Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Elliptic problems”

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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Novel techniques and devices for in-situ film coatings of long, small diameter tubes or elliptical and other surface contours

In this study, devices and techniques that can, via physical vapor deposition,coat various surface contours or very long small aperture pipes, are described. Recently, a magnetron mole was developed in order to in-situ coat accelerator tube sections of the Brookhaven National Lab relativistic heavy ion collider that have 7.1 cm diameter with access points that are 500 m apart, for copper coat the accelerator vacuum tube in order to alleviate the problems of unacceptable ohmic heating and of electron clouds. A magnetron with a 50 cm long cathode was designed fabricated and successfully operated to copper coat a whole assembly containing a full-size, stainless steel, cold bore, of the accelerator magnet tubing connected to two types bellows, to which two additional pipes made of accelerator tubing were connected. The magnetron is mounted on a carriage with spring loaded wheels that successfully crossed bellows and adjusted for variations in vacuum tube diameter, while keeping the magnetron centered. Electrical power and cooling water were fed through a cable bundle. The umbilical cabling system, which is enclosed in a flexible braided metal sleeve, is driven by a motorized spool. To increase cathode lifetime, movable magnet package was developed, and thickest possible cathode was made, with a rather challenging target to substrate distance of less than 1.5 cm. Optimized process to ensure excellent adhesion was developed. Coating thickness of 10 μm Cu passed all industrial tests and even exceeded maximum capability of a 12 kg pull test fixture. Room temperature radio frequency (RF) resistivity measurement indicated that 10 μm Cu coated stainless steel accelerator tube has conductivity close to copper tubing. Work is in progress to repeat the RF resistivity measurement at cryogenic temperatures. Over 20 years ago, a device using multi axis robotic manipulators controlling separate robotic assemblies resulted in nine-axes of motion combined with conformal shape of the cathodes that can adapt to various curved surface contours was developed and successfully used for depositing optical coating on aircraft canopies. The techniques can be utilized for in situ coating of elliptical and other surface contour RF cavities and long beam pipes with thick superconducting films. Plans are to incorporate ion assisted deposition in those techniques for attaining dense, adherent and defect free coatings.

43 PARTICLE ACCELERATORS↗
DOE OSTI2020

Demonstration and performance testing of extreme-resolution simulations with static meshes on Summit (CPU & GPU) for a parked-turbine configuration and an actuator-line (mid-fidelity model) wind farm configuration (ECP-Q4 FY2020 Milestone Report)

The goal of the ExaWind project is to enable predictive simulations of wind farms comprised of many megawatt-scale turbines situated in complex terrain. Predictive simulations will require computational fluid dynamics (CFD) simulations for which the mesh resolves the geometry of the turbines and captures the rotation and large deflections of blades. Whereas such simulations for a single turbine are arguably petascale class, multi-turbine wind farm simulations will require exascale-class resources. The primary physics codes in the ExaWind simulation environment are Nalu-Wind, an unstructured-grid solver for the acoustically incompressible Navier-Stokes equations, AMR-Wind, a block-structured-grid solver with adaptive mesh refinement capabilities, and OpenFAST, a wind-turbine structural dynamics solver. The Nalu-Wind model consists of the mass-continuity Poisson-type equation for pressure and Helmholtz-type equations for transport of momentum and other scalars. For such modeling approaches, simulation times are dominated by linear-system setup and solution for the continuity and momentum systems. For the ExaWind challenge problem, the moving meshes greatly affect overall solver costs as reinitialization of matrices and recomputation of preconditioners is required at every time step. The choice of overset-mesh methodology to model the moving and non-moving parts of the computational domain introduces constraint equations in the elliptic pressure-Poisson solver. The presence of constraints greatly affects the performance of algebraic multigrid preconditioners.

17 WIND ENERGY↗
DOE OSTI2015

Interaction of elliptically polarised cross-degenerate cnoidal waves in an isotropic gyrotropic medium with spatial dispersion of cubic nonlinearity

Three unusual classes of particular analytical solutions to a system of four nonlinear equations are found for slowly varying complex amplitudes of circularly polarised components of the electric field. The system describes the self-action and interaction of two elliptically polarised plane waves collinearly propagating in an isotropic medium with second-order frequency dispersion and spatial dispersion of cubic nonlinearity. The solutions correspond to self-consistent combinations of two elliptically polarised cnoidal waves whose mutually orthogonal polarisation components vary in accordance with pairwise identical laws during propagation. At the same time, the amplitudes of the component with the same circular polarisation are proportional to two different elliptic Jacobi functions with the same periods. (nonlinear optical phenomena)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Application of Lagrangian techniques for calculating the on-axis rotational transform

