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At least 37 records · Page 2

Sound propagation in realistic interactive 3D scenes with parameterized sources using deep neural operators

We address the challenge of acoustic simulations in three-dimensional (3D) virtual rooms with parametric source positions, which have applications in virtual/augmented reality, game audio, and spatial computing. The wave equation can fully describe wave phenomena such as diffraction and interference. However, conventional numerical discretization methods are computationally expensive when simulating hundreds of source and receiver positions, making simulations with parametric source positions impractical. To overcome this limitation, we propose using deep operator networks to approximate linear wave-equation operators. This enables the rapid prediction of sound propagation in realistic 3D acoustic scenes with parametric source positions, achieving millisecond-scale computations. By learning a compact surrogate model, we avoid the offline calculation and storage of impulse responses for all relevant source/listener pairs. Our experiments, including various complex scene geometries, show good agreement with reference solutions, with root mean squared errors ranging from 0.02 to 0.10 Pa. Notably, our method signifies a paradigm shift as—to our knowledge—no prior machine learning approach has achieved precise predictions of complete wave fields within realistic domains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Optimal Transfer Operators in Algebraic Two-Level Methods for Nonsymmetric and Indefinite Problems

Consider an algebraic two-level method applied to the 𝑛-dimensional linear system 𝐴⁢𝒙 = 𝒃 using fine-space preconditioner (i.e., “relaxation” or “smoother”) 𝑀, with 𝑀 ≈ 𝐴, restriction and interpolation 𝑅 and 𝑃, and algebraic coarse-space operator 𝐴 𝑐 : = 𝑅 ∗ ⁢𝐴⁢𝑃. Then, what are the best possible transfer operators 𝑅 and 𝑃 of a given dimension 𝑛 𝑐 < 𝑛? Brannick et al. [12] showed that when 𝐴 and 𝑀 are Hermitian positive definite (HPD), the optimal interpolation is such that its range contains the 𝑛 𝑐 smallest generalized eigenvectors of the matrix pencil (𝐴, 𝑀). Recently, in Ali et al. [5] we generalized this framework to the non-HPD setting, by considering both right (interpolation) and left (restriction) generalized eigenvectors of (𝐴, 𝑀) and defining corresponding nonsymmetric transfer operators {𝑅#, 𝑃#}. Tight convergence bounds for {𝑅#, 𝑃#} are derived in spectral radius, as well as a proof of pseudo-optimality. Note, {𝑅#, 𝑃#} are typically complex valued, which is not practical for real-valued problems. Here, in this work, we build on [5], first characterizing all inner products in which the coarse-space correction defined by {𝑅#, 𝑃#} is orthogonal. We then develop tight two-level convergence bounds in these norms, and prove that the underlying transfer operators {𝑅#, 𝑃#} are genuinely optimal. As a special case, our theory both recovers and extends the HPD results from [12]. Finally, we show how to construct optimal, real-valued transfer operators in the case of that 𝐴 and 𝑀 are real valued, but are not HPD. Numerical examples arising from a discretized advection-reaction equation, wave-equation, and Stokes equations are used to verify and illustrate the theory.

97 MATHEMATICS AND COMPUTING↗

Full wave modeling of radio-frequency beams in tokamaks in the electron cyclotron frequency range

Simulation of full wave, without paraxial approximation, high-resolution solution of wave equations in frequency domain in the electron cyclotron resonance (ECR) frequency range for realistic Tokamak plasma parameters became possible by using recently formulated hybrid iterative algorithm [Svidzinski et al., Phys. Plasmas 25, 082509 (2018)] for numerically solving discretized wave equations. This approach combines time evolution and iterative relaxation techniques into iteration cycles. This algorithm is implemented in 2D code FullWave, solving wave equations in Tokamaks in cold and hot plasma models, and it has been tested in 3D full wave iterative RF beams simulation tool, which is presently being developed to model 3D ECRH RF beams in fusion devices using dynamic grid adaptation. The results of 2D full wave modeling, assuming specified toroidal mode number, of ECRH RF beams in DIII-D plasma, performed in the cold and hot plasma models for outboard and top launch scenarios using FullWave are presented. Nonlocal hot plasma response model, based on accurate numerical solution of linearized Vlasov equation, is used to model beam propagation and absorption in the 2nd electron cyclotron harmonic region. Demonstration of capability of the hybrid iterative algorithm to model ECRH RF beams in 3D is made by simulating a substantial part of realistic beam in DIII-D, launched from outboard side of the machine. All relevant physics of RF beam propagation, most of which is not captured in paraxial approximation, such as beam's divergence, interference between the X and O modes in the beam, X-O mode conversion, beam splitting into the X and O mode beams, transformation of beam's cross section, and absorption at the 2nd electron cyclotron harmonic, is captured in the simulations. A numerical technique to find an optimal beam polarization at the launcher to launch a nearly pure X or O mode beam in plasma is developed and tested.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part I: Model Formulation

