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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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At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Comparison of momentum transport models for numerical relativity

The main problems of nonvacuum numerical relativity, compact binary mergers and stellar collapse, involve hydromagnetic instabilities and turbulent flows, so that kinetic energy at small scales leads to mean effects at large scale that drive the secular evolution. Notable among these effects is momentum transport. We investigate two models of this transport effect, a relativistic Navier-Stokes system and a turbulent mean stress model, that are similar to all of the prescriptions that have been attempted to date for treating subgrid effects on binary neutron star mergers and their aftermath. Our investigation involves both stability analysis and numerical experimentation on star and disk systems. We also begin the investigation of the effects of particle and heat transport on postmerger simulations. Here, we find that correct handling of turbulent heating is crucial for avoiding unphysical instabilities. Given such appropriate handling, the evolution of a differentially rotating star and the accretion rate of a disk are reassuringly insensitive to the choice of prescription. However, disk outflows can be sensitive to the choice of method, even for the same effective viscous strength. We also consider the effects of eddy diffusion in the evolution of an accretion disk and show that it can interestingly affect the composition of outflows.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Non-equilibrium simulations of hydraulic permeation: Role of mechanical boundary conditions in dense membranes

Understanding the mechanisms of water transport in reverse osmosis membranes is critical for improving membrane performance and guiding material design. While classical models describe transport as either solution-diffusion (SD)—involving concentration-driven diffusion through a homogeneous medium—or pore-flow (PF)—involving pressure-driven convection through percolated water channels—their applicability to crosslinked polyamide membranes remains debated. Here, using non-equilibrium molecular dynamics simulations, we investigate the impact of mechanical support conditions on pressure-driven water transport in polyamide membranes across varying crosslink densities and pressure differentials (1000–5000 bar). Two support conditions are considered: graphene-restrained, representing experimentally relevant supported membranes, and freeze-restrained, mimicking a self-supported structure. In graphene-restrained systems, water concentration gradients and constant pressure profiles emerge, consistent with SD theory and incompatible with PF assumptions due to the absence of percolated pores and sub-nanometer voids. In contrast, freeze-restrained systems display uniform water concentration and linearly decreasing pressure at 1000 bar, and exhibit compressibility-induced water gradients and partial percolation at 5000 bar, resembling PF-like behavior. However, the underlying assumptions of PF theory—continuous solvent pathways and pressure transmission through water-filled pores—are not met under most conditions. Our results demonstrate that accurate modeling of reverse osmosis membranes must incorporate realistic mechanical boundary conditions to distinguish between transport mechanisms. For dense polyamide membranes supported by porous substrates, graphene-restrained simulations best reflect experimental setups and support the SD model as the dominant mechanism of water permeation.

molecular dynamics↗
DOE OSTI2021

As a Matter of Tension: Kinetic Energy Spectra in MHD Turbulence

While magnetized turbulence is ubiquitous in many astrophysical and terrestrial systems, our understanding of even the simplest physical description of this phenomena, ideal magnetohydrodynamic (MHD) turbulence, remains substantially incomplete. As such, in this work we highlight the shortcomings of existing theoretical and phenomenological descriptions of MHD turbulence that focus on the joint (kinetic and magnetic) energy fluxes and spectra by demonstrating that treating these quantities separately enables fundamental insights into the dynamics of MHD turbulence. This is accomplished through the analysis of the scale-wise energy transfer over time within an implicit large eddy simulation of subsonic, super-Alfvénic MHD turbulence. Our key finding is that the kinetic energy spectrum develops a scaling of approximately k –4/3 in the stationary regime as magnetic tension mediates large-scale kinetic to magnetic energy conversion and significantly suppresses the kinetic energy cascade. This motivates a reevaluation of existing MHD turbulence theories with respect to a more differentiated modeling of the energy fluxes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Toward an event-level analysis of hadron structure using differential programming

