Order Unity Research Articles

An exact solution of the lubrication equations for the Oldroyd-B model in a hyperbolic pipe

An exact analytical solution of the lubrication equations for the steady, isothermal, incompressible flow of a viscoelastic Oldroyd-B fluid in a hyperbolic cylindrical contracting pipe is derived. The solution is valid for values of the Deborah number, De, up to order unity (De is defined as the ratio of the longest relaxation time of the polymer to the characteristic residence time of the fluid in the pipe), all values of the ratio of the polymer viscosity to the total viscosity of the fluid, η, and typical values of the contraction ratio, Λ, encountered in experiments and practical applications. It is provided in terms of the streamfunction only and is used in the momentum balance to derive a strongly non-linear ordinary differential equation of second order with unknown a function which corresponds to a modified fluid velocity along the main flow direction. The final equation is solved semi-numerically using a fully spectral (Legendre)-Galerkin approach to resolve the unknown function almost down to machine accuracy. The exact solution for the polymer extra-stresses, which is emphasized is not the full solution of the complete lubrication equations, allows for the derivation of a variety of theoretical expressions for the average pressure-drop along the pipe. In all cases, a decrease in the pressure drop compared to the Newtonian value with increasing De, η and/or Λ is predicted. The differences between the corresponding analytical solution for the planar geometrical configuration are also identified and discussed.

Free movement of a near-wall particle in fluid of comparable density

The fundamental problem of nonlinear interaction between a freely moving particle and surrounding fluid flow is investigated for a density ratio of order unity, with potential applications to biomedical, environmental, and aerodynamic configurations. The interaction takes place near a fixed wall, with the particle being relatively thin. A mathematical model is presented, showing the fluid pressure forces to be dominant over the mass-acceleration effects in the particle motion (in contrast with previous analyses). The added mass due to the fluid motion, thus, greatly exceeds the body mass. Numerical simulations and asymptotic analysis reveal a range of possible particle motions. The main properties emerging are: (a) the distinction between collisions with the wall and fly-away responses; (b) the time scales involved in such behaviors; (c) the pressures and velocities induced at collision; (d) the occurrence of flow reversal in certain cases; and (e) the results being independent of the particle mass and moment of inertia as well as independent of the density ratio provided that the ratio is of order unity (0–7, say) or only slightly larger (8–30, say).

Symmetry and structure in the “Generalized Plasma Focus problem”

The “Generalized Plasma Focus problem” refers to a generic class of plasma propagation phenomena that share many features of a dense plasma focus device. Its recent theoretical development has been shown to predict some features of the pinch phase in PF-1000 and POSEIDON. The theory attempts to decompose the plasma propagation problem into two weakly interdependent subproblems. This is achieved by expressing every physical variable of an applicable continuum model of the plasma as the product of a scaling parameter, which contains device-related information and represents its numerical magnitude, and a scaled variable that is devoid of device-related information, is of order unity, and represents the spatiotemporal structure of that variable. The first subproblem seeks a traveling surface of revolution whose local normal velocity equals the scaling parameter for velocity and is aligned with the magnetic force density. Spatiotemporal distributions of all the scaled variables must move along with this reference surface by definition. This paper explores the resulting scaling theory and its symmetry properties. A new coordinate transformation results in a formula for the spatiotemporal distribution of the magnetic field of the curved and non-steady plasma sheath. New insights into the snowplow effect are obtained. A current sheath with a rear boundary exists only when the current is decreasing and only when the current carrying plasma is less dense than the fill gas. The current sheath thickness is the same for small and large devices. The geomagnetic flux compression problem has an exact solution.

Magnetically Driven Turbulence in the Inner Regions of Protoplanetary Disks

Given the important role turbulence plays in the settling and growth of dust grains in protoplanetary disks, it is crucial that we determine whether these disks are turbulent and to what extent. Protoplanetary disks are weakly ionized near the midplane, which has led to a paradigm in which largely laminar magnetic field structures prevail deeper in the disk, with angular momentum being transported via magnetically launched winds. Yet, there has been little exploration of the precise behavior of the gas within the bulk of the disk. We carry out 3D, local shearing box simulations that include all three low-ionization effects (ohmic diffusion, ambipolar diffusion, and the Hall effect) to probe the nature of magnetically driven gas dynamics 1–30 au from the central star. We find that gas turbulence can persist with a generous yet physically motivated ionization prescription (order unity Elsässer numbers). The gas velocity fluctuations range from 0.03 to 0.09 of the sound speed c s at the disk midplane to ∼c s near the disk surface, and are dependent on the initial magnetic field strength. However, the turbulent velocities do not appear to be strongly dependent on the field polarity, and thus appear to be insensitive to the Hall effect. The midplane turbulence has the potential to drive dust grains to collision velocities exceeding their fragmentation limit, and likely reduces the efficacy of particle clumping in the midplane, though it remains to be seen if this level of turbulence persists in disks with lower ionization levels.

