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Results for “Hyperdiffusion”

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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15 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Comparison of the telegraph and hyperdiffusion approximations in cosmic-ray transport

The telegraph equation and its generalizations have been repeatedly considered in the models of diffusive cosmic-ray transport. Yet the telegraph model has well-known limitations, and analytical arguments suggest that a hyperdiffusion model should serve as a more accurate alternative to the telegraph model, especially on the timescale of a few scattering times. We present a detailed side-by-side comparison of an evolving particle density profile, predicted by the telegraph and hyperdiffusion models in the context of a simple but physically meaningful initial-value problem, compare the predictions with the solution based on the Fokker–Planck equation, and discuss the applicability of the telegraph and hyperdiffusion approximations to the description of strongly anisotropic particle distributions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Hyperdiffusion of dust particles in a turbulent tokamak plasma

In this work, the effect of plasma turbulence on the trajectories of dust particles is investigated for the first time. The dynamics of dust particles is computed using the ad hoc developed Dust Injection Simulator code, using a 3D turbulent plasma background computed with the TOKAM3X code. As a result, the evolution of the particle trajectories is governed by the ion drag force, and the shape of the trajectory is set by the Stokes number St∝a d /n 0 , with a d the dust radius and n 0 the density at the separatrix. The plasma turbulence is observed to scatter the dust particles, exhibiting a hyperdiffusive regime in all cases. The amplitude of the turbulent spread of the trajectories Δr 2 is shown to depend on the ratio Ku/St, with Ku∝u rms the Kubo number and urms the fluctuation level of the plasma flow. These results are compared with a simple analytical model, predicting Δr 2 ∝(Ku/St) 2 t 3 , or Δr 2 ∝(u rms n 0 /a d ) 2 t 3 . As the dust is heated by the plasma fluxes, thermionic emission sets the dust charge, originally negative, to slightly positive values. This results in a substantial reduction of the ion drag force through the suppression of its Coulomb scattering component. The dust grain inertia is then no longer negligible and drives the transition from a hyperdiffusive regime toward a ballistic one.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Hyperdiffusion of dust particles in a turbulent tokamak plasma

The effect of plasma turbulence on the trajectories of dust particles is investigated for the first time. The dynamics of dust particles is computed using the ad-hoc developed Dust Injection Simulator code, using a 3D turbulent plasma background computed with the TOKAM3X code. As a result, the evolution of the particle trajectories is governed by the ion drag force, and the shape of the trajectory is set by the Stokes number $St\propto a_d/n_0$, with $a_d$ the dust radius and $n_0$ the density at the separatrix. The plasma turbulence is observed to scatter the dust particles, exhibiting a hyperdiffusive regime in all cases. The amplitude of the turbulent spread of the trajectories $\Delta r^2$ is shown to depend on the ratio $Ku/St$, with $Ku\propto u_{rms}$ the Kubo number and $u_{rms}$ the fluctuation level of the plasma flow. These results are compared with a simple analytical model, predicting $\Delta r^2\propto (Ku/St)^2t^3$, or $\Delta r^2\propto (u_{rms}n_0/a_d)^2t^3$. As the dust is heated by the plasma fluxes, thermionic emission sets the dust charge, originally negative, to slightly positive values. This results in a substantial reduction of the ion drag force through the suppression of its Coulomb scattering component. The dust grain inertia is then no longer negligible, and drives the transition from a hyperdiffusive regime towards a ballistic one.

dust↗
DOE OSTI2015

The static structure and dynamics of cadmium sulfide nanoparticles within poly(styrene- block -isoprene) diblock copolymer melts

Here, the static structure and dynamic behavior of cadmium sulfide nanoparticles suspended in block copolymer matrix are investigated using transmission electron microscopy, small-angle X-ray scattering, and X-ray photon correlation spectroscopy. The transmission electron micro- scopy study shows that cadmium sulfide nanoparticles are preferentially segregated within the polyisoprene domain of a poly(styrene- block -isoprene) diblock copolymer. For the dynamics study, X-ray photon correlation spectroscopy captures the relaxation process of cadmium sulfide nanoparticles. The measured characteristic relaxation time reveals that the observed dynamics are hyperdiffusive. The characteristic velocity and corresponding activation energy, which are hallmarks of a hyperdiffusive system, are determined from the relationship between the characteristic relaxation time and the wavevector.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Exploring the impacts of physics and resolution on aqua-planet simulations from a nonhydrostatic global variable-resolution modeling framework

