Search NASA⌕ Search

SEARCH · Search NASA

Results for “elliptical”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

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

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

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A variational mimetic finite difference method for elliptic interface problems on non-matching polytopal meshes with geometric interface inconsistencies

A new variational mimetic finite difference method for elliptic interface problems with perfect and imperfect thermal contacts on non-matching polytopal meshes with geometric interface inconsistencies is developed and analyzed theoretically and numerically. The method is defined on multiple non-matching submeshes with gaps and overlaps along their interfaces. The discrete equations are derived from a minimization problem for the augmented Dirichlet functional. For a perfect thermal contact, the functional uses a modified mimetic gradient with extended stencil which couples unknowns from both sides of an interface, as well as penalty terms to enforce weak continuity of temperature across the interface. The method leads to a symmetric positive definite matrix for any scaling of the penalty terms. For an imperfect thermal contact, the Dirichlet functional is supplemented with a quadratic jump term along the interface related to the interface thermal resistance. We prove that the method conserves the total heat flux across each interface. In conclusion, the obtained results are verified with numerical experiments showing convergence in the discrete L 2 and L ∞ norms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Elliptic flow of heavy-flavor decay electrons in Au+Au collisions at s NN = 27 and 54.4 GeV at RHIC

We report on new measurements of elliptic flow (v 2 ) of electrons from heavy-flavor hadron decays at mid-rapidity (|y| < 0.8) in Au+Au collisions at $\sqrt{s{NN}}$ = 27 and 54.4 GeV from the STAR experiment. Heavy-flavor decay electrons (eHF) in Au+Au collisions at $\sqrt{s{NN}}$ = 54.4 GeV exhibit a non-zero v 2 in the transverse momentum (p T ) region of p T < 2 GeV/c with the magnitude comparable to that at $\sqrt{s{NN}}$=200 GeV. The measured e HF v 2 at 54.4 GeV is also consistent with the expectation of their parent charm hadron v 2 following number-of-constituent-quark scaling as other light and strange flavor hadrons at this energy. These suggest that charm quarks gain significant collectivity through the evolution of the QCD medium and may reach local thermal equilibrium in Au+Au collisions at $\sqrt{s{NN}}$=54.4 GeV. The measured e HF v 2 in Au+Au collisions at $\sqrt{s{NN}}$ = 27 GeV is consistent with zero within large uncertainties. The energy dependence of v 2 for different flavor particles (π,Φ,D 0 /e HF ) shows an indication of quark mass hierarchy in reaching thermalization in high-energy nuclear collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs

Physics informed neural networks (PINNs) are deep learning based techniques for solving partial differential equations (PDEs) encountered in computational science and engineering. Guided by data and physical laws, PINNs find a neural network that approximates the solution to a system of PDEs. Such a neural network is obtained by minimizing a loss function in which any prior knowledge of PDEs and data are encoded. Despite its remarkable empirical success in one, two or three dimensional problems, there is little theoretical justification for PINNs. As the number of data grows, PINNs generate a sequence of minimizers which correspond to a sequence of neural networks. We want to answer the question: Does the sequence of minimizers converge to the solution to the PDE? We consider two classes of PDEs: linear second-order elliptic and parabolic. By adapting the Schauder approach and the maximum principle, we show that the sequence of minimizers strongly converges to the PDE solution in C 0 . Furthermore, we show that if each minimizer satisfies the initial/boundary conditions, the convergence mode becomes H 1 . Computational examples are provided to illustrate our theoretical findings. To the best of our knowledge, this is the first theoretical work that shows the consistency of PINNs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Higher-order moments of the elliptic flow distribution in PbPb collisions at $ \sqrt{s_{\textrm{NN}}}$ = 5.02 TeV

The hydrodynamic flow-like behavior of charged hadrons in high-energy lead-lead collisions is studied through multiparticle correlations. The elliptic anisotropy values based on different orders of multiparticle cumulants, v$_{2}${2k}, are measured up to the tenth order (k = 5) as functions of the collision centrality at a nucleon-nucleon center-of-mass energy of $ \sqrt{s_{\textrm{NN}}} $ = 5.02 TeV. The data were recorded by the CMS experiment at the LHC and correspond to an integrated luminosity of 0.607 nb$^{–1}$. A hierarchy is observed between the coefficients, with v$_{2}${2} > v$_{2}${4} ≳ v$_{2}${6} ≳ v$_{2}${8} ≳ v$_{2}${10}. Based on these results, centrality-dependent moments for the fluctuation-driven event-by-event v$_{2}$ distribution are determined, including the skewness, kurtosis and, for the first time, superskewness. Assuming a hydrodynamic expansion of the produced medium, these moments directly probe the initial-state geometry in high-energy nucleus-nucleus collisions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Loop-by-loop differential equations for dual (elliptic) Feynman integrals

