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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.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Spatio-temporal dynamics induced by competing instabilities in two asymmetrically coupled nonlinear evolution equations

Pattern formation often occurs in spatially extended physical, biological, and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and their characteristic length scales. However, patterns resulting from the simultaneous occurrence of instabilities cannot be expected to be simple superposition of the patterns associated with the considered instabilities. To address this issue, we design two simple models composed by two asymmetrically coupled equations of non-conserved (Swift-Hohenberg equations) or conserved (Cahn-Hilliard equations) order parameters with different characteristic wave lengths. The patterns arising in these systems range from coexisting static patterns of different wavelengths to traveling waves. A linear stability analysis allows to derive a two parameter phase diagram for the studied models, in particular, revealing for the Swift-Hohenberg equations, a co-dimension two bifurcation point of Turing and wave instability and a region of coexistence of stationary and traveling patterns. The nonlinear dynamics of the coupled evolution equations is investigated by performing accurate numerical simulations. These reveal more complex patterns, ranging from traveling waves with embedded Turing patterns domains to spatio-temporal chaos, and a wide hysteretic region, where waves or Turing patterns coexist. For the coupled Cahn-Hilliard equations the presence of a weak coupling is sufficient to arrest the coarsening process and to lead to the emergence of purely periodic patterns. The final states are characterized by domains with a characteristic length, which diverges logarithmically with the coupling amplitude.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Restricted Hartree Fock using complex-valued orbitals: A long-known but neglected tool in electronic structure theory

Restricted Hartree Fock using complex-valued orbitals (cRHF) is studied. We introduce an orbital pairing theorem, with which we obtain a concise connection between cRHF and real-valued RHF, and use it to uncover the close relationship between cRHF, unrestricted Hartree Fock, and generalized valence bond perfect pairing. This enables an intuition for cRHF, contrasting with the generally unintuitive nature of complex orbitals. We also describe an efficient computer implementation of cRHF and its corresponding stability analysis. By applying cRHF to the Be + H{sub 2} insertion reaction, a Woodward-Hoffmann violating reaction, and a symmetry-driven conical intersection, we demonstrate in genuine molecular systems that cRHF is capable of removing certain potential energy surface singularities that plague real-valued RHF and related methods. This complements earlier work that showed this capability in a model system. We also describe how cRHF is the preferred RHF method for certain radicaloid systems like singlet oxygen and antiaromatic molecules. For singlet O{sub 2}, we show that standard methods fail even at the equilibrium geometry. An implication of this work is that, regardless of their individual efficacies, cRHF solutions to the HF equations are fairly commonplace.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

The linear tearing instability in three dimensional, toroidal gyro-kinetic simulations

Linear gyro-kinetic simulations of the classical tearing mode in three-dimensional toroidal geometry were performed using the global gyro-kinetic turbulence code, GKW. The results were benchmarked against a cylindrical ideal MHD and analytical theory calculations. The stability, growth rate, and frequency of the mode were investigated by varying the current profile, collisionality, and the pressure gradients. Both collisionless and semi-collisional tearing modes were found with a smooth transition between the two. A residual, finite, rotation frequency of the mode even in the absence of a pressure gradient is observed, which is attributed to toroidal finite Larmor-radius effects. When a pressure gradient is present at low collisionality, the mode rotates at the expected electron diamagnetic frequency. However, the island rotation reverses direction at high collisionality. The growth rate is found to follow a η{sup 1∕7} scaling with collisional resistivity in the semi-collisional regime, closely following the semi-collisional scaling found by Fitzpatrick. The stability of the mode closely follows the stability analysis as performed by Hastie et al. using the same current and safety factor profiles but for cylindrical geometry, however, here a modification due to toroidal coupling and pressure effects is seen.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Nonlinear effects of inertial Alfvén wave in low beta plasmas

This paper is devoted to the study of the nonlinear interaction and propagation of high frequency pump inertial Alfvén wave (IAW) with comparatively low frequency IAW with emphasis on nonlinear effects and applications within space plasma and astrophysics for low β-plasma (β≪m{sub e}/m{sub i}). We have developed a set of dimensionless equations in the presence of ponderomotive nonlinearity due to high frequency pump IAW in the dynamics of comparatively low frequency IAW. Stability analysis and numerical simulation have been carried out for the coupled system comprising of pump IAW and low frequency IAW to study the localization and turbulent spectra, applicable to auroral region. The result reveals that localized structures become more complex and intense in nature at the quasi steady state. From the obtained result, we found that the present model may be useful to study the turbulent fluctuations in accordance with the observations of FAST/THEMIS spacecraft.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Understanding the effects of strain on morphological instabilities of a nanoscale island during heteroepitaxial growth

