Energy balance of turbulence in the upper atmosphere.
Energy balance equation obtained from turbulent winds from chemical release studies and turbulent diffusion analysis of globule expansion
TURBULENT DIFFUSION↗
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Results for “diffusion equation”
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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Numerical simulation of electrophoresis separation processes
A new Petrov-Galerkin finite element formulation has been proposed for transient convection-diffusion problems. Most Petrov-Galerkin formulations take into account the spatial discretization, and the weighting functions so developed give satisfactory solutions for steady state problems. Though these schemes can be used for transient problems, there is scope for improvement. The schemes proposed here, which consider temporal as well as spatial discretization, provide improved solutions. Electrophoresis, which involves the motion of charged entities under the influence of an applied electric field, is governed by equations similiar to those encountered in fluid flow problems, i.e., transient convection-diffusion equations. Test problems are solved in electrophoresis and fluid flow. The results obtained are satisfactory. It is also expected that these schemes, suitably adapted, will improve the numerical solutions of the compressible Euler and the Navier-Stokes equations.
Ganjoo, D. K.↗
Specular reflection treatment for the 3D radiative transfer equation solved with the discrete ordinates method
The contribution of this paper relies in the development of numerical algorithms for the mathematical treatment of specular reflection on borders when dealing with the numerical solution of radiative transfer problems. The radiative transfer equation being integro-differential, the discrete ordinates method allows to write down a set of semi-discrete equations in which weights are to be calculated. The calculation of these weights is well known to be based on either a quadrature or on angular discretization, making the use of such method straightforward for the state equation. Also, the diffuse contribution of reflection on borders is usually well taken into account. However, the calculation of accurate partition ratio coefficients is much more tricky for the specular condition applied on arbitrary geometrical borders. This paper presents algorithms that calculate analytically partition ratio coefficients needed in numerical treatments. The developed algorithms, combined with a decentered finite element scheme, are validated with the help of comparisons with analytical solutions before being applied on complex geometries.
97 MATHEMATICS AND COMPUTING↗
Elastic wave propagation in a highly scattering medium - A diffusion approach
The propagation of elastic waves in the moon, where the first seismograms were characterized by the presence of a long coda attributed to strongly scattered waves, is modeled with the aid of the time-dependent equation of radiative transfer. The average energy density as a function of time and space is described by the diffusion equation with linear dissipation on the assumption that all the energy present has been scattered many times and the time and distance scales of the problem are long compared to the scales of the scattering process. Ultrasonic experiments in the laboratory confirm the applicability of the formalism.
Dainty, A. M.↗
Enhancing statistical moment calculations for stochastic Galerkin solutions with Monte Carlo techniques
Here, we provide a method for enhancing stochastic Galerkin moment calculations to the linear elliptic equation with random diffusivity using an ensemble of Monte Carlo solutions. This hybrid approach combines the accuracy of low-order stochastic Galerkin and the computational efficiency of Monte Carlo methods to provide statistical moment estimates which are significantly more accurate than performing each method individually. The hybrid approach involves computing a low-order stochastic Galerkin solution, after which Monte Carlo techniques are used to estimate the residual. We show that the combined stochastic Galerkin solution and residual is superior in both time and accuracy for a one-dimensional test problem and a more computational intensive two-dimensional linear elliptic problem for both the mean and variance quantities.
