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At least 19 records

Periodic GFN1-xTB Tight Binding: A Generalized Ewald Partitioning Scheme for the Klopman–Ohno Function

A novel formulation is presented for the treatment of electrostatics in the periodic GFN1-xTB tight-binding model. Periodic GFN1-xTB is hindered by the functional form of the second-order electrostatics, which only recovers Coulombic behavior at large interatomic distances and lacks a closed-form solution for its Fourier transform. We address this by introducing a binomial expansion of the Klopman–Ohno function to partition short- and long-range interactions, enabling the use of a generalized Ewald summation for the solution of the electrostatic energy. This approach is general and is applicable to any damped potential of the form |R n + c| –m . Benchmarks on the X23 molecular crystal dataset and a range of prototypical bulk semiconductors demonstrate that this systematic treatment of the electrostatics eliminates unphysical behavior in the equation of state curves. In the bulk systems studied, we observe a mean absolute error in total energy of 35 meV/atom, comparable to the machine-learned universal force field, M3GNet, and sufficiently precise for structure relaxation. These results highlight the promising potential of GFN1-xTB as a universal tight-binding parametrization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

pyEF: A Python Framework for QM and QM/MM Atom-Wise Electric Field Analysis

We introduce pyEF, a software package for computing molecular electric fields, electrostatic interaction energies, and electrostatic potentials from quantum mechanical (QM) atom-centered multipole expansions with atom-wise decomposable contributions. We demonstrate the computational efficiency and accuracy of this QM-derived electric field evaluation tool through several tests. To assess the influence of the underlying QM method and charge partitioning scheme on these electrostatic quantities, we analyze over 250 configurations of an acetone solute molecule in five solvents of variable polarity. We find that electric field calculations are highly sensitive to the choice of charge partitioning method. Even among real-space charge schemes, acetone Stark tuning rates differ by up to a factor of 2. Benchmarking computed solvent dipole moments against experimental bulk values, we conclude that the CM5, ADCH, and Hirshfeld-I charge schemes most reliably capture solvent electrostatics and therefore provide a more faithful foundation for computing electric fields. When constructed from these real-space charges, electric fields are nearly insensitive to basis set size and monotonically increase in magnitude with higher Fock exchange. We also demonstrate efficient convergence of QM electrostatics when more distant molecules are represented solely by MM point charges, reducing computational overhead. Leveraging these findings, we demonstrate the use of pyEF to deduce environmental effects on a transition metal complex from a Ga 4 L 6 12– nanocage and quantify the dominant role of organic linkers in orchestrating electrostatic preorganization.

electric fields

Implications of reduced-complexity aerosol thermodynamics on organic aerosol mass concentration and composition over North America

Atmospheric organic aerosol (OA) mass concentrations can be affected by water uptake through its impact on the gas–particle partitioning of semi-volatile compounds. Current chemical transport models (CTMs) neglect this process. We have implemented the Binary Activity Thermodynamics model coupled to a volatility basis set partitioning scheme in the GEOS-Chem CTM, providing an efficient reduced-complexity OA model that predicts relative-humidity-dependent mixing and partitioning thermodynamics, while limiting the impact on computational efficiency. We provide a quantitative assessment of this water-sensitive OA treatment, focusing on a subdomain over North America. The updated OA scheme predicts a spatiotemporal mean enhancement in surface-level OA mass concentration of 145 % for January 2019 and 76 % for July 2019 compared to GEOS-Chem's most advanced OA scheme. The temporal mean surface-level OA organic mass concentration can increase by up to ∼590 % for January 2019 and ∼280 % for July 2019, with the greatest enhancements occurring over the ocean. The updated OA scheme also quantifies the OA-associated water content. The simulations show how different OA precursors and related OA surrogates contribute and respond to water uptake, including that due to changes in temperature and relative humidity over the diurnal cycle in selected winter and summer months. These results are independent of future CTM improvements involving updates to chemical reaction schemes and emission inventories. Our water-sensitive OA scheme allows for a better representation of the seasonal and regional variations in OA mass concentration in CTMs.