A comprehensive morphological stability analysis of a nanoscale circular island during heteroepitaxial growth is presented based on continuum elasticity theory. The interplay between kinetic and thermodynamic mechanisms is revealed by including strain-related kinetic processes. In the kinetic regime, the Burton-Cabrera-Frank model is adopted to describe the growth front of the island. Together with kinetic boundary conditions, various kinetic processes including deposition flow, adatom diffusion, attachment-detachment kinetics, and the Ehrlich-Schwoebel barrier can be taken into account at the same time. In the thermodynamic regime, line tension, surface energy, and elastic energy are considered. As the strain relief in the early stages of heteroepitaxy is more complicated than commonly suggested by simple consideration of lattice mismatch, we also investigate the effects of external applied strain and elastic response due to perturbations on the island shape evolution. The analytical expressions for elastic fields induced by mismatch strain, external applied strain, and relaxation strain are presented. A systematic approach is developed to solve the system via a perturbation analysis which yields the conditions of film morphological instabilities. Consistent with previous experimental and theoretical work, parametric studies show the kinetic evolution of elastic relaxation, island morphology, and film composition under various conditions. Our present work offers an effective theoretical approach to get a comprehensive understanding of the interplay between different growth mechanisms and how to tailor the growth mode by controlling the nature of the crucial factors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Effective photon mass and exact translating quantum relativistic structures

Using a variation of the celebrated Volkov solution, the Klein-Gordon equation for a charged particle is reduced to a set of ordinary differential equations, exactly solvable in specific cases. The new quantum relativistic structures can reveal a localization in the radial direction perpendicular to the wave packet propagation, thanks to a non-vanishing scalar potential. The external electromagnetic field, the particle current density, and the charge density are determined. The stability analysis of the solutions is performed by means of numerical simulations. The results are useful for the description of a charged quantum test particle in the relativistic regime, provided spin effects are not decisive.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Verification of BOUT++ by the method of manufactured solutions

BOUT++ is a software package designed for solving plasma fluid models. It has been used to simulate a wide range of plasma phenomena ranging from linear stability analysis to 3D plasma turbulence and is capable of simulating a wide range of drift-reduced plasma fluid and gyro-fluid models. A verification exercise has been performed as part of a EUROfusion Enabling Research project, to rigorously test the correctness of the algorithms implemented in BOUT++, by testing order-of-accuracy convergence rates using the Method of Manufactured Solutions (MMS). We present tests of individual components including time-integration and advection schemes, non-orthogonal toroidal field-aligned coordinate systems and the shifted metric procedure which is used to handle highly sheared grids. The flux coordinate independent approach to differencing along magnetic field-lines has been implemented in BOUT++ and is here verified using the MMS in a sheared slab configuration. Finally, we show tests of three complete models: 2-field Hasegawa-Wakatani in 2D slab, 3-field reduced magnetohydrodynamics (MHD) in 3D field-aligned toroidal coordinates, and 5-field reduced MHD in slab geometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Gyrokinetic theory of slab universal modes and the non-existence of the gradient drift coupling (GDC) instability

A gyrokinetic linear stability analysis of a collisionless slab geometry in the local approximation is introduced. We focus on k ∥ =0 universal (or entropy) modes driven by plasma gradients at small and large plasma β. These are small scale non-MHD instabilities with growth rates that typically peak near k ⊥ ρi~1 and vanish in the long wavelength k ⊥ →0 limit. This report also discusses a mode known as the Gradient Drift Coupling (GDC) instability previously reported in the gyrokinetic literature, which has a finite growth rate γ= $\sqrt{β/[2(1+β)]C_{s}/|L_{p}|}$ with C$^{2}_{s}$ =p 0 /ρ 0 for k ⊥ →0 and is universally unstable for 1/L p ≠0. Here, we show that the GDC instability is a spurious, unphysical artifact that erroneously arises due to the failure to respect the total equilibrium pressure balance p 0 +B$^{2}_{0}$ /(8π)=constant, which renders the assumption B$^{\prime}_{0}$ 0 =0 inconsistent if p$^{\prime}_{0}$ ≠0.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Optimization of electrical treatment strategy for surface roughness reduction in conducting thin films

