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Results for “periodicity- preserving approximation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Approximation of nearly-periodic symplectic maps via structure-preserving neural networks

A continuous-time dynamical system with parameter ε is nearly-periodic if all its trajectories are periodic with nowhere-vanishing angular frequency as ε approaches 0. Nearly-periodic maps are discrete-time analogues of nearly-periodic systems, defined as parameter-dependent diffeomorphisms that limit to rotations along a circle action, and they admit formal U(1) symmetries to all orders when the limiting rotation is non-resonant. For Hamiltonian nearly-periodic maps on exact presymplectic manifolds, the formal U(1) symmetry gives rise to a discrete-time adiabatic invariant. In this paper, we construct a novel structure-preserving neural network to approximate nearly-periodic symplectic maps. This neural network architecture, which we call symplectic gyroceptron, ensures that the resulting surrogate map is nearly-periodic and symplectic, and that it gives rise to a discrete-time adiabatic invariant and a long-time stability. This new structure-preserving neural network provides a promising architecture for surrogate modeling of non-dissipative dynamical systems that automatically steps over short timescales without introducing spurious instabilities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Code Demonstration: Approximation of nearly-periodic symplectic maps via structure-preserving neural networks

In this notebook, we use the symplectic gyroceptron architecture from [Duruisseaux et al., 2022] to learn a surrogate map for the nearly-periodic symplectic flow map associated to a nearly-periodic Hamiltonian system composed of two nonlinearly coupled oscillators, where one of them oscillates significantly faster than the other: $\Big\lbrace$ $ {\dot{q}_1 = p_1 \hspace{5mm} \dot{p}_1 = -q_1 - \epsilon \partial_{q1}U(q_1 , q_2 )} \atop {\dot{q}_2 = \epsilon p_2 \hspace{4mm} \dot{p}_2 = -\epsilon q_2 - \epsilon \partial_{q2}U(q_1 , q_2 )}$. These equations of motion are the Hamilton's equations associated to the Hamiltonian $H_{\epsilon}(q_1,q_2,p_1,p_2)=\frac{1}{2}(q^2_1+p^2_1)+\frac{1}{2}\epsilon(q^2_2+p^2_2)+\epsilon$$U(q_1,q_2)$.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A Method for Dimensionally Adaptive Sparse Trigonometric Interpolation of Periodic Functions

We present a method for dimensionally adaptive sparse trigonometric interpolation of multidimensional periodic functions belonging to a smoothness class of finite order. This method targets applications where periodicity must be preserved and the precise anisotropy is not known a priori. To the authors' knowledge, this is the first instance of a dimensionally adaptive sparse interpolation algorithm that uses a trigonometric interpolation basis. The motivating application behind this work is the adaptive approximation of a multi-input model for a molecular potential energy surface (PES) where each input represents an angle of rotation. Our method is based on an anisotropic quasi-optimal estimate for the decay rate of the Fourier coefficients of the model; a least-squares fit to the coefficients of the interpolant is used to estimate the anisotropy. Thus, our adaptive approximation strategy begins with a coarse isotropic interpolant, which is gradually refined using the estimated anisotropic rates. The procedure takes several iterations where ever-more accurate interpolants are used to generate ever-improving anisotropy rates. We present several numerical examples of our algorithm where the adaptive procedure successfully recovers the theoretical “best” convergence rate, including an application to a periodic PES approximation. An open-source implementation of our algorithm resides in the Tasmanian UQ library developed at Oak Ridge National Laboratory.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Pulse: An Outlier Sensitive Downsampling Algorithm For Timeseries Data

Pulse is a downsampling algorithm for timeseries data. Frequently datasets become so large that visualization tools and web browsers cannot effectively render graphics due to memory constraints. Downsampling algorithms are commonly applied to minimize the quantity of data required to visualize important features or trends in the data, but some datasets are composed by distinct enough features and trends that most existing downsampling algorithms fail to preserve them. Pule was developed to downsample timeseries data for galvanostatic stack test data at the Idaho National Laboratory. These datasets were composed by approximately 4 million records, most of them being extremely uniform. However, during relatively brief time periods when the stack test changes state, for example when the test article is powered on, or a load is added, the data produce sparse asymptotes. No existing downsampling algorithm was capable of preserving the sparse asymptotes in electrolysis stack test data. Instead, we develop a downsampling algorithm that preserves important outliers in data, and otherwise aggressively downsamples uniform data. The algorithm has applications in other domains like seismology, in the measurement of earthquakes, or astronomy, in the measurement of quasars or transit photometry.

