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At least 19 records

Projective Representations, Bogomolov Multiplier, and Their Applications in Physics

We present a pedagogical review of projective representations of finite groups and their physical applications in quantum many-body systems. Some of our physical results are new. We begin with a self-contained introduction to projective representations, highlighting the role of group cohomology, representation theory, and classification of irreducible projective representations. We then focus on a special subset of cohomology classes, known as the Bogomolov multiplier, which consists of cocycles that are symmetric on commuting pairs but remain nontrivial in group cohomology. Such cocycles have important physical implications: they characterize (1+1)D SPT phases that cannot be detected by string order parameters and give rise, upon gauging, to distinct gapped phases with completely broken non-invertible Rep(G) symmetry. We construct explicit lattice models for these phases and demonstrate how they are distinguished by the fusion rules of local order parameters. We show that a pair of completely broken Rep(G) SSB phases host nontrivial interface modes at their domain walls. As an example, we construct a lattice model where the ground state degeneracy on a ring increases from 32 without interfaces to 56 with interfaces.

Bogomolov multiplier↗

Vegetation Representation Influences Projected Streamflow Changes in the Colorado River Basin

Vegetation parameters for the Variable Infiltration Capacity (VIC) hydrologic model were recently updated using observations from the Moderate Resolution Imaging Spectroradiometer (MODIS). Previous work showed that these MODIS-based parameters improved VIC evapotranspiration simulations when compared to eddy covariance observations. Due to the importance of evapotranspiration within the Colorado River basin, this study provided a basin-by-basin calibration of VIC soil parameters with updated MODIS-based vegetation parameters to improve streamflow simulations. Interestingly, while both configurations had similar historic streamflow performance, end-of-century hydrologic projections, driven by 29 downscaled global climate models under the RCP8.5 emissions scenario, differed between the two configurations. The calibrated MODIS-based configuration had an ensemble mean that simulated little change in end-of-century annual streamflow volume (+0.4%) at Lees Ferry, Arizona, relative to the historical period (1960–2005). In contrast, the previous VIC configuration, which is used to inform decisions about future water resources in the Colorado River basin, projected an 11.7% decrease in annual streamflow. Both VIC configurations simulated similar amounts of evapotranspiration in the historical period. However, the MODIS-based VIC configuration did not show as much of an increase in evapotranspiration by the end of the century, primarily within the upper basin’s forested areas. Differences in evapotranspiration projections were the result of the MODIS-based vegetation parameters having lower leaf area index values and less forested area compared to previous vegetation estimates used in recent Colorado River basin hydrologic projections. These results highlight the need to accurately characterize vegetation and better constrain climate sensitivities in hydrologic models.

54 ENVIRONMENTAL SCIENCES↗

Exploring Afro-Asian water fluxes in CMIP5 and CMIP6 models: Present-day evaluation and future projections

Accurate representation and projection of water fluxes are vital, particularly in monsoon regions where seasonal variability and changes significantly impact water resources, agriculture, hydroelectric power generation, and the economy. This study uses both CMIP5 and CMIP6 models to investigate the present-day representation of key water flux components (including precipitation, evaporation, water vapor, and moisture advection) over the Afro-Asian region during the summer monsoon (JJAS). We also examine future changes under two emission scenarios and assess the underlying physical mechanisms driving these changes while identifying sources of projection uncertainty. Our results show that both models reasonably capture the present-day characteristics of water flux components, although with noticeable biases. Across most regions, we find that CMIP6 models demonstrate slight improvements over CMIP5 in the representation of these components. In a warmer future, a robust intensification of JJAS precipitation (exceeding 0.25 mm/day) is projected across the Afro-Asian region. This increase is largely driven by the vertical thermodynamic term associated with increasing temperature. We find that model uncertainty is the primary source of uncertainty in water flux projections, accounting for over 50 % of the total variance.