Complete quasilinear model for the acceleration-driven lower hybrid drift instability and a computational assessment of its validity.

A complete quasilinear model is derived for the electrostatic acceleration-driven lower hybrid drift instability in a uniform two-species low-beta plasma in which current is perpendicular to the background magnetic field. The model consists of coupled nonlinear velocity space diffusion equationsfor the volume-averaged ion and electron distribution functions. Each species' diffusion coefficient depends on a time-evolving spectral density of the electric-field energy per unit volume and a time-evolving dispersion relation. The dispersion relation is expressed analytically in integral form without the use of asymptotic limits and applies to arbitrary distribution functions, so long as they can be expressed as a function of one velocity coordinate, e.g., f(v_{y}) or f(v_{⊥}). The quasilinear model conserves energy and is complete in that it fully describes the evolution of the distribution functions, including resonant and nonresonant particle-wave interactions, while accounting for distribution-function-dependent mixed-complex frequencies. The quasilinear diffusion model is solved numerically and self-consistently using a Crank-Nicolson temporal discretization and a second-order finite-volume velocity-space discretization. Numerical solutions are compared to nonlinear fourth-order accurate continuum kinetic Vlasov-Poisson simulations. Evolution of electric-field energy, growth rates, distribution functions, and diffusion coefficients are shown to be in agreement with Vlasov simulations. The quasilinear model is shown to predict anomalous transport terms, like resistivity and heating, to within a factor of order unity. Discrepancies between the quasilinear model and Vlasov simulations are assessed and attributed primarily to lack of damping in the quasilinear description and to the use of unperturbed-orbit susceptibilities in the linear theory dispersion relation. The results illuminate the predictive accuracy of the quasilinear model, place approximate bounds on its validity, and provide much needed vetting of quasilinear theory's ability to predict the nonlinear state of a microturbulent plasma.

Soiling, cleaning, and abrasion: The results of the 5-year photovoltaic glass coating field study

External contamination (“soiling”) of the incident surface is a major limiting factor for solar technologies. A 5-year field glass coupon study was conducted to better understand external contamination and its effects; compare cleaning methods and the use of preventative coatings; and explore the abrasion resulting from cleaning to advise on accelerated abrasion testing. Test sites included the cities of Dubai (UAE), Kuwait City (Kuwait), Mesa (AZ), Mumbai (India), and Sacramento (CA). Through the 5-year cumulative study, dry brush, water spray, and wet sponge and squeegee cleaning methods were compared to no cleaning. Optical microscopy was used to obtain images, including representative color images, grayscale images for object analysis, and oblique images for coating integrity assessment. A thresholding protocol was developed to analyze and distinguish specimens using the ImageJ software. Optical performance was quantified using a spectrophotometer, including comprehensive optical characterization (transmittance, reflectance, and absorptance in addition to forward- and back-scattering). Atomic force microscopy was used to verify the abrasion damage morphology, including the width and depth of surface scratches. Analysis of the results included correlation of optical performance and particle area coverage, rank order (by coating or location), and the acceleration factor for abrasion damage. The efficacy of external cleaning was more readily distinguished from the effectiveness of antisoiling coatings. The acceleration factor for dry brush cleaning of a porous silica coating was found to be on the order of unity.

Chain-Length Dependence of Peptide-Lipid Bilayer Interaction Strength and Binding Kinetics: A Combined Theoretical and Experimental Approach.