Woodruff, Nathan [Idaho National Laboratory (INL),↗
DOE OSTI2024

Coarse-graining Hamiltonian systems using WSINDy

Abstract Weak form equation learning and surrogate modeling has proven to be computationally efficient and robust to measurement noise in a wide range of applications including ODE, PDE, and SDE discovery, as well as in coarse-graining applications, such as homogenization and mean-field descriptions of interacting particle systems. In this work we extend this coarse-graining capability to the setting of Hamiltonian dynamics which possess approximate symmetries associated with timescale separation. A smooth $$\varepsilon$$ ε -dependent Hamiltonian vector field $$X_\varepsilon$$ X ε possesses an approximate symmetry if the limiting vector field $$X_0=\lim _{\varepsilon \rightarrow 0}X_\varepsilon$$ X 0 = lim ε → 0 X ε possesses an exact symmetry. Such approximate symmetries often lead to the existence of a Hamiltonian system of reduced dimension that may be used to efficiently capture the dynamics of the symmetry-invariant dependent variables. Deriving such reduced systems, or approximating them numerically, is an ongoing challenge. We demonstrate that WSINDy can successfully identify this reduced Hamiltonian system in the presence of large perturbations imparted in the $$\varepsilon >0$$ ε > 0 regime, while remaining robust to extrinsic noise. This is significant in part due to the nontrivial means by which such systems are derived analytically. WSINDy naturally preserves the Hamiltonian structure by restricting to a trial basis of Hamiltonian vector fields. The methodology is computationally efficient, often requiring only a single trajectory to learn the global reduced Hamiltonian, and avoiding forward solves in the learning process. In this way, we argue that weak-form equation learning is particularly well-suited for Hamiltonian coarse-graining. Using nearly-periodic Hamiltonian systems as a prototypical class of systems with approximate symmetries, we show that WSINDy robustly identifies the correct leading-order system, with dimension reduced by at least two, upon observation of the relevant degrees of freedom. While our main contribution is computational, we also provide a contribution to the literature on averaging theory by proving that first-order averaging at the level of vector fields preserves Hamiltonian structure in nearly-periodic Hamiltonian systems. This provides theoretical justification for our approach as WSINDy’s computations occur at the level of Hamiltonian vector fields. We illustrate the efficacy of our proposed method using physically relevant examples, including coupled oscillator dynamics, the Hénon–Heiles system for stellar motion within a galaxy, and the dynamics of charged particles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Physics informed deep neural network embedded in a chemical transport model for the Amazon rainforest

Secondary organic aerosols (SOA) are fine particles in the atmosphere, which interact with clouds, radiation and affect the Earth’s energy budget. SOA formation involves chemistry in gas phase, aqueous aerosols, and clouds. Simulating these chemical processes involve solving a stiff set of differential equations, which are computationally expensive steps for three-dimensional chemical transport models. Deep neural networks (DNNs) are universal function approximators that could be used to represent the complex nonlinear changes in aerosol physical and chemical processes; however, key challenges such as generalizability to extended time periods, preservation of mass balance, simulating sparse model outputs, and maintaining physical constraints have limited their use in atmospheric chemistry. Here, we develop an approach of using a physics-informed DNN that overcomes previous such challenges and demonstrates its applicability for the chemical formation processes of isoprene epoxydiol SOA (IEPOX-SOA) over the Amazon rainforest. The DNN is trained with data generated by simulating IEPOX-SOA over the entire atmospheric column, using the Weather Research and Forecasting Model coupled with Chemistry (WRF-Chem). The trained DNN is then embedded within WRF-Chem to replace the computationally expensive default solver of IEPOX-SOA formation. The trained DNN predictions generalizes well with the default model simulation of the IEPOX-SOA mass concentrations and its size distribution (20 size bins) over several days of simulations in both dry and wet seasons. The embedded DNN reduces the computational expense of WRF-Chem by a factor of 2. Our approach shows promise in terms of application to other computationally expensive chemistry solvers in climate models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

A Practical Framework for Simulating Time-Resolved Spectroscopy Based on a Real-Time Dyson Expansion

