Kinetic Scales Research Articles

Clustering of magnetic reconnection exhausts in the solar wind: An automated detection study

Context. Magnetic reconnection is a fundamental process in astrophysical plasmas that enables the dissipation of magnetic energy at kinetic scales. Detecting this process in situ is therefore key to furthering our understanding of energy conversion in space plasmas. However, reconnection jets typically scale from seconds to minutes in situ, and as such, finding them in the decades of data provided by solar wind missions since the beginning of the space era is an onerous task. Aims. In this work, we present a new approach for automatically identifying reconnection exhausts in situ in the solar wind. We apply the algorithm to Solar Orbiter data obtained while the spacecraft was positioned at between 0.6 and 0.8 AU and perform a statistical study on the jets we detect. Methods. The method for automatic detection is inspired by the visual identification process and strongly relies on the Walén relation. It is enhanced through the use of Bayesian inference and physical considerations to detect reconnection jets with a consistent approach. Results. Applying the detection algorithm to one month of Solar Orbiter data near 0.7 AU, we find an occurrence rate of seven jets per day, which is significantly higher than in previous studies performed at 1 AU. We show that they tend to cluster in the solar wind and are less likely to occur in the tenuous solar wind (< 10 cm−3 near 0.7 AU). We discuss why the source and the degree of Alfvénicity of the solar wind might have an impact on magnetic reconnection occurrence. Conclusions. By providing a tool to quickly identify potential magnetic reconnection exhausts in situ, we pave the way for broader statistical studies on magnetic reconnection in diverse plasma environments.

Electromagnetic electron Kelvin–Helmholtz instability

On electron kinetic scales, ions and electrons decouple, and electron velocity shear on electron inertial length ∼de can trigger electromagnetic (EM) electron Kelvin–Helmholtz instability (EKHI). In this paper, we present an analytic study of EM EKHI in an inviscid collisionless plasma with a step-function electron shear flow. We show that in incompressible collisionless plasma, the ideal electron frozen-in condition E+ve×B/c=0 must be broken for the EM EKHI to occur. In a step-function electron shear flow, the ideal electron frozen-in condition is replaced by magnetic flux conservation, i.e., ∇×(E+ve×B/c)=0, resulting in a dispersion relation similar to that of the standard ideal and incompressible magnetohydrodynamics KHI. The magnetic field parallel to the electron streaming suppresses the EM EKHI due to magnetic tension. The threshold for the EM mode of the EKHI is (k·ΔUe)2>ne1+ne2ne1ne2[ne1(vAe1·k)2+ne2(vAe2·k)2], where vAe=B/(4πmene)1/2, ΔUe, and ne are the electron streaming velocity shear and densities, respectively. The growth rate of the EM mode is γem∼Ωce, which is the electron gyro-frequency.

Transition metal embedded in nonmetal-doped T-carbon [110]: A superior synergistic trifunctional electrocatalyst for HER, OER and ORR

The design of efficient and low-cost multifunctional electrocatalysts for hydrogen evolution reaction (HER), oxygen evolution reaction (OER) and oxygen reduction reaction (ORR) is critical for the development of clean energy. Two-dimensional (2D) carbon-based nano-materials are becoming more and more popular in heterogeneous catalysis due to their cost-effective and multi-scale tunability as single-atom catalysis (SACs) substrates. In this paper, by using first-principles calculation, we designed and demonstrated a novel macropore T-carbon [110] (TC) monolayer as 2D electrocatalyst substrate for HER/OER/ORR, and the synergistic modification of the transition metal and nonmetal atoms (TM-X) were investigated to enhance the multifunctional electrocatalytic performance. We screened out the Co embedded in N-doped TC (Co3@N-TC) from 30 TM@X-TC monolayers as a trifunctional electrocatalysts, which exhibits superior performance for HER/ORR/OER on both thermodynamic and kinetic scales, and with excellent thermal and electrochemical stability. Then, the TC monolayer is naturally macropore with a diameter of 5.36 Å and exhibits excellent adsorption capacity for the intermediates and products of the redox reactions. Moreover, we revealed the origin of the electrocatalytic activity using the crystal orbital Hamilton population (COHP) and the molecular orbitals (MOs). The d orbital of Co3@N-TC is significantly hybridized with the p orbital of the intermediates, so that the lone electrons initially occupied in the antibonding state pair up and occupy the downward bonding state, allowing *OH to be appropriately adsorbed onto the TC monolayer. This work not only demonstrates that the TM@X-TC monolayer is a superior synergistic trifunctional electrocatalyst, but also reveals a macropore monolayer material with potential applications in electrocatalysis.