Reconstructing the internal properties of hadrons in terms of fundamental quark and gluon de- grees of freedom is a central goal in nuclear and particle physics. This effort lies at the core of major experimental programs, such as the Jefferson Lab 12 GeV program and the upcoming Electron-Ion Collider. A primary challenge is the inherent inverse problem: converting large-scale observational data from collision events into the fundamental QCD-defined densities that characterize the micro- scopic structure of hadronic systems. Recent advances in AI and machine learning have opened new avenues for addressing this challenge using deep learning techniques. A particularly promising direction is the integration of complex theoretical calculations and experimental simulations into a unified framework capable of reconstructing these densities directly from event-level information. In this document, we introduce a key algorithm called LOITS, which enables differentiable program- ming within such a framework, facilitating the use of AI/ML techniques to solve the inverse problem of QCF reconstruction at the event level.

Braga, Kevin [College of William and Mary, William↗
DOE OSTI2021

Measurement of the production cross section of prompt $ {\Xi}_{\mathrm{c}}^0 $ baryons at midrapidity in pp collisions at $ \sqrt{s} $ = 5.02 TeV

The transverse momentum (p T ) differential cross section of the charm-strange baryon $ {\Xi}_{\mathrm{c}}^0 $ is measured at midrapidity (|y| < 0.5) via its semileptonic decay into e + Ξ - ν e in pp collisions at $\sqrt{s}$ = 5.02 TeV with the ALICE detector at the LHC. The ratio of the p T -differential $ {\Xi}_{\mathrm{c}}^0 $-baryon and D 0 -meson production cross sections is also reported. The measurements are compared with simulations with different tunes of the PYTHIA 8 event generator, with predictions from a statistical hadronisation model (SHM) with a largely augmented set of charm-baryon states beyond the current lists of the Particle Data Group, and with models including hadronisation via quark coalescence. The p T -integrated cross section of prompt $ {\Xi}_{\mathrm{c}}^0 $-baryon production at midrapidity is also reported, which is used to calculate the baryon-to-meson ratio $ {\Xi}_{\mathrm{c}}^0 $/D 0 = 0.20 ± 0.04 (stat.)$^{+0.08}_{-0.07}$ (syst.). These results provide an additional indication of a modification of the charm fragmentation from e + e - and e - p collisions to pp collisions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Explicit physics-informed neural networks for nonlinear closure: The case of transport in tissues

In upscaling methods, closures for nonlinear problems present a well-known challenge. While a number of theoretical methods have been proposed for handling such closures, nonlinearities still remain a significant obstacle for many problems. In this work, we use a combination of formal upscaling and data-driven machine learning for explicitly closing a nonlinear transport and reaction process in multiscale tissues. The classical effectiveness factor model is used to formulate the macroscale reaction kinetics. We train a multilayer perceptron network using training data generated by direct numerical simulations over microscale examples. Once trained, the network is used in an algorithm for numerically solving the upscaled (coarse-grained) differential equation describing mass transport and reaction in two example tissues. The network is described as being explicit in the sense that the network is trained using macroscale concentrations and gradients of concentration as components of the feature space rather than incorporating them as part of a constraint in the optimization process. Network training and solutions to the macroscale transport equations were computed for two different tissues. The two tissue types (brain and liver) exhibit markedly different geometrical complexity and spatial scale (cell size and sample size). The upscaled solutions for the average concentration are compared with numerical solutions derived from the microscale concentration fields by a posteriori averaging. There are three outcomes of this work of particular note. 1) Our overall approach results in an upscaled nonlinear PDE. The PDE is closed using a neural network, and our approach results in the definition of the classical effectiveness factor for effecting closure. 2) We identify particular source terms for the closure problem that are important for representing the structure of the closure. These source terms involve macroscale concentrations and their gradients. We adopt these source terms to use as explicit features in the learning algorithm. We find the trained networks that include the macroscale source terms generate models that are able to predict the correction factor with increased fidelity over those that do not. 3) We find that the trained network exhibits good generalizability, and it is able to predict the effectiveness factor with high fidelity for realistically-structured tissues despite the significantly different scale and geometrical complexity of the two example tissue types. This latter result emphasizes our purposeful connection between conventional averaging methods with the use of machine learning for closure; this contrasts with some machine learning methods for upscaling where the exact form of the macroscale equation remains unknown.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Emulating climate extreme indices

