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DOE OSTI2021

Some aspects of the five-dimensional Lovelock black hole spacetime: Strong homotopy retract, perihelion precession and quasistationary levels

Highlights: • Some topological aspects are explored. • The perihelion precession is calculated. • The general Heun functions are applied to obtain analytical solutions. • The quasibound states and the radial wave eigenfunctions are obtained. In this work we explore some mathematical physics aspects of the spherically symmetric Lovelock black hole in high dimensions. Intended for this aim, we thoroughly consider the metric corresponding to the five-dimensional Lovelock black hole spacetime. We construct the strong retractions by the geodesic equations on the background under consideration. As a result, from the topological point of view, we construct the theory of strong homotopy retract, which will allow us, in principle, to better understand some of its suitable applications on astrophysics and cosmology, in particular, in the analysis of the spacetime singularities. We find the solutions of the equation of motion for both radial and angular coordinates, and then we describe the outer (“exterior”) and lower (“interior”) apparent horizons. Indeed, the outer apparent horizon is the last surface from which the light waves could still escape from the black hole. Thus, it is meaningful to analyze some physical phenomena related to quantum particles propagating outside the exterior apparent horizon, in particular, we discuss the quasistationary levels of scalar fields and their radial wave functions, which are given in terms of the general Heun functions. We also calculate the perihelion precession in this background.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

High resolution variability in wet deposition in the southeastern United States

Rainwater chemistry is determined by atmospheric pollutants and particles which vary spatially and temporally. Industrial and agricultural activities and meteorological events (e.g. sea breezes, severe weather, blowing dust) alter atmospheric particle and trace gas compositions. These gases and particles are scavenged by cloud and rain droplets that drive wet deposition. During an Intensive Operation Period (IOP) from April to October 2021, rainwater was collected at higher frequency intervals, usually daily, after precipitation events at three locations on the Savannah River Site (SRS). The farthest locations were separated by approximately 20 km. The mean concentration (μeq/L) of seven ions followed the Cl⁻ > SO 4 2− > Na⁺ > NO 3 ⁻ > K⁺ > Mg 2+ > Ca 2+ downward trend. Ion concentrations were compared to background ion concentrations from the National Atmospheric Deposition Program (NADP). The high frequency monthly averaged SRS data compared well with the monthly averaged NADP background but demonstrated extensive variability. In some months in 2021, the high frequency data compared better to the NADP site near the coast while in other months inland sites compared better. Strong spatial variability for ion concentrations was observed across SRS which was attributed to localized impacts in rainfall spatial variability. High frequency measurements allowed for comparison to regional weather patterns indicating influences from the Atlantic Ocean, Gulf of Mexico, and cities. This can account for spatial variability in the wet deposition flux. Sea breezes, Saharan dust, and anthropogenic sources were shown to impact wet deposition flux variability. Higher frequency precipitation chemistry sampling at numerous locations better captures ion concentration variability and improves measurement representativeness.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Pulsed laser synthesis of mesoporous metal chalcogenide thin films

Mesoporous films of the metal chalcogenide B-FeSe were grown on MgO substrates by KrF pulsed laser deposition (PLD) in an argon background. At 100 mTorr, gated intensified charge-coupled device imaging and ion probe measurements showed that the plasma plume responsible for crystal growth initially comprised three components, with distinct expansion velocities. Plume interactions with the substrate heater and ablation target gave rise to complex dynamics, including collisions between the charged leading edge—rebounding between the substrate and the target—and slower-moving species in the plume interior. Film growth was dominated by species with kinetic energies ≤0.5 eV/atom. X-ray reflectivity revealed that films grown in this environment—with a substrate temperature of 350 ° C, a laser fluence of 1.0 J cm −2 , and a 7.5 mm 2 spot area—formed a porous framework with 15% porosity. Atomic force microscopy showed surface features that suggest pore sizes below 100 nm. X-ray diffraction indicated that the porous films were epitaxial with respect to the substrate and likely grew by oriented-attachment of gas-phase molecular clusters or very small nanoparticles, in contrast to the conventional epitaxy of vacuum films from atomic constituents. The in-plane orientation of the mesoporous films was B-FeSe [100]||[110] MgO, attributed to the soft landing of pre-formed crystallites on the MgO substrates, where protruding Se rows of B-FeSe aligned with corrugations of the MgO surface. In conclusion, this work implies that growth of candidate electrocatalyst materials by PLD in inert gas background may allow mesoporous frameworks with a single crystallographic orientation that expose specific crystal facets for electrochemical reactions and active site engineering.

cluster epitaxy↗

DOE OSTI2021

Simulations of Events for the LUX-ZEPLIN (LZ) Dark Matter Experiment

The LUX-ZEPLIN dark matter search aims to achieve a sensitivity to the WIMP-nucleon spin-independent cross-section down to (1–2) ×10−12 pb at a WIMP mass of 40 GeV/ c 2 . This paper describes the simulations framework that, along with radioactivity measurements, was used to support this projection, and also to provide mock data for validating reconstruction and analysis software. Of particular note are the event generators, which allow us to model the background radiation, and the detector response physics used in the production of raw signals, which can be converted into digitized waveforms similar to data from the operational detector. Inclusion of the detector response allows us to process simulated data using the same analysis routines as developed to process the experimental data.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

The MIGDAL experiment: Measuring a rare atomic process to aid the search for dark matter

We present the Migdal In Galactic Dark mAtter expLoration (MIGDAL) experiment aiming at the unambiguous observation and study of the so-called Migdal effect induced by fast-neutron scattering. It is hoped that this elusive atomic process can be exploited to enhance the reach of direct dark matter search experiments to lower masses, but it is still lacking experimental confirmation. Our goal is to detect the predicted atomic electron emission which is thought to accompany nuclear scattering with low, but calculable, probability, by deploying an Optical Time Projection Chamber filled with a low-pressure gas based on CF 4 . Initially, pure CF 4 will be used, and then in mixtures containing other elements employed by leading dark matter search technologies — including noble species, plus Si and Ge. High resolution track images generated by a Gas Electron Multiplier stack, together with timing information from scintillation and ionisation readout, will be used for 3D reconstruction of the characteristic event topology expected for this process — an arrangement of two tracks sharing a common vertex, with one belonging to a Migdal electron and the other to a nuclear recoil. Different energy-loss rate distributions along both tracks will be used as a powerful discrimination tool against background events. In this article we present the design of the experiment, informed by extensive particle and track simulations and detailed estimations of signal and background rates. In pure CF 4 we expect to observe 8.9 (29.3) Migdal events per calendar day of exposure to an intense D–D (D–T) neutron generator beam at the NILE facility located at the Rutherford Appleton Laboratory (UK). With our nominal assumptions, 5σ median discovery significance can be achieved in under one day with either generator.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2026

Atmospheric pion, kaon, and muon fluxes for sub-orbital experiments

Cosmic rays interacting with the Earth's atmosphere generate extensive air showers, which produce Cherenkov, fluorescence and radio emissions. These emissions are key signatures for detection by ground-based, sub-orbital, and satellite-based telescopes aiming to study high energy cosmic ray and neutrino events. However, detectors operating at ground and balloon altitudes are also exposed to a background of atmospheric charged particles, primarily pions, kaons, and muons, that can mimic or obscure the signals from astrophysical sources. In this work, we use coupled cascade equations to calculate the atmospheric pion, kaon and muon fluxes reaching detectors at various altitudes. Our analysis focuses on energies above 10 GeV, where the influence of the Earth's magnetic field on particle trajectories is minimal. We provide angular and energy-resolved flux estimates and discuss their relevance as background for extensive air shower detection. Furthermore, our results are potentially relevant for interpreting data from current and future balloon-borne experiments such as EUSO-SPB2 and for refining trigger and veto strategies in Cherenkov and fluorescence telescopes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

A worldwide aerosol phenomenology: Elemental and organic carbon in PM 2.5 and PM 10