97 MATHEMATICS AND COMPUTING↗
Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach
Here, we develop numerical methods for stochastic reaction-diffusion systems based on approaches used for fluctuating hydrodynamics (FHD). For hydrodynamic systems, the FHD formulation is formally described by stochastic partial differential equations (SPDEs). In the reaction-diffusion systems we consider, our model becomes similar to the reaction-diffusion master equation (RDME) description when our SPDEs are spatially discretized and reactions are modeled as a source term having Poisson fluctuations. However, unlike the RDME, which becomes prohibitively expensive for an increasing number of molecules, our FHD-based description naturally extends from the regime where fluctuations are strong, i.e., each mesoscopic cell has few (reactive) molecules, to regimes with moderate or weak fluctuations, and ultimately to the deterministic limit. By treating diffusion implicitly, we avoid the severe restriction on time step size that limits all methods based on explicit treatments of diffusion and construct numerical methods that are more efficient than RDME methods, without compromising accuracy. Guided by an analysis of the accuracy of the distribution of steady-state fluctuations for the linearized reaction-diffusion model, we construct several two-stage (predictor-corrector) schemes, where diffusion is treated using a stochastic Crank-Nicolson method, and reactions are handled by the stochastic simulation algorithm of Gillespie or a weakly second-order tau leaping method. We find that an implicit midpoint tau leaping scheme attains second-order weak accuracy in the linearized setting and gives an accurate and stable structure factor for a time step size of an order of magnitude larger than the hopping time scale of diffusing molecules. We study the numerical accuracy of our methods for the Schlögl reaction-diffusion model both in and out of thermodynamic equilibrium. We demonstrate and quantify the importance of thermodynamic fluctuations to the formation of a two-dimensional Turing-like pattern and examine the effect of fluctuations on three-dimensional chemical front propagation. Furthermore, by comparing stochastic simulations to deterministic reaction-diffusion simulations, we show that fluctuations accelerate pattern formation in spatially homogeneous systems and lead to a qualitatively different disordered pattern behind a traveling wave.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
AutoTandemML: Active Learning Enhanced Tandem Neural Networks for Inverse Design Problems
Inverse design in science and engineering involves determining optimal design parameters that achieve desired performance outcomes, a process often hindered by the complexity and high dimensionality of design spaces, leading to significant computational costs. To tackle this challenge, we propose a novel hybrid approach that combines active learning with Tandem Neural Networks to enhance the efficiency and effectiveness of solving inverse design problems. Active learning allows to selectively sample the most informative data points, reducing the required dataset size without compromising accuracy. We investigate this approach using three benchmark problems: airfoil inverse design, photonic surface inverse design, and scalar boundary condition reconstruction in diffusion partial differential equations. We demonstrate that integrating active learning with Tandem Neural Networks outperforms standard approaches across the benchmark suite, achieving better accuracy with fewer training samples.
97 MATHEMATICS AND COMPUTING↗
A multiphase electrokinetic flow model for electrolytes with liquid/liquid interfaces
A numerical model for electrokinetic flow of multiphase systems with deformable interfaces is presented, based on a combined level set-volume of fluid technique. A new feature is a multiphase formulation of the Nernst–Planck transport equation for advection, diffusion and conduction of individual charge carrier species that ensures their conservation in each fluid phase. The numerical model is validated against the analytical results of Zholkovskij et al. (2002) [1], and results for the problem of two drops coalescing in the presence of mobile charge carriers are presented. The time taken for two drops containing ions to coalesce decreases with increasing ion concentration.
42 ENGINEERING↗
Realistic multisite lattice-gas modeling and KMC simulation of catalytic surface reactions: Kinetics and multiscale spatial behavior for CO-oxidation on metal (100) surfaces
A realistic molecular-level description of catalytic reactions on single-crystal metal surfaces can be provided by stochastic multisite lattice-gas (msLG) models. This approach has general applicability, although in this report, we will focus on the example of CO-oxidation on the unreconstructed fcc metal (100) or M(100) surfaces of common catalyst metals M = Pd, Rh, Pt and Ir (i.e., avoiding regimes where Pt and Ir reconstruct). These models can capture the thermodynamics and kinetics of adsorbed layers for the individual reactants species, such as CO/M(100) and O/M(100), as well as the interaction and reaction between different reactant species in mixed adlayers, such as (CO + O)/M(100). The msLG models allow population of any of hollow, bridge, and top sites. This enables a more flexible and realistic description of adsorption and adlayer ordering, as well as of reaction configurations and configuration-dependent barriers. Adspecies adsorption and interaction energies, as well as barriers for various processes, constitute key model input. The choice of these energies is guided by experimental observations, as well as by extensive Density Functional Theory analysis. Model behavior is assessed via Kinetic Monte Carlo (KMC) simulation. We also address the simulation challenges and theoretical ramifications associated with very rapid diffusion and local equilibration of reactant adspecies such as CO. These msLG models are applied to describe adsorption, ordering, and temperature programmed desorption (TPD) for individual CO/M(100) and O/M(100) reactant adlayers. In addition, they are also applied to predict mixed (CO + O)/M(100) adlayer structure on the nanoscale, the complete bifurcation diagram for reactive steady-states under continuous flow conditions, temperature programmed reaction (TPR) spectra, and titration reactions for the CO-oxidation reaction. Extensive and reasonably successful comparison of model predictions is made with experimental data. Furthermore, we discuss the possible transition from traditional mean-field-type bistability and reaction kinetics for lower-pressure to multistability and enhanced fluctuation effects for moderate- or higher-pressure. Behavior in the latter regime reflects a stronger influence of adspecies interactions and also lower diffusivity in the higher-coverage mixed adlayer. We also analyze mesoscale spatiotemporal behavior including the propagation of reaction diffusion fronts between bistable reactive and inactive states, and associated nucleation-mediated transitions between these states. This behavior is controlled by complex surface mass transport processes, specifically chemical diffusion in mixed reactant adlayers for which we provide a precise theoretical formulation. The msLG models together with an appropriate treatment of chemical diffusivity enable equation-free heterