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NASA NTRS1988

Semi-discrete approximations to nonlinear systems of conservation laws; consistency and L(infinity)-stability imply convergence

A convergence theory for semi-discrete approximations to nonlinear systems of conservation laws is developed. It is shown, by a series of scalar counter-examples, that consistency with the conservation law alone does not guarantee convergence. Instead, a notion of consistency which takes into account both the conservation law and its augmenting entropy condition is introduced. In this context it is concluded that consistency and L(infinity)-stability guarantee for a relevant class of admissible entropy functions, that their entropy production rate belongs to a compact subset of H(loc)sup -1 (x,t). One can now use compensated compactness arguments in order to turn this conclusion into a convergence proof. The current state of the art for these arguments includes the scalar and a wide class of 2 x 2 systems of conservation laws. The general framework of the vanishing viscosity method is studied as an effective way to meet the consistency and L(infinity)-stability requirements. How this method is utilized to enforce consistency and stability for scalar conservation laws is shown. In this context we prove, under the appropriate assumptions, the convergence of finite difference approximations (e.g., the high resolution TVD and UNO methods), finite element approximations (e.g., the Streamline-Diffusion methods) and spectral and pseudospectral approximations (e.g., the Spectral Viscosity methods).

Tadmor, Eitan↗

NASA NTRS1993

A new flux conserving Newton's method scheme for the two-dimensional, steady Navier-Stokes equations

A new numerical method is developed for the solution of the two-dimensional, steady Navier-Stokes equations. The method that is presented differs in significant ways from the established numerical methods for solving the Navier-Stokes equations. The major differences are described. First, the focus of the present method is on satisfying flux conservation in an integral formulation, rather than on simulating conservation laws in their differential form. Second, the present approach provides a unified treatment of the dependent variables and their unknown derivatives. All are treated as unknowns together to be solved for through simulating local and global flux conservation. Third, fluxes are balanced at cell interfaces without the use of interpolation or flux limiters. Fourth, flux conservation is achieved through the use of discrete regions known as conservation elements and solution elements. These elements are not the same as the standard control volumes used in the finite volume method. Fifth, the discrete approximation obtained on each solution element is a functional solution of both the integral and differential form of the Navier-Stokes equations. Finally, the method that is presented is a highly localized approach in which the coupling to nearby cells is only in one direction for each spatial coordinate, and involves only the immediately adjacent cells. A general third-order formulation for the steady, compressible Navier-Stokes equations is presented, and then a Newton's method scheme is developed for the solution of incompressible, low Reynolds number channel flow. It is shown that the Jacobian matrix is nearly block diagonal if the nonlinear system of discrete equations is arranged approximately and a proper pivoting strategy is used. Numerical results are presented for Reynolds numbers of 100, 1000, and 2000. Finally, it is shown that the present scheme can resolve the developing channel flow boundary layer using as few as six to ten cells per channel width, depending on the Reynolds number.

Scott, James R.↗

NASA NTRS2002

International Conference on Remote Sensing Applications for Archaeological Research and World Heritage Conservation