Climate change↗

Matrix ensembles with global symmetries and ’t Hooft anomalies from 2d gauge theory

The Hilbert space of a quantum system with internal global symmetry $\textit{G}$ decomposes into sectors labelled by irreducible representations of $\textit{G}$. If the system is chaotic, the energies in each sector should separately resemble ordinary random matrix theory. We show that such “sector-wise” random matrix ensembles arise as the boundary dual of two- dimensional gravity with a $\textit{G}$ gauge field in the bulk. Within each sector, the eigenvalue density is enhanced by a nontrivial factor of the dimension of the representation, and the ground state energy is determined by the quadratic Casimir. We study the consequences of ’t Hooft anomalies in the matrix ensembles, which are incorporated by adding specific topological terms to the gauge theory action. The effect is to introduce projective representations into the decomposition of the Hilbert space. Finally, we consider ensembles with $\textit{G}$ symmetry and time reversal symmetry, and analyze a simple case of a mixed anomaly between time reversal and an internal $\mathbb{Z}$ 2 symmetry.

2D Gravity↗

ROSE LCOM Tools

This project provides a tool to compute LCOM metrics for important Ada abstraction mechanisms (e.g., packages, protected objects). It analyzes data accesses and routine calls to compute an abstract representation of an Ada package (or some other abstraction). Different LCOM metrics (1-5) are computed from the abstract representation. The project also provides support for representing the abstraction graphically (via graphviz). The LCOM tool requires an existing ROSE installation configured with the GNAT 2019 compiler.

Lamar, KennethM↗

A spatial evaluation of Arctic sea ice and regional limitations in CMIP6 historical simulations

The Arctic sea ice response to a warming climate is assessed in a subset of models participating in Phase 6 of the Coupled Model Intercomparison Project (CMIP6), using several metrics in comparison with satellite observations and results from the Pan-Arctic Ice Ocean Modeling and Assimilation System and the Regional Arctic System Model. Our study examines the historical representation of sea ice extent, volume, and thickness using spatial analysis metrics, such as the integrated ice-edge error, Brier score, and Spatial Probability Score. We find that the CMIP6 multi-model mean captures the mean annual cycle and 1979-2014 sea ice trends remarkably well. However, individual models experience a wide range of uncertainty in the spatial distribution of sea ice when compared against satellite measurements and reanalysis data. Our metrics expose common and individual regional model biases, which sea ice temporal analyses alone do not capture. We identify large ice edge and ice thickness errors in Arctic sub-regions, implying possible model specific limitations in or lack of representation of some key physical processes. We postulate that many of them could be related to the oceanic forcing, especially in the marginal and shelf seas, where seasonal sea ice changes are not adequately simulated. We therefore conclude that an individual model’s ability to represent the observed/reanalysis spatial distribution still remains a challenge. We propose the spatial analysis metrics as useful tools to diagnose model limitations, narrow down possible processes affecting them, and guide future model improvements critical to the representation and projections of Arctic climate change.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Cloud response to co-condensation of water and organic vapors over the boreal forest

