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The Draco Dwarf Spheroidal Galaxy in the First Year of Dark Energy Spectroscopic Instrument Data

We investigate the spatial distribution, kinematics, and metallicity of stars in the Draco dwarf spheroidal galaxy using data from the Dark Energy Spectroscopic Instrument (DESI). We identify 155 high-probability members of Draco using line-of-sight velocity and metallicity information derived from DESI spectroscopy along with Gaia Data Release 3 proper motions. We find a mean line-of-sight velocity of −290.62 ± 0.80 km s −1 with dispersion = $9.57$$^{+0.66}_{–0.62}$ km s −1 and mean metallicity [Fe/H] = −2.10 ± 0.04, consistent with previous results. We also find that Draco has a steep metallicity gradient within the half-light radius, and a metallicity gradient that flattens beyond the half-light radius. We identify eight high-probability members outside the King tidal radius, four of which we identify for the first time. These extratidal stars are not preferentially aligned along the orbit of Draco. We compute an average surface brightness of 34.02 mag arsec –2 within an elliptical annulus from the King tidal radius of 48'.1–81′.

79 ASTRONOMY AND ASTROPHYSICS↗

The DECam Local Volume Exploration Survey: Overview and First Data Release

The DECam Local Volume Exploration survey (DELVE) is a 126-night survey program on the 4 m Blanco Telescope at the Cerro Tololo Inter-American Observatory in Chile. DELVE seeks to understand the characteristics of faint satellite galaxies and other resolved stellar substructures over a range of environments in the Local Volume. DELVE will combine new DECam observations with archival DECam data to cover ~15,000 deg 2 of high Galactic latitude (|b| > 10°) southern sky to a 5σ depth of g, r, i, z ~ 23.5 mag. In addition, DELVE will cover a region of ~2200 deg 2 around the Magellanic Clouds to a depth of g, r, i ~ 24.5 mag and an area of ~135 deg 2 around four Magellanic analogs to a depth of g, i ~ 25.5 mag. Here, we present an overview of the DELVE program and progress to date. Furthermore, we also summarize the first DELVE public data release (DELVE DR1), which provides point-source and automatic aperture photometry for ~520 million astronomical sources covering ~5000 deg 2 of the southern sky to a 5σ point-source depth of g = 24.3 mag, r = 23.9 mag, i = 23.3 mag, and z = 22.8 mag. DELVE DR1 is publicly available via the NOIRLab Astro Data Lab science platform.

79 ASTRONOMY AND ASTROPHYSICS↗

The DECam Local Volume Exploration Survey Data Release 2

We present the second public data release (DR2) from the DECam Local Volume Exploration survey (DELVE). DELVE DR2 combines new DECam observations with archival DECam data from the Dark Energy Survey, the DECam Legacy Survey, and other DECam community programs. DELVE DR2 consists of ∼160,000 exposures that cover >21,000 deg$^{2}$ of the high-Galactic-latitude (∣b∣ > 10°) sky in four broadband optical/near-infrared filters (g, r, i, z). DELVE DR2 provides point-source and automatic aperture photometry for ∼2.5 billion astronomical sources with a median 5σ point-source depth of g = 24.3, r = 23.9, i = 23.5, and z = 22.8 mag. A region of ∼17,000 deg$^{2}$ has been imaged in all four filters, providing four-band photometric measurements for ∼618 million astronomical sources. DELVE DR2 covers more than 4 times the area of the previous DELVE data release and contains roughly 5 times as many astronomical objects. DELVE DR2 is publicly available via the NOIRLab Astro Data Lab science platform.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Observation and modeling of energetic particles at synchronous orbit on July 29, 1977

In the twelve hours following a worldwide storm, there was a series of at least four magnetospheric substorms, the last and largest of which exhibited an expansion phase onset at approximately 1200 UT. Data from six spacecraft in three general local time groupings (0300, 0700, and 1300 LT) were examined and vector magnetic field data and energetic electron and ion data from approximately 15 keV to 2 MeV were employed.

