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DOE OSTI2022

Physics-Informed Sparse Gaussian Process for Probabilistic Stability Analysis of Large-Scale Power System with Dynamic PVs and Loads

This work proposes a physics-informed sparse Gaussian process (SGP) for probabilistic stability assessment of large-scale power systems in the presence of uncertain dynamic PVs and loads. The differential and algebraic equations considering uncertainties from dynamic PVs and loads are reformulated to a nonlinear mapping relationship that allows the application of SGP. Thanks to the nonparametric characteristic of Gaussian process, the proposed framework does not require distributions of uncertain inputs and this distinguishes it from existing approaches. As the original Gaussian process is not scalable to large-scale systems with high dimensional uncertain inputs, this paper develops the SGP with a stochastic variational inference technique. It leads to approximately two orders of complex reduction. A data pre-processing step is also introduced to tackle the coexistence of stable and unstable cases by sample clustering and constructing separate SGPs. The probabilistic transient stability index is analyzed to assess system stability under different uncertain dynamics loads and PVs. Comparisons are performed with the sampling-based, the polynomial chaos expansion-based, and traditional Gaussian process-based methods on the modified IEEE 118-bus and Texas 2000-bus systems under various scenarios, including different levels of uncertainties and the existence of nonlinear correlations among dynamic PVs. The impacts of data quality and quantity issues are also investigated. It is shown that the proposed SGP achieves significantly improved computational efficiency while maintaining high accuracy with a limited number of data.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

An Empirical Model For Intrinsic Alignments: Insights From Cosmological Simulations

We extend current models of the halo occupation distribution (HOD) to include a flexible, empirical framework for the forward modeling of the intrinsic alignment (IA) of galaxies. A primary goal of this work is to produce mock galaxy catalogs for the purpose of validating existing models and methods for the mitigation of IA in weak lensing measurements. This technique can also be used to produce new, simulation-based predictions for IA and galaxy clustering. Our model is probabilistically formulated, and rests upon the assumption that the orientations of galaxies exhibit a correlation with their host dark matter (sub)halo orientation or with their position within the halo. We examine the necessary components and phenomenology of such a model by considering the alignments between (sub)halos in a cosmological dark matter only simulation. We then validate this model for a realistic galaxy population in a set of simulations in the Illustris-TNG suite. We create an HOD mock with Illustris-like correlations using our method, constraining the associated IA model parameters, with the $\mathcal{X}$$^{2}_{dof}$ between our model’s correlations and those of Illustris matching as closely as 1.4 and 1.1 for orientation–position and orientation–orientation correlation functions, respectively. By modeling the misalignment between galaxies and their host halo, we show that the 3-dimensional two-point position and orientation correlation functions of simulated (sub)halos and galaxies can be accurately reproduced from quasi-linear scales down to 0.1 $\mathcal{h}$ –1 Mpc. We also find evidence for environmental influence on IA within a halo. Our publicly-available software provides a key component enabling efficient determination of Bayesian posteriors on IA model parameters using observational measurements of galaxy-orientation correlation functions in the highly nonlinear regime.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Tomography of the gamma-ray sky from cross-correlation with DESI DR2 and unWISE galaxies

We study the origin of extragalactic gamma-ray emission observed by Fermi-LAT, using the cross-correlation of the gamma-ray sky with maps of large-scale structure provided by the DESI and unWISE surveys. Tomographic cross-correlation reveals the bias-weighted redshift distributions of gamma-ray sources. We first illustrate this method by cross-correlating detected gamma-ray point sources with large-scale structure. We find a significant cross-correlation and infer a point source redshift distribution broadly consistent with the distribution of identified optical counterparts previously reported in the literature, as well as a similar linear bias ($b \approx 2$) to massive galaxies that host bright active galactic nuclei. We then study the clustering of the Fermi unresolved gamma-ray background (UGRB), both in auto-correlation and in cross-correlation with large-scale structure. We detect the cross-correlation of the UGRB and LSS at $\sim 10σ$ in total, with highly significant detections from both DESI and unWISE. Our measurements suggest that the redshift distribution of the UGRB is broadly consistent with the redshift distribution of detected point sources. Additionally, we find a relatively weak amplitude for the cross-correlation with large-scale structure at z < 2, suggesting a significant fraction of the UGRB does not come from z < 2 large-scale structure. A natural candidate is contamination of from residual Galactic emission, and our best estimate of the contamination level derived from the UGRB auto-spectrum suggests that the mean bias of UGRB sources is indeed quite similar to the bias of detected Fermi point sources. However, we cannot exclude additional emission from gamma-ray sources at high redshift, z > 2, and we suggest that cross-correlation with tracers at z > 2, including CMB lensing, would be the ideal way to determine the fraction of z > 2 emission.

