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Results for “Highly oscillatory solutions”

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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18 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Magnus method for electronic structure calculations at extreme conditions

We present the application of Magnus based methods to the solution of first order coupled ordinary differential equations in High Energy Density (HED) physics applications. Our focus is on the application to quantum mechanical methods, specifically on the solution of the radial Dirac equation for real and complex energies. HED applications require accurate solutions across a wide range of spatial and energy domains, including regimes where the solutions exhibit pronounced oscillatory behavior. Such cases pose significant computational challenges. We demonstrate that Magnus-based integrators can efficiently and accurately address these challenges. We discuss the implementation of the Magnus method for the solution of the radial Dirac equation, including practical considerations such as the evaluation of matrix exponentials, numerical integration, error estimation, and adaptive step size control. We also discuss the application of these methods to complex energy Green’s function techniques and the efficient approximation of integrals of the solutions relevant to HED electronic structure calculations. Here, we demonstrate the accuracy and robustness of the resulting method in applications to the free-particle case, for which analytic solutions are available for comparison, as well as the challenging case of gold at HED conditions.

general physics↗
DOE OSTI2021

Error estimates of finite difference methods for the Dirac equation in the massless and nonrelativistic regime

We present four frequently used finite difference methods and establish the error bounds for the discretization of the Dirac equation in the massless and nonrelativistic regime, involving a small dimensionless parameter 0 < ε &NestedLessLess; 1 inversely proportional to the speed of light. In the massless and nonrelativistic regime, the solution exhibits rapid motion in space and is highly oscillatory in time. Specifically, the wavelength of the propagating waves in time is at O(ε), while in space, it is at O(1) with the wave speed at O(ε -1 ). We adopt one leap-frog, two semi-implicit, and one conservative Crank-Nicolson finite difference methods to numerically discretize the Dirac equation in one dimension and establish rigorously the error estimates which depend explicitly on the time step τ, mesh size h, and the small parameter ε. The error bounds indicate that, to obtain the “correct” numerical solution in the massless and nonrelativistic regime, i.e., 0 < ε &NestedLessLess; 1, all these finite difference methods share the same ε-scalability as time step τ = O(ε 3/2 ) and mesh size h = O(ε 1/2 ). A large number of numerical results are reported to verify the error estimates.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Space-time dependent thermal conductivity in nonlocal thermal transport

Nonlocal thermal transport is generally described by the Peierls-Boltzmann transport equation (PBE). However, solving the PBE for a general space-time dependent problem remains a challenging task due to the high dimensionality of the integro-differential equation. In this work, we present a direct solution to the space-time dependent PBE with a linearized collision matrix using an eigendecomposition method. We show that there exists a generalized Fourier-type relation that links heat flux to the local temperature, and this constitutive relation defines a thermal conductivity that depends on both time and space. Combining this approach with ab initio calculations of phonon properties, we demonstrate that the space-time dependent thermal conductivity gives rise to an oscillatory response in temperature in a transient grating geometry in high thermal conductivity materials. The present solution method allows us to extend the reach of our computational capability for heat conduction to space-time dependent nondiffusive transport regimes. Here, this capability will not only enable a more accurate interpretation of thermal measurements that observe nonlocal thermal transport, but also enhance our physical understanding of nonlocal thermal transport in high thermal conductivity materials that are promising candidates for nanoscale thermal management applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Solution Structure and Hydration Forces between Mica and Hydrophilic Versus Hydrophobic Surfaces

Solid-liquid interfaces are central to a range of interesting phenomena including catalysis, heterogeneous nucleation, water desalination, and biomolecular assembly. While three-dimensional Fast Force Mapping (3D FFM) has emerged as a technique for resolving interfacial solution structure at the molecular scale, key challenges for data interpretation persist, most notably regarding the influence of the probe on the measured structure. Using the mica-water system as a case study, we investigate the effect of hydrophilic and hydrophobic probes on interfacial solution structure measured by 3D FFM. Data from hydrophilic silicon-based probes are in good agreement with molecular dynamics simulations, wherein the innermost water molecules adsorb preferentially at the surface ditrigonal cavity sites followed by two subsequent hydration layers. In contrast, the hydrophobic carbon-based probes detect vertical oscillatory features, but do not show lateral patterning that matches the underlying mica lattice. At high ionic strength, up to six of these oscillatory features are observed extending 2 nm into the solution phase with an average spacing of 0.29 ± (0.04) nm. Further, we also determine that the repulsive hydration force between mica and the hydrophilic probe depends on the nature and concentration of ions in solution. Specifically, solutions with stronger ion-water and ion-ion interactions increase the interfacial viscosity, which results in a stronger repulsive hydration force as the probe approaches the surface. Based on these observations, we present a scheme for controlling the outcomes of particle attachment and aggregation by varying the solution conditions to tune the hydration force.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Kinetics of Shear-Induced Structural Ordering in Dense Colloids

