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At least 811 records · Page 45

Mapping the Gas Turbulence in the Coma Cluster: Predictions for Astro-H

Astro-H will be able for the first time to map gas velocities and detect turbulence in galaxy clusters. One of the best targets for turbulence studies is the Coma cluster, due to its proximity, absence of a cool core, and lack of a central active galactic nucleus. To determine what constraints Astro-H will be able to place on the Coma velocity field, we construct simulated maps of the projected gas velocity and compute the second-order structure function, an analog of the velocity power spectrum. We vary the injection scale, dissipation scale, slope, and normalization of the turbulent power spectrum, and apply measurement errors and finite sampling to the velocity field. We find that even with sparse coverage of the cluster, Astro-H will be able to measure the Mach number and the injection scale of the turbulent power spectrum-the quantities determining the energy flux down the turbulent cascade and the diffusion rate for everything that is advected by the gas (metals, cosmic rays, etc.). Astro-H will not be sensitive to the dissipation scale or the slope of the power spectrum in its inertial range, unless they are outside physically motivated intervals. We give the expected confidence intervals for the injection scale and the normalization of the power spectrum for a number of possible pointing configurations, combining the structure function and velocity dispersion data. Importantly, we also determine that measurement errors on the line shift will bias the velocity structure function upward, and show how to correct this bias.

clusters: intracluster medium↗

EMAPS: An Efficient Multiscale Approach to Plasma Systems with Non-MHD Scale Effects

Using Discrete-Event Simulation (DES) as a novel paradigm for time integration of large-scale physics-driven systems, we have achieved significant breakthroughs in simulations of multi-dimensional magnetized plasmas where ion kinetic and finite Larmor radius (FLR) and Hall effects play a crucial role. For these purposes we apply a unique asynchronous simulation tool: a parallel, electromagnetic Particle-in-Cell (PIC) code, HYPERS (Hybrid Particle Event-Resolved Simulator), which treats plasma electrons as a charge neutralizing fluid and solves a self-consistent set of non-radiative Maxwell, electron fluid equations and ion particle equations on a structured computational grid. HYPERS enables adaptive local time steps for particles, fluid elements and electromagnetic fields. This ensures robustness (stability) and efficiency (speed) of highly dynamic and nonlinear simulations of compact plasma systems such spheromaks, FRCs, ion beams and edge plasmas. HYPERS is a unique asynchronous code that has been designed to serve as a test bed for developing multi-physics applications not only for laboratory plasma devices but generally across a number of plasma physics fields, including astrophysics, space physics and electronic devices. We have made significant improvements to the HYPERS core: (1) implemented a new asynchronous magnetic field integration scheme that preserves local divB=0 to within round-off errors; (2) Improved staggered-grid discretizations of electric and magnetic fields. These modifications have significantly enhanced the accuracy and robustness of 3D simulations. We have conducted first-ever end-to-end 3D simulations of merging spheromak plasmas. The preliminary results show: (1) tilt-driven relaxation of a freely expanding spheromak to an m=1 Taylor helix configuration and (2) possibility of formation of a tilt-stable field-reversed configuration via merging and magnetic reconnection of two double-sided spheromaks with opposite helicities.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Study of an electrodynamic system consisting of a laser cavity and an external weakly reflecting element

The behaviour of the electromagnetic field in a three-mirror laser cavity is described using the method of integral equations. The results of numerical calculations and experimental studies for particular examples implementing the considered configuration are presented. The conditions for optimal tuning of a laser interferometer-deformograph with a three-mirror cavity are determined. The contribution of the reflected and scattered light and arising additional seismic noises to the resulting error of laser gravitational wave detectors is studied. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Ambient and Cryogenic Alignment Verification and Performance of the Infrared Multi-Object Spectrometer