The surface roughness of deposited conducting thin films is responsible for various materials reliability problems in nanoelectronics and nanofabrication technologies. In this work, we report a modeling and simulation study that aims at optimizing the electrical surface treatment of deposited conducting thin films as a physical processing strategy for their surface roughness reduction. Our research is based on a continuum model of film surface morphological evolution that accounts for the residual stress in the deposited conducting thin film, the film’s wetting of the substrate layer that it is deposited on, film texture and surface diffusional anisotropy, and surface electromigration. Through systematic linear stability analysis and dynamical simulation protocols, we examine in detail the effects of film surface crystallographic orientation and applied electric field direction toward minimizing the electric field strength required for film surface smoothening. We believe that the critical electric field strength requirement for surface roughness reduction on {110}, {100}, and {111} surfaces of face-centered cubic crystalline conducting thin films exhibits a very strong dependence on the applied electric field direction, expressed as the electric field misalignment with respect to the principal residual stress directions in the film and the fast surface diffusion directions. Due to these findings, we optimize the electrical treatment strategy for surface roughness reduction of conducting thin films with respect to all relevant processing and material parameters.

42 ENGINEERING↗
DOE OSTI2018

Symmetry breaking in high frequency, symmetric capacitively coupled plasmas

Two radially propagating surface wave modes, “symmetric,” in which the upper and lower axial sheath fields ( E z ) are aligned, and “anti-symmetric,” in which they are opposed, can exist in capacitively coupled plasma (CCP) discharges. For a symmetric (equal electrode areas) CCP driven symmetrically, we expected to observe only the symmetric mode. Instead, we find that when the applied rf frequency f is above or near an anti-symmetric spatial resonance, both modes can exist in combination and lead to unexpected non-symmetric equilibria. We use a fast 2D axisymmetric fluid-analytical code to study a symmetric CCP reactor at low pressure (7.5 mTorr argon) and low density (~3 × 10 15 m -3 ) in the frequency range of f = 55 to 100 MHz which encompasses the first anti-symmetric spatial resonance frequency f a but is far below the first symmetric spatial resonance f s . For lower frequencies such that f is well below f a> , the symmetric CCP is in a stable symmetric equilibrium, as expected, but at higher frequencies such that f is near or greater than f a , a non-symmetric equilibrium appears which may be stable or unstable. In our study, we develop a nonlinear lumped circuit model of the symmetric CCP to better understand these unexpected results, indicating that the proximity to the anti-symmetric spatial resonance allows self-exciting of the anti-symmetric mode even in a symmetric system. The circuit model results agree well with the fluid simulations. A linear stability analysis of the symmetric equilibrium describes a transition with increasing frequency from stable to unstable.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Creation of large temperature anisotropies in a laboratory plasma

Ion temperature anisotropy in an expanding magnetized plasma is investigated using laser induced fluorescence. Parallel and perpendicular ion velocity distribution functions (IVDFs) were measured simultaneously with high spatial resolution in the expanding plasma. Large ion temperature anisotropies (T ⊥i /T ∥i ~ 10) are observed in a conical region at the periphery of the expanding plasma plume. A simple 2D Boris stepper model that incorporates the measured electric field structure is able to reproduce the gross features of the measured perpendicular IVDFs. Here, a Nyquist stability analysis of the measured IVDFs suggests that multiple instabilities with k ⊥ρi ~ 1 and k ||ρi ~ 0.2 are likely to be excited in these plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Direct numerical simulation of supercritical oxy-methane mixing layers with CO 2 substituted counterparts

Direct numerical simulations (DNS) of temporally developing, three dimensional, CH 4 /CO 2 , CH 4 /O 2 and CO 2 /O 2 mixing layers, are conducted at a supercritical pressure of 300 atm. To effectively model the supercritical regime, the employed formulation includes the compressible form of the governing equations, the cubic Peng-Robinson equation of state and a generalized formulation for heat and mass flux vectors derived from non-equilibrium thermodynamics and fluctuation theory. A linear inviscid stability analysis is also performed for each case, to determine its most unstable wavelength. Flow visualizations reveal the presence of high density gradient magnitude regions for all three mixing layers, with conditional averages indicating increased presence of heavier fluid species within these regions. No significant departures are observed from perfect gas behavior, with compressibility factors very close to unity for all three mixing cases. Applicability of presumed probability density function methods (PDF) is examined for the three supercritical mixing layers. An a priori analysis is also conducted to investigate various simplifying assumptions employed in modeling various subgrid scale (SGS) flux models. Two additional terms are identified in the large eddy simulations (LES) equations, the gradient of SGS contribution of pressure in the momentum equation and the gradient of SGS contribution of heat flux in energy equation, whose magnitudes are similar and comparable with their respective resolved terms. The performance of the scale similarity model to represent these additional terms is investigated. Lastly, the performance of Smagorinsky, gradient and scale similarity models are also investigated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Droplet formation simulation using mixed finite elements