54 ENVIRONMENTAL SCIENCES

Many-Body Benchmark of Electronic Charge and Spin Densities for Li 1–x NiO 2

Accurate benchmarks are particularly important for highly correlated oxides as mean-field approximations often fail to describe the subtle balance of charge transfer and magnetism in these materials with an accuracy comparable to experimental needs. Here we present accurate diffusion Monte Carlo (DMC) results of the electronic charge and spin densities for the tunable highly correlated oxide Li 1–x NiO 2 for x = 0, 1/2, and 1. To enable quantitative comparisons, we introduce a robust density-partitioning scheme, extending Voronoi analysis to assign atomic charges from spatially noisy DMC densities. We then benchmark common approximations used in density functional theory (DFT). Comparison against DMC shows that r 2 SCAN delivers the most balanced performance across charge, spin, and radial density descriptors, nearly reproducing DMC results for LiNiO 2 and apical Ni sites in Li 0.5 NiO 2 . Hybrid functionals (PBE0, SCAN0) perform unexpectedly poorly, and PBE + U + V yields inconsistent trends between charge and spin densities. Therefore, the r 2 SCAN functional minimizes errors relative to DMC while capturing the variable valence of the Ni ion and also retaining the computational efficiency of DFT for large-scale simulations of the tunable structural and electronic phases of Li1−xNiO2. Our study highlights the importance of accurate benchmarking of the fundamental quantities involved in DFT to select appropriate DFT approximations in order to advance the predictive modeling of charge-transfer-driven phenomena in correlated electron systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Communication Lower Bounds and Optimal Algorithms for Symmetric Matrix Computations

In this article, we focus on the communication costs of three symmetric matrix computations: (i) multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK) (ii) adding the result of the multiplication of a matrix with the transpose of another matrix and the transpose of that result, known as a symmetric rank-2k update (SYR2K) (iii) performing matrix multiplication with a symmetric input matrix (SYMM). All three computations appear in the Level 3 Basic Linear Algebra Subroutines (BLAS) and have wide use in applications involving symmetric matrices. We establish communication lower bounds for these kernels using sequential and distributed-memory parallel computational models, and we show that our bounds are tight by presenting communication-optimal algorithms for each setting. Our lower bound proofs rely on applying a geometric inequality for symmetric computations and analytically solving constrained nonlinear optimization problems. As a result, the symmetric matrix and its corresponding computations are accessed and performed according to a triangular block partitioning scheme in the optimal algorithms.

Al Daas, Hussam [Rutherford Appleton Laboratory, D

Design of Zone-Based Hierarchical Protection System for 100% Renewable Microgrids

Design of a reliable and secure protection system for a 100% renewable microgrid with only inverter-based resources (IBRs), is quite challenging. Most of the existing protection schemes in the state-of-the-art are suitable for microgrids with mixed-type of distributed energy resources (DERs) that covers both rotating machine-based DERs as well as IBR-based DERs, where the fault current level is moderately high. Due to drastic reduction in fault current level based on mode of operation and the variation of the low fault current level based on the operating level of the IBRs, the existing protection schemes face critical challenges, in case of a 100% renewable microgrid. This article proposes a zone-based hierarchical protection scheme that partitions a microgrid into various zones-of-protection and assigns speed-based hierarchical protection schemes in order to address the fundamental challenges of such microgrids. The performance of the proposed scheme is evaluated using time-domain simulation study on a microgrid test system. The results corroborates that the proposed hierarchical zone-based protection scheme exhibits enhanced reliability, security and dependability while tested with various fault cases (fault types, locations, and impedances), and non-fault cases during both grid-tied and islanded mode.

grid-forming inverter

Design of Zone-Based Hierarchical Protection System for 100% Renewable Microgrids: Preprint

Design of a reliable and secure protection system for a 100% renewable microgrid with only inverter-based resources (IBRs), is quite challenging. Most of the existing protection schemes in the state-of-the-art are suitable for microgrids with mixed-type of distributed energy resources (DERs) that covers both rotating machine-based DERs as well as IBR-based DERs, where the fault current level is moderately high. Due to drastic reduction in fault current level based on mode of operation and the variation of the low fault current level based on the operating level of the IBRs, the existing protection schemes face critical challenges, in case of a 100% renewable microgrid. This article proposes a zone-based hierarchical protection scheme that partitions a microgrid into various zones-of-protection and assigns speed-based hierarchical protection schemes in order to address the fundamental challenges of such microgrids. The performance of the proposed scheme is evaluated using time-domain simulation study on a microgrid test system. The results corroborates that the proposed hierarchical zone-based protection scheme exhibits enhanced reliability, security and dependability while tested with various fault cases (fault types, locations, and impedances), and non-fault cases during both grid-tied and islanded mode.

