arXiv subjects

J. R. King

Publications and source records attributed to J. R. King.

At least 19 recordsLinked to original sources

arXiv2023

Complex-plane singularity dynamics for blow up in a nonlinear heat equation: analysis and computation

Blow-up solutions to a heat equation with spatial periodicity and a quadratic nonlinearity are studied through asymptotic analyses and a variety of numerical methods. The focus is on the dynamics of the singularities in the complexified space domain. Blow up in finite time is caused by these singularities eventually reaching the real axis. The analysis provides a distinction between small and large nonlinear effects, as well as insight into the various time scales on which blow up is approached. It is shown that an ordinary differential equation with quadratic nonlinearity plays a central role in the asymptotic analysis. This equation is studied in detail, including its numerical computation on multiple Riemann sheets, and the far-field solutions are shown to be given at leading order by a Weierstrass elliptic function.

math.AP↗

arXiv2021

Growing Neoclassical Tearing Modes Seeded via Transient-Induced-Multimode Interactions

Nonlinear extended MHD simulations demonstrating seeding of neoclassical tearing modes (NTMs) via MHD-transient-induced multimode interactions are presented. Simulations of NTMs are enabled by two recent NIMROD code developments: the implementation of heuristic neoclassical stresses and the application of transient magnetic perturbations (MPs) at the boundary. NTMs are driven unstable by the inherently pressure driven kinetic bootstrap current, which arises due to collisional viscosity between passing and trapped electrons. These simulations use heuristic closures that model the neoclassical electron and ion stresses. NTM growth requires a seed island, which is generated by a transiently applied MP in simulations. The capability is demonstrated using kinetic-based reconstructions with flow of a DIII-D ITER Baseline Scenario discharge [R.J. La Haye, et al., Proceedings IAEA FEC 2020]. The applied MP seeds a 2/1 NTM that grows in two phases: a slow growth phase followed by a faster robust growth phase like that observed experimentally. Additionally, an evolving sequence of higher order core modes are excited at first. Power transfer analysis shows that nonlinear interactions between the core modes and the 2/1 helps drive the initial slow growth. Once the induced 2/1 magnetic island reaches a critical width, the NTM transitions to faster robust growth which is well described by the nonlinear modified Rutherford equation. This work highlights the role of nonlinear mode coupling in seeding NTMs.

physics.plasm-ph↗

arXiv2021

Solutions with snaking singularities for the fast diffusion equation

We construct solutions of the fast diffusion equation, which exist for all $t\in\mathbb{R}$ and are singular on the set $Γ(t):= \{ ξ(s) ; -\infty 0$, where $ξ\in C^3(\mathbb{R};\mathbb{R}^n)$, $n\geq 2$. We also give a precise description of the behavior of the solutions near $Γ(t)$.

math.AP↗

arXiv2021

Cross-Code verification and sensitivity analysis to effectively model the electrothermal instability

This manuscript presents verification cases that are developed to study the electrothermal instability (ETI). Specific verification cases are included to ensure that the unit physics components necessary to model the ETI are accurate, providing a path for fluid-based codes to effectively simulate ETI in the linear and nonlinear growth regimes. Two software frameworks with different algorithmic approaches are compared for accuracy in their ability to simulate diffusion of a magnetic field, linear growth of the ETI, and a fully nonlinear ETI evolution. The nonlinear ETI simulations show early time agreement, with some differences emerging, as noted in the wavenumber spectrum, late into the nonlinear development of ETI. A sensitivity study explores the role of equation-of-state (EOS), vacuum density, and vacuum resistivity. EOS and vacuum resistivity are found to be the most critical factors in the modeling of nonlinear ETI development.

physics.plasm-ph↗

arXiv2020

Multidimensional tests of a finite-volume solver for MHD with a real-gas equation of state

