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At least 55 records · Page 3

Numerical simulation of asteroid geometry variance on airburst threat

For an atmospheric airburst the primary source of concern when assessing uncertainty is the size and velocity. Determining these properties provides the basis for threat assessment, as the total energy of the asteroid may then be estimated, and the threat investigated thoroughly. Even with clarity as to how much energy an asteroid may deposit, a great deal of uncertainty still exists for the actual energy deposition process. One such source of uncertainty is the geometry of the incoming asteroid. The geometry of an asteroid will alter the stress distribution during entry, which adds uncertainty to when fracture will occur. Here, in this study, we use Smoothed Particle Hydrodynamics to model the atmospheric airburst of Tunguska-scale asteroids with varying geometric profiles, including a sphere, ellipsoid, binary and superellipsoid. Each asteroid is modeled as a homogenous structure with strength. We assess uncertainty through a series of planar 2D simulation cases for each geometry, comparing the source of stochasticity across geometries. A single 3D airburst simulation for each geometry is also analyzed. Additionally, the 3D cases are compared to the highly uncertain Tunguska event, predicting variance in burst height across geometries, but all bounded by theoretical burst heights proposed for Tunguska.

Airburst↗

Volumetric analysis and mesh generation of real and artificial microstructural geometries

Producing a viable finite element mesh of realistic microstructural structural geometry is a critical step in analyzing the thermo-mechanical behavior of complex multi-material composites. Advancements in imaging technology such as micro computed tomography have allowed modelers to access high resolution mesoscale geometries for direct numerical simulation. However, converting from voxel based 3D images to usable finite element meshes has been challenging. A robust method including algorithms and software scripts for generating finite element meshes from 3D imaged microstructures is presented in this paper. It includes a routine for inserting cohesive elements around material interfaces to enable modeling of interface properties including delamination and damage. The algorithms and procedures presented in this method leverage currently available software packages for processing surface based geometry into volume based meshes. In addition to converting real geometry from physical imaging systems, algorithms for producing numerically generated and statistically equivalent microstructural geometry are also included. These artificial microstructures can be a valuable resource for modelers when physical specimens do not exist or are limited in quantity: Method establishes a workflow from voxel data to viable finite element mesh including interface information, and Includes a method for synthetic geometry generation based on metrics from real microstructures.

36 MATERIALS SCIENCE↗

Spectral Element Applications in Complex Nuclear Reactor Geometries: Tet-to-Hex Meshing

The spectral element code Nek5000 is an open-source, higher-order computational fluid dynamics code developed at Argonne National Laboratory. It is designed to solve incompressible Navier-Stokes equations, but it also has a low-Mach-number approximation feature available. Large eddy simulation is approached by explicit filtering of the velocity field (and other fields) to mimic the effect of dissipation due to the unresolved scale. The computational domain is decomposed into second-order hexahedral elements that conform to the boundaries. However, generating a high-quality pure-hexahedral mesh can be challenging for some problems. For simple geometries, traditional blocking methods can be used to decompose the domain into smaller blocks to generate a so-called structural mesh. A structural mesh can maintain good orthogonality but can have a highly skewed mesh to conform to the geometry, as well as unnecessary refinement in the far field. Moreover, for geometries with relative complexity, blocking the geometry becomes impossible. To address these issues, we adopted a let-to-hex strategy to generate a pure hexahedral mesh for Nek5000. First, we generate a pure tetrahedral mesh for the geometry; then we divide one tetrahedral element into four hexahedral elements. A pure tetrahedral mesh could be easily generated for complex geometries by using many current meshing codes. In this paper, we use the commercial codes ANSYS meshing and ANSYSICEM to generate the pure tetrahedral mesh and then convert it to a pure hexahedral mesh. Boundary layers are extruded in ANSYSICEM to maintain near-wall resolution.