The Floquet exponents of periodic field lines are studied through the variations of the magnetic action on the magnetic axis, which is assumed to be elliptical. The near-axis formalism developed by Mercier, Solov'ev and Shafranov is combined with a Lagrangian approach. The on-axis Floquet exponent is shown to coincide with the on-axis rotational transform. A discrete solution suitable for numerical implementation is introduced, which gives the Floquet exponents as solutions to an eigenvalue problem. This discrete formalism expresses the exponents as the eigenvalues of a $6$ X $6$ matrix.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Image segmentation for analyzing galaxy-galaxy strong lensing systems

The goal of this Letter is to develop a machine learning model to analyze the main gravitational lens and detect dark substructure (subhalos) within simulated images of strongly lensed galaxies. Using the technique of image segmentation, we turn the task of identifying subhalos into a classification problem, where we label each pixel in an image as coming from the main lens, a subhalo within a binned mass range, or neither. Our network is only trained on images with a single smooth lens and either zero or one subhalo near the Einstein ring. On an independent test set with lenses with large ellipticities, quadrupole and octopole moments, and for source apparent magnitudes between 17–25, the area of the main lens is recovered accurately. On average, only 1.3% of the true area is missed and 1.2% of the true area is added to another part of the lens. In addition, subhalos as light as 10 8.5 M ⊙ can be detected if they lie in bright pixels along the Einstein ring. Furthermore, the model is able to generalize to new contexts it has not been trained on, such as locating multiple subhalos with varying masses or more than one large smooth lens.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Integrated Simulation of Weld Residual Stress Evolution and Crack Propagation Using XFEM

Nuclear power plant components operate in environments that promote multiple degradation mecha- nisms, several of which involve crack initiation and growth. An ongoing effort in the U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program is developing a general capability within the Multiphysics Object Oriented Simulation Environment (MOOSE) framework for simulating three-dimensional crack growth under a range of driving conditions, including fatigue, stress corrosion cracking (SCC), brittle fracture, and stress-relaxation cracking. This report demonstrates an end-to-end workflow that uses this capability to model weld-residual-stress-driven SCC in the J-groove weld of a pressurized-water reactor control rod drive mechanism penetration in the vessel head. The workflow consists of a thermomechanical welding simulation with temperature-dependent plasticity, followed by cooldown to ambient conditions, and a restart of the simulation using the MOOSE extended finite element method (XFEM) module to propagate a three-dimensional crack through the residual stress field. New welding capabilities were developed to properly initialize newly activated elements in the weld region, and robustness improvements were made to the mesh-based algorithm for defining cutting planes in the 3D XFEM algorithm, allowing it to handle complex crack fronts and stress fields. Together these advances allowed the simulated SCC crack to grow from an initial elliptical flaw in the weld, across the weld, through the tube wall, and almost to the triple point (where the weld, tube, and reactor pressure vessel head intersect) over roughly 36 years of simulated service. These results demonstrate a workflow that can be extended to fully three-dimensional welding simulations and more complex crack interaction problems.

42 - ENGINEERING↗
DOE OSTI2015

Electron temperature gradient mode instability and stationary vortices with elliptic and circular boundary conditions in non-Maxwellian plasmas

Linear and nonlinear dynamics of electron temperature gradient mode along with parallel electron dynamics is investigated by considering hydrodynamic electrons and non-Maxwellian ions. It is noticed that the growth rate of η{sub e}-mode driven linear instability decreases by increasing the value of spectral index and increases by reducing the ion/electron temperature ratio along the magnetic field lines. The eigen mode dispersion relation is also found in the ballooning mode limit. Stationary solutions in the form of dipolar vortices are obtained for both circular and elliptic boundary conditions. It is shown that the dynamics of both circular and elliptic vortices changes with the inclusion of inhomogeneity and non-Maxwellian effects.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes

In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered considerable interest due to their flexibility, robust theoretical guarantees, and close ties to traditional methods. They can transform the solving of general nonlinear PDEs into solving quadratic optimization problems with nonlinear, PDE-induced constraints. However, the complexity bottleneck lies in computing with dense kernel matrices obtained from pointwise evaluations of the covariance kernel, and its partial derivatives, a result of the PDE constraint and for which fast algorithms are scarce. The primary goal of this paper is to provide a near-linear complexity algorithm for working with such kernel matrices. We present a sparse Cholesky factorization algorithm for these matrices based on the near-sparsity of the Cholesky factor under a novel ordering of pointwise and derivative measurements. The near-sparsity is rigorously justified by directly connecting the factor to GP regression and exponential decay of basis functions in numerical homogenization. We then employ the Vecchia approximation of GPs, which is optimal in the Kullback-Leibler divergence, to compute the approximate factor. This enables us to compute ϵ-approximate inverse Cholesky factors of the kernel matrices with complexity O(N log d (N/ϵ)) in space and O(N log 2d (N/ϵ)) in time. We integrate sparse Cholesky factorizations into optimization algorithms to obtain fast solvers of the nonlinear PDE. We numerically illustrate our algorithm’s near-linear space/time complexity for a broad class of nonlinear PDEs such as the nonlinear elliptic, Burgers, and Monge-Ampère equations. In summary, we provide a fast, scalable, and accurate method for solving general PDEs with GPs and kernel methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Force-free Jacobian equilibria for Vlasov-Maxwell plasmas

New analytic force-free Vlasov-Maxwell equilibria for thin current sheets are presented. The magnetic flux densities are expressed in terms of Jacobian elliptic functions of one Cartesian spatial coordinate. The magnetic flux densities reduce to previously reported hyperbolic functions in one limit and sinusoidal functions in another limit of the modulus k. A much wider class of nonlinear force-free Vlasov-Maxwell equilibria open expanded possibilities for modeling of solar system, astrophysical and laboratory plasmas. Modified Maxwellian distribution functions are determined explicitly in terms of Jacobian elliptic functions. Conditions for double peaked distribution functions that could be unstable are developed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Nonlinear coupling of left and right handed circularly polarized dispersive Alfvén wave

The nonlinear phenomena are of prominent interests in understanding the particle acceleration and transportation in the interplanetary space. The ponderomotive nonlinearity causing the filamentation of the parallel propagating circularly polarized dispersive Alfvén wave having a finite frequency may be one of the mechanisms that contribute to the heating of the plasmas. The contribution will be different of the left (L) handed mode, the right (R) handed mode, and the mix mode. The contribution also depends upon the finite frequency of the circularly polarized waves. In the present paper, we have investigated the effect of the nonlinear coupling of the L and R circularly polarized dispersive Alfvén wave on the localized structures formation and the respective power spectra. The dynamical equations are derived in the presence of the ponderomotive nonlinearity of the L and R pumps and then studied semi-analytically as well as numerically. The ponderomotive nonlinearity accounts for the nonlinear coupling between both the modes. In the presence of the adiabatic response of the density fluctuations, the nonlinear dynamical equations satisfy the modified nonlinear Schrödinger equation. The equations thus obtained are solved in solar wind regime to study the coupling effect on localization and the power spectra. The effect of coupling is also studied on Faraday rotation and ellipticity of the wave caused due to the difference in the localization of the left and the right modes with the distance of propagation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Novel spherical hohlraum with cylindrical laser entrance holes and shields

Our recent works [K. Lan et al., Phys. Plasmas 21, 010704 (2014); K. Lan et al., Phys. Plasmas 21, 052704 (2014)] have shown that the octahedral spherical hohlraums are superior to the cylindrical hohlraums in both higher symmetry during the capsule implosion and lower backscatter without supplementary technology. However, both the coupling efficiency from the drive laser energy to the capsule and the capsule symmetry decrease remarkably when larger laser entrance holes (LEHs) are used. In addition, the laser beams injected at angles > 45° transport close to the hohlraum wall, thus the wall blowoff causes the LEH to close faster and results in strong laser plasma interactions inside the spherical hohlraums. In this letter, we propose a novel octahedral hohlraum with LEH shields and cylindrical LEHs to alleviate these problems. From our theoretical study, with the LEH shields, the laser coupling efficiency is significantly increased and the capsule symmetry is remarkably improved in the spherical hohlraums. The cylindrical LEHs take advantage of the cylindrical hohlraum near the LEH and mitigate the influence of the blowoff on laser transport inside a spherical hohlraum. The cylindrical LEHs can also be applied to the rugby and elliptical hohlraums.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Large-Time Behavior of Solutions to Vlasov-Poisson-Fokker-Planck Equations: From Evanescent Collisions to Diffusive Limit

