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At least 1,387 records · Page 77

Genuine k -partite correlations and entanglement in the ground state of the Dicke model for interacting qubits

Here, in this work, we calculate and study correlations of the Dicke model in the presence of qubit–qubit interaction. Whereas the analysis of correlations among its subsystems is essential for the understanding of corresponding critical phenomena and for performing quantum information tasks, the majority of correlation measures are restricted to bipartitions due to the inherent challenges associated with handling multiple partitions. To circunvent this we employ the calculation of Genuine Multipartite Correlations (GMC) based on the invariance of our model under particle permutation. We then quantify the correlations within each subpart of the system, as well as the percentage contribution of each GMC of order $k$, highlighting the many-body behaviors for different regimes of parameters. Additionally, we show that GMC signal both first- and second-order quantum phase transitions present in the model. Furthermore, as GMC encompasses both classical and quantum correlations, we employ Quantum Fisher Information (QFI) to detect genuine multipartite entanglement. Ultimately, we map the Dicke model with interacting qubits to spin in solids interacting with a quantum field of magnons, thus demonstrating a potential experimental realization of this model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

An empirical analysis of supply offers in the ERCOT operating reserves markets

Here, this paper seeks to improve theoretical and empirical understanding of supplier dynamics in wholesale markets for operating reserves, which have been understudied compared to energy markets. We begin by identifying several economic factors that unit owners may consider when submitting offers into operating reserves auctions in two-stage, co-optimized markets common across much of North America. Next, we analyze historical offer data from the Electric Reliability Council of Texas (ERCOT) market to assess whether actual reserve market behavior aligns with expectations based on economic theory, as well as with commonly used assumptions in electricity market modeling efforts. We find that the aggregate supply of operating reserves in ERCOT varies meaningfully over time, becoming more expensive during summer afternoons, which is consistent with theoretical expectations but contradicts the typical modeling assumption of temporally invariant reserve offers. Analysis of offers made by individual units uncovers additional insights, such as the existence of large offer pattern differences by unit owner and the tendency of battery storage units to submit very low offer prices. We conclude by discussing how our findings can be integrated into electricity market modeling assumptions to improve alignment with observed operating reserve offer inputs and pricing outcomes.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

A consistent and conservative Phase-Field method for multiphase incompressible flows

In the present study, a consistent and conservative Phase-Field method, including both the model and scheme, is developed for multiphase flows with an arbitrary number of immiscible and incompressible fluid phases. The consistency of mass conservation and the consistency of mass and momentum transport are implemented to address the issue of physically coupling the Phase-Field equation, which locates different phases, to the hydrodynamics. These two consistency conditions, as illustrated, provide the “optimal” coupling because (i) the new momentum equation resulting from them is Galilean invariant and implies the kinetic energy conservation, regardless of the details of the Phase-Field equation, and (ii) failures of satisfying the second law of thermodynamics or the consistency of reduction of the multiphase flow model only result from the same failures of the Phase-Field equation but are not due to the new momentum equation. Physical interpretation of the consistency conditions and their formulations are first provided, and general formulations that are obtained from the consistency conditions and independent of the interpretation of the velocity are summarized. Then, the present consistent and conservative multiphase flow model is completed by selecting a reduction consistent Phase-Field equation. Several novel techniques are developed to inherit the physical properties of the multiphase flows after discretization, including the gradient-based phase selection procedure, the momentum conservative method for the surface force, and the general theorems to preserve the consistency conditions on the discrete level. Equipped with those novel techniques, a consistent and conservative scheme for the present multiphase flow model is developed and analyzed. The scheme satisfies the consistency conditions, conserves the mass and momentum, and assures the summation of the volume fractions to be unity, on the fully discrete level and for an arbitrary number of phases. All those properties are numerically validated. Finally, numerical applications demonstrate that the present model and scheme are robust and effective in studying complicated multiphase dynamics, especially for those with large-density ratios.