This work considers two algorithms of a finite-volume solver for the MHD equations with a real-gas equation of state (EOS). Both algorithms use a multistate form of Harten-Lax-Van Leer approximate Riemann solver as formulated for MHD discontinuities. This solver is modified to use the generalized sound speed from the real-gas EOS. Two methods are tested: EOS evaluation at cell centers and at flux interfaces where the former is more computationally efficient. A battery of 1D and 2D tests are employed: convergence of 1D and 2D linearized waves, shock tube Riemann problems, a 2D nonlinear circularly polarized Alfvén wave, and a 2D magneto-Rayleigh-Taylor instability test. The cell-centered EOS evaluation algorithm produces unresolvable thermodynamic inconsistencies in the intermediate states leading to spurious solutions while the flux-interface EOS evaluation algorithm robustly produces the correct solution. The linearized wave tests show this inconsistency is associated with the magnetosonic waves and the magneto-Rayleigh-Taylor instability test demonstrates simulation results where the spurious solution leads to an unphysical simulation.

physics.comp-ph↗

arXiv2018

GPU acceleration and performance of the particle-beam-dynamics code Elegant

Elegant is an accelerator physics and particle-beam dynamics code widely used for modeling and design of a variety of high-energy particle accelerators and accelerator-based systems. In this paper we discuss a recently developed version of the code that can take advantage of CUDA-enabled graphics processing units (GPUs) to achieve significantly improved performance for a large class of simulations that are important in practice. The GPU version is largely defined by a framework that simplifies implementations of the fundamental kernel types that are used by Elegant: particle operations, reductions, particle loss, histograms, array convolutions and random number generation. Accelerated performance on the Titan Cray XK-7 supercomputer is approximately 6-10 times better with the GPU than all the CPU cores associated with the same node count. In addition to performance, the maintainability of the GPU-accelerated version of the code was considered a key design objective. Accuracy with respect to the CPU implementation is also a core consideration. Four different methods are used to ensure that the accelerated code faithfully reproduces the CPU results.

physics.comp-ph↗

arXiv2017

MHD modeling of a DIII-D low-torque QH-mode discharge and comparison to observations

Extended-MHD modeling of DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] quiescent H-mode (QH-mode) discharges with nonlinear NIMROD [C. R. Sovinec et al., J. Comput. Phys. 195, 355 (2004)] simulations saturates into a turbulent state but does not saturate when the steady-state flow inferred from measurements is not included. This is consistent with the experimental observations of the quiescent regime on DIII-D. The simulation with flow develops into a saturated turbulent state where the n=1 and 2 toroidal modes become dominant through an inverse cascade. Each mode in the range of n=1-5 is dominant at a different time. Consistent with experimental observations during QH-mode, the simulated state leads to large particle transport relative to the thermal transport. Analysis shows that the amplitude and phase of the density and temperature perturbations differ resulting in greater fluctuation-induced convective particle transport relative to the convective thermal transport. Comparison to magnetic-coil measurements shows that rotation frequencies differ between the simulation and experiment, which indicates that more sophisticated extended-MHD two-fluid modeling is required.

physics.plasm-ph↗

arXiv2017

The Impact of Collisionality, FLR and Parallel Closure Effects on Instabilities in the Tomakak Pedestal: Numerical Studies with the NIMROD code

The extended-MHD NIMROD code [C.R. Sovinec and J.R. King, J. Comput. Phys. 229, 5803 (2010)] is verified against the ideal-MHD ELITE code [H.R. Wilson et al. Phys. Plasmas 9, 1277 (2002)] on a diverted tokamak discharge. When the NIMROD model complexity is increased incrementally, resistive and first-order finite-Larmour radius effects are destabilizing and stabilizing, respectively. The full result is compared to local analytic calculations which are found to overpredict both the resistive destabilization and drift stabilization in comparison to the NIMROD computations.

physics.plasm-ph↗

arXiv2017

Effect of Scrape-Off-Layer Current on Reconstructed Tokamak Equilibrium

Methods are described that extend fields from reconstructed equilibria to include scrape-off-layer current through extrapolated parametrized and experimental fits. The extrapolation includes both the effects of the toroidal-field and pressure gradients which produce scrape-off-layer current after recomputation of the Grad-Shafranov solution. To quantify the degree that inclusion of scrape-off-layer current modifies the equilibrium, the $χ$-squared goodness-of-fit parameter is calculated for cases with and without scrape-off-layer current. The change in $χ$-squared is found to be minor when scrape-off-layer current is included however flux surfaces are shifted by up to 3 cm. The impact on edge modes of these scrape-off-layer modifications is also found to be small and the importance of these methods to nonlinear computation is discussed.

