3D Parameter Space Research Articles

A Framework for Assessing Ocean Mixed Layer Depth Evolution

AbstractThe ocean surface mixed layer plays a crucial role as an entry or exit point for heat, salt, momentum, and nutrients from the surface to the deep ocean. In this study, we introduce a framework to assess the evolution of the mixed layer depth (MLD) for realistic forcings and preconditioning conditions. Our approach involves a physically‐based parameter space defined by three dimensionless numbers: λs representing the relative contribution of the buoyancy flux and the wind stress at the air‐sea interface, Rh the Richardson number which characterizes the stability of the water column relative to the wind shear, and f/Nh which characterizes the importance of the Earth's rotation (ratio of the Coriolis frequency f and the pycnocline stratification Nh). Four MLD evolution regimes (“restratification,” “stable,” “deepening,” and “strong deepening”) are defined based on the values of the normalized temporal evolution of the MLD. We evaluate the 3D parameter space in the context of 1D simulations and we find that considering only the two dimensions (λs, Rh) is the best choice of 2D projection of this 3D parameter space. We then demonstrate the utility of this two‐dimensional λs − Rh parameter space to compare 3D realistic ocean simulations: we discuss the impact of the horizontal resolution (1°, 1/12°, or 1/60°) and the Gent‐McWilliams parameterization on MLD evolution regimes. Finally, a proof of concept of using observational data as a truth indicates how the parameter space could be used for model calibration.

Void drift in narrow rectangular channels for highly advective bubbly flows: A macroscopic drift-flux model derived from two-fluid local simulations

This article addresses the issue of reduced models to describe turbulent two-phase flows in industrial applications. This work is an application based on Bois (2021) theoretical derivations to connect the spatially-averaged drift-flux model (DFM) to the local Reynolds-averaged two-fluid model (TFM). It presents new opportunities to calibrate closure laws or propose new models based on finer-scale descriptions. Highly convective steady bubbly flows with wall-peaking void fraction profiles are considered. Dispersed bubbles are weakly deformable. A new model dedicated to void fraction dispersion in flat rectangular channels is developed for application into the DFM. The model is calibrated based on reference local Euler-Euler two-fluid simulations of pressurised water and steam mono-dispersed bubbles, in adiabatic conditions. 64 conditions are considered to cover regularly the 3D parameter space in void fraction, Reynolds and Eötvös numbers. The new formulation proposed shows a very good fit with the post-processed predictions of local CFD simulations along with a substantial reduction in grid requirement. The model contains sub-filter correlations between vapour concentration and mixture or relative velocities. This model derived from local simulations is validated a posteriori in an industrial component scale code where the full space-filtered DFM is implemented and resolved. This work proves the benefits and feasibility of one-by-one model development and calibration based on two-fluid simulations.

2D Embeddings of Multi-dimensional Partitionings.

Partitionings (or segmentations) divide a given domain into disjoint connected regions whose union forms again the entire domain. Multi-dimensional partitionings occur, for example, when analyzing parameter spaces of simulation models, where each segment of the partitioning represents a region of similar model behavior. Having computed a partitioning, one is commonly interested in understanding how large the segments are and which segments lie next to each other. While visual representations of 2D domain partitionings that reveal sizes and neighborhoods are straightforward, this is no longer the case when considering multi-dimensional domains of three or more dimensions. We propose an algorithm for computing 2D embeddings of multi-dimensional partitionings. The embedding shall have the following properties: It shall maintain the topology of the partitioning and optimize the area sizes and joint boundary lengths of the embedded segments to match the respective sizes and lengths in the multi-dimensional domain. We demonstrate the effectiveness of our approach by applying it to different use cases, including the visual exploration of 3D spatial domain segmentations and multi-dimensional parameter space partitionings of simulation ensembles. We numerically evaluate our algorithm with respect to how well sizes and lengths are preserved depending on the dimensionality of the domain and the number of segments.