The present contribution investigates the dynamics generated by the two-dimensional Vlasov-Poisson-Fokker-Planck equation for charged particles in a steady inhomogeneous background of opposite charges. We provide global in time estimates that are uniform with respect to initial data taken in a bounded set of a weighted L{sup 2} space, and where dependencies on the mean-free path τ and the Debye length δ are made explicit. In our analysis the mean free path covers the full range of possible values: from the regime of evanescent collisions τ→∞ to the strongly collisional regime τ→0. As a counterpart, the largeness of the Debye length, that enforces a weakly nonlinear regime, is used to close our nonlinear estimates. Accordingly we pay a special attention to relax as much as possible the τ-dependent constraint on δ ensuring exponential decay with explicit τ-dependent rates towards the stationary solution. In the strongly collisional limit τ→0, we also examine all possible asymptotic regimes selected by a choice of observation time scale. Here also, our emphasis is on strong convergence, uniformity with respect to time and to initial data in bounded sets of a L{sup 2} space. Our proofs rely on a detailed study of the nonlinear elliptic equation defining stationary solutions and a careful tracking and optimization of parameter dependencies of hypocoercive/hypoelliptic estimates.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

A unified hp-HDG framework for Friedrichs' PDE systems

Here, this work proposes a unified hp-adaptivity framework for hybridized discontinuous Galerkin (HDG) method for a large class of partial differential equations (PDEs) of Friedrichs' type. In particular, we present unified hp-HDG formulations for abstract one-field and two-field structures and prove their well-posedness. In order to handle non-conforming interfaces we simply take advantage of HDG built-in mortar structures. With split-type mortars and the approximation space of trace, a numerical flux can be derived via Godunov approach and be naturally employed without any additional treatment. As a consequence, the proposed formulations are parameter-free. We perform several numerical experiments for time-independent and linear PDEs including elliptic, hyperbolic, and mixed-type to verify the proposed unified hp-formulations and demonstrate the effectiveness of hp-adaptation. Two adaptivity criteria are considered: one is based on a simple and fast error indicator, while the other is rigorous but more expensive using an adjoint-based error estimate. The numerical results show that these two approaches are comparable in terms of convergence rate even for problems with strong gradients, discontinuities, and singularities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Modeling electric charge distribution on insulator under electron bombardment: Case of rectangular surface implantation

Despite progress in the study of dielectric properties and the formation of secondary electrons images and especially in the understanding of their mirror curve shape, since the first models for mirror equation were developed, an exact quantitative prediction of the mirror curve for most materials has remained an unsolved problem. In this paper, recent development in the characterization of charge trapping ability of insulators using the scanning electron microscope mirror method (SEMMM) is reviewed. All this work has resulted in unprecedented insights into the early stage of dielectric study and it is also relevant for a deeper understanding of this anomalous effect (mirror effect) as well as for discussion of the factors affecting it. So the dependency of elliptic mirror and the anisotropic effect in the trapping phenomena of charge is highlighted.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Building a quantum computing architecture using 3D superconducting cavities

Quantum computers promise advantages over classical machines for solving certain complex problems, but building processors that truly deliver this advantage remains a central challenge, particularly due to limited coherence times. Three-dimensional superconducting radio-frequency (SRF) cavities offer an attractive platform due to their exceptionally long lifetimes. However, since these harmonic systems require nonlinear elements, such as transmons, for control, additional losses are often introduced. In this talk, I will present a multimode quantum system based on an elliptical SRF cavity hosting two cavity modes weakly coupled to an ancillary transmon circuit. This architecture is carefully engineered to preserve coherence while enabling efficient control. By optimizing the design to mitigate transmon-induced decoherence, we realize single-photon lifetimes of 20.6 ms and 15.6 ms in the two modes, with pure dephasing times exceeding 40 ms. Using sideband interactions and error-resilient protocols, such as measurement-based correction and post-selection, we demonstrate high-fidelity state control, including preparation of Fock states up to N=20 with fidelities above 95% (to our knowledge, the highest reported to date), as well as high-fidelity two-mode entanglement. These results highlight 3D SRF cavities as a robust foundation for qudit-based quantum information processing, harnessing the large Hilbert space of cavity modes. I will conclude by outlining strategies to further enhance coherence in both cavities and ancilla qubits, and discuss pathways toward scaling this architecture into a larger quantum computing platform.