physics.plasm-ph↗

arXiv2017

NIMROD Modeling of Quiescent H-mode: Reconstruction Considerations and Saturation Mechanism

The extended-MHD NIMROD code [C.R. Sovinec and J.R. King, J. Comput. Phys. 229, 5803 (2010)] models broadband-MHD activity from a reconstruction of a quiescent H-mode shot on the DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)]. Computations with the reconstructed toroidal and poloidal ion flows exhibit low-n perturbations (n=1-5) that grow and saturate into a turbulent-like MHD state. The workflow used to project the reconstructed state onto the NIMROD basis functions re-solves the Grad-Shafranov equation and extrapolates profiles to include scrape-off-layer currents. Evaluation of the transport from the turbulent-like MHD state leads to a relaxation of the density and temperature profiles.

physics.plasm-ph↗

arXiv2016

Pattern formation in a pseudo-parabolic equation

We address the propagation into an unstable state of a localised disturbance in a forward-backward diffusion pseudo-parabolic equation. Three asymptotic regimes are distinguished as t tends to infinity, the first being a regime ahead of the propagating disturbance that is dominated by the linearised equation. The analysis of this leads to the determination of the speed of the leading edge of the propagating disturbance and implies that in the second, transition, regime the solution takes the form of a modulated travelling wave. In a third regime the solution approaches a nearly periodic steady state, where the period is obtained on matching with the modulated travelling wave. Detailed analysis of this pattern is also presented. The analysis is completed by contrasting the formal asymptotic description of the solution with numerical computations. It is assumed for the above analysis that the initial disturbance decays faster than an exponential rate; in this case a critical exponential decay rate at the leading edge of the front and propagation speed are found. We investigate the wave speed selection mechanism for exponentially decaying initial conditions. It is found that whenever the initial data behave as a real exponential (no matter how slow the rate of the decay) the speed selected is that selected by fast decaying initial conditions. However, for initial conditions with a complex exponential we find regimes of the decay rate and the wavelength for which the front propagates at a faster wave speed. This is investigated numerically and is worth emphasising since it gives a different scenario for wave speed behaviour than that exhibited by well-studied semilinear reaction-diffusion equations: there are initial conditions with exponential decay faster than the critical one for which the front propagates with a speed faster than the critical one.

math.AP↗

arXiv2015

Lie symmetry properties of nonlinear reaction-diffusion equations with gradient-dependent diffusivity

Complete descriptions of the Lie symmetries of a class of nonlinear reaction-diffusion equations with gradient-dependent diffusivity in one and two space dimensions are obtained. A surprisingly rich set of Lie symmetry algebras depending on the form of diffusivity and source (sink) in the equations is derived. It is established that there exists a subclass in 1-D space admitting an infinite-dimensional Lie algebra of invariance so that it is linearisable. A special power-law diffusivity with a fixed exponent, which leads to wider Lie invariance of the equations in question in 2-D space, is also derived. However, it is shown that the diffusion equation without a source term (which often arises in applications and is sometimes called the Perona-Malik equation) possesses no rich variety of Lie symmetries depending on the form of gradient-dependent diffusivity. The results of the Lie symmetry classification for the reduction to lower dimensionality, and a search for exact solutions of the nonlinear 2-D equation with power-law diffusivity, also are included.

math-ph↗

arXiv2011

Detailed Abundances of the Solar Twins 16 Cygni A and B: Constraining Planet Formation Models

Results of a detailed abundance analysis of the solar twins 16 Cyg A and 16 Cyg B based on high-resolution, high signal-to-noise ratio echelle spectroscopy are presented. 16 Cyg B is known to host a giant planet while no planets have yet been detected around 16 Cyg A. Stellar parameters are derived directly from our high-quality spectra, and the stars are found to be physically similar, with Delta_T_eff = +43 K, Delta_logg = -0.02 dex, and Delta_xi = +0.10 km/s (in the sense of A - B), consistent with previous findings. Abundances of 15 elements are derived and are found to be indistinguishable between the two stars. The abundances of each element differ by <= 0.026 dex, and the mean difference is +0.003 +/- 0.015 (sigma) dex. Aside from Li, which has been previously shown to be depleted by a factor of at least 4.5 in 16 Cyg B relative to 16 Cyg A, the two stars appear to be chemically identical. The abundances of each star demonstrate a positive correlation with the condensation temperature of the elements (T_c); the slopes of the trends are also indistinguishable. In accordance with recent suggestions, the positive slopes of the [m/H]-T_c relations may imply that terrestrial planets have not formed around either 16 Cyg A or 16 Cyg B. The physical characteristics of the 16 Cyg system are discussed in terms of planet formation models, and plausible mechanisms that can account for the lack of detected planets around 16 Cyg A, the disparate Li abundances of 16 Cyg A and B, and the eccentricity of the planet 16 Cyg B b are suggested.