ANSYS ICEM↗

Molecular Geometry and Electronic Structure of Copper Corroles

Copper corroles are known for their unique multiconfigurational electronic structures in the ground state, which arise from the transfer of electrons from the π orbitals of the corrole to the d-orbital of copper. While density functional theory (DFT) provides reasonably good molecular geometries, the determination of the ground spin state and the associated energetics is heavily influenced by functional choice, particularly the percentage of the Hartree–Fock exchange. Using extended multireference perturbation theory methods (XMS-CASPT2), the functional choice can be assessed. The molecular geometries and electronic structures of both the unsubstituted and the meso-triphenyl copper corroles were investigated. A minimal active space was employed for structural characterization, while larger active spaces are required to examine the electronic structure. The XMS-CASPT2 investigations conclusively identify the ground electronic state as a multiconfigurational singlet (S o ) with three dominant electronic configurations in its lowest energy and characteristic saddled structure. In contrast, the planar geometry corresponds to the triplet state (T o ), which is approximately 5 kcal/mol higher in energy compared to the S o state for both the bare and substituted copper corroles. Notably, the planarity of the T o geometry is reduced in the substituted corrole compared with that in the unsubstituted one. By analyzing the potential energy surface (PES) between the S o and T o geometries using XMS-CASPT2, the multiconfigurational electronic structure is shown to transition toward a single electron configuration as the saddling angle decreases (i.e., as one approaches the planar geometry). Despite the ability of the functionals to reproduce the minimum energy structures, only the TPSSh-D 3 PES is reasonably close to the XMS-CASPT2 surface. Significant deviations along the PES are observed with other functionals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nanocrystal Geometry Governs Phase Transformation Pathways in Palladium Hydride

Pathways and structural dynamics of phase transformations impact performance of materials in energy and information storage technologies. Palladium hydride (PdH x ) nanocrystals are an ideal model system for studying solute-induced phase transformations, where elastic energy from lattice mismatch between α-PdH x and β-PdH x phases is often considered a key to determining the transformation pathways. α/β-PdH x interfacial elastic energy is affected by the confined geometry of a nanocrystal. However, how nanocrystal geometry influences phase transformation pathways is largely unknown. Using in situ liquid phase transmission electron microscopy, we directly visualize hydrogenation in Pd nanocrystals with two geometries, a nanocube and a hexagonal nanoplate. Both follow similar sequences of an initially curved nucleus, interface flattening, and reverse-stage nucleation; however, their evolving α/β-PdH x interfaces exhibit geometry-dependent crystallographic alignments. In nanocubes, {100}-aligned configurations conform to static elastic energy ordering, representing a pathway that maintains a local mechanical equilibrium, whereas nanoplates display both {110}- and {211}-aligned interfaces. Theoretical simulations show that geometry determines the accessibility of alternative phase transformation pathways as the system is driven far from equilibrium during hydrogenation. In conclusion, these findings identify geometry as a fundamental parameter for directing phase transformation pathways, offering design principles for accessing atypical configurations and improving properties of intercalation-based devices.

Lee, Daewon [Lawrence Berkeley National Laboratory↗

CASPT2 molecular geometries of Fe( II ) spin-crossover complexes

Using fully internally contracted (FIC)-CASPT2 analytical gradients, geometry optimizations of spin-crossover complexes are reported. This approach is tested on a series of Fe(II) complexes with different sizes, ranging from 13 to 61 atoms. A combination of active space and basis set choices are employed to investigate their role in determining reliable molecular geometries. The reported strategy demonstrates that a wave function-based level of theory can be used to optimize the geometries of metal complexes in reasonable times and enables one to treat the molecular geometry and electronic structure of the complexes using the same level of theory. For a series of smaller Fe(II) SCO complexes, strong field ligands in the LS state result in geometries with the largest differences between DFT and CASPT2; however, good agreement overall is observed between DFT and CASPT2. For the larger complexes, moderate sized basis sets yield geometries that compare well with DFT and available experimental data. Here we recommend using the (10e,12o) active space since convergence to a minimum structure was more efficient than with truncated active spaces despite having similar Fe–ligand bond distances.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Torus geometry eigenfunctions of an interacting multi-Landau-level Hamiltonian

A short-ranged, rotationally symmetric multi-Landau-level model Hamiltonian for strongly interacting electrons in a magnetic field was proposed [A. Anand et al., Phys. Rev. Lett. 126, 136601 (2021)] with the key feature that it allows exact many-body eigenfunctions on the disk not just for quasiholes but for all charged and neutral excitations of the entire Jain sequence filling fractions. We extend this to geometries without full rotational symmetry, namely, the torus and cylinder geometries, and present their spectra. Exact diagonalization of the interaction on the torus produces the low-energy spectra at filling fraction v = n/(2⁢pn + 1) that is identical, up to a topological (2⁢pn + 1)-fold multiplicity, to that of the integer quantum Hall spectra at v = n, for the incompressible state as well as all excitations. While the ansatz eigenfunctions in the disk geometry cannot be generalized to closed geometries such as torus or sphere, we show how to extend them to cylinder geometry. Meanwhile, we show eigenfunctions for charged excitations at filling fractions between 1/3 and 2/5 can be written on the torus and the spherical geometries.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DES Y1 results: Splitting growth and geometry to test $\Lambda$CDM

