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At least 1,099 records · Page 61
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Quantum Computation of Dynamical Quantum Phase Transitions and Entanglement Tomography in a Lattice Gauge Theory

Strongly coupled gauge theories far from equilibrium may exhibit unique features that could illuminate the physics of the early universe and of hadron and ion colliders. Studying real-time phenomena has proven challenging with classical-simulation methods but is a natural application of quantum simulation. To demonstrate this prospect, we quantum compute nonequal-time correlation functions and perform entanglement tomography of nonequilibrium states of a simple lattice gauge theory, the Schwinger model, using a trapped-ion quantum computer by IonQ Inc. As an ideal target for near-term devices, a recently predicted dynamical quantum phase transition in this model is studied by preparing, quenching, and tracking the subsequent nonequilibrium dynamics in three ways: (i) overlap echos signaling dynamical transitions, (ii) nonequal-time correlation functions with an underlying topological nature, and (iii) the entanglement structure of nonequilibrium states, including entanglement Hamiltonians. These results constitute the first observation of a dynamical quantum phase transition in a lattice gauge theory on a quantum computer and are a first step toward investigating topological phenomena in nuclear and high-energy physics using quantum technologies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Atomistic Simulations of the Elastic Compression of Platinum Nanoparticles

Abstract The elastic behavior of nanoparticles depends strongly on particle shape, size, and crystallographic orientation. Many prior investigations have characterized the elastic modulus of nanoscale particles using experiments or simulations; however their reported values vary widely depending on the methods for measurement and calculation. To understand these discrepancies, we used classical molecular dynamics simulation to model the compression of platinum nanoparticles with two different polyhedral shapes and a range of sizes from 4 to 20 nm, loaded in two different crystal orientations. Multiple standard methods were used to calculate the elastic modulus from stress-vs-strain data for each nanoparticle. The magnitudes and particle-size dependence of the resulting moduli varied with calculation method and, even for larger nanoparticles where bulk-like behavior may be expected, the effective elastic modulus depended strongly on shape and orientation. Analysis of per-atom stress distributions indicated that the shape- and orientation-dependence arise due to stress triaxiality and inhomogeneity across the particle. When the effective elastic modulus was recalculated using a representative volume element in the center of a large nanoparticle, the elastic modulus had the expected value for each orientation and was shape independent. It is only for single-digit nanoparticles that meaningful differences emerged, where even the very center of the particle had a lower modulus due to the effect of the surface. These findings provide better understanding of the elastic properties of nanoparticles and disentangle geometric contributions (such as stress triaxiality and spatial inhomogeneity) from true changes in elastic properties of the nanoscale material.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Subsurface electrical conductivity across the BEO site inferred using a capacitively coupled resistivity survey in May 2013, Utqiagvik, Alaska

Multiple transects across and around the Barrow Environmental Observatory (BEO) site were surveyed using a capacitively coupled resistivity tool to infer the subsurface electrical conductivity in the top ~6 m in order to improve the understanding of heterogeneity in ice and salinity content. This work was led by the environmental geophysics team from Lawrence Berkeley National Laboratory as part of the Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic). The acquisition was performed in May 2013 using a capacitively coupled resistivity tool (OhmMapper from Geometrics, Inc) mounted behind a sled hooked to a snowmobile. Twenty-eight ~750 m long transects cover the NGEE intensive site (polygon areas A, B, C, D) in the BEO with a measurement (apparent resistivity for 5 different geometries) taken every 1.5 to 2 m. The survey also includes other transects that have been acquired along Electrical Resistivity Tomography (ERT) transects previously acquired at the site (Site 0, AB, and BD), and several long transects (up to 7 km each) around the BEO site crossing several Drained Thawed Lake Basins (DTLB). The various transects acquired during this survey cover a distance of about 100 km. All the datasets are provided with the acquisition geometry and the associated subsurface apparent electrical conductivity. In addition, the 28 transects at the BEO intensive site were inverted to infer the subsurface electrical conductivity. Unprocessed and processed data products are included in this package. This metadata document contains a description of the survey and processing steps and the inferred products.The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic) was a 15-year research effort (2012-2027) to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy’s Office of Biological and Environmental Research. The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska, and 2) multiple areas in the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska. Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy’s Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Quantum Gravity in the Lab. I. Teleportation by Size and Traversable Wormholes