Here, this paper formulates a new particle-in-cell method for the Vlasov–Maxwell system. Under the Lorenz gauge condition, Maxwell’s equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The use of potentials for the fields motivates the adoption of a Hamiltonian formulation for particles that employs the generalized (conjugate) momentum. A notable advantage offered by the Hamiltonian formulation is the elimination of time derivatives in the Lorenz gauge formulation that are required by the standard Newton–Lorentz treatment of the particles. This allows the fields to retain the full time-accuracy guaranteed by the field solver. The resulting updates for particles require only knowledge of the fields and their spatial derivatives. An analytical method for constructing these spatial derivatives is presented that exploits the underlying integral solution used in the field solver for the wave equations. Moreover, these derivatives are demonstrated to converge at the same rate as the fields in both time and space. The Method of Lines Transpose field solver we consider in this work is globally first-order accurate in time and high-order accurate in space (e.g., fourth- and fifth-order) and belongs to a larger class of methods which are unconditionally stable, can address geometry, and leverage $\mathcal {O}(N)$ fast summation methods for efficiency. We demonstrate the method on several well-established benchmark problems on bounded domains, including a plasma sheath as well as a relativistic particle beam. The efficacy of the proposed formulation is established by comparing with a second-order accurate finite-difference time-domain method that employs a leapfrog time advance for particles and a charge conserving map suitable for bounded domains. The new method shows mesh-independent numerical heating properties even in cases where the plasma Debye length is smaller than the grid spacing. This is an important feature of the new method for problems defined on bounded domains, because it permits the use of coarser grids in space in the representation of the fields. Such a capability has significant implications for the simulation of plasmas in bounded domains with complex geometry, where the ratio between the largest and smallest cells can vary significantly. The use of high-order spatial approximations in the new method also means that fewer grid points are required in order to achieve a fixed accuracy. Our results also suggest that the new method can be used with fewer simulation particles per cell compared to the benchmark explicit method, which permits further computational savings.

97 MATHEMATICS AND COMPUTING↗

Quasi-periodic travelling gravity–capillary waves

We present a numerical study of spatially quasi-periodic travelling waves on the surface of an ideal fluid of infinite depth. This is a generalization of the classic Wilton ripple problem to the case when the ratio of wavenumbers satisfying the dispersion relation is irrational. We propose a conformal mapping formulation of the water wave equations that employs a quasi-periodic variant of the Hilbert transform to compute the normal velocity of the fluid from its velocity potential on the free surface. We develop a Fourier pseudo-spectral discretization of the travelling water wave equations in which one-dimensional quasi-periodic functions are represented by two-dimensional periodic functions on the torus. This leads to an overdetermined nonlinear least-squares problem that we solve using a variant of the Levenberg–Marquardt method. We investigate various properties of quasi-periodic travelling waves, including Fourier resonances, time evolution in conformal space on the torus, asymmetric wave crests, capillary wave patterns that change from one gravity wave trough to the next without repeating and the dependence of wave speed and surface tension on the amplitude parameters that describe a two-parameter family of waves.