astro-ph.SR↗

arXiv2010

Fe I and Fe II Abundances of Solar-Type Dwarfs in the Pleiades Open Cluster

We have derived Fe abundances of 16 solar-type Pleiades dwarfs by means of an equivalent width analysis of Fe I and Fe II lines in high-resolution spectra obtained with the Hobby - Eberly Telescope and High Resolution Spectrograph. Abundances derived from Fe II lines are larger than those derived from Fe I lines (herein referred to as over-ionization) for stars with Teff < 5400 K, and the discrepancy (deltaFe = [Fe II/H] - [Fe I/H]) increases dramatically with decreasing Teff, reaching over 0.8 dex for the coolest stars of our sample. The Pleiades joins the open clusters M 34, the Hyades, IC 2602, and IC 2391, and the Ursa Major moving group, demonstrating ostensible over-ionization trends. The Pleiades deltaFe abundances are correlated with Ca II infrared triplet and Halpha chromospheric emission indicators and relative differences therein. Oxygen abundances of our Pleiades sample derived from the high-excitation O I triplet have been previously shown to increase with decreasing Teff, and a comparison with the deltaFe abundances suggests that the over-excitation (larger abundances derived from high excitation lines relative to low excitation lines) and over-ionization effects that have been observed in cool open cluster and disk field main sequence (MS) dwarfs share a common origin. Star-to-star Fe I abundances have low internal scatter, but the abundances of stars with Teff < 5400 K are systematically higher compared to the warmer stars. The cool star [Fe I/H] abundances cannot be connected directly to over-excitation effects, but similarities with the deltaFe and O I triplet trends suggest the abundances are dubious. Using the [Fe I/H] abundances of five stars with Teff > 5400 K, we derive a mean Pleiades cluster metallicity of [Fe/H] = +0.01 +/- 0.02.

astro-ph.SR↗

arXiv2010

Li I and K I Scatter in Cool Pleiades Dwarfs

We utilize high-resolution (R~60,000), high S/N (~100) spectroscopy of 17 cool Pleiades dwarfs to examine the confounding star-to-star scatter in the 6707 Li I line strengths in this young cluster. Our Pleiads, selected for their small projected rotational velocity and modest chromospheric emission, evince substantial scatter in the linestrengths of 6707 Li I feature that is absent in the 7699 K I resonance line. The Li I scatter is not correlated with that in the high-excitation 7774 O I feature, and the magnitude of the former is greater than the latter despite the larger temperature sensitivity of the O I feature. These results suggest that systematic errors in linestrength measurements due to blending, color (or color-based T_eff) errors, or line formation effects related to an overlying chromosphere are not the principal source of Li I scatter in our stars. There do exist analytic spot models that can produce the observed Li scatter without introducing scatter in the K I line strengths or the color-magnitude diagram. However, these models predict factor of >3 differences in abundances derived from the subordinate 6104 and resonance 6707 Li I features; we find no difference in the abundances determined from these two features. These analytic spot models also predict CN line strengths significantly larger than we observe in our spectra. The simplest explanation of the Li, K, CN, and photometric data is that there must be a real abundance component to the Pleiades Li dispersion. We suggest that this real abundance component is the manifestation of relic differences in erstwhile pre-main-sequence Li burning caused by effects of surface activity on stellar structure. We discuss observational predictions of these effects.