Advances in computing resources are gradually moving regional and global numerical forecasting simulations towards sub-10 km resolution, but global high resolution climate simulations remain a challenge. The non-hydrostatic Model for Prediction Across Scales (MPAS) provides a global framework to achieve very high resolution using regional mesh refinement. Previous studies using the hydrostatic version of MPAS (H-MPAS) with the physics parameterizations of Community Atmosphere Model version 4 (CAM4) found notable resolution dependent behaviors. This study revisits the resolution sensitivity using the non-hydrostatic version of MPAS (NH-MPAS) with both CAM4 and CAM5 physics. A series of aqua-planet simulations at global quasi-uniform resolutions ranging from 240 km to 30 km and global variable resolution simulations with a regional mesh refinement of 30 km resolution over the tropics are analyzed, with a primary focus on the distinct characteristics of NH-MPAS in simulating precipitation, clouds, and large-scale circulation features compared to H-MPAS-CAM4. The resolution sensitivity of total precipitation and column integrated moisture in NH-MPAS is smaller than that in H-MPAS-CAM4. This contributes importantly to the reduced resolution sensitivity of large-scale circulation features such as the inter-tropical convergence zone and Hadley circulation in NH-MPAS compared to H-MPAS. In addition, NH-MPAS shows almost no resolution sensitivity in the simulated westerly jet, in contrast to the obvious poleward shift in H-MPAS with increasing resolution, which is partly explained by differences in the hyperdiffusion coefficients used in the two models that influence wave activity. With the reduced resolution sensitivity, simulations in the refined region of the NH-MPAS global variable resolution configuration exhibit zonally symmetric features that are more comparable to the quasi-uniform high-resolution simulations than those from H-MPAS that displays zonal asymmetry in simulations inside the refined region. Overall, NH-MPAS with CAM5 physics shows less resolution sensitivity compared to CAM4. These results provide a reference for future studies to further explore the use of NH-MPAS for high-resolution climate simulations in idealized and realistic configurations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Dynamics of High Molecular Weight Cylindrical and Lamellar Block Copolymers with X‐ray Photon Correlation Spectroscopy

Here, the structure and dynamics of polystyrene (PS)-b-poly(ethylene oxide) block copolymers (BCPs) are studied. The BCPs exhibit microphase-separated cylindrical and lamellar morphologies. Structural dynamics are measured with X-ray photon correlation spectroscopy in the small-angle regime. Morphologies and domain sizes are evaluated using small-angle X-ray scattering (SAXS), scanning electron microscopy, and atomic force microscopy. Different solvent processing conditions are investigated. Grain sizes evaluated using SAXS are found to depend on processing only for the rubbery majority BCP. The structural relaxation times are examined as a function of PS volume fraction, temperature, morphology, and structural sizes. Well above the glass transition temperature (T g ) of PS, all samples exhibit stretched autocorrelation decays and diffusive dynamics. Near T g of PS, the dynamics of all samples are anomalous with compressed autocorrelation decays and hyperdiffusive dynamics. This transition occurs at 153 °C or 1.13 T g of PS. In the diffusive regime (at high temperature), structural relaxation times are dependent on the processing method. Near PS T g (at low temperature), structural relaxation times scale with the PS volume fraction. Structural relaxation times do not correlate with grain size, indicating that the out-of-equilibrium state of PS dominates the structural dynamics of these strongly phase-segregated BCPs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Conservative discontinuous Galerkin interpolation: Sheared boundary conditions

Local studies of accretion disks and laboratory magnetized plasmas employ analytical coordinate mappings that introduce sheared boundary conditions (BCs). Here, we present a discontinuous Galerkin (DG) algorithm to apply such BCs based on projections and quadrature-free integration. The procedure is high-order accurate, preserves moments exactly and works in multiple dimensions. Tests of increasing complexity are provided, beginning with translations of one and two dimensional fields, followed by 3D and 5D simulations with sheared (twist-shift) BCs. Results show that the algorithm is (p + 1)-order accurate in the DG representation and (p + 2) -order accurate in the cell averages, with p being the order of the polynomial basis. Quantification of the algorithm's hyperdiffusion and discussion of aliasing errors are given. This technique enables conservative local simulations of plasma turbulence with DG, not possible until now.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Smectite phase separation is driven by hydration-mediated interfacial charge