Baker, D. N.↗

Teleparallelism as a universal connection on null hypersurfaces in general relativity

It is shown that a close relationship between the inner geometry of a null hypersurface N3 and the Newman-Penrose (NP) (1962, 1963) spin coefficient formalism exists. Projecting the null complex NP tetrad onto N3, two triads of basis vectors in N3 are obtained. The inner geometry of N3 is based on the assumption that these vectors are parallelly transported along the surface; this gives rise to the teleparallel connection as a metric nonsymmetric affine connection. The gauge freedom for the choice of the basis triads is given by the isotropy subgroup of the local Lorentz group leaving invariant the direction of the null generators of N3, and teleparallelism is determined by the equivalence class of the basis triads with respect to the global gauge group. Nine of the twelve NP coefficients are identified as the triad components of the torsion and the second fundamental form of N3. The resulting generalized Gauss-Codazzi equations are identical to nine of the NP equations, i.e., to the half of the Ricci identities. This result gives a geometrical meaning to the entire formalism. Finally a general proof of Penrose's theorem that the shear of the null generators of N3 is the only initial null datum for a gravitational field on N3 is presented.

Mazur, P. O.↗

Three-Dimensional Aerodynamic Instabilities In Multi-Stage Axial Compressors

This thesis presents the conceptualization and development of a computational model for describing three-dimensional non-linear disturbances associated with instability and inlet distortion in multistage compressors. Specifically, the model is aimed at simulating the non-linear aspects of short wavelength stall inception, part span stall cells, and compressor response to three-dimensional inlet distortions. The computed results demonstrated the first-of-a-kind capability for simulating short wavelength stall inception in multistage compressors. The adequacy of the model is demonstrated by its application to reproduce the following phenomena: (1) response of a compressor to a square-wave total pressure inlet distortion; (2) behavior of long wavelength small amplitude disturbances in compressors; (3) short wavelength stall inception in a multistage compressor and the occurrence of rotating stall inception on the negatively sloped portion of the compressor characteristic; (4) progressive stalling behavior in the first stage in a mismatched multistage compressor; (5) change of stall inception type (from modal to spike and vice versa) due to IGV stagger angle variation, and "unique rotor tip incidence" at these points where the compressor stalls through short wavelength disturbances. The model has been applied to determine the parametric dependence of instability inception behavior in terms of amplitude and spatial distribution of initial disturbance, and intra-blade-row gaps. It is found that reducing the inter-blade row gaps suppresses the growth of short wavelength disturbances. It is also concluded from these parametric investigations that each local component group (rotor and its two adjacent stators) has its own instability point (i.e. conditions at which disturbances are sustained) for short wavelength disturbances, with the instability point for the compressor set by the most unstable component group. For completeness, the methodology has been extended to describe finite amplitude disturbances in high-speed compressors. Results are presented for the response of a transonic compressor subjected to inlet distortions.

Tan, Choon S.↗

Task I: A Computational Model for Short Wavelength Stall Inception and Development In Multi-Stage Compressors

A computational model is presented for simulating axial compressor stall inception and development via disturbances with length scales on the order of several (typically about three) blade pitches. The model was designed for multi-stage compressors in which stall is initiated by these short wavelength disturbances, also referred to as spikes. The inception process described is fundamentally nonlinear, in contrast to the essentially linear behavior seen in so-called modal stall inception . The model was able to capture the following experimentally observed phenomena: (1) development of rotating stall via short wavelength disturbances, (2) formation and evolution of localized short wavelength stall cells in the first stage of a mismatched compressor, (3) the switch from long to short wavelength stall inception resulting from the re-staggering of the inlet guide vane, (4) the occurrence of rotating stall inception on the negatively sloped portion of the compressor characteristic. Parametric investigations indicated that (1) short wavelength disturbances were supported by the rotor blade row, (2) the disturbance strength was attenuated within the stators, and (3) the reduction of inter-blade row gaps can suppress the growth of short wavelength disturbances. It is argued that each local component group (rotor plus neighboring stators) has its own instability point (i.e. conditions at which disturbances are sustained) for short wavelength disturbances, with the instability point for the compressor set by the most unstable component group.