The Infrared Multi-Object Spectrometer (IRMOS) is a facility instrument for the Kitt Peak National Observatory 4 and 2.1 meter telescopes. IRMOS is a near-IR (0.8 - 2.5 micron) spectrometer with low- to mid-resolving power (R = 300 - 3000). IRMOS produces simultaneous spectra of approximately 100 objects in its 2.8 x 2.0 arc-min field of view using a commercial Micro Electro-Mechanical Systems (MEMS) Digital Micro-mirror Device (DMD) from Texas Instruments. The IRMOS optical design consists of two imaging subsystems. The focal reducer images the focal plane of the telescope onto the DMD field stop, and the spectrograph images the DMD onto the detector. We describe ambient breadboard subsystem alignment and imaging performance of each stage independently, and the ambient and cryogenic imaging performance of the fully assembled instrument. Interferometric measurements of subsystem wavefront error serve to venfy alignment, and are accomplished using a commercial, modified Twyman-Green laser unequal path interferometer. Image testing provides further verification of the optomechanical alignment method and a measurement of near-angle scattered light due to mirror small-scale surface error. Image testing is performed at multiple field points. A mercury-argon pencil lamp provides spectral lines at 546.1 nm and 1550 nm, and a CCD camera and IR camera are used as detectors. We use commercial optical modeling software to predict the point-spread function and its effect on instrument slit transmission and resolution. Our breadboard test results validate this prediction. We conclude with an instrument performance prediction for first light.

Connelly, Joseph A.↗

Superselection rules, quantum error correction, and quantum chromodynamics

We investigate the relationship between superselection rules and quantum error correcting codes. We demonstrate that the existence of a superselection rule implies the Knill-Laflamme condition in quantum error correction. As an example, we examine the code built from quantum chromodynamics, where the proton and neutron states in the model are explored as different superselection sectors that protect logical information. Finally we comment on topological quantum error correcting codes and supersymmetric quantum field theory within this framework.

97 MATHEMATICS AND COMPUTING↗

Finite grid instability and spectral fidelity of the electrostatic Particle-In-Cell algorithm

The origin of the Finite Grid Instability (FGI) is studied by resolving the dynamics in the 1D electrostatic Particle-In-Cell (PIC) model in the spectral domain at the single particle level and at the collective motion level. The spectral fidelity of the PIC model is contrasted with the underlying physical system or the gridless model. The systematic spectral phase and amplitude errors from the charge deposition and field interpolation are quantified for common particle shapes used in the PIC models. Lastly, it is shown through such analysis and in simulations that the lack of spectral fidelity relative to the physical system due to the existence of aliased spatial modes is the major cause of the FGI in the PIC model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The impact of capillary heterogeneity on CO 2 flow and trapping across scales

Capillary heterogeneity has been identified over the last decade as a key control on subsurface CO 2 flow behavior during geological CO 2 sequestration. These heterogeneities can be formed in all sedimentary rocks, ranging from slight variations in the sand grain sizes to extensive sequences of interbedded sands, shales, and limestones. Capillary heterogeneity has been largely, although not entirely, overlooked in subsurface flow modeling because it is assumed to only directly influence fluid redistribution over scales of centimeters to meters. However, even small-scale fluid movements can result in dramatic impacts on the mobility and trapping of the CO 2 over kilometers. Therefore, neglecting capillary heterogeneity at multiple scales could potentially lead to errors in modeling and predicting field-scale plume migration. In this review paper, we aim to provide a consistent overview to (1) establish that capillary heterogeneity can have a major impact on CO 2 plume migration, (2) establish the respective length scales at which capillary heterogeneity matters, and (3) provide guidance for numerical modeling. This review covers pertinent literature and extracts key observations from the core to the field scales. Experimental studies have shown that millimeter-decimeter scale capillary heterogeneity can cause the so-called capillary heterogeneity trapping in addition to pore-scale residual trapping. Even at such a small scale, capillary heterogeneity can already lead to complex upscaled constitutive relationships, such as flow-rate dependent and anisotropic relative permeability, which affects field-scale CO 2 migration even when field-scale heterogeneities are present. Under gravity-dominated flow regimes, centimeter-meter scale capillary heterogeneity can entrap a significant amount of CO 2 at field scale, not just after imbibition but also during drainage. In certain cases, the presence of capillary heterogeneity can even completely stop the vertical movement of the CO 2 plume, hence greatly reducing leakage risks. At meter-kilometer scale, the influence of capillary heterogeneity is more pronounced and can hinder or redirect CO 2 migration in both lateral and vertical directions. The impact of capillary heterogeneity across multiple spatial scales poses a great challenge in modeling CO 2 migration at field scale, because it is practically impossible to build a field-scale earth model with grid blocks at millimeter scale. We recommend a hierarchical modeling approach to address this challenge. At field scale, earth models are built to capture geological features and heterogeneities in high but still practical grid resolutions. For each facies or rock type of the field-scale model, high- resolution meter-scale “conceptual” models are built with millimeter-scale grid blocks to capture representative fine-scale bedding geometries and heterogeneities in various environments of deposition, bridging the gap from subcore scale to the size of a field-scale simulation grid block. Upscaling is then used to preserve the smaller-scale flow dynamics of various rock types in field-scale simulations. Here, future work is needed to (1) refine, improve, and validate the hierarchical modeling approach; (2) build libraries of fine-scale bedding models for facies in various environments of deposition; (3) quantify multiscale capillary heterogeneity effects under subsurface uncertainties; (4) gain learning from different storage formations; and (5) establish best practices that balance accuracy and computational speed.