Elemental carbon (EC), organic carbon (OC), and particulate matter (PM) concentrations in the inhalable (PM 10 ) and fine (PM 2.5 ) size fractions are measured worldwide, albeit with different analytical methods. These measurements from many researchers were collected and analyzed for Africa, America, Asia, and Europe for 2012–2019. EC/PM, OC/PM, and OC/EC ratios were examined based on region, site type, and season to infer potential sources and impacts. These analyses demonstrate that carbonaceous materials are important PM constituents throughout the world. Mean EC/PM ratios were lowest in PM 10 in Sahelian Africa and Europe (∼0.01), highest (>0.07) in PM 2.5 at urban sites in North America, South America, and Japan. Mean OC/PM ratios were lowest in PM 10 in the Sahel (∼0.06) and in PM 2.5 in China and Thailand (0.10), and highest in central and eastern Europe (∼0.3) and North America (∼0.4). OC/EC ratios were elevated in western and northern Europe, and at regional background sites in North America. EC/PM increased with PM 10 in Thailand, while OC/PM increased with higher PM mass in Thailand, India, and North America, highlighting the specific contribution of carbonaceous aerosols to PM pollution in these regions. At European and North American background sites, OC/EC ratios increased with PM mass. Higher OC/EC ratios in dry periods indicate influence of wildfires, prescribed burns, and secondary aerosol formation. Elevated wintertime EC/PM ratios coincide with residential heating in temperate climate zones.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Characteristics of upward-connecting-leader current leading to attachment in downward negative cloud-to-ground lightning strokes

For this work, we analyzed currents associated with upward connecting leaders (UCLs) initiated from the Kennedy Space Center Industrial Area Tower in two negative cloud-to-ground strokes that struck the tower. One stroke was also recorded using a high-speed video camera located 760 m from the KSC IAT. The NLDN-reported peak currents for the two strokes were – 31.7 and – 98.5 kA. During the UCL development phase the current waveforms exhibited a monotonically (quasi-exponentially) increasing “background” current overlaid with 10-μs scale pulses with a median amplitude of 51.1 A. The UCL current durations for the two strokes were 1039 and 449 μs, respectively. During the pre-attachment processes (UCL and slow front) the total negative charge effectively transferred to ground were 70.2 and 55 mC, respectively. For the stroke captured on high-speed video, the average line-charge-density for the 109-m long UCL was found to be 0.5 mC/m. The average UCL 2-D speed was 2.4 × 10 5 m/s, and it was observed to accelerate toward the downward leader prior to attachment. We observed that UCL-pulse amplitudes are larger, background currents are higher, and interpulse intervals are shorter at later times during UCLs, which can be attributed to the intensification of the local electric field due to the approaching downward negative leader. The median positive charge injected into the UCL by a pulse was 297 μC. The UCL associated with the higher peak-current stroke produced the highest injected pulse-charge values about three times sooner during its development, likely due to the 2–2.7 times faster average downward leader vertical speeds.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Lattice light-sheet microscopy allows for super-resolution imaging of receptors in leaf tissue

Plant leaf tissues are difficult to image via fluorescent microscopy, largely due to the presence of chlorophyll and other pigments that provide large background fluorescence. An advantage of Lattice Light-Sheet microscopy is its use of Bessel beams that illuminate a thin focal region of interest for microscopy, allowing for the excitation of fluorescent molecules within this region without surrounding chlorophyll-like objects outside of the region of interest. Here, we apply STORM Super-resolution techniques to observe Receptor-Like Kinases in Arabidopsis thaliana leaf cells. By applying this technique with the Lattice Light-Sheet, we can localize immune response proteins in sub-100 nm length scales and reconstruct three-dimensional locations of proteins within individual leaf cells. Using this technique, we observed the effect of the elicitors ATP and flg22, where we observed a significant degree of internalization of cognate receptors P2K1 and FLS2. We were also able to similarly observe differences in colocalization due to stimulation with these elicitors, where we observe proteins on the membrane becoming less colocalized as a result of stimulation, suggesting an immune response mechanism involving receptors internalizing via pathways distinct to the receptor. Further, these data show the Lattice Light-Sheet’s capabilities for imaging tissue with problematic background fluorescence that otherwise makes super-resolution fluorescence microscopy difficult.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Nonlinear dynamics of combustor azimuthal modes: Experiments and modeling