Abstract. Accounting for the condensation of organic vapors along with water vapor (co-condensation) has been shown in adiabatic cloud parcel model (CPM) simulations to enhance the number of aerosol particles that activate to form cloud droplets. The boreal forest is an important source of biogenic organic vapors, but the role of these vapors in co-condensation has not been systematically investigated. In this work, the environmental conditions under which strong co-condensation-driven cloud droplet number enhancements would be expected over the boreal biome are identified. Recent measurement technology, specifically the Filter Inlet for Gases and AEROsols (FIGAERO) coupled to an iodide-adduct chemical ionization mass spectrometer (I-CIMS), is utilized to construct volatility distributions of the boreal atmospheric organics. Then, a suite of CPM simulations initialized with a comprehensive set of concurrent aerosol observations collected in the boreal forest of Finland during spring 2014 is performed. The degree to which co-condensation impacts droplet formation in the model is shown to be dependent on the initialization of temperature, relative humidity, updraft velocity, aerosol size distribution, organic vapor concentration, and the volatility distribution. The predicted median enhancements in cloud droplet number concentration (CDNC) due to accounting for the co-condensation of water and organics fall on average between 16 % and 22 %. This corresponds to activating particles 10–16 nm smaller in dry diameter that would otherwise remain as interstitial aerosol. The highest CDNC enhancements (ΔCDNC) are predicted in the presence of a nascent ultrafine aerosol mode with a geometric mean diameter of ∼ 40 nm and no clear Hoppel minimum, indicative of pristine environments with a source of ultrafine particles (e.g., via new particle formation processes). Such aerosol size distributions are observed 30 %–40 % of the time in the studied boreal forest environment in spring and fall when new particle formation frequency is the highest. To evaluate the frequencies with which such distributions are experienced by an Earth system model over the whole boreal biome, 5 years of UK Earth System Model (UKESM1) simulations are further used. The frequencies are substantially lower than those observed at the boreal forest measurement site (< 6 % of the time), and the positive values, peaking in spring, are modeled only over Fennoscandia and the western parts of Siberia. Overall, the similarities in the size distributions between observed and modeled (UKESM1) are limited, which would limit the ability of this model, or any model with a similar aerosol representation, to project the climate relevance of co-condensation over the boreal forest. For the critical aerosol size distribution regime, ΔCDNC is shown to be sensitive to the concentrations of semi-volatile and some intermediate-volatility organic compounds (SVOCs and IVOCs), especially when the overall particle surface area is low. The magnitudes of ΔCDNC remain less affected by the more volatile vapors such as formic acid and extremely low- and low-volatility organic compounds (ELVOCs and LVOCs). The reasons for this are that most volatile organic vapors condense inefficiently due to their high volatility below the cloud base, and the concentrations of LVOCs and ELVOCs are too low to gain significant concentrations of soluble mass to reduce the critical supersaturations enough for droplet activation to occur. A reduction in the critical supersaturation caused by organic condensation emerges as the main driver of the modeled ΔCDNC. The results highlight the potential significance of co-condensation in pristine boreal environments close to sources of fresh ultrafine particles. For accurate predictions of co-condensation effects on CDNC, also in larger-scale models, an accurate representation of the aerosol size distribution is critical. Further studies targeted at finding observational evidence and constraints for co-condensation in the field are encouraged.

54 ENVIRONMENTAL SCIENCES↗

Reduced‐Order Modeling of Energetic Materials Using Physics‐Aware Recurrent Convolutional Neural Networks in a Latent Space (LatentPARC)

Physics-aware deep learning (PADL) has gained popularity for use in spatiotemporal dynamics simulations, such as those in computational modeling of energetic materials (EM). We show that the challenge PADL methods face while learning complex field evolution problems can be simplified and accelerated by decoupling it into two tasks: learning complex geometric features in evolving fields and modeling dynamics over these features in a lower-dimensional feature space. We build upon our previous work on physics-aware recurrent convolutional neural networks (PARC). PARC embeds knowledge of underlying physics into its neural network architecture for more robust and accurate prediction of evolving physical fields. PARC was shown to effectively learn complex nonlinear features such as the formation of hotspots and coupled shock fronts in various initiation scenarios of EMs, as a function of microstructures, serving effectively as a microstructure-aware burn model. Here, we further accelerate PARC and reduce its computational cost by projecting the original dynamics onto a lower-dimensional invariant manifold, or “latent space.” The projected latent representation encodes the complex geometry of evolving fields (e.g., temperature and pressure) in a set of data-driven features. The reduced dimension of this latent space allows us to learn the dynamics during the initiation of EM with a lighter and more efficient model. We observe a significant decrease in training and inference time while maintaining results comparable to PARC at inference. This work takes steps towards enabling rapid prediction of EM thermomechanics at larger scales and characterization of EM structure–property–performance linkages at a full application scale.