RLC resonator with diode nonlinearity: Bifurcation comparison of numerical predictions and circuit measurements

A nonlinear RLC resonator is investigated experimentally and numerically using bifurcation analysis. The nonlinearity is due to the parallel combination of a semiconductor rectifier diode and a fixed capacitor. The diode’s junction capacitance, diffusion capacitance, and DC current–voltage relation each contribute to the nonlinearity. The closely related RL-diode resonator has been of interest for many years since its demonstration of period-doubling cascades to chaos. In this study, a direct comparison is made of dynamical regime maps produced from simulations and circuit measurements. The maps show the variety of limit cycles, their bifurcations, and regions of chaos over the 2D parameter space of the source voltage’s frequency and amplitude. The similar structures of the simulated and experimental maps suggest that the diode models commonly used in circuit simulators (e.g., SPICE) work well in bifurcation analyses, successfully predicting complex and chaotic dynamics detected in the circuit. These results may be useful for applications of varactor-loaded split ring resonators.

Symmetry-induced higher-order exceptional points in two dimensions

Exceptional points of order n (EPns) appear in non-Hermitian systems as points where the eigenvalues and eigenvectors coalesce. They emerge if 2(n−1) real constraints are imposed, such that EP2s generically appear in two dimensions (2D). Local symmetries have been shown to reduce this number of constraints. In this work, we provide a complete characterization of the appearance of symmetry-induced higher-order EPs in 2D parameter space. We find that besides EP2s only EP3s, EP4s, and EP5s can be stabilized in 2D. Moreover, these higher-order EPs must always appear in pairs with their dispersion determined by the symmetries. Upon studying the complex spectral structure around these EPs, we find that depending on the symmetry, EP3s are accompanied by EP2 arcs, and two- and three-level open Fermi structures. Similarly, EP4s and closely related EP5s, which arise due to multiple symmetries, are accompanied by exotic EP arcs and open Fermi structures. For each case, we provide an explicit example. We also comment on the topological charge of these EPs, and discuss similarities and differences between symmetry-protected higher-order EPs and EP2s. Published by the American Physical Society 2024

Adaptive design of experiments to fit surrogate Gaussian process regression models allows fast sensitivity analysis of the input waveform for patient-specific 3D CFD models of liver radioembolization

Background and objectivePatient-specific 3D computational fluid dynamics (CFD) models are increasingly being used to understand and predict transarterial radioembolization procedures used for hepatocellular carcinoma treatment. While sensitivity analyses of these CFD models can help to determine the most impactful input parameters, such analyses are computationally costly. Therefore, we aim to use surrogate modelling to allow relatively cheap sensitivity analysis. As an example, we compute Sobol's sensitivity indices for three input waveform shape parameters. MethodsWe extracted three characteristic shape parameters from our input mass flow rate waveform (peak systolic mass flow rate, heart rate, systolic duration) and defined our 3D input parameter space by varying these parameters within 75 %-125 % of their nominal values. To fit our surrogate model with a minimal number of costly CFD simulations, we developed an adaptive design of experiments (ADOE) algorithm. The ADOE uses 100 Latin hypercube sampled points in 3D input space to define the initial design of experiments (DOE). Subsequently, we re-sample input space with 10,000 Latin Hypercube sampled points and cheaply estimate the outputs using the surrogate model. In each of 27 equivolume bins which divide our input space, we determine the most uncertain prediction of the 10,000 points, compute the true outputs using CFD, and add these points to the DOE. For each ADOE iteration, we calculate Sobol's sensitivity indices, and we continue to add batches of 27 samples to the DOE until the Sobol indices have stabilized. ResultsWe tested our ADOE algorithm on the Ishigami function and showed that we can reliably obtain Sobol's indices with an absolute error <0.1. Applying ADOE to our waveform sensitivity problem, we found that the first-order sensitivity indices were 0.0550, 0.0191 and 0.407 for the peak systolic mass flow rate, heart rate, and the systolic duration, respectively. ConclusionsAlthough the current study was an illustrative case, the ADOE allows reliable sensitivity analysis with a limited number of complex model evaluations, and performs well even when the optimal DOE size is a priori unknown. This enables us to identify the highest-impact input parameters of our model, and other novel, costly models in the future.