97 MATHEMATICS AND COMPUTING↗

Reducing Frequency Bias of Fourier Neural Operators in 3D Seismic Wavefield Simulations Through Multistage Training

The recent development of neural operator (NeurOp) learning for solutions to the elastic wave equation shows promising results and provides the basis for fast large-scale simulations for different seismological applications. In this article, we use the Fourier neural operator (FNO) model to directly solve the 3D Helmholtz wave equation for fast seismic ground-motion simulations on different frequencies and show the frequency bias of the FNO model, that is, it learns the lower frequencies better comparing to the higher frequencies. To reduce the frequency bias, we adopt the multistage FNO training, that is, after training a stage 1 FNO model for estimating the ground motion, we use a second FNO model as the stage 2 to learn from the residual, which greatly reduced the errors on the higher frequencies. By adopting this multistage training, the FNO models show reduced biases on higher frequencies, which enhanced the overall results of the ground-motion simulations. Thus the multistage training FNO improves the accuracy and realism of the ground-motion simulations.

earthquakes↗

Local enhancement in transient absorption spectroscopy by gating the resonance in the time domain

The concept of resonant perfect absorption, enabled by the combined action of pulse propagation and an auxiliary gate pulse, was recently proposed and demonstrated in a group of two-level systems [Y. He , ]. Here we exploit this method in a more realistic scenario by solving the coupled time-dependent Schrödinger equation and the Maxwell wave equation in helium. Through emptying the population of the 1 s 2 p excited state after its excitation, we explore the evolution of the spectral profile with time delay and propagation distance and link the observations to the controlled interference between the original field and the gated new field. We find that resonant absorption for higher-lying states can also be strongly enhanced, in spite of the congestion of multiple resonances and the presence of complex laser-induced couplings. Our results show that interferometric control of absorption using intense laser fields can be applied selectively in both the temporal and spatial domains. Published by the American Physical Society 2024

He, Yu (ORCID:0000000152120176)↗

Resonant propagation of extreme-ultraviolet pulses through strongly driven high-density media

We show that by combining strong-field dressing and resonant propagation of XUV pulses, the transition of absorption lines from their natural Lorentzian profiles through Fano and complex multipeak shapes all the way back to broadened near-Lorentzian profiles can be achieved, in the limit of optically thick samples. The final stage of this spectral modification can be understood in terms of a significant temporal stretching and delay of the resonant XUV pulse as it propagates through the dense gas, which alters the ultrafast absorption that is modified by the time-synchronized few-femtosecond laser pulse. We first demonstrate this concept in numerical calculations, both using a model system and through a fully coupled solution of the time-dependent Schrödinger equation and the Maxwell wave equation. The applicability and generality of the underlying mechanism is then illustrated in proof-of-principle attosecond transient absorption measurements in a helium gas with a widely varying atomic density. These results provide insights into the interaction of ultrashort laser pulses with dense media and its coherent control. Published by the American Physical Society 2025

He, Yu (ORCID:0000000152120176)↗

DPFEHM: a differentiable subsurface physics simulator

The Earth’s subsurface is a key resource that provides energy via fossil fuels and geothermal sources, stores drinking water, and is used in the fight against climate change via carbon sequestration. Simulating the physical processes that occur in the Earth’s subsurface with computers enables better use of this resource. DPFEHM is a Julia package that includes computer models with a focus on the Earth’s subsurface, especially fluid flow, which is critical for the aforementioned applications. DPFEHM is able to solve the groundwater flow equations (single phase flow), Richards equation (air/water), the advection-dispersion equation, and the 2d wave equation. One of the key features of DPFEHM is that it supports automatic differentiation, so it can be integrated into machine learning workflows using frameworks such as Flux or PyTorch. The automatic differentiation capabilities give it the same performance as adjoint methods.

54 ENVIRONMENTAL SCIENCES↗

Exponential Runge-Kutta Parareal for non-diffusive equations

Parareal is a well-known parallel-in-time algorithm that combines a coarse and fine propagator within a parallel iteration. It allows for large-scale parallelism that leads to significantly reduced computational time compared to serial time-stepping methods. However, like many parallel-in-time methods it can fail to converge when applied to non-diffusive equations such as hyperbolic systems or dispersive nonlinear wave equations. Here, this paper explores the use of exponential integrators within the Parareal iteration. Exponential integrators are particularly interesting candidates for Parareal because of their ability to resolve fast-moving waves, even at the large stepsizes used by coarse propagators. This work begins with an introduction to exponential Parareal integrators followed by several motivating numerical experiments involving the nonlinear Schrödinger equation. These experiments are then analyzed using linear analysis that approximates the stability and convergence properties of the exponential Parareal iteration on nonlinear problems. The paper concludes with two additional numerical experiments involving the dispersive Kadomtsev-Petviashvili equation and the hyperbolic Vlasov-Poisson equation. These experiments demonstrate that exponential Parareal methods offer improved time-to-solution compared to serial exponential integrators when solving certain non-diffusive equations.