97 MATHEMATICS AND COMPUTING↗

High-yield growth kinetics and spatial mapping of single-walled carbon nanotube forests at wafer scale

Emerging commercial applications of vertically aligned, single-walled carbon nanotube (SWCNT) “forests” require synthesis that minimizes nanotube diameter while maximizing number density across substrate areas exceeding centimeter scale. To address this need, we synthesized SWCNT forests on full silicon wafers with notable reproducibility and uniformity, and co-optimized growth for small diameters and high densities across large areas to access new territory in this 3D parameter space. We mapped the spatial uniformity of key structural features using Raman microscopy, synchrotron X-ray scattering, and Rutherford backscattering spectrometry. Low C 2 H 2 flux over sub-nm Fe/Mo catalysts produced small-diameter SWCNTs (2.1 nm) at high number densities (2.26 × 10 12 cm -2 ) on wafers up to 6 in. Although removing Mo resulted in larger SWCNT diameters and lower densities (<0.7 × 10 12 cm -2 ), mass conversion rates from C 2 H 2 to SWCNT product were high and remarkably invariant for catalyst compositions and densities (i.e., 47.7% or 1.30 × 10 6 % g-catalyst -1 on 4-in. wafers). These carbon conversion efficiencies far exceed typical benchtop reactors and are on par with the best reported literature values. Our detailed elucidation of correlations among structural characteristics within this resource-efficient process is expected to guide future scale-up efforts of SWCNT forest growth beyond wafer scale.

36 MATERIALS SCIENCE↗

Synthesis of Hf 6 Ta 2 O 17 superstructure via spark plasma sintering for improved oxidation resistance of multi-component ultra-high temperature ceramics

Ultra-high temperature ceramics (UHTCs) have shown aspiration to overcome challenges in the thermal protection system (TPS) by designing new materials referred to as multi-component UHTCs (MC-UHTCs) in the compositional space. MC-UHTCs have shown remarkable improvement in oxidation resistance due to the formation of the Hf6Ta2O17 superstructure during plasma exposure. Herein, the Hf 6 Ta 2 O 17 superstructure is synthesized via a solid-state reaction between HfO 2 and Ta 2 O 5 powder mixtures during spark plasma sintering (SPS). The compositions chosen are 50 vol% of HfO 2 -50 vol% of Ta 2 O 5 (50HO-50TO) and 70 vol% of HfO 2 -30 vol% of Ta 2 O 5 (70HO-30TO). The phase quantification via Rietveld analysis showed Hf 6 Ta 2 O 17 as a principal phase with some residual Ta 2 O 5 phase in both the samples. The high-temperature thermal stability of the samples was evaluated using high-velocity plasma jet exposure for up to 3 min. 50HO-50TO was able to withstand the intense plasma condition, which is attributed to the higher content of the Hf 6 Ta 2 O 17 phase (~84%) and lower strain in the Ta 2 O 5 phase. The augmentation in the Hf 6 Ta 2 O 17 phase to 94.7% (in 50HO-50TO) post plasma exposure has been attributed to the invariant transformation from a liquid state to Hf 6 Ta 2 O 17 at temperatures >2500 °C during testing. The mechanical integrity is elucidated from the insignificant change in the hardness ~13.3 GPa before and 11.2 GPa after plasma exposure of the 50HO-50TO sample. As a result, the Hf 6 Ta 2 O 17 superstructure's thermo-mechanical stability suggests developing novel oxidation-resistant MC-UHTCs in compositional space for reusable space vehicle applications.