Suder, Kenneth↗

Joint Non-kinetic Effects Model (JNEM)

This slide presentation reviews the development of the Joint Non-kinetic Effects Model (JNEM), which is tool to support Battle Command Training that links simulation-generated non-kinetic events and outcomes to Training Audience Command and Staff decisions. JNEM helps create the operating environment for the following population groups (P-groups): (1) Local Civilians on the Battlefield, (2) Inter-Governmental Organizations (3) Non-Governmental Organizations (4) Contractors on the battlefield.

wargaming↗

Predicting the Likelihood of Human-Elephant Conflict and Assessing Patterns in Elephant Movements Over Varying Habitat Conditions in the Kavango-Zambezi Area

In the Kavango-Zambezi area of southern Africa, three million people live within areas frequently traveled by free-ranging elephants. As the region continues to develop rapidly, urban and agricultural settlements further encroach upon the land that these elephants use. As elephants come into more frequent contact with urban and agricultural areas, human populations face financial loss through crop damage and the potential for injury from direct conflict with elephants. Elephant populations are also at risk of injuries from conflict as well as illness related to the consumption of waste. In order to implement human-elephant conflict mitigation strategies, local conservation groups need to be informed on best practices for coexistence. This project aided The Ecoexist Project and Connected Conservation in understanding the ecological factors that drive elephant movement into human settlements and provided Earth observation data to support conflict management in the future. The team used Landsat 5 Thematic Mapper (TM), Landsat 8 Operational Land Imager (OLI) data to create land use land cover maps and calculate vegetation indices, and used TerraClimate data to analyze drought conditions. These classified maps allowed us to display a time series of human settlement from 1990 to the present and were made explorable alongside other environmental variables in an updated Google Earth Engine (GEE) tool. This project also provided heat maps that show the risk of human-elephant conflict based on historical data of HEC locations. This analysis will provide support for conservation experts in determining best practices for future mitigation and prevention of human-elephant conflict.

Ariel Calle↗

An Unbiased CO Survey Toward the Northern Region of the Small Magellanic Cloud with the Atacama Compact Array. II. CO Cloud Catalog

The nature of molecular clouds and their statistical behavior in subsolar metallicity environments are not fully explored yet. We analyzed data from an unbiased CO (J = 2–1) survey at the spatial resolution of ∼2 pc in the northern region of the Small Magellanic Cloud with the Atacama Compact Array to characterize the CO cloud properties. A cloud-decomposition analysis identified 426 spatially/velocity-independent CO clouds and their substructures. Based on the cross-matching with known infrared catalogs by Spitzer and Herschel, more than 90% CO clouds show spatial correlations with point sources. We investigated the basic properties of the CO clouds and found that the radius–velocity linewidth (R–σ v ) relation follows the Milky Way-like power-law exponent, but the intercept is ∼1.5 times lower than that in the Milky Way. The mass functions (dN/dM) of the CO luminosity and virial mass are characterized by an exponent of ∼1.7, which is consistent with previously reported values in the Large Magellanic Cloud and in the Milky Way.

Local Group↗

EERC Final Topical Report – Findings on Subtask 3.2 – Produced Water Management Through Geologic Homogenization, Conditions, and Reuse

