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At least 181 records · Page 10

Active learning of polarizable nanoparticle phase diagrams for the guided design of triggerable self-assembling superlattices

Polarizable nanoparticles are of interest in materials science because of their rich and complex phase behavior that can be used to engineer nanostructured materials with long-range crystalline order. To understand and rationally navigate the design space of polarizable nanoparticles for self-assembling highly ordered superlattices, we developed a coarse-grained computational model to describe the nanoparticle-nanoparticle interactions in implicit solvent and employ the computationally efficient image method to model many-body polarization interactions. We conducted high-throughput virtual screening over a five-dimensional particle design space spanned by temperature, particle size, particle charge, particle dielectric, and solvent dielectric using enhanced sampling molecular dynamics calculations within an active learning framework to efficiently map out the regions of thermodynamic stability of the self-assembled aggregates. We validate our predictions in comparisons against small angle x-ray scattering measurements of gold nanoparticles surface functionalized with metal chalcogenide ligands. Lastly, we use our validated phase maps to computationally design switchable nanostructured materials capable of triggered assembly and disassembly as a function of temperature and solvent dielectric with potential applications as sensors, smart windows, optoelectronic devices, and in medical diagnostics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Fierro Version 2.x

FIERRO is a parallel C++ code designed to simulate fluid mechanics, heat transfer, and solid mechanics in two- and three-dimensional space. FIERRO is written to run on homogeneous (CPU) and heterogeneous (CPU+GPU) high performance computing machines. Fierro can aid a) modeling and design efforts that have historically relied on commercial implicit and explicit finite element codes, b) numerical methods research, c) manufacturing research, and d) computer science research. The code contains diverse numerical methods to solve the governing physics equations for both quasi-static and dynamic problems. Mathematical optimization solvers are coupled to the numerical methods to research topology and shape optimization that has application to additive manufacturing, and to create novel numerical approaches. Phase-field methods with micromechanical solvers are provided to simulate microstructure formation and evolution in manufacturing processes. The micromechanical solvers can also help research efforts create continuum-scale constitutive models for solids, as a function of the microstructure, in situ in a calculation or in a stand-alone manner. No physical data exists within the code.

Morgan, Nathaniel↗

Fierro

FIERRO is a parallel C++ code designed to simulate fluid mechanics, heat transfer, and solid mechanics in two- and three dimensional space. FIERRO is written to run on homogeneous (CPU) and heterogeneous (CPU+GPU) high performance computing machines. Fierro can aid a) modeling and design efforts that have historically relied on commercial implicit and explicit finite element codes, b) numerical methods research, c) manufacturing research, and d) computer science research. The code contains diverse numerical methods to solve the governing physics equations for both quasi-static and dynamic problems. Mathematical optimization solvers are coupled to the numerical methods to research topology and shape optimization that has application to additive manufacturing, and to create novel numerical approaches. Phase-field methods with micromechanical solvers are provided to simulate microstructure formation and evolution in manufacturing processes. The micromechanical solvers can also help research efforts create continuum-scale constitutive models for solids, as a function of the microstructure, in situ in a calculation or in a stand-alone manner. No physical data exists within the code.

Morgan, Nathaniel↗

Lens Modeling of STRIDES Strongly Lensed Quasars Using Neural Posterior Estimation

Strongly lensed quasars can be used to constrain cosmological parameters through time-delay cosmography. Models of the lens masses are a necessary component of this analysis. To enable time-delay cosmography from a sample of $\mathcal{O}(10^3)$ lenses, which will soon become available from surveys like the Rubin Observatory’s Legacy Survey of Space and Time and the Euclid Wide Survey, we require fast and standardizable modeling techniques. To address this need, we apply neural posterior estimation (NPE) for modeling galaxy-scale strongly lensed quasars from the Strong Lensing Insights into the Dark Energy Survey (STRIDES) sample. NPE brings two advantages: speed and the ability to implicitly marginalize over nuisance parameters. We extend this method by employing sequential NPE to increase precision of mass model posteriors. We then fold individual lens models into a hierarchical Bayesian inference to recover the population distribution of lens mass parameters, accounting for out-of-distribution shift. After verifying our method using simulated analogs of the STRIDES lens sample, we apply our method to 14 Hubble Space Telescope single-filter observations. We find the population mean of the power-law elliptical mass distribution slope, γ lens , to be $\mathcal{M}_γ$ lens = 2.13 ± 0.06. Our result represents the first population-level constraint for these systems. This population-level inference from fully automated modeling is an important stepping stone toward cosmological inference with large samples of strongly lensed quasars.