Physical interactions between polypeptide chains and lipid membranes underlie critical cellular processes. Yet, despite fundamental importance, key mechanistic aspects of these interactions remain elusive. Bulk experiments have revealed a linear relationship between free energy and peptide chain length in a model system, but does this linearity extend to the interaction strength and to the kinetics of lipid binding? To address these questions, we utilized a combination of coarse-grained molecular dynamics (CG MD) simulations, analytical modeling, and atomic force microscopy (AFM)-based single molecule force spectroscopy. Following previous bulk experiments, we focused on interactions between short hydrophobic peptides (WLn, n = 1, ..., 5) with 1-palmitoyl-2-oleoyl-glycero-3-phosphocholine (POPC) bilayers, a simple system that probes peptide primary structure effects. Potentials of mean force extracted from CG MD recapitulated the linearity of free energy with the chain length. Simulation results were quantitatively connected to bulk biochemical experiments via a single scaling factor of order unity, corroborating the methodology. Additionally, CG MD revealed an increase in the distance to the transition state, a result that weakens the dependence of the dissociation force on the peptide chain length. AFM experiments elucidated rupture force distributions and, through modeling, intrinsic dissociation rates. Taken together, the analysis indicates a rupture force plateau in the WLn-POPC system, suggesting that the final rupture event involves the last 2 or 3 residues. In contrast, the linear dependence on chain length was preserved in the intrinsic dissociation rate. This study advances the understanding of peptide-lipid interactions and provides potentially useful insights for the design of peptides with tailored membrane-interacting properties.

The three-dimensional structure of black hole accretion flows within the plunging region

ABSTRACT We analyse, using new analytical models and numerical general relativistic magnetohydrodynamic simulations, the three-dimensional properties of accretion flows inside the plunging region of black hole spacetimes (i.e. at radii smaller than the innermost stable circular orbit). These simulations are of thick discs, with aspect ratios of order unity $h/r \sim 1$, and with a magnetic field geometry given by the standard low-magnetization ‘SANE’ configuration. This work represents the first step in a wider analysis of this highly relativistic region. We show that analytical expressions derived in the ‘thin disc’ limit describe the numerical results remarkably well, despite the large aspect ratio of the flow. We further demonstrate that accretion within this region is typically mediated via spiral arms, and that the geometric properties of these spiral structures can be understood with a simple analytical model. These results highlight how accretion within the plunging region is fundamentally two-dimensional in character, which may have a number of observational implications. We derive a modified theoretical description of the pressure within the plunging region which accounts for turbulent heating and may be of use to black hole image modelling.

Investigation of the Gamma-Ray Bursts Prompt Emission Under the Relativistically Expanding Fireball Scenario

The spectral properties of a composite thermal emission arising from a relativistic expanding fireball can be remarkably different from the Planck function. We perform a detailed study of such a system to explore the features of the prompt emission spectra from gamma-ray bursts (GRBs). In particular, we address the effect of optical opacity and its dependence on the density profile between the expanding gas and the observer. This results in a nontrivial shape of the photospheric radius, which in combination with the constraints derived from the equal arrival time can result in a mild broader spectrum compared to the Planck function. Further, we show the time-integrated spectrum from the expanding fireball deviates significantly from the instantaneous emission and is capable of explaining the observed broad spectral width of GRBs. We also show that the demand of the spectral width of the order of unity, obtained through statistical analysis, is consistent with the scenario where the dynamics of the expanding fireball are governed predominantly by the energy content of the matter.

Calculation of toroidal Alfvén eigenmode mode structure in general axisymmetric toroidal geometry

A workflow is developed based on the ideal MHD model to investigate the linear physics of various Alfvén eigenmodes in general axisymmetric toroidal geometry by solving the coupled shear Alfvén wave (SAW) and ion sound wave (ISW) equations in ballooning space. The model equations are solved by the FALCON code in the singular layer, and the corresponding solutions are then taken as the boundary conditions for calculating parallel mode structures in the whole ballooning space. As an application of the code, the frequencies and mode structures of toroidal Alfvén eigenmode (TAE) are calculated in the reference equilibria of the Divertor Tokamak Test facility with positive and negative triangularities, respectively. As typical result for reactor relevant plasma conditions, which are strongly triangular in the outer core region where magnetic shear is of order unity, we show that the triangularity effect on TAE is generally small. Furthermore, by properly handling the boundary conditions, we demonstrate finite TAE damping due to coupling with the local acoustic continuum and find that the damping rate is small for typical plasma parameters.