astro-ph.SR↗

arXiv2009

Stellar Nucleosynthesis in the Hyades Open Cluster

We report a comprehensive light element (Li, C, N, O, Na, Mg, and Al) abundance analysis of three solar-type main sequence (MS) dwarfs and three red giant branch (RGB) clump stars in the Hyades open cluster using high-resolution and high signal-to-noise spectroscopy. For each group (MS or RGB), the CNO abundances are found to be in excellent star-to-star agreement. Our results confirm that the giants have undergone the first dredge-up and that material processed by the CN cycle has been mixed to the surface layers. The observed abundances are compared to predictions of a standard stellar model based on the Clemson-American University of Beirut (CAUB) stellar evolution code. The model reproduces the observed evolution of the N and O abundances, as well as the previously derived 12C/13C ratio, but it fails to predict by a factor of 1.5 the observed level of 12C depletion. Li abundances are derived to determine if non-canonical extra mixing has occurred in the Hyades giants. The Li abundance of the giant gamma Tau is in good accord with the predicted level of surface Li dilution, but a ~0.35 dex spread in the giant Li abundances is found and cannot be explained by the stellar model. Possible sources of the spread are discussed; however, it is apparent that the differential mechanism responsible for the Li dispersion must be unrelated to the uniformly low 12C abundances of the giants. Na, Mg, and Al abundances are derived as an additional test of our stellar model. All three elements are found to be overabundant by 0.2-0.5 dex in the giants relative to the dwarfs. Such large enhancements of these elements are not predicted by the stellar model, and non-LTE effects significantly larger (and, in some cases, of opposite sign) than those implied by extant literature calculations are the most likely cause.

astro-ph.SR↗

arXiv2005

Hyades Oxygen Abundances from the Lambda 6300 [O I] Line: The Giant-Dwarf Discrepancy Revisited

We present the results of our abundance analysis of Fe, Ni, and O in high S/N, high-resolution VLT/UVES and McDonald/2dcoude spectra of nine dwarfs and three giants in the Hyades open cluster. The difference in Fe abundances derived from Fe II and Fe I lines ([Fe II/H] - [Fe I/H]) and Ni I abundances derived from moderately high-excitation (Chi ~ 4.20 eV) lines are found to increase with decreasing T_eff for the dwarfs. Both of these findings are in concordance with previous results of over-excitation/ionization in cool young dwarfs. Oxygen abundances are derived from the Lambda 6300 [O I] line, with careful attention given to the Ni I blend. The dwarf O abundances are in star-to-star agreement within uncertainties, but the abundances of the three coolest dwarfs (4573 < T_eff < 4834 K) evince an increase with decreasing T_eff. Possible causes for the apparent trend are considered, including the effects of over-dissociation of O-containing molecules. O abundances are derived from the near-UV Lambda 3167 OH line in high-quality Keck/HIRES spectra, and no such effects are found- indeed, the OH-based abundances show an increase with decreasing T_eff, leaving the nature and reality of the cool dwarf [O I]-based O trend uncertain. The mean relative O abundance of the six warmest dwarfs (5075 < T_eff < 5978 K) is [O/H] = +0.14 +/- 0.02, and we find a mean abundance of [O/H] = +0.08 +/- 0.02 for the giants. Thus, our updated analysis of the Lambda 6300 [O I] line does not confirm the Hyades giant-dwarf oxygen discrepancy initially reported by King & Hiltgen (1996), suggesting the discrepancy was a consequence of analysis-related systematic errors....

astro-ph↗

arXiv2005

Beryllium Enhancement as Evidence for Accretion in a Lithium-Rich F Dwarf

The early F dwarf star ``J37'' in the open cluster NGC6633 shows an unusual pattern of photospheric abundances, including an order of magnitude enhancement of lithium and iron-peak elements, but an under-abundance of carbon. As a consequence of its thin convection zone these anomalies have been attributed to either radiative diffusion or the accretion of hydrogen-depleted material. By comparing high resolution VLT/UVES spectra of J37 (and other F stars in NGC 6633) with syntheses of the Be ii doublet region at 3131 Ang, we establish that J37 also has a Be abundance (A(Be)=3.0+/-0.5) that is at least ten times the cosmic value. This contradicts radiative diffusion models that produce a Li over-abundance, as they also predict photospheric Be depletion. Instead, since Be is a highly refractory element, it supports the notion that J37 is the first clear example of a star that has accreted volatile-depleted material with a composition similar to chondritic meteorites, although some diffusion may be necessary to explain the low C and O abundances.

astro-ph↗