We use simple pattern scaling and time-shift to emulate changes in a set of climate extreme indices under future scenarios, and evaluate the emulators' accuracy. We propose a metric for the error in emulation in the context of initial condition ensembles, to specifically characterize the role of internal variability in the emulation performance. Our metric separates systematic emulation errors from unavoidable discrepancies between emulated and target values due to internal variability. We compute the metricis at grid-point scale, and we show geographically resolved results, or aggregate them at global scale. We demonstrate the use of our error metric in the emulation of a suite of temperature and precipitation extreme indices. We test and compare simple pattern scaling and time-shift using a range of trajectories spanning targets inspired by the Paris agreement -- warming to 1.5C and 2.0C from the pre-industrial baseline -- and two of the longer-established trajectories, RCP4.5 and RCP8.5. With this suite of scenarios we can test the effects on the performance of the size of the temperature gap between emulation origin and target. We find that for most indices emulation the dominant source of discrepancy is internal variability. For at least one index, however, counting exceedances of a high temperature threshold, significant portions of the globally aggregated discrepancy and its regional pattern originate from the systematic emulation error. This error exceeds internal variability of both the target and the emulated quantities in large coherent regions at low latitudes, and the explanation can be found in the differential behavior of temperature distributions across latitudes. The metric also highlights a fundamental difference in the two methods related to the simulation of internal variability, which is dampened significantly by simple pattern scaling. This aspect is of consequence when using these methods for specific applications, where preserving variability for uncertainty quantification is deemed important. With this study we offer our metric as a diagnostic tool, facilitating the formulation of scientific hypotheses on the reasons for the error. In the meantime, we show that for many impact relevant indices by now traditional emulation techniques can be accurate within the variations unavoidably introduced by internal variability, establishing the fundamental condition for using their emulation in impact modeling.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Adaptive Uncertainty Quantification for Stochastic Hyperbolic Conservation Laws

Here, we propose a predictor-corrector adaptive method for the study of hyperbolic partial differential equations (PDEs) under uncertainty. Constructed around the framework of stochastic finite volume (SFV) methods, our approach circumvents sampling schemes or simulation ensembles while also preserving fundamental properties, in particular hyperbolicity of the resulting systems and conservation of the discrete solutions. Furthermore, we augment the existing SFV theory with a priori convergence results for statistical quantities, in particular push-forward densities, which we demonstrate through numerical experiments. By linking refinement indicators to regions of the physical and stochastic spaces, we drive anisotropic refinements of the discretizations, introducing new degrees of freedom where deemed profitable. To illustrate our proposed method, we consider a series of numerical examples for nonlinear hyperbolic PDEs based on Burgers’ and Euler’s equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Ultimate Precision on Sin^2 Theta_23 With the Numi Experiments

There were two major goals to this proposal: the study of the discrepancy between data and MC in the NuMI Medium Energy neutrino beam and the incorporation of the MINOS and NOVA neutrino oscillation datasets. The first topic was approached via development of a simulation of the NuMI beam monitoring instrumentation suite. Initially, the Horn-Off current data sets were used to measure a set of hadron production parameters which improved the data/MC agreement in a way which was independent of the focusing parameters. The peak position discrepancy was only explained by a large (10kA) reduction in the horn current. A full simulation of the muon monitors was developed to attempt to make an independent measurement of the horn current by means of differential data taken by those monitors. While only at the 5kA level, the result corroborated the former findings. The second goal has not yet been completed but progress has focused on understanding how to modify the MINOS MC to take into account the MEC contribution which is missing from the underlying NEUGEN MC. A number of improvements to the MINOS reconstruction have been necessary. The framework to run the fits on the combined data has been completed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Parallel Algebraic Multigrid for Fusion and Higher-Order PDEs

Multigrid methods play a key role in large-scale scientific simulation because they are among the fastest and most scalable approaches for solving the underlying sparse linear systems of equations that arise from a wide array of Partial Differential Equation (PDE) discretizations. Algebraic multigrid (AMG) is a special type of multigrid method that depends only on the description of the linear system, giving it better portability and broader applicability than geometric multigrid, as it requires no explicit knowledge of the problem geometry. Even though these methods are widely used today, there are still applications where further development is needed. In this report, we focus on PDEs with higher-order terms (e.g., fourth order), concentrating on a PDE that arises in tokamak edge plasma simulations (a tokamak is a machine that confines a plasma using magnetic fields and is believed to be the leading plasma confinement concept for future fusion power plants). General multigrid relaxes a linear system on coarser grids and reverses this process with interpolation, but standard AMG methods struggle with the aforementioned higher-order PDEs. We investigate cyclic coarsening and interpolation heuristics, as well as new iterative approximation methods of refining the solution at each grid to improve the existing multigrid approach. To this end, we ensure that these techniques are transferable to a parallelized setting with LLNL’s supercomputers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Seabed bathymetry and friction modeling in MoorDyn

This paper presents the implementation and verification of a seabed bathymetry feature and seabed friction feature to the open-source, lumped-mass mooring system dynamics modeler, MoorDyn, which is part of the National Renewable Energy Laboratory’s aero-hydro-servo-elastic simulation tool, OpenFAST. Variations in seabed slope, as well as the frictional effects of mooring lines moving along the seabed, will affect the mooring line tensions of a floating platform and the consequent platform response. These new features are especially relevant for modeling mooring systems in deep-water coastal areas where seabed depth can change significantly over an entire mooring footprint. The bathymetry feature models the seabed as a rectangular grid of variable water depths in place of the existing, uniform water depth in MoorDyn. The friction force is primarily represented as a Coulombic friction force, or the product of a kinetic friction coefficient and the seabed contact normal force, with the ability to differentiate between transverse and axial motion of a line node on the seabed in any bathymetry grid. These capabilities were tested by running MoorDyn and OpenFAST simulations over a variety of seabed and environmental conditions; the resulting fairlead tensions, node tensions, and mooring line kinematics were verified against equivalent OrcaFlex simulations. The results match closely, meaning the features are verified, which will increase the overall fidelity of OpenFAST and FAST.Farm simulations.

17 WIND ENERGY↗
DOE OSTI2023

Uncertain role of clouds in shaping summertime atmosphere-sea ice connections in reanalyses and CMIP6 models

Downwelling longwave radiation (DLR) driven by the atmospheric and cloud conditions in the troposphere is suggested to be a dominant factor to determine the summertime net surface energy budget over the Arctic Ocean and thus plays a key role to shape the September sea ice. We use reanalyses and the self-organizing map (SOM) method to distinguish CMIP6 model performance in replicating the observed strong atmosphere-DLR connection. We find all models can reasonably simulate the linkage between key atmosphere variables and the clear sky DLR but behave differently in replicating the atmosphere-DLR connection due to cloud forcing. In ERA5 and strongly coupled models, tropospheric high pressure is associated with decreased clouds in the mid- and high-levels and increased clouds near the surface. This out-of-phase structure indicates that DLR cloud forcing is nearly neutral, making the clear sky DLR more important to bridge JJA circulation to late-summer sea ice. In MERRA-2 and weakly coupled models, tropospheric clouds display a vertically homogeneous reduction; the cloud DLR is thus strongly reduced due to the cooling effect, which partially cancels out the clear sky DLR and makes the total DLR less efficient to translate circulation forcing to sea ice. The differences of cloud vertical distribution in CMIP6 appear to be differentiated by circulation related relative humidity. Therefore, a better understanding of the discrepancy of different reanalyses and remote sensing products is critical to comprehensively evaluate simulated interactions among circulation, clouds, sea ice and energy budget at the surface in summer.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Statistical Treatment of Inverse Problems Constrained by Differential Equations-based Models with Stochastic Terms