36 MATERIALS SCIENCE↗

A multi-region approach for the analysis of porous materials and gas-solid reactions using USAXS-SAXS-WAXS: application to CaO carbonation

The reaction rate of gas-solid non-catalytic reactions is typically investigated using reactant conversion data over time and ex-situ measurements of the porous solid reactant textural properties; these data enable the experimental estimation of the initial intrinsic reaction rate, whereas the evolution of the textural properties and the reaction rate over time are evaluated theoretically using reaction models. In this work, a different methodology is presented, based on: a) in-situ time-resolved USAXS-SAXS-WAXS measurements of the solid sample, and b) a multi-region modeling approach; this methodology allows for the estimation of the textural properties and the intrinsic reaction rate at any time during the reaction. Referring to a reaction in which a solid product is obtained from a solid reactant and a gaseous reactant, the porous particle is described as consisting of several distinct regions with different microstructural properties, and both a gas-solid reaction model and a SAXS model are derived and applied to the carbonation of porous CaO. The proposed reaction model highlights the role of the inaccessible reactant and accurately predicts the solid reactant conversion versus time profile. The SAXS model accurately predicts the measured linear trends of the Porod invariant and of the pre-factor of the power law scattering profile versus CaO mass fraction; in the absence of chemical reactions, the proposed equations extend classical SAXS theory to porous materials containing macropores and nonporous solid phases in addition to standard nanoscale inhomogeneous regions.

CO2 solid sorbents↗

An extended three-field principle to scale-bridge the granular micromechanics of polymer-bonded particulate materials

Observed phenomena of damage, viscoelasticity, and viscoplasticity in polymer-bonded particulate materials (PBPM), like polymer-bonded explosive (PBX), are accommodated in a scale-bridging constitutive model based on granular micromechanics. An extended three-field variational principle with min - max optimization problem is introduced to homogenize the bonded aggregates’ grain-scale contact mechanics. Similarly to prior applications of a three-field principle, volume constraints are invoked to embed microscale-to-macroscale correspondences for kinematic and static volumetric measures, like mean strain and its energy-conjugate stress invariant. Unlike prior applications, our three-field principle realizes a strain-driven model for effective constitutive behavior due to bonded intergranular contact. In conclusion, the resultant micro-sphere integration-based homogenization is demonstrated in comparison to existing publicly-available measurements to capture the extreme tension/compression constitutive asymmetry exhibited by PBPMs (specifically PBX-9501) during material softening.

42 ENGINEERING↗

A conservative discontinuous-Galerkin-in-time (DGiT) multirate time integration framework for interface-coupled problems with applications to solid–solid interaction and air–sea models

In this paper we extend the DGiT multirate framework, developed in Connors and Sockwell (2022) for scalar transmission problems, to a solid–solid interaction (SSI) problem involving two coupled elastic solids and a coupled air–sea model with the rotating, thermal shallow water equations. In so doing we aim to demonstrate the broad applicability of the mathematical theory and governing principles established in Connors and Sockwell (2022) to coupled problems characterized by subproblems evolving at different temporal scales. Further, multirate time integration algorithms employing different time steps, optimized for the dynamics of each subproblem, can significantly improve simulation efficiency for such coupled problems. However, development of multirate algorithms is a highly non-trivial task due to the coupling, which can impact accuracy, stability or other desired properties such as preservation of system invariants. DGiT provides a general template for multirate time integration that can achieve these properties. To elucidate the manner in which DGiT accomplishes this task, we fully detail each step in the application of the framework to the SSI and air–sea coupled problems. Numerical examples illustrate key properties of the resulting multirate schemes for both problems.

42 ENGINEERING↗

D2NO: Efficient handling of heterogeneous input function spaces with distributed deep neural operators

Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems. However, challenges arise when dealing with input functions that exhibit heterogeneous properties, requiring multiple sensors to handle functions with minimal regularity. To address this issue, discretization-invariant neural operators have been used, allowing the sampling of diverse input functions with different sensor locations. However, existing frameworks still require an equal number of sensors for all functions. We propose a novel distributed approach to further relax the discretization requirements and solve the heterogeneous dataset challenges. Our method involves partitioning the input function space and processing individual input functions using independent and separate neural networks. A centralized neural network is used to handle shared information across all output functions. This distributed methodology reduces the number of gradient descent back-propagation steps, improving efficiency while maintaining accuracy. Here, we demonstrate that the corresponding neural network is a universal approximator of continuous nonlinear operators and present three numerical examples to validate its performance.

97 MATHEMATICS AND COMPUTING↗

Divide and conquer: Learning chaotic dynamical systems with multistep penalty neural ordinary differential equations

Forecasting high-dimensional dynamical systems is a fundamental challenge in various fields, such as geosciences and engineering. Neural Ordinary Differential Equations (NODEs), which combine the power of neural networks and numerical solvers, have emerged as a promising algorithm for forecasting complex nonlinear dynamical systems. However, classical techniques used for NODE training are ineffective for learning chaotic dynamical systems. In this work, we propose a novel NODE-training approach that allows for robust learning of chaotic dynamical systems. Here, our method addresses the challenges of non-convexity and exploding gradients associated with underlying chaotic dynamics. Training data trajectories from such systems are split into multiple, non-overlapping time windows. In addition to the deviation from the training data, the optimization loss term further penalizes the discontinuities of the predicted trajectory between the time windows. The window size is selected based on the fastest Lyapunov time scale of the system. Multi-step penalty(MP) method is first demonstrated on Lorenz equation, to illustrate how it improves the loss landscape and thereby accelerates the optimization convergence. MP method can optimize chaotic systems in a manner similar to least-squares shadowing with significantly lower computational costs. Our proposed algorithm, denoted the Multistep Penalty NODE, is applied to chaotic systems such as the Kuramoto-Sivashinsky equation, the two-dimensional Kolmogorov flow, and ERA5 reanalysis data for the atmosphere. It is observed that MP-NODE provide viable performance for such chaotic systems, not only for short-term trajectory predictions but also for invariant statistics that are hallmarks of the chaotic nature of these dynamics.

Chaotic dynamical systems↗

Transient anisotropic kernel for probabilistic learning on manifolds

PLoM (Probabilistic Learning on Manifolds) is a method introduced in 2016 for handling small training datasets by projecting an Itô equation from a stochastic dissipative Hamiltonian dynamical system, acting as the MCMC generator, for which the KDE-estimated probability measure with the training dataset is the invariant measure. PLoM performs a projection on a reduced-order vector basis related to the training dataset, using the diffusion maps (DMAPS) basis constructed with a time-independent isotropic kernel. In this paper, we propose a new ISDE projection vector basis built from a transient anisotropic kernel, providing an alternative to the DMAPS basis to improve statistical surrogates for stochastic manifolds with heterogeneous data. The construction ensures that for times near the initial time, the DMAPS basis coincides with the transient basis. For larger times, the differences between the two bases are characterized by the angle of their spanned vector subspaces. The optimal instant yielding the optimal transient basis is determined using an estimation of mutual information from Information Theory, which is normalized by the entropy estimation to account for the effects of the number of realizations used in the estimations. Consequently, this new vector basis better represents statistical dependencies in the learned probability measure for any dimension. Three applications with varying levels of statistical complexity and data heterogeneity validate the proposed theory, showing that the transient anisotropic kernel improves the learned probability measure.

Diffusion maps↗

A new method to compute periodic orbits in general symplectic maps

The search of high-order periodic orbits has been typically restricted to problems with symmetries that help to reduce the dimension of the search space. Well-known examples include reversible maps with symmetry lines. The present work proposes a new method to compute high-order periodic orbits in twist maps without the use of symmetries. The method is a combination of the parameterization method in Fourier space and a Newton–Gauss multiple shooting scheme. The parameterization method has been successfully used in the past to compute quasi-periodic invariant circles. However, this is the first time that this method is used in the context of periodic orbits. Numerical examples are presented showing the accuracy and efficiency of the proposed method. Furthermore, the method is also applied to verify the renormalization prediction of the residues’ convergence at criticality (extensively studied in reversible maps) in the relatively unexplored case of maps without symmetries.