The macroscopic rheological response of a colloidal solution is highly correlated with the local microscopic structure, as revealed by an in situ Rheo-SAXS experiment with a high temporal resolution. Oscillatory shear can induce a strain-controlled ordering-to-disorder transition, resulting in a shear-thickening process that is different from the normal shear-thickening behavior that is driven by hydrodynamics and particle friction. Here, we reveal that there is a complex time-dependent kinetics toward structural ordering under different applied strains. When the strain amplitude reaches a critical value that starts to induce disordering in the system, the pathway toward the dynamic equilibrium can also become highly non-monotonic. Within the same oscillatory cycle, there is a strong correlation of ordering with different phases of the oscillation, with the system oscillating between two dynamic metastable states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Nanometer-Scale Correlations in Aqueous Salt Solutions

The intermediate-range (1–4 nm) correlation of cations, an- ions, and water in aqueous alkaline earth salt solutions is measured using synchrotron X-ray diffraction. We differentiate from the entire solution structure factor, S(Q), a separate region at low Q (<1 °A-1) containing local diffraction maxima (pre-peaks) that indicate nanometer-scale oscillatory behavior. These features are quantitatively reproduced with classical molecular dynamics simulations. At high concentrations, the pre-peaks emerge from correlations arising from existence of small quasi close-packed lattice- like structures comprised of cation hydration spheres. We also analyze the concentration dependence of the pre-peak and discuss the overall results in light of the rich literature dealing with intermediate-range correlations underlying universal phenomena in concentrated electrolytes. The authors were supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Biosciences. Pacific Northwest National Laboratory (PNNL) is operated by Battelle for the U.S. Department of Energy under Contract No. DE-AC05-76RL01830. Computing resources were generously allocated by PNNL's Institutional Computing program. DOE Contract No. DEAC02- 06CH11357 supports operation of the Advanced Photon Source at Argonne National Laboratory.

Chemical physics, nucleation, Madelung potential↗
DOE OSTI2022

Spin-piston problem for a ferromagnetic thin film: Shock waves and solitons

In this report the unsteady, nonlinear magnetization dynamics induced by spin injection in an easy-plane ferromagnetic channel subject to an external magnetic field are studied analytically. Leveraging a dispersive hydrodynamic description, the Landau-Lifshitz equation is recast in terms of hydrodynamic-like variables for the magnetization's perpendicular component (spin density) and azimuthal phase gradient (fluid velocity). Spin injection acts as a moving piston that generates nonlinear, dynamical spin textures in the ferromagnetic channel with downstream quiescent spin density set by the external field. In contrast to the classical problem of a piston accelerating a compressible gas, here, variable spin injection and field lead to a rich variety of nonlinear wave phenomena from oscillatory spin shocks to solitons and rarefaction (expansion) waves. A full classification of solutions is provided using nonlinear wave modulation theory by identifying two key aspects of the fluid-like dynamics: subsonic/supersonic conditions and convex/nonconvex hydrodynamic flux. Familiar waveforms from the classical piston problem such as rarefaction waves and shocks manifest in their spin-based counterparts as smooth and highly oscillatory transitions, respectively, between two distinct magnetic states. The spin shock is an example of a dispersive shock wave, which arises in many physical systems. New features without a gas dynamics counterpart include composite wave complexes with “contact” spin shocks and rarefactions. Magnetic supersonic conditions lead to two pronounced piston edge behaviors including a stationary soliton and an oscillatory wave train. These coherent wave structures have physical implications for the generation of high frequency spin waves from pulsed injection and persistent, stable stationary and/or propagating solitons in the presence of magnetic damping. The analytical results are favorably compared with numerical simulations.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Development of a Performance Portable Non-Equilibrium Plasma Fluid Solver on Adaptive Grids

This presentation will describe the numerical techniques, programming paradigms, verification, and performance of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures. Our plasma fluid model solves the conservation equations for self-consistent electrostatic Poisson, electron and heavy species transport, and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive mesh management library, AMReX (Zhang et al., JOSS, 4 (37) 1370, 2019), and can be built and run on widely available vendor specific GPU architectures (NVIDIA/AMD/Intel). We utilize a non-subcycled second order semi-implicit time-stepping method where all adaptive mesh refinement (AMR) levels are advanced with the same time step. The composite multi-level multigrid solver from within AMReX is used for each of the governing equations that are cast into a Helmholtz equation form. We have also developed a python based chemical mechanism parser framework that uses a similar format as CANTERA (Goodwin et al., Zenodo, 2018) yaml files as input. Our custom parser reads the yaml file and provides C++ files with transport and production rate functions that can be executed on both host (CPU) and device (GPU). We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on low-pressure capacitive and high-pressure streamer discharges. Our initial performance studies indicate 10X speed-up using 20 NVIDIA GPUs versus 200 CPUs for an atmospheric streamer discharge problem solved on a 512 x 1024 x 512 grid.