The Energy & Environmental Research Center (EERC) was awarded a contract by the North Dakota Industrial Commission (NDIC) Oil and Gas Research Program (NDIC No. G-051-101) to conduct a study on the recycling of water used in oil and gas operations, also known as produced water, from oil- and gas-producing regions of North Dakota as directed by Section 19 of North Dakota House Bill 1014. This final report provides a compilation of results of the study, which include regulatory, scientific, technological, and feasibility methods and considerations associated with North Dakota produced water management. The report provides a synopsis of this project’s previously submitted produced water assessment report entitled “Produced Water Management and Recycling Options in North Dakota” (Energy & Environmental Research Center, 2020), with updated values provided as appropriate. The report provides the results from the investigation of a novel produced water management strategy, referred to as geologic homogenization, conditioning, and reuse (GHCR), which aims to use a subsurface geologic formation as a natural medium for managing produced water recycling and reuse. Water management is a significant technical and economic challenge for sustainable oil and gas production, and water volumes are intrinsically linked to oil production volumes. North Dakota oil production rose to over 1.5 million barrels (MMbbl)/day in 2019, and despite a downturn in oil price in early 2020, North Dakota oil production has recovered to 1.1 MMbbl/day as of August 2021. Bakken petroleum system development between 2008 and 2020 has resulted in a nearly fourfold increase in produced water volumes to 642 MMbbl/yr in 2020 after peaking at 740 MMbbl/yr in 2019 and a fivefold increase in saltwater disposal (SWD) volumes to 565 MMbbl/yr in 2020 after a peak of 682 MMbbl/yr in 2019. Produced water and SWD volumes are forecasted to double by 2030. SWD is the primary method of produced water management used in North Dakota, with approximately 95% of the SWD volume occurring through subsurface injection into sandstones of the Dakota Group (Dakota). Localized pressurization of the Dakota resulting from SWD and projected increases in produced water volumes could impact the economics of North Dakota oil production. As a result, there is an emerging need to pursue alternative produced water management approaches, including recycling and reuse. While produced water recycling is not yet widespread, commercial operators are making strides in overcoming the technical challenges of using high salinity produced water in completion operations (Marathon Oil, 2020). As water management continues to be a key focal point in companies’ environmental, social, and governance (ESG) initiatives, focus on water management, including recycling, will likely continue to increase. Laboratory column testing, field sample collection, geologic modeling and numerical simulation, and techno-economic analysis all indicate that GHCR could feasibly be implemented as a potential water management option. Laboratory column testing and field sample collection indicate that the Inyan Kara sandstone and native formation fluid are capable of homogenizing with the Bakken produced water to a point where the fluid composition appears to stabilize. Extracting that stabilized fluid could be considered homogeneous and capable of providing individual batches of hydraulic fracturing fluid. Numerical simulation results indicate that extraction of fluids from the Inyan Kara in a GHCR implementation scenario is capable of reducing formation pressure, which would help ease localized pressurization of the Inyan Kara and extend the available capacity for nearby existing SWD wells. Economic analysis indicates that there are scenarios where GHCR implementation can be a competitive or even lower-cost option than a conventional water management approach. Site-specific conditions will dictate the economic potential of GHCR, but potentially attractive sites for GHCR implementation will be those that are located above a pressurized zone of the Inyan Kara, need six or more Bakken infill wells, and face high costs for conventional SWD and/or freshwater. Based on the regulatory review, drilling into the Inyan Kara for SWD and to harness as a source water for industrial use have precedent in North Dakota, and a workable regulatory solution for GHCR seems likely. However, restrictions in the state regarding surface storage and transport of produced fluids may limit some activities, which will affect how GHCR could ultimately be implemented. In summary, this study reveals pursuing GHCR can be a viable approach to water management in North Dakota. The GHCR concept addresses some of the challenges that hinder the more traditional approaches to recycling in the industry. Furthermore, an assessment of the current landscape of water management within the state reveals the ongoing trend of increasing volumes of produced water and SWD. Projections reveal that the volumes of produced water that need to be managed are expected to double over the next decade (Energy & Environmental Research Center, 2020). With the continued development of the Bakken and continuing driving factors related to ESG initiatives, implementing a practice such as GHCR is a feasible approach to adding recycling of produced water to industry within the state. This subtask was cofunded through the EERC–U.S. Department of Energy Joint Program on Research and Development for Fossil Energy-Related Resources Cooperative Agreement No. DE-FE0024233. Nonfederal funding was provided by the North Dakota Industrial Commission Oil and Gas Research Program. References Energy & Environmental Research Center, 2020, Produced water management and recycling options in North Dakota: Final Report for North Dakota Legislative Management Energy Development and Transmission Committee and North Dakota Industrial Commission. Marathon Oil, 2020, Sustainability report: https://cdn.sanity.io/files/ghcnw9z2/website/ 91744eb6ef8fbe59505a911c6b8d2e8dd9a537fa.pdf?dl (accessed November 2021).

