A Case Study to Quantify Variability in Building Load Profiles
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32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
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Quantum-inspired tempering for ground state approximation using artificial neural networks
A large body of work has demonstrated that parameterized artificial neural networks (ANNs) can efficiently describe ground states of numerous interesting quantum many-body Hamiltonians. However, the standard variational algorithms used to update or train the ANN parameters can get trapped in local minima, especially for frustrated systems and even if the representation is sufficiently expressive. We propose a parallel tempering method that facilitates escape from such local minima. This methods involves training multiple ANNs independently, with each simulation governed by a Hamiltonian with a different "driver" strength, in analogy to quantum parallel tempering, and it incorporates an update step into the training that allows for the exchange of neighboring ANN configurations. We study instances from two classes of Hamiltonians to demonstrate the utility of our approach using Restricted Boltzmann Machines as our parameterized ANN. The first instance is based on a permutation-invariant Hamiltonian whose landscape stymies the standard training algorithm by drawing it increasingly to a false local minimum. The second instance is four hydrogen atoms arranged in a rectangle, which is an instance of the second quantized electronic structure Hamiltonian discretized using Gaussian basis functions. We study this problem in a minimal basis set, which exhibits false minima that can trap the standard variational algorithm despite the problem’s small size. We show that augmenting the training with quantum parallel tempering becomes useful to finding good approximations to the ground states of these problem instances.
Albash, Tameem↗
Cross-code comparison of the impact of the fill tube on high yield implosions on the National Ignition Facility
Fill tubes are used to inject deuterium and tritium fuel into inertial confinement fusion capsules fielded on the National Ignition Facility. These fill tubes have been shown to have a detrimental effect on capsule performance, primarily by introducing a low-density pathway into the central fuel region that enables the jetting of ablation material into the hot spot. Due to the complexity of the highly nonlinear flow associated with the fill tube and the challenge of diagnosing the evolution of the fill tube jet late in the implosion experiments, the uncertainty in how this perturbation source evolves is great. In this work, we report on the results of a detailed code comparison performed to understand uncertainties in computational modeling of the impact of fill tubes on implosion performance. The study employed two radiation-hydrodynamics codes, HYDRA and xRAGE, which employ very different meshing strategies and hydrodynamics solvers, as well as two radiation transport methodologies, discrete ordinates and multi-group diffusion. Our results demonstrate generally good agreement between codes through most of the implosion although they indicate sensitivity to opacity averaging methods. Late in the implosion, differences arise in the distribution and amount of contaminant although these differences have a remarkably small impact on the amount of yield reduction due to the fill tube. While these results demonstrate sensitivity in fill tube modeling to algorithmic choices, the observed differences between codes are small relative to known sensitivities due to expected variations in the fill tube geometry. Finally, we have developed a methodology for performing multi-group diffusion simulations that show good agreement with the more accurate discrete ordinates method
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Landslide monitoring using seismic refraction tomography – The importance of incorporating topographic variations
Seismic refraction tomography provides images of the elastic properties of subsurface materials in landslide settings. Seismic velocities are sensitive to changes in moisture content, which is a triggering factor in the initiation of many landslides. However, the application of the method to long-term monitoring of landslides is rarely used, given the challenges in undertaking repeat surveys and in handling and minimizing the errors arising from processing time-lapse surveys. This work presents a simple method and workflow for producing a reliable time-series of inverted seismic velocity models. This method is tested using data acquired during a recent, novel, long-term seismic refraction monitoring campaign at an active landslide in the UK. Potential sources of error include those arising from inaccurate and inconsistent determination of first-arrival times, inaccurate receiver positioning, and selection of inappropriate inversion starting models. At our site, a comparative analysis of variations in seismic velocity to real-world variations in topography over time shows that topographic error alone can account for changes in seismic velocity of greater than ±10% in a significant proportion (23%) of the data acquired. The seismic velocity variations arising from real material property changes at the near-surface of the landslide, linked to other sources of environmental data, are demonstrated to be of a similar magnitude. Over the monitoring period we observe subtle variations in the bulk seismic velocity of the sliding layer that are demonstrably related to variations in moisture content. This highlights the need to incorporate accurate topographic information for each time-step in the monitoring time-series. The goal of the proposed workflow is to minimize the sources of potential errors, and to preserve the changes observed by real variations in the subsurface. Following the workflow produces spatially comparable, time-lapse velocity cross-sections formulated from disparate, discretely-acquired datasets. These practical steps aim to aid the use of the seismic refraction tomography method for the long-term monitoring of landslides prone to hydrological destabilization.