This paper introduces a statistical treatment of inverse problems constrained by models with stochastic terms. The solution of the forward problem is given by a distribution represented numerically by an ensemble of simulations. The goal is to formulate the inverse problem, in particular the objective function, to find the closest forward distribution (i.e., the output of the stochastic forward problem) that best explains the distribution of the observations in a certain metric. We use proper scoring rules, a concept employed in statistical forecast verification, namely energy, variogram, and hybrid (i.e., combination of the two) scores. We study the performance of the proposed formulation in the context of two applications: a coefficient field inversion for subsurface flow governed by an elliptic partial differential equation with a stochastic source and a parameter inversion for power grid governed by differential-algebraic equations. In both cases we show that the variogram and the hybrid scores produce better parameter inversion results than does the energy score, whereas the energy score leads to better probabilistic predictions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker–Planck Equations

The Fokker-Planck (FP) equation is a foundational partial differential equation (PDE) in stochastic processes involving Brownian motions. However, the curse of dimensionality (CoD) poses a formidable challenge when dealing with high-dimensional FP equations. Although Monte Carlo simulation and (vanilla) Physics-Informed Neural Networks (PINNs) have shown the potential to tackle CoD, both methods exhibit significant numerical errors in high dimensions when dealing with the probability density function (PDF) associated with Brownian motion. The point-wise PDF values tend to decrease exponentially as dimensionality increases, surpassing the precision of numerical simulations and resulting in substantial errors. In addition, due to its massive sampling, Monte Carlo fails to offer fast sampling. Modeling the logarithm likelihood (LL) via vanilla PINNs transforms the FP equation into a notoriously difficult Hamilton-Jacobi-Bellman (HJB) equation, which is impractical for PINN learning, whose error grows rapidly with dimension. To this end, we propose a novel approach utilizing a score-based solver to fit the score function in stochastic differential equations (SDEs). The score function, defined as the gradient of the LL, plays a fundamental role in inferring LL and PDF and enables fast SDE sampling, offering an effective means to overcome the CoD. Three fitting methods, Score Matching (SM), Sliced Score Matching (SSM), and Score-PINN, are introduced, each contributing unique advantages in computational complexity, accuracy, and generality. The proposed score-based SDE solver operates in two stages: first, employing score matching or Score-PINN to acquire the score function; and second, solving the LL via an ordinary differential equation (ODE) using the obtained score function. Comparative evaluations across these methods showcase varying trade-offs. The proposed methodology is evaluated across diverse SDEs, including anisotropic Ornstein-Uhlenbeck processes, geometric Brownian motion, and Brownian motion with varying eigenspace. We also test various distributions, including Gaussian, Log-normal, Laplace, and Cauchy distributions. The numerical results demonstrate the score-based SDE solver’s stability, speed, and performance across different experimental settings, solidifying its potential as a solution to CoD for high-dimensional FP equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Accelerating phase field simulations through a hybrid adaptive Fourier neural operator with U-net backbone

Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying. For one such process as liquid-metal dealloying (LMD), phase field models have been developed to understand the mechanisms leading to complex morphologies. However, the LMD governing equations in these models often involve coupled non-linear partial differential equations (PDE), which are challenging to solve numerically. In particular, numerical stiffness in the PDEs requires an extremely refined time step size (on the order of 10 -12 s or smaller). This computational bottleneck is especially problematic when running LMD simulation until a late time horizon is required. This motivates the development of surrogate models capable of leaping forward in time, by skipping several consecutive time steps at-once. In this paper, we propose a U-shaped adaptive Fourier neural operator (U-AFNO), a machine learning (ML) based model inspired by recent advances in neural operator learning. U-AFNO employs U-Nets for extracting and reconstructing local features within the physical fields, and passes the latent space through a vision transformer (ViT) implemented in the Fourier space (AFNO). We use U-AFNOs to learn the dynamics of mapping the field at a current time step into a later time step. We also identify global quantities of interest (QoI) describing the corrosion process (e.g., the deformation of the liquid-metal interface, lost metal, etc.) and show that our proposed U-AFNO model is able to accurately predict the field dynamics, in spite of the chaotic nature of LMD. Most notably, our model reproduces the key microstructure statistics and QoIs with a level of accuracy on par with the high-fidelity numerical solver, while achieving a significant 11, 200 × speed-up on a high-resolution grid when comparing the computational expense per time step. Finally, we also investigate the opportunity of using hybrid simulations, in which we alternate forward leaps in time using the U-AFNO with high-fidelity time stepping. We demonstrate that while advantageous for some surrogate model design choices, our proposed U-AFNO model in fully auto-regressive settings consistently outperforms hybrid schemes.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Simulating Alpha Particles Incident on MKID Chips for Quantum Sensitivity Analysis