We present a loop-by-loop method for computing the differential equations of Feynman integrals using the recently developed dual form formalism. We give explicit prescriptions for the loop-by-loop fibration of multi-loop dual forms. Then, we test our formalism on a simple, but non-trivial, example: the two-loop three-mass elliptic sunrise family of integrals. We obtain an ε-form differential equation within the correct function space in a sequence of relatively simple algebraic steps. In particular, none of these steps relies on the analysis of q-series. Then, we discuss interesting properties satisfied by our dual basis as well as its simple relation to the known ε-form basis of Feynman integrands. The underlying K3-geometry of the three-loop four-mass sunrise integral is also discussed. Finally, we speculate on how to construct a “good” loop-by-loop basis at three-loop.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

J/ ψ elliptic and triangular flow in Pb-Pb collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 5 . 02 TeV

The inclusive J/ ψ elliptic ( v 2 ) and triangular ( v 3 ) flow coefficients measured at forward rapidity (2 . 5 < y < 4) and the v 2 measured at midrapidity (| y | < 0 . 9) in Pb-Pb collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 5 . 02 TeV using the ALICE detector at the LHC are reported. The entire Pb-Pb data sample collected during Run 2 is employed, amounting to an integrated luminosity of 750 μ b – 1 at forward rapidity and 93 μ b – 1 at midrapidity. The results are obtained using the scalar product method and are reported as a function of transverse momentum p T and collision centrality. At midrapidity, the J/ ψ v 2 is in agreement with the forward rapidity measurement. The centrality averaged results indicate a positive J/ ψ v 3 with a significance of more than 5 σ at forward rapidity in the p T range 2 < p T < 5 GeV/ c . The forward rapidity v 2 , v 3 , and v 3 /v 2 results at low and intermediate p T ( p T ≲ 8 GeV/ c ) exhibit a mass hierarchy when compared to pions and D mesons, while converging into a species-independent curve at higher p T . At low and intermediate p T , the results could be interpreted in terms of a later thermalization of charm quarks compared to light quarks, while at high p T , path-length dependent effects seem to dominate. The J/ ψ v 2 measurements are further compared to a microscopic transport model calculation. Using a simplified extension of the quark scaling approach involving both light and charm quark flow components, it is shown that the D-meson v n measurements can be described based on those for charged pions and J/ ψ flow.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Method of Green’s Potentials for Elliptic PDEs in Domains with Random Apertures

Problems with topological uncertainties appear in many fields ranging from nano-device engineering to the design of bridges. In many of such problems, a part of the domains boundaries is subjected to random perturbations making inefficient conventional schemes that rely on discretization of the whole domain. Here, we study elliptic PDEs in domains with boundaries comprised of a deterministic part and random apertures, and apply the method of modified potentials with Green’s kernels defined on the deterministic part of the domain. This approach allows to reduce the dimension of the original differential problem by reformulating it as a boundary integral equation posed on the random apertures only. The multilevel Monte Carlo method is then applied to this modified integral equation and its optimal ϵ -2 asymptotical complexity is shown. Finally, we provide the qualitative analysis of the proposed technique and support it with numerical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Enhanced harmonic generation accompanying Ferromagnetic resonance in thin permalloy elliptical disks

Throughout this work, large amplitude magnetization dynamics in elliptical permalloy nano-disks are studied via simulation of the Landau-Lifshitz equation. When the external magnetic field is applied in the plane of the disk two low-lying resonant modes exist. The higher frequency mode corresponds to the Kittel-like uniform ferromagnetic resonance mode and is consistent with previous experimental observations. The second mode with the lower frequency, termed the "cap mode", is localized near the two ends of the ellipse. At certain fields the ratio of the frequencies of these modes is equal to two or three and here one can efficiently generate the Kittel mode as the 2nd or 3rd harmonic of the "cap mode" when the magnitude of the input microwave field is of order 0.1 Oe, which can easily be achieved in practice. The nonlinear responses depend strongly on the equilibrium, field-dep-endent, behavior of the magnetization which is non-uniform and displays features not captured by the Stoner-Wohlfarth model for an ellipsoid.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Highly Elliptic Circular Dichroism of Copper Aspartate One-Dimensional Nanostructures across the Ultraviolet to Terahertz Ranges