Contents include the following: Monitoring the Ancient Countryside: Remote Sensing and GIS at the Chora of Chersonesos (Crimea, Ukraine). Integration of Remote Sensing and GIS for Management Decision Support in the Pendjari Biosphere Reserve (Republic of Benin). Monitoring of deforestation invasion in natural reserves of northern Madagascar based on space imagery. Cartography of Kahuzi-Biega National Park. Cartography and Land Use Change of World Heritage Areas and the Benefits of Remote Sensing and GIS for Conservation. Assessing and Monitoring Vegetation in Nabq Protected Area, South Sinai, Egypt, using combine approach of Satellite Imagery and Land Surveys. Evaluation of forage resources in semi-arid savannah environments with satellite imagery: contribution to the management of a protected area (Nakuru National Park) in Kenya. SOGHA, the Surveillance of Gorilla Habitat in World Heritage sites using Space Technologies. Application of Remote Sensing to monitor the Mont-Saint-Michel Bay (France). Application of Remote Sensing & GIS for the Conservation of Natural and Cultural Heritage Sites of the Southern Province of Sri Lanka. Social and Environmental monitoring of a UNESCO Biosphere Reserve: Case Study over the Vosges du Nord and Pfalzerwald Parks using Corona and Spot Imagery. Satellite Remote Sensing as tool to Monitor Indian Reservation in the Brazilian Amazonia. Remote Sensing and GIS Technology for Monitoring UNESCO World Heritage Sites - A Pilot Project. Urban Green Spaces: Modern Heritage. Monitoring of the technical condition of the St. Sophia Cathedral and related monastic buildings in Kiev with Space Applications, geo-positioning systems and GIS tools. The Murghab delta palaeochannel Reconstruction on the Basis of Remote Sensing from Space. Acquisition, Registration and Application of IKONOS Space Imagery for the cultural World Heritage site at Mew, Turkmenistan. Remote Sensing and VR applications for the reconstruction of archaeological landscapes. Archaeology through Space: Experience in Indian Subcontinent. The creation of a GIS Archaeological Site Location Catalogue in Yucatan: A Tool to preserve its Cultural Heritage. Mapping the Ancient Anasazi Roads of Southeast Utah. Remote Sensing and GIS Technology for Identification of Conservation and Heritage sites in Urban Planning. Mapping Angkor: For a new appraisal of the Angkor region. Angkor and radar imaging: seeing a vast pre-industrial low-density, dispersed urban complex. Technical and methodological aspects of archaeological CRM integrating high resolution satellite imagery. The contribution of satellite imagery to archaeological survey: an example from western Syria. The use of satellite images, digital elevation models and ground truth for the monitoring of land degradation in the "Cinque Terre" National park. Remote Sensing and GIS Applications for Protection and Conservation of World Heritage Site on the coast - Case Study of Tamil Nadu Coast, India. Multispectral high resolution satellite imagery in combination with "traditional" remote sensing and ground survey methods to the study of archaeological landscapes. The case study of Tuscany. Use of Remotely-Sensed Imagery in Cultural Landscape. Characterisation at Fort Hood, Texas. Heritage Learning and Data Collection: Biodiversity & Heritage Conservation through Collaborative Monitoring & Research. A collaborative project by UNESCO's WHC (World Heritage Center) & The GLOBE Program (Global Learning and Observations to Benefit the Environment). Practical Remote Sensing Activities in an Interdisciplinary Master-Level Space Course.

Source record↗

NASA NTRSDate not supplied

Conserved Function of RNA Binding Motif Protein48 (RBM48) and Armadillo Repeat Containing 7 (ARMC7) in Maize and Human U12 Splicing

Splicing of pre-mRNA is fundamental for genes containing introns. Emerging data points to a deeply conserved role of this process in eukaryotic cell differentiation and proliferation. The vast majority of introns termed U2-type introns are spliced by a major spliceosome; however, there also exist rare and more conserved U12-type introns that are spliced by a minor spliceosome. Mutations that disrupt U12 splicing inhibit cell differentiation in both maize endosperm and human blood cells. However, the mechanism underlying this process is not well understood. The maize RNA Binding Motif Protein 48 (RBM48) plays an essential role as a U12 splicing factor and is required for proper maize kernel development. Using human cell lines, CRISPR-Cas9 knockdown of RBM48 demonstrated a conserved function in human U12 intron splicing. RBM48 and Armadillo Repeat Containing 7 (ARMC7) protein interact in both maize and human as part of the activated minor spliceosome. Here we show RBM48 and ARMC7 co-localization in the nucleus of human cell lines. Vertebrate ARMC7 is normally localized in the cytosol, whereas RBM48 is found in the nucleus. Our data suggests that the interaction plays a role in regulating ARMC7 localization or the efficiency of U12 intron splicing. We also performed comprehensive transcriptome profiling and identified a common subset of conserved Minor Intron Containing Genes (MIGs) impacted in both human and maize RBM48 knockout mutants. Of importance, the vast majority of these MIGs are associated with developmental defects in both plants and animals. This suggests that aberrant splicing of these targets has a high likelihood of mediating abnormal cell phenotypes. These data support evolutionarily conserved U12 splicing mechanisms between maize and humans with both RBM48 and ARMC7 having roles in the activated spliceosome.

maize↗

DOE OSTI2022

Draft Environmental Impact Statement for Proposed Energy Conservation Standards for Manufactured Housing