Superconducting quantum devices, such as microwave kinetic inductance detectors (MKIDs), are highly sensitive instruments used in quantum computing and advanced sensing technologies. However, their extreme sensitivity also makes them vulnerable to background noise from natural sources like radiation. One significant contributor to this noise is alpha particles emitted by 210Po, a radon decay daughter that accumulates on surfaces near the detector. This project investigates how alpha particles emitted from 210Po interact with MKID chips. These particles can deposit energy on the detector surface, disrupting its operation and generating false signals. Understanding the energy and behavior of these particles is crucial for improving the design and reliability of quantum devices. To explore this, we first modeled the decay chain starting from 210Pb to 210Po using differential equations. This allowed us to predict how the activity of alpha-emitting isotopes changes over time, reaching a steady state after about two years. Next, we simulated alpha particle interactions with the MKID chip using the Geant4 software toolkit. We built a detailed computer model of the detector housing, including the copper lid where alpha particles originate, the silicon chip, and a thin aluminum sensor layer. Alpha particles were emitted isotropically from just beneath the copper lid’s surface, mimicking natural decay conditions. The simulation tracked how these particles deposit energy on the chip, generating electron-hole pairs and phonons. The results provide insight into the behavior of the resultant electron-hole pairs and phonons, giving us a clear understanding of the energy deposition distribution on the chip. This work supports efforts to mitigate background noise in superconducting sensors, advancing their use in quantum computing and sensitive physics experiments.

Hall, Matthew [Fermilab; UCLA]↗
DOE OSTI2020

Polarimetric Radar Characteristics of Simulated and Observed Intense Convective Cores for a Midlatitude Continental and Tropical Maritime Environment

This study contrasts midlatitude continental and tropical maritime deep convective cores using polarimetric radar observables and retrievals from selected deep convection episodes during the MC3E and TWPICE field campaigns. The continental convective cores produce stronger radar reflectivities throughout the profiles, while maritime convective cores produce more positive differential reflectivity Z dr and larger specific differential phase K dp above the melting level. Hydrometeor identification retrievals revealed the presence of large fractions of rimed ice particles (snow aggregates) in the continental (maritime) convective cores, consistent with the Z dr and K dp observations. The regional cloud-resolving model simulations with bulk and size-resolved bin microphysics are conducted for the selected cases, and the simulation outputs are converted into polarimetric radar signals and retrievals identical to the observational composites. Both the bulk and the bin microphysics reproduce realistic land and ocean (L-O) contrasts in reflectivity, polarimetric variables of rain drops, and hydrometeor profiles, but there are still large uncertainties in describing Z dr and K dp of ice crystals associated with the ice particle shapes/orientation assumptions. Sensitivity experiments are conducted by swapping background aerosols between the continental and maritime environments, revealing that background aerosols play a role in shaping the distinct L-O contrasts in radar reflectivity associated with raindrop sizes, in addition to the dominant role of background thermodynamics.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

An energy-based coupling approach to nonlocal interface problems.

Nonlocal models provide accurate representations of physical phenomena ranging from fracture mechanics to complex subsurface flows, settings in which traditional partial differential equation models fail to capture effects caused by long-range forces at the microscale and mesoscale. However, the application of nonlocal models to problems involving interfaces, such as multimaterial simulations and fluid-structure interaction, is hampered by the lack of a physically consistent interface theory which is needed to support numerical developments and, among other features, reduces to classical models in the limit as the extent of nonlocal interactions vanish. In this paper, we use an energy-based approach to develop a formulation of a nonlocal interface problem which provides a physically consistent extension of the classical perfect interface formulation for partial differential equations. Numerical examples in one and two dimensions validate the proposed framework and demonstrate the scope of our theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