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Proton diffusion and hydrogen/deuterium exchange in amorphous solid water at temperatures from 114 to 134 K

The reaction coefficient for hydrogen/deuterium (H/D) exchange and the diffusion of hydrated excess protons within amorphous solid water (ASW) are characterized as a function of temperature. For these experiments, water films are deposited on a Pt(111) substrate at 108 K, and reactions with pre-adsorbed hydrogen atoms produce hydrated protons. Upon heating, protons diffuse within the water, and H/D exchange occurs when they encounter D2O probe molecules deposited in the films. The time-dependent concentration of D2O is monitored with infrared spectroscopy, and it indicates the protons diffusion from the substrate and establish an equilibrium distribution prior to significant H/D exchange for temperatures 114 K ≤T≤ 134 K. By controlling the distance between the D2O molecules and the substrate, we probe the distribution of protons within the film. It decays as x−2 for the examined range of x (12–52 nm) due to the electric field that develops between the diffusing protons and their image charges in the metal substrate. This agrees with the theoretical distance scaling for the equilibrated proton concentration in a dielectric near a metal boundary. From the proton concentration and the measured D2O decay rate, a lower bound for the proton diffusion coefficient ranging from 10−20 m2/s at 114 K to 10−18 m2/s at 134 K is estimated. The diffusion coefficient has an activation energy of 0.40 eV, which is comparable to energies reported for molecular translations and rotations of H2O, suggesting they may play a critical role in the proton diffusion mechanism within ASW.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Accelerating high-order continuum kinetic plasma simulations using multiple GPUs

Kinetic plasma simulations solve the Vlasov-Poisson or Vlasov-Maxwell equations to evolve scalar-variable distribution functions in position-velocity phase space and vector-variable electromagnetic fields in configuration space. The immense computational cost of evolving high-dimensional variables, and their large number of degrees of freedom, often limits the utility of continuum kinetic simulations and presents a challenge when it comes to accurately simulating real-world physical phenomena. To address this challenge, we present techniques that accelerate and minimize the computational work required for a scalable Vlasov-Poisson solver. We show theoretical hardware compute and communication bounds for solving a fourth-order finite-volume Vlasov-Poisson system. These bounds are then used to inform and evaluate the design of performance portable algorithms for a multiple graphics processing unit (GPU) accelerated version of the Vlasov-Poisson solver VCK-CPU [1]. We demonstrate that the multi-GPU Vlasov solver implementation, VCK-GPU, simultaneously minimizes required inter-process data transfer while also being bounded by the machine network performance limits. This results in an overall strong scaling speedup per timestep of up to 40x in three-dimensional phase space (one position, two velocity coordinates) and 54x in four dimensional phase space (two position, two velocity coordinates) and a 341x increase in simulation throughput of the GPU accelerated code over the existing CPU code. The GPU code is also able to weak scale up to 256 compute nodes and 1024 GPUs. In conclusion, we demonstrate that the improved compute performance enables exploring configurations which were previously computationally infeasible, including resolving fine-scale distribution function filamentation and multi-species dynamics with realistic electron-proton mass ratios.

Continuum kinetics

Vidyut3d: A GPU accelerated fluid solver for non-equilibrium plasmas on adaptive grids

We present the numerical methods, programming methodology, verification, and performance assessment of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures, in this work. Our plasma fluid model solves the coupled conservation equations for species transport, electrostatic Poisson and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive-grid/particle management library, AMReX, and is portable over widely available vendor specific GPU architectures. We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth-order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on capacitive discharges and atmospheric pressure streamer propagation. We demonstrate the use of our solver on two 3D simulation cases: an atmospheric streamer propagation in Ar-H2 mixtures and a low pressure three-electrode radio frequency reactor. Our performance studies on three different CPU+GPU architectures indicate ~ 150-400X speed-up using AMD and NVIDIA GPUs per time step compared to a single CPU core for a 4 million cell simulation with 15 species.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Vidyut3d: A Gpu Accelerated Fluid Solver for Non-Equilibrium Plasmas on Adaptive Grids

We present the numerical methods, programming methodology, verification, and performance assessment of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures, in this work. Our plasma fluid model solves the coupled conservation equations for species transport, electrostatic Poisson and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive-grid/particle management library, AMReX, and is portable over widely available vendor specific GPU architectures. We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth-order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on capacitive discharges and atmospheric pressure streamer propagation. We demonstrate the use of our solver on two 3D simulation cases: an atmospheric streamer propagation in Ar-H2 mixtures and a low pressure twin electrode radio frequency reactor. Our performance studies on three different CPU+GPU architectures indicate approximately 150-400X speed-up using AMD and NVIDIA GPUs per time step compared to a single CPU core for a 4 million cell simulation with 15 species.