This draft environmental impact statement (EIS) analyzes the impacts related to DOE’s proposed energy conservation standards for manufactured homes. DOE’s proposed energy conservation standards are based on the 2021 International Energy Conservation Code (IECC) and relate to the building thermal envelope; air sealing; installation of insulation; duct sealing; heating, ventilation and air conditioning (HVAC); service hot water systems; mechanical ventilation fan efficacy; and heating and cooling equipment sizing. The draft EIS evaluates DOE’s proposed action (energy conservation standards tiered based the manufacturers retail list price), alternatives to the proposed action (including energy conservation standards tiered based on size of the manufactured home and untiered standards), and a no action alternative. The draft EIS presents analysis of impacts related to (1) energy resources; (2) air resources (including greenhouse gases, climate change, ambient air quality and indoor air quality); (3) health and safety; (4) socioeconomics; and (5) environmental justice.

MacDonell, Margaret↗

DOE OSTI2026

Entropy Stable Conservative Flux Form Neural Networks

We propose an entropy-stable conservative flux form neural network (CFN) to predict the dynamics of unknown governing conservation laws. The design of the network is based on the entropy-stable, second-order, and non-oscillatory Kurganov-Tadmor (KT) scheme. The proposed entropy-stable CFN, hereafter referred to as ESCFN, uses slope limiting as a denoising mechanism, ensuring accurate predictions in both noisy and sparse observation environments, as well as in both smooth and discontinuous regions. Importantly, our method is designed to predict long term dynamics of the unknown conservation law exclusively from a short temporal window of observed data, that is, without oracle knowledge of the PDE or later-time solution profiles. Numerical experiments demonstrate that the ESCFN achieves both stability and conservation while maintaining accuracy over extended time domains, and successfully predicts shock propagation speeds in long-term simulations. Furthermore, it is also robust to both noisy and sparse data environments.

Hyperbolic conservation laws↗

DOE OSTI2021

Using Change Models to Envision Better Applications of Animal Behavior Research in Conservation Management and Beyond

While most animal behavior researchers have mastered the process of knowledge creation, generating knowledge that can readily be applied requires a different set of skills. The process and timeframe of fundamental scientific knowledge production is often not relevant to those who might apply it, such as conservation or wildlife managers. Additionally, the complex challenges that policy makers, managers and practitioners face are often not adequately communicated to and among scientists. This mutual disconnect in discourse, relationships, common terms, and practices is especially apparent when animal behavior researchers seek to have applied impact. We argue that bridging the complex implementation gap in animal behavior requires a formalized vision for change. We turn to change model theory, a tool commonly used in other fields for identifying the links between actions and outcomes necessary for enacting large-scale change. We focus on the subfield of conservation behavior with a change model that outlines specific ways to improve collaboration and coordination between animal behavior science and conservation practice. We present this targeted change model, review each strategy the model outlines, and highlight pressing actions that people from various career stages and backgrounds can take. We encourage researchers to further the alignment of science with management needs by developing the proper communication mechanisms for improved cultural exchange and plan future change model efforts directly targeting managers. Beyond the conservation behavior change model we present, we also discuss the broad applicability of change models to enhance the application of academic research to other fields. Fundamental science researchers are increasingly required to show impact of their work on society; the change model process we describe here can enable further impact.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Path-Integrated Stereo X-Ray Digital Image Correlation: Resolving the Violation of Conservation of Intensity

In this study, x-ray imaging addresses many challenges with visible light imaging in extreme environments, where optical diagnostics such as digital image correlation (DIC) and particle image velocimetry (PIV) suffer biases from index of refraction changes and/or cannot penetrate visibly occluded objects. However, conservation of intensity—the fundamental principle of optical image correlation algorithms—may be violated if ancillary components in the X-ray path besides the surface or fluid of interest move during the test. The test series treated in this work sought to characterize the safe use of fiber-epoxy composites in aerospace and aviation industries during fire accident scenarios. Stereo X-ray DIC was employed to measure test unit deformation in an extreme thermal environment involving a visibly occluded test unit, incident surface heating to temperatures above 600°C, and flames and soot from combusting epoxy decomposition gasses. The objective of the current work is to evaluate two solutions to resolve the violation of conservation of intensity that resulted from both the test unit and the thermal chamber deforming during the test. The first solution recovered conservation of intensity by pre-processing the path-integrated X-ray images to isolate the DIC pattern of the test unit from the thermal chamber components. These images were then correlated with standard, optical DIC software. The second solution, called Path-Integrated Digital Image Correlation (PI-DIC), modified the fundamental matching criterion of DIC to account for multiple, independently-moving components contributing to the final image intensity. The PI-DIC algorithm was extended from a 2D framework to a stereo framework and implemented in a custom DIC software. Both solutions accurately measured the cylindrical shape of the undeformed test unit, recovering radii values of R = 76.20±0.12 mm compared to the theoretical radius of R theor = 76.20 mm. During the test, the test unit bulged asymmetrically as decomposition gasses pressurized the interior and eventually burned in a localized jet. Both solutions measured the heterogeneous radius of this bulge, which reached a maximum of approximately R = 91 mm, with a discrepancy of 2–3% between the two solutions. Two solutions that resolve the violation of conservation of intensity for path-integrated X-ray images were developed. Both were successfully employed in a stereo X-ray DIC configuration to measure deformation of an aluminum-skinned, fiber-epoxy composite test unit in a fire accident scenario.