Effects of surface tension on the collapse time of an empty bubble

The collapse of an empty spherical bubble in an ideal liquid, in the absence of viscosity and surface tension, was studied by Lord Rayleigh. Using energy conservation, he derived an exact expression for the total collapse time as a function of the initial radius of the bubble, the density of the liquid, and the far-field pressure. In the present work, we extend Rayleigh's expression to include surface tension effects. Results are found to depend on a dimensionless parameter ϵ that measures the ratio between the work done by surface tension and that done by pressure during the collapse. This parameter is small for large bubbles but can be of order unity or larger for bubbles of small radius and, eventually, small pressure. We show that the ratio between the collapse time in the presence of surface tension and Rayleigh's collapse time is proportional to a definite integral that is a smooth, monotonically decreasing function of ϵ. This function can be easily bounded analytically for any value of ϵ, yielding a simple and accurate approximation for the collapse time that, for all practical purposes, provides a complete analytical solution to the problem at hand. We finally extend results to the case of a hyperspherical collapsing empty bubble.

Luminous giants populate the dense Cosmic Web

Context. Giant radio galaxies (GRGs, giant RGs, or giants) are megaparsec-scale, jet-driven outflows from accretion disks of supermassive black holes, and represent the most extreme pathway by which galaxies can impact the Cosmic Web around them. A long-standing but unresolved question is why giants are so much larger than other radio galaxies. Aims. It has been proposed that, in addition to having higher jet powers than most RGs, giants might live in especially low-density Cosmic Web environments. In this work, we aim to test this hypothesis by pinpointing Local Universe giants and other RGs in physically principled, Bayesian large-scale structure reconstructions. Methods. More specifically, we localised a LOFAR Two-metre Sky Survey (LoTSS) DR2–dominated sample of luminous (lν(ν = 150 MHz)≥1024 W Hz−1) giants and a control sample of LoTSS DR1 RGs, both with spectroscopic redshifts up to zmax = 0.16, in the BORG SDSS Cosmic Web reconstructions. We measured the Cosmic Web density on a smoothing scale of ∼2.9 Mpc h−1 for each RG; for the control sample, we then quantified the relation between RG radio luminosity and Cosmic Web density. With the BORG SDSS tidal tensor, we also measured for each RG whether the gravitational dynamics of its Cosmic Web environment resemble those of clusters, filaments, sheets, or voids. Results. For both luminous giants and general RGs, the Cosmic Web density distribution is gamma distribution–like. Luminous giants populate large-scale environments that tend to be denser than those of general RGs. This result is corroborated by gravitational dynamics classification and a cluster catalogue crossmatching analysis. We find that the Cosmic Web density around RGs with 150 MHz radio luminosity lν is distributed as 1 + ΔRG | Lν = lν ∼ Γ(k, θ), where k = 4.8 + 0.2 · √, θ = 1.4 + 0.02 · √, and √:= log10(lν (1023 W Hz−1)−1). Conclusions. This work presents more than a thousand inferred megaparsec-scale densities around radio galaxies, which may be correct up to a factor of order unity – except in clusters of galaxies, where the densities can be more than an order of magnitude too low. We pave the way to a future in which megaparsec-scale densities around RGs are common inferred quantities, which help to better understand their dynamics, morphology, and interaction with the enveloping Cosmic Web. Our data demonstrate that luminous giants inhabit denser environments than general RGs. This shows that – at least at high jet powers – low-density environments are no prerequisite for giant growth. Using general RGs, we quantified the relation between radio luminosity at 150 MHz and Cosmic Web density on a smoothing scale of ∼2.9 Mpc h−1. This positive relation, combined with the discrepancy in radio luminosity between known giants and general RGs, reproduces the discrepancy in Cosmic Web density between known giants and general RGs. Our findings are consistent with the view that giants are regular, rather than mechanistically special, members of the radio galaxy population.

Mechanical structure of the nucleon and the baryon octet: twist-2 case

We investigate the gravitational form factors (GFFs) of the nucleon and the baryon octet, decomposed into their flavor components, utilizing a pion mean-field approach grounded in the large Nc limit of Quantum Chromodynamics (QCD). Our focus is on the contributions from the twist-2 operators to the flavor-triplet and octet GFFs, and we decompose the mass, angular momentum, and D-term form factors of the nucleon into their respective flavors. The strange quark contributions are found to be relatively mild for the mass and angular momentum form factors, while providing significant corrections to the D-term form factor. In the course of examining the flavor decomposition of the GFFs, we uncover that the effects of twist-4 operators play a crucial role. While the gluonic contributions are suppressed by the packing fraction of the instanton vacuum in the twist-2 case, contributions from twist-4 operators are of order unity, necessitating its explicit consideration.