A Heating Mechanism via Magnetic Pumping in the Intracluster Medium

Turbulence driven by active galactic nuclei activity, cluster mergers, and galaxy motion constitutes an attractive energy source for heating the intracluster medium (ICM). How this energy dissipates into the ICM plasma remains unclear, given its low collisionality and high magnetization (precluding viscous heating by Coulomb processes). Kunz et al. proposed a viable heating mechanism based on the anisotropy of the plasma pressure under ICM conditions. The present paper builds upon that work and shows that particles can be heated by large-scale turbulent fluctuations via magnetic pumping. We study how the anisotropy evolves under a range of forcing frequencies, what waves and instabilities are generated, and demonstrate that the particle distribution function acquires a high-energy tail. For this, we perform particle-in-cell simulations where we periodically vary the mean magnetic field B (t). When B (t) grows (dwindles), a pressure anisotropy P ⊥ > P ∥(P ⊥ < P ∥) builds up (P ⊥ and P ∥ are, respectively, the pressures perpendicular and parallel to B (t)). These pressure anisotropies excite mirror (P ⊥ > P ∥) and oblique firehose (P ∥ > P ⊥) instabilities, which trap and scatter the particles, limiting the anisotropy, and providing a channel to heat the plasma. The efficiency of this mechanism depends on the frequency of the large-scale turbulent fluctuations and the efficiency of the scattering the instabilities provide in their nonlinear stage. We provide a simplified analytical heating model that captures the phenomenology involved. Our results show that this process can be relevant in dissipating and distributing turbulent energy at kinetic scales in the ICM.

Laboratory study of Kelvin–Helmholtz instability at ion kinetic scales

Kelvin–Helmholtz instability (KHI) is considered important in transporting energy and mass at the magnetopause of Earth and other planets. However, the ion kinetic effect influences the generation and evolution of KHI, as the spatial length of the magnetopause may be smaller than the Larmor radius of the ion; this influence is not yet fully understood. In this investigation, laboratory experiments were designed to study the excitation of KHI at the ion kinetic scale. The ion kinetic scale was modeled by controlling the ratio of the Larmor radius and the electric scale length ρ i / L E &amp;gt; 1, and the KHI was excited at the spatial scale of LE by a controllable sheared E × B flow. It was found that the ion kinetic effect on KHI growth manifests as the ion Larmor radius reaches the shear length scale, and the KHI is suppressed as the ion Larmor radius increases. Incorporating a theoretical analysis by substituting our experimental parameters, the suppression of the KHI was attributed to the fact that the KHI linear growth rate decreases with the ratio change of the ion Larmor radius because the relative orientations of the ion diamagnetic drift velocity ( V d) and the shear flow velocity ( V 0) are opposite. Our experimental conditions ( V d / V 0 &amp;lt; 0) are similar to the dusk-side conditions of the magnetospheres of Earth and Mercury under northward interplanetary magnetic fields; therefore, this result can be extended to understand the evolution of KHI in the planetary boundary layer.

The effect of variations in the magnetic field direction from turbulence on kinetic-scale instabilities

At kinetic scales in the solar wind, instabilities transfer energy from particles to fluctuations in the electromagnetic fields while restoring plasma conditions towards thermodynamic equilibrium. We investigate the interplay between background turbulent fluctuations at the small-scale end of the inertial range and kinetic instabilities acting to reduce proton temperature anisotropy. We analyse in situ solar wind observations from the Solar Orbiter mission to develop a measure for variability in the magnetic field direction. We find that non-equilibrium conditions sufficient to cause micro-instabilities in the plasma coincide with elevated levels of variability. We show that our measure for the fluctuations in the magnetic field is non-ergodic in regions unstable to the growth of temperature anisotropy-driven instabilities. We conclude that the competition between the action of the turbulence and the instabilities plays a significant role in the regulation of the proton-scale energetics of the solar wind. This competition depends not only on the variability of the magnetic field but also on the spatial persistence of the plasma in non-equilibrium conditions.