Time-resolved spectroscopy is a powerful tool for probing electron dynamics in molecules and solids, revealing transient phenomena on subfemtosecond time scales. The interpretation of experimental results is often enhanced by parallel numerical studies, which can provide insight and validation for experimental hypotheses. However, developing a theoretical framework for simulating time-resolved spectra remains a significant challenge. The most suitable approach involves the many-body nonequilibrium Green's function formalism, which accounts for crucial dynamical many-body correlations during time evolution. While these dynamical correlations are essential for observing emergent behavior in time-resolved spectra, they also render the formalism prohibitively expensive for large-scale simulations. Substantial effort has been devoted to reducing this computational cost─through approximations and numerical techniques─while preserving the key dynamical correlations. The ultimate goal is to enable first-principles simulations of time-dependent systems ranging from small molecules to large, periodic, multidimensional solids. Here, in this perspective, we outline key challenges in developing practical simulations for time-resolved spectroscopy, with a particular focus on Green's function methodologies. We highlight a recent advancement toward a scalable framework: the real-time Dyson expansion (RT-DE) [Phys. Rev. Lett. 2024, 133, 226902]. We introduce the theoretical foundation of RT-DE and discuss strategies for improving scalability, which have already enabled simulations of system sizes beyond the reach of previous fully dynamical approaches. We conclude with an outlook on future directions for extending RT-DE to first-principles studies of dynamically correlated, nonequilibrium systems.

Reeves, Cian C. [Univ. of California, Santa Barbar↗
DOE OSTI2026

Heterogeneous Multi-Domain Dataset Synthesis to Facilitate Privacy and Risk Assessments in Smart City IoT

The emergence of the Smart Cities paradigm and the rapid expansion and integration of Internet of Things (IoT) technologies within this context have created unprecedented opportunities for high-resolution behavioral analytics, urban optimization, and context-aware services. However, this same proliferation intensifies privacy risks, particularly those arising from cross-modal data linkage across heterogeneous sensing platforms. To address these challenges, this paper introduces a comprehensive, statistically grounded framework for generating synthetic, multimodal IoT datasets tailored to Smart City research. The framework produces behaviorally plausible synthetic data suitable for preliminary privacy risk assessment and as a benchmark for future re-identification studies, as well as for evaluating algorithms in mobility modeling, urban informatics, and privacy-enhancing technologies. As part of our approach, we formalize probabilistic methods for synthesizing three heterogeneous and operationally relevant data streams—cellular mobility traces, payment terminal transaction logs, and Smart Retail nutrition records—capturing the behaviors of a large number of synthetically generated urban residents over a 12-week period. The framework integrates spatially explicit merchant selection using K-Dimensional (KD)-tree nearest-neighbor algorithms, temporally correlated anchor-based mobility simulation reflective of daily urban rhythms, and dietary-constraint filtering to preserve ecological validity in consumption patterns. In total, the system generates approximately 116 million mobility pings, 5.4 million transactions, and 1.9 million itemized purchases, yielding a reproducible benchmark for evaluating multimodal analytics, privacy-preserving computation, and secure IoT data-sharing protocols. To show the validity of this dataset, the underlying distributions of these residents were successfully validated against reported distributions in published research. We present preliminary uniqueness and cross-modal linkage indicators; comprehensive re-identification benchmarking against specific attack algorithms is planned as future work. This framework can be easily adapted to various scenarios of interest in Smart Cities and other IoT applications. By aligning methodological rigor with the operational needs of Smart City ecosystems, this work fills critical gaps in synthetic data generation for privacy-sensitive domains, including intelligent transportation systems, urban health informatics, and next-generation digital commerce infrastructures.

IoT↗
DOE OSTI2021

Fourier Neural Networks as Function Approximators and Differential Equation Solvers

We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a straightforward architecture with a single hidden layer. The simplicity of this network architecture facilitates the integration with any other higher-complexity networks, at a data pre- or postprocessing stage. We validate this FNN on naturally periodic smooth functions and on piecewise continuous periodic functions. We showcase the use of this FNN for modeling or solving partial differential equations with periodic boundary conditions. The main advantages of the current approach are the validity of the solution outside the training region, interpretability of the trained model, and simplicity of use.