With the long-term goal of studying models of quantum gravity in the lab, we propose holographic teleportation protocols that can be readily executed in table-top experiments. These protocols exhibit similar behavior to that seen in the recent traversable-wormhole constructions of Gao et al. [J. High Energy Phys., 2017, 151 (2017)] and Maldacena et al. [Fortschr. Phys., 65, 1700034 (2017)]: information that is scrambled into one half of an entangled system will, following a weak coupling between the two halves, unscramble into the other half. We introduce the concept of teleportation by size to capture how the physics of operator-size growth naturally leads to information transmission. The transmission of a signal through a semiclassical holographic wormhole corresponds to a rather special property of the operator-size distribution that we call size winding. For more general systems (which may not have a clean emergent geometry), we argue that imperfect size winding is a generalization of the traversablewormhole phenomenon. In addition, a form of signaling continues to function at high temperature and at large times for generic chaotic systems, even though it does not correspond to a signal going through a geometrical wormhole but, rather, to an interference effect involving macroscopically different emergent geometries. Finally, we outline implementations that are feasible with current technology in two experimental platforms: Rydberg-atom arrays and trapped ions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Quasioptical modeling of wave beams with and without mode conversion. IV. Numerical simulations of waves in dissipative media

We report the first quasi-optical simulations of wave beams in a hot plasma using the quasi-optical code PARADE (PAraxial RAy DEscription) [K. Yanagihara, I. Y. Dodin, and S. Kubo, Phys. Plasmas 26, 072112 (2019)]. This code is unique in that it accounts for inhomogeneity of the dissipation-rate across the beam and mode conversion simultaneously. We show that the dissipation-rate inhomogeneity shifts beams relative to their trajectories in cold plasma and that the two electromagnetic modes are coupled via this process, an effect that was ignored in the past. Additionally, we propose a simplified approach to account for the dissipation-rate inhomogeneity. This approach is computationally inexpensive and simplifies the analysis of actual experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Computational study of Li 3 BO 3 and Li 3 BN 2 II: Stability analysis of pure phases and of model interfaces with Li anodes

Both Li 3 BO 3 and Li 3 BN 2 materials have promising properties for use in all solid-state batteries and other technologies dependent on electrolytes with significant ionic conductivity. As the second of a two-part study, the structural properties of Li 3 BO 3 and three reported phases of Li 3 BN 2 are investigated using first-principles modeling techniques. For alpha- Li 3 BN 2 , the tetragonal P4 2 / mnm structure reported in the literature is found to be unstable as evidenced by imaginary phonon modes near the M point of its Brillouin zone. Our simulations within the harmonic approximation suggest that the real α phase has the orthorhombic space group symmetry Pmmn formed with twice as many formula units and tiny adjustments of the equivalent lattice parameters and fractional coordinates. Extending the analysis of the Pmmn α- Li 3 BN 2 structure to the quasiharmonic approximation improves the agreement between the room-temperature x-ray pattern reported in the literature and the corresponding simulation results. In anticipation of the use of the monoclinic phases of Li 3 BO 3 and Li 3 BN 2 in Li ion conducting applications, chemical stability is investigated in terms of free-energy differences of possible decomposition and Li reaction processes, finding encouraging results. As further investigations of Li 3 BO 3 and β- Li 3 BN 2 as electrolyte or coating materials, particularly for use with Li metal anodes, idealized electrolyte/Li interfaces were investigated in terms of their geometric, energetic, and electronic properties. The results find the electrolyte/Li interfaces to be quite favorable, perhaps comparable to the pioneering LiPON/Li system.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Magnetohydrodynamic Wave Mode Conversion in a Pseudostreamer Structure

