. In this work, we pioneer a solvent-based approach for the synthesis of argyrodite solid electrolytes Li7PS6 and Li6PS5Xinstead of a stringent solid-state synthesis. Nontoxic ethanol is employed as the solvent, enabling a rapid synthetic approach to produce argyrodite solid electrolytes with high phase purity and compositional flexibility. Compared with Li7PS6, halogen doping (i.e. X = F, Cl, Br, I) not only increases the ionic conductivity, but also enhances the electrochemical stability at the interface towards Li metal. Specifically, F-doped argyrodites produce a robust SEI layer containing LiF, contributing to enhanced interfacial stability. Finally, to address the air instability challenge, argyrodite-incorporated composite solid electrolytes (CSEs) are designed and prepared to produce stable and flexible membranes that are demonstrated in solid-state Li metal batteries. These advances push argyrodite sulfide solid electrolyte research further and pave the way for the proliferation of next generation lithium metal batteries.

25 ENERGY STORAGE↗

DOE OSTI2022

Electrochemical energy storage systems

Electrochemical energy storage systems are crucial components for the realization of a carbon-neutral/carbon-negative energy sector globally. Industrial applications require energy storage technologies that cater to a wide range of specifications in terms of form factor, gravimetric and volumetric energy density, charging rates, and safety, among others. The key electrochemical technologies for industrial applications are supercapacitors and batteries. Supercapacitors are high-power devices while batteries typically cater to high energy density requirements. This chapter provides an in-depth understanding of these technologies in terms of materials, processing, working principle, and architecture. Subsequently, state-of-the-art of these technologies is discussed with an emphasis on materials, manufacturing, and end-use systems. Finally, emerging technologies in the electrochemical energy storage field are highlighted.

Dixit, Marm↗

DOE OSTI2022

WBG-Enabled Current-Source Inverters for Integrated PM Motor Drives

This project takes advantage of the special capabilities of wide-bandgap (WBG) power semiconductor devices to develop innovative power electronics in the form of new current-source inverters (CSIs) that offer promising advantages over the dominant voltage-source inverter (VSI) topology. These CSIs, in turn, are extremely well-suited for integration into the housings of permanent magnet synchronous machines (PMSMs) to form integrated motor drives (IMDs). These new IMDs offer great promise for achieving major energy savings in a wide variety of applications that benefit from adjustable-speed control, including air conditioners, laundry appliances, industrial pumps/compressors, electric vehicles, and aerospace drives. WBG devices play a critical enabling role in these new IMDs because of their transformative features including much higher switching frequencies, lower losses, and compatibility with high operating temperatures. When incorporated into new CSI-based IMDs with PM machines, these WBG switches open the door to achieving major increases in power density, drive system efficiency, and fault tolerance, as well as substantial reductions in electromagnetic interference (EMI), manufacturing cost, and temperature-induced failures. The higher operating temperature capability of WBG devices compared to conventional silicon power devices is very appealing in IMD applications because the power electronics is mounted in close proximity to the motors which typically operate at temperatures well above the maximum limits of today’s silicon-based power electronics. This project has succeeded in designing, building, and testing multiple prototype versions of this CSI-IMD that have overcome many technical challenges in order to demonstrate the impressive performance improvements that can be achieved by the WBG-enabled CSI-IMD. The preliminary demo and bench-top versions of the current-source inverter developed during the first two years of the project were critical to laying the technical foundations for the 3 kW prototype CSI-IMD unit that was successfully built and tested during the third year. This prototype CSI-IMD unit was designed to fit within the housing envelope of the original permanent magnet (PM) synchronous machine in order to meet the demanding power density requirements that were set at the beginning of the project. All of the remaining performance objectives set for the prototype CSI-IMD unit including efficiency and electromagnetic interference (EMI) were also met. The last 18 months of the project were devoted to developing further enhancements of the WBG-enabled CSI-IMD technology that better prepare it for commercial production. More specifically, an upgraded version of the prototype CSI-IMD unit was developed that moved the power electronics into the same machine housing chamber as the motor, substantially raising the thermal demands on the power electronics. Tests with five different combinations of motor enclosure types and air cooling configurations were evaluated. Importantly, this work confirmed that the power electronics can deliver its full rated power and still operate well within its maximum temperature limits even for worst-case conditions when the housing is “totally-enclosed” without any openings for air to enter or exit the enclosure, and no blower/fan is provided to blow air over the outside surface of the enclosure. Reaching the full performance and energy-savings potential of this disruptive CSI-IMD motor drive technology is highly consistent with ARPA-E’s stated mission to “enhance the economic and energy security of the United States” while also supporting its commitment to “ensure that the U.S. maintains a technological lead in developing and deploying advanced energy technologies”. Follow-on projects are under way to explore the scalability of WBG-enabled CSI-IMD technology to 100 kW (peak) electric vehicle traction drives and fault-tolerant modular motor drives for future electrified aircraft propulsion applications.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2024