97 MATHEMATICS AND COMPUTING↗

Elastic Wave Propagation in Curvilinear Coordinates with Mesh Refinement Interfaces by a Fourth Order Finite Difference Method

In this work, we develop a fourth order accurate finite difference method for the three dimensional elastic wave equation in isotropic media with the piecewise smooth material property. In our model, the material property can be discontinuous at curved interfaces. The governing equations are discretized in second order form on curvilinear meshes by using a fourth order finite difference operator satisfying a summation-by-parts property. The method is energy stable and high order accurate. The highlight is that mesh sizes can be chosen according to the velocity structure of the material so that computational efficiency is improved. At the mesh refinement interfaces with hanging nodes, physical interface conditions are imposed by using ghost points and interpolation. With a fourth order predictor-corrector time integrator, the fully discrete scheme is energy conserving. Numerical experiments are presented to verify the fourth order convergence rate and the energy conserving property.

58 GEOSCIENCES↗

Validation of finite element analysis strategy to investigate acoustic levitation in a two-axis acoustic levitator

A two-axis acoustic levitator can be used to generate a standing pressure wave capable of levitating solid and liquid particles at appropriate input conditions. This work proposes a simulation framework to investigate the two-axis levitation particle stability using a commercial, computational fluid dynamics software based on the harmonic solution to the acoustic wave equation. The simulation produced predictions of the standing wave that include a strong "+" shaped pattern of nodes and anti-nodes that are aligned with the levitator axes. To verify the simulation, a levitator was built and used to generate the standing wave. The field was probed with a microphone and a motorized-scanning system. After scaling the simulated pressure to the measured pressure, the magnitudes of the sound pressure level at corresponding high-pressure locations were different by no more than 5%. This is the first time a measurement of a two-axis levitator standing pressure wave has been presented and shown to verify simulations. Furthermore, as an additional verification, the authors consulted high speed camera measurements of a reference-levitator transducer, which was found to have a maximum peak-to-peak displacement of 50 +/- 5 mu m. The reference-levitator is known to levitate water at 160 dB. The system for this work was simulated to match the operation of the reference-levitator so that it produced sound pressure levels of 160 dB. This pressure was achieved when the transducer maximum peak-to-peak displacement was 50.8 mu m. The agreement between the two levitators' displacements provides good justification that the modeling approach presented here produces reliable results.

2 axis levitator↗

Separability in consistent truncations

The separability of the Hamilton-Jacobi equation has a well-known connection to the existence of Killing vectors and rank-two Killing tensors. This paper combines this connection with the detailed knowledge of the compactification metrics of consistent truncations on spheres. The fact that both the inverse metric of such compactifications, as well as the rank-two Killing tensors can be written in terms of bilinears of Killing vectors on the underlying “round metric,” enables us to perform a detailed analyses of the separability of the Hamilton-Jacobi equation for consistent truncations. We introduce the idea of a separating isometry and show that when a consistent truncation, without reduction gauge vectors, has such an isometry, then the Hamilton-Jacobi equation is always separable. When gauge vectors are present, the gauge group is required to be an abelian subgroup of the separating isometry to not impede separability. We classify the separating isometries for consistent truncations on spheres, S n , for n = 2, …, 7, and exhibit all the corresponding Killing tensors. These results may be of practical use in both identifying when supergravity solutions belong to consistent truncations and generating separable solutions amenable to scalar probe calculations. Finally, while our primary focus is the Hamilton-Jacobi equation, we also make some remarks about separability of the wave equation.