Whiteley, J. S.↗
Combining Distributed Electrochemical Measurements with a Semi-Empirical Model to Identify Local Variations in Overpotentials for PEM Water Electrolyzers
Abstract A segmented cell and PCB approach was used to demonstrate an advanced technique for measuring and understanding the electrochemical behavior of PEM water electrolyzers. By employing a semi-empirical model, discrete modes of overpotential and their spatial distributions were identified in an operating cell. Distributed area-specific resistance (DASR measurements indicate that local dehydration of the polymer electrolyte membrane is the primary driver of increased polarization, behaving similarly to mass transport-limited currents at low flow rates due to ineffective gas-phase bubble removal. To improve quantification, the overall ohmic overpotential is divided into background (η Ohm,b ) and mass transport-coupled (η Ohm,mt ) components. Two types of anode diffusion media, a baseline PTL and a thin foil liquid/gas diffusion layer (LGDL), were examined. The results show significant variations in η Ohm,b and highlight that ineffective bubble removal leads to pronounced local dehydration. The effect of cell temperature on various overpotentials was also examined. Negligible differences in diffusion overpotential were observed when comparing PEWE performance using the PTL and LGDL, despite major differences in two-phase fluid transport within each diffusion media. This underscores the critical role of the catalyst layer's micro-porous structure in diffusion processes. The study highlights the complex nature and intricacies of mass transport limitations within PEWEs.
Roy, Anirban (ORCID:0000000163803386)↗
On a nonlocal Cahn–Hilliard model permitting sharp interfaces
A nonlocal Cahn–Hilliard model with a non-smooth potential of double-well obstacle type that promotes sharp interfaces in the solution is presented. To capture long-range interactions between particles, a nonlocal Ginzburg–Landau energy functional is defined which recovers the classical (local) model as the extent of nonlocal interactions vanish. In contrast to the local Cahn–Hilliard problem that always leads to diffuse interfaces, the proposed nonlocal model can lead to a strict separation into pure phases of the substance. In this work, the lack of smoothness of the potential is essential to guarantee the aforementioned sharp-interface property. Mathematically, this introduces additional inequality constraints that, in a weak formulation, lead to a coupled system of variational inequalities which at each time instance can be restated as a constrained optimization problem. We prove the well-posedness and regularity of the semi-discrete and continuous in time weak solutions, and derive the conditions under which pure phases are admitted. Moreover, we develop discretizations of the problem based on finite element methods and implicit–explicit time-stepping methods that can be realized efficiently. Finally, we illustrate our theoretical findings through several numerical experiments in one and two spatial dimensions that highlight the differences in features of local and nonlocal solutions and also the sharp interface properties of the nonlocal model.
97 MATHEMATICS AND COMPUTING↗
Introducing the SLICE Method for estimating pebble-bed reactor inventories at equilibrium operation with SCALE
This paper introduces the SCALE Leap-In method for Cores at Equilibrium (SLICE) for estimating pebble-bed reactor equilibrium core isotopic inventories using capabilities in the SCALE code system, requiring only a small computational cluster and a few days of computation. This method uses an iterative approach that relies on (1) a surrogate spectrum model that captures spatial and time-dependent spectral conditions, (2) a multi-pass model that captures the pebble’s evolving nuclide inventory as a function of location and time in the core, and (3) a full-core model that captures the core’s spatial neutron flux distribution. The SLICE approach is applied to a generic fluoride salt–cooled high-temperature reactor, demonstrating fuel inventory convergence through nuclide concentration inspection across iterations and comparisons for core realizations with varying discretizations. Results agree within ~5% with another state-of-the-art code, with differences attributed to input parameter or modeling assumption variations in the equilibrium generation methods.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Modeling of deformation of battery cells using thick shell element formulation
Here, we describe a new approach for modeling nonlinear deformation and stress distribution of battery cells using a new thick shell finite element formulation with a through-thickness calculation of stresses and strains that satisfy equilibrium conditions. Battery cells are transversely layered materials that contain numerous thin layers in a repeating sequence. The layers are made of materials with significantly different mechanical responses. Explicit discretization of the layers is computationally impractical except for very small domains, while homogenized material models cannot account for stress and strain variations and partition through the thickness. The new formulation allows for calculation of the transverse and interlayer stresses based on the material properties of the individual cell layers. The application to problems where the transverse stresses have strong influence is also possible.
