Results for “discontinuous coefficients”

DOE OSTI2025

Adaptive Interface-PINNs (AdaI-PINNs): An Efficient Physics-Informed Neural Networks Framework for Interface Problems

Here, we present an efficient physics-informed neural networks (PINNs) framework, termed Adaptive Interface-PINNs (AdaI-PINNs), to improve the modeling of interface problems with discontinuous coefficients and/or interfacial jumps. This framework is an enhanced version of its predecessor, Interface PINNs or I-PINNs (Sarma et al.; https://doi.org/10.1016/j.cma.2024.117135), which involves domain decomposition and assignment of different predefined activation functions to the neural networks in each subdomain across a sharp interface, while keeping all other parameters of the neural networks identical. In AdaI-PINNs, the activation functions vary solely in their slopes, which are trained along with the other parameters of the neural networks. This makes the AdaI-PINNs framework fully automated without requiring preset activation functions. Comparative studies on one-dimensional, two-dimensional, and three-dimensional benchmark elliptic interface problems reveal that AdaI-PINNs outperform I-PINNs, reducing computational costs by 2-6 times while producing similar or better accuracy.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

A high order Cartesian grid, finite volume method for elliptic interface problems

We present a higher-order finite volume method for solving elliptic PDEs with jump conditions on interfaces embedded in a 2D Cartesian grid. Second, fourth, and sixth order accuracy is demonstrated on a variety of tests including problems with high-contrast and spatially varying coefficients, large discontinuities in the source term, and complex interface geometries. We include a generalized truncation error analysis based on cell-centered Taylor series expansions, which then define stencils in terms of local discrete solution data and geometric information. In the process, we develop a simple method based on Green's theorem for computing exact geometric moments directly from an implicit function definition of the embedded interface. This approach produces stencils with a simple bilinear representation, where spatially-varying coefficients and jump conditions can be easily included and finite volume conservation can be enforced.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Discontinuity in RG flows across dimensions: entanglement, anomaly coefficients and geometry

We study the entanglement entropy associated with a holographic RG flow from AdS 7 to AdS 4 × $\mathbb{H}$ 3 , where $\mathbb{H}$ 3 is a 3-dimensional hyperbolic manifold with curvature κ. The dual six-dimensional RG flow is disconnected from Lorentz-invariant flows. In this context we address various notions of central charges and identify a monotonic candidate c-function that captures IR aspects of the flow. The UV behavior of the holographic entanglement entropy and, in particular its universal term, display an interesting dependence on the curvature, κ. We then contrast our holographic results with existing field theory computations in six dimensions and find a series of new corrections in curvature to the universal term in the entanglement entropy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Interface-aware Methods for Diffusion Equations [Slides]

In this talk, we will present interface-aware methods for diffusion equation. The focus is on the necessity of interface-aware, mixed cells, interface reconstruction, discontinuity of material diffusion coefficients, order of accuracy in time, property for large time steps, and simpler interface-aware methods. Numerical examples are provided to demonstrate the features on these aspects of the methods

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Calculation fo the Reflection and Transmission Coefficients for Gradual Tapered Waveguide Structures

It is required to find the reflection and transmission coefficients for a tapered waveguide. It is assumed that the taper is very long and gradual such that no higher order modes are excited from the discontinuity of the waveguide. Three different methods are presented for finding the reflection coefficient and two methods are presented for finding the transmission coefficient. A traditional differential equation method which finds only the reflection coefficient is presented. An additional set of differential equations are presented which finds both the reflection and transmission coefficients. A FEM (finite element method), which solves for both the reflection and transmission coefficients, is presented with its limitations. An example of a tapered coaxial line and waveguide is presented with the different methods compared and contrasted.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Magnetoelastic-coupling-assisted first-order antiferromagnetic transitions in the corrugated honeycomb-lattice compounds (Ca, Sr) ⁢Mn 2 ⁢ P 2