We analyze Dark Energy Survey (DES) data to constrain a cosmological model where a subset of parameters—focusing on Ωm—are split into versions associated with structure growth (e.g., Ωmgrow) and expansion history (e.g., Ωmgeo). Once the parameters have been specified for the ΛCDM cosmological model, which includes general relativity as a theory of gravity, it uniquely predicts the evolution of both geometry (distances) and the growth of structure over cosmic time. Any inconsistency between measurements of geometry and growth could therefore indicate a breakdown of that model. Our growth-geometry split approach therefore serves both as a (largely) model-independent test for beyond-ΛCDM physics, and as a means to characterize how DES observables provide cosmological information. We analyze the same multiprobe DES data as [Phys. Rev. Lett. 122, 171301 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.171301] : DES Year 1 (Y1) galaxy clustering and weak lensing, which are sensitive to both growth and geometry, as well as Y1 BAO and Y3 supernovae, which probe geometry. We additionally include external geometric information from BOSS DR12 BAO and a compressed Planck 2015 likelihood, and external growth information from BOSS DR12 RSD. We find no significant disagreement with Ωmgrow=Ωmgeo. When DES and external data are analyzed separately, degeneracies with neutrino mass and intrinsic alignments limit our ability to measure Ωmgrow, but combining DES with external data allows us to constrain both growth and geometric quantities. We also consider a parametrization where we split both Ωm and w, but find that even our most constraining data combination is unable to separately constrain Ωmgrow and wgrow. Relative to ΛCDM, splitting growth and geometry weakens bounds on σ8 but does not alter constraints on h.

79 ASTRONOMY AND ASTROPHYSICS↗

Numerical Model Development of a Variable-Geometry Attenuator Wave Energy Converter

Because the wave energy industry is still in its infancy, an optimal design for wave energy converters (WECs) has yet to be established; more work is needed to explore various cost-reduction pathways. The primary cost-reduction pathway considered for this work is the optimization of the geometric profile on an attenuator WEC to maximize power production while, at the same time, minimizing capital expenditures through the use of variable-geometry modules. In this investigation, the variable-geometry modules consist of inflatable bags placed on either side of a base central steel cylinder that would be inflated in low-moderate sea states to maximize power capture and then deflated in moderate-extreme sea states to minimize wave loading. The numerical model and simulation of the attenuator WEC were developed and completed using WEC-Sim, which is an open-source code that is appropriate for use in evaluating the dynamic response of the different WEC models in operational seas. The power production estimates were obtained from the Wave Energy Prize (WEP) sea states, which are representative of U. S. deployment sites, to calculate the average climate capture width that is used in the WEP ACE calculation. Preliminary capital expenditure costs were obtained assuming the base central steel cylinder mass was equal to the fluid displaced mass, minus the mass of the variable-geometry bags. The additional weight required to offset the additional buoyancy from the variable-geometry bags was assumed to come from the addition of seawater ballast. The variable-geometry attenuator model was found to have a similar power capture efficiency as a fixed-body model, but is expected to have a lower characteristic capital expenditure given its more streamlined profile, which demonstrates that variable-geometry modules may provide a realistic cost-reduction pathway to help design a more cost-competitive WEC.

50 EE - Wind and Water Power Program - Water (EE-4↗

Optimal Geometry for Focused Ion Beam-Milled Samples for Direct-Pull Micro-Tensile Testing Performed In Situ in a Scanning Electron Microscope

A thorough procedure was developed to efficiently manufacture dogbone samples using focused ion beam (FIB) milling for micro-tensile testing. A Bruker PI 89 PicoIndenter, Billerica, MA, USA, was used as a case study, although the analysis and results are applicable to other micro-mechanical testing systems capable of mounting a standard, Ø12.7 mm × Ø3.2 mm pin, scanning electron microscopy (SEM) pin stub (Ted Pella, Redding, CA, USA). Nine dogbones were made from an Fe-45Cu alloy additively manufactured using powder-fed laser-directed energy deposition (DED-LB). Testing showed that fracture was confined to the gauge section for all dogbones and that the fracture mode, ductile vs. brittle, was entirely dependent on the grain orientation relative to the loading direction. The analysis showed that the measured plastic strain to failure can vary from >11% (optimal geometry) to <1% (non-optimal geometry) in micro-tensile testing of high-tensile-strength (>1 GPa) metallic materials. Subsequently, a finite element analysis (FEA) was conducted to identify the improved dogbone geometries. A total of ten thousand dogbone geometries were tested, and their dimensions were defined by a set of four adjustable parameters (corner radius, load surface angle, load surface length, and dogbone head length). The gauge width and gauge length were fixed to 4 µm and 10 µm, respectively. Three-dimensional surface plots of the stress concentration as a function of two parameters were used to identify the optimal ranges of parameter values. The addition of maximum width and length constraints, measuring 25 µm and 30 µm, respectively, allowed us to identify an optimal geometry at load surface angles of 30° and 45°. Their respective dimensions (corner radius, load surface length, and dogbone head length) are, in µm, 12, 6, and 7 and 10, 7, and 7. Testing these two optimal geometries with a range of gauge lengths from 4 to 20 µm showed that smaller gauge lengths only slightly reduced the detrimental stress concentration outside the gauge section. However, smaller gauge lengths will notably improve the FIB surface polishing step as tapering is reduced with smaller dogbone lengths.

Chemistry↗

Numerical Model Development of a Variable-Geometry Attenuator Wave Energy Converter: Preprint

Because the wave energy industry is still in its infancy, an optimal design for wave energy converters (WECs) has yet to be established; more work is needed to explore various cost reduction pathways. The primary cost-reduction pathway considered for this work is the optimization of the geometric profile on an attenuator WEC to maximize power production while, at the same time, minimizing capital expenditures through the use of variable-geometry modules. In this investigation, the variable geometry modules consist of inflatable bags placed on either side of a base central steel cylinder that would be inflated in low moderate sea states to maximize power capture and then deflated in moderate-extreme sea states to minimize wave loading. The numerical model and simulation of the attenuator WEC were developed and completed using WEC-Sim, which is an open-source code that is appropriate for use in evaluating the dynamic response of the different WEC models in operational seas. The power production estimates were obtained from the Wave Energy Prize (WEP) sea states, which are representative of U. S. deployment sites, to calculate the average climate capture width that is used in the WEP ACE calculation. Preliminary capital expenditure costs were obtained assuming the base central steel cylinder mass was equal to the fluid displaced mass, minus the mass of the variable-geometry bags. The additional weight required to offset the additional buoyancy from the variable-geometry bags was assumed to come from the addition of seawater ballast. The variable-geometry attenuator model was found to have a similar power capture efficiency as a fixed-body model, but is expected to have a lower characteristic capital expenditure given its more streamlined profile, which demonstrates that variable-geometry modules may provide a realistic cost-reduction pathway to help design a more cost-competitive WEC.

50 EE - Wind and Water Power Program - Water (EE-4↗

Very high cycle fatigue characteristics of laser beam powder bed fused AlSi10Mg: A systematic evaluation of part geometry

This study explores the influence of geometry and part size on defect distribution, melt pool size, and mechanical characteristics in laser beam powder bed fused (LB-PBF) AlSi10Mg. Five distinct geometries—hourglass, small rod, small block, large block, and large rod—were fabricated under identical process parameters. Fully reversed ultrasonic fatigue testing, operating at a frequency of 20 kHz, was conducted to assess the very high cycle fatigue properties. The findings indicated that part geometry had a major impact on the fatigue properties of the material in the very high cycle fatigue regime. Specimens machined from large rods and large blocks had the lowest porosity and highest fatigue resistance. Microstructural analysis indicated that hourglass, small rod, and small block specimens had shallower melt pools and overlap depths compared to other geometries. This observation suggests a higher cooling rate in specimens with smaller cross-sectional areas, leading to the increased presence of entrapped gas pores and a lack of fusion defects. Understanding the relationship between part geometry and fatigue properties in LB-PBF components offers insights for optimizing design and manufacturing processes in additive manufacturing applications.