25 ENERGY STORAGE↗
Post-Transcriptional Mechanisms Respond Rapidly to Ecologically Relevant Thermal Fluctuations During Temperature-Dependent Sex Determination
An organism’s ability to integrate transient environmental cues experienced during development into molecular and physiological responses forms the basis for adaptive shifts in phenotypic trajectories. During temperature-dependent sex determination (TSD), thermal cues during discrete periods in development coordinate molecular changes that ultimately dictate sexual fate and contribute to patterns of inter- and intra-sexual variation. How these mechanisms interface with dynamic thermal environments in nature remain largely unknown. By deploying thermal loggers in wild nests of the American alligator (Alligator mississippiensis) over two consecutive breeding seasons, we observed that 80% of nests exhibit both male- and female-promoting thermal cues during the thermosensitive period, and of these nests, all exhibited both male- and female-promoting temperatures within the span of a single day. These observations raise a critical question—how are opposing environmental cues integrated into sexually dimorphic transcriptional programs across short temporal scales? To address this question, alligator embryos were exposed to fluctuating temperatures based on nest thermal profiles and sampled over the course of a daily thermal fluctuation. We examined the expression dynamics of upstream genes in the temperature-sensing pathway and find that post-transcriptional alternative splicing and transcript abundance of epigenetic modifier genes JARID2 and KDM6B respond rapidly to thermal fluctuations while transcriptional changes of downstream effector genes, SOX9 and DMRT1, occur on a delayed timescale. Our findings reveal how the basic mechanisms of TSD operate in an ecologically relevant context. We present a hypothetical hierarchical model based on our findings as well as previous studies, in which temperature-sensitive alternative splicing incrementally influences the epigenetic landscape to affect the transcriptional activity of key sex-determining genes.
59 BASIC BIOLOGICAL SCIENCES↗
Error Estimates of Residual Minimization Using Neural Networks for Linear PDES
We propose an abstract framework for analyzing the convergence of least-squares methods based on residual minimization when feasible solutions are neural networks. With the norm relations and compactness arguments, we derive error estimates for both continuous and discrete formulations of residual minimization in strong and weak forms. The formulations cover recently developed physicsinformed neural networks based on strong and variational formulations.
97 MATHEMATICS AND COMPUTING↗
Smoothed aggregation for difficult stretched mesh and coefficient variation problems
Abstract Four adaptations of the smoothed aggregation algebraic multigrid (SA‐AMG) method are proposed with an eye toward improving the convergence and robustness of the solver in situations when the discretization matrix contains many weak connections. These weak connections can cause higher than expected levels of fill‐in within the coarse discretization matrices and can also give rise to suboptimal smoothing within the prolongator smoothing phase. These smoothing drawbacks are due to the relatively small size of some diagonal entries within the filtered matrix that one obtains after dropping the weak connections. The new algorithms consider modifications to the Jacobi‐like step that defines the prolongator smoother, modifications to the filtered matrix, and also direct modifications to the resulting grid transfer operators. Numerical results are given illustrating the potential benefits of the proposed adaptations.