graphics processing units↗
DOE OSTI2024

Revisiting Artifacts of Kohn–Sham Density Functionals for Biosimulation

We revisit the problem of unphysical charge density delocalization/fractionalization induced by the self-interaction error of common approximate Kohn–Sham (KS) density functional theory functionals on simulation of small to medium-sized proteins in a vacuum. Aside from producing unphysical electron densities and total energies, the vanishing of the HOMO–LUMO gap associated with the unphysical charge delocalization leads to an unphysical low-energy spectrum and catastrophic failure of most popular solvers for the KS self-consistent field (SCF) problem. We apply a robust quasi-Newton SCF solver to obtain solutions for some of these difficult cases. The anatomy of the charge delocalization is revealed by the natural deformation orbitals obtained from the density matrix difference between the Hartree–Fock and KS solutions; the charge delocalization not only can occur between charged fragments (such as in zwitterionic polypeptides) but also involves neutral fragments. The vanishing-gap phenomenon and troublesome SCF convergence are both attributed to the unphysical KS Fock operator eigenspectra of molecular fragments (e.g., amino acids or their side chains). Analysis of amino acid pairs suggests that the unphysical charge delocalization can be partially ameliorated by the use of some range-separated hybrid functionals but not by semilocal or standard hybrid functionals. Last, we demonstrate that solutions without the unphysical charge delocalization can be located even for semilocal KS functionals highly prone to such defects, but such solutions have non-Aufbau character and are unstable with respect to mixing of the non-overlapping “frontier” orbitals. Caution should be exercised when unexpectedly small (or vanishing) HOMO–LUMO gaps and atypical SCF convergence patterns (e.g., oscillatory) are observed in KS DFT simulations in any context (bio or otherwise).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Multigrid-Reduction-in-Time for the Rotating Shallow Water Equations

We consider multilevel time-parallel methods for the numerical solution of the rotating shallow water equations. In particular, the multigrid-reduction-in-time (MGRIT) algorithm is used for the parallel time integration. An asymptotic model is used at the coarse levels while the full model is employed at the finer levels. The asymptotic model is well-suited for highly oscillatory partial differential equations like the rotating shallow water equations because it can accurately and stably take the required large time-steps on coarse levels. Our work exploits the flexibility of the MGRIT algorithm in terms of the number of levels and relaxation schemes to show some computational benefits, especially with respect to FCF-relaxation and data reuse.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Shear-Induced Conformations of Salt-Free Polyelectrolytes in Semidilute Solutions

Here, we present coarse-grained molecular dynamics simulations of salt-free polyelectrolyte chains in semidilute solutions under simple shear flow, with full hydrodynamic interactions and explicit dipolar solvent. At equilibrium, chain orientation statistics follow a pseudo-Voigt distribution, and the structural correlation length and chain end-to-end vector autocorrelation function exhibit scaling behavior consistent with theoretical predictions for polyelectrolytes. Under shear, chains transition from coiled to stretched states and the end-to-end vector autocorrelation function reveals oscillatory dynamics at high Weissenberg numbers. Analysis of the gyration tensor and shear strain distributions identified three distinct chain populations with directional alignment along and against the shear gradient. Compared with their neutral polymer counterparts, polyelectrolytes exhibit stronger shear thinning and enhanced chain alignment under the same Weissenberg number, which is attributed to electrostatic interactions and shear-induced counterion release. These findings provide molecular insight into the distinct flow response of charged polymers and have implications for tailoring the rheological properties of polyelectrolyte-based materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Direct numerical simulations of turbulent reacting flows with shock waves and stiff chemistry using many-core/GPU acceleration