47 OTHER INSTRUMENTATION↗

DOE OSTI2022

Performance Analysis of Speculative Parallel Adaptive Local Timestepping for Conservation Laws

Stable simulation of conservation laws, such as those used to model fluid dynamics and plasma physics applications, requires the satisfaction of the so-called Courant-Friedrichs-Lewy condition. By allowing regions of the mesh to advance with different timesteps that locally satisfy this stability constraint, significant work reduction can be attained when compared to a time integration scheme using a single timestep size. However, parallelizing this algorithm presents considerable difficulty. Since the stability condition depends on the state of the system, dependencies become dynamic and potentially non-local. In this article, we present an adaptive local timestepping algorithm using an optimistic (Timewarp-based) parallel discrete event simulation. We introduce waiting heuristics to limit misspeculation and a semi-static load balancing scheme to eliminate load imbalance as parts of the mesh require finer or coarser timesteps. Last, we outline an interface for separating the physics of the specific conservation law from the temporal integration allowing for productive adoption of our proposed algorithm. We present a misspeculation study for three conservation laws, demonstrating both the productivity of the local timestepping API, for which 74% of the lines of code are reused across different conservation laws, and the robustness of the waiting heuristics—at most 1.5% of element updates are rolled back. Our performance studies demonstrate up to a 2.8× speedup versus a baseline unoptimized local timestepping approach, a 4x improvement in per-node throughput compared to an MPI parallelization of synchronous timestepping, and scalability up to 3,072 cores on NERSC’s Cori Haswell partition.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Machine Learning for Conservative-to-Primitive in Relativistic Hydrodynamics

The numerical solution of relativistic hydrodynamics equations in conservative form requires root-finding algorithms that invert the conservative-to-primitive variables map. These algorithms employ the equation of state of the fluid and can be computationally demanding for applications involving sophisticated microphysics models, such as those required to calculate accurate gravitational wave signals in numerical relativity simulations of binary neutron stars. This work explores the use of machine learning methods to speed up the recovery of primitives in relativistic hydrodynamics. Artificial neural networks are trained to replace either the interpolations of a tabulated equation of state or directly the conservative-to-primitive map. The application of these neural networks to simple benchmark problems shows that both approaches improve over traditional root finders with tabular equation-of-state and multi-dimensional interpolations. In particular, the neural networks for the conservative-to-primitive map accelerate the variable recovery by more than an order of magnitude over standard methods while maintaining accuracy. Neural networks are thus an interesting option to improve the speed and robustness of relativistic hydrodynamics algorithms.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

A pseudospectral implicit particle-in-cell method with exact energy and charge conservation

The standard particle-in-cell (PIC) method employs explicit finite-difference (FD) methods (e.g. the leap-frog scheme) for both spatial and temporal integrations. Here, we employ a pseudospectral method for solving the Poisson equation and a fully implicit time integration to achieve exact energy conservation. The advantage of a pseudospectral field solver is its spectral accuracy in solving field solutions. Earlier studies of implicit time integration of PIC FD equations can enforce exact energy exchange between field and particles, resulting in exact energy-conserving schemes. Here, we prove that the exact energy conservation property can be carried over to the pseudospectral scheme. Simultaneously, we provide a solution to ensure a pseudospectral charge continuity equation. We demonstrate the new scheme in a 2D electrostatic PIC code. In conclusion, theoretical results are confirmed via numerical examples.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

A heuristic tool to assess regional impacts of renewable energy infrastructure on conservation areas