This paper provides an experimental and theoretical investigation of azimuthal instabilities in a lean, premixed combustor. It presents data from a high Reynolds number, industrial-scale facility with multiple fuel stages that enable variation of radial and azimuthal symmetries. The combustor exhibits a variety of behaviors – including standing, spinning, mixed waves, and intermittent behaviors, as well as periodic limit cycles and quasi-periodic oscillations – depending upon varying power and azimuthal symmetry. A second key objective of this paper is to present a weakly nonlinear framework that is used to understand and interpret these results, showing the influence of eigenmode degeneracy, background noise, and azimuthal non-uniformities in mean quantities such as temperature and flame-acoustic coupling. In particular, this analysis shows the importance of the linear instability growth/damping rate and azimuthal non-uniformities in controlling the relative prominence of standing, spinning, or mixed waves at the limit cycle, as well as the preference in the spinning direction. It also shows the conditions under which single frequency or quasi-periodic oscillations are dominant, and how these are more fundamentally influenced by azimuthal non-uniformities and background noise.

42 ENGINEERING↗

DOE OSTI2021

Simulation of lithium transport using the BOUT++ framework

A numerical model that calculates the collisional interactions between the lithium atoms from a lithium pellet and the background plasmas has been upgraded. The ion density ($N_t$), electron temperature ($T_e$), ion temperature ($T_i$) and parallel ion velocity ($V_{∥, i}$) are used to characterize the background plasmas. The lithium atom density ($N^{a}_{Li}$) and parallel velocity ($V_{∥,a}$) of lithium atoms evolve with time. For each lithium ion, the density ($N_{Li^{n+}}$), temperature ($T_{Li^{n+}}$) and parallel velocity ($V_{∥, Li^{n+}}$) are self-consistently calculated. A C-mod lower single null equilibrium is used to generate the grid for the BOUT++ simulation. The lithium atoms can be fully ionized to $Li^{3+}$ in ~2 μs. The rapid radial and poloidal expansion of the lithium ions are found in the simulation. After the collision interaction process, the electron temperature rapidly decreases at the pellet location; then, it rapidly poloidally expands, and the temperature at the pellet location starts to recover. The electron pressure increases at the pellet location despite the decrease in electron temperature because of the extra electrons from the lithium ionization. The ion pressure profile decreases in the pellet location due to the decrease in ion temperature.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2020

Process intensification education contributes to sustainable development goals. Part 1

In 2015 all the United Nations (UN) member states adopted 17 sustainable development goals (UN-SDG) as part of the 2030 Agenda, which is a 15-year plan to meet ambitious targets to eradicate poverty, protect the environment, and improve the quality of life around the world. Although the global community has progressed, the pace of implementation must accelerate to reach the UN-SDG time-line. For this to happen, professionals, institutions, companies, governments and the general public must become cognizant of the challenges that our world faces and the potential technological solutions at hand, including those provided by chemical engineering. Process intensification (PI) is a recent engineering approach with demonstrated potential to significantly improve process efficiency and safety while reducing cost. It offers opportunities for attaining the UN-SDG goals in a cost-effective and timely manner. However, the pedagogical tools to educate undergraduate, graduate students, and professionals active in the field of PI lack clarity and focus. This paper sets out the state-of-the-art, main discussion points and guidelines for enhanced PI teaching, deliberated by experts in PI with either an academic or industrial background, as well as representatives from government and specialists in pedagogy gathered at the Lorentz Center (Leiden, The Netherlands) in June 2019 with the aim of uniting the efforts on education in PI and produce guidelines. In this Part 1, we discuss the societal and industrial needs for an educational strategy in the framework of PI. The terminology and background information on PI, as it relates to educational implementation in industry and academia, are provided as a preamble to Part 2, which presents practical examples that will help educating on Process Intensification.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Melting and phase relations of Fe-Ni-Si determined by a multi-technique approach