Smectite clay minerals have an outsize impact on the response of clay-rich media to common stimuli, such as hydration and ion exchange, motivating extensive effort to understand behaviors resulting from these processes such as swelling and exfoliation. Smectites are common and historic systems for investigating colloidal and interfacial phenomena, with two swelling regimes commonly identified across myriad clays: osmotic swelling at high water activity and crystalline swelling at low water activity. However, no current swelling model seamlessly spans the full ranges of water, salt and clay content encountered in natural or engineered settings. Here, we show that structures previously rationalized as either osmotic or crystalline coexist as a rich array of distinct colloidal phases that differ by water content, layer stacking thickness, and curvature. We present an analytical model for intermolecular potentials among water, salt and clay in both mono- and divalent electrolytes that predicts swelling pressures across high and low water activities. Our results indicate that all clay swelling is osmotic swelling, but that the osmotic pressure of charged mineral interfaces becomes attractive and dominates that of the electrolyte at high clay activities. Global energy minima are often not reached on experimental timescales due to many local energy minima that promote long-lived intermediate states with vast differences in clay, ion, and water mobilities, leading to hyperdiffusive layer dynamics driven by variable hydration-mediated interfacial charge.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2016

Implementation of the full viscoresistive magnetohydrodynamic equations in a nonlinear finite element code

Numerical simulations form an indispensable tool to understand the behavior of a hot plasma that is created inside a tokamak for providing nuclear fusion energy. Various aspects of tokamak plasmas have been successfully studied through the reduced magnetohydrodynamic (MHD) model. The need for more complete modeling through the full MHD equations is addressed here. Our computational method is presented along with measures against possible problems regarding pollution, stability, and regularity. The problem of ensuring continuity of solutions in the center of a polar grid is addressed in the context of a finite element discretization of the full MHD equations. A rigorous and generally applicable solution is proposed here. Useful analytical test cases are devised to verify the correct implementation of the momentum and induction equation, the hyperdiffusive terms, and the accuracy with which highly anisotropic diffusion can be simulated. A striking observation is that highly anisotropic diffusion can be treated with the same order of accuracy as isotropic diffusion, even on non-aligned grids, as long as these grids are generated with sufficient care. This property is shown to be associated with our use of a magnetic vector potential to describe the magnetic field. Several well-known instabilities are simulated to demonstrate the capabilities of the new method. The linear growth rate of an internal kink mode and a tearing mode are benchmarked against the results of a linear MHD code. The evolution of a tearing mode and the resulting magnetic islands are simulated well into the nonlinear regime. The results are compared with predictions from the reduced MHD model. Finally, a simulation of a ballooning mode illustrates the possibility to use our method as an ideal MHD method without the need to add any physical dissipation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Dynamics of Nanoparticles in Entangled Polymer Solutions

The mean square displacement < r 2 > of nanoparticle probes dispersed in simple isotropic liquids and in polymer solutions is interrogated using fluorescence correlation spectroscopy and single-particle tracking (SPT) experiments. Probe dynamics in different regimes of particle diameter (d), relative to characteristic polymer length scales, including the correlation length (ξ), the entanglement mesh size (a), and the radius of gyration (R g ), are investigated. In simple fluids and for polymer solutions in which d >> R g , long-time particle dynamics obey random-walk statistics < r 2 >:t, with the bulk zero-shear viscosity of the polymer solution determining the frictional resistance to particle motion. In contrast, in polymer solutions with d < R g , polymer molecules in solution exert noncontinuum resistances to particle motion and nanoparticle probes appear to interact hydrodynamically only with a local fluid medium with effective drag comparable to that of a solution of polymer chain segments with sizes similar to those of the nanoparticle probes. Under these conditions, the nanoparticles exhibit orders of magnitude faster dynamics than those expected from continuum predictions based on the Stokes–Einstein relation. SPT measurements further show that when d > a, nanoparticle dynamics transition from diffusive to subdiffusive on long timescales, reminiscent of particle transport in a field with obstructions. This last finding is in stark contrast to the nanoparticle dynamics observed in entangled polymer melts, where X-ray photon correlation spectroscopy measurements reveal faster but hyperdiffusive dynamics. As a result, we analyze these results with the help of the hopping model for particle dynamics in polymers proposed by Cai et al. and, on that basis, discuss the physical origins of the local drag experienced by the nanoparticles in entangled polymer solutions.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2018