79 ASTRONOMY AND ASTROPHYSICS↗

Shear wave generation by mode conversion in picosecond ultrasonics: Impact of grain orientation and material properties

Abstract Picosecond ultrasonics has seen wide application in the investigation of interfaces in semiconductors and 3D imaging in biological systems. Shear ultrasonic waves are important for elastic constant and grain orientation measurement in ceramic materials. In this study, we investigate the impact of grain orientation and material's elastic properties on the generation efficiency of shear waves by mode conversion at a transducer thin film/substrate interface. The solution of acoustic wave equations suggests that crystal grain orientation has a strong impact on the generated shear wave amplitude. This dependence is found to be closely related to the magnitude of longitudinal component of wave displacements. The applicability of analytical model is validated by the experimental results from time‐domain Brillouin scattering. Moreover, material properties determine acoustic wave amplitudes based on the acoustic mismatch model and, particularly, large elastic anisotropy defined by Zener ratio favors strong shear waves. In the light of this analysis, several recommendations on suitable grain orientations and film materials are made to facilitate shear wave detection.

Wang, Yuzhou↗

Near-global summer circulation response to the spring surface temperature anomaly in Tibetan Plateau –– the GEWEX/LS4P first phase experiment

Subseasonal to seasonal (S2S) prediction of droughts and floods is one of the major challenges of weather and climate prediction. Recent studies suggest that the springtime land surface temperature/subsurface temperature (LST/SUBT) over the Tibetan Plateau (TP) can be a new source of S2S predictability. The project “Impact of Initialized Land Surface Temperature and Snowpack on Subseasonal to Seasonal Prediction (LS4P)” was initiated to study the impact of springtime LST/SUBT anomalies over high mountain areas on summertime precipitation predictions. The present work explores the simulated global scale response of the atmospheric circulation to the springtime TP land surface cooling by 16 current state-of-the-art Earth System Models (ESMs) participating in the LS4P Phase I (LS4P-I) experiment. The LS4P-I results show, for the first time, that springtime TP surface anomalies can modulate a persistent quasi-barotropic Tibetan Plateau-Rocky Mountain Circumglobal (TRC) wave train from the TP via the northeast Asia and Bering Strait to the western part of the North America, along with the springtime westerly jet from TP across the whole North Pacific basin. The TRC wave train modulated by the TP thermal anomaly play a critical role on the early summer surface air temperature and precipitation anomalies in the regions along the wave train, especially over the northwest North America and the southern Great Plains. The participant models that fail in capturing the TRC wave train greatly under-predict climate anomalies in reference to observations and the successful models. These results suggest that the TP LST/SUBT anomaly via the TRC wave train is the first order source of the S2S variability in the regions mentioned. Furthermore, the TP surface temperature anomaly can influence the Southern Hemispheric circulation by generating cross-equator wave trains. However, the simulated propagation pathways from the TP into the Southern Hemisphere show large inter-model differences. More dynamical understanding of the TRC wave train as well as its cross-equator propagation into the Southern Hemisphere will be explored in the newly launched LS4P phase II experiment.

54 ENVIRONMENTAL SCIENCES↗

3D Seismic Anatomy of a Watershed Reveals Climate–Topography Coupling That Drives Water Flowpaths and Bedrock Weathering

To investigate how bedrock transforms to soil, we mapped the topography of the interface demarcating onset of weathering under an east-west trending shale watershed in the Valley and Ridge province in the U.S.A. Using wave-equation travel-time tomography from a seismic array of >4000 geophones, we obtained a 3D P-wave velocity (Vp) model that resolves structures ~20 m below land surface (mbls). The depth of mobile soil and the onset of dissolution of chlorite roughly match Vp = 600 m/s and Vp = 2700 m/s, respectively. Chlorite dissolution initiates porosity growth in the shale matrix. Depth to the 2700 m/s contour is greater under the N- as compared to S-facing hillslopes and under sub-planar as compared to concave-up land surfaces. Broadly, the geometries of the ‘soil’ and ‘chlorite’ Vp contours are consistent with the calculated potential for shear fracture opening under weak regional compression. However, this calculated fracture potential does not consistently explain observations related to N- vs. S-facing aspect nor fracture density observed by borehole televiewer. Apparently, regional compression is only a secondary influence on Vp: the primary driver of P-wave slowing in the upper layers of this catchment is topographic control of reactive water flowpaths and their integrated effects on weathering. Here, the Vp result is best explained as the long-term integrated effect of groundwater flow-induced geochemical weathering of shale in response to climate-driven patterns of micro- and macro-topography.

54 ENVIRONMENTAL SCIENCES↗