CSST large-scale structure analysis pipeline: I. Constructing reference mock galaxy redshift surveys

ABSTRACT In this paper, we set out to construct a set of reference mock galaxy redshift surveys (MGRSs) for the future Chinese Space-station Survey Telescope (CSST) observation, where subsequent survey selection effects can be added and evaluated. This set of MGRSs is generated using the dark matter subhaloes extracted from a high-resolution Jiutian N-body simulation of the standard lambda-cold dark matter cosmogony with Ωm = 0.3111, ΩΛ = 0.6889, and σ8 = 0.8102. The simulation has a box size of 1 h−1Gpc, and consists of 61443 particles with mass resolution $3.723 \times 10^{8} \:h^{-1}\rm M_\odot$. In order to take into account the effect of redshift evolution, we first use all 128 snapshots in the Jiutian simulation to generate a light-cone halo/subhalo catalogue. Next, galaxy luminosities are assigned to the main and subhalo populations using the subhalo abundance matching (SHAM) method with the DESI (Dark Energy Spectroscopic Instrument) z-band luminosity functions at different redshifts. Multiband photometries, as well as images, are then assigned to each mock galaxy using a 3D parameter space nearest-neighbour sampling of the DESI LS (Legacy Imaging Survey) observational galaxies and groups. Finally, the CSST and DESI LS survey geometry and magnitude limit cuts are applied to generate the required MGRSs. As we have checked, this set of MGRSs can generally reproduce the observed galaxy luminosity/mass functions within 0.1 dex for galaxies with L &amp;gt; 108 h-2 L⊙ (or M* &amp;gt; 108.5 h-2M⊙) and within 1σ level for galaxies with L &amp;lt; 108 h-2 L⊙ (or M* &amp;lt; 108.5 h-2 M⊙). Together with the CSST slitless spectra and redshifts for our DESI LS seed galaxies that are under construction, we will set out to test various slitless observational selection effects in subsequent probes.

From Feast to Famine: A Systematic Study of Accretion onto Oblique Pulsars with 3D GRMHD Simulations

Disk-fed accretion onto neutron stars can power a wide range of astrophysical sources ranging from X-ray binaries, to accretion-powered millisecond pulsars, ultraluminous X-ray sources, and gamma-ray bursts. A crucial parameter controlling the gas–magnetosphere interaction is the strength of the stellar dipole. In addition, coherent X-ray pulsations in many neutron star systems indicate that the star's dipole moment is oblique relative to its rotation axis. Therefore, it is critical to systematically explore the 2D parameter space of the star's magnetic field strength and obliquity, which is what this work does, for the first time, in the framework of 3D general-relativistic magnetohydrodynamics. If the accretion disk carries its own vertical magnetic field, this introduces an additional factor: the relative polarity of the disk and stellar magnetic fields. We find that depending on the strength of the stellar dipole and the star–disk relative polarity, the neutron star's jet power can either increase or decrease with increasing obliquity. For weak dipole strength (equivalently, high accretion rate), the parallel polarity results in a positive correlation between jet power and obliquity, whereas the antiparallel orientation displays the opposite trend. For stronger dipoles, the relative-polarity effect disappears, and jet power always decreases with increasing obliquity. The influence of the relative polarity gradually disappears as obliquity increases. Highly oblique pulsars tend to have an increased magnetospheric radius, a lower mass accretion rate, and enter the propeller regime at lower magnetic moments than aligned stars.

Adaptive smoothing of retinotopic maps based on Teichmüller parametrization

Retinotopic mapping, the mapping between visual inputs on the retina and neural responses on the cortical surface, is one of the fundamental topics in visual neuroscience. In human studies, retinotopic maps are conventionally constructed and processed by decoding blood oxygenation-level dependent (BOLD) functional magnetic resonance imaging (fMRI) responses to designed visual stimuli on the cortical surface. However, these methods frequently generate retinotopic maps that do not preserve topology, contradicting a fundamental property of retinotopic maps observed in neurophysiology. To address this problem, we propose an integrated approach to simultaneously refine the flattening from the 3D cortical surface to the 2D parametric space and adaptively smooth retinotopic perception centers in the visual space to make the retinotopic maps topological. One key element of the approach is the enhanced error tolerant Teichmüller mapping, which refines the parametrization by minimizing angle distortions and maximizing alignment to noisy landmarks. We validated our overall approach with synthetic and real retinotopic mapping datasets and applied it to compute cortical magnification factor (CMF). The results showed that the proposed approach was superior to other conventional retinotopic mapping methods in predicting BOLD fMRI time series and preserving topology.