grid-forming inverter

Dynamic flux surrogate-based partitioned methods for interface problems

Loosely coupled partitioned methods for multiphysics problems treat each subproblem as a separate entity and advance them independently in time. In so doing these methods enable code reuse, increase concurrency and provide a convenient framework for plug-and-play multiphysics simulations. However, mathematically loosely coupled schemes are equivalent to a single step of an iterative solution method, which can compromise their accuracy and stability. We present a new data-driven partitioned method for coupled parametric PDEs that can improve upon the accuracy of traditional loosely coupled methods without incurring a performance penalty. To that end, we replace conventional field transfers across the interface by a surrogate for the dynamics of the interface flux exchanged between the subdomains. To develop this surrogate we apply dynamic mode decomposition to a non-standard staggered-in-time state, comprising the interface flux and small solution patches near the interface. The new approach shifts the main computational burden to an offline training phase, whereas application of the surrogate in the online phase amounts to a single matrix–vector multiplication. In conclusion, we provide stability analysis of the surrogate-based partitioned scheme and include numerical results that demonstrate its potential.

Dynamic mode decomposition (DMD)

Learning linear optical circuits with coherent states

We analyze the energy and training data requirements for supervised learning of an M-mode linear optical circuit by minimizing an empirical risk defined solely from the action of the circuit on coherent states. When the linear optical circuit acts non-trivially only on k < M unknown modes (i.e. a linear optical k-junta), we provide an energy-efficient, adaptive algorithm that identifies the junta set and learns the circuit. We compare two schemes for allocating a total energy, E, to the learning algorithm. In the first scheme, each of the T random training coherent states has energy E/T. In the second scheme, a single random MT-mode coherent state with energy E is partitioned into T training coherent states. The latter scheme exhibits a polynomial advantage in training data size sufficient for convergence of the empirical risk to the full risk due to concentration of measure on the $(2MT-1)$-sphere. Specifically, generalization bounds for both schemes are proven, which indicate that for ε-approximation of the full risk by the empirical risk with high probability, $O(E^{2/3}M^{2/3}/\epsilon^{2/3})$ training states are sufficient for the first scheme and $O(E^{1/3}M^{1/3}/\epsilon^{2/3})$ training states are sufficient for the second scheme.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Stage-local partitioned two-step runge-kutta methods for large systems of ordinary differential equations

We introduce stage-local partitioned two-step Runge-Kutta methods are an extension of standard two-step Runge-Kutta methods, which are an alternative to the standard additive two-step Runge-Kutta methods currently existing in the literature. Furthermore, these new schemes are designed with an eye towards truly N-partitioned systems and leverage local stage approximations to make several computationally interesting approximations viable. Specifically, the focus on local stage approximations makes possible the construction of truly asynchronous schemes, in the parallel sense, possible. In addition, we show that an implicit-explicit approach to these schemes can lead to methods that require the inversion of only local nonlinear systems.

Applied Dynamical Systems

A High-Order Eulerian–Lagrangian Runge–Kutta Finite Volume (EL–RK–FV) Method for Scalar Nonlinear Conservation Laws

Abstract We present a class of high-order Eulerian–Lagrangian Runge–Kutta finite volume methods that can numerically solve Burgers’ equation with shock formations, which could be extended to general scalar conservation laws. Eulerian–Lagrangian (EL) and semi-Lagrangian (SL) methods have recently seen increased development and have become a staple for allowing large time-stepping sizes. Yet, maintaining relatively large time-stepping sizes post shock formation remains quite challenging. Our proposed scheme integrates the partial differential equation on a space-time region partitioned by linear approximations to the characteristics determined by the Rankine–Hugoniot jump condition. We trace the characteristics forward in time and present a merging procedure for the mesh cells to handle intersecting characteristics due to shocks. Following this partitioning, we write the equation in a time-differential form and evolve with Runge–Kutta methods in a method-of-lines fashion. High-resolution methods such as ENO and WENO-AO schemes are used for spatial reconstruction. Extension to higher dimensions is done via dimensional splitting. Numerical experiments demonstrate our scheme’s high-order accuracy and ability to sharply capture post-shock solutions with large time-stepping sizes.