Sitaraman, Hariswaran

Development of a Performance Portable Non-Equilibrium Plasma Fluid Solver on Adaptive Grids

This presentation will describe the numerical techniques, programming paradigms, verification, and performance of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures. Our plasma fluid model solves the conservation equations for self-consistent electrostatic Poisson, electron and heavy species transport, and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive mesh management library, AMReX (Zhang et al., JOSS, 4 (37) 1370, 2019), and can be built and run on widely available vendor specific GPU architectures (NVIDIA/AMD/Intel). We utilize a non-subcycled second order semi-implicit time-stepping method where all adaptive mesh refinement (AMR) levels are advanced with the same time step. The composite multi-level multigrid solver from within AMReX is used for each of the governing equations that are cast into a Helmholtz equation form. We have also developed a python based chemical mechanism parser framework that uses a similar format as CANTERA (Goodwin et al., Zenodo, 2018) yaml files as input. Our custom parser reads the yaml file and provides C++ files with transport and production rate functions that can be executed on both host (CPU) and device (GPU). We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on low-pressure capacitive and high-pressure streamer discharges. Our initial performance studies indicate 10X speed-up using 20 NVIDIA GPUs versus 200 CPUs for an atmospheric streamer discharge problem solved on a 512 x 1024 x 512 grid.

graphics processing units

CLPNets: Coupled Lie–Poisson neural networks for multi-part Hamiltonian systems with symmetries

To accurately compute data-based prediction of Hamiltonian systems, it is essential to utilize methods that preserve the structure of the equations over time. We consider a particularly challenging case of systems with interacting parts that do not reduce to pure momentum evolution. Such systems are essential in scientific computations, such as discretization of a continuum elastic rod, which can be viewed as the group of rotations and translations $SE(3)$. The evolution involves not only the momenta but also the relative positions and orientations of the particles. The presence of Lie group-valued elements, such as relative positions and orientations, poses a problem for applying previously derived methods for data-based computing. We develop a novel method of data-based computation and complete phase space learning of such systems. We follow the original framework of SympNets (Jin et al., 2020) and LPNets (Eldred et al., 2024), building the neural network from phase space mappings that preserve the Lie–Poisson structure. We derive a novel system of mappings that are built into neural networks describing the evolution of such systems. We call such networks Coupled Lie–Poisson Neural Networks, or CLPNets. We consider increasingly complex examples for the applications of CLPNets, starting with the rotation of two rigid bodies about a common axis, progressing to the free rotation of two rigid bodies, and finally to the evolution of two connected and interacting $SE(3)$ components, describing the discretization of an elastic rod into two elements. Our method preserves all Casimir invariants to machine precision, preserves energy to high accuracy, and shows good resistance to the curse of dimensionality, requiring only a few thousand data points for all cases studied (three to eighteen dimensions). Additionally, the method is highly economical in memory requirements, requiring only about 200 parameters for the most complex case considered.

Data-based modeling

A Statistician’s Overview of Physics-Informed Neural Networks for Spatio-Temporal Data

The recent success of deep neural network models with physical constraints (so-called, Physics-Informed Neural Networks, PINNs) has led to renewed interest in the incorporation of mechanistic information in predictive models. Statisticians and others have long been interested in this problem, which has led to several practical and innovative solutions dating back decades. In this overview, we focus on the problem of data-driven prediction and inference of dynamic spatio-temporal processes that include mechanistic information, such as would be available from partial differential equations, with a strong focus on the quantification of uncertainty associated with data, process, and parameters. Here, we give a brief review of several paradigms and focus our attention on Bayesian implementations given they naturally accommodate uncertainty quantification. We then show that it is straight-forward to include the Bayesian PINN (B-PINN) within the Bayesian hierarchical model (BHM) framework that has long been considered for modeling dynamic spatio-temporal processes. Such a BHM-PINN is illustrated via a simulation study in which a latent nonlinear Burgers’ equation PDE governs the dynamics of Poisson distributed spatio-temporal data. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Bayesian