Capillary heterogeneity↗

Scaling open-weight large language models for hydropower regulatory information extraction: A systematic analysis

Information extraction from regulatory and technical documents using large language models (LLMs) involves practical trade-offs between extraction quality and computational cost. We evaluate eight open-weight LLMs spanning 0.6B–70B parameters on hydropower licensing documents and report deployment-oriented evidence under a unified extraction schema and evaluation protocol. Across the model set, we observe clear scale-dependent trends in both baseline extraction quality and the effectiveness of reflective reasoning (self-checking) under our fixed-prompt, no-augmentation setting. Mid-scale models often provide a favorable balance of accuracy and efficiency, whereas the smallest models show limited or inconsistent gains from the reasoning variants tested. Larger models achieve the highest overall F1 scores but incur substantially greater compute and infrastructure requirements. We further find that reliability failure modes can distort conventional metrics in this domain: in particular, high recall can coincide with systematic extraction errors when models fabricate values for fields that are absent from the source text, underscoring the importance of conservative null handling and evidence-grounded evaluation. Overall, our study provides a reproducible resource–performance comparison for open-weight LLM-based extraction in hydropower regulatory documentation and offers practical guidance for model selection under different deployment constraints.

Evaluation protocol↗

Lens models and magnification maps of the six Hubble Frontier Fields clusters

We present strong-lensing models as well as mass and magnification maps for the cores of the six Hubble Space Telescope (HST) Frontier Fields galaxy clusters. Our parametric lens models are constrained by the locations and redshifts of multiple image systems of lensed background galaxies. We use a combination of photometric redshifts and spectroscopic redshifts of the lensed background sources obtained by us (for A2744 and AS1063), collected from the literature, or kindly provided by the lensing community. Using our results, we (1) compare the derived mass distribution of each cluster to its light distribution, (2) quantify the cumulative magnification power of the HST Frontier Fields clusters, (3) describe how our models can be used to estimate the magnification and image multiplicity of lensed background sources at all redshifts and at any position within the cluster cores, and (4) discuss systematic effects and caveats resulting from our modeling methods. We specifically investigate the effect of the use of spectroscopic and photometric redshift constraints on the uncertainties of the resulting models. We find that the photometric redshift estimates of lensed galaxies are generally in excellent agreement with spectroscopic redshifts, where available. However, the flexibility associated with relaxed redshift priors may cause the complexity of large-scale structure that is needed to account for the lensing signal to be underestimated. Our findings thus underline the importance of spectroscopic arc redshifts, or tight photometric redshift constraints, for high precision lens models. All products from our best-fit lens models (magnification, convergence, shear, deflection field) and model simulations for estimating errors are made available via the Mikulski Archive for Space Telescopes.

