Sinusoidal Perturbation Research Articles

Same-sided successive-shock HED instability experiments

Inertial confinement fusion (ICF) and high-energy density (HED) physics experiments experience complicated forcing for instability growth and mix due to the ubiquitous presence of multiple shocks interacting with perturbations on multiple material interfaces. One common driver of instability growth is successive shocks from the same direction. However, there is a severe lack of analytic work and modeling validation for same-sided successive shocks since they are extremely difficult to achieve with conventional (non-HED) drivers. Successive shocks access a large instability parameter space; idealized fluid theory [K. O. Mikaelian, Phys. Rev. A 31, 410 (1985)] predicts 15 different interface evolution scenarios for a sinusoidal perturbation. Growth becomes more complex for multi-mode, compressible HED systems. The Mshock campaign is the first experiment in any fluid regime to probe a wide portion of successive shock parameter space. This is enabled by our development of a hybrid direct/indirect drive platform capable of creating independently controllable successive shocks on the National Ignition Facility. These experiments have delivered the first data capable of rigorously challenging our models and their ability to accurately capture Richtmyer–Meshkov growth under successive shocks. Single-mode and two-mode experiments have successfully demonstrated the ability to access and control the various growth scenarios of the shocked interface, including re-inversion, freeze out, and continued growth. Simulations and theoretical modeling are shown to accurately capture the experimental observations in the linear growth phase, giving us confidence in our ICF/HED design codes.

A numerical method for two-phase flow with its application to the Kelvin–Helmholtz instability problem

This article uses the artificial compressibility-based high-order finite difference method to simulate the two-phase Kelvin–Helmholtz (KH) instability problem. The equations are based on the mass-conserving Allen–Cahn equation coupled with the incompressible Navier–Stokes equations. One of the advantages of the artificial compressibility approach is that many high-order numerical schemes based on hyperbolic conservation law can be applied. A fifth-order weighted essentially non-oscillatory (WENO) scheme is used for discretizing the convective terms while a standard central finite difference scheme is used for the viscous and surface tension terms. The system of equations is then solved using the Beam-Warming approximate factorization technique. For validation, the effects of both single- and double-mode sinusoidal perturbations on the Kelvin–Helmholtz instability dynamics are analyzed. When there is a single-mode sinusoidal perturbation, the interface roll-up at the center of the domain. Additionally, the role of the surface tension parameter in the instability’s dynamics is investigated. The development of Kelvin–Helmholtz instability is shown to be sensitive to the surface tension value. The analysis of grid convergence is also performed to capture the interface dynamics at varying resolutions. The comparison of the computed results is in good agreement with those from the literature. It is observed that the proposed technique effectively resolves the dynamics of the chaotically distorted interfaces of the Kelvin–Helmholtz instability in two-phase flow.

The response of small-scale shear layers to perturbations in turbulence

The perturbation response of small-scale shear layers in turbulence is investigated with direct numerical simulations (DNS). The analysis of shear layers in isotropic turbulence suggests that the typical layer thickness is about four times the Kolmogorov scale $\eta$ . Response for sinusoidal perturbations is investigated for an isolated shear layer, which models a mean flow around the shear layers in turbulence. The vortex formation in the shear layer is optimally promoted by the perturbation whose wavelength divided by the layer thickness is about 7. These results indicate that the small-scale shear instability in turbulence is efficiently promoted by velocity fluctuations with a wavelength of about $30\eta$ . Furthermore, DNS are carried out for decaying turbulence initialised by the artificially modified velocity field of isotropic turbulence. The vortex formation from shear layers is accelerated under the influence of external perturbations with the efficient wavelength to promote the instability. When velocity fluctuations with this wavelength are eliminated by a band-cut filter, the shear layers tend to persist for a long time without producing vortices. These behaviours affect the number of vortices in turbulence, which increases and decreases when velocity perturbations with the unstable wavelength of the instability are artificially amplified and damped, respectively. The increase in the number of vortices results in the enhancement of kinetic energy dissipation, enstrophy production and strain self-amplification. These results indicate that the perturbation response of shear layers is important in the small-scale dynamics of turbulence as well as the modulation of small-scale turbulent motions by external disturbance.

Thermoelastic instability on a frictional surface and its implication for size effect in friction experiments

Recent laboratory friction experiments on large rock samples revealed that dynamic weakening, a remarkable reduction in the friction coefficient at elevated slip rates, occurs at lower slip rates in larger samples. There is a large difference between the sizes of natural faults and those in laboratory experiments. Therefore, it is crucial to understand the effect of size on rock friction. In the field of tribology, the interaction between frictional heating and thermoelastic effect has long been investigated. It was shown that higher slip rates than the critical value {V}_{mathrm{cr}} causes growth of temperature and normal stress heterogeneity (thermoelastic instability), and {V}_{mathrm{cr}} is proportional to the wavenumber of the heterogeneity. Severely heterogeneous normal stress may cause concentration of frictional power, thus locally activating dynamic weakening and leading to macroscopic weakening. Because a larger sample hosts a perturbation of a smaller wavenumber, it is expected to weaken at a lower slip rate than a smaller sample. In this study, a new numerical method was developed for analysis of thermoelastic instability based on the definition of memory variables and numerical approximation to the integration kernel, for the 2-dimensional problem of a planar fault embedded in an infinite medium. This method was advantageous over the standard integral equation method in terms of numerical costs. Numerical solutions with the new method on sinusoidal perturbations in the normal stress were compared with previously derived steady-state solution and its stability for validation. The typical thermoelastic properties of gabbro yield {V}_{mathrm{cr}} in a range of experimentally adopted slip rates, indicating that the thermoelastic effect may play an important role in high-velocity friction experiments. Because the temperature rise and the resulting normal stress change smear out after the friction experiments, measurement of the temperature distribution in a sample during a friction experiment is important for further understanding the dynamic weakening and scale effect of rock friction.Graphical

Analogue circuit realisation of surface-confined redox reaction kinetics

The literature on voltammetry and electrochemical impedance spectroscopy (EIS) recognises the importance of using large-amplitude sinusoidal perturbations to better characterise electrochemical systems. To identify the parameters of a given reaction, various electrochemical models with different sets of values are simulated and compared against the experimental data to determine the best-fit set of parameters. However, the process of solving these nonlinear models is computationally expensive. This paper proposes analogue circuit elements for synthesising surface-confined electrochemical kinetics at the electrode interface. The resultant analogue model could be used as a solver to compute reaction parameters as well as a tracker for ideal biosensor behaviour. The performance of the analogue model was verified against numerical solutions to theoretical and experimental electrochemical models. Results show that the proposed analogue model has a high accuracy of at least 97% and a wide bandwidth of up to 2 kHz. The circuit consumed an average power of 9 μW.

Influence of the Shock Wave Intensity on Instability Development at Rough Interfaces of a Three-Layer Gas System

The influence exerted by the intensity of a shock wave transmitted through rough interfaces on instability development in a three-layer gas system at Mach numbers M = 1.3 and M = 3 is studied. The three-layer system is obtained by placing two thin films (interfaces) across a shock tube. A heavy gas (sulfur hexafluoride) occupies the space between the interfaces (the central layer of the system), while the spaces to the left and right of the central layer are filled with air. The initial roughness of the interfaces is specified as a two-mode sinusoidal perturbation. The computations are carried out using the MIMOZA code based on implicit large eddy simulation (ILES) with the Euler equations integrated on a mesh with square cells. The numerical results are compared with each other and, at M = 1.3, with experimental data.

The Effect of On-Site Potentials on Supratransmission in One-Dimensional Hamiltonian Lattices.

We investigated a class of one-dimensional (1D) Hamiltonian N-particle lattices whose binary interactions are quadratic and/or quartic in the potential. We also included on-site potential terms, frequently considered in connection with localization phenomena, in this class. Applying a sinusoidal perturbation at one end of the lattice and an absorbing boundary on the other, we studied the phenomenon of supratransmission and its dependence on two ranges of interactions, 0<α<∞ and 0<β<∞, as the effect of the on-site potential terms of the Hamiltonian varied. In previous works, we studied the critical amplitude As(α,Ω) at which supratransmission occurs, for one range parameter α, and showed that there was a sharp threshold above which energy was transmitted in the form of large-amplitude nonlinear modes, as long as the driving frequency Ω lay in the forbidden band-gap of the system. In the absence of on-site potentials, it is known that As(α,Ω) increases monotonically the longer the range of interactions is (i.e., as α⟶0). However, when on-site potential terms are taken into account, As(α,Ω) reaches a maximum at a low value of α that depends on Ω, below which supratransmission thresholds decrease sharply to lower values. In this work, we studied this phenomenon further, as the contribution of the on-site potential terms varied, and we explored in detail their effect on the supratransmission thresholds.