Species Scale and Primordial Gravitational Waves

AbstractThe species scale is a field‐dependent UV cut‐off for any effective field theory weakly coupled to gravity. In this letter, it is shown that in the context of inflationary cosmology, a detection of primordial gravitational waves will set an upper bound on the decay rate of the species scale. Specifically, this is derived in terms of the tensor‐to‐scalar ratio of power spectra of primordial perturbations. Given the targets of current and next generation experiments, it is shown that any successful detection would signify that this upper limit is of the order of unity, which is consistent with recent discussions in the literature.

Effect of near-wall distance on velocity slip and temperature jump conditions in hypersonic rarefied gas flows

In nonequilibrium slip and jump conditions, normal gas velocity and temperature gradients are used to calculate the gas slip velocity and temperature at the surface, respectively. Gökçen et al. (Computational fluid dynamics near the continuum limit, AIAA Paper No. 87-1115, 1987, and Gökçen and MacCormack, Nonequilibrium effects for hypersonic transitional flows using continuum approach, AIAA Paper No. 89-0461, 1989) stated that the tangential velocity and temperature of the gas molecules before a collision with the surface could be interpreted as the macroscopic tangential velocity and temperature of the gas molecules at the so-called near-wall distances auλ and aTλT away from the surface, respectively. The coefficients au and aT are the order of unity. In the present work, new forms of the slip and jump conditions are proposed by modifying the Gökçen slip and jump conditions to include the coefficients (au, aT). Numerical investigations are comprehensively conducted to determine the numerically proper values (au, aT) for the hypersonic rarefied gas flows. Cases such as the circular cylinder in cross-flow and sharp and blunted leading edge wedge are considered in the present work, with nitrogen as the working gas. The simulation results show the significant effects of the coefficients (au, aT) on the accuracy of the slip velocity and surface gas temperature predictions, and the values of au = 1.2 and aT = 1.1 show good agreement with the direct simulation Monte Carlo data.

Effective Hamiltonian approach to kinetic Ising models: Application to an infinitely long-range Husimi-Temperley model.

The probability distribution (PD) of spin configurations in kinetic Ising models has been cast in the form of the canonical Boltzmann PD with a time-dependent effective Hamiltonian (EH). It has been argued that in systems with extensive energy EH depends linearly on the number of spins N leading to the exponential dependence of PD on the system size. In macroscopic systems the argument of the exponential function may reach values of the order of the Avogadro number which is impossible to deal with computationally, thus making unusable the linear master equation (ME) governing the PD evolution. To overcome the difficulty, it has been suggested to use instead the nonlinear ME (NLME) for the EH density per spin. It has been shown that in spatially homogeneous systems NLME contains only terms of order unity even in the thermodynamic limit. The approach has been illustrated with the kinetic Husimi-Temperley model (HTM) evolving under the Glauber dynamics. At finite N the known numerical results has been reproduced and extended to broader parameter ranges. In the thermodynamic limit an exact nonlinear partial differential equationof the Hamilton-Jacobi type for EH has been derived. It has been shown that the average magnetization in HTM evolves according to the conventional kinetic mean field equation.

MRI turbulence in vertically stratified accretion discs at large magnetic Prandtl numbers

ABSTRACT The discovery of the first binary neutron star merger, GW170817, has spawned a plethora of global numerical relativity simulations. These simulations are often ideal (with dissipation determined by the grid) and/or axisymmetric (invoking ad hoc mean-field dynamos). However, binary neutron star mergers (similar to X-ray binaries and active galactic nuclei inner discs) are characterized by large magnetic Prandtl numbers, $\rm Pm$, (the ratio of viscosity to resistivity). $\rm Pm$ is a key parameter determining dynamo action and dissipation but it is ill-defined (and likely of order unity) in ideal simulations. To bridge this gap, we investigate the magnetorotational instability (MRI) and associated dynamo at large magnetic Prandtl numbers using fully compressible, three-dimensional, vertically stratified, isothermal simulations of a local patch of a disc. We find that, within the bulk of the disc (z ≲ 2H, where H is the scale-height), the turbulent intensity (parametrized by the stress-to-thermal-pressure ratio α), and the saturated magnetic field energy density, Emag, produced by the MRI dynamo, both scale as a power with Pm at moderate Pm (4 ≲ Pm ≲ 32): Emag ∼ Pm0.74 and α ∼ Pm0.71, respectively. At larger Pm (≳ 32), we find deviations from power-law scaling and the onset of a plateau. Compared to our recent unstratified study, this scaling with Pm becomes weaker further away from the disc mid-plane, where the Parker instability dominates. We perform a thorough spectral analysis to understand the underlying dynamics of small-scale MRI-driven turbulence in the mid-plane and of large-scale Parker-unstable structures in the atmosphere.