Many studies have suggested silicon as a candidate light element for the cores of Earth and Mercury. However, the effect of silicon on the melting temperatures of core materials and thermal profiles of cores is poorly understood, due to disagreements among melt detection techniques, uncertainties in sample pressure evolution during heating, and sparsity of studies investigating the combined effects of nickel and silicon on the phase diagram of iron. Here, in this study we develop a multi-technique approach for measuring the high-pressure melting and solid phase relations of iron alloys and apply it to Fe 0.8 Ni 0.1 Si 0.1 (Fe-11wt%Ni-5.3wt%Si), a composition compatible with recent estimates for the cores of Earth and Mercury. This approach combines results (20-83 GPa) from two atomic-level techniques: synchrotron Mossbauer spectroscopy (SMS) and synchrotron x-ray diffraction (XRD). Melting is independently detected by the loss of the Mossbauer signal, produced exclusively by solid-bound iron nuclei, and the onset of a liquid diffuse x-ray scattering signal. The use of a burst heating and background updating method for quantifying changes in the reference background during heating facilitates the determination of liquid diffuse signal onsets and leads to strong reproducibility and excellent agreement in melting temperatures determined separately by the two techniques. XRD measurements additionally constrain the hcp-fcc phase boundary and in-situ pressure evolution of the samples during heating. We apply our updated thermal pressure model to published SMS melting data on fcc-Fe and fcc-Fe 0.9 Ni 0.1 to precisely evaluate the effect of silicon on melting temperatures. We find that the addition of 10 mol% Si to Fe 0.9 Ni 0.1 reduces melting temperatures by ~250 K at low pressures (<60 GPa) and flattens the hcp-fcc phase boundary. Extrapolating our results, we constrain the location of the hcp-fcc-liquid quasi-triple point at 147±14 GPa and 3140±90 K, which implies a melting temperature reduction of 500 K compared with Fe 0.9 Ni 0.1 . The results demonstrate the advantages of combining complementary experimental techniques in investigations of melting under extreme conditions.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Overview of oxygen opacity experiments at the National Ignition Facility and investigation of potential systematic errors

Experiments to measure oxygen opacity at stellar interior conditions have been performed at the National Ignition Facility in a Discovery Science campaign. These experiments utilize the Opacity-on-NIF platform with a sample comprised of O, Mg, and Si. The spectral data from the Opacity Spectrometer cover the 1000–2000 eV photon energy range showing bound-free continuum absorption from O and line absorption from Mg and Si. DANTE and the Gated X-ray Detector are employed to measure the sample plasma’s temperature and density, respectively. Initial data show lower transmission than expected by theoretical models, raising questions of whether potential background or data uniformity concerns could produce systematic errors in the inferred transmission. Here, we investigate three concerns thought to be important for the oxygen opacity data, including instrumental scattered background, sample self-emission non-uniformity, and backlight continuum non-uniformity. Additionally, we show the effect of a recently developed method to account for 2nd order crystal reflection. The total effect of these concerns on one experiment is found to be small compared to the observed difference between the inferred transmission and a model calculation at the inferred temperature and density. Thus, we conclude that these potential sources of systematic error cannot account for the observed difference, increasing the likelihood of a real effect due to the high temperature and density conditions. However, because this is only a single experiment, we cannot make a firm conclusion. More experiments measuring the opacity and necessary calibrations are needed to assess the reproducibility and uncertainty of this result.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Analytical Determination of Radioactive Strontium and Cesium by Thermal Ionization Mass Spectrometry

Thermal ionization mass spectrometry (TIMS) has been evaluated for the detection of the radioactive isotopes of strontium and cesium. The instrument was investigated for the analysis of isotopic ratios of 89Sr to 90Sr and 135Cs to 137Cs in the presence of atomic isobars (Y and Zr for Sr analysis and Ba for Cs analysis). Signicant discrimination using TIMS was found for both Sr and Cs through evaluation using stable isotopes. Fusion procedures with different flux were evaluated for preparation of sample matrices. Chemical separations were developed and used after fusion to isolate the Sr and Cs from a prepared background matrix (i.e., Montana Soil). A graded approach, increasing in stable background isotopes, was performed to monitor the chemistry and instrument response. A thermal neutron irradiation was performed to produce a sample that contained the radioisotopes of Sr and Cs. Even though the irradiated sample was not a certified standard it does provide accurate expectation values via published, well understood cumulative fission yield data. The results presented in this work correlate extremely well with the published data. Furthermore, a significant decrease in uncertainty (by a factor of 5 { 10) was found for the isotopic ratios measured with TIMS compared to the published values.