Topological Singularity Pair in Nonreciprocal Non-Hermitian Lossy-dielectric Gyromagnetic Metasurface

The transmission properties of a nonreciprocal non-Hermitian metasurface composed of lossy dielectric and gyromagnetic materials are studied with closed-form analytical solutions. It is found that a pair of opposite topological singularities of isolation ratio exist in a two-dimensional (2D) parameter space, and their evolution with parameter adjustment is preliminarily studied. These results provide clues for the design of optical devices. Further study of the mechanism of this singular behavior may reveal the complex systematic effect of non-Hermiticity and non-reciprocity on optical performance.

The e-MANTIS emulator: fast predictions of the non-linear matter power spectrum in f(R)CDM cosmology

ABSTRACT In order to probe modifications of gravity at cosmological scales, one needs accurate theoretical predictions. N-body simulations are required to explore the non-linear regime of structure formation but are very time consuming. In this work, we release a new public emulator, dubbed e-mantis, that performs an accurate and fast interpolation between the predictions of f(R) modified gravity cosmological simulations, run with ecosmog. We sample a wide 3D parameter space given by the current background scalar field value $10^{-7}\lt \left|f_{R_0}\right|\lt 10^{-4}$, matter density 0.24 &amp;lt; Ωm &amp;lt; 0.39, and primordial power spectrum normalization 0.6 &amp;lt; σ8 &amp;lt; 1.0, with 110 points sampled from a Latin hypercube. For each model we perform pairs of f(R)CDM and ΛCDM simulations covering an effective volume of $\left(560 \, h^{-1}\, \mathrm{Mpc}\right)^3$ with a mass resolution of ∼2 × 1010h−1M⊙. We build an emulator for the matter power spectrum boost B(k) = Pf(R)(k)/PΛCDM(k) using a Gaussian process regression method. The boost is mostly independent of h, ns, and Ωb, which reduces the dimensionality of the relevant cosmological parameter space. Additionally, it is more robust against statistical and systematic errors than the raw power spectrum, thus strongly reducing our computational needs. According to our dedicated study of numerical systematics, the resulting emulator has an estimated maximum error of 3 per cent across the whole cosmological parameter space, for scales $0.03 \ h\, \mathrm{Mpc}^{-1} \lt k \lt 7 \ h\, \mathrm{Mpc}^{-1}$, and redshifts 0 &amp;lt; z &amp;lt; 2, while in most cases the accuracy is better than 1 per cent. Such an emulator could be used to constrain f(R) gravity with weak lensing analyses.

Codimension-2 Bifurcations in a Quantum Decision Making Model

We consider a discrete-time model of a population of agents participating in a minority game using a quantum cognition in an approach with binary choices. As the agents make decisions based on both their present and past states, the model is inherently two-dimensional, but can be reduced to a one-dimensional system governed by a bi-valued function. Through this reduction, we prove how the complex bifurcation structure in the model’s 2D parameter space can be explained by a few codimension-2 bifurcation points of a type not yet reported in the literature. These points act as organizing centers for period-adding structures that partially overlap, leading to bistability.

Segmentation of Brain Metastases Using Background Layer Statistics (BLAST).

Accurate segmentation of brain metastases is important for treatment planning and evaluating response. The aim of this study was to assess the performance of a semiautomated algorithm for brain metastases segmentation using Background Layer Statistics (BLAST). Nineteen patients with 48 parenchymal and dural brain metastases were included. Segmentation was performed by 4 neuroradiologists and 1 radiation oncologist. K-means clustering was used to identify normal gray and white matter (background layer) in a 2D parameter space of signal intensities from postcontrast T2 FLAIR and T1 MPRAGE sequences. The background layer was subtracted and operator-defined thresholds were applied in parameter space to segment brain metastases. The remaining voxels were back-projected to visualize segmentations in image space and evaluated by the operators. Segmentation performance was measured by calculating the Dice-Sørensen coefficient and Hausdorff distance using ground truth segmentations made by the investigators. Contours derived from the segmentations were evaluated for clinical acceptance using a 5-point Likert scale. The median Dice-Sørensen coefficient was 0.82 for all brain metastases and 0.9 for brain metastases of ≥10 mm. The median Hausdorff distance was 1.4 mm. Excellent interreader agreement for brain metastases volumes was found with an intraclass correlation coefficient = 0.9978. The median segmentation time was 2.8 minutes/metastasis. Forty-five contours (94%) had a Likert score of 4 or 5, indicating that the contours were acceptable for treatment, requiring no changes or minor edits. We show accurate and reproducible segmentation of brain metastases using BLAST and demonstrate its potential as a tool for radiation planning and evaluating treatment response.