Krolewski, Alex [Waterloo U., Math. Dept.; Waterlo↗

DOE OSTI2025

Multi-GPU porting of a phase-change cascaded lattice Boltzmann method for three-dimensional pool boiling simulations

The Lattice Boltzmann method (LBM) has proven effective in simulating phase-change phenomena, such as melting, solidification, evaporation, and boiling. In this work, we develop a highly parallelized multi-GPU implementation of LBM for three-dimensional pool boiling simulations. The code is based on the OpenACC programming model, which enables the code to be deployed efficiently on multi-core CPUs, GPUs, and potentially other accelerators, without the need for architecture-specific rewrites. To support large-scale simulations, the domain is decomposed and distributed across multiple compute nodes using MPI. We demonstrate that the code exhibits excellent scaling properties, with ideal strong-scaling running with up to 256 GPUs on the MareNostrum5 cluster.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Resilience-Oriented DG Siting and Sizing Considering Stochastic Scenario Reduction

In this paper, a fuel-based distributed generator (DG) allocation strategy is proposed to enhance the distribution system resilience against extreme weather. The long-term planning problem is formulated as a two-stage stochastic mixed-integer programming (SMIP). The first stage is to make decisions of DG siting and sizing under the given budget constraint. In the second stage, a post-extreme-event-restoration (PEER) is employed to minimize the operating cost in an uncertain fault scenario. In particular, this study proposes a method to select the most representative scenarios for the SMIP. First, a Monte Carlo Simulation (MCS) is introduced to generate sufficient scenarios considering random fault locations and load profiles. Then, the number of scenarios is reduced by the K-means clustering algorithm. The advantage of scenario reduction is to make a trade-off between accuracy and computational efficiency. Finally, the SMIP is solved by the progressive hedging algorithm. Here, the case studies of the IEEE 33-bus and 123-bus test systems demonstrate the effectiveness of the proposed algorithm in reducing the expected energy not served (EENS), which is a critical criterion of resilience.

42 ENGINEERING↗

DOE OSTI2020

Distributed non-negative matrix factorization with determination of the number of latent features

The holistic analysis and understanding of the latent (that is, not directly observable) variables and patterns buried in large datasets is crucial for data-driven science, decision making and emergency response. Such exploratory analyses require devising unsupervised learning methods for data mining and extraction of the latent features, and non-negative matrix factorization (NMF) is one of the prominent such methods. NMF is based on compute-intense non-convex constrained minimization, which, for large datasets requires fast and distributed algorithms. However, current parallel implementations of NMF fail to estimate the number of latent features. In practice, identifying these features is both difficult and significant for pattern recognition and latent feature analysis, especially for large dense matrices. Here, we introduce a distributed NMF algorithm coupled with distributed custom clustering followed by a stability analysis on dense data, which we call DnMFk, to determine the number of latent variables. The results on synthetic data and the classical Swimmer data set demonstrate the accuracy of model determination while scaling nearly linearly across multiple processors for large data. Further, we employ DnMFk to determine the number of hidden features from a terabyte matrix.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

A Clustering-Based Scenario Generation Framework for Power Market Simulation with Wind Integration

A critical step in stochastic optimization models of power system analysis is to select a set of appropriate scenarios and significant numbers of scenario generation methods exist in the literature. This paper develops a clustering based scenario generation method, which aims to improve the performance of existing scenario generation techniques by grouping a set of correlated wind sites into clusters according to their cross-correlations. Copula based models are utilized to model spatiotemporal correlations and the Gibbs sampling is then used to generate scenarios for day-ahead markets. Our results show that the generated scenarios based on clustered wind sites outperform existing approaches in terms of reliability and sharpness and can reduce the total computational time for scenario generation and reduction significantly. The clustering-based framework can therefore provide a better support for real-world market simulations with high wind penetration.