Chen, Jiajie

Fast and Invertible Simplicial Approximation of Magnetic‐Following Interpolation for Visualizing Fusion Plasma Simulation Data

We introduce a fast and invertible approximation for fusion plasma simulation data represented as 2D planar meshes with connectivities approximating magnetic field lines along the toroidal dimension in deformed 3D toroidal spaces. Scientific variables (e.g., density and temperature) in these fusion data are interpolated following a complex magnetic-field-line-following scheme in the toroidal space represented by a cylindrical coordinate system. This deformation in the 3D space poses challenges for root-finding and interpolation. To this end, we propose a novel paradigm for visualizing and analyzing such data based on a newly developed algorithm for constructing a 3D simplicial mesh within the deformed 3D space. Our algorithm generates a tetrahedral mesh that connects the 2D meshes using tetrahedra while adhering to the constraints on node connectivities imposed by the magnetic field-line scheme. Specifically, we first divide the space into smaller partitions to reduce complexity based on the input geometries and constraints on connectivities. Then, we independently search for a feasible tetrahedralization of each partition, considering nonconvexity. We demonstrate our method with two X-Point Gyrokinetic Code (XGC) simulation datasets on the International Thermonuclear Experimental Reactor (ITER) and Wendelstein 7-X (W7-X), and use an ocean simulation dataset to substantiate broader applicability of our method. An open source implementation of our algorithm is available at https://github.com/rcrcarissa/DeformedSpaceTet.

Ren, Congrong [The Ohio State Univ., Columbus, OH

Implicit-explicit Runge-Kutta for radiation hydrodynamics I: Gray diffusion

Radiation hydrodynamics are a challenging multiscale and multiphysics set of equations. To capture the relevant physics of interest, one typically must time step on the hydrodynamics timescale, making explicit integration the obvious choice. On the other hand, the coupled radiation equations have a scaling such that implicit integration is effectively necessary in non-relativistic regimes. A first-order Lie-Trotter-like operator split is the most common time integration scheme used in practice, alternating between an explicit hydrodynamics step and an implicit radiation solve and energy deposition step. However, such a scheme is limited to first-order accuracy, and nonlinear coupling between the radiation and hydrodynamics equations makes a more general additive partitioning of the equations non-trivial. Here, we develop a new formulation and partitioning of radiation hydrodynamics with gray diffusion that allows us to apply (linearly) implicit-explicit Runge-Kutta time integration schemes. In conclusion, we prove conservation of total energy in the new framework, and demonstrate 2nd-order convergence in time on multiple radiative shock problems, achieving error 3–5 orders of magnitude smaller than the first-order Lie-Trotter operator split at the hydrodynamic CFL, even when Lie-Trotter applies a 3rd-order TVD Runge-Kutta scheme to the hydrodynamics equations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Urban weather modeling using WRF: linking physical assumptions, code implementation, and observational needs

The Weather Research and Forecasting (WRF) model includes urban schemes that simulate the influence of urban surfaces on the atmosphere using parameterizations for flux, and radiative exchanges. Three core schemes – the Bulk urban parameterization, Single-Layer Urban Canopy Model (SLUCM), and Multi-Layer Urban Canopy Model (MLUCM) – represent increasing levels of complexity. Although the parameterizations within these urban schemes are described in the literature, their specific implementation remains poorly documented, thus slowing down model development efforts. This manuscript provides a roadmap to the three urban schemes in WRF version 4.5.2, presenting equations using the same symbols as in the model code, along with references to code lines, and including graphics and explanations that connect the code to its physical foundations. Our thorough review of the urban parameterizations implemented in WRF version 4.5.2 highlighted a handful of parameters that may introduce discontinuities in simulations: (i) in the SLUCM, a 1 mm h −1 rain rate threshold is employed to switch between two minimum moisture availability parameterizations, thus impacting latent heat flux calculations; (ii) in the SLUCM a threshold is used to partition shortwave radiation into direct and diffuse components; (iii) in all three urban schemes, the bulk Richardson number is employed to select the similarity function, which influences the vertical distribution of heat and momentum. We also identified a highly simplified treatment of the radiative balance on roof surfaces. The implications of these simplifications can be assessed through targeted observations across relevant conditions, including varying precipitation rates, cloud cover, and transitions between stability regimes. Furthermore, the widespread application of the Monin-Obukhov similarity theory in these urban schemes warrants model evaluation under highly stable and unstable conditions and in heterogeneous urban settings with variable land cover and building heights on scales finer than model resolution. To address these challenges, we offer guidance on observational strategies, emphasizing the need for multi-parametric measurements to capture potential compensating biases and multi-height measurements that align with the levels where quantities are diagnostic and prognosed in the model (i.e., the lowest atmospheric level of the WRF model). Finally, our inspection of the code revealed implementation bugs that have now been corrected in WRF versions 4.6.0 and 4.6.1. Sensitivity tests over the Atlanta urban area show that these corrections affect surface temperatures, underscoring the importance of performing rigorous documentation and verification of the implementation of parameterizations in model code.