74 ATOMIC AND MOLECULAR PHYSICS↗

Understanding how chemical structure affects ignition-delay-time $\phi$-sensitivity

$\phi$-sensitivity is the change in ignition delay time (IDT) with respect to the fuel-to-air equivalence ratio ($\phi$). High $\phi$-sensitivity is a desirable fuel property for applications in advanced compression ignition and multi-mode engine designs. Understanding how $\phi$-sensitivity depends on chemical structure is essential for selecting promising biofuels from the ever-growing list of proposed candidates. Here, we investigate the effect of chemical structure on $\phi$-sensitivity with experiment, simulation, and theory. Experimental Advanced Fuel Ignition Delay Analyzer (AFIDA) measurements for 2,4-dimethylpentane and diisopropyl ether provide evidence that branching and functional groups strongly impact $\phi$-sensitivity. Further insights into this dependence are obtained with 0-D kinetic simulations with existing mechanisms for n-pentane, diethyl ether, 3-pentanone, n-heptane, 2-methylhexane, 2,4-dimethylpentane, and 2,2,3-trimethylbutane. Quantum mechanical (QM) G4 calculations of low-temperature reactions help explain the observed experimental and simulation trends. Specifically, these QM calculations provide theoretical estimates of the ketohydroperoxide (KHP) dissociation rates, the HO 2 formation rates from peroxy radical (ROO), and the “cross-over” temperatures, i.e., the temperature at which ROO dissociation is favored compared to hydroperoxyl radical (QOOH) formation. Each of these reaction rates is compared to the n-alkane reference point to determine the impact of branching and different functional groups. Although kinetic mechanisms typically assume that KHP dissociation rates are invariant of chemical environment, our QM results suggest that this rate can span a range of roughly two orders of magnitude. We also discuss the importance of including the peroxy-hydroperoxy (OO-OOH) hydrogen transfer reaction for branched ethers. Finally, the insights gained assist in proposing a highly $\phi$-sensitive compound, namely, isopropyl propyl ether.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Towards physics-informed explainable machine learning and causal models for materials research

From emergent material descriptions to estimation of properties stemming from structures to optimization of process parameters for achieving best performance – all key facets of materials science and related fields have experienced tremendous growth with the introduction of data-driven models. This gradual progression goes at par with developments of machine learning workflows, from purely data-driven shallow models to those that are well-capable in encoding more complex graphs, symbolic representations, invariances, and positional embeddings. Furthermore, this perspective aims at summarizing strategic aspects of such transitions while providing insights into the requirements of bringing in explainable, interpretable predictive models, and causal learning to aid in materials design and discovery. Although the focus remains on a variety of functional materials by providing a handful of case studies, the applications of such integrated methodologies are universal to facilitate fundamental understandings of materials physics while enabling autonomous experiments.

36 MATERIALS SCIENCE↗

An adaptive adversarial domain adaptation approach for corn yield prediction

Recently, statistical machine learning and deep learning methods have been widely explored for corn yield prediction. Though successful, machine learning models generated within a specific spatial domain often lose their validity when directly applied to new regions. To address this issue, we designed an unsupervised adaptive domain adversarial neural network (ADANN). Specifically, through domain adversarial training, the ADANN model reduced the impact of domain shift by projecting data from different domains into the same subspace. Also, the ADANN model was designed to be trained in an adaptive way, which guaranteed the model can learn the domain-invariant features and perform accurate yield prediction simultaneously. Informative variables including time-series vegetation indices and sequential weather observations were first collected from multiple data sources and aggregated to the county level. Then, we trained the ADANN model with the extracted features and corresponding reported county-level corn yield from the U.S. Department of Agriculture (USDA). Finally, the trained model was evaluated in four testing years 2016–2019. The U.S. corn belt was used as the study area and counties under study were grouped into two diverse ecological regions. Overall, the experimental results showed that the developed ADANN model had better performance than three other state-of-the-art machine learning models in both local experiments (train and test in the same region) and transfer experiments (train and test in different regions). As the first study using adversarial learning for crop yield prediction, this research demonstrates a novel solution for improving model transferability on crop yield prediction.

59 BASIC BIOLOGICAL SCIENCES↗

Using dorsal surface for individual identification of dairy calves through 3D deep learning algorithms

Advances in machine learning techniques have allowed the development of computer vision systems (CVS) that can accurately predict several phenotypes of interest for livestock operations. In this context, 3D images taken from a top-down view are particularly useful for estimating body condition score, growth development, and body biometrics in cattle. Frequently, such CVS rely on identification (ID) systems, such as electronic tags, as a way to match animal ID and the predicted phenotype. However, the same 3D images used to predict body weight and other animal biometrics could be adopted for animal recognition as well. Such alternative would optimize CVS to recognize animal ID and monitor growth development simultaneously while leveraging the same hardware infrastructure. Furthermore, this strategy could be used to recognize animals with similar color patterns. Nonetheless, growing animals are continuously changing body shape, which could limit its use as an invariant feature for pattern recognition. Thus, the objectives of this study were: (1) to compare algorithms for different 3D object representations to identify individual animals; and (2) to evaluate how short-term changes in body shape due to animal growth affect the predictive performance of these algorithms. For objective 1, the algorithms were trained (n = 4,558) and tested (n = 1,139) using images from 38 Holstein calves. For objective 2, we designed three different experiments using images (n = 2,347) from five Holstein calves taken over six weeks during their growing period, always training and testing on different weeks. Each experiment evaluated how changing a different parameter of the image capturing procedure affected the predictive ability of the trained algorithms. In the first experiment, we varied the total number of images per animal in the training set; in the second experiment, we varied the number of weeks while keeping a fixed number of images in the training set; and in the third experiment, we skipped weeks between images in the training and test sets. The F 1 score for objective (1) was up to 0.804 when testing with the last frames of each video, and up to 0.959 when using random frames for testing. For objective (2), the F 1 score was up to 0.947 for the first experiment when using 130 images per animal; up to 0.979 for the second experiment when using all five weeks; and up to 0.917 when not skipping weeks between training and testing. In conclusion, these results show that deep learning algorithms can be used to identify individual animals through their dorsal area 3D surfaces, and, from our experiments using calves in their growing period, that they are robust enough to account for changes in body shape and size, making them a promising tool for animal recognition during growth.

3D neural networks↗

Particlization in fluid dynamical simulations of heavy-ion collisions: The IS3D module

The IS3D particlization module simulates the emission of hadrons from heavy-ion collisions via Monte-Carlo sampling of the Cooper–Frye formula which converts fluid dynamical information into local phase-space distributions for hadrons. The code package includes multiple choices for the non-equilibrium correction to these distribution functions: the 14-moment approximation, first-order Chapman–Enskog expansion, and two types of modified equilibrium distributions. This makes it possible to explore to what extent heavy-ion experimental data are sensitive to different choices for δf n , presently the main source of theoretical uncertainty in the particlization stage. Here, we validate our particle sampler with a high degree of precision by generating several million hadron emission events from a longitudinally boost-invariant hypersurface and comparing the event-averaged particle spectra and space–time distributions to the Cooper–Frye formula.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Ensemble Monte Carlo calculations with five novel moves

We introduce five novel types of Monte Carlo (MC) moves that brings the number of moves of ensemble MC calculations from three to eight. So far such calculations have relied on affine invariant stretch moves that were originally introduced by Christen (2007), walk moves by Goodman and Weare (2010) and quadratic moves by Militzer (2023). Ensemble MC methods have been very popular because they harness information about the fitness landscape from a population of walkers rather than relying on expert knowledge. Here we modified the affine method and employed a simplex of points to set the stretch direction. We adopt the simplex concept to quadratic moves. We also generalize quadratic moves to arbitrary order. Finally, we introduce directed moves that employ the values of the probability density while all other types of moves rely solely on the location of the walkers. We apply all algorithms to the Rosenbrock density in 2 and 20 dimensions and to the ring potential in 12 and 24 dimensions. We evaluate their efficiency by comparing error bars, autocorrelation time, travel time, and the level of cohesion that measures whether any walkers were left behind. Our code is open source.

97 MATHEMATICS AND COMPUTING↗