data visualization↗

DOE OSTI2024

Quest for Multifunctionality: Current Progress in the Characterization of Heterometallic Metal–Organic Frameworks

Metal–organic frameworks (MOFs) are a class of porous, crystalline materials that have been systematically developed for a broad range of applications. Incorporation of two or more metals into a single crystalline phase to generate heterometallic MOFs has been shown to lead to synergistic effects, in which the whole is oftentimes greater than the sum of its parts. Because geometric proximity is typically required for metals to function cooperatively, deciphering and controlling metal distributions in heterometallic MOFs is crucial to establish structure–function relationships. However, determination of short- and long-range metal distributions is nontrivial and requires the use of specialized characterization techniques. Advancements in the characterization of metal distributions and interactions at these length scales is key to rapid advancement and rational design of functional heterometallic MOFs. Further, this perspective summarizes the state-of-the-art in the characterization of heterometallic MOFs, with a focus on techniques that allow metal distributions to be better understood. Using complementary analyses, in conjunction with computational methods, is critical as this field moves toward increasingly complex, multifunctional systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

The cosmic DANCe of Perseus

Context. Star-forming regions are excellent benchmarks for testing and validating theories of star formation and stellar evolution. The Perseus star-forming region, being one of the youngest (< 10 Myr), closest (280-320 pc), and most studied in the literature, is a fundamental benchmark. Aims. We aim to study the membership, phase-space structure, mass, and energy (kinetic plus potential) distribution of the Perseus star-forming region using public catalogues (Gaia, APOGEE, 2MASS, and Pan-STARRS). Methods. We used Bayesian methodologies that account for extinction to identify the Perseus physical groups in the phase-space, retrieve their candidate members, derive their properties (age, mass, 3D positions, 3D velocities, and energy), and attempt to reconstruct their origin. Results. We identify 1052 candidate members in seven physical groups (one of them new) with ages between 3 and 10 Myr, dynamical super-virial states, and large fractions of energetically unbounded stars. Their mass distributions are broadly compatible with that of Chabrier for masses ≳0.1 M ⊙ and do not show hints of over-abundance of low-mass stars in NGC 1333 with respect to IC 348. These groups’ ages, spatial structure, and kinematics are compatible with at least three generations of stars. Future work is still needed to clarify if the formation of the youngest was triggered by the oldest. Conclusions. The exquisite Gaia data complemented with public archives and mined with comprehensive Bayesian methodologies allow us to identify 31% more members than previous studies, discover a new physical group (Gorgophone: 7 Myr, 191 members, and 145 M ⊙ ), and confirm that the spatial, kinematic, and energy distributions of these groups support the hierarchical star formation scenario.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Critical magnetic Reynolds number of the turbulent dynamo in collisionless plasmas

The intracluster medium of galaxy clusters is an extremely hot and diffuse, nearly collisionless plasma, which hosts dynamically important magnetic fields of ~μG strength. Seed magnetic fields of much weaker strength of astrophysical or primordial origin can be present in the intracluster medium. In collisional plasmas, which can be approximated in the magnetohydrodynamical (MHD) limit, the turbulent dynamo mechanism can amplify weak seed fields to strong dynamical levels efficiently by converting turbulent kinetic energy into magnetic energy. However, the viability of this mechanism in weakly collisional or completely collisionless plasma is much less understood. In this study, we explore the properties of the collisionless turbulent dynamo using three-dimensional hybrid-kinetic particle-in-cell simulations. We explore the properties of the collisionless turbulent dynamo in the kinematic regime for different values of the magnetic Reynolds number, Rm, initial magnetic-to-kinetic energy ratio, (E mag /E kin ) i , and initial Larmor ratio, (r Larmor /L box ) i , i.e. the ratio of the Larmor radius to the size of the turbulent system. We find that in the ‘un-magnetized’ regime, (r Larmor /L box ) i > 1, the critical magnetic Reynolds number for the dynamo action Rm crit ≈ 107 ± 3. In the ‘magnetized’ regime, (r Larmor /L box ) i ≲ 1, we find a marginally higher Rm crit = 124 ± 8. We find that the growth rate of the magnetic energy does not depend on the strength of the seed magnetic field when the initial magnetization is fixed. We also study the distribution and evolution of the pressure anisotropy in the collisionless plasma and compare our results with the MHD turbulent dynamo.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Q-BEEP: Quantum Bayesian Error Mitigation Employing Poisson Modeling over the Hamming Spectrum