Fourier decomposition↗
DOE OSTI2022

Historic Architectural Resource Survey of the Dosimetry Applications Research (DOSAR) Facility in the 7700 Area of the Oak Ridge National Laboratory

In May 2022, Cultural Resource Analysts, Inc., completed a historic architectural resource survey of buildings associated with the Dosimetry Applications Research Facility at the Oak Ridge National Laboratory. The laboratory is one of three Department of Energy facilities located on the Oak Ridge Reservation in Roane and Anderson Counties, Tennessee. The Dosimetry Applications Research Facility is located approximately 2 mi southeast of the main Oak Ridge National Laboratory campus. The survey included Buildings 7709, 7710, and 7712, which date to the 1960s. An additional DOSAR building (Building 7735) dates to the late 1980s and was not surveyed since it is outside the period of significance. The survey was conducted at the request of UT-Battelle, LLC, on behalf of the Department of Energy. As stipulated by the National Historic Preservation Act of 1966, as amended, the Department of Energy is required to identify any properties under its jurisdiction that are included in or eligible for inclusion in the National Register of Historic Places. In order to identify historic properties at the Oak Ridge National Laboratory, in 2017–2018 Cultural Resource Analysts, Inc., conducted a survey of the main campus as well as outlying facilities, publishing the findings in a 2018 report entitled Oak Ridge National Laboratory Historic Architectural Resource Survey. At the time of the 2017–2018 survey, buildings associated with the Dosimetry Applications Research Facility were not accessible for security reasons and the current report serves as an addendum to the 2018 report. In addition, the current survey incorporates information included in a documentation report on Building 7709 completed in 2019. The properties included in the current survey were also evaluated for their collective potential as a historic district. The identification of archaeological properties that are eligible for inclusion in the National Register of Historic Places is beyond the scope of this report. Cultural Resource Analysts, Inc., recommends that none of the buildings surveyed for the current report are individually eligible for listing in the National Register of Historic Places. However, the collective of buildings represents a facility that made notable contributions to the Oak Ridge National Laboratory’s scientific research endeavors from the 1960s to the 1980s, specifically in the field of Health Physics. The buildings and their associated features have also maintained their integrity of setting, materials, design, location, and association. Therefore, Cultural Resource Analysts, Inc., proposes the Dosimetry Applications Research Facility Historic District, which is recommended eligible for listing under Criterion A. The three buildings addressed in the current survey (Buildings 7709, 7710, and 7712) are recommended eligible as contributing resources of the historic district. The district boundary is scribed to incorporate the environs of these three facilities, as well as additional relevant features.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2022

Downscaled hyper-resolution (400 m) gridded datasets of daily precipitation and temperature (2008–2019) for the East–Taylor subbasin (western United States)

Abstract. High-resolution gridded datasets of meteorological variables are needed in order to resolve fine-scale hydrological gradients in complex mountainous terrain. Across the United States, the highest available spatial resolution of gridded datasets of daily meteorological records is approximately 800 m. This work presents gridded datasets of daily precipitation and mean temperature for the East–Taylor subbasin (in the western United States) covering a 12-year period (2008–2019) at a high spatial resolution (400 m). The datasets are generated using a downscaling framework that uses data-driven models to learn relationships between climate variables and topography. We observe that downscaled datasets of precipitation and mean temperature exhibit smoother spatial gradients (while preserving the spatial variability) when compared to their coarser counterparts. Additionally, we also observe that when downscaled datasets are upscaled to the original resolution (800 m), the mean residual error is almost zero, ensuring no bias when compared with the original data. Furthermore, the downscaled datasets are observed to be linearly related to elevation, which is consistent with the methodology underlying the original 800 m product. Finally, we validate the spatial patterns exhibited by downscaled datasets via an example use case that models lidar-derived estimates of snowpack. The presented dataset constitutes a valuable resource to resolve fine-scale hydrological gradients in the mountainous terrain of the East–Taylor subbasin, which is an important study area in the context of water security for the southwestern United States and Mexico. The dataset is publicly available at https://doi.org/10.15485/1822259 (Mital et al., 2021).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Vibrational Spectroscopy of Hexahalo Complexes

Halogenated inorganic complexes A x [MHal y ] (A = alkali metal or alkaline earth, M = transition or main group metal, x = 1–3, and y = 2–9) are an archetypal class of compounds that provide entry points to large areas of inorganic and physical chemistry. All of the hexahalo complexes adopt an octahedral, O h , symmetry (or nearly so). Consequently, one of the bending modes is forbidden in both the infrared and Raman spectra. In the solid state, many of the complexes crystallize in the cubic space group Fm3̅m, which preserves the octahedral symmetry. Even for those that are not cubic, the octahedral symmetry of the [MHal 6 ] n- ion is largely retained and, to a good approximation, so are the selection rules. In the present work, we show that by using the additional information provided by neutron vibrational spectroscopy, in combination with conventional optical spectroscopies, we can generate complete and unambiguous assignments for all the modes. Comparison of the experimental and calculated transition energies for the systems where periodic-density functional theory was possible (i.e., those for which the crystal structure is known) shows that the agreement is almost quantitative. We also provide a linear relationship that enables the prediction of the forbidden mode.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Big Hole Drilling Support for Nuclear Testing, 1985-1992: An Architectural Survey of the Area 1 Subdock, Nevada National Security Site, Nye County, Nevada

The U.S. Department of Energy, National Nuclear Security Administration Nevada Field Office (NNSA/NFO) planned to demolish two buildings at the Area 1 Subdock at the Nevada National Security Site (NNSS) in Nye County, Nevada, to meet environmental management mission requirements. A review was conducted under Title 54 United States Code (USC) § 306101 (commonly known as Section 106 of the National Historic Preservation Act) and its implementing regulations, 36 Code of Federal Regulations (CFR) Part 800. As a result, a Memorandum of Agreement (MOA) was developed to mitigate the effects of the building demolitions. Stipulation III.B of the MOA requires an architectural survey of the Area 1 Subdock. Prior to this survey, the Subdock had not been systematically recorded. Therefore, an area of approximately 33 hectares (81 acres) was surveyed for historic properties by Desert Research Institute personnel. This effort resulted in the identification, recording, and evaluation of the potential Area 1 Subdock Historic District (SHPO Resource No. D377), including the identification of its contributing components. This district is recommended as eligible for the National Register of Historic Places (NRHP) under Criteria A and C. It contains 14 primary resources which include individual buildings, structures, storage yards, and infrastructure. Of these resources, all except one are recommended as elements that contribute to the district during its period of significance corresponding to nuclear testing from 1985 through 1992. Four of the resources (B18847, B18848, S2772, S2773) are recommended as individually eligible for the NRHP.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Noise and error analysis and optimization in particle-based kinetic plasma simulations

In this paper we analyze the noise in macro-particle methods used in plasma physics and fluid dynamics, leading to approaches for minimizing the total error, focusing on electrostatic models in one dimension. We begin by describing kernel density estimation for continuous values of the spatial variable x, expressing the kernel in a form in which its shape and width are represented separately. The covariance matrix of the noise in the density is computed, first for uniform true density. The bandwidth of the covariance matrix C(x,y) is related to the width of the kernel. A feature that stands out is the presence of constant negative terms in the elements of the covariance matrix both on and off-diagonal. These negative correlations are related to the fact that the total number of particles is fixed at each time step; they also lead to the property ∫C(x,y)dy = 0. We investigate the effect of these negative correlations on the electric field computed by Gauss's law, finding that the noise in the electric field is related to a process called the Ornstein-Uhlenbeck bridge, leading to a covariance matrix of the electric field with variance significantly reduced relative to that of a Brownian process. For non-constant density, p(x), still with continuous x, we analyze the total error in the density estimation and discuss it in terms of bias-variance optimization (BVO). For some characteristic length l, determined by the density and its second derivative, and kernel width h, having too few particles within h leads to too much variance; for h that is large relative to l, there is too much smoothing of the density. The optimum between these two limits is found by BVO. For kernels of the same width, it is shown that this optimum (minimum) is weakly sensitive to the kernel shape. Next, we repeat the analysis for x discretized on a grid. In this case the charge deposition rule is determined by a particle shape. An important property to be respected in the discrete system is the exact preservation of total charge on the grid; this property is necessary to ensure that the electric field is equal at both ends, consistent with periodic boundary conditions. We find that if the particle shapes satisfy a partition of unity property, the particle charge deposited on the grid is conserved exactly. Further, if the particle shape is expressed as the convolution of a kernel with another kernel that satisfies the partition of unity, then the particle shape obeys the partition of unity. This property holds for kernels of arbitrary width, including widths that are not integer multiples of the grid spacing. Furthermore, we show results relaxing the approximations used to do BVO optimization analytically, by doing numerical computations of the total error as a function of the kernel width, on a grid in x. The comparison between numerical and analytical results shows good agreement over a range of particle shapes. We discuss the practical implications of our results, including the criteria for design and implementation of computationally efficient particle shapes that take advantage of the developed theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

The Architecture of Area 12 Camp - Nevada's Atomic Ghost Town. An Architectural Survey of Area 12 Camp, Nevada National Security Site, Nye County, Nevada

The U.S. Department of Energy, National Nuclear Security Administration Nevada Field Office (NNSA/NFO) plans to demolish 10 buildings and one structure in Area 12 Camp at the Nevada National Security Site (NNSS) in Nye County, Nevada, to meet current and future National Weapons Science, Global and Homeland Security Program, and Environmental Management mission requirements and to reduce dangers to site workers from some of these resources. These demolitions constitute an undertaking subject to review under Title 54 U.S.C. § 306108, commonly known as Section 106 of the National Historic Preservation Act, Title 54 U.S.C. § 300101, et seq., and its implementing regulations, 36 C.F.R. Part 800. These resources were recorded and evaluated as individually ineligible for the National Register of Historic Places (National Register or NRHP) by Menocal and Shaw (2019). Upon review by the Nevada State Historic Preservation Office (SHPO) and internal review by Desert Research Institute (DRI) and NNSA/NFO staff, it was determined that these resources needed to be rerecorded and evaluated in relation to what appeared to be a National Register-eligible Historic District made up of the entirety of Area 12 Camp. Based on preliminary information, it appeared that all 11 resources would likely be contributing elements of that historic district. With that assumption in mind, recording of the entire proposed Area 12 Camp Historic District was done for three purposes. First, it would result in a definitive significance evaluation of the 11 resources in question. Second, recording of the entire camp would be offered as an appropriate mitigation measure for the demolition of these resources. Third, it would present an essential background for future management of resources within the district boundaries. Prior to the present survey, Area 12 Camp had not yet been systematically recorded; therefore, DRI surveyed an area of approximately 229 acres for architectural resources. This effort resulted in the identification, recording, and evaluation of the Area 12 Camp Historic District (SHPO Resource No. D372), including the identification of its contributing components. This district is recommended eligible for the National Register of Historic Places under Criteria A and C. It is unevaluated under Criteria B and D. The Area 12 Historic District contains 71 Principal Resources, which include landscapes, buildings, and structures. Of these resources, 69 (including 10 of the 11 resources to be removed) are recommended as contributing elements of the historic district during its period of significance corresponding to nuclear testing from 1960 through 1992. During most of the Cold War, the government reservation now called the NNSS was named the Nevada Test Site (NTS).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

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↗
DOE OSTI2025

A provably stable numerical method for the anisotropic diffusion equation in confined magnetic fields

We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial boundary value problem. A discrete formulation is presented using operator splitting in time with the summation by parts finite difference approximation of spatial derivatives for the perpendicular diffusion operator. Weak penalty procedures are derived for implementing both boundary conditions and parallel diffusion operator obtained by field line tracing. We prove that the fully-discrete approximation is unconditionally stable. Discrete energy estimates are shown to match the continuous energy estimate given the correct choice of penalty parameters. A nonlinear penalty parameter is shown to provide an effective method for tuning the parallel diffusion penalty and significantly minimises rounding errors. Several numerical experiments, using manufactured solutions, the “NIMROD benchmark” problem and a single island problem, are presented to verify numerical accuracy, convergence, and asymptotic preserving properties of the method. Finally, we present a magnetic field with chaotic regions and islands and show the contours of the anisotropic diffusion equation reproduce key features in the field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

The Preservation of Super-Earths and the Emergence of Gas Giants after Their Progenitor Cores Have Entered the Pebble-isolation Phase

The omnipresence of super-Earths suggests that they are able to be retained in natal disks around low-mass stars, whereas exoplanets' mass distributions indicate that some cores have transformed into gas giants through runaway gas accretion at ≳1 au from solar-type stars. In this paper, we show that transition to runaway gas accretion by cores may be self-impeded by an increase of the grain opacity in their envelope after they have acquired sufficient mass (typically ~ 10M ⊕ ) to enter a pebble-isolation phase. The accumulation of approximately millimeter- to meter-sized pebbles in their migration barriers enhances their local fragmentation rates. The freshly produced submillimeter grains pass through the barrier, elevate the effective dust opacity, and reduce the radiative flux in the core's envelope. These effects alone are adequate to suppress the transition to runaway accretion and preserve super-Earths in the stellar proximity (~0.1 au), albeit entropy advection between the envelope and the disk can further reduce the accretion rate. At an intermediate distance (~1 au) from their host stars, the escalation in the dust opacity dominates over entropy advection in stalling the transition to runaway accretion for marginally pebble-isolated cores. Beyond a few astronomical unit, the transformation of more-massive cores to gas giants is reachable before severe depletion of disk gas. This requirement can be satisfied either in extended disks with large scale height via orderly accretion of migrating pebbles or through the mergers of oligarchic protoplanetary embryos, and can account for the correlated occurrence of long-period gas giants and close-in super-Earths.

79 ASTRONOMY AND ASTROPHYSICS↗