Droplet formation happens in finite time due to the surface tension force. The linear stability analysis is useful to estimate the size of a droplet but fails to approximate the shape of the droplet. This is due to a highly nonlinear flow description near the point where the first pinch-off happens. A one-dimensional axisymmetric mathematical model was first developed by Eggers and Dupont [“Drop formation in a one-dimensional approximation of the Navier–Stokes equation,” J. Fluid Mech. 262, 205–221 (1994)] using asymptotic analysis. This asymptotic approach to the Navier–Stokes equations leads to a universal scaling explaining the self-similar nature of the solution. Numerical models for the one-dimensional model were developed using the finite difference [Eggers and Dupont, “Drop formation in a one-dimensional approximation of the Navier–Stokes equation,” J. Fluid Mech. 262, 205–221 (1994)] and finite element method [Ambravaneswaran et al., “Drop formation from a capillary tube: Comparison of one-dimensional and two-dimensional analyses and occurrence of satellite drops,” Phys. Fluids 14, 2606–2621 (2002)]. The focus of this study is to provide a robust computational model for one-dimensional axisymmetric droplet formation using the Portable, Extensible Toolkit for Scientific Computation. The code is verified using the Method of Manufactured Solutions and validated using previous experimental studies done by Zhang and Basaran [“An experimental study of dynamics of drop formation,” Phys. Fluids 7, 1184–1203 (1995)]. The present model is used for simulating pendant drops of water, glycerol, and paraffin wax, with an aspiration of extending the application to simulate more complex pinch-off phenomena.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Evolution of coupled weakly driven waves in a dissipative plasma

The nonlinear collisional dynamics of coupled driven plasma waves in the presence of background dissipation is studied analytically within kinetic theory. Sufficiently near marginal stability, phase space correlations are poorly preserved and time delays become unimportant. The system is then shown to be governed by two first-order coupled autonomous differential equations of cubic order for the wave amplitudes and two complementary first-order equations for the evolution of their phases. That system of equations can be decoupled and further simplified to a single second-order differential equation of Liénard's type for each amplitude. Numerical solutions for this equation are obtained in the general case, while analytic solutions are obtained for special cases in terms of parameters related to the spacing of the resonances of the two waves in frequency space, e.g., wave lengths and oscillation frequencies. These parameters are further analyzed to find classes of quasi-steady saturation and pulsating scenarios. To classify equilibrium points, local stability analysis is applied, and bifurcation conditions are determined. When the two waves saturate at similar amplitude levels, their combined signal is shown to invariably exhibit amplitude beating and phase jumps of nearly π. In conclusion, the obtained analytical results can be used to benchmark simulations and to interpret eigenmode amplitude measurements in fusion experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Including the parallel mass flow in calculating the steady-state solutions and stability of the momentum balance equations for a quasisymmetric stellarator

The Helically Symmetric Experiment (HSX) is a quasisymmetric stellarator with minimal parallel viscous damping in a helical direction. The parallel flow (Vǁ) along the magnetic field is similarly weakly damped by viscosity. In this paper, the self-consistent steady-state parallel and poloidal momentum balance equations are used to show that a large Vǁ on the order of the ion thermal velocity can increase the ion resonant radial electric field (Er) beyond the value calculated using the typical approximation that Vǁ is zero. By altering the damping of Vǁ, either by degrading the quasisymmetry or varying the neutral density, the ion resonant Er can shift in a controllable fashion. It is shown explicitly that there exist stable and unstable steady-state solutions in the two-dimensional space of Vǁ and Er. A stability analysis of each solution is performed by calculating the eigenvalues and eigenvectors of the Jacobian. The unstable solution corresponds to a saddle point in which the eigenvalues have opposite signs. The analysis leads to the conclusion that unstable solutions occur when the derivative of the total poloidal damping with respect to Er is positive. A hysteresis in Er and Vǁ is observed when the radial current density is linearly increased to a maximum and then decreased back to zero. Jumps in the radial electric field and the parallel flow are observed as the radial current density drives the evolution from one stable point to the next. This result is similar to experimental data observed on several devices.