Quantum computing technology has grown rapidly in recent years, with new technologies being explored, error rates being reduced, and quantum processor’s qubit capacity growing. However, near-term quantum algorithms are still unable to be induced without compounding consequential levels of noise, leading to non-trivial erroneous results. Quantum Error Correction (in-situ error mitigation) and Quantum Error Mitigation (post-induction error mitigation) are promising fields of research within the quantum algorithm scene, aiming to alleviate quantum errors, increasing the overall fidelity and hence the overall quality of circuit induction. Earlier this year, a pioneering work, namely HAMMER, published in ASPLOS-22 demonstrated the existence of a latent structure regarding post-circuit induction errors when mapping to the Hamming spectrum. However, they intuitively assumed that errors occur in local clusters, and that at higher average Hamming distances this structure falls away. In this work, we show that such a correlation structure is not only local but extends certain non-local clustering patterns which can be precisely described by a Poisson distribution model taking the input circuit, the device run time status (i.e., calibration statistics) and qubit topology into consideration. Using this quantum error characterizing model, we developed an iterative algorithm over the generated Bayesian network state-graph for post-induction error mitigation. Thanks to more precise modeling of the error distribution latent structure and the new iterative method, our Q-Beep approach provides state of the art performance and can boost circuit execution fidelity by up to 234.6% on Bernstein-Vazirani circuits and on average 71.0% on QAOA solution quality, using 16 practical IBMQ quantum processors. For other benchmarks such as those in QASMBench, the fidelity improvement is up to 17.8%. Q-Beep is a light-weight post-processing technique that can be performed offline and remotely, making it a useful tool for quantum vendors to integrate and provide more reliable circuit induction results.

Stein, Samuel A.↗

DOE OSTI2025

Introducing the SLICE Method for estimating pebble-bed reactor inventories at equilibrium operation with SCALE

This paper introduces the SCALE Leap-In method for Cores at Equilibrium (SLICE) for estimating pebble-bed reactor equilibrium core isotopic inventories using capabilities in the SCALE code system, requiring only a small computational cluster and a few days of computation. This method uses an iterative approach that relies on (1) a surrogate spectrum model that captures spatial and time-dependent spectral conditions, (2) a multi-pass model that captures the pebble’s evolving nuclide inventory as a function of location and time in the core, and (3) a full-core model that captures the core’s spatial neutron flux distribution. The SLICE approach is applied to a generic fluoride salt–cooled high-temperature reactor, demonstrating fuel inventory convergence through nuclide concentration inspection across iterations and comparisons for core realizations with varying discretizations. Results agree within ~5% with another state-of-the-art code, with differences attributed to input parameter or modeling assumption variations in the equilibrium generation methods.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Distributed-Memory Parallel Symmetric Nonnegative Matrix Factorization

We develop the first distributed-memory parallel implementation of Symmetric Nonnegative Matrix Factorization (SymNMF), a key data analytics kernel for clustering and dimensionality reduction. Our implementation includes two different algorithms for SymNMF, which give comparable results in terms of time and accuracy. The first algorithm is a parallelization of an existing sequential approach that uses solvers for non symmetric NMF. The second algorithm is a novel approach based on the Gauss-Newton method. It exploits second-order information without incurring large computational and memory costs. We evaluate the scalability of our algorithms on the Summit system at Oak Ridge National Laboratory, scaling up to 128 nodes (4,096 cores) with 70% efficiency. Additionally, we demonstrate our software on an image segmentation task.

Eswar, Srinivas↗

DOE OSTI2025

Electronic Spin Relaxation and Clustering in High-Pressure High-Temperature Synthesized Microcrystalline Diamond Particles with Reduced Nitrogen Content

The negatively charged nitrogen-vacancy (NV – ) color center in diamonds is widely studied because of numerous applications of this unique quantum system in sensing and quantum information sciences. While substitutional nitrogen is required to form the NV – centers in diamond, it also yields other paramagnetic defects─primarily the neutrally charged substitutional nitrogen centers (P1)─that decrease NV – spin coherence, which in turn degrades performance in applications. Herein, we investigate high-pressure high-temperature synthesized diamond microparticles (ca. 140–185 μm) having lower─ranging from 3 to 38 ppm─than the typical nitrogen content of type 1b diamond ( ca. 100 ppm and higher) typically used for the production of fluorescent diamond particles with NV – centers. A suite of electron paramagnetic resonance, optically detected magnetic resonance, and nuclear magnetic resonance methods are used to characterize spin properties of P1 and NV – centers in the particles. Upon decreasing the nitrogen content from 29 to 3 ppm, the ensemble NV – T 2 relaxation time increased by about 3-fold as measured directly in the Hahn Echo experiment at magnetic field of 1.2 T. Analysis of electronic relaxation of P1 centers revealed the existence of at least two distinct populations of P1 centers, consisting of fast and slower relaxing spins and allowed for an estimation of local concentrations. Even with <10 ppm nitrogen contents, the analysis indicated a highly heterogeneous distribution of P1 centers, suggesting the possibility of P1 spin clustering even at low nitrogen concentrations. The combined data demonstrate that the particles prepared from HPHT diamond with a low nitrogen content offer improved spin properties that are beneficial for NV – sensing applications.

Carbon↗

DOE OSTI2023

Modeling Short-Range Order in Disordered Rocksalt Cathodes by Pair Distribution Function Analysis

Pair distribution function (PDF) analysis is a powerful technique for the characterization of short-range order (SRO) in disordered materials. Accurate interpretation of experimental PDF data is critically reliant on the development of structural models that can account for local variations in site occupancies and bond lengths. To this end, we outline an approach to model SRO using first-principles calculations based on the cluster-expansion formalism. These methods are validated on neutron scattering data from two disordered rocksalt oxyfluorides, Li 1.3 Mn 0.4 Ti 0.3 O 1.7 F 0.3 and Li 1.3 Mn 0.4 Nb 0.2 Ti 0.1 O 1.7 F 0.3 . For each composition, we demonstrate that an average structure without any SRO fails to reproduce several key features in the experimental PDF. To pinpoint the origin of the suspected SRO in these materials, configurational and displacive effects were separately investigated using two disparate models. Special quasi-random structures were relaxed using density functional theory to account for local changes in bond lengths while maintaining a near-random ionic configuration. This leads to slightly improved accuracy but still misrepresents asymmetry in the first few peaks of the PDF. Monte Carlo simulations were performed to model configurational SRO on a fixed lattice, which by itself is shown to have a minimal influence on the PDF. Instead, we find that it is the bond length relaxations within environments created by SRO which controls the details of the PDF, thereby highlighting the subtle but important coupling between configurational and displacive SRO in disordered materials.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Coordinated JWST Imaging of Three Distance Indicators in a Supernova Host Galaxy and an Estimate of the Tip of the Red Giant Branch Color Dependence

Boasting a 6.5 m mirror in space, JWST can increase by several times the number of supernovae (SNe) to which a redshift-independent distance has been measured with a precision distance indicator (e.g., tip of the red giant branch (TRGB) or Cepheids); the limited number of such SN calibrators currently dominates the uncertainty budget in distance ladder Hubble constant (H 0 ) experiments. JWST/NIRCAM imaging of the Virgo Cluster galaxy NGC 4536 is used here to preview JWST program GO-1995, which aims to measure H 0 using three stellar distance indicators (Cepheids, TRGB, and J-branch asymptotic giant branch/carbon stars). Each population of distance indicator was here successfully detected—with sufficiently large number statistics, well-measured fluxes, and characteristic distributions consistent with ingoing expectations—so as to confirm that we can acquire distances from each method precise to about 0.05 mag (statistical uncertainty only). We leverage overlapping Hubble Space Telescope imaging to identify TRGB stars, crossmatch them with the JWST photometry, and present a preliminary constraint on the slope of the TRGB's F115W versus (F115W – F444W) relation equal to -0.99 ± 0.16 mag mag -1 . This slope is consistent with prior slope measurements in the similar Two Micron All-Sky Survey J band, as well as with predictions from the BaSTI isochrone suite. We use the new TRGB slope estimate to flatten the 2D TRGB feature and measure a (blinded) TRGB distance relative to a set of fiducial TRGB colors, intended to represent the absolute fiducial calibrations expected from geometric anchors such as NGC 4258 and the Magellanic Clouds. In doing so, we empirically demonstrate that the TRGB can be used as a standardizable candle at the IR wavelengths accessible with JWST.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Constraining the scatter in the galaxy–halo connection at Milky Way masses