Compressible reacting flows may display sharp spatial variation related to shocks, contact discontinuities or reactive zones embedded within relatively smooth regions. The presence of such phenomena emphasizes the relevance of shock-capturing schemes such as the weighted essentially non-oscillatory (WENO) scheme as an essential ingredient of the numerical solver. However, these schemes are complex and have more computational cost than the simple high-order compact or non-compact schemes. In this paper, we present the implementation of a seventh-order, minimally-dissipative mapped WENO (WENO7M) scheme in a newly developed direct numerical simulation (DNS) code called KAUST Adaptive Reactive Flows Solver (KARFS). In order to make efficient use of the computer resources and reduce the solution time, without compromising the resolution requirement, the WENO routines are accelerated via graphics processing unit (GPU) computation. The performance characteristics and scalability of the code are studied using different grid sizes and block decomposition. Furthermore, the performance portability of KARFS is demonstrated on a variety of architectures including NVIDIA Tesla P100 GPUs and NVIDIA Kepler K20X GPUs. In addition, the capability and potential of the newly implemented WENO7M scheme in KARFS to perform DNS of compressible flows is also demonstrated with model problems involving shocks, isotropic turbulence, detonations and flame propagation into a stratified mixture with complex chemical kinetics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Capturing Carbonation: Understanding Kinetic Complexities through a New Era of Electron Microscopy

Cryogenic plasma focused ion beam (PFIB) electron microscopy analysis is applied to visualizing ex situ (surface industrial) and in situ (subsurface geologic) carbonation products, to advance understanding of carbonation kinetics. Ex situ carbonation is investigated using NIST fly ash standard #2689 exposed to aqueous sodium bicarbonate solutions for brief periods of time. In situ carbonation pathways are investigated using volcanic flood basalt samples from Schaef et al. (2010) exposed to aqueous CO 2 solutions by them. The fly ash reaction products at room temperature show small amounts of incipient carbonation, with calcite apparently forming via surface nucleation. Reaction products at 75° C show beginning stages of an iron carbonate phase, e.g., siderite or ankerite, common phases in subsurface carbon sequestration environments. This may suggest an alternative to calcite in carbonation low calcium-bearing fly ashes. Flood basalt carbonation reactions show distinct zonation with high calcium and calcium-magnesium bearing zones alternating with high iron-bearing zones. The calcium-magnesium zones are notable with occurrence of localized pore space. Oscillatory zoning in carbonate minerals is distinctly associated with far-from-equilibrium conditions where local chemical environments fluctuate via a coupling of reaction with transport. The high porosity zones may reflect a precursor phase (e.g., aragonite) with higher molar volume that then “ripens” to the high-Mg calcite phase-plus-porosity. These observations reveal that carbonation can proceed with evolving local chemical environments, formation and disappearance of metastable phases, and evolving reactive surface areas. Together this work shows that future application of cryo-PFIB in carbonation studies would provide advanced understanding of kinetic mechanisms for optimizing industrial-scale and commercial-scale applications.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Impact of Backbone Rigidity on the Thermomechanical Properties of Semiconducting Polymers with Conjugation Break Spacers

There remains a lack of fundamental understanding in theroleofbackbonerigidityonthe thermomechanical properties of conjugated polymers. Here, we provide the first holistic approach to understand the fundamental influence of backbone rigidity on an n-type naphthalene diimide-based conjugated polymer, denoted by PNDI-Cx, through insertion of a flexible conjugation break spacer (CBS). CBS lengths are varied from fully conjugated with zero alkyl spacer (PNDI-C0) to a seven- carbon alkyl spacer (PNDI-C 7 ), with the CBS engineered into each repeat unit for systematic evaluation. Solution small-angle neutron scattering and oscillatory shear rheometry were employed to provide the first quantitative evidence of CBS influence over conjugated polymer chain rigidity and entanglement molecular weight (M e ), demonstrating a reduction in the Kuhn length from 521 to 36 Å for fully conjugated PNDI-C0 and PNDI-C6, respectively, as well as a nearly consistent Me of ~15 kDa upon the addition of CBS. Thermomechanical properties, such as elastic modulus and glass-transition temperature, were shown to decrease with an increasing length of CBS. An extraordinary ductility, upwards of 400% tensile strain before fracture, was observed for high-molecular-weight PNDI-C4, which we attribute to a high number of entanglements and disruption of crystallization. Furthermore, the deformation mechanism for PNDI-Cx was studied under strain through X-ray diffraction, polarized UV-vis spectroscopy, and atomic force microscopy. Overall, this work sheds light on the important role of backbone rigidity in designing flexible and stretchable conjugated polymers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Mean Flow from Phase Averages in the 2D Boussinesq Equations

The atmosphere and ocean are described by highly oscillatory PDEs that challenge both our understanding of their dynamics and their numerical approximation. This paper presents a preliminary numerical study of one type of phase averaging applied to mean flows in the 2D Boussinesq equations that also has application to numerical methods. The phase averaging technique, well-known in dynamical systems theory, relies on a mapping using the exponential operator, and then an averaging over the phase. The exponential operator has connections to the Craya–Herring basis pioneered by Jack Herring to study the fluid dynamics of oscillatory, nonlinear fluid dynamics. In this paper, we perform numerical experiments to study the effect of this averaging technique on the time evolution of the solution. We explore its potential as a definition for mean flows. We also show that, as expected from theory, the phase-averaging method can reduce the magnitude of the time rate of change in the PDEs, making them potentially suitable for time stepping methods.