Since the discovery of chirality, circular dichroism (CD) of mirror-asymmetric molecules has been studied across the ultraviolet, visible, and near-infrared ranges. Recently, chiroptical activity studies have expanded to the terahertz (THz) range, where resonance peaks originate from collective vibrations of tens and hundreds of atoms. Here, in this study, we synthesized Cu 2+ coordination complexes with L- and D-aspartic acid as nanowires and nanorods and characterized their chiroptical activity across multiple frequency ranges. Both chiral nanostructures exhibit strong electronic CD (ECD), primarily from Cu 2+ d-d transitions, while vibrational CD (VCD) spectra show sharp C=O, C–H, and O–H vibronic peaks, indicating higher atomic defect densities in nanorods than nanowires. Although THz CD (TCD) spectra are broad, they exhibit ∼1000× greater ellipticity than ECD and VCD, perhaps warranting previous references to circular dichroism of nanostructures as giant. Comparative TCD analysis highlights strong chiral phonon sensitivity, underscoring its potential for probing defect densities and structural changes for various chiral nanostructures and (bio)crystals.

THz spectroscopy↗
DOE OSTI2025

Elliptic anisotropy measurement of the f 0 (980) hadron in proton-lead collisions and evidence for its quark-antiquark composition

Despite the f 0 (980) hadron having been discovered half a century ago, the question about its quark content has not been settled: it might be an ordinary quark-antiquark ($q\bar{q}$) meson, a tetraquark ($q\bar{q}$$q\bar{q}$) exotic state, a kaon-antikaon ($K\bar{K}$) molecule, or a quark-antiquark-gluon ($q\bar{q}$g) hybrid. This paper reports strong evidence that the f 0 (980) state is an ordinary $q\bar{q}$ meson, inferred from the scaling of elliptic anisotropies (v 2 ) with the number of constituent quarks (n q ), as empirically established using conventional hadrons in relativistic heavy ion collisions. The f 0 (980) state is reconstructed via its dominant decay channel f 0 (980) → π + π − , in proton-lead collisions recorded by the CMS experiment at the LHC, and its v 2 is measured as a function of transverse momentum (p T ). It is found that the n q = 2 ($q\bar{q}$ state) hypothesis is favored over n q = 4 ($q\bar{q}$$q\bar{q}$ or $K\bar{K}$ states) by 7.7, 6.3, or 3.1 standard deviations in the p T < 10, 8, or 6 GeV/c ranges, respectively, and over n q = 3 ($q\bar{q}$g hybrid state) by 3.5 standard deviations in the p T < 8 GeV/c range. This result represents the first determination of the quark content of the f 0 (980) state, made possible by using a novel approach, and paves the way for similar studies of other exotic hadron candidates.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Risk-averse optimal control of semilinear elliptic PDEs

In this paper, we consider the optimal control of semilinear elliptic PDEs with random inputs. These problems are often nonconvex, infinite-dimensional stochastic optimization problems for which we employ risk measures to quantify the implicit uncertainty in the objective function. In contrast to previous works in uncertainty quantification and stochastic optimization, we provide a rigorous mathematical analysis demonstrating higher solution regularity (in stochastic state space), continuity and differentiability of the control-to-state map, and existence, regularity and continuity properties of the control-to-adjoint map. Our proofs make use of existing techniques from PDE-constrained optimization as well as concepts from the theory of measurable multifunctions. We illustrate our theoretical results with two numerical examples motivated by the optimal doping of semiconductor devices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Verification of the Shafranov shift in free-boundary VMEC, DESC, and SPEC calculations with elliptical geometry

Here, given a set of current-carrying filaments that create a magnetic field with rotating elliptical flux surfaces, we present verification calculations using the VMEC, DESC, and SPEC free-boundary magnetohydrostatic equilibrium codes for both the “vacuum” equilibrium, for which there is no plasma pressure and no plasma currents, and for a non-zero pressure, zero toroidal current equilibrium. For the vacuum case, these codes are quantitatively compared to the magnetic field produced by the coils. For the non-zero pressure case, they are compared to each other. As the stepped pressure profile used in SPEC approaches the continuous profile used in VMEC and DESC, the SPEC magnetic axis approaches the VMEC and DESC axes. To within an error given by the difference between the pressure profiles, the VMEC, DESC, and SPEC calculations give the same pressure-induced geometric shift of the magnetic axis, known as the Shafranov shift.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Resonances of electromagnetically induced transparency and absorption in a light field of elliptically polarised waves

Electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) resonances excited by a strong two-frequency field are considered for various values of the total angular momenta of the ground (F{sub g}) and excited (F{sub e}) states at a degenerated optical closed transition F{sub g} → F{sub e}. The light field is formed by two co-propagating waves with arbitrary elliptical polarisations. The process of spontaneous transfer of anisotropy from the excited state to the ground state is shown to determine the formation of the EIA resonance at the transition F{sub g} = F → F{sub e} = F + 1. The results obtained generalise the classification of transitions into ‘bright’ (F{sub g} = F → F{sub e} = F + 1) and ‘dark’ (F{sub g} = F → F{sub e} = F and F{sub g} = F → F{sub e} = F – 1) transitions with respect to the direction of a subnatural resonance. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Modeling of Additively Manufactured Ceramic Heat Exchangers with Semi-Elliptical Cross-Section Flow Channels

An approximate and easily applied analytical model was developed for heat transfer calculations of heat exchangers consisting of multiple rows and columns of heat transfer fluid flow channels with semi-elliptical cross sections. Heat exchangers of this type are being developed by using ceramic material and additive manufacturing for high temperature and pressure-concentrating solar electric power plants. Calculations using the model require only the geometrical dimensions and flow conditions of the heat exchanger. Comparisons of modeling predictions, with both simulation results and experimental data, were conducted to verify the viability of the model. The results showed good agreement where almost all the modeling predictions were within 20% of the simulation results or the experimental data. Finally, the proposed modeling approach is more generally applicable to heat transfer analysis of heat exchangers with similar flow channel configurations to those considered in this study.

Ceramic↗
DOE OSTI2021

Dark matter haloes of massive elliptical galaxies at z ∼ 0.2 are well described by the Navarro–Frenk–White profile

ABSTRACT We investigate the internal structure of elliptical galaxies at z ∼ 0.2 from a joint lensing–dynamics analysis. We model Hubble Space Telescope images of a sample of 23 galaxy–galaxy lenses selected from the Sloan Lens ACS (SLACS) survey. Whereas the original SLACS analysis estimated the logarithmic slopes by combining the kinematics with the imaging data, we estimate the logarithmic slopes only from the imaging data. We find that the distribution of the lensing-only logarithmic slopes has a median 2.08c ± 0.03 and intrinsic scatter 0.13 ± 0.02, consistent with the original SLACS analysis. We combine the lensing constraints with the stellar kinematics and weak lensing measurements, and constrain the amount of adiabatic contraction in the dark matter (DM) haloes. We find that the DM haloes are well described by a standard Navarro–Frenk–White halo with no contraction on average for both of a constant stellar mass-to-light ratio (M/L) model and a stellar M/L gradient model. For the M/L gradient model, we find that most galaxies are consistent with no M/L gradient. Comparison of our inferred stellar masses with those obtained from the stellar population synthesis method supports a heavy initial mass function (IMF) such as the Salpeter IMF. We discuss our results in the context of previous observations and simulations, and argue that our result is consistent with a scenario in which active galactic nucleus feedback counteracts the baryonic-cooling-driven contraction in the DM haloes.

Shajib, Anowar J.↗
DOE OSTI2020

Elliptic flow coalescence to identify the $f_0$(980) content

Here we use a simple coalescence model to generate $f_0$(980) particles for three configurations: a $s\bar{s}$ meson, a $u\bar{u}s\bar{s}$ tetraquark, and a $K^+K^–$ molecule. The phase-space information of the coalescing constituents is taken from a multiphase transport (AMPT) simulation of heavy-ion collisions. It is shown that the number of constituent quarks scaling of the elliptic flow anisotropy can be used to discern $s\bar{s}$ from $u\bar{u}s\bar{s}$ and $K^+K^–$ configurations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Baseline predictions of elliptic flow and fluctuations for the RHIC Beam Energy Scan using response coefficients

Currently the RHIC Beam Energy Scan is exploring a new region of the Quantum Chromodynamic phase diagram at large baryon densities that approaches nuclear astrophysics regimes. This provides an opportunity to study relativistic hydrodynamics in a regime where the net conserved charges of baryon number, strangeness, and electric charge play a role, which will significantly change the theoretical approach to simulating the baryon-dense Quark-Gluon Plasma. In this work, we detail many of the important changes needed to adapt both initial conditions and the medium to baryon-rich matter. Then, we make baseline predictions for the elliptical flow and fluctuations based on extrapolating the physics at LHC and top RHIC energies to support future analyses of where and how the new baryon-dense physics causes these extrapolations to break down. First we compare eccentricities across beam energies, exploring their underlying assumptions; we find the the extrapolated initial state is predicted to be nearly identical to that at AuAu $\sqrt{s_{NN}}$ = 200 GeV. Then the final flow harmonic predictions are based on linear+cubic response. We discuss preliminary STAR results in order to determine the implications that they have for linear+cubic response coefficients at the lowest beam energy of AuAu $\sqrt{s_{NN}}$ = 7 GeV.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