Stellarators with enhanced tritium confinement and edge radiation control

A stellarator design is described with the purpose of achieving three goals: (1) enhance the confinement time of tritium. (2) Have a sufficient density of high-Z impurities to radiate the thermal power escaping from the core while having an extremely low impurity density in the core. (3) Maintain a large fraction of the plasma in a burning plasma state with an optimal tritium fraction. Some features of this design could be used in tokamaks. Although having three confinement zones is natural for stellarators, it is not for tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Tailoring activity of iron phthalocyanine by edge-nitrogen sites induced electronic delocalization

Fe-N-C catalysts have been recognized as the most satisfactory candidates alternatively to Pt-based catalysts for oxygen reduction reaction (ORR). However, fine-tailoring of their intrinsic ORR catalytic activity still remains a great challenge due to the inferior accessibility and intrinsic activity of FeN x moieties. Herein, one order of magnitude activity enhancement of pristine Fe-N-C through cooperating with nitrogen-doped carbon micro-flower is achieved. The axial coordination effect between Fe active center and nitrogen atoms in support can break the electronic distribution symmetry of FeN x moieties and induce the electron delocalization on Fe active center and the electron localization on N, respectively, which favor the adsorption behavior of *OH intermediate. As a result, the catalyst exhibits a remarkable half-wave potential of 0.9 V and a high kinetic current density of 74.04 mA cm -2 at 0.85 V. In addition, when utilized as a cathode catalyst of liquid Zn-air batteries (ZABs), it possesses excellent electrochemical performance, for example, a high open circuit voltage (OCV) and peak power density of 1.59 V and 170.09 mW cm -2 , respectively. In conclusion, this work provides a new understanding into the activity enhancement mechanism of Fe-N-C catalysts, and inspires electronic delocalization of active sites for adjusting catalytic activity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Highly Durable Fluorinated High Oxygen Permeability Ionomers for Proton Exchange Membrane Fuel Cells

For proton exchange membrane fuel cells to be cost-competitive in light- and heavy-duty vehicle applications, their Pt content in the catalyst layers needs to be lowered. However, lowering the Pt content results in voltage losses due to high local oxygen transport resistances at the ionomer–Pt interface. It is therefore crucial to use ionomers that have higher oxygen permeability than Nafion. In this paper, novel high oxygen permeability ionomers (HOPIs) are presented, with up to five times higher oxygen permeability than Nafion, synthesized by copolymerization of perfluoro-2,2-dimethyl-1,3-dioxole (PDD) with perfluoro(4-methyl-3,6-dioxaoct-7-ene) sulfonyl fluoride (PFSVE). PDD is the source of higher permeability due to its open ring structure, while PFSVE provides ionic conductivity. Optimization of PDD content and equivalent weight enables increased fuel cell performance, mainly at high current densities, where HOPIs can achieve power densities >1.25 W cm -2 and exceed the 0.8 A cm -2 U.S. Department of Energy durability target by losing only 4.5 mV, which is over six times less than 30 mV. Finally, the interactions between HOPI and SO 3 - groups with a PtCo/C catalyst are also elucidated here at a fundamental level.

25 ENERGY STORAGE↗

DOE OSTI2024

Data-driven search for promising intercalating ions and layered materials for metal-ion batteries