Benefiting from information‐rich multi‐frequency AC voltammetry coupled with chemometrics on the example of on‐line monitoring of leveler component of electroplating bath

AbstractSimultaneous application of multiple sinusoidal waveforms perturbations superimposed onto DC staircase step significantly enriches current response. The measured current is characterized by a matrix of data rather than a conventional voltammetric output in a form of a vector. This increase of the dimensionality of the current response and therefore the wealth of analytical information is achieved without compromising the time of analysis. The natural approach for compression of such data and extraction of relevant information is by utilizing multi‐way chemometric decomposition techniques. An electroplating solution presents a very challenging analyte for electroanalysis as its constituents interact synergistically with each other during both the plating process and its simulation during electroanalysis. For some components the mechanism is not entirely understood. Therefore, the only way to benefit from the analytical data is by employing soft modeling. The electrode processes involving additives rely heavily on adsorption and, indirectly, on electron transfer kinetics for which AC voltammetry is an analytical technique capable of delivering informative signals. This paper presents a rigorous universal method for calculating and validating an exemplary multi‐way calibration of a leveler component in a copper electroplating bath used in the semiconductor industry. The method presented employs comparatively Parallel Factor Analysis coupled with Inverse Least Squares Regression and multi‐linear Partial Least Squares. The calibration training set consists of multi‐frequency AC voltammetric data subjected to pretreatments aiming to select informative independent variables and exclude outliers.

Behaviour and onset of low-dimensional chaos with a periodically varying loss in single-mode homogeneously broadened laser

Abstract In this work, we numerically study the behaviour of the single-mode homogeneously broadened laser versus a large perturbation of the steady state. Periodic behaviour develops for suitable values of the ratio of the population decay rates ℘ \wp , which has been analytically predicted by the analytical approach developed in the previous works, and for a pumping parameter 2 C 2C situated below and above the instability threshold 2 C 2 th 2{C}_{2{\rm{th}}} . We here show that the adiabatic elimination of the polarisation with sinusoidal time-dependent perturbation of the cavity rate leads the single-mode homogenously broadened laser to exhibit chaotic emission, if the frequency ω \omega is equal to the natural frequency Δ P {\Delta }_{P} . Increasing the pumping parameter 2 C 2C , the laser undergoes a period-doubling sequence. This cascade of period doubling drives the laser towards chaos. We also propose a reformulation of our analytical procedure, which describes the self-pulsing regime of the single-mode homogeneously broadened laser. We here report that asymmetric aspect that appears in the time evolution of the electric field is due to phase effects between the electric field components.

Transient wave-leak interaction analysis for improved leak detection in viscoelastic pipelines

Transient wave reflection methods (TWRMs) have exhibited favorable capability in leak detection for elastic pipelines, but applications have demonstrated their relatively low accuracy for viscoelastic pipelines. This paper investigates the transient wave behaviour, the principal tenet for leak detection by TWRMs, in a leaky viscoelastic pipeline to understand the mechanism of wave modification by leaks and viscoelasticity. Based on the correspondence principle, this research derives analytical formulations of the leak-induced wave reflection and phase difference at any measurement point in a viscoelastic pipe. According to the measured reflection coefficient, an optimization algorithm is further developed to detect the leak. The methodologies are then assessed and discussed through sinusoidal and sigmoid perturbations in numerical and laboratory tests. The extensive analyses indicate that measurement distance and leak ratio affect the magnitude of the reflected wave, yet, the wave phase shift is relatively independent of the leak ratio for practical applications.