79 ASTRONOMY AND ASTROPHYSICS↗

On the estimation of gravitational wave spectrum from cosmic domain walls

We revisit the production of gravitational waves from unstable domain walls analyzing their spectrum by the use of field theoretic lattice simulations with grid size 1024{sup 3}, which is larger than the previous study. We have recognized that there exists an error in the code used in the previous study, and the correction of the error leads to the suppression of the spectrum of gravitational waves at high frequencies. The peak of the spectrum is located at the scale corresponding to the Hubble radius at the time of the decay of domain walls, and its amplitude is consistent with the naive estimation based on the quadrupole formula. Using the numerical results, the magnitude and the peak frequency of gravitational waves at the present time are estimated. It is shown that for some choices of parameters the signal of gravitational waves is strong enough to be probed in the future gravitational wave experiments.

79 ASTRONOMY AND ASTROPHYSICS↗

Tensor-decomposition techniques for ab initio nuclear structure calculations: From chiral nuclear potentials to ground-state energies

The computational resources needed to generate the ab initio solution of the nuclear many-body problem for increasing mass number and/or accuracy necessitates innovative developments to improve upon (i) the storage of many-body operators and (ii) the scaling of many-body methods used to evaluate nuclear observables. The storing and efficient handling of many-body operators with high particle ranks is currently one of the major bottlenecks limiting the applicability range of ab initio studies with respect to mass number and accuracy. Recently, the application of tensor decomposition techniques to many-body tensors has proven highly beneficial to reduce the computational cost of ab initio calculations in quantum chemistry and solid-state physics. The impact of applying state-of-the-art tensor factorization techniques to modern nuclear Hamiltonians derived from chiral effective field theory is investigated. Subsequently, the error induced by the tensor decomposition of the input Hamiltonian on ground-state energies of closed-shell nuclei calculated via second-order many-body perturbation theory is benchmarked. The first proof-of-principles application of tensor-decomposition techniques to the nuclear Hamiltonian is performed. Two different tensor formats are investigated by systematically benchmarking the approximation error on matrix elements stored in various bases of interest. The analysis is achieved while including normal-ordered three-nucleon interactions that are nowadays used as input to the most advanced ab initio calculations in medium-mass nuclei. With the aid of the factorized Hamiltonian, the second-order perturbative correction to ground-state energies is decomposed and the scaling properties of the underlying tensor network are discussed. The employed tensor formats are found to lead to an efficient data compression of two-body matrix elements of the nuclear Hamiltonian. In particular, the sophisticated tensor hypercontraction scheme yields low tensor ranks with respect to both harmonic-oscillator and Hartree-Fock single-particle bases. It is found that the tensor rank depends on the two-body total angular momentum J for which one performs the decomposition, which is itself directly related to the sparsity of the corresponding tensor. Furthermore, including normal-ordered two-body contributions originating from three-body interactions does not compromise the efficient data compression. Ultimately, the use of factorized matrix elements authorizes controlled approximations of the exact second-order ground-state energy corrections. In particular, a small enough error is obtained from low-rank factorizations in He4,O16, and Ca40. It is presently demonstrated that tensor-decomposition techniques can be efficiently applied to systematically approximate the nuclear many-body Hamiltonian in terms of lower-rank tensors. Beyond the input Hamiltonian, tensor-decomposition techniques can be envisioned to scale down the cost of state-of-the-art nonperturbative many-body methods in order to extend ab initio studies to (i) higher precisions, (ii) larger masses, and (iii) nuclei of doubly open-shell character.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A General Framework for Progressive Data Compression and Retrieval