Integrable higher-spin deformations of sigma models from auxiliary fields

We construct a new infinite family of integrable deformations of the principal chiral model (PCM) parametrized by an interaction function of several variables, which extends the formalism of [C. Ferko and L. Smith, An infinite family of integrable sigma models using auxiliary fields, .] and includes deformations of the PCM by functions of both the stress tensor and higher-spin conserved currents. We show in detail that every model in this class admits a Lax representation for its equations of motion, and that the Poisson bracket of the Lax connection takes the Maillet form, establishing the existence of an infinite set of Poisson-commuting conserved charges. We argue that the non-Abelian T-dual of any model in this family is classically integrable, and that T-duality “commutes” with a general deformation in this class, in a sense which we make precise. Finally, we demonstrate that these higher-spin auxiliary field deformations can be extended to accommodate the addition of a Wess-Zumino term, and we exhibit the Lax connection in this case. Published by the American Physical Society 2025

Bielli, Daniele (ORCID:0009000640034768)

High-pressure elasticity and equation of state of the fluoroelastomer Viton® A-500

Viton® A is a semi-crystalline copolymer of polyvinylidene fluoride and hexafluoropropylene used in various engineering applications due to its mechanical properties and chemical inertness. In situ ultrasonic spectroscopy and x-ray radiography measurements were performed in a Paris–Edinburgh press to measure the pressure dependence of the transverse and longitudinal acoustic velocity of the fluoroelastomer A-500 from 2.7 to 5.7 GPa at 296 K. In addition, we performed high-pressure Brillouin scattering measurements to obtain acoustic velocities from ambient pressure to 5.7 GPa to supplement the ultrasonic measurements, especially at low pressures. The acoustic velocities were then used to calculate a pressure–volume (P–V) equation of state, the bulk and shear moduli, and the Poisson's ratio. These quantities are compared with the reported pressure-dependent properties of related polymers over this range of pressures.

Acoustical properties

Sound Velocities in Vanadium Reveal Complex Elastic Behavior at High Pressures

Compressional (VP) and shear (VS) wave velocities of polycrystalline vanadium were measured simultaneously up to 11.5 GPa at room temperature using ultrasonic interferometry in a multi-anvil press. Complex softening behavior in VS and resulting shear moduli are discovered, possibly revealing a precursor to the reported phase transition within 30–60 GPa. The current data enables a comprehensive assessment of the elastic and mechanical properties of vanadium at high pressures, including bulk and shear moduli, Young’s modulus, Poisson’s ratio, and Pugh’s ratio. Through fitting to the 3rd-order finite strain equations, the elastic moduli and their pressure derivatives were determined to be K S0 = 151 (2) GPa, G 0 = 46.9 (8) GPa, K$^{’}_{S0}$ = 3.47 (5), and G$^{’}_{0}$ = 0.62 (1). These experimental results allow us to compare with and benchmark the existing Steinberg–Guinan models for extrapolations to extreme pressure and temperature conditions.

36 MATERIALS SCIENCE

Analysis of the weighted shifted boundary method for the Poisson and Stokes problems

The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. Accuracy is maintained by properly shifting the location and values of the boundary conditions. This avoids integration over cut cells and the associated implementation issues. Recently, the Weighted SBM (WSBM) was proposed for the Navier-Stokes equations with free surfaces and the Stokes flow with moving boundaries. The attribute “weighted” in the name WSBM stems from the fact that its variational form is weighted with the elemental volume fraction of active fluid. The motivation for the development of the WSBM was the preservation of the volume of active fluid to a higher degree of accuracy, which in turn resulted in improved stability and robustness characteristics in moving-boundary, time-dependent simulations. In this article, we present the numerical analysis of the WSBM formulations for the Poisson and Stokes problems. We give mathematical conditions under which the bilinear forms defining the discrete variational formulations are uniformly coercive (Poisson problem) or inf-sup stable (Stokes problem). By these results, stability and optimal convergence is proven in the natural norm; L2-error estimates can also be derived.

Approximate domain boundaries

Non-linear dynamics of jet quenching

We develop a comprehensive analytic framework for jet quenching in QCD media, based on a medium-induced parton cascade sourced by collinear virtual splittings. We show that the energy flow out of the jet cone, driven by turbulent gluon cascades, is governed by a non-linear rate equation that resums gluon splittings at arbitrary angles and is enhanced by the medium length, L. The solution of this equation sets the initial condition for a non-linear DGLAP-like evolution equation, which describes the collinear early vacuum cascade resolved by the medium at angles exceeding the medium resolution angle, θ c . For asymptotic jet energies, the medium-induced cascade displays an exponential behavior that generalizes the Poisson-like distribution of parton energy loss. This formulation enables the resummation of leading contributions in α s ln(1/R), and α s ln(R/θ c ), and powers of α s L. We briefly explore the limit of strong quenching, where analytic treatments are feasible, offering insights into the impact of parton cascades on jet quenching. These results provide guidance for future numerical simulations and analytical investigations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Additional considerations in analytical solution for time-dependent heat conduction in a three-dimensional multilayer sphere

This work presents an analytical method to solve the heat conduction equation in three dimensions for problems consisting of multilayer concentric spheres. The method can be used to treat time-varying heat conduction problems where the heat source that drives the transient is time-invariant. Equally applicable to all Poisson-type problems with concentric spherical geometry, the method consists of representing the solution as a summation of weighted eigenfunctions. The weights for each eigenfunction are computed algebraically. Previous work has already established the core constituents of the methodology. The current work augments the existing methods by including consideration of nonzero interface resistance between layers and explicit discussion on the boundary condition homogenization required to treat inhomogeneous problems. Also, two demonstration problems are presented. One demonstration problem is based on the method of manufactured solutions and therefore allows for comparison with exact expressions for the solution temperature distribution. The second, more complex, demonstration problem relies on the finite element method for comparisons. The expected convergence behavior is observed for both demonstration problems.

97 - MATHEMATICS AND COMPUTING

Algebra of invariants for the Vlasov–Maxwell system

The algebra of invariants for both the relativistic and nonrelativistic multispecies Vlasov–Maxwell system is examined, including the case with a fixed ion background. Invariants and their associated fluxes are obtained directly from the Vlasov–Maxwell system. The invariants are shown to Poisson commute with the Hamiltonian and the rest of the Poisson bracket algebra of invariants is identified. Special attention is given to the role played by the monopole condition, ∇ · B.

Fundamental invariants

Numerical simulations of three-dimensional ion crystal dynamics in a Penning trap using the fast multipole method

We simulate the dynamics, including laser cooling, of three-dimensional (3-D) ion crystals confined in a Penning trap using a newly developed molecular dynamics-like code. The numerical integration of the ions’ equations of motion is accelerated using the fast multipole method to calculate the Coulomb interaction between ions, which allows us to efficiently study large ion crystals with thousands of ions. In particular, we show that the simulation time scales linearly with ion number, rather than with the square of the ion number. By treating the ions’ absorption of photons as a Poisson process, we simulate individual photon scattering events to study laser cooling of 3-D ellipsoidal ion crystals. Initial simulations suggest that these crystals can be efficiently cooled to ultracold temperatures, aided by the mixing of the easily cooled axial motional modes with the low frequency planar modes. In our simulations of a spherical crystal of 1000 ions, the planar kinetic energy is cooled to several millikelvin in a few milliseconds while the axial kinetic energy and total potential energy are cooled even further. This suggests that 3-D ion crystals could be well suited as platforms for future quantum science experiments.