79 ASTRONOMY AND ASTROPHYSICS↗

Error estimates of finite difference methods for the Dirac equation in the massless and nonrelativistic regime

We present four frequently used finite difference methods and establish the error bounds for the discretization of the Dirac equation in the massless and nonrelativistic regime, involving a small dimensionless parameter 0 < ε &NestedLessLess; 1 inversely proportional to the speed of light. In the massless and nonrelativistic regime, the solution exhibits rapid motion in space and is highly oscillatory in time. Specifically, the wavelength of the propagating waves in time is at O(ε), while in space, it is at O(1) with the wave speed at O(ε -1 ). We adopt one leap-frog, two semi-implicit, and one conservative Crank-Nicolson finite difference methods to numerically discretize the Dirac equation in one dimension and establish rigorously the error estimates which depend explicitly on the time step τ, mesh size h, and the small parameter ε. The error bounds indicate that, to obtain the “correct” numerical solution in the massless and nonrelativistic regime, i.e., 0 < ε &NestedLessLess; 1, all these finite difference methods share the same ε-scalability as time step τ = O(ε 3/2 ) and mesh size h = O(ε 1/2 ). A large number of numerical results are reported to verify the error estimates.

97 MATHEMATICS AND COMPUTING↗

Uniform accuracy of implicit-explicit Runge-Kutta (IMEX-RK) schemes for hyperbolic systems with relaxation

Implicit-explicit Runge-Kutta (IMEX-RK) schemes are popular methods to treat multiscale equations that contain a stiff part and a non-stiff part, where the stiff part is characterized by a small parameter. Here, in this work, we prove rigorously the uniform stability and uniform accuracy of a class of IMEX-RK schemes for a linear hyperbolic system with stiff relaxation. The result we obtain is optimal in the sense that it holds regardless of the value of and the order of accuracy is the same as the design order of the original scheme, i.e., there is no order reduction.

97 MATHEMATICS AND COMPUTING↗

Physics-based adaptivity of a spectral method for the Vlasov–Poisson equations based on the asymmetrically-weighted Hermite expansion in velocity space

We propose a spectral method for the 1D-1V Vlasov–Poisson system where the discretization in velocity space is based on asymmetrically-weighted Hermite functions, dynamically adapted via a scaling α and shifting u of the velocity variable. Specifically, at each time instant an adaptivity criterion selects new values of α and u based on the numerical solution of the discrete Vlasov–Poisson system obtained at that time step. Once the new values of the Hermite parameters α and u are fixed, the Hermite expansion is updated and the discrete system is further evolved for the next time step. The procedure is applied iteratively over the desired temporal interval. The key aspects of the adaptive algorithm are: the map between approximation spaces associated with different values of the Hermite parameters that preserves total mass, momentum and energy; and the adaptivity criterion to update α and u based on physics considerations relating the Hermite parameters to the average velocity and temperature of each plasma species. For the discretization of the spatial coordinate, we rely on Fourier functions and use the implicit midpoint rule for time stepping. The resulting numerical method possesses intrinsically the property of fluid-kinetic coupling, where the low-order terms of the expansion are akin to the fluid moments of a macroscopic description of the plasma, while kinetic physics is retained by adding more spectral terms. Moreover, the scheme features conservation of total mass, momentum and energy associated in the discrete, for periodic boundary conditions. A set of numerical experiments confirms that the adaptive method outperforms the non-adaptive one in terms of accuracy and stability of the numerical solution.

97 MATHEMATICS AND COMPUTING↗

A Full-Induction Magnetohydrodynamics Solver for Liquid Metal Fusion Blankets in Vertex-CFD