Structural Dynamics of Strongly Segregated Block Copolymer Electrolytes

Polymer electrolytes are promising materials for high energy density rechargeable batteries. However, they have low ion transport rates and gradually lose electrode adhesion during cycling. These effects are dependent on polymer structure and dynamics. This motivates an investigation of diblock copolymer electrolyte dynamics. Structural and stress relaxations have been measured with X-ray photon correlation spectroscopy (XPCS) and rheology, respectively, as a function of salt concentration and temperature. The polymer electrolyte studied in this work is a mixture of poly(styrene-b-ethylene oxide), SEO, and lithium bistrifluoromethanesulfonimide (LiTFSI). Results from XPCS experiments showed hyperdiffusive motion for various lithium salt concentrations and at varying temperatures, which is indicative of soft glassy materials. This behavior is attributed to cooperative dynamics. The decay time was a weak, nonmonotonic function of salt concentration and decreased with increasing temperature, in an Arrhenius fashion. In contrast, the shear modulus decreased with increasing salt concentration and increasing temperature. The entanglement relaxation from rheological measurements followed Vogel-Fulcher-Tammann behavior. The structural decay time was slower than the entanglement relaxation time at temperatures above the glass transition temperature, but they were approximately equal at T g regardless of salt concentration. This may indicate a fundamental connection between cooperative structural motion and polymer chain motion in this material.

25 ENERGY STORAGE↗
DOE OSTI2016

Structure and Entanglement Factors on Dynamics of Polymer-Grafted Nanoparticles

Nanoparticles functionalized with long polymer chains at low graft density are interesting systems to study structure–dynamic relationships in polymer nanocomposites since they are shown to aggregate into strings in both solution and melts and also into spheres and branched aggregates in the presence of free polymer chains. Our work investigates structure and entanglement effects in composites of polystyrene-grafted iron oxide nanoparticles by measuring particle relaxations using X-ray photon correlation spectroscopy. And for particles within highly ordered strings and aggregated systems, they experience a dynamically heterogeneous environment displaying hyperdiffusive relaxation commonly observed in jammed soft glassy systems. Furthermore, particle dynamics is diffusive for branched aggregated structures which could be caused by less penetration of long matrix chains into brushes. These results suggest that particle motion is dictated by the strong interactions of chains grafted at low density with the host matrix polymer.

36 MATERIALS SCIENCE↗
DOE OSTI2023

The Flux-Differencing Discontinuous Galerkin Method Applied to an Idealized Fully Compressible Nonhydrostatic Dry Atmosphere

Dynamical cores used to study the circulation of the atmosphere employ various numerical methods ranging from finite-volume, spectral element, global spectral, and hybrid methods. In this work, we explore the use of Flux-Differencing Discontinuous Galerkin (FDDG) methods to simulate a fully compressible dry atmosphere at various resolutions. We show that the method offers a judicious compromise between high-order accuracy and stability for large-eddy simulations and simulations of the atmospheric general circulation. In particular, filters, divergence damping, diffusion, hyperdiffusion, or sponge-layers are not required to ensure stability; only the numerical dissipation naturally afforded by FDDG is necessary. We apply the method to the simulation of dry convection in an atmospheric boundary layer and in a global atmospheric dynamical core in the standard benchmark of Held and Suarez

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Multigrid treatment of implicit continuum diffusion

Implicit treatment of diffusive terms of various differential orders common in continuum mechanics modeling, such as computational fluid dynamics, is investigated with spectral and multigrid algorithms in non-periodic 2D domains. In doubly periodic time dependent problems these terms are handled efficiently by spectral methods, but in non-periodic systems solved with distributed memory parallel computing and 2D domain decomposition, this efficiency is lost for a large number of processors. Here, we built and present here a multigrid algorithm for these types of problems that outperforms a spectral solution employing the highly optimized FFTW library. This solver is suitable for high performance computing and may be able to efficiently treat implicit diffusion of arbitrary order by introducing auxiliary equations of lower order. We test these solvers for fourth and sixth order diffusion with harmonic test functions as well as turbulent 2D magnetohydrodynamic simulations. It is also shown that an anisotropic operator without mixed-derivative terms improves model accuracy and speed, and we examine the impact that the various diffusion operators have on the energy, the enstrophy, and the qualitative aspect of a simulation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