02 PETROLEUM↗

A group finder algorithm optimised for the study of local galaxy environments

Context. The majority of galaxy group catalogues available in the literature use the popular friends-of-friends algorithm which links galaxies using a linking length. One potential drawback to this approach is that clusters of points can be linked with thin bridges which may not be desirable. In order to study galaxy groups, it is important to obtain realistic group structures. Aim. Here, in this study, we present a new simple group finder algorithm, TD-ENCLOSER, that finds the group that encloses a target galaxy of interest. Methods. TD-ENCLOSER is based on the kernel density estimation method which treats each galaxy, represented by a zero-dimensional particle, as a two-dimensional circular Gaussian. The algorithm assigns galaxies to peaks in the density field in order of density in descending order (‘top down’) so that galaxy groups ‘grow’ around the density peaks. Outliers in under-dense regions are prevented from joining groups by a specified hard threshold, while outliers at the group edges are clipped below a soft (blurred) interior density level. Results. The group assignments are largely insensitive to all free parameter variations apart from the hard density threshold and the kernel standard deviation, although this is a known feature of density-based group finder algorithms and it operates with a computing speed that increases linearly with the size of the input sample. In preparation for a companion paper, we also present a simple algorithm to select unique representative groups when duplicates occur. Conclusions. TD-ENCLOSER is tested on a mock galaxy catalogue using a smoothing scale of 0.3 Mpc and is found to be able to recover the input group distribution with sufficient accuracy to be applied to observed galaxy distributions.

79 ASTRONOMY AND ASTROPHYSICS↗

Renormalization and conformal invariance of non-local quantum electrodynamics

We study renormalization group flow in a non-local version of quantum electrodynamics (QED). We determine the regime in which the theory flows to a local theory in the infrared and study a possible UV completion of four-dimensional QED. In addition, we find that there exist non-local conformal theories with a one-dimensional conformal manifold and non-local deformations of QED in three dimensions that are exactly marginal. Along the way we develop methods for coupling non-local derivatives to external sources and discuss unitarity and conformal vs. scale invariance of these theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Symmetries of coupled harmonic oscillators

It is shown that the system of two coupled harmonic oscillators possesses many interesting symmetries. It is noted that the symmetry of a single oscillator is that of the three-parameter group Sp(2). Thus two uncoupled oscillator exhibits a direct product of two Sp(2) groups, with six parameters. The coupling can be achieved through a rotation in the two-dimensional space of two oscillator coordinates. The closure of the commutation relations for the generators leads to the ten-parameter group Sp(4) which is locally isomorphic to the deSitter group O(3,2).

Han, D.↗

Majorana zero modes in Y -shape interacting Kitaev wires

Motivated by the recent experimental realization of minimal Kitaev chains using quantum dots, we investigate the Majorana zero modes (MZM) in Y-shape Kitaev wires. We solve the associated Kitaev models analytically at the sweet spot (t h = Δ) and derive the exact form of MZM wave-functions in this geometry. We observed exotic multi-site MZMs located near the junction center, on the nearby edge sites of each leg. This result is important for potential braiding of Majoranas and the performance of Y-junctions made from arrays of quantum dots. Furthermore, we study the stability of local (single-site) and multi-site MZMs modes in the presence of Coulomb repulsion, using density matrix renormalization group theory. Our local density-of-states calculation shows that these multi-site MZMs are as equally topologically protected as the single-site MZMs when in the presence of Coulomb repulsion or when away from the sweet-spot.