Understanding the origin of unconventional magnetic order is a central theme in the research field of functional quantum materials for spin-dependent applications. In general, a paramagnetic (PM) to antiferromagnetic (AFM) transition is of thermodynamically second order in nature in the absence of a magnetic field. In the magnetically frustrated corrugated-honeycomb lattice compounds (Ca, Sr) ⁢Mn 2 ⁢ P 2 , electrical resistivity 𝜌 measurements in the 𝑎⁢𝑏 plane are reported to exhibit sharp discontinuities at the respective PM to AFM ordering temperatures 𝑇 N = 69.5 and 53 K, respectively, signifying the unusual first-order nature of the AFM transition. To reveal the origin of such anomalous transitions, high-resolution linear thermal-expansion measurements are reported for both CaMn 2 ⁢P 2 and SrMn 2 ⁢ P 2 in the 𝑎⁢𝑏 plane and along the 𝑐 axis using capacitance dilatometry. The thermal expansion measurements show a sharp discontinuity in Δ⁢𝐿/𝐿 at 𝑇 N , yielding a diverging behavior in the thermal expansion coefficient 𝛼⁡(𝑇) associated with strong magnetoelastic coupling, driving the first-order AFM transition in CaMn 2 ⁢P 2 . However, this effect is weaker in SrMn 2 ⁢P 2 , consistent with the magnetic entropy changes 𝑆⁡(𝑇) obtained from the heat-capacity measurements. Temperature-dependent 𝑎⁢𝑏-plane x-ray diffraction measurements for CaMn 2 ⁢ P 2 near its 𝑇 N yield a volume thermal expansion coefficient consistent with literature data for other materials. The uniaxial pressure derivatives of 𝑇 N in the two compounds are found to be respectively opposite in sign, presumably due to the different magnetic structures.

Pakhira, Santanu [Maulana Azad National Institute ↗

DOE OSTI2024

Impact of Variable Perpendicular Transport Coefficients in WEST Simulations Using SolEdge-HDG

Plasma–wall interaction is one of the key research topics on the way to controlled fusion. To study the best operational designs with reduced heat and particle fluxes onto tokamak plasma facing components (PFCs) comprehensive plasma simulations are required. A recent implementation of a hybridized discontinuous Galerkin scheme into a new version of SolEdge code has the advantage of using magnetic equilibrium-free mesh. This allows us to conduct pioneering 2-D transport simulations of a full discharge in the WEST tokamak. In this work, we implemented plasma transport coefficients as functions of coordinate in the poloidal plane and neutral diffusion as a function of neutral mean free path. Moreover, the perpendicular convection flux terms were added to the code. Using the new features, a few test cases were investigated. Finally, the influence of nonconstant transport coefficients on the simulated particle and heat fluxes onto the WEST tokamak PFCs are demonstrated.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

A phase-field diffraction model for thermo-hydro-mechanical propagating fractures

This paper introduces a novel diffraction based thermo-hydraulic–mechanical (THM) model for fracture propagation using a phase-field fracture (PFF) approach. The key innovation of the THM-PFF model lies in its integrated treatment of four solution variables—displacements, phase-field, pressure, and temperature—each governed by a combination of conservation of momentum (mechanics problem), a variational inequality (constrained minimization problem), mass conservation (pressure problem), and energy conservation (temperature problem). This leads to a new formulation of a coupled variational inequality system. A major advancement is the development of an extended fixed-stress algorithm, where displacements, phase-field, pressures, and temperatures are solved in a staggered sequence. An important aspect of this work is the global coupling of pressures and temperatures across the domain using diffraction systems, with diffraction coefficients defined by material parameters weighted by the diffusive phase-field variable. To ensure robust local mass conservation, we employ enriched Galerkin finite elements (EG) for both pressure and temperature diffraction equations. By enriching the continuous Galerkin basis functions with discontinuous piecewise constants, EG accurately represents solution and parameter discontinuities while preserving local mass and energy conservation—crucial aspects for THM problems and realistic behavior. Moreover, the use of a predictor–corrector local mesh adaptivity scheme is employed, allowing the model to handle small phase-field length-scale parameters while maintaining high numerical accuracy and reasonable computational cost. Furthermore, these new model and algorithmic developments represent significant advances in the field and have been substantiated through rigorous numerical tests.

Diffraction systems↗

DOE OSTI2024

A Verification Suite of Test Cases for the Barotropic Solver of Ocean Models

Abstract The development of any atmosphere or ocean model warrants a suite of test cases (TCs) to verify its spatial and temporal discretizations, order of accuracy, stability, reproducibility, portability, scalability, etc. In this paper, we present a suite of shallow water TCs designed to verify the barotropic solver of atmosphere and ocean models. These include the non‐dispersive coastal Kelvin wave; the dispersive inertia‐gravity wave; the dispersive planetary and topographic Rossby waves; the barotropic tide; and a non‐linear manufactured solution. These TCs check the implementation of the linear pressure gradient term; the linear constant or variable‐coefficient Coriolis and bathymetry terms; and the non‐linear advection terms. Simulation results are presented for a variety of time‐stepping methods as well as two spatial discretizations: a mimetic finite volume method based on the TRiSK scheme, and a high‐order discontinuous Galerkin spectral element method. The experimental procedure for conducting these numerical experiments is detailed. It underscores several key considerations that vary depending on the chosen spatial discretization method. Finally, convergence studies of every TC are conducted with refinement in both space and time, only in space, and only in time. The convergence slopes match the expected theoretical predictions.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Determining Optimal Magnetometer Configuration on MAGIS-100

Long-baseline atom interferometers such as the Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100) require stringent control and continuous characterization of background magnetic fields and spatial gradients to prevent systemic phase shifts that mimic ultralight dark matter or gravitational wave signatures. Because direct sensor placement within the ultra-high vacuum beam pipe is infeasible, in-situ magnetic field monitoring relies on external sensor arrays situated in the surrounding annular region. This work demonstrates a field reconstruction framework for a 5.3-meter MAGIS-100 modular section using finite-element Opera simulations. Transverse magnetic fields are expanded using a cylindrical multipole framework as informed by Fermilab’s Muon g-2 experiment, with magnetometer array configurations optimized via Fisher information matrix D-optimality. Inverting external sensor readings through a Gauss-Newton scheme recovers interior tube fields across distinct axial positions. In the discontinuity-averse uniform region (slice pair P4), the model achieves sub-noise-floor performance with a cross-validated root-mean-square error (RMSE) of $6.7227 \times 10^{-4}\text{ A/m}$ ($0.845\times$ sensor noise floor) and an interior field coefficient of variation of $1.71\%$. An elbow criterion in the Fisher bounds establishes $n_{\text{max}} = 2$ as the optimal multipole truncation order to prevent noise amplification from over-parameterization, with $n_{\text{max}} = 3$ (sextupole) order chosen for analysis to demonstrate further complexity and cross-pair comparison. Furthermore, analytical differentiation of the fitted multipole coefficients yields dense spatial maps of the transverse Jacobian gradient matrix $\nabla \mathbf{H}$ along with propagated $1\sigma$ uncertainty bounds across the beam region ($r \le 2.75\text{ in}$). This operational framework confirms that external magnetometer arrays can reliably monitor magnetic field uniformity and spatial gradients along the 100-meter flight path given appropriate sampling for any complexity order.

Appleby, Darwin [William Rainey Harper Coll.] (ORC↗

DOE OSTI2026

Determining Optimal Magnetometer Configuration on MAGIS-100

Long-baseline atom interferometers such as the Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100) require stringent control and continuous characterization of background magnetic fields and spatial gradients to prevent systemic phase shifts that mimic ultralight dark matter or gravitational wave signatures. Because direct sensor placement within the ultra-high vacuum beam pipe is infeasible, in-situ magnetic field monitoring relies on external sensor arrays situated in the surrounding annular region. This work demonstrates a field reconstruction framework for a 5.3-meter MAGIS-100 modular section using finite-element Opera simulations. Transverse magnetic fields are expanded using a cylindrical multipole framework as informed by Fermilab’s Muon g-2 experiment, with magnetometer array configurations optimized via Fisher information matrix D-optimality. Inverting external sensor readings through a Gauss-Newton scheme recovers interior tube fields across distinct axial positions. In the discontinuity-averse uniform region (slice pair P4), the model achieves sub-noise-floor performance with a cross-validated root-mean-square error (RMSE) of $6.7227 \times 10^{-4}\text{ A/m}$ ($0.845\times$ sensor noise floor) and an interior field coefficient of variation of $1.71\%$. An elbow criterion in the Fisher bounds establishes $n_{\text{max}} = 2$ as the optimal multipole truncation order to prevent noise amplification from over-parameterization, with $n_{\text{max}} = 3$ (sextupole) order chosen for analysis to demonstrate further complexity and cross-pair comparison. Furthermore, analytical differentiation of the fitted multipole coefficients yields dense spatial maps of the transverse Jacobian gradient matrix $\nabla \mathbf{H}$ along with propagated $1\sigma$ uncertainty bounds across the beam region ($r \le 2.75\text{ in}$). This operational framework confirms that external magnetometer arrays can reliably monitor magnetic field uniformity and spatial gradients along the 100-meter flight path given appropriate sampling for any complexity order.

Appleby, Darwin [William Rainey Harper Coll.] (ORC↗

DOE OSTI2026

In-Situ Magnetic Field Reconstruction in the MAGIS-100 Experiment

Long-baseline atom interferometers such as the Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100) require stringent control and continuous characterization of background magnetic fields and spatial gradients to prevent systemic phase shifts that mimic ultralight dark matter or gravitational wave signatures. Because direct sensor placement within the ultra-high vacuum beam pipe is infeasible, in-situ magnetic field monitoring relies on external sensor arrays situated in the surrounding annular region. This work demonstrates a field reconstruction framework for a 5.3-meter MAGIS-100 modular section using finite-element Opera simulations. Transverse magnetic fields are expanded using a cylindrical multipole framework as informed by Fermilab’s Muon g-2 experiment, with magnetometer array configurations optimized via Fisher information matrix D-optimality. Inverting external sensor readings through a Gauss-Newton scheme recovers interior tube fields across distinct axial positions. In the discontinuity-averse uniform region (slice pair P4), the model achieves sub-noise-floor performance with a cross-validated root-mean-square error (RMSE) of $6.7227 \times 10^{-4}\text{ A/m}$ ($0.845\times$ sensor noise floor) and an interior field coefficient of variation of $1.71\%$. An elbow criterion in the Fisher bounds establishes $n_{\text{max}} = 2$ as the optimal multipole truncation order to prevent noise amplification from over-parameterization, with $n_{\text{max}} = 3$ (sextupole) order chosen for analysis to demonstrate further complexity and cross-pair comparison. Furthermore, analytical differentiation of the fitted multipole coefficients yields dense spatial maps of the transverse Jacobian gradient matrix $\nabla \mathbf{H}$ along with propagated $1\sigma$ uncertainty bounds across the beam region ($r \le 2.75\text{ in}$). This operational framework confirms that external magnetometer arrays can reliably monitor magnetic field uniformity and spatial gradients along the 100-meter flight path given appropriate sampling for any complexity order.

Appleby, Darwin [William Rainey Harper Coll.; Ferm↗

DOE OSTI2023

Phase transformations and thermal expansion coefficients of unirradiated U-X wt.% Zr (X = 6, 10, 20, 30) measured via neutron diffraction

This work characterizes the crystallographic evolution of unirradiated U-X wt.% Zr (X = 6, 10, 20, 30) while cooling from equilibration, single phase γ-U-Zr, at 900 °C to ambient temperature using time-of-flight neutron diffraction. The β-U phase was unobserved during cooling at 1 °C/min in all alloys. All alloys followed the phase transformation pathway of γ-U-Zr→γ-U-Zr+α-U→α-U +δ-UZr2 with an observed miscibility gap in γ-U-Zr. The α-U and δ-UZr2 transformation took place simultaneously in the U-30 wt.% Zr sample. These findings strengthen the need to re-approach the U-Zr phase diagram in entirety. Bulk volumetric CTEs agree well with published data, strengthening the quantification of lattice-specific CTEs reported in this study. A compositionally dependent discontinuity in thermal expansion, increasing in magnitude with decreasing U content, occurs during the γ-U-Zr→α-U+δ-UZr2 transformation. The γ-U-Zr lattice parameter was measured to have a compositional dependency.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Underlying mechanism of structural transformation between GaSb and GaAs response to intense electronic excitation

Ion irradiation of semiconductors has emerged as a promising approach for fabricating self-organized nanosystems with high atomic precision, despite often being accompanied by undesirable phenomena. Exploring the mechanisms underlying structural transformations is crucial for assessing nanostructure array types under complex irradiation environments. By quantitatively calculating the thermodynamically driven processes and analyzing the impact of intrinsic structural parameters, distinct structural transformations in response to intense electronic excitation are systematically investigated in gallium antimonide (GaSb) and gallium arsenide (GaAs) systems. In high-energy regimes, the nanofibers layer of GaSb exhibits intriguing structural discrepancy, characterized by partial nanofibers with coherent boundaries, interspersed nanopores accompanied by antisite defects and Ga precipitates, distinguishing to a series of discontinuous latent tracks that emerged within cylindrical trajectories in GaAs. Furthermore, significant diffusion behaviors of the nanohillocks are discovered in GaAs, with higher average roughness than GaSb, driven by the gradient stress distribution influenced by the free-surface effects. The deposition energy for melting phase formation, Gibbs free energy, and Ga diffusion coefficients contribute to the distinctive structural features, evidencing relatively stable morphological configurations and higher irradiation resistance in GaAs. Consequently, special optoelectronic properties associated with structural discrepancies facilitate the design and optimization of material functionalities by irradiation technologies.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Analyticity of replica correlators and modular ETH

We study the two point correlation function of a local operator on an n -sheeted replica manifold corresponding to the half-space in the vacuum state of a conformal field theory. In analogy with the inverse Laplace transform, we define the Renyi transform of this correlation function, which is a function of one complex variable w, dual to the Renyi parameter n . Inspired by the inversion formula of Caron-Huot, we argue that if the Renyi transform ƒ(w) has bounded behavior at infinity in the complex w plane, the discontinuity of the Renyi transform disc ƒ(w) provides the unique analytic continuation in n of the original replica correlation function. We check our formula by explicitly calculating the Renyi transform of a particular replica correlator in a large N holographic CFT d in dimensions d > 2. We also discover that the discontinuity of the Renyi transform is related to the matrix element of local operators between two distinct eigenstates of the modular Hamiltonian. We calculate the Renyi transform in 2 d conformal field theories, and use it to extract the off-diagonal elements of (modular) ETH. We argue that in 2 d , this is equivalent to the off-diagonal OPE coefficients of a CFT and show that our technique exactly reproduces recent results in the literature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Calculating a minimum overlap period for successful intercalibration of soil moisture sensors

Abstract Long‐term in situ soil moisture monitoring inevitably requires sensors to be replaced. Ensuing discontinuities in the data record can be mitigated by intercalibration, however it is unclear how long the existing sensor needs to remain alongside the newly installed before there is enough overlapping data to generate a robust intercalibration. We used 154 pairs of established and newly installed sensors within the Marena, Oklahoma, In Situ Sensor Testbed to determine if there is a minimum overlap time that should be considered when planning upcoming replacements. Hourly observations of the existing sensor were linearly calibrated to those of the newly installed sensor with coefficients determined from overlap periods incremented by 30 days until a reference period of 2 years was reached. The resulting bias, root‐mean‐square error, and correlation coefficient for sensor pairs indicate that a minimum of 6 to 9 months of overlapping data are required to generate a successful intercalibration. Extending that to a full year before decommissioning the old sensor results in a stable intercalibration with higher confidence.

Agriculture↗

DOE OSTI2025

Adaptive Interface-PINNs (AdaI-PINNs) for transient diffusion: Applications to forward and inverse problems in heterogeneous media

We model transient diffusion in heterogeneous materials using a novel physics-informed neural networks framework (PINNs) termed Adaptive interface physics-informed neural networks or AdaI-PINNs (Roy et al. arXiv preprint arXiv:2406.04626, 2024). AdaI-PINNs utilize different activation functions with trainable slopes tailored to each material region within the computational domain, allowing for a fully automated and adaptive PINNs approach to model interface problems with strongly and weakly discontinuous solutions. To enhance its performance in highly heterogeneous transient diffusion systems, we prescribe a suite of robust practices, including appropriate non-dimensionalization of equations, a biased sampling method, Glorot initialization, and the hard enforcement of boundary and initial conditions. Here we evaluate the efficacy of the proposed method on several benchmark forward and inverse problems. Comparative studies on one-dimensional and two-dimensional benchmark problems reveal that the modified AdaI-PINNs outperform its unmodified counterpart, achieving root-mean-square errors that are at least two orders of magnitude better in forward problems. For inverse problems, the maximum errors in the approximated diffusion coefficients by modified AdaI-PINNs are four orders of magnitude better than those of the unmodified version. Additionally, modified AdaI-PINNs demonstrate improved stability in problems with large material mismatches.

42 ENGINEERING↗

DOE OSTI2023

Linear-depth quantum circuits for loading Fourier approximations of arbitrary functions

Abstract The ability to efficiently load functions on quantum computers with high fidelity is essential for many quantum algorithms, including those for solving partial differential equations and Monte Carlo estimation. In this work, we introduce the Fourier series loader (FSL) method for preparing quantum states that exactly encode multi-dimensional Fourier series using linear-depth quantum circuits. Specifically, the FSL method prepares a (Dn)-qubit state encoding the 2 Dn -point uniform discretization of aD-dimensional function specified by aD-dimensional Fourier series. A free parameter,m, which must be less thann, determines the number of Fourier coefficients, 2 D ( m + 1 ) , used to represent the function. The FSL method uses a quantum circuit of depth at most 2 ( n − 2 ) + ⌈ log 2 ( n − m ) ⌉ + 2 D ( m + 1 ) + 2 − 2 D ( m + 1 ) , which is linear in the number of Fourier coefficients, and linear in the number of qubits (Dn) despite the fact that the loaded function’s discretization is over exponentially many (2 Dn ) points. The FSL circuit consists of at most D n + 2 D ( m + 1 ) + 1 − 1 single-qubit and D n ( n + 1 ) / 2 + 2 D ( m + 1 ) + 1 − 3 D ( m + 1 ) − 2 two-qubit gates; we present a classical compilation algorithm with runtime O ( 2 3 D ( m + 1 ) ) to determine the FSL circuit for a given Fourier series. The FSL method allows for the highly accurate loading of complex-valued functions that are well-approximated by a Fourier series with finitely many terms. We report results from noiseless quantum circuit simulations, illustrating the capability of the FSL method to load various continuous 1D functions, and a discontinuous 1D function, on 20 qubits with infidelities of less than 10 −6 and 10 −3 , respectively. We also demonstrate the practicality of the FSL method for near-term quantum computers by presenting experiments performed on the Quantinuum H1-1 and H1-2 trapped-ion quantum computers: we loaded a complex-valued function on 3 qubits with a fidelity of over 95 % , as well as various 1D real-valued functions on up to 6 qubits with classical fidelities ≈99%, and a 2D function on 10 qubits with a classical fidelity ≈94%.

Physics↗