Zaris, John (ORCID:0009000196476323)

Randomized Adiabatic Quantum Linear Solver Algorithm with Optimal Complexity Scaling and Detailed Running Costs

Solving linear systems of equations is a fundamental problem with a wide variety of applications across many fields of science, and there is increasing effort to develop quantum linear solver algorithms. Subaşı et al. [Phys. Rev. Lett. 122, 060504 (2019)] proposed a randomized algorithm inspired by adiabatic quantum computing, based on a sequence of random Hamiltonian simulation steps, with suboptimal scaling in the condition number 𝜅 of the linear system and the target error 𝜖. Here we go beyond these results in several ways. Firstly, using filtering [Lin and Tong, Quantum 4, 361 (2020)] and Poissonization techniques [Cunningham and Roland, ArXiv:2406.03972 (2024)], the algorithm complexity is improved to the optimal scaling 𝑂⁡(𝜅⁢log (1/𝜖))—an exponential improvement in 𝜖, and a shaving of a log 𝜅 scaling factor in 𝜅. Secondly, the algorithm is further modified to achieve constant factor improvements, which are vital as we progress towards hardware implementations on fault-tolerant devices. We introduce a cheaper randomized walk operator method replacing Hamiltonian simulation—which also removes the need for potentially challenging classical precomputations; randomized routines are sampled over optimized random variables; circuit constructions are improved. We obtain a closed formula rigorously upper bounding the expected number of times one needs to apply a block-encoding of the linear system matrix to output a quantum state encoding the solution to the linear system. The upper bound is 837⁢𝜅 at 𝜖 = 10 −10 for Hermitian matrices.

97 MATHEMATICS AND COMPUTING

Thermodynamically consistent Cahn–Hilliard–Navier–Stokes equations using the metriplectic dynamics formalism

Cahn–Hilliard–Navier–Stokes (CHNS) systems describe flows with two-phases, e.g., a liquid with bubbles. Obtaining constitutive relations for general dissipative processes for such systems, which are thermodynamically consistent, can be a challenge. We show how the metriplectic 4-bracket formalism (Morrison and Updike, 2024) achieves this in a straightforward, in fact algorithmic, manner. First, from the noncanonical Hamiltonian formulation for the ideal part of a CHNS system we obtain an appropriate Casimir to serve as the entropy in the metriplectic formalism that describes the dissipation (e.g. viscosity, heat conductivity and diffusion effects). General thermodynamics with the concentration variable and its thermodynamics conjugate, the chemical potential, are included. Having expressions for the Hamiltonian (energy), entropy, and Poisson bracket, we describe a procedure for obtaining a metriplectic 4-bracket that describes thermodynamically consistent dissipative effects. The 4-bracket formalism leads naturally to a general CHNS system that allows for anisotropic surface energy effects. Furthermore, this general CHNS system reduces to cases in the literature, to which we can compare.

Cahn–Hilliard

Elastic constants in monocrystalline tungsten under quasi-hydrostatic pressures to 11.3 GPa

Compressional (P) and shear (S) wave velocities of tungsten single crystals along the [100] and [110] directions were measured using ultrasonic interferometry at room temperature up to 11.3 GPa. Least-squares fitting of $V$$^{[100]}_{P}$, $V$$^{[100]}_{S}$, $V$$^{[110]}_{P}$, and pressure to finite strain (FS) equations yields the elastic constants: C 11 = 523.5(5) GPa, C 12 = 205.1(32) GPa, and C 44 = 160.8(4) GPa, along with their respective pressure derivatives: $C$$^{′}_{11}$ = 6.20(2), $C$$^{′}_{12}$ = 3.35(1), and $C$$^{′}_{44}$ = 1.65(6). Using the Voigt–Reuss–Hill approximation, the elastic moduli were derived as K S0 = 311.2(22) GPa and G 0 = 160.2(7)GPa, along with their respective pressure derivatives: $K$$^{′}_{S0}$ = 4.30(4) and $G$$^{′}_{0}$ = 1.56(1). The Debye temperature of tungsten was determined to be 380.7(8) K, showing good agreement with previous calorimetric measurements. The elastic anisotropy increases slightly from 1.01(1) at ambient pressure to 1.03(1) at 11.3 GPa, suggesting that tungsten remains nearly isotropic under compression. Poisson's ratio slightly increased from 0.281(3) to 0.288(3) with pressure. Additionally, Pugh's ratio decreased from 0.512(4) to 0.494(4), while Pettifor's ratio increased from 0.148(10) to 0.175(10) as pressure reached 11.3 GPa. These results suggest that tungsten is weakly ductile compared to the critical thresholds for ductile behavior (i.e., Pugh's ratio <0.6 and Pettifor's ratio >0, indicating ductile behavior), but that its ductility increases marginally under pressure.

Wang, Ran [Stony Brook University, NY (United Stat