In this work, we develop and implement two new methods for constraining the scatter in the relationship between galaxies and dark matter haloes. These new techniques are sensitive to the scatter at low halo masses, making them complementary to previous constraints that are dependent on clustering amplitudes or rich galaxy groups, both of which are only sensitive to more massive haloes. In both of our methods, we use a galaxy group finder to locate central galaxies in the Sloan Digital Sky Survey main galaxy sample. Our first technique uses the small-scale cross-correlation of central galaxies with all lower mass galaxies. This quantity is sensitive to the satellite fraction of low-mass galaxies, which is in turn driven by the scatter between haloes and galaxies. The second technique uses the kurtosis of the distribution of line-of-sight velocities between central galaxies and neighbouring galaxies. This quantity is sensitive to the distribution of halo masses that contain the central galaxies at fixed stellar mass. Theoretical models are constructed using peak halo circular velocity, Vpeak, as our property to connect galaxies to haloes, and all comparisons between theory and observation are made after first passing the model through the group-finding algorithm. We parametrize scatter as a lognormal distribution in M* at fixed Vpeak, σ[M*|Vpeak]. The cross-correlation technique yields a constraint of σ[M*|Vpeak] = 0.27 ± 0.05 dex at a mean Vpeak of 168 km s-1, corresponding to a scatter in log M* at fixed Mh of σ[M*|Mh] = 0.38 ± 0.06 dex at $M_\text{h}=10^{11.8}\, \text{M}_\odot$. The kurtosis technique yields σ[M*|Vpeak] = 0.30 ± 0.03 at Vpeak = 209 km s-1, corresponding to σ[M*|Mh] = 0.34 ± 0.04 at $M_\text{h}=10^{12.2}\, \text{M}_\odot$. The values of σ[M*|Mh] are significantly larger than the constraints at higher masses, in agreement with the results of hydrodynamic simulations. This increase is only partly due to the scatter between Vpeak and Mh, and it represents an increase of nearly a factor of 2 relative to the values inferred from clustering and group studies at high masses.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

An Investigation of Poorly Studied Open Cluster NGC 4337 Using Multicolor Photometric and Gaia DR2 Astrometric Data

We present a comprehensive analysis (photometric and kinematical) of the poorly studied open cluster NGC 4337 using 2MASS, WISE, APASS, and Gaia DR2 databases. By determining the membership probabilities of stars, we identified the 624 most probable members with membership probability higher than 50% by using proper motion and parallax data taken from Gaia DR2. The mean proper motion of the cluster is obtained as μ{sub x}=−8.83±0.01 and μ {sub y} = 1.49 ± 0.006 mas yr{sup −1}. We find the normal interstellar extinction toward the cluster region. The radial distribution of members provides a cluster radius of 7.′75 (5.63 pc). The estimated age of 1600 ± 180 Myr indicates that NGC 4337 is an old open cluster with a bunch of red giant stars. The overall mass function slope for main-sequence stars is found as 1.46±0.18 within the mass range 0.75−2.0 M{sub ⊙}, which is in fair agreement with Salpeter’s value (x = 1.35) within uncertainty. The present study demonstrates that NGC 4337 is a dynamically relaxed open cluster. Using the Galactic potential model, Galactic orbits are obtained for NGC 4337. We found that this object follows a circular path around the Galactic center. Under the kinematical analysis, we compute the apex coordinates (A, D) by using two methods: (i) the classical convergent point method and (ii) the AD-diagram method. The obtained coordinates are (A {sub conv}, D {sub conv}) = (96.°27 ± 0.°10, 13.°14 ± 0.°27) and (A {sub ◦}, D {sub ◦}) = (100.°282 ± 0.°10, 9.°577 ± 0.°323) respectively. We also computed the Velocity Ellipsoid Parameters, matrix elements (μ {sub ij}), direction cosines (l {sub j}, m {sub j}, n {sub j}), and the Galactic longitude of the vertex (l {sub 2}).

79 ASTRONOMY AND ASTROPHYSICS↗