Effects of buoyancy on the dispersion of drugs released intrathecally in the spinal canal.

This paper investigates the transport of drugs delivered by direct injection into the cerebrospinal fluid (CSF) that fills the intrathecal space surrounding the spinal cord. Because of the small drug diffusivity, the dispersion of neutrally buoyant drugs has been shown in previous work to rely mainly on the mean Lagrangian flow associated with the CSF oscillatory motion. Attention is given here to effects of buoyancy, arising when the drug density differs from the CSF density. For the typical density differences found in applications, the associated Richardson number is shown to be of order unity, so that the Lagrangian drift includes a buoyancy-induced component that depends on the spatial distribution of the drug, resulting in a slowly evolving cycle-averaged flow problem that can be analysed with two-time scale methods. The asymptotic analysis leads to a nonlinear integro-differential equation for the spatiotemporal solute evolution that describes accurately drug dispersion at a fraction of the cost involved in direct numerical simulations of the oscillatory flow. The model equation is used to predict drug dispersion of positively and negatively buoyant drugs in an anatomically correct spinal canal, with separate attention given to drug delivery via bolus injection and constant infusion.

COSMOS-Web: Intrinsically Luminous z ≳ 10 Galaxy Candidates Test Early Stellar Mass Assembly

We report the discovery of 15 exceptionally luminous 10 ≲ z ≲ 14 candidate galaxies discovered in the first 0.28 deg2 of JWST/NIRCam imaging from the COSMOS-Web survey. These sources span rest-frame UV magnitudes of −20.5 > M UV > −22, and thus constitute the most intrinsically luminous z ≳ 10 candidates identified by JWST to date. Selected via NIRCam imaging, deep ground-based observations corroborate their detection and help significantly constrain their photometric redshifts. We analyze their spectral energy distributions using multiple open-source codes and evaluate the probability of low-redshift solutions; we conclude that 12/15 (80%) are likely genuine z ≳ 10 sources and 3/15 (20%) likely low-redshift contaminants. Three of our z ∼ 12 candidates push the limits of early stellar mass assembly: they have estimated stellar masses ∼ 5 × 109 M ⊙, implying an effective stellar baryon fraction of ϵ ⋆ ∼ 0.2−0.5, where ϵ ⋆ ≡ M ⋆/(f b M halo). The assembly of such stellar reservoirs is made possible due to rapid, burst-driven star formation on timescales < 100 Myr where the star formation rate may far outpace the growth of the underlying dark matter halos. This is supported by the similar volume densities inferred for M ⋆ ∼ 1010 M ⊙ galaxies relative to M ⋆ ∼ 109 M ⊙—both about 10−6 Mpc−3—implying they live in halos of comparable mass. At such high redshifts, the duty cycle for starbursts would be of order unity, which could cause the observed change in the shape of the UV luminosity function from a double power law to a Schechter function at z ≈ 8. Spectroscopic redshift confirmation and ensuing constraints of their masses will be critical to understand how, and if, such early massive galaxies push the limits of galaxy formation in the Lambda cold dark matter paradigm.

Anthropogenic Coal Ash as a Contaminant in an Underwater Search. II. Beyond Beryllium, Lanthanum, and Uranium

It has been shown that the Beryllium, Lanthanum and Uranium concentrations in the “BeLaU” spherules are in the expected ranges of coal ash. It is reported that the average elemental concentration of 12 microspherules can be found in the COALQUAL database in 98% (49/50) of the elements examined. The “BeLaU pattern” is found to be not unique, it can be reproduced using a coal ash standard (SRM1633a) and a chondritic normalization. The ratio of rare-earth elements in the “BeLaU” spherules and the SMR1633a sample is of order unity. Comparisons against SRM1633a return only two elements with abundances statistically significantly lower than the coal ash standard of reference (or fractions of order unity), agreeing in 96% (52/54) of the elements tested. No elements show higher abundance than 10× the reference standard. Terrestrial coal ash is curiously very similar to the collected spherules. Origin from a recent meteoritic event remains uncertain.