Multiphysics modeling of liquid metal fusion blankets, which produce tritium and convert energy of neutrons created via fusion reactions into heat, is crucial for predicting performance, ensuring structural integrity, and optimizing energy production. While traditional blanket modeling of liquid metal flows during normal steady operating conditions commonly employs the inductionless approximation of the magnetohydrodynamics (MHD) equations, transient scenarios, when the plasma-confining magnetic field varies on millisecond time scales, require a full-induction MHD approach that dynamically evolves the magnetic field via the time-dependent induction equation. This paper presents the formulation, implementation, and initial verification of a full-induction MHD solver integrated within the open-source Vertex-CFD framework, which aims to achieve tight multiphysics coupling, a flexible software design enabling easy extension and addition of physics models, and performance portability across computing platforms. The solver utilizes finite element spatial discretization, implicit Runge–Kutta time integration, and an inexact Newton method to solve the resulting discrete nonlinear system, leveraging Trilinos packages for efficient computation. Verification against selected benchmark problems demonstrates accuracy and robustness of the solver. Furthermore, when the solver is applied to an idealized blanket model in 2.5D and full 3D, results obtained with Vertex-CFD are in good agreement with recently published quasi-2D simulations. These findings establish a computational foundation for future simulations of transient MHD phenomena in liquid metal blankets with Vertex-CFD, and open avenues for future extensions and performance optimizations.

Endeve, Eirik [ORNL] (ORCID:0000000312519507)↗

Confinement and String Breaking in the Compact Abelian Higgs Model

While real-time simulation of Quantum Chromodynamics remains technologically out of reach, simplified models for studying elements of QCD phenomenology abound. This work presents a simple model, a spin-1 truncation of the Compact Abelian Higgs Model simulated on qutrit sites, in which confinement and string breaking is accessible to current simulation methods. In the low-energy regime of 1+1D scalar electrodynamics, the heavy modes are integrated out, producing a spin chain effective Hamiltonian in which Gauss' law is implicitly satisfied. We study the spectrum of string-like excitations using DMRG methods on the order of 100 sites. We demonstrate that an added, local chemical potential, playing a role analogous to external charges, permits parameter-dependent measurements of physical features of interest like the string tension and effective meson mass. Varying the chemical potential also permits a characterization of string stability not assessed in prior studies of confining lattice models.

Senseman, Blake [Iowa U.]↗

Fast HARDI Uncertainty Quantification and Visualization with Spherical Sampling

In this paper, we study uncertainty quantification and visualization of orientation distribution functions (ODF), which corresponds to the diffusion profile of high angular resolution diffusion imaging (HARDI) data. The shape inclusion probability (SIP) function is the state‐of‐the‐art method for capturing the uncertainty of ODF ensembles. The current method of computing the SIP function with a volumetric basis exhibits high computational and memory costs, which can be a bottleneck to integrating uncertainty into HARDI visualization techniques and tools. We propose a novel spherical sampling framework for faster computation of the SIP function with lower memory usage and increased accuracy. In particular, we propose direct extraction of SIP isosurfaces, which represent confidence intervals indicating spatial uncertainty of HARDI glyphs, by performing spherical sampling of ODFs. Our spherical sampling approach requires much less sampling than the state‐of‐the‐art volume sampling method, thus providing significantly enhanced performance, scalability, and the ability to perform implicit ray tracing. Our experiments demonstrate that the SIP isosurfaces extracted with our spherical sampling approach can achieve up to 8164× speedup, 37282× memory reduction, and 50.2% less SIP isosurface error compared to the classical volume sampling approach. We demonstrate the efficacy of our methods through experiments on synthetic and human‐brain HARDI datasets.

97 MATHEMATICS AND COMPUTING↗

One-sweep moment-based semi-implicit-explicit integration for gray thermal radiation transport

Thermal radiation transport (TRT) is a time dependent, high dimensional partial integro-differential equation. In practical applications such as inertial confinement fusion, TRT is coupled to other physics such as hydrodynamics, plasmas, etc., and the timescales one is interested in capturing are often much slower than the radiation timescale. As a result, TRT is treated implicitly, and due to its stiffness and high dimensionality, is often a dominant computational cost in multiphysics simulations. Here we develop a new approach for implicit-explicit (IMEX) integration of gray TRT in the deterministic SN setting, which requires only one sweep per stage, with the simplest first-order method requiring only one sweep per time step. The partitioning of equations is done via a moment-based high-order low-order formulation of TRT, where the streaming operator and first two moments are used to capture the asymptotic stiff regimes of the streaming limit and diffusion limit. Absorption-reemission is treated explicitly, and although stiff, is sufficiently damped by the implicit solve that we achieve stable accurate time integration without incorporating the coupling of the high order and low order equations implicitly. Due to nonlinear coupling of the high-order and low-order equations through temperature-dependent opacities, to facilitate IMEX partitioning and higher-order methods, we use a semi-implicit integration approach amenable to nonlinear partitions. In conclusion, results are demonstrated on thick Marshak and crooked pipe benchmark problems, demonstrating orders of magnitude improvement in accuracy and wallclock compared with the standard first-order implicit integration typically used.