Physics↗
DOE OSTI2025

3D pattern formation of a protein–membrane suspension

Many essential cellular processes, including cell division and the establishment of cell polarity during embryogenesis, are regulated by pattern-forming proteins. These proteins often need to bind to a substrate, such as the cell membrane, onto which they interact and form two-dimensional (2D) patterns. It is unclear how the membrane’s continuity and dimensionality impact pattern formation. Here, we address this gap using the MinDE system, a prototypical example of pattern-forming membrane proteins. We show that when the lipid substrate is fragmented into submicrometer-sized diffusive liposomes, adenosine triphosphate-driven protein–protein interactions generate three-dimensional (3D) spatially extended patterns, despite the complete loss of membrane continuity. Remarkably, these 3D patterns emerge at scales four orders of magnitude larger than the individual liposomes. By systematically varying protein concentration, liposome size, and density, we observed and characterized a variety of 3D dynamical patterns not seen on continuous 2D membranes, including traveling waves, dynamical spirals, and a coexistence phase. Simulations and linear stability analysis of a coarse-grained model revealed that the physical properties of the dispersed membrane effectively rescale both the protein–membrane binding rates and diffusion, two key parameters governing pattern formation and wavelength selection. These findings highlight the robustness of Min’s pattern-forming ability, suggesting that protein–membrane suspensions could serve as an adaptable template for studying out-of-equilibrium self-organization in 3D, beyond in vivo contexts.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Four decades of implicit Monte Carlo

In 1971, Fleck and Cummings derived a system of equations to enable robust Monte Carlo simulations of time-dependent, thermal radiative transfer problems. Denoted the “Implicit Monte Carlo” (IMC) equations, their solution remains the de facto standard of high-fidelity radiative transfer simulations. Over the course of 44 years, their numerical properties have become better understood, and accuracy enhancements, novel acceleration methods, and variance reduction techniques have been suggested. In this review, we rederive the IMC equations—explicitly highlighting assumptions as they are made—and outfit the equations with a Monte Carlo interpretation. We put the IMC equations in context with other approximate forms of the radiative transfer equations and present a new demonstration of their equivalence to another well-used linearization solved with deterministic transport methods for frequency-independent problems. We discuss physical and numerical limitations of the IMC equations for asymptotically small time steps, stability characteristics and the potential of maximum principle violations for large time steps, and solution behaviors in an asymptotically thick diffusive limit. We provide a new stability analysis for opacities with general monomial dependence on temperature. Here, we consider spatial accuracy limitations of the IMC equations and discussion acceleration and variance reduction techniques.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

RADIALLY MAGNETIZED PROTOPLANETARY DISK: VERTICAL PROFILE

This paper studies the response of a thin accretion disk to an external radial magnetic field. Our focus is on protoplanetary disks (PPDs), which are exposed during their later evolution to an intense, magnetized wind from the central star. A radial magnetic field is mixed into a thin surface layer, wound up by the disk shear, and pushed downward by a combination of turbulent mixing and ambipolar and ohmic drift. The toroidal field reaches much greater strengths than the seed vertical field that is usually invoked in PPD models, even becoming superthermal. Linear stability analysis indicates that the disk experiences the magnetorotational instability (MRI) at a higher magnetization than a vertically magnetized disk when both the effects of ambipolar and Hall drift are taken into account. Steady vertical profiles of density and magnetic field are obtained at several radii between 0.06 and 1 AU in response to a wind magnetic field B{sub r} ∼ (10{sup −4}–10{sup −2})(r/ AU){sup −2} G. Careful attention is given to the radial and vertical ionization structure resulting from irradiation by stellar X-rays. The disk is more strongly magnetized closer to the star, where it can support a higher rate of mass transfer. As a result, the inner ∼1 AU of a PPD is found to evolve toward lower surface density. Mass transfer rates around 10{sup −8} M{sub ⊙} yr{sup −1} are obtained under conservative assumptions about the MRI-generated stress. The evolution of the disk and the implications for planet migration are investigated in the accompanying paper.

79 ASTRONOMY AND ASTROPHYSICS↗