In scientific simulations, observations, and experiments, the transfer of data to and from disk and across networks has become a major bottleneck for data analysis and visualization. Compression techniques have been employed to tackle this challenge, but traditional lossy methods often demand conservative error tolerances to meet the numerical accuracy requirements of both anticipated and unknown data analysis tasks. Progressive data compression and retrieval has emerged as a promising solution, where each analysis task dictates its own accuracy needs. However, few analysis algorithms inherently support progressive data processing, and adapting compression techniques, file formats, client/server frameworks, and APIs to support progressivity can be challenging. Here, this paper presents a framework that enables progressive-precision data queries for any data compressor or numerical representation. Our strategy hinges on a multi-component representation that successively reduces the error between the original and compressed field, allowing each field in the progressive sequence to be expressed as a partial sum of components. We have implemented this approach with four established scientific data compressors and assessed its effectiveness using real-world data sets from the SDRBench collection. The results show that our framework competes in accuracy with the standalone compressors it is based upon. Additionally, (de)compression time is proportional to the number of components requested by the user. Finally, our framework allows for fully lossless compression using lossy compressors when a sufficient number of components are employed.

97 MATHEMATICS AND COMPUTING↗

WE-G-BRA-04: Common Errors and Deficiencies in Radiation Oncology Practice

Purpose: Dosimetric errors in radiotherapy dose delivery lead to suboptimal treatments and outcomes. This work reviews the frequency and severity of dosimetric and programmatic errors identified by on-site audits performed by the IROC Houston QA center. Methods: IROC Houston on-site audits evaluate absolute beam calibration, relative dosimetry data compared to the treatment planning system data, and processes such as machine QA. Audits conducted from 2000-present were abstracted for recommendations, including type of recommendation and magnitude of error when applicable. Dosimetric recommendations corresponded to absolute dose errors >3% and relative dosimetry errors >2%. On-site audits of 1020 accelerators at 409 institutions were reviewed. Results: A total of 1280 recommendations were made (average 3.1/institution). The most common recommendation was for inadequate QA procedures per TG-40 and/or TG-142 (82% of institutions) with the most commonly noted deficiency being x-ray and electron off-axis constancy versus gantry angle. Dosimetrically, the most common errors in relative dosimetry were in small-field output factors (59% of institutions), wedge factors (33% of institutions), off-axis factors (21% of institutions), and photon PDD (18% of institutions). Errors in calibration were also problematic: 20% of institutions had an error in electron beam calibration, 8% had an error in photon beam calibration, and 7% had an error in brachytherapy source calibration. Almost all types of data reviewed included errors up to 7% although 20 institutions had errors in excess of 10%, and 5 had errors in excess of 20%. The frequency of electron calibration errors decreased significantly with time, but all other errors show non-significant changes. Conclusion: There are many common and often serious errors made during the establishment and maintenance of a radiotherapy program that can be identified through independent peer review. Physicists should be cautious, particularly in areas highlighted herein that show a tendency for errors.

60 APPLIED LIFE SCIENCES↗

SU-F-T-540: Comprehensive Fluence Delivery Optimization with Multileaf Collimation

Purpose: Multileaf collimator (MLC) leaf sequencing is performed via commercial black-box implementations, on which a user has limited to no access. We have developed an explicit, generic MLC sequencing model to serve as a tool for future investigations of fluence map optimization, fluence delivery optimization, and rotational collimator delivery methods. Methods: We have developed a novel, comprehensive model to effectively account for a variety of transmission and penumbra effects previously treated on an ad hoc basis in the literature. As the model is capable of quantifying a variety of effects, we utilize the asymmetric leakage intensity across each leaf to deliver fluence maps with pixel size smaller than the narrowest leaf width. Developed using linear programming and mixed integer programming formulations, the model is implemented using state of the art open-source solvers. To demonstrate the versatility of the algorithm, a graphical user interface (GUI) was developed in MATLAB capable of accepting custom leaf specifications and transmission parameters. As a preliminary proof-ofconcept, we have sequenced the leaves of a Varian 120 Leaf Millennium MLC for five prostate cancer patient fields and one head and neck field. Predetermined fluence maps have been processed by data smoothing methods to obtain pixel sizes of 2.5 cm{sup 2}. The quality of output was analyzed using computer simulations. Results: For the prostate fields, an average root mean squared error (RMSE) of 0.82 and gamma (0.5mm/0.5%) of 91.4% were observed compared to RMSE and gamma (0.5mm/0.5%) values of 7.04 and 34.0% when the leakage considerations were omitted. Similar results were observed for the head and neck case. Conclusion: A model to sequence MLC leaves to optimality has been proposed. Future work will involve extensive testing and evaluation of the method on clinical MLCs and comparison with black-box leaf sequencing algorithms currently used by commercial treatment planning systems.

60 APPLIED LIFE SCIENCES↗

Spatially Local Surrogate Modeling of Subgrid-Scale Effects in Idealized Atmospheric Flows: A Deep Learned Approach Using High-Resolution Simulation Data

Abstract We introduce a machine learned surrogate model from high-resolution simulation data to capture the subgrid-scale effects in dry, stratified atmospheric flows. We use deep neural networks (NNs) to model the spatially local state differences between a coarse-resolution simulation and a high-resolution simulation. The setup enables the capture of both dissipative and antidissipative effects in the state differences. The NN model is able to accurately capture the state differences in offline tests outside the training regime. In online tests intended for production use, the NN-coupled coarse simulation has higher accuracy over a significant period of time compared to the coarse-resolution simulation without any correction. We provide evidence of the capability of the NN model to accurately capture high-gradient regions in the flow field. With the accumulation of the errors, the NN-coupled simulation becomes computationally unstable after approximately 90 coarse simulation time steps. Insights gained from these surrogate models further pave the way for formulating stable, complex, physics-based spatially local NN models which are driven by traditional subgrid-scale turbulence closure models. Significance Statement Flows in the atmosphere are highly chaotic and turbulent, comprising flow structures of broad scales. For effective computational modeling of atmospheric flows, the effects of the small- and large-scale structures need to be captured by the simulations. Capturing the small-scale structures requires fine-resolution simulations. Even with the current state-of-the-art supercomputers, it can be prohibitively expensive to simulate these flows when computed for the entire earth over climate time scales. Thus, it is necessary to focus on the larger-scale structures using a coarse-resolution simulation while capturing the effects of the smaller-scale structures using some parameterization (approximation) scheme and incorporating it into the coarse-resolution simulation. We use machine learning to model the effects of the small-scale structures (subgrid-scale effects) in atmospheric flows. Data from a fine-resolution simulation is used to compute the missing subgrid-scale effects in coarse-resolution simulations. We then use machine learning models to approximate these differences between the coarse- and fine-resolution simulations. We see improved accuracy for the coarse-resolution simulations when corrected using these machine learned models.

54 ENVIRONMENTAL SCIENCES↗

Deep-ultraviolet ptychographic pocket-scope (DART): mesoscale lensless molecular imaging with label-free spectroscopic contrast

The mesoscale characterization of biological specimens has traditionally required compromises between resolution, field-of-view, depth-of-field, and molecular specificity, with most approaches relying on external labels. Here we present the Deep-ultrAviolet ptychogRaphic pockeT-scope (DART), a handheld platform that transforms label-free molecular imaging through intrinsic deep-ultraviolet spectroscopic contrast. By leveraging biomolecules’ natural absorption fingerprints and combining them with lensless ptychographic microscopy, DART resolves down to 308-nm linewidths across centimeter-scale areas while maintaining millimeter-scale depth-of-field. The system’s virtual error-bin methodology effectively eliminates artifacts from limited temporal coherence and other optical imperfections, enabling high-fidelity molecular imaging without lenses. Through differential spectroscopic imaging at deep-ultraviolet wavelengths, DART quantitatively maps nucleic acid and protein distributions with femtogram sensitivity, providing an intrinsic basis for explainable virtual staining. We demonstrate DART’s capabilities through imaging of tissue sections, cytopathology specimens, blood cells, and neural populations, revealing detailed molecular contrast without external labels. The combination of high-resolution molecular mapping and broad mesoscale imaging in a portable platform opens new possibilities from rapid clinical diagnostics, tissue analysis, to biological characterization in space exploration.

60 APPLIED LIFE SCIENCES↗

Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media

This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative L2 errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state).

German, Péter (ORCID:0000000307285283)↗