The interaction of a fast magnetoacoustic wave with a magnetic null point in a pseudostreamer magnetic configuration is modeled. The incident fast wave is excited by an impulsive velocity driver located in the corona outside the Alfvén-acoustic equipartition layer. The fast wave front experiences refraction and wraps around the null point, while the front segment approaching the null point along the magnetic bisector passes through it. In the equipartition layer surrounding the null point, part of the fast wave energy is converted into slow magnetoacoustic waves. Slow waves propagate outward from the null point along the magnetic separatrices. The fronts of slow waves exhibit a characteristic chevron shape. The fast-to-slow mode conversion efficiency increases with the width of the initial perturbation, following a power-law dependence with an index of approximately 1.06. For initial wave amplitudes below about 10% of the local Alfvén speed, the dependence of the conversion efficiency on the initial amplitude is weak. After interacting with the null point, the amplitudes of the fast waves decrease significantly owing to energy conversion and the spreading of wave energy over a broad spatial domain. In contrast, the energy of slow waves remains concentrated in the vicinity of the magnetic separatrices, resulting in less pronounced geometric attenuation of these waves. These findings are consistent with observational reports of the interaction of a coronal fast wave with a pseudostreamer.

Zhong, Yu [Univ. of Warwick, Coventry (United King↗
DOE OSTI2021

Modeling the spectral modification of lower hybrid wave in the presence of drift-wave type density fluctuation in the scrape-off-layer of the EAST tokamak

In this work, the spectrum change of the lower hybrid (LH) waves caused by a low-frequency density fluctuation in the scrape-off-layer is studied by applying the wave scattering model developed by Bonoli and Ott [Phys. Fluids 25, 359 (1982)] via a Monte Carlo method. A ray-tracing model specific to this purpose is developed to evaluate the probability distribution of both the poloidal refractive index (N θ ) and the parallel refractive index (N ∥ ) of the LH wave at the last closed flux surface (LCFS).The probability distributions of N ∥ and N θ at the LCFS are studied using the EAST parameters as a function of wave frequency, the initial N ∥ , and the polar injection position, which may influence the lower hybrid current drive efficiency.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Blue Rock CropSpanPV - Low Cost Racking for Agricultural Solar Photovoltaics

In this work, a total of four solar panel layouts, applied to Agrivoltaics, are investigated. This study presents two hypotheses: 1. Prefabrication - Lower total cost can be achieved by constructing a pre-assembled, pre-wired solar array in a factory, with automation, then rapidly deploying it in the field. 2. Tension Structures - Using tension structures in a way to suspend an overhead solar array also reduces costs when compared to conventional support methods. Designs are presented for frames to hold the panels. Configurations are advanced to connect the frames into arrays. Supports and foundations to hold the arrays in the desired layout are calculated, selected and presented. Cost models are prepared for the four layouts, which include definition of the business enterprise, the manufacturing operation, and the required facility for production at scale. Cost models include, detail material and task/labor take-offs for both manufacturing and installation. Comparisons with conventional system adapted to Agrivoltaics reveal that the two hypotheses do not hold true. A prefabricated array requires additional material that is not needed in the base system and the cost of this additional material is not outweighed by the cost savings of reduced field installation. The cost of wire rope for a tension structure does result in an economy of material, however, the cost of end connections and tensioning devices adds significantly to the cost of the overall tension structure. Foundation loads with tension structures, especially the large wind uplift seen with a fixed tilt solar array, impose significant constraints and high costs. The following conclusions are recommended for further consideration: 1. Best Case Agrivoltaic Configuration - The best value/lowest cost configuration for agrivoltaics is the installation of solar panels mounted on a single axis tracker in either a 2-in-portrait or 2-in landscape arrangement. This is useful for grazing lands and for staple crops which require high light levels. These applications represent the vast majority of the potential agrivoltaic market. Important elements in this configuration are the specific geometric layout coordinated with the various field operations and a control system linked between the farm equipment and single axis tracker. The control system is to monitor location and orientation, then actively tilt the solar panels or brake the field equipment to provide clearance and avoid collisions. 2. Long Span Applications - The use of tension structures for an overhead fixed tilt array is beneficial where long spans are a necessity, especially where the base support in the project location has consolidated rock near the surface or some other solid structure. One application is spanning wide irrigation canals. Another may be as an installation at the top deck of parking structures. 3. Direct Ground Mount Configuration – Having skids at the base of a pre-fabricated array that extend when the array is deployed, could be a successful design. This could be a useful strategy for dense, flat, ground-mount configurations like that employed by a couple of successful commercial operations (5G Maverick and Erthos). Arrays would be orientated north and south, deployed very low on prepared grade. Arrays would be aligned closely next to each other and anchored with small ground screws or simply with ballast. This same product arrangement could be very useful for rapid deployment and set-up of solar arrays for temporary deployments, disaster response and the military operations