36 MATERIALS SCIENCE↗

Diversity and conservation of plant small secreted proteins associated with arbuscular mycorrhizal symbiosis

Arbuscular mycorrhizal symbiosis (AMS) is widespread mutualistic association between plants and fungi, which plays an essential role in nutrient exchange, enhancement in plant stress resistance, development of host, and ecosystem sustainability. Previous studies have shown that plant small secreted proteins (SSPs) are involved in beneficial symbiotic interactions. However, the role of SSPs in the evolution of AMS has not been well studied yet. In this study, we performed computational analysis of SSPs in 60 plant species and identified three AMS-specific ortholog groups containing SSPs only from at least 30% of the AMS species in this study and three AMS-preferential ortholog groups containing SSPs from both AMS and non-AMS species, with AMS species containing significantly more SSPs than non-AMS species. We found that independent lineages of monocot and eudicot plants contained genes in the AMS-specific ortholog groups and had significant expansion in the AMS-preferential ortholog groups. Also, two AMS-preferential ortholog groups showed convergent changes, between monocot and eudicot species, in gene expression in response to arbuscular mycorrhizal fungus Rhizophagus irregularis. Furthermore, conserved cis-elements were identified in the promoter regions of the genes showing convergent gene expression. We found that the SSPs, and their closely related homologs, in each of three AMS-preferential ortholog groups, had some local variations in the protein structural alignment. We also identified genes co-expressed with the Populus trichocarpa SSP genes in the AMS-preferential ortholog groups. This first plant kingdom-wide analysis on SSP provides insights on plant-AMS convergent evolution with specific SSP gene expression and local diversification of protein structures.

59 BASIC BIOLOGICAL SCIENCES↗

Large Primtive Asteroids: Thermal and Dynamical Context

Primitiveasteroids, most of which are located in the outer belt and Jupiter’s Trojan clouds, provide information related to the origin and evolution of the solar system and the conditions in which the solar nebula was formed. These asteroids are widely thought to be the origin of the least-altered car-bonaceous chondrite that allow us to put crucial con-straints on the current dynamical and thermal theories of the formation and evolution of the early solar sys-tem. The nature of surface composition of large and low-albedo asteroids, like (1) Ceres, (10) Hygiea and (52) Europa, is still under intense debate and different interpretations have beenput forth to explain the ab-sorption features in these objects (e.g.,[1, 2, 3,4,5,6]). Laboratory and spectroscopic experiments on me-teorites that represent all nine carbonaceous chondrite types also found no spectral matches for these large asteroids (e.g.,[7]). Previous studies of asteroid Ceres (the largest primitive asteroid in the solar system) have been conducted to constrain and estimate its surface composition (e.g., [2, 5]). Using linear mixing,[2]found hydroxide brucite, serpentines, and carbonates, to be consistent with Ceres’ ground-based spectra.[5]estimated the surface composition of Ceres and found evidence of widespread NH3-phyllosilicates across its surface using best-fit solutions to Dawn’s NIR spectra. The presence of NH3-phyllosilicates implies that mate-rial from the outer solar system was incorporated into large primitive asteroids, either during their formation at great heliocentric distance or by incorporation of material transported into the Main Belt region. Here we presentnew largeand primitive asteroidsthat share the same spectral similaritieswith the largest asteroid in the solar system, Ceres.We also present the context of these new observations in terms oftheirthermal and dynamicalevolution.Large Primitive Asteroids: Dynamical and Thermal Context:Orbital Distribution of LargePrimitiveAsteroids: Constraining the mineralogy and surface composition of large primitive asteroids will place crucial con-straints on existing dynamical and thermal theories of the formation of the early solar system. We identified several additional asteroids in the Europa-like group in addition to asteroids Europa, Euphrosyne, and Patien-tia, that wereidentified in [8]using NASA IRTFtele-scope (e.g.,Figure 1). These new asteroids along with the already-observed Ceres-and Europa-like group members are localized in the 2.8 < a < 3.4 AU region and characterized by larger sizes, showing an interest-ing orbital distribution (Figure 2). Ceres-likeand Eu-ropa-like groups, which include the largest asteroids in the solar system, show an interesting orbital distribu-tion. These groups are located in the 2.6 < a < 3.6 AU region that contains the snow-line. The snow-line’s location may have been driftedinwards due to the disk’s cooling and evolution[9,10]. Recent dynamical models[11,12]suggested that a substantial fraction of primitive asteroids originated between or beyond the giant planets (a > 5 AU), where water ice would have been stable, and then implanted in the outer Main Belt region because of the giant planets’ growth.Figure 1. Two asteroids, 94 Aurora and 423 Diotima, showing spectra similar to asteroids (1)Ceres and (52)Europa.Thermal modeling and evolution of primitive aster-oids:Primitive water-rich asteroids are thought to be originally composed of mixtures of anhydrous materi-als and water ice that waslater melted by heating sources such as the decay of 26Al, reacting with anhy-drous materials to form H2O/OH-rich minerals. Calcu-lations of the evolution of the temperature and struc-ture of icy planetesimals were performedusing a 1D finite differences thermal evolution model[13, 14] for 26Al-heated planetesimals. In particular, thermally activated compaction due to hot pressing of bodies with an initially unconsolidated porous structure is included. An ice-rich initial composition that leads to a material dominated by phyllosilicates upon aqueous alteration (with 25 vol% H2O and a rock fraction that contains 85 vol% phyllosilicates and 15 vol% olivine upon aque-ous alteration, similar to CIand CM chondrites) was assumed. Atypical initial porosity of 40%[15] is re-duced following the change of the strain rate that is calculated as Voigt approximation from the strain rates of components[16]. Material properties (thermal con-ductivity, density, heat capacity, etc.) correspond to the composition assumed and are adjusted with tempera-ture and porosity. Melting of the water ice as well as water-rock separation are included[14]. Both short-and long-lived radionuclides are consideredas heat sources. Figure 3 shows the maximum temperature calculated as a function of radius and accretion time. A variety of internal structures is obtained, ranging from primordial (no melting of water ice) over partially melted or partially differentiated (melting of water ice, hydration, formation of a rocky core and water ocean below an undifferentiated layer) to completely differ-entiated ones (rocky core, water mantle, Enceladus-like case). The heating and differentiation of planetesi-mals is determined by the availability of 26Al, i.e., by the accretion time t0 relative to the formation of the calcium-aluminum-rich inclusions (CAIs), such that maximum temperatures and structures vary stronglyfor t0< 6 Myr rel. to CAIs. However, for a later accre-tion only the size of the body determines its maximum tempera-ture and structure due to the nearly constant heating by long-lived radionuclides. Average densities of Ceres-and Europa-like group membersimply high-ly porous interiors and, consequently, relatively late accretion at t0> 3 Myr rel. to CAIs with a maximum temperature of < 600 K (Figure3)