AlSi10Mg↗

Hypervelocity impact flash expansion geometry under various spacecraft surface electrical conditions

A more congested space environment due to increasing space activities introduces new threats to spacecraft operators. Among these threats include hypervelocity impacts from microparticles (< 1 µg) in the form of meteoroids and space debris. These microparticles travel at speeds between 11.2 and 72.8 km/s with respect to the Earth and can impact spacecraft forming a small (~1 µm) and dense (~ 10 26 m -3 ) plasma. This plasma can generate a strong optical emission (impact flash) and a radio frequency (RF) emission. These emissions can lead to spacecraft electrical anomalies when the impacted spacecraft surface (target) carries high electrical potential due to various space weather effects. To understand the microparticle hypervelocity impact plasma and its associated threat to spacecraft electronics, we studied the hypervelocity impact flash expansion geometry under various spacecraft surface electrical conditions. Three high-speed broadband photomultiplier tubes (PMT) are used to capture the temporal evolution of the impact flash and the temporal evolution of the angular distribution of the impact flash expansion geometry in a 3 MV electrostatic dust accelerator during a ground-based experiment. Overall, results indicate that the impact surface electrical condition has a statistically significant influence on the impact flash geometry, and a strong similarity between the impact plasma and flash expansion geometry. Thus, this paper provides new experimental support for the impact flash origin from and connection with the impact plasma, and serves as the first impact flash expansion geometry characterization under various impact surface electrical conditions in a collisionless environment (< 10 -5 Torr).

42 ENGINEERING↗

A multi-dimensional Child–Langmuir law for any diode geometry

While prior theoretical studies of multi-dimensional space-charge limited current (SCLC) assumed emission from a small patch on infinite electrodes, none have considered emission from an entire finite electrode. In this paper, we apply variational calculus (VC) and conformal mapping, which have previously been used to derive analytic solutions for SCLC density (SCLCD) for nonplanar one-dimensional geometries, to obtain mathematical relationships for any multi-dimensional macroscopic diode with finite cathode and anode. We first derive a universal mathematical relationship between space-charge limited potential and vacuum potential for any diode and apply this technique to determine SCLCD for an eccentric spherical diode. We then apply VC and the Schwartz–Christoffel transformation to derive an exact equation for SCLCD in a general two-dimensional planar geometry with emission from a finite emitter. Particle-in-cell simulations using VSim agreed within 4%–13% for a range of ratios of emitter width to gap distance using the thinnest electrodes practical for the memory constraints of our hardware, with the difference partially attributed to the theory's assumption of infinitesimally thin electrodes. After generalizing this approach to determine SCLCD for any orthogonal diode as a function of only the vacuum capacitance and vacuum potential, we derive an analytical formulation of the three-dimensional Child–Langmuir law for finite parallel rectangular and disk geometries. These results demonstrate the utility for calculating SCLCD for any diode geometry using vacuum capacitance and vacuum potential, which are readily obtainable for many diode geometries, to guide experiment and simulation development.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Flow structures of the cross-flow over a five-layer helically coiled steam generator geometry

The helically-coiled heat exchanger (HCSG) offers advantages over straight tubes such as compactness in geometry, increased heat transfer coefficients, and capability to absorb thermal expansion. In this study, the time-resolved velocity field data of shell-side crossflow over a five-layer helically coiled steam generator geometry was obtained using Particle Image Velocimetry (PIV) between adjacent rods in four regions with up to 5000 frames per second (5 kHz) at approximately Re u = 3600. The slant rod bundle created different flow patterns in different regions. Proper Orthogonal Decomposition (POD) revealed high-energy-mode flow structures. Due to the confined flow channel geometry, the large flow structures were not advected resulting in no strong POD mode paring. Continuous Wavelet Transform (CWT) visualized the characteristics of flow fluctuation in time and frequency domain simultaneously, which ranged in Strouhal number, S u , between 0.03 and 1.17. In the wake regions of the rods, flows changed in both pattern and magnitude over time. Once a pattern formed, it continued for relatively shorter than straight tube arrays, before changing the pattern again. The histograms of the POD time coefficients presented this multimodal flow characteristics. The current study focuses more on whole flow field analyses in the selected regions rather than local point-wise analyses. Finally, this study revealed that various Strouhal numbers can exist in the helically coiled heat exchanger geometry, which was not observed in straight tube arrays. In particular, Strouhal numbers smaller than 0.1 do not seem to be caused by vortex shedding but seem to be the result of the combination of complex geometry and possible multimodal trends. Based on the current observation, further works would involve intensive instantaneous point-wise analyses on the interactions between important locations such as separation points, stagnation points, shear layers, etc.