14 SOLAR ENERGY↗
DOE OSTI2021

EGR Dilution and Fuel Property Effects on High-Efficiency Spark-Ignition Flames

Modern spark ignition internal combustion engines rely on fast combustion rates and high dilution to achieve high brake thermal efficiencies. To accomplish this, new engine designs have moved towards increased tumble ratios and stroke-to-bore ratios. Increased tumble ratios correlate positively with increases in turbulent kinetic energy and improved fuel and residual gas mixing, all of which favor faster and more efficient combustion. Longer stroke-to-bore ratios allow higher geometric compression ratios and use of late intake valve closing to control peak compression pressures and temperatures. The addition of dilution to improve efficiency is limited by the resulting increase in combustion instabilities manifested by cycle-to-cycle variability. A number of effects - preferential diffusion, turbulence-combustion interactions, stochastic flow patterns, laminar-turbulent flame kernel transitions, and relative length and velocity scales between flame and turbulence - are believed to be responsible for the increase in cycle-to-cycle variations, where their contributions are likely interlinked. Several studies have shown the influence of stochastic flow characteristics on the nature of combustion instabilities, such as velocity patterns on flame kernel formation and cycle-to-cycle variations in residual gas. However, few have focused on the specific effects of fuel properties. The objective of this work is to contrast the effects of dilution on propane stoichiometric combustion against gasoline. Dilution tolerance experiments were conducted in a purpose-built high stroke-to-bore ratio single cylinder engine with both gasoline and LPG. Three-dimensional full cycle computational fluid dynamics (CFD) simulations employing a level-set combustion approach and Reynolds averaged Navier-Stokes (RANS) turbulence modeling was used to qualitatively assess the changes in length and velocity scales for turbulence and the flame. The experimental results showed that LPG can tolerate higher exhaust gas recirculation (EGR) dilution under a variety of conditions. Analysis of CFD simulations showed that propane flames are likely less sensitive to influences from the flow field due to less thickening of the flame and higher effective flame speeds.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2021

Delaying the inevitable: tidal disruption in microstate geometries

Microstate geometries in string theory replace the black-hole horizon with a smooth geometric “cap” at the horizon scale. In geometries constructed using superstratum technology, this cap has the somewhat surprising property that induces very large tidal deformations on infalling observers that are far away from it. We find that this large-distance amplification of the tidal effects is also present in horizonless microstate geometries constructed as bubbling solutions, but can be tamed by suitably arranging the bubbles to reduce the strength of some of the gravitational multipole moments. However, despite this taming, these tidal effects still become large at a significant distance from the microstructure. This result suggests that an observer will not fall unharmed into the structure replacing the black hole horizon.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Symmetric U(1) and Z 2 spin liquids on the pyrochlore lattice