Production and transport of turbulent kinetic energy from premixed flames subjected to mean pressure gradients

The influence of mean favorable pressure gradients on the production and transport of turbulent kinetic energy is experimentally investigated in a premixed bluff-body combustor. The combustor wall geometry is modified into converging, straight, or diverging configurations to experimentally alter the mean pressure gradient in the reacting flow field. For each configuration, turbulent kinetic energy production and transport dynamics are characterized with high-speed particle image velocimetry and simultaneous CH* chemiluminescence imaging. For all cases, the premixed reaction increases the turbulent kinetic energy and integral length scales in the flow. However, increasing the magnitude of the mean favorable pressure gradient increases the turbulent kinetic energy produced by the flame. The source of increased turbulent fluctuations from reactants to products is first investigated with a steady flow energy analysis, and is accompanied with a Reynolds decomposed investigation of the kinetic energy in the flow. As the mean pressure gradient increases, the turbulent kinetic energy in the flow increases due to stronger magnitudes of flame-generated turbulence in the form of baroclinic torque. The evolution of the flame-generated turbulence is examined by decomposing the transport equation of turbulent kinetic energy. Increasing the mean favorable pressure gradient augments the largest magnitude transport terms, and the budget of turbulent kinetic energy is primarily driven by pressure gradient work and viscous dissipation. The results here differ from previous direct numerical simulation (DNS) studies, and should ultimately motivate additional research to aid the development of computational models which can better predict turbulent flame-flow dynamics in confined environments with mean pressure gradients.

The Failure of Both Einstein’s Space-time Theory and His Equivalence Principle and Their Resolution by the Uniform Scaling Method

The Lorentz transformation (LT) makes three predictions which are not consistent with one another: Lorentz-FitzGerald length contraction (FLC), time dilation (TD) and light-speed equality for observers in relative motion to one another. The LT also stands in violation of the Law of Causality because it fails to recognize that inertial clocks can never change their rate spontaneously. Einstein’s light-speed postulate (LSP) is shown to be unviable by considering a case in which a light source passes by a stationary observer at the same time that it emits a light pulse in the same direction. It is found that, in contradiction to the LSP, that the classical velocity (Galilean) transformation (GVT) is applicable when two observers in relative motion deduce the speed of a light wave. The Newton-Voigt transformation (NVT) is consistent with the Law of Causality because it assumes space and time do not mix. The NVT is nonetheless consistent with the relativistic velocity transformation (RVT) and also with Einstein’s mass-energy equivalence relation E=mc2. The ratio Q of clock rates for two inertial rest frames S and S’ is required input for the NVT. Experimental data obey the Universal Time-dilation Law (UTDL) which states that the measured time Δt obtained by a inertial clock for a given event is inversely proportional to γ(v)= (1-v2c-2)-0.5v, where v is the speed of the clock relative to a specific rest frame referred to as the objective rest frame ORS. The value of Q when the clock of the observer in at rest in S while that of another observer is at rest in the object’s rest frame S’ is obtained from the UTDL as the ratio γ(v’)/γ(v). The Uniform Scaling method considers Q to be a conversion factor between the units of time in the two rest frames. It is found that the conversion factors for all other physical properties are integral multiples of Q. Kinetic scaling of the properties insures that the laws of physics are the same in each inertial frame, as required .........

Boosting the convergence of low-variance DSMC by GSIS

The low-variance direct simulation Monte Carlo (LVDSMC) is a powerful method to simulate low-speed rarefied gas flows. However, in the near-continuum flow regime, due to limitations on the time step and spatial cell size, it takes plenty of time to find the steady-state solution. Here we remove these deficiencies by coupling the LVDSMC with the general synthetic iterative scheme (GSIS) which permits the simulation at the hydrodynamic scale rather than the much smaller kinetic scale. As a proof of concept, we propose the stochastic-deterministic coupling method based on the Bhatnagar-Gross-Krook kinetic model. First, macroscopic synthetic equations are derived exactly from the kinetic equation, which not only contain the Navier-Stokes-Fourier constitutive relation, but also encompass the higher-order terms describing the rarefaction effects. Then, the high-order terms are extracted from LVDSMC and fed into synthetic equations to predict the macroscopic properties which are closer to the steady-state solution than LVDSMC. Finally, the state of simulation particles in LVDSMC is updated to reflect the change of macroscopic properties. As a result, the convergence to steady state is greatly accelerated, and the restrictions on cell size and the time step are removed. We conduct the Fourier stability analysis and simulate several canonical rarefied gas flows to demonstrate the advantages of LVDSMC-GSIS: when the Knudsen number is lower than 0.1, it can use the grid size about 10 times larger than that in traditional DSMC, and it can reduce the computational cost by two orders of magnitude in the flow regime.