42 ENGINEERING↗

Geometry and size dependent microstructure and crack formation in Rene 41 superalloy fabricated by laser powder bed fusion

This study provides a systematic investigation into the size and geometry-dependent microstructural evolution and cracking susceptibility of LPBF-fabricated Rene 41. By coupling experimental microstructural analysis with thermal modeling, this research uniquely identifies the relationship between geometry-specific thermal histories, carbide coarsening, and liquation cracking. Four different geometries with varying thickness were fabricated with the identical process parameters. It was found that the grain size and morphology are not affected by the part size. However, the thinner parts exhibited coarser sub-grain structures compared to the thicker ones. The crack formation was observed for the parts with cross-sections smaller than 1 mm, whereas thicker parts had high density without any defects. Further, the cracks were observed in the interdendritic regions, suggesting that liquation cracking was the active micro-crack formation mechanism. The detailed microstructural analysis combined with a thermal finite element analysis proved that the heat extraction efficiency was lower for thinner parts causing a lower cooling rate and coarser carbides, making them more susceptible to constitutional liquation. Microhardness measurements were conducted for each geometry and correlated with the observed microstructural variations. The findings highlight the critical need for geometry-specific optimization of LPBF process parameters to mitigate cracking and achieve microstructural uniformity, offering valuable insights into the fabrication of complex, high-performance aerospace components.

36 MATERIALS SCIENCE↗

Effect of crystallite geometries on electrochemical performance of porous intercalation electrodes by multiscale operando investigation

Lithium-ion batteries are yet to realize their full promise because of challenges in the design and construction of electrode architectures that allow for their entire interior volumes to be reversibly accessible for ion storage. Electrodes constructed from the same material and with the same specifications, which differ only in terms of dimensions and geometries of the constituent particles, can show surprising differences in polarization, stress accumulation and capacity fade. Here, using operando synchrotron X-ray diffraction and energy dispersive X-ray diffraction (EDXRD), we probe the mechanistic origins of the remarkable particle geometry-dependent modification of lithiation-induced phase transformations in V2O5 as a model phase-transforming cathode. A pronounced modulation of phase coexistence regimes is observed as a function of particle geometry. Specifically, a metastable phase is stabilized for nanometre-sized spherical V2O5 particles, to circumvent the formation of large misfit strains. Spatially resolved EDXRD measurements demonstrate that particle geometries strongly modify the tortuosity of the porous cathode architecture. Greater ion-transport limitations in electrode architectures comprising micrometre-sized platelets result in considerable lithiation heterogeneities across the thickness of the electrode. These insights establish particle geometry-dependent modification of metastable phase regimes and electrode tortuosity as key design principles for realizing the promise of intercalation cathodes. Designing electrode architectures for Li-ion batteries that can be reversibly accessible for ion storage can be challenging. Using operando techniques the mechanistic origin of lithiation-induced phase transformations in a V2O5 model cathode is now clarified.

Luo, Yuting↗

Programmable interactions and emergent geometry in an array of atom clouds

Interactions govern the flow of information and the formation of correlations between constituents of many-body quantum systems, dictating phases of matter found in nature and forms of entanglement generated in the laboratory. Typical interactions decay with distance and thus produce a network of connectivity governed by geometry—such as the crystalline structure of a material or the trapping sites of atoms in a quantum simulator. However, many envisioned applications in quantum simulation and computation require more complex coupling graphs including non-local interactions, which feature in models of information scrambling in black hole, and mappings of hard optimization problems onto frustrated classical magnets. Here we describe the realization of programmable non-local interactions in an array of atomic ensembles within an optical cavity, in which photons carry information between atomic spins. By programming the distance dependence of the interactions, we access effective geometries for which the dimensionality, topology and metric are entirely distinct from the physical geometry of the array. As examples, we engineer an antiferromagnetic triangular ladder, a Möbius strip with sign-changing interactions and a treelike geometry inspired by concepts of quantum gravity. The tree graph constitutes a toy model of holographic duality, in which the quantum system lies on the boundary of a higher-dimensional geometry that emerges from measured correlations. Overall, our work provides broader prospects for simulating frustrated magnets and topological phases, investigating quantum optimization paradigms and engineering entangled resource states for sensing and computation.

74 ATOMIC AND MOLECULAR PHYSICS↗