TIMS, environmental contamination, radiostrontium,↗

DOE OSTI2025

Coupled geomechanical investigation of depletion-induced fault reactivation

Fault reactivation during subsurface fluid production pose significant challenges to safe and sustainable resource extraction. Here, this study presents a three-dimensional coupled geomechanical framework to investigate the processes driving fault reactivation, capturing the interactions between reservoir dynamics and geomechanical responses. Verification against theoretical estimations based on linear poroelasticity confirms the model's capacity in representing reservoir background stress responses. However, the study reveals that relying solely on background stress states can underestimate or overestimate fault reactivation potential, emphasizing the importance of including localized stress perturbations such as differential compaction and stress redistribution. Applied to a fault (M1) inspired by the geological characteristics of the Groningen field, the model shows slip initiation at 2965 m depth with 16.0 MPa depletion, aligning with field observations where seismicity occurred at approximately 3 km depth after 15.8 MPa depletion. Parametric studies reveal: (1) inelastic reservoir compaction delays fault reactivation and mitigates fault slip by reducing stress concentration, (2) higher intermediate in-situ stress magnitudes decrease the Coulomb Failure Stress (CFS) increase rate and reduce fault slip, (3) larger fault offsets amplify shear stress near the offset zone, promoting earlier reactivation and longer rupture propagation, and (4) fault permeability significantly influences pressure diffusion, with low-permeability faults leading to sharper stress changes and earlier fault destabilization. These insights highlight the critical role of geological and mechanical parameters in fault reactivation and provide a predictive framework for mitigating induced seismicity risks.

Coupled geomechanical modeling↗

DOE OSTI2023

Plasmonic hybrid core-shell (HyCoS) AgPt NP template hybridized with GQDs for SERS enhancement of 4-MBA and BT

Surface-enhanced Raman spectroscopy (SERS) is an attractive vibrational spectroscopic technique that can enable a non-destructive and ultra-sensitive detection down to the single-molecule level. Herein, a novel hybrid SERS platform is developed based on hybrid core-shell (HyCoS) AgPt nanoparticles (NPs) and graphene quantum dots (GQDs) for the enhancement of Raman vibration of 4-mercaptobenzoic acid (4-MBA) and benzenethiol (BT). The unique design of HyCoS AgPt NPs induces strong electromagnetic mechanism (EM) enhancement through the amplification of electromagnetic fields by the excitation of high-density surface plasmons and hot spots. Superior localized surface plasmon resonance (LSPR) is generated by the AgPt core-shell and background Ag NP coupling, which is systematically investigated by the optical properties and FDTD simulations. The background Ag NPs can further increase the coverage of metallic NPs, leading to higher-density hot spots and enhanced SERS response. At the same time, GQDs can provide plentiful accessible edges for the charge transfer to the HOMO and LUMO of 4-MBA and BT based on the chemical mechanism (CM) enhancement. The mixing approach of GQDs and target molecules on the HyCoS AgPt NPs can significantly amplify the Raman signals via the strong adsorption of probe molecules by the π – π interaction. The enhancement factors of proposed SERS platform can reach ~107 and ~105 for the 4-MBA and BT respectively.

36 MATERIALS SCIENCE↗

DOE OSTI2020

A conservative, consistent, and scalable meshfree mimetic method

Mimetic methods discretize divergence by restricting the Gauss theorem to mesh cells. Because point clouds lack such geometric entities, construction of a compatible meshfree divergence remains a challenge. In this work, we define an abstract Meshfree Mimetic Divergence (MMD) operator on point clouds by contraction of field and virtual face moments. This MMD satisfies a discrete divergence theorem, provides a discrete local conservation principle, and is first-order accurate. We consider two MMD instantiations. The first one assumes a background mesh and uses generalized moving least squares (GMLS) to obtain the necessary field and face moments. This MMD instance is appropriate for settings where a mesh is available but its quality is insufficient for a robust and accurate mesh-based discretization. The second MMD operator retains the GMLS field moments but defines virtual face moments using computationally efficient weighted graph-Laplacian equations. This MMD instance does not require a background grid and is appropriate for applications where mesh generation creates a computational bottleneck. It allows one to trade an expensive mesh generation problem for a scalable algebraic one, without sacrificing compatibility with the divergence operator. We demonstrate the approach by using the MMD operator to obtain a virtual finite-volume discretization of conservation laws on point clouds. Finally, numerical results in the paper confirm the mimetic properties of the method and show that it behaves similarly to standard finite volume methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