The geometrically frustrated three-dimensional pyrochlore lattice has been long predicted to host a quantum spin liquid, an intrinsic long-range entangled state with fractionalized excitations. To date, most proposals for pyrochlore materials have focused on quantum spin ice, a U(1) quantum spin liquid whose only low energy excitations are emergent photons of Maxwell type. Here, we explore the possibility of finding pyrochlore quantum spin liquids whose low energy theories go beyond this standard one. We give a complete classification of symmetric U ( 1 ) and Z 2 spin liquids on the pyrochlore lattice within the projective symmetry group framework for fermionic spinons. We find 18 U ( 1 ) spin liquids and 28 Z 2 spin liquids that preserve pyrochlore space-group symmetry while, upon further imposing time-reversal symmetry, the numbers of classes become 16 and 48, respectively. For each class, the most general symmetry-allowed spinon mean-field Hamiltonian is given. Interestingly, we find that several U(1) spin liquid classes possess an unusual gapless multi-nodal-line structure (“nodal star”) in the spinon bands, which is protected by the projective actions of the threefold rotation and screw symmetries of the pyrochlore space group. Through a simple model, we study the effect of gauge fluctuations on such a nodal star spin liquid and propose that the leading terms in the low temperature specific heat have the scaling form C / T ~ T + T / ln T , in contrast to the form C / T ~ T 2 of the standard U(1) pyrochlore spin liquid with gapped spinons.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Raytracing the long trace profiler

The optical design of the Long Trace Profiler optical system is explored with a commercial raytrace program, Zemax OpticStudio™ (ZOS)1, with the intent of finding and correcting sources of systematic error. ZOS provides both geometric raytracing tools and physical optics Gaussian beam propagation and diffraction image calculation tools, and two design modes, sequential component (SC) and non-sequential component (NSC) that are optimized for different aspects of the design process. The original LTP-II system employs a singlet lens with a 1250 mm focal length. It is optimized to provide minimum distortion over a surface slope angle range of ±5 mrad. Using the ZOS tools, we are able to simulate ghost rays that produce distortion in the beam spot image and can minimize the distortion by deliberate misalignment of the beamsplitter (BS) components. Unfortunately, the reference beam is compromised because of the component tilts. The most recent LTP500 system design simplifies the optical system and makes the reference beam usable again, even with misalignment of the polarizing beamsplitter (PBS). Two lenses are designed for the LTP500 - a cemented doublet that has been fabricated, and a singlet with one aspheric surface. Both have focal distances of 500 mm with an expanded angular measurement range of ±10 mrad. The aspheric singlet provides superior performance. ZOS allows the import of wavefront measurement data produced by commercial interferometer software. We apply the wavefront error measurement from the cemented doublet to the model to show that the 19nm RMS wavefront error needs to be improved by at least a factor of ten in order to reduce the systematic error to a level that will allow the LTP to approach its design limit of a few tens of nanoradians.

Takacs, Peter Z.↗
DOE OSTI2022

Geometric soft theorems

We derive a universal soft theorem for every scattering amplitude with at least one massless particle in an arbitrary theory of scalars. Our results follow from the geometry of field space and are valid for any choice of mass spectrum, potential terms, and higher-derivative interactions. For a vanishing potential, the soft limit of every amplitude is equal to the field-space covariant derivative of an amplitude with one fewer particle. Furthermore, the Adler zero and the dilaton soft theorem are special cases of our results. We also discuss more exotic scenarios in which the soft limit is non-trivial but still universal. Last but not least, we derive new theorems for multiple-soft limits which directly probe the field-space curvature, as well as on-shell recursion relations applicable to two-derivative scalar field theories exhibiting no symmetries whatsoever.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Measurement of the angular dependence of the spontaneous Raman scattering in anisotropic crystalline materials using spherical samples: Potassium dihydrogen phosphate as a case example