97 MATHEMATICS AND COMPUTING↗

Semi-Lagrangian nodal discontinuous Galerkin method for the BGK model

In this work, we propose a semi-Lagrangian (SL) nodal discontinuous Galerkin (DG) solver for the BGK equation. The BGK model was introduced by Bhatnagar, Gross, and Krook [1] as a relaxation model for the fundamental Boltzmann equation [5], which describes the kinetic dynamic of rarefied gases with a probability distribution function. The challenges of designing efficient numerical schemes for the Boltzmann equation mainly come from its high dimensionality and complicated nonlinear collision operator. The BGK model gains interests since it has much lower computational cost, due to the relatively simple structure of the relaxation operator in replacement of the collision operator, while simultaneously preserving several important physical properties, such as macroscopic quantities and dissipation of entropy.

97 MATHEMATICS AND COMPUTING↗

Sparse chronology strategy for integrating seasonal energy storage in capacity expansion models

Here, this study develops the sparse chronology method to enhance the representative period framework in capacity expansion models, enabling the effective integration of long-duration energy storage modeling. Traditional representative period methods cannot capture the state of charge of seasonal energy storage systems because they do not establish effective inter-day linkages to connect the state of charge between periods. The sparse chronology approach addresses this limitation by establishing inter-day linkages that allow state of charge to shift inter-seasonally. At the same time, it groups identical representative days into partitions, applying constraints sparsely and implicitly to reduce computational load further. Validation results demonstrate that this method successfully simulates long-duration energy storage patterns, achieving close alignment with a continuous yearly benchmark model, with seasonal trends and state of charge cycles clearly represented. The computational load analysis reveals that the sparse chronology method efficiently applies constraints on maximum and minimum state of charge limits within the representative day framework, eliminating the need for detailed constraints on each individual day. By partitioning representative days and constraining only the start and end of each partition, the method significantly decreases computational requirements. Simulation results show that sparse chronology closely approximates the continuous yearly method's accuracy, even with as few as 20 representative days, achieving correlation values with the benchmark of nearly 0.9 in state of charge plots. Furthermore, it maintains computational efficiency, requiring only 4 % of the solver time compared to the continuous yearly method with 20 representative days. This approach allows capacity expansion models to incorporate long-duration energy storage with high temporal, spatial, and technological resolution, enabling more detailed modeling for large-scale power systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A DG-IMEX Method for Two-moment Neutrino Transport: Nonlinear Solvers for Neutrino–Matter Coupling

Neutrino-matter interactions play an important role in core-collapse supernova (CCSN) explosions as they contribute to both lepton number and/or four-momentum exchange between neutrinos and matter, and thus act as the agent for neutrino-driven explosions. Due to the multiscale nature of neutrino transport in CCSN simulations, an implicit treatment of neutrino-matter interactions is desired, which requires solutions of coupled nonlinear systems in each step of the time integration scheme. In this paper we design and compare nonlinear iterative solvers for implicit systems with energy coupling neutrino-matter interactions commonly used in CCSN simulations. Specifically, we consider electron neutrinos and antineutrinos, which interact with static matter configurations through the Bruenn 85 opacity set. The implicit systems arise from the discretization of a nonrelativistic two-moment model for neutrino transport, which employs the discontinuous Galerkin (DG) method for phase-space discretization and an implicit-explicit (IMEX) time integration scheme. In the context of this DG-IMEX scheme, we propose two approaches to formulate the nonlinear systems — a coupled approach and a nested approach. For each approach, the resulting systems are solved with Anderson-accelerated fixedpoint iteration and Newton’s method. The performance of these four iterative solvers has been compared on relaxation problems with various degree of collisionality, as well as proto-neutron star deleptonization problems with several matter profiles adopted from spherically symmetric CCSN simulations. Here, numerical results suggest that the nested Anderson-accelerated fixed-point solver is more efficient than other tested solvers for solving implicit nonlinear systems with energy coupling neutrino-matter interactions.