Mathematics and Computing↗

Duality defect of the monster CFT

Abstract We show that the fermionization of the Monster CFT with respect to Z 2 A is the tensor product of a free fermion and the Baby Monster CFT. The chiral fermion parity of the free fermion implies that the Monster CFT is self-dual under the Z 2 A orbifold, i.e. it enjoys the Kramers–Wannier duality. The Kramers–Wannier duality defect extends the Monster group to a larger category of topological defect lines that contains an Ising subcategory. We introduce the defect McKay – Thompson series defined as the Monster partition function twisted by the duality defect, and find that the coefficients can be decomposed into the dimensions of the (projective) irreducible representations of the Baby Monster group. We further prove that the defect McKay–Thompson series is invariant under the genus-zero congruence subgroup 16 D 0 of P S L ( 2 , Z ) .

Physics↗

A variant selection framework for genome graphs

Abstract Motivation Variation graph representations are projected to either replace or supplement conventional single genome references due to their ability to capture population genetic diversity and reduce reference bias. Vast catalogues of genetic variants for many species now exist, and it is natural to ask which among these are crucial to circumvent reference bias during read mapping. Results In this work, we propose a novel mathematical framework for variant selection, by casting it in terms of minimizing variation graph size subject to preserving paths of length α with at most δ differences. This framework leads to a rich set of problems based on the types of variants [e.g. single nucleotide polymorphisms (SNPs), indels or structural variants (SVs)], and whether the goal is to minimize the number of positions at which variants are listed or to minimize the total number of variants listed. We classify the computational complexity of these problems and provide efficient algorithms along with their software implementation when feasible. We empirically evaluate the magnitude of graph reduction achieved in human chromosome variation graphs using multiple α and δ parameter values corresponding to short and long-read resequencing characteristics. When our algorithm is run with parameter settings amenable to long-read mapping (α = 10 kbp, δ = 1000), 99.99% SNPs and 73% SVs can be safely excluded from human chromosome 1 variation graph. The graph size reduction can benefit downstream pan-genome analysis. Availability and implementation https://github.com/AT-CG/VF. Supplementary information Supplementary data are available at Bioinformatics online.

59 BASIC BIOLOGICAL SCIENCES↗

Finite and infinite matrix product states for Gutzwiller projected mean-field wave functions

Matrix product states (MPS) and “dressed” ground states of quadratic mean fields (e.g., Gutzwiller projected Slater determinants) are both important classes of variational wave functions. This latter class has played important roles in understanding superconductivity and quantum spin liquids. We present a method to obtain both the finite and infinite MPS (iMPS) representation of the ground state of an arbitrary fermionic quadratic mean-field Hamiltonian (which in the simplest case is a Slater determinant and in the most general case is a Pfaffian). We also show how to represent products of such states (e.g., determinants times Pfaffians). From this representation one can project to single occupancy and evaluate the entanglement spectra after Gutzwiller projection. We then obtain the MPS and iMPS representation of Gutzwiller projected mean-field states that arise from the variational slave-fermion approach to the S = 1 bilinear-biquadratic quantum spin chain. To accomplish this, we develop an approach to orthogonalize degenerate iMPS to find all the states in the degenerate ground-state manifold. We find the energies of the MPS and iMPS states match the variational energies closely, indicating the method is accurate and there is minimal loss due to truncation error. We then present an exploration of the entanglement spectra of projected slave-fermion states, exploring their qualitative features and finding good qualitative agreement with the respective exact ground-state spectra found from density matrix renormalization group.

1-dimensional spin chains↗

Closed-Loop Pumped Storage Hydropower Resource Assessment for the United States. Final Report on HydroWIRES Project D1: Improving Hydropower and PSH Representations in Capacity Expansion Models

Pumped storage hydropower represents the bulk of the United States' current energy storage capacity: 23 gigawatts (GW) of the 24-GW national total (Denholm et al. 2021). This capacity was largely built between 1960 and 1990. PSH is a mature and proven method of energy storage with competitive round-trip efficiency and long life spans. These qualities make PSH a very attractive potential solution to energy storage needs, particularly for longer-duration storage (8 hours or more); such storage will be crucial to bridge gaps in electricity production as variable wind and solar production continue to comprise an ever-larger portion of the United States' energy portfolio (Cole et al. 2021; Frazier et al. 2021). However, it is unclear how much potential the United States has for the development of new PSH. No new large PSH has been constructed in the United States since the 1990s, and attempts to quantify technical potential capacity from PSH project applications to the Federal Energy Regulatory Commission (FERC) suffer from inconsistent site and cost evaluation methodologies and likely are not representative of all PSH opportunities. This study seeks to better under understand the technical potential for PSH development in the United States by developing a national-scale resource assessment for closed-loop PSH. Individual sites are not modeled in sufficient detail for project-level development, but they do provide valuable insights into potential resource areas across the United States, including the ability to provide estimates for a range of long-term development scenarios.

13 HYDRO ENERGY↗

Nitrate loading projection is sensitive to freeze-thaw cycle representation

Climate change can have substantial impacts on nitrogen runoff, which is a major cause of eutrophication, harmful algal blooms, and hypoxia in freshwaters and coastal regions. We examined responses of nitrate loading to climate change in the Upper Mississippi River Basin (UMRB) with an enhanced Soil and Water Assessment Tool with physically based Freeze-Thaw cycle representation (SWAT-FT), as compared with the original SWAT model that employs an empirical equation. Driven by future climate projections from five General Circulation Models (GCMs) from 1960 to 2099 under the Representative Concentrations Pathways (RCP) 8.5 scenario, we analyzed changes in riverine nitrate loadings, as well as terrestrial surface and subsurface contributions of the UMRB in the 21st century relative to the baseline period of 1960–1999. By the end of the 21st century, the original SWAT model predicted about a 50% increase in riverine nitrate loadings which is nearly twice as much as that estimated by SWAT-FT (ca. 25%). Such a large difference in projected nitrate changes can potentially mislead mitigation strategies that aim to reduce nitrogen runoff from the UMRB. Further analysis shows that the difference between the original SWAT model and SWAT-FT led to substantial discrepancies in the spatial distribution of surface and subsurface nitrate loadings in the UMRB. In general, SWAT-FT predicted more nitrate leaching for northwestern parts of the UMRB which are more sensitive to freeze-thaw cycle, mainly because SWAT-FT simulated less frequent frozen soils. This study highlights the importance of using physically based freeze-thaw cycle representation in water quality modeling. Design of future nitrogen runoff reduction strategies should include careful assessment of effects that land management has on the freeze-thaw cycles to provide reliable projection of water quality under climate change.

Wang, Qianfeng↗

SynopFrame: Multiscale time-dependent visual abstraction framework for analyzing DNA nanotechnology simulations

We present an open-source framework, SynopFrame, that allows DNA nanotechnology (DNA-nano) experts to analyze and understand molecular dynamics simulation trajectories of their designs. We use a multiscale multi-dimensional abstraction space, connect the representations to a projected conformational space plot of the structure’s temporal sequence, and thus enable experts to analyze the dynamics of their structural designs and, specifically, failure cases of the assembly. In addition, our time-dependent abstraction representation allows the biologists, for the first time in a smooth and structurally clear way, to identify and observe temporal transitions of a DNA-nano design from one configuration to another, and to highlight important periods of the simulation for further analysis. We realize SynopFrame as a dashboard of the different synchronized 3D spatial and 2D schematic visual representations, with a color overlay to show essential properties such as the status of hydrogen bonds. The linking of the spatial, schematic, and abstract views ensures that users can effectively analyze the high-frequency motion. We also categorize the status of the hydrogen bonds into a new format to allow us to color-encode it and overlay it on the representations. To demonstrate the utility of SynopFrame, we describe example usage scenarios and report user feedback.