Hu, Jonathan J.↗
The latent variable proximal point algorithm for variational problems with inequality constraints
The latent variable proximal point (LVPP) algorithm is a framework for solving infinite-dimensional variational problems with pointwise inequality constraints. The algorithm is a saddle point reformulation of the Bregman proximal point algorithm. At the continuous level, the two formulations are equivalent, but the saddle point formulation is more amenable to discretization because it introduces a structure-preserving transformation between a latent function space and the feasible set. Working in this latent space is much more convenient for enforcing inequality constraints than the feasible set, as discretizations can employ general linear combinations of suitable basis functions, and nonlinear solvers can involve general additive updates. LVPP yields numerical methods with observed mesh-independence for obstacle problems, contact, fracture, plasticity, and others besides; in many cases, for the first time. The framework also extends to more complex constraints, providing means to enforce convexity in the Monge–Ampère equation and handling quasi-variational inequalities, where the underlying constraint depends implicitly on the unknown solution. Here, in this paper, we describe the LVPP algorithm in a general form and apply it to ten problems from across mathematics.
Inequality constraints↗
Microbubble dynamics and heat transfer in boiling droplets
Dissipating large heat fluxes from a surface is critically important in numerous industrial and natural applications. Boiling based spray cooling and surface texturing are two of the most promising methods being investigated to address this problem. Although our understanding on these topics has significantly improved over past decades, critical gaps remain in the knowledgebase stymieing the realization of their full potential. As an example, while bubble growth in pool boiling have been investigated in detail, comparatively little is known about how the bubbles evolve inside boiling drops. In the present work, we have investigated for the first time, the microbubble dynamics inside water droplets boiling on superhydrophilic textured substrates using high-speed X-ray phase contrast imaging (XRPCI). Our observations show that the transient bubble density variation follows similar characteristics irrespective of the texture spacing at a given surface temperature. For an example microstructure, we found that the number of discrete bubbles on the surface decreases as temperature is increased although their growth rate increases. Here, we observe that bubble growth is highly non-uniform during the lifetime of a drop on the surface. Initially, bubbles grow under diffusion-limited regime, but at later times they grow as ~t 1.45 due to combined effects of coalescence and evaporation. In some conditions, we found that bubbles shrink dramatically af- ter the initial growth spurt presumably due to severe quenching of the surface, and migration of bubbles on the surface. Using the bubble sizes, for the first time we analyzed the heat flux removed by a single bubble and also by all the bubbles at a given time. We find that the highest dissipation through latent- heat component (~600 W/cm 2 ) occurs just in the beginning and thereafter it decreases. We expect that our findings and the analysis would guide further work on the topic and will aid in the overarching goal of engineering surfaces that are more efficient in boiling heat transfer.
42 ENGINEERING↗
Quantum dynamics simulation of the advection-diffusion equation
The advection-diffusion equation is simulated via several quantum algorithms. Three formulations are considered: (1) Trotterization, (2) variational quantum time evolution (VarQTE), and (3) adaptive variational quantum dynamics simulation (AVQDS). These schemes were originally developed for the Hamiltonian simulation of many-body quantum systems. The finite-difference discretized operator of the transport equation is formulated as a Hamiltonian and solved without the need for ancillary qubits. Computations are conducted on a quantum simulator (IBM Qiskit Aer) and a superconducting quantum hardware (IBM Fez). The former emulates the latter without the noise. The actual hardware implementation experiences significant noise. The results of the quantum simulator are compared with data from direct numerical simulation (DNS) with infidelities of the order 10 −5 . In the quantum simulator, Trotterization is observed to have the lowest infidelity and is suitable for fault-tolerant computation. The AVQDS algorithm requires the lowest gate count and circuit depth. The VarQTE algorithm is the next best in terms of gate counts, but the number of its optimization variables is directly proportional to the number of qubits. Due to current hardware limitations, Trotterization cannot be implemented, as it has an overwhelmingly large number of operations. Meanwhile, AVQDS and VarQTE can be executed at the hardware level. These algorithms present a new paradigm for computational transport phenomena on quantum computers.
Alipanah, Hirad [Univ. of Pittsburgh, PA (United S↗
Challenges of measuring spin Seebeck noise
Just as electronic shot noise in driven conductors results from the granularity of charge and the statistical variation in the arrival times of charge carriers, there are predictions for fundamental noise in magnon currents due to angular momentum being carried by discrete excitations. The inverse spin Hall effect as a transduction mechanism to convert spin current into charge current raises the prospect of experimental investigations of such magnon shot noise. Spin Seebeck effect measurements have demonstrated the electrical detection of thermally driven magnon currents and have been suggested as an avenue for accessing spin current fluctuations. Using spin Seebeck structures made from yttrium iron garnet on gadolinium gallium garnet, we demonstrate the technical challenges inherent in such noise measurements. While there is a small increase in voltage noise in the inverse spin Hall detector at low temperatures associated with adding a magnetic field, the dependence on field orientation implies that this is not due to magnon shot noise. We describe theoretical predictions for the expected magnitude of magnon shot noise, highlighting ambiguities that exist. Further, we show that magnon shot noise detection through the standard inverse spin Hall approach is likely impossible due to geometric factors. Implications for future attempts to measure magnon shot noise are discussed.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Fault Network Geometry Modulates Earthquake Source Spectra Across Scales
Earthquake source spectra provide unique insights into the earthquake rupture process. Motivated by previous research suggesting that complex fault geometries enhance high‐frequency seismic radiation, we study the influence of fault network geometry on earthquake source spectra using multiple independent observations. At regional scales, we examine correlations of stress drop measurements with surface fault trace misalignment in Southern California, Japan, and Central Italy. At a global scale, we examine correlations of moment‐rate function complexity of large earthquakes with focal mechanism variability, a proxy for local fault complexity. Despite significant scatter in the observations, we find overall consistent positive correlations. The concept that elastic interactions of discrete fault structures during the earthquake rupture process generates high‐frequency ground motions offers a coherent framework for interpreting our observations. These findings suggest that variations in fault complexity explain why some earthquakes produce stronger high‐frequency ground motions than others.
Lee, Jaeseok [Brown Univ., Providence, RI (United ↗
Low-Memory, Discrete Ordinates, Discontinuous Galerkin Methods for Radiative Transport
The discrete ordinates discontinuous Galerkin (SN-DG) method is a well-established and practical approach for solving the radiative transport equation. In this paper, we study a low-memory variation of the upwind SN-DG method. The proposed method uses a smaller finite element space that is constructed by coupling spatial unknowns across collocation angles, thereby yielding an approximation with fewer degrees of freedom than the standard method. Like the original SN-DG method, the low-memory variation still preserves the asymptotic diffusion limit and maintains the characteristic structure needed for mesh sweeping algorithms. While we observe second-order convergence in the scattering dominated, diffusive regime, the low-memory method is in general only first-order accurate. To address this issue, we use upwind reconstruction to recover second-order accuracy. Finally, for both methods, numerical procedures based on upwind sweeps are proposed to reduce the system dimension in the underlying Krylov solver strategy.
97 MATHEMATICS AND COMPUTING↗
Mining for Metal–Organic Systems: Chemistry Frontiers of Th-, U-, and Zr-Materials
The conceptual framework presented in this Perspective overviews the design principles of innovative thorium-based materials that could address urgent needs of the medicinal, nuclear energy, and waste remediation sectors from the lens of zirconium and uranium analogs. We survey the intersections of Zr, Th, and U chemistry with a focus on how the intrinsic behavior of each metal translates to broader material properties, including, but not limited to, structural and topological diversity, preferential metal–ligand binding, and reactivity. On the example of several classes of materials, including organometallic complexes, polyoxometalates, and the primary focus of this Perspective, metal–organic frameworks (MOFs), the design principles that govern the preparation of Zr-, Th-, and U-compounds, including oxophilicity, variation in oxidation states, and stable coordination environments have been considered. Further, we highlight how the impact of the mentioned variables may shift throughout the progression from discrete molecular systems to extended structures. We discuss the common assumption that zirconium-organic materials are typically considered a close analog of thorium-based congeners in areas such as material design and preparation. Through consideration of fundamental chemistry principles, we shed light on the relationships between Zr-, Th-, and U-based materials and highlight how a critical analysis of their distinct properties can be used to target a desired material performance. Finally, we provide a detailed understanding of Th-based materials chemistry by anchoring their fundamental properties between two well-studied reference points, zirconium- and uranium-containing analogs.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