The rise in demand for lithium-ion batteries has led to a large-scale search for electrode materials and intercalating ion species to meet the demands of next-generation energy technologies. Recent efforts largely focus on searching for cathodes that can accommodate large amounts of intercalating ions, but similar work on anodes is relatively limited. This study utilizes machine learning methods to find alternative two-dimensional (2D) materials and intercalating ions beyond Li for metal-ion batteries with high-power efficiencies. The approach first uses density functional theory (DFT) calculations to estimate the theoretical capacities and voltages of various metal ions on 2D materials. The DFT-generated data also provide insights into the local structural accommodation upon ion intercalation on various 2D materials. Significant changes to the lattice can result in irreversible changes to the bonding environments in the anode material, resulting in poor cycling stability. Next, this study develops a binding energy and structural accommodation-based classification model to screen anode materials for next-generation batteries. The classification model selects intercalating ions and 2D material pairs suitable for batteries based on the calculated voltage and volumetric changes in the 2D material upon intercalation. Finally, this study builds a regression model to accurately predict the binding energies of the various intercalating ions on 2D materials. The approach highlights the importance of different elemental and structural features for classification and regression tasks. In conclusion, the insights gained from this study on the role of involved features, such as electronegativities of the constituent ions and the presence of unfilled electronic levels, will help to streamline further studies towards the search for future layered battery materials.

36 MATERIALS SCIENCE↗

DOE OSTI2025

The total neutron cross section of liquid and solid ammonia

Ammonia is a material of interest for future neutron moderators at high-power sources due to its high hydrogen density, low melting point, and resistance to polymerization in an intense radiation field. Its performance in such applications cannot currently be calculated due to the absence of suitable computer models for the interaction of neutrons with ammonia under relevant conditions. In an effort to develop suitable scattering kernels for computer simulations of moderator performance, we have conducted a series of Density Functional Theory and Molecular Dynamics calculations of the molecular-level thermal properties of ammonia at various temperatures within both the solid and liquid phases. In this paper, we compare computer calculations for the energy-dependent total neutron cross section of ammonia, based on these models, to experimental measurements of those cross sections at temperatures of 221 K, 180 K, and 35 K. The experimental data were collected over an energy range from 0.1 meV to 10 eV using time-of-flight techniques at the Low Energy Neutron Source (LENS) facility at Indiana University. This comparison provides a first validation in the development of thermal scattering libraries for Monte Carlo source design simulations based on liquid and solid ammonia. In conclusion, we also provide some insights into where additional development of tools for creating such models may be needed.

Ammonia↗

DOE OSTI2026

Translating Fundamental Insights into Ag-Based Bimetallic Electrocatalysts to Anion-Exchange Membrane Fuel Cells

To address challenges of high costs and scalability for fuel cells, it is essential to develop af-fordable and earth-abundant materials that are Pt-group-metal (PGM)-free. Recent advance-ments in PGM-free electrocatalysis for the oxygen reduction reaction (ORR) in alkaline media show that high catalyst loadings are needed to achieve high reaction rates; however, there are associated mass transport limitations. To address this issue, we develop low-loading ionomer-less Ag-bimetallic thin films by alloying with 3d block elements or Sn. We bridge knowledge from fundamental rotating disk electrode (RDE) studies to gas-diffusion cathodes in high-temperature anion-exchange membrane fuel cells (HT-AEMFCs), resulting in high-activity ORR catalysis and peak power densities up to 1.2 W cm-² geo for the Ag-Sn and Ag-Co alloys. Here, experimental post-characterization and theoretical calculations reveal small Co or Sn oxide nano-islands on Ag as likely active sites enhancing ORR activity, ultimately offering these low-loading PGM-free ORR materials as a viable path towards sustainable energy conversion.

Catalysts↗

DOE OSTI2020

Phase separation and state oscillation of active inertial particles

Active matter systems are of great interest for their novel out-of-equilibrium collective behavior. Active Brownian particles (ABPs) are known to exhibit clustering and motility-induced phase separation, and there have been many studies revealing this rich behavior in the overdamped limit of Brownian motion, where inertial effects are insignificant. In this work, we simulate an Active Inertial Particle (AIP) model where we focus on the underdamped, rather than overdamped limit, to study the interplay between particle inertia and collective behavior, such as phase separation. We show that inertia reduces particle motility due to collisions and a longer time delay for particles to regain speed, thereby suppressing phase separation relative to that observed in the overdamped limit. Additionally, we observe interesting oscillatory behavior between a phase separated steady-state and a homogeneous fluid state that results from inertia-induced collective motion within active clusters due to momentum transfer. Such oscillatory behavior has been reported for ABP systems with particle shape anisotropy, where collective motion is mediated by particle shape anisotropy. Furthermore, we confirm that there is no single characteristic frequency for the oscillatory behavior. The power spectral density is a power law in the high frequency domain, with an exponent close to -2.5.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