A Space Mission for Cross‐Scale Coupling in the Earth's Magnetosphere

AbstractThe Earth's magnetosphere occupies a huge volume in space. Past space missions have identified the basic structures and revealed several phenomena that release significant energy explosively. These activities are discovered through point‐wise measurements in space. Consequently, there is a severe lack of knowledge on the coupling between different activities. A space mission that can address this deficiency is proposed here, building on what previous space missions have revealed. A fleet of eight identical spacecraft in two sets of tetrahedral constellations will enable evaluation of how localized kinetic activities may lead to global changes and vice versa in the Earth's magnetosphere. This mission uses the full capability of a tetrahedral constellation to yield a quantitative determination of physical parameters that govern the mass, momentum, and energy flows between space disturbances at kinetic and global scales. It will also resolve the ambiguity in single‐point measurements to differentiate their temporal and spatial variations. Examples on how to use this mission to extract cross‐scale coupling of activities and tackle outstanding questions in magnetospheric research are discussed.

A simplified semi-empirical model for long-range low-frequency noise propagation in the turbulent atmosphere

We present a semi-empirical long-range low-frequency acoustic propagation model, which accounts for atmospheric turbulence. Ostashev and Wilson’s scattering model is combined with a ray-theory based refraction model to account for turbulent scattering and refraction via a turbulent absorption coefficient. The coefficient is ascertained via integration of scattered energy. The model is formulated, calibrated, and validated via corresponding experiments conducted within the National Science Foundation Boundary Layer Wind Tunnel. The predictions of the newly proposed ‘bridging model’ match the wind tunnel experimental data with an average error of 11.9%. Example predictions are shown to quantify the effect of turbulent kinetic energy and turbulent integral length scale on long-range infrasound propagation. To demonstrate the approach, we present predictions of the propagation of noise from a tornado and a nonlinear wave.

Unified preserving properties of kinetic schemes.

The kinetic theory provides a physical basis for developing multiscale methods for gas flows covering a wide range of flow regimes. A particular challenge for kinetic schemes is whether they can capture the correct hydrodynamic behaviors of the system in the continuum regime (i.e., as the Knudsen number ε≪1) without enforcing kinetic scale resolution. At the current stage, the main approach to analyze such a property is the asymptotic preserving (AP) concept, which aims to show whether a kinetic scheme reduces to a solver for the hydrodynamic equationsas ε→0, such as the shock capturing scheme for the Euler equations. However, the detailed asymptotic properties of the kinetic scheme are indistinguishable when ε is small but finite under the AP framework. To distinguish different characteristics of kinetic schemes, in this paper we introduce the concept of unified preserving (UP) aiming at assessing asymptotic orders of a kinetic scheme by employing the modified equationapproach and Chapman-Enskon analysis. It is shown that the UP properties of a kinetic scheme generally depend on the spatial and temporal accuracy and closely on the interconnections among three scales (kinetic scale, numerical scale, and hydrodynamic scale) and their corresponding coupled dynamics. Specifically, the numerical resolution and specific discretization of particle transport and collision determine the flow physics of the scheme in different regimes, especially in the near continuum limit. As two examples, the UP methodology is applied to analyze the discrete unified gas-kinetic scheme and a second-order implicit-explicit Runge-Kutta scheme in their asymptotic behaviors in the continuum limit.

Decomposition rate as an emergent property of optimal microbial foraging

Decomposition kinetics are fundamental for quantifying carbon and nutrient cycling in terrestrial and aquatic ecosystems. Several theories have been proposed to construct process-based kinetics laws, but most of these theories do not consider that microbial decomposers can adapt to environmental conditions, thereby modulating decomposition. Starting from the assumption that a homogeneous microbial community maximizes its growth rate over the period of decomposition, we formalize decomposition as an optimal control problem where the decomposition rate is a control variable. When maintenance respiration is negligible, we find that the optimal decomposition kinetics scale as the square root of the substrate concentration, resulting in growth kinetics following a Hill function with exponent 1/2 (rather than the Monod growth function). When maintenance respiration is important, optimal decomposition is a more complex function of substrate concentration, which does not decrease to zero as the substrate is depleted. With this optimality-based formulation, a trade-off emerges between microbial carbon-use efficiency (ratio of growth rate over substrate uptake rate) and decomposition rate at the beginning of decomposition. In environments where carbon substrates are easily lost due to abiotic or biotic factors, microbes with higher uptake capacity and lower efficiency are selected, compared to environments where substrates remain available. The proposed optimization framework provides an alternative to purely empirical or process-based formulations for decomposition, allowing exploration of the effects of microbial adaptation on element cycling.