A specialized experimental configuration was created to allow for more-accurate characterization of the spontaneous Raman scattering properties in anisotropic materials. This need stems from the challenges, arising from the complexity of light propagation, in obtaining accurate measurements of the angular dependence of the Raman scattering cross section in birefringent materials. The nonlinear optical material KH 2 PO 4 (KDP) is used as a model medium. Our report is motivated by the need to improve our understanding and management of transverse stimulated Raman scattering in KDP crystals and its deuterated analog, DKDP, typically used for frequency conversion and polarization control in large-aperture laser systems. Key to this experimental platform is the use of high-quality spherical samples that enable one to measure the Raman scattering cross section in a wide range of geometries using only a single sample. The effect of polarization rotation of both the pump light and the collected Raman signal must be carefully considered in data analysis and can give rise to artifacts, which can, in part, be mitigated by reducing the input and collection cone angles.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Multidimensional simulations of Mckenna-driven flow tube configuration: Investigating non-ideality in NO x formation flow tube experiments

Multidimensional simulations have been conducted to simulate atmospheric pressure, flat-flame/McKenna-burner-driven-flow tube experiments targeted to obtain NO x speciation data for predicting/analyzing syngas combustion emissions. In a prior work, we demonstrated the impacts of multidimensional transport on post flame region prediction departures from those assuming unidimensional flow/transport conditions. In this work, we develop and utilize a multidimensional laminar reacting flow solver to simulate the fully coupled flame and post flame regions to further elucidate the impacts of the earlier unidimensional modeling assumptions on interpreting post flame NO x experimental data. The model is used to simulate a lean, premixed syngas/air flame and its associated post flame regions within a cylindrical flow-tube-like arrangement. The combustion process takes place under atmospheric condition with trace amount of NO x seeding fed into the inlet gas stream. The spatial evolution of NO x species (NO and NO 2 ) in the flame and in the post-combustion zone suggests two distinct regions: 1) a region encompassing the flame structure itself; and 2) a post flame region in which the temperature decays due to both axial and radial transport processes. The predictions show that for the conditions studied, a pulsatile flow field exists due to the formation of an expanding and contracting recirculation zone in the outer periphery of the flow tube. By resolving the nature of the flow, the resulting time-averaged temperature and species concentrations show improved agreement with existing experimental measurements. The flow-field interaction results in radial inhomogeneities in the NO 2 profiles with the maximum concentration offset from the flow centerline. The location of the peak in NO 2 is coupled with radial temperature gradients from wall cooling effects and their significant influence on NO/NO 2 interconversion kinetics, producing notable NO 2 accumulation in regions near the wall. Geometrical configurations capable of suppressing/minimizing the pulsatile nature are also investigated and the results are compared. Other experimental configurations could be considered in parametric simulations to determine the optimal configuration that would minimize non-idealities in the observations. The work shows the value in performing such computations in advance of settling on a particular design for flow tube/flow reactor experiments.

42 ENGINEERING↗
DOE OSTI2022

Lagrangian conditional statistics and flow topology in edge plasma turbulence

Lagrangian statistics and particle transport in edge plasma turbulence are investigated using the Hasegawa–Wakatani model and its modified version. The latter shows the emergence of pronounced zonal flows. Different values of the adiabaticity parameter are considered. The main goal is to characterize the role of coherent structures, i.e., vortices and zonal flows, and their impact on the Lagrangian statistics of particles. Computationally intensive long time simulations following ensembles of test particles over hundreds of eddy turnover times are considered in statistically stationary turbulent flows. The flow topology is characterized using the Lagrangian Okubo–Weiss criterion in order to split the flow into topologically different domains. In elliptic and hyperbolic regions, the probability density functions (PDFs) of the residence time have self-similar algebraic decaying tails. However, in the intermediate regions, the PDFs exhibit exponentially decaying tails. Topologically conditioned PDFs of the Lagrangian velocity, and acceleration and density fluctuations are likewise computed. The differences between the classical Hasegawa–Wakatani system and its modified version are assessed, and the role of zonal flows is highlighted. Here, the density flux spectrum, which characterizes the contributions of different length scales, is studied, and its inertial scaling is found to be in agreement with predictions based on dimensional arguments. Analyzing the angular change of particle tracers at different time scales, corresponding to coarse grained curvature, completes the study, and these multiscale geometric statistics quantify the directional properties of the particle motion in different flow regimes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