Wind and hydropower are important renewable components of national energy portfolios, but their infrastructure negatively affects biodiversity. Regional development requires identification of scenarios that minimize the cumulative impacts of multiple facilities. We introduce the cumulative impact plot (CIP) to quantify cumulative impacts of renewable energy development within a region. Summed impacts of facilities are plotted as a function of the number of facilities, with facilities ranked by increasing (the best-case scenario) or decreasing (worst-case scenario) individual impact. These curves represent lower and upper bounds to which alternative development scenarios (e.g., facilities ranked by generating capacity) can be compared. We used CIPs to assess overlap of potential wind and hydropower facilities with two types of conservation area in the United States: (1) federally protected lands and (2) critical habitats of federally threatened and endangered species. Here, we evaluated two alternative scenarios: facilities ranked by (A) decreasing generating capacity and (B) increasing distance from urban centers. Differences between the best-case and worst-case scenarios were large, thus revealing opportunities to develop facilities with limited impact on conservation areas. Alternative scenarios maximizing energy density generally resulted in conservation area overlap intermediate to best-case and worst-case scenarios. CIPs can also identify the proportion of wind versus hydropower favored under alternative scenarios. Build-out scenarios aimed at minimizing conservation area overlap favor hydropower, whereas alternative scenarios favor wind power. We conclude that CIPs can (1) complement—but should not replace—project-level environmental impact assessment, (2) integrate strategic, cumulative, and scenario-based assessments, and (3) harness rapidly growing geospatial data.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

A conservative Galerkin solver for the quasilinear diffusion model in magnetized plasmas

We propose a conservative Galerkin scheme for the quasilinear model in three-dimensional momentum space and three-dimensional spectral space, with cylindrical symmetry. We construct an unconditionally conservative weak form and use a discretization that preserves conservation properties independent of the wave emission probability. The discrete operators, combined with a consistent quadrature rule, preserve all the conservation laws rigorously. The proposed scheme is quite general: it works for both relativistic and non-relativistic systems, for both magnetized and unmagnetized plasmas, and even for problems with time-dependent dispersion relations. We represent the particle distribution by continuous basis functions and use discontinuous basis functions for the wave spectral energy density, which enables the application of a positivity-preserving technique. We adopt the marching simplex algorithm, designed initially for computer graphics, for numerical integration on the resonance manifold. Furthermore, the numerical examples with a bump-on-tail initial configuration show how the unstable waves produce strong momentum space diffusion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Surrogate modeling for efficiently, accurately and conservatively estimating measures of risk

We present a surrogate modeling framework for conservatively estimating measures of risk from limited realizations of an expensive physical experiment or computational simulation. Risk measures combine objective probabilities with the subjective values of a decision maker to quantify anticipated outcomes. Given a set of samples, we construct a surrogate model that produces estimates of risk measures that are always greater than their empirical approximations obtained from the training data. These surrogate models limit over-confidence in reliability and safety assessments and produce estimates of risk measures that converge much faster to the true value than purely sample-based estimates. We first detail the construction of conservative surrogate models that can be tailored to a stakeholder’s risk preferences and then present an approach, based on stochastic orders, for constructing surrogate models that are conservative with respect to families of risk measures. Our surrogate models include biases that permit them to conservatively estimate the target risk measures. We provide theoretical results that show that these biases decay at the same rate as the L 2 error in the surrogate model. Numerical demonstrations confirm that risk-adapted surrogate models do indeed overestimate the target risk measures while converging at the expected rate.