Magnetospheric Multiscale Observations of Markov Turbulence on Kinetic Scales

In our previous studies we have examined solar wind and magnetospheric plasma turbulence, including Markovian character on large inertial magnetohydrodynamic scales. Here we present the results of the statistical analysis of magnetic field fluctuations in the Earth’s magnetosheath, based on the Magnetospheric Multiscale mission at much smaller kinetic scales. Following our results on spectral analysis with very large slopes of about −16/3, we apply a Markov-process approach to turbulence in this kinetic regime. It is shown that the Chapman–Kolmogorov equation is satisfied and that the lowest-order Kramers–Moyal coefficients describing drift and diffusion with a power-law dependence are consistent with a generalized Ornstein–Uhlenbeck process. The solutions of the Fokker–Planck equation agree with experimental probability density functions, which exhibit a universal global scale invariance through the kinetic domain. In particular, for moderate scales we have the kappa distribution described by various peaked shapes with heavy tails, which, with large values of the kappa parameter, are reduced to the Gaussian distribution for large inertial scales. This shows that the turbulence cascade can be described by the Markov processes also on very small scales. The obtained results on kinetic scales may be useful for a better understanding of the physical mechanisms governing turbulence.

Multipoint Observations of Dispersive Scale Alfvénic Field‐Line Resonances Associated With Substorm Auroral Beads

AbstractWe present a case study of the field‐aligned current (FAC) systems that transpire within the high‐altitude auroral acceleration region of an “auroral bead” initiated double oval substorm observed on 23 February 2001 by the Cluster fleet. Conjunctive Cluster measurements and auroral images from IMAGE reveal that auroral bead current system formation and evolution is a multi‐scale, injection‐mediated process. The FACs at large scales vary on substorm evolution time scales (∼minutes) in response to the injection and evolution of hotter denser magnetospheric plasma. Embedded within the large‐scale FACs are intense short‐scale (≲ few 10s of km) currents comprising dispersive scale Alfvén wave (DAW) fluctuations. The DAWs are a complex mixture of ingoing and reflected components that regularly interfere to form a broad spectrum of kinetic (dispersive) scale Alfvénic field‐line resonances (KFLRs). The Alfvénic currents appear as a nested series of upward and downward FAC densities with amplitudes reaching a few 100 nA/m2. Energized field‐aligned or counterstreaming electrons near keV energies and below are observed with parallel skews that vary in concert with variations in the DAW current sense. Positive correlations between DAW electric field energy densities and the energies of energized H+, He+, and O+ outflow are observed, indicative of ion energization within the DAW fields. Due to their L‐shell location (L ∼5.8–7.0) and associations with injections, the KFLRs are interpreted as the high‐altitude auroral zone analog of KFLRs observed in the equatorial inner magnetosphere.

Kinetic Scale Magnetic Reconnection with a Turbulent Forcing: Particle-in-cell Simulations

Turbulent magnetic reconnection has been observed by spacecraft to occur commonly in terrestrial magnetosphere and the solar wind, providing a new scenario of kinetic scale magnetic reconnection. Here by imposing a turbulent forcing on ions in particle-in-cell simulations, we simulate kinetic scale turbulent magnetic reconnection. We find formation of fluctuated electric and magnetic fields and filamentary currents in the diffusion region. Reconnection rate does not change much compared to that in laminar Hall reconnection. At the X-line, the electric and magnetic fields both exhibit a double power-law spectrum with a spectral break near local lower-hybrid frequency. The energy conversion rate is high in turbulent reconnection, leading to significant electron acceleration at the X-line. The accelerated electrons form a power-law spectrum in the high energy range, with a power-law index of about 3.7, much harder than one can obtain in laminar reconnection.