Robust atomic states for quantum information with continuous variables

Using a set of Zeeman sublevels of an alkali atom such as rubidium or sodium, we propose to construct a pair of coherentc population trap (CPT) states, which can be individually addressed and populated at will. The system can be arranged such that there exists a dressed state that is a linear combination of these two CPT states. We have earlier shown the capability of forming discrete quantum gates using this configuration [J.Phys. B, (2006), 39, 3919]. In the present communication, we will show how the same configuration can be used to prepare and operate continuously varying states. The state can be mapped to a 2D parametric space in such a way that any desired vector within it can be prepared, and a continuous, adiabatic evolution from one vector to another is also possible. A method to exploit a continuous interaction potential, which can be used in quantum computation, is also suggested. We discuss how a continuous variable quantum computation can be performed using such states.

CAD-integrated stiffener sizing-topology design via force flow members (FFM)

Stiffener design plays a crucial role in the lightweight design of stiffened panels. We propose a CAD-integrated stiffener design approach for shells. The problem is partitioned into two steps: (1) generating clear force flow members (FFM) based on the direction of principal stress, and (2) introducing a nodal variable-based sizing-topology optimization for further lightweight design enhancement. Specifically, we generate dense principal stress trajectory families using the iterative tracing technique, and extract FFM through hierarchical clustering. Generating high-precision principal stress trajectories on free-form surfaces is a challenging task. Our method differs from previous approaches in that we employ tensor transformations to convert principal stress directions from the 3D physical space into the 2D parameter space. We then create NURBS curve-based FFM in the 2D parameter space. The NURBS-based free-form deformations (NFFD) technique is utilized to map FFM from the 2D parameter space to the 3D physical space, ensuring FFMs are precise and watertight constructions of geometries. We propose a nodal variable-based sizing-topology method for the lightweight design of FFM. The heights of FFM control points are designated as design variables. Steadily eliminating pseudo-heights is achieved by using the Sigmoid function to penalize the design variables. Moreover, we introduce an NFFD-based isogeometric analysis method for stiffened panels modeled by NFFD-based FFM to realize the integration of design and analysis. The effectiveness and robustness of the presented method are demonstrated through various benchmarks and examples with industrial backgrounds. The proposed optimization framework exhibits strong application potential in the lightweight design of stiffened panels.

Visualization of simulated coating efficiency and uniformity.

For a line-of-sight coating uniformity model, the source distribution is normalized such that all material can be traced. This is validated for a point source in an empty coating chamber. We can now quantify the source utilization of a coating geometry to determine what fraction of the evaporated source material is collected on the optics of interest. For the example of a planetary motion system, we calculate this utilization and two nonuniformity parameters for a large range of two input parameters, here the distance between the source and the rotary drive system and the lateral displacement of the source from the machine centerline. Contour plot visualizations in this 2D parameter space assist understanding geometry trade-offs.

Tensor network investigation of the hard-square model

Using the corner-transfer matrix renormalization group to contract the tensor network that describes its partition function, we investigate the nature of the phase transitions of the hard-square model, one of the exactly solved models of statistical physics for which Baxter has found an integrable manifold. The motivation is twofold: assess the power of tensor networks for such models, and probe the 2D classical analog of a 1D quantum model of hard-core bosons that has recently attracted significant attention in the context of experiments on chains of Rydberg atoms. Accordingly, we concentrate on two planes in the 3D parameter space spanned by the activity and the coupling constants in the two diagonal directions. We first investigate the only case studied so far with Monte Carlo simulations, the case of opposite coupling constants. We confirm that, away and not too far from the integrable 3-state Potts point, the transition out of the period-3 phase appears to be unique in the Huse-Fisher chiral universality class, albeit with significantly different exponents as compared to Monte Carlo. We also identify two additional phase transitions not reported so far for that model, a Lifshitz disorder line, and an Ising transition for large enough activity. To make contact with 1D quantum models of Rydberg atoms, we then turn to a plane where the ferromagnetic coupling is kept fixed, and we show that the resulting phase diagram is very similar, the only difference being that the Ising transition becomes first-order through a tricritical Ising point, in agreement with Baxter's prediction that this plane should contain a tricritical Ising point, and in remarkable, almost quantitative agreement with the phase diagram of the 1D quantum version of the model.