Roy, Tanay [Fermilab]↗
DOE OSTI2015

Dark matter voids in the SDSS galaxy survey

What do we know about voids in the dark matter distribution given the Sloan Digital Sky Survey (SDSS) and assuming the ΛCDM model? Recent application of the Bayesian inference algorithm BORG to the SDSS Data Release 7 main galaxy sample has generated detailed Eulerian and Lagrangian representations of the large-scale structure as well as the possibility to accurately quantify corresponding uncertainties. Building upon these results, we present constrained catalogs of voids in the Sloan volume, aiming at a physical representation of dark matter underdensities and at the alleviation of the problems due to sparsity and biasing on galaxy void catalogs. To do so, we generate data-constrained reconstructions of the presently observed large-scale structure using a fully non-linear gravitational model. We then find and analyze void candidates using the VIDE toolkit. Our methodology therefore predicts the properties of voids based on fusing prior information from simulations and data constraints. For usual void statistics (number function, ellipticity distribution and radial density profile), all the results obtained are in agreement with dark matter simulations. Our dark matter void candidates probe a deeper void hierarchy than voids directly based on the observed galaxies alone. The use of our catalogs therefore opens the way to high-precision void cosmology at the level of the dark matter field. We will make the void catalogs used in this work available at http://www.cosmicvoids.net.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

On the offset of barred galaxies from the black hole M {sub BH}-σ relationship

We use collisionless N-body simulations to determine how the growth of a supermassive black hole (SMBH) influences the nuclear kinematics in both barred and unbarred galaxies. In the presence of a bar, the increase in the velocity dispersion σ (within the effective radius) due to the growth of an SMBH is on average ≲ 10%, whereas the increase is only ≲ 4% in an unbarred galaxy. In a barred galaxy, the increase results from a combination of three separate factors: (1) orientation and inclination effects; (2) angular momentum transport by the bar that results in an increase in the central mass density; and (3) an increase in the vertical and radial velocity anisotropy of stars in the vicinity of the SMBH. In contrast, the growth of the SMBH in an unbarred galaxy causes the velocity distribution in the inner part of the nucleus to become less radially anisotropic. The increase in σ following the growth of the SMBH is insensitive to a variation of a factor of 10 in the final mass of the SMBH, showing that it is the growth process rather than the actual SMBH mass that alters bar evolution in a way that increases σ. We argue that using an axisymmetric stellar dynamical modeling code to measure SMBH masses in barred galaxies could result in a slight overestimate of the derived M {sub BH}, especially if a constant M/L ratio is assumed. We conclude that the growth of a black hole in the presence of a bar could result in an increase in σ that is roughly 4%-8% larger than the increase that occurs in an axisymmetric system. While the increase in σ due to SMBH growth in a barred galaxy might partially account for the claimed offset of barred galaxies and pseudo bulges from the M {sub BH}-σ relation obtained for elliptical galaxies and classical bulges in unbarred galaxies, it is inadequate to account for all of the offset.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

The High Fraction of Thin Disk Galaxies Continues to Challenge ΛCDM Cosmology

Any viable cosmological framework has to match the observed proportion of early- and late-type galaxies. In this contribution, we focus on the distribution of galaxy morphological types in the standard model of cosmology (Lambda cold dark matter, ΛCDM). Using the latest state-of-the-art cosmological ΛCDM simulations known as Illustris, IllustrisTNG, and EAGLE, we calculate the intrinsic and sky-projected aspect ratio distribution of the stars in subhalos with stellar mass M * > 10 10 M ⊙ at redshift z = 0. There is a significant deficit of intrinsically thin disk galaxies, which however comprise most of the locally observed galaxy population. Consequently, the sky-projected aspect ratio distribution produced by these ΛCDM simulations disagrees with the Galaxy And Mass Assembly (GAMA) survey and Sloan Digital Sky Survey at ≥12.52σ (TNG50-1) and ≥14.82σ (EAGLE50) confidence. The deficit of intrinsically thin galaxies could be due to a much less hierarchical merger-driven build-up of observed galaxies than is given by the ΛCDM framework. It might also arise from the implemented sub-grid models, or from the limited resolution of the above-mentioned hydrodynamical simulations. We estimate that an 8 5 times better mass resolution realization than TNG50-1 would reduce the tension with GAMA to the 5.58σ level. Finally, we show that galaxies with fewer major mergers have a somewhat thinner aspect ratio distribution. Given also the high expected frequency of minor mergers in ΛCDM, the problem may be due to minor mergers. In this case, the angular momentum problem could be alleviated in Milgromian dynamics because of a reduced merger frequency arising from the absence of dynamical friction between extended dark matter halos.

79 ASTRONOMY AND ASTROPHYSICS↗