42 ENGINEERING↗

DOE OSTI2025

Carbon-conserving bioproduction of malate in an E. coli -based cell-free system

Formate, a biologically accessible form of CO 2 , has attracted interest as a renewable feedstock for bioproduction. However, approaches are needed to investigate efficient routes for biological formate assimilation due to its toxicity and limited utilization by microorganisms. Cell-free systems hold promise due to their potential for efficient use of carbon and energy sources and compatibility with diverse feedstocks. However, bioproduction using purified cell-free systems is limited by costly enzyme purification, whereas lysate-based systems must overcome loss of flux to background reactions in the cell extract. Here, we engineer an E. coli-based system for an eight-enzyme pathway from DNA and incorporate strategies to regenerate cofactors and minimize loss of flux through background reactions. We produce the industrial di-acid malate from glycine, bicarbonate, and formate by engineering the carbon-conserving reductive TCA and formate assimilation pathways. We show that in situ regeneration of NADH drives metabolic flux towards malate, improving titer by 15-fold. Background reactions can also be reduced 6-fold by diluting the lysate following expression and introducing chemical inhibitors of competing reactions. Together, these results establish a carbon-conserving, lysate-based cell-free platform for malate production, producing 64 μM malate after 8 h. This system conserves 43 % of carbon otherwise lost as CO 2 through the TCA cycle and incorporates 0.13 mol CO 2 equivalents/mol glycine fed. Finally, techno-economic analysis of cell-free malate production from formate revealed that the high cost of lysate is a key challenge to the economic feasibility of the process, even assuming efficient cofactor recycling. This work demonstrates the capabilities of cell-free expression systems for both the prototyping of carbon-conserving pathways and the sustainable bioproduction of platform chemicals.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2022

Momentum conservation in current drive and alpha-channeling-mediated rotation drive

Alpha channeling uses waves to extract hot ash from a fusion plasma, transferring energy from the ash to the wave. It has been proposed that this process could create a radial electric field, efficiently driving E × B rotation. However, existing theories ignore the nonresonant particles, which play a critical role in enforcing momentum conservation in quasilinear theory. Because cross field charge transport and momentum conservation are fundamentally linked, this non-consistency throws the rotation drive into question. This paper has two main goals. First, we provide a pedantic and cohesive introduction to the recently developed simple, general, self-consistent quasilinear theory for electrostatic waves that explains the torques which allow for current drive parallel to the magnetic field, and charge extraction across it; a theory that has largely resolved the question of rotation drive by alpha channeling. We show how the theory reveals a fundamental difference between the reaction of nonresonant particles to plane waves that grow in time vs steady-state waves that have a nonuniform spatial structure, allowing rotation drive in the latter case while precluding it in the former, and we review the local and global conservation laws that lead to this result. Second, we provide two new results in support of the theory. First, we provide a novel two-particle Hamiltonian model that rigorously establishes the relationship between charge transport and momentum conservation. Second, we compare the new quasilinear theory to the oscillation-center theories of ponderomotive forces, showing how the latter often obscure the time-dependent nonresonant recoil, but ultimately lead to similar results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Conservation of angular momentum in ultrafast spin dynamics

The total angular momentum of a closed system is a conserved quantity, which should remain constant in time for any excitation experiment once the pumping signal has been extinguished. Such conservation, however, is never satisfied in practice in any real-time first-principles description of the demagnetization process. Furthermore, there is growing experimental evidence that the same takes place in experiments. The missing angular momentum is usually associated to lattice vibrations, which are not measured experimentally and are never considered in real-time simulations. Here, in this study, we critically analyze the issue and conclude that current state-of-the-art simulations violate angular momentum conservation already at the electronic level of description. This shortcoming originates from an oversimplified description of the spin-orbit coupling, which includes atomic contributions but neglects completely that of itinerant electrons. We corroborate our findings with time-dependent simulations using model tight-binding Hamiltonians, and show that indeed such conservation can be reintroduced by an appropriate choice of spin-orbit coupling. The consequences of our findings on recent experiments are also discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Slow thermalization and subdiffusion in $U$(1) conserving Floquet random circuits

Random quantum circuits are paradigmatic models of minimally structured and analytically tractable chaotic dynamics. We study a family of Floquet unitary circuits with Haar random U(1) charge conserving dynamics; the minimal such model has nearest-neighbor gates acting on spin-1/2 qubits, and a single layer of even/odd gates repeated periodically in time. We find that this minimal model is not robustly thermalizing at numerically accessible system sizes, and displays slow subdiffusive dynamics for long times. We map out the thermalization dynamics in a broader parameter space of charge conserving circuits, and understand the origin of the slow dynamics in terms of proximate localized and integrable regimes in parameter space. In contrast, we find that small extensions to the minimal model are sufficient to achieve robust thermalization; these include (i) increasing the interaction range to three-site gates, (ii) increasing the local Hilbert space dimension by appending an additional unconstrained qubit to the conserved charge on each site, or (iii) using a larger Floquet period comprised of two independent layers of gates. Furthermore, our results should inform future studies of charge conserving circuits, which are relevant for a wide range of topical theoretical questions.

1-dimensional spin chains↗