D Takir↗

Spontaneously Broken Noninvertible Symmetries in Transverse-Field Ising Qudit Chains

Recent developments have revealed that symmetries need not form a group, but instead can be noninvertible. Here we use analytical arguments and numerical evidence to illuminate how spontaneous symmetry breaking of a noninvertible symmetry is similar yet distinct from ordinary, invertible, symmetry breaking. We consider one-dimensional chains of group-valued qudits, whose local Hilbert space is spanned by elements of a finite group 𝐺 (reducing to ordinary qubits when 𝐺=ℤ 2 ). We construct Ising-type transverse-field Hamiltonians with Rep⁡(𝐺) symmetry whose generators multiply according to the tensor product of irreducible representations (irreps) of the group 𝐺 . For non-Abelian 𝐺 , the symmetry is noninvertible. In the symmetry broken phase there is one ground state per irrep on a closed chain. The symmetry breaking can be detected by local order parameters but, unlike the invertible case, different ground states have distinct entanglement patterns. We show that for each irrep of dimension greater than one the corresponding ground state exhibits string order, entanglement spectrum degeneracies, and has gapless edge modes on an open chain—features usually associated with symmetry-protected topological order. Consequently, domain wall excitations behave as one-dimensional non-Abelian anyons with nontrivial internal Hilbert spaces and fusion rules. Our Letter identifies properties of noninvertible symmetry breaking that existing quantum hardware can probe.

1-dimensional spin chains↗