79 ASTRONOMY AND ASTROPHYSICS↗

Machine Learning for Memory Reduction in the Implicit Monte Carlo Simulations of Thermal Radiative Transfer [Slides]

Project Goal: Use parametric Machine Learning methods in order to reduce memory requirements at checkpointing & restarting in the IMC simulations of Thermal Radiative Transfer using: Expectation Maximization and Weighted Gaussian Mixture Model-based approach for `particle-data compression', introduced in Plasma Physics to model Maxwellian particle distributions by Luis Chacon and Guangye Chen; Expectation Maximization with Weighted Hyper-Erlang Model in order to compress isotropic IMC particle data in the frequency domain; and Expectation Maximization and von Mises-Fisher Mixture Model for compression of anisotropic IMC particle data in the angular domain (work-in-progress).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Explicit dispersion relations for warm fluid waves in a uniform plasma (invited)

Classical dispersion relations for waves in a fluid plasma are expressed as implicit functions of wave frequency and wave- number. The implicit dispersion relation must in general be solved numerically. This work introduces an astute method for obtaining an explicit dispersion relation for waves in a fluid plasma. The explicit expression has an advantage of providing eigenmodes without numerical computations and giving a dispersion relation more detailed than the implicit expression. As in the case of cold waves, the wavenumber for an arbitrary frequency can be directly obtained from the explicit formula. The explicit formula also enables an accurate evaluation of finite-temperature effects on a dispersion relation even near the cyclotron resonance, where a numerical analysis of the implicit relation is impractical. As a result, the analytic formula can be used to investigate temperature effects on electromagnetic waves.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks

One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs), especially with arbitrary initial data. We address this problem by taking advantage of recent advances in scientific machine learning and the spectral dynamically orthogonal (DO) and borthogonal (BO) methods for representing stochastic processes. The recently introduced DO/BO methods reduce the SPDE to solving a system of deterministic PDEs and a system of stochastic ordinary differential equations. Specifically, we propose two new physics-informed neural networks (PINNs) for solving time-dependent SPDEs, namely the neural network (NN)-DO/BO methods. The proposed methods incorporate the DO/BO constraints into the loss function (along with the modal decomposition of the SPDE) with an implicit form instead of generating explicit expressions for the temporal derivatives of the DO/BO modes. Hence, the NN-DO/BO methods can overcome some of the drawbacks of the original DO/BO methods. For example, we do not need the assumption that the covariance matrix of the random coefficients is invertible as in the original DO method, and we can remove the assumption of no eigenvalue crossing as in the original BO method. Moreover, the NN-DO/BO methods can be used to solve time-dependent stochastic inverse problems with the same formulation and same computational complexity as for forward problems. Furthermore, we demonstrate the capability of the proposed methods via several numerical examples, namely: (1) A linear stochastic advection equation with deterministic initial condition: we obtain good results with the proposed methods, while the original DO/BO methods cannot be applied directly in this case. (2) Long-time integration of the stochastic Burgers' equation: we show the good performance of NN-DO/BO methods, especially the effectiveness of the NN-BO approach for such problems with many eigenvalue crossings during the whole time evolution, while the original BO method fails. (3) Nonlinear reaction diffusion equation: we consider both the forward problem and the inverse problems, including very noisy initial point values, to investigate the flexibility of the NN-DO/BO methods in handling inverse and mixed type problems. Taken together, these simulation results demonstrate that the NN-DO/BO methods can be employed to effectively quantify uncertainty propagation in a wide range of physical problems, but future work should address the efficiency issue of PINNs for forward problems.

97 MATHEMATICS AND COMPUTING↗

A two-fluid single-column model of turbulent shallow convection. Part II: Single-column model formulation and numerics

The two-fluid single-column model of Thuburn et al. (Quart. J. R. Meteorol. Soc., 2019, 145, 1535–1550) is extended to include moisture and horizontal wind shear. Turbulent kinetic energy is introduced as a prognostic variable, dependence on a diagnosed boundary-layer height is removed, and subfilter fluxes are approximated using a two-fluid version of a Mellor–Yamada scheme. Three mechanisms for entrainment and detrainment processes are introduced, which represent entrainment of unstable air at the surface, forced detrainment of air at the top of the boundary/cloud layers, and turbulent mixing that relaxes the convective fluid to a reference profile. A semi-implicit Eulerian discretization replaces the semi-implicit semi-Lagrangian implementation of Thuburn et al. (Quart. J. R. Meteorol. Soc., 2019, 145, 1535–1550) to improve numerical stability and conservation. The equations for the implicit time step are solved using a quasi-Newton method, which is shown to perform well in numerical tests for conservation and convergence. The two-fluid single-column model presented in this article will be applied to simulations of shallow cumulus convection in Part III.

54 ENVIRONMENTAL SCIENCES↗