Pattern formation and front stability for a moving-boundary model of biological invasion and recession

We investigate pattern formation in a two-dimensional (2D) Fisher–Stefan model, which involves solving the Fisher–KPP equation on a compactly-supported region with a moving boundary. The boundary evolves analogously to the classical one-phase Stefan problem, such that boundary speed is proportional to the local population density gradient. By combining the Fisher–KPP and classical Stefan theory, the Fisher–Stefan model alleviates two limitations of the Fisher–KPP equation for biological populations. Unlike the Fisher–KPP equation, solutions to the Fisher–Stefan model have compact support, explicitly defining the region occupied by the population. Furthermore, the Fisher–Stefan model admits travelling wave solutions with non-negative density for all wave speeds c∈(−∞,∞), and can thus model both population invasion and population recession. In this work, we investigate whether the 2D Fisher–Stefan model predicts pattern formation, by analysing the linear stability of planar travelling wave solutions to sinusoidal transverse perturbations. Planar fronts of the Fisher–KPP equation are linearly stable. Similarly, we demonstrate that invading planar fronts (c>0) of the Fisher–Stefan model are linearly stable to perturbations of all wave numbers. However, our analysis demonstrates that receding planar fronts (c<0) of the Fisher–Stefan model are linearly unstable for all wave numbers. This is analogous to unstable solutions for planar solidification in the classical Stefan problem. Introducing a surface tension regularisation stabilises receding fronts for short-wavelength perturbations, giving rise to a range of unstable modes and a most unstable wave number. We supplement linear stability analysis with level-set numerical solutions that corroborate theoretical results. Overall, front instability in the Fisher–Stefan model suggests a new mechanism for pattern formation in receding biological populations.

Heaving foil propulsion performance under combined base and perturbation signal inputs

The thrust variation, efficiency, and wake evolution of a flapping foil were investigated for a variety of base and perturbation frequencies. The study was inspired by the complex environment in which fish swim. In this numerical study, the waveform of the perturbation signal was adjusted by the waveform parameter k. The results demonstrate that the addition of perturbations increases thrust in the majority of cases, with square wave perturbations having the most substantial effect. However, the addition of a perturbation signal reduces the propulsion efficiency; a square wave perturbation significantly reduces the propulsion efficiency, while a sinusoidal or approximate sawtooth wave perturbation slightly decrease the propulsion efficiency. The change in the wake structure is closely related to the perturbation signal waveform, base frequency magnitude, and perturbation frequency magnitude, according to the wake structure analysis. The present work provides useful findings for optimizing underwater vehicle motion parameters.

Thermoacoustic response of fully compressible counterflow diffusion flames to acoustic perturbations

The goal of this research is to study the thermoacoustic response of diffusion flames due to their relevance in applications such as rocket engines. An in-house code is extended to solve the fully compressible counterflow diffusion flame equations, allowing for a spatially- and temporally-varying pressure field. Various hydrogen-air flames with a range of strain rates are simulated using detailed chemistry. After introducing sinusoidal pressure perturbations at the inlet, the gain and phase of various quantities of interest are extracted. As the frequency is increased, the gain of the temperature source term transitions from the perturbed steady flamelet value to a first plateau at intermediate frequencies, and finally to a second plateau at the highest frequencies. At these high frequencies, the gain of the integrated heat release decays to zero, underscoring the importance of compressibility. These three regimes can be identified and explained through a linearization and frequency domain analysis of the governing equations. The validity of the low Mach number assumption and importance of detailed chemistry are assessed.

Surface instability of sheared active skeletal muscle tissue with loss of muscle mass

In the present work, we study the surface instability of the wrinkling kind for the active-elastic skeletal muscle tissue subject to shear when the tissues are modeled by the mixture active strain approach. We consider two different models for the strain energy density functions, one as a sum of an incompressible neo-Hookean for the isotropic tissue constituents with the shear modulus μ and the anisotropic standard reinforcing model with the fiber stiffness E, and the other as a sum of the Gent material as an isotropic part and a function of the anisotropic variant I4 to model the anisotropic part. In both models, we introduce the activation parameter γ which describes the microstructural degree of contraction of the muscle. With the help of incremental deformation over the equations of equilibrium and incremental boundary conditions in the form of sinusoidal perturbations, we investigate the solutions for the surface instabilities of the wrinkling kind. First, we show that the critical amount of shear for instability, Kcr, decreases with an increasing E/μ ratio for the first model and the surface loses its stability with an increase in γ for a given E/μ ratio up to that angle Φ between the fibers and the direction of shear at which Kcr abruptly drops to a very low value for γ=0. For the second model, we find that Kcr increases with an increase in limiting chain extensibility of the Gent model and it either increases or almost remains constant with an increase in γ. Then we also introduce a decay deformation tensor involving a dimensionless parameter g into the multiplicative decomposition of the deformation gradient tensor, which helps model the loss of muscle mass during sarcopenia. We find that Kcr is almost independent with an increase in g for the first model but decreases with the increase in g for the second model for most Φ’s. Based on our results, we suggest that the second model is more compatible with the intuitive reasoning that the stability of the skeletal muscle surface should decrease with an increase in the loss of muscle mass.