54 ENVIRONMENTAL SCIENCES

Hierarchical Truncations for Many-Body Expansion Potentials

In this work, a new strategy to truncate high-order terms in the many-body expansion (MBE) is proposed. This new approach, which we call a hierarchical many-body expansion (HMBE), is based on a hierarchical partition of the system into multitier fragments and can in principle be applied to any large molecular system. Numerical tests on a series of (H 2 O) 64 structures are presented, demonstrating satisfactory relative energies between the clusters and binding energies of individual clusters compared with full-cluster calculations, with significantly fewer high-order terms computed than conventional MBE. The hierarchical truncation can be augmented by certain many-body terms for fragments at the interface between the partitions (called “Schengen terms”) to further improve accuracy. This work establishes the HMBE scheme as a promising framework to model very large systems (e.g., proteins), which are naturally built on a hierarchical structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Stability analysis of the Eulerian–Lagrangian finite volume methods for nonlinear hyperbolic equations in one space dimension

In this paper, we construct a novel Eulerian–Lagrangian finite volume (ELFV) method for nonlinear scalar hyperbolic equations in one space dimension. It is well known that the exact solutions to such problems may contain shocks though the initial conditions are smooth, and direct numerical methods may suffer from restricted time step sizes. To relieve the restriction, we propose an ELFV method, where the space-time domain was separated by the partition lines originated from the cell interfaces whose slopes are obtained following the Rakine–Hugoniot junmp condition. Unfortunately, to avoid the intersection of the partition lines, the time step sizes are still limited. To fix this gap, we detect effective troubled cells (ETCs) and carefully design the influence region of each ETC, within which the partitioned space-time regions are merged together to form a new one. Then with the new partition of the space-time domain, we theoretically prove that the proposed first-order scheme with Euler forward time discretization is total-variation-diminishing and maximum-principle-preserving with at least twice larger time step constraints than the classical first order Eulerian method for Burgers’ equation. Numerical experiments verify the optimality of the designed time step sizes.

97 MATHEMATICS AND COMPUTING

Advancing Organized Convection Representation in the Unified Model: Implementing and Enhancing Multiscale Coherent Structure Parameterization

To address the effect of stratiform latent heating on meso- to large-scale circulations, an enhanced implementation of the Multiscale Coherent Structure Parameterization (MCSP) is developed for the Met Office Unified Model. MCSP represents the top-heavy stratiform latent heating from under-resolved organized convection in general circulation models. We couple the MCSP with a mass-flux convection scheme (CoMorph-A) to improve storm lifecycle continuity. The improved MCSP trigger is specifically designed for mixed-phase deep convective cloud, combined with a background vertical wind shear, both known to be crucial for stratiform development. We also test a cloud top temperature dependent convective-stratiform heating partitioning, in contrast to the earlier fixed partitioning. Assessments from ensemble weather forecasts and decadal simulations demonstrate that MCSP directly reduces cloud deepening and precipitation areas by moderating mesoscale circulations. Indirectly, it amends tropical precipitation biases, notably correcting dry and wet biases over India and the Indian Ocean, respectively. Remarkably, the scheme outperforms a climate model ensemble by improving seasonal precipitation cycle predictions in these regions. The scheme also improves Madden-Julian Oscillation (MJO) spectra, achieving better alignment with observational and reanalysis data by intensifying the simulated MJO over the Indian Ocean during phases 4 to 5. However, the scheme increases precipitation overestimation over the Western Pacific. Shifting from fixed to temperature-dependent convective-stratiform partitioning reduces the Pacific precipitation overestimation and further improves the seasonal cycle in India. Spatially correlated biases highlight the necessity for advances beyond deterministic approaches to align MCSP with environmental conditions.

54 ENVIRONMENTAL SCIENCES