Wingate, Beth A.↗
DOE OSTI2023

Perivascular network segmentations derived from high-field MRI and their implications for perivascular and parenchymal mass transport in the rat brain

A custom segmentation workflow was applied to ex vivo high-field MR images of rat brains acquired following in vivo intraventricular contrast agent infusion to generate maps of the perivascular spaces (PVS). The resulting perivascular network segmentations enabled analysis of perivascular connections to the ventricles, parenchymal solute clearance, and dispersive solute transport within PVS. Numerous perivascular connections between the brain surface and the ventricles suggest the ventricles integrate into a PVS-mediated clearance system and raise the possibility of cerebrospinal fluid (CSF) return from the subarachnoid space to the ventricles via PVS. Assuming rapid solute exchange between the PVS and CSF spaces primarily by advection, the extensive perivascular network decreased the mean clearance distance from parenchyma to the nearest CSF compartment resulting in an over 21-fold reduction in the estimated diffusive clearance time scale, irrespective of solute diffusivity. This corresponds to an estimated diffusive clearance time scale under 10 min for amyloid-beta which suggests that the widespread distribution of PVS may render diffusion an effective parenchymal clearance mechanism. Additional analysis of oscillatory solute dispersion within PVS indicates that advection rather than dispersion is likely the primary transport mechanism for dissolved compounds greater than 66 kDa in the long (> 2 mm) perivascular segments identified here, although dispersion may be significant for smaller compounds in shorter perivascular segments.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Specular-reflection contributions to static and dynamic radiation forces on circular cylinders

Interest in the response of highly reflecting objects in water to modulated acoustical radiation forces makes it appropriate to consider contributions to such forces from perfectly reflecting objects to provide insight into radiation forces. The acoustic illumination can have wavelengths much smaller than the object's size, and objects of interest may have complicated shapes. Here, the specular contribution to the oscillating radiation force on an infinite circular cylinder at normal incidence is considered for double-sideband-suppressed carrier-modulated acoustic illumination. The oscillatory magnitude of the specular force decreases monotonically with increasing modulation frequency, and the phase of the oscillating force depends on the relative phase of the sidebands. The phase dependence on the modulation frequency can be reduced with the appropriate selection of a sideband relative-phase parameter. That is a consequence of the significance of rays that are incident on the cylinder having small impact parameters that are nearly backscattered. For one choice of a relative sideband phase, a prior partial wave series (PWS) solution is available, which supports the specular analysis when the PWS is evaluated for a rigid cylinder. The importance of specular contributions for aluminum cylinders in water is noted. A specular analysis for an analogous spherical reflector is also summarized.

Marston, Philip L. (ORCID:0000000306778537)↗
DOE OSTI2021

Sodium dodecyl sulfate modulates the structure and rheological properties of Pluronic F108–poly(acrylic acid) coacervates)

Micelles formed within coacervate phases can impart functional properties, but it is unclear if this micellization provides mechanical reinforcement of the coacervate whereby the micelles act as high functionality crosslinkers. Here, we examine how sodium dodecyl sulfate (SDS) influences the structure and properties of Pluronic F108–polyacrylic acid (PAA) coacervates as SDS is known to decrease the aggregation number of Pluronic micelles. Increasing the SDS concentration leads to larger water content in the coacervate and an increase in the relative concentration of PAA to the other solids. Rheological characterization with small angle oscillatory shear (SAOS) demonstrates that these coacervates are viscoelastic liquids with the moduli decreasing with the addition of the SDS. The loss factor (tan δ) initially increases linearly with the addition of SDS, but a step function increase in the loss factor occurs near the reported CMC of SDS. However, this change in rheological properties does not appear to be correlated with any large scale structural differences in the coacervate as determined by small angle X-ray scattering (SAXS) with no signature of Pluronic micelles in the coacervate when SDS concentration is >4 mM during formation of the coacervate, which is less than that observed (6 mM SDS) in initial Pluronic F108 solution despite the higher polymer concentration in the coacervate. Finally, these results suggest that the mechanical properties of polyelectrolyte-non-ionic surfactant coacervates are driven by the efficicacy of binding between the complexing species driving the coacervate, which can be disrupted by competitive binding of the SDS to the Pluronic.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