Nonlinear fractional diffusion model for space-time neutron dynamics

In this work, a new fractional multidimensional neutron diffusion model is introduced using Cattaneo equation instead of the commonly used Fick's law for two neutron energy groups. The model represents a coupled system of nonlinear hyperbolic fractional partial differential equations considering finite fast and finite thermal neutron velocities. The model provides new quantities that relate some of the most important nuclear parameters together producing some newly physical concepts. These quantities include fast and thermal neutron relaxation times, Riemann-Liouville fractional integrals of the neutron densities and derivatives of macroscopic absorption cross sections. This model can be useful for mathematicians and physicists since the anomalous subdiffusion process describes the neutron movement closer to reality. The effect of the anomalous subdiffusion exponent (0<γ≤1) on the neutron flux is discussed. The model is successfully applied to simple homogenous and heterogonous reactor cores with step, ramp and sinusoidal perturbations for different values ofγ to estimate the average reactor powers in the fuel and moderator regions. Also, the new fractional model is applied to LRA BWR benchmark problem including adiabatic heating and Doppler feedback. On the other hand and based on the concept of prompt jump, the proposed fractional model is simplified and then analytically solved using Mittag-Liffler function. Solving fractional models numerically consumes considerable computational time costs due to the persistent memory of fractional operators, especially for smaller values of γ. For this regard, adaptively multi-step differential transform MDTM method is implemented to solve the proposed fractional model. The MDTM is developed using step size control technique for which the length of the step integration varies according to the solution behaviour.

Structural stability of a lightsail for laser-driven interstellar flight

The structural stability of a lightsail under the intense laser flux necessary for interstellar flight is studied analytically and numerically. A sinusoidal perturbation is introduced into a two-dimensional thin-film sail to determine if the sail remains stable or if the perturbations grow in amplitude. A perfectly reflective sail material that gives specular reflection of the laser illumination is assumed in determining the resulting loading on the sail, although other reflection models can be incorporated as well. The quasi-static solution of the critical point between shape stability and instability is found by equating the bending moments induced on the sail due to radiation pressure with the restoring moments caused by the strength of the sail material and the tension applied at the edges of the sail. From this quasi-static solution, analytical expressions for the critical value of elastic modulus and boundary tension magnitude are found as a function of sail properties (e.g., thickness) and the amplitude and wave number of the initial sinusoidal perturbation. These same expressions are also derived from a more formal variational energy (virtual work) approach. A numerical model of the complete lightsail dynamics is developed by discretizing the lightsail into rectangular finite elements. By introducing torsional and rectilinear springs between the elements into the numerical model, a hierarchy of models is produced that can incorporate the effects of bending and applied tension. The numerical models permit the transient dynamics of a perturbed lightsail to be compared to the analytic results of the quasi-static analysis, visualized as stability maps that show the rate of perturbation growth as a function of sail thickness, elastic modulus, and applied tension. The analytic theory is able to correctly predict the stability boundary found in the numerical simulations. The stiffness required to make a thin lightsail stable against uncontrolled perturbation growth appears to be unfeasible for known materials, however, a relatively modest tensioning of the sail (e.g., via an inflatable structure or spinning of the sail) is able to maintain the sail shape under all wavelengths and amplitudes of perturbations.

Resonance in the flow past a highly confined circular cylinder

A three-dimensional direct numerical simulation is carried out to investigate the response of the flow past a highly confined circular cylinder to single-mode sinusoidal perturbations. The Reynolds number is fixed at 1000, and the blockage ratio (the ratio of the cylinder diameter to the distance between two lateral walls) is fixed at 0.6. Local perturbations are introduced upstream of the cylinder at normalized excitation frequencies (fe/f0) from 0.2 to 3.4, where f0 is the vortex shedding frequency in an unperturbed flow. It is observed that the vortex shedding frequency of the perturbed flows (fs) and the excitation frequency (fe) are locked-on in four distinct modes including fs = 2.0fe, fs = 1.5fe, fs = 1.0fe, and fs = 0.5fe, respectively. Among them, the fundamental lock-on with fs = 0.5fe appears over a wide range of excitation frequencies (fe/f0 = 1.4–2.8). By contrast, only the fundamental lock-on regime of fs = 0.5fe is observed when perturbing an unconfined flow at the same Reynolds number, highlighting the significant impact of confinement on the lock-on behavior. It is further revealed that the lock-on behavior is controlled by the responses of separated shear layers in the near wake, which switch from higher modes to lower modes with increasing excitation frequency in the confined flow.