Abstraction space↗

The Schwarz Alternating Method for the Seamless Coupling of Nonlinear Reduced Order Models and Full Order Models

Projection-based model order reduction allows for the parsimonious representation of full order models (FOMs), typically obtained through the discretization of a set of partial differential equations (PDEs) using conventional techniques (e.g., finite element, finite volume, finite difference methods) where the discretization may contain a very large number of degrees of freedom. As a result of this more compact representation, the resulting projection-based reduced order models (ROMs) can achieve considerable computational speedups, which are especially useful in real-time or multi-query analyses. One known deficiency of projection-based ROMs is that they can suffer from a lack of robustness, stability and accuracy, especially in the predictive regime, which ultimately limits their useful application. Another research gap that has prevented the widespread adoption of ROMs within the modeling and simulation community is the lack of theoretical and algorithmic foundations necessary for the “plug-and-play” integration of these models into existing multi-scale and multi-physics frameworks. This paper describes a new methodology that has the potential to address both of the aforementioned deficiencies by coupling projection-based ROMs with each other as well as with conventional FOMs by means of the Schwarz alternating method [41]. Leveraging recent work that adapted the Schwarz alternating method to enable consistent and concurrent multiscale coupling of finite element FOMs in solid mechanics [35, 36], we present a new extension of the Schwarz framework that enables FOM-ROM and ROM-ROM coupling, following a domain decomposition of the physical geometry on which a PDE is posed. In order to maintain efficiency and achieve computation speed-ups, we employ hyper-reduction via the Energy-Conserving Sampling and Weighting (ECSW) approach [13]. We evaluate the proposed coupling approach in the reproductive as well as in the predictive regime on a canonical test case that involves the dynamic propagation of a traveling wave in a nonlinear hyper-elastic material.

97 MATHEMATICS AND COMPUTING↗

Understanding the Physics Representation of Deep Learning Models in Environmental Applications

Deep learning (DL) models have been popular in earth and environmental modeling and analysis, which exhibit huge potential in capturing and reconstructing the non-linearity of relevant environmental processes. They are extensively used as analytical tools or emulators for multiple domains (atmosphere, land surface, ocean, and biogeochemistry). Despite their success, their internal working mechanism remains largely unknown. Such a lack of knowledge hinders the identification of physically consistent models that are fully adaptive to non-stationary climate, as well as the development of physics-informed machine learning such as physics-informed neural network (PINN). To establish preliminary knowledge and framework of such physics representation evaluation, this project focuses on an improved understanding of DL models in the environmental applications. DL models are increasingly applied to environmental modeling and prediction. However, they have been evaluated mostly from a performance perspective, and there is a gap in understanding how they represent the known physics internally. Such knowledge is especially critical when applying DL models under climate change conditions, where new inputs are likely outside the ranges of the training datasets. In this project, we reveal how the known physical processes are represented within DL models from both statistical and mechanistic perspectives. Leveraging the traditional model evaluations that focus more on the accuracies of predictions, we establish a framework that examines both the accuracy and physics representation of DL models. This analysis framework can identify DL models that make the correct predictions based on correct physics, thus enhancing the existing explainable artificial intelligence (explainable-AI) portfolio. It lays a foundation for developing novel metrics to evaluate the emerging DL models in environmental applications. This knowledge also informs the development of physics-informed DL models by revealing the direct connections between the known physical processes and specific model components or structures.

54 ENVIRONMENTAL SCIENCES↗

Data Centers Gap Analysis [Slides]

Data centers and other large loads are a significant driver of unprecedented, near-term demand growth in the United States. Power system planners, utilities, regulators, and other stakeholders are grappling with how to integrate data centers on the system without comprising reliability, resiliency, and energy affordability. NLR is pursuing work to develop a siting and decision-making tool that would draw on power systems modeling expertise to achieve granular representation of trade-offs involved in data center sitting and development. This slide deck supports the same workstream by reviewing the literature to identify mitigation options to facilitate near-term integration of large loads and by presenting options for pursuing data development and/or modeling projects to improve representation of siting options.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