Direct driving of simulated planetary jets by upscale energy transfer

Context. The precise mechanism that forms jets and large-scale vortices on the giant planets is unknown. An inverse cascade has been suggested by several studies. Alternatively, energy may be directly injected by small-scale convection. Aims. Our aim is to clarify whether an inverse cascade feeds zonal jets and large-scale eddies in a system of rapidly rotating, deep, geostrophic spherical-shell convection. Methods. We analyze the nonlinear scale-to-scale transfer of kinetic energy in such simulations as a function of the azimuthal wave number, m. Results. We find that the main driving of the jets is associated with upscale transfer directly from the small convective scales to the jets. This transfer is very nonlocal in spectral space, bypassing large-scale structures. The jet formation is thus not driven by an inverse cascade. Instead, it is due to a direct driving by Reynolds stresses, statistical correlations of velocity components of the small-scale convective flows. Initial correlations are caused by the effect of uniform background rotation and shell geometry on the flows and provide a seed for the jets. While the jet growth suppresses convection, it increases the correlation of the convective flows, which further amplifies the jet growth until it is balanced by viscous dissipation. To a much smaller extent, energy is transferred upscale to large-scale vortices directly from the convective scales, mostly outside the tangent cylinder. There, large-scale vortices are not driven by an inverse cascade either. Inside the tangent cylinder, the transfer to large-scale vortices is even weaker, but more local in spectral space, leaving open the possibility of an inverse cascade as a driver of large-scale vortices. In addition, large-scale vortices receive kinetic energy from the jets via forward transfer. We therefore suggest a jet instability as an alternative formation mechanism of large-scale vortices. Finally, we find that the jet kinetic energy scales approximatively as ℓ−5, the same as for the so-called zonostrophic regime.

Topology of Magnetic and Velocity Fields at Kinetic Scales in Incompressible Plasma Turbulence

AbstractThe topology of the magnetic and velocity fields at the kinetic scales are investigated in the context of nearly incompressible magnetosheath plasma turbulence. Using the unprecedented high‐resolution data from the Magnetospheric MultiScale mission, the joint probability distribution functions of geometrical invariants characterizing the magnetic and velocity fields gradient tensor at the kinetic scales are computed. The topological features of the magnetic and velocity field gradient tensors and their symmetric component tensors present axisymmetric distribution patterns, indicating that the structure of the plasma turbulence at the kinetic scales are different from those in hydrodynamic and magnetohydrodynamic turbulence. Moreover, a strong correlation between the straining and rotational parts of the magnetic and velocity field gradient tensors was found, which manifests the dominance of sheet‐like structures at the kinetic‐scales dissipation in incompressible plasma turbulence.

The role of particle precipitation on plasma structuring at different altitudes by in-situ measurements

The plasma in the cusp ionosphere is subject to particle precipitation, which is important for the development of large-scale irregularities in the plasma density. These irregularities can be broken down into smaller scales which have been linked to strong scintillations in the Global Navigation Satellite System (GNSS) signals. We present power spectra for the plasma density irregularities in the cusp ionosphere for regions with and without auroral particle precipitation based on in-situ measurements from the Twin Rockets to Investigate Cusp Electrodynamics-2 (TRICE-2) mission, consisting of two sounding rockets flying simultaneously at different altitudes. The electron density measurements taken from the multi-needle Langmuir probe system (m-NLP) were analyzed for the whole flight duration for both rockets. Due to their high sampling rates, the probes allow for a study of plasma irregularities down to kinetic scales. A steepening of the slope in the power spectra may indicate two regimes, a frequency interval with a shallow slope, where fluid-like processes are dominating, and an interval with a steeper slope which can be addressed with kinetic theory. The steepening occurs at frequencies between 20 Hz and 100 Hz with a median similar to the oxygen gyrofrequency. Additionally, the occurrence of double slopes increases where precipitation starts and throughout the rest of the flight. In addition, strong electron density fluctuations were found in regions poleward of the cusp, thus in regions immediately after precipitation. Furthermore, by investigating the integrated power of the fluctuations within different frequency ranges, we show that at low frequencies (10–100 Hz), the power is pronounced more evenly while the rocket encounters particle precipitation, while at high frequencies (100–1000 Hz) fluctuations essentially coincide with the passing through a flow channel.

Flat bands arising from spin-orbit assisted orbital frustration

We present general design principles for engineering and discovering periodic systems with flat bands. Our paradigm exploits spin-orbit assisted orbital frustration on a lattice to produce band structures that contain multiplets of narrowly dispersing bands whose bandwidth is smaller than all other energy scales of the problem including the band gap surrounding the flat bands. We present a series of models in 1D and 2D on various lattices with different intracellular spin-orbit like potentials that hybridize the degrees of freedom in the unit cell. As an alternative to machine learning based exhaustive searches, these design principles and models can be used to search for flat band systems in a variety of physical settings and can be used to investigate the role of weakly dispersing highly orbitally frustrated degrees of freedom in systems where the interactions dominate over the kinetic energy scales of the system.