Generalized multistability and its control in a laser.

We revisit the laser model with cavity loss modulation, from which evidence of chaos and generalized multistability was discovered in 1982. Multistability refers to the coexistence of two or more attractors in nonlinear dynamical systems. Despite its relative simplicity, the adopted model shows us how the multistability depends on the dissipation of the system. The model is then tested under the action of a secondary sinusoidal perturbation, which can remove bistability when a suitable relative phase is chosen. The surviving attractor is the one with less dissipation. This control strategy is particularly useful when one of the competing attractors is a chaotic attractor.

Sinusoidal Optic Flow Perturbations Reduce Transient but Not Continuous Postural Stability: A Virtual Reality-Based Study

Optic flow perturbations induced by virtual reality (VR) are increasingly used in the rehabilitation of postural control and gait. Here, VR offers the possibility to decouple the visual from the somatosensory and vestibular system. By this means, it enables training under conflicting sensorimotor stimulation that creates additional demands on sensory reweighting and balance control. Even though current VR-interventions still lack a well-defined standardized metric to generate optic flow perturbations that can challenge balance in a repeatable manner, continuous oscillations of the VR are typically used as a rehabilitation tool. We therefore investigated if continuous sensory conflicts induced by optic flow perturbations can challenge the postural system sustainably. Eighteen young adults (m = 8, f = 10, age = 24.1 ± 2.0 yrs) were recruited for the study. The VR was provided using a state-of-the-art head-mounted display including the virtual replica of the real environment. After familiarization in quiet stance without and with VR, bipedal balance was perturbed by sinusoidal rotations of the visual scenery in the sagittal plane with an amplitude of 8° and a frequency of 0.2 Hz. Postural stability was quantified by mean center of mass speed derived from 3D-kinematics. A rmANOVA found increased postural instability only during the first perturbation cycle, i.e., the first 5 s. Succeeding the first perturbation cycle, visual afferents were downregulated to reduce the destabilizing influence of the sensory conflicts. In essence, only the transient beginning of sinusoidal oscillation alters balance compared to quiet standing. Therefore, continuous sinusoidal optic flow perturbations appear to be not suitable for balance training as they cannot trigger persisting sensory conflicts and hence challenge the postural system sustainably. Our study provides rationale for using unexpected and discrete optic flow perturbation paradigms to induce sustainable sensory conflicts.

Studying the Richtmyer–Meshkov instability in convergent geometry under high energy density conditions using the Decel platform

The “Decel” platform at Sandia National Laboratories investigates the Richtmyer–Meshkov instability (RMI) in converging geometry under high energy density conditions [Knapp et al., Phys. Plasmas 27, 092707 (2020)]. In Decel, the Z machine magnetically implodes a cylindrical beryllium liner filled with liquid deuterium, launching a converging shock toward an on-axis beryllium rod machined with sinusoidal perturbations. The passage of the shock deposits vorticity along the Be/D2 interface, causing the perturbations to grow. In this paper, we present platform improvements along with recent experimental results. To improve the stability of the imploding liner to the magneto Rayleigh–Taylor instability, we modified its acceleration history by shortening the Z electrical current pulse. Next, we introduce a “split rod” configuration that allows two axial modes to be fielded simultaneously in different axial locations along the rod, doubling our data per experiment. We then demonstrate that asymmetric slots in the return current structure modify the magnetic drive pressure on the surface of the liner, advancing the evolution on one side of the rod by multiple ns compared to its 180° counterpart. This effectively enables two snapshots of the instability at different stages of evolution per radiograph with small deviations of the cross-sectional profile of the rod from the circular. Using this platform, we acquired RMI data at 272 and 157 μm wavelengths during the single shock stage. Finally, we demonstrate the utility of these data for benchmarking simulations by comparing calculations using ALEGRA MHD and RageRunner.