Model order reduction by radial basis function network for sparse reconstruction of an industrial natural gas boiler

The radial basis function network (RBFN) is compared with gappy interpolation for sparse reconstruction of a reduced order model (ROM) for an industrial natural gas boiler. It is a non-intrusive method based on proper orthogonal decomposition (POD) and sensor measurements substituted by full order model (FOM) results at specified locations. The FOM was formed by steady-state computational fluid dynamic simulation at training and validation points selected by Latin hypercube and adaptive sampling in the 2D parameter space. Parametric study was performed for a varying number of sensors located on the boiler walls as a realistic measurement option. The optimal numbers of training samples and truncated eigenmodes were determined according to the relative L 2 norm error between FOM and ROM by the truncated eigenmodes. Results showed RBFN outperforming gappy interpolation with a lower relative L 2 norm error and less dependence on the number of sensors for both temperature and nitric oxide concentration fields. The RBFN may be a better choice for reconstruction of multidimensional scalar fields as a digital twin through fusion of simulation and online data for smart operation of complicated thermofluid facilities.

A new approach to feature-based asteroid taxonomy in 3D color space

The taxonomic classification of asteroids has been mostly based on spectroscopic observations with wavelengths spanning from the visible (VIS) to the near-infrared (NIR). VIS-NIR spectra of ~2500 asteroids have been obtained since the 1970s; the Sloan Digital Sky Survey (SDSS) Moving Object Catalog 4 (MOC 4) was released with ~4 × 105 measurements of asteroid positions and colors in the early 2000s. A number of works then devised methods to classify these data within the framework of existing taxonomic systems. Some of these works, however, used 2D parameter space (e.g., gri slope vs. z-i color) that displayed a continuous distribution of clouds of data points resulting in boundaries that were artificially defined. We introduce here a more advanced method to classify asteroids based on existing systems. This approach is simply represented by a triplet of SDSS colors. The distributions and memberships of each taxonomic type are determined by machine learning methods in the form of both unsupervised and semi-supervised learning. We apply our scheme to MOC 4 calibrated with VIS-NIR reflectance spectra. We successfully separate seven different taxonomy classifications (C, D, K, L, S, V, and X) with which we have a sufficient number of spectroscopic datasets. We found the overlapping regions of taxonomic types in a 2D plane were separated with relatively clear boundaries in the 3D space newly defined in this work. Our scheme explicitly discriminates between different taxonomic types (e.g., K and X types), which is an improvement over existing systems. This new method for taxonomic classification has a great deal of scalability for asteroid research, such as space weathering in the S-complex, and the origin and evolution of asteroid families. We present the structure of the asteroid belt, and describe the orbital distribution based on our newly assigned taxonomic classifications. It is also possible to extend the methods presented here to other photometric systems, such as the Johnson-Cousins and LSST filter systems.

Ensemble-based unsupervised machine learning method for membership determination of open clusters using Mahalanobis distance

ABSTRACT We present an improved method for the determination of membership of an open cluster using ensemble-based unsupervised machine learning techniques. The working principle of this method relies on two stages: (i) choosing a suitable range of three astrometric parameters (π, μαcos δ, μδ) using k-nearest neighbour (kNN) algorithm on the data downloaded for the cluster within a smaller search radius; (ii) application of two component Gaussian mixture modelling (GMM) on the resulting one dimensional Gaussian distribution of Mahalanobis distance (MD) of stars using the range of parameters obtained from the earlier step, but with the data downloaded within a bigger search radius. MD is calculated from the mean of each of the parameters in three dimensions. Thus the use of MD reduces the input of the GMM from the 3D parameter space into a 1D parameter space for the cluster membership determination. The method has been tested on a few clusters including those which have overlaps in some/all the parameters using the data obtained from the Gaia DR3 data base. It is found that the approach can easily separate the cluster members from the field stars. The clean colour-magnitude diagrams and similar direction of proper motions of the member stars obtained for the clusters shows that this method is very efficient and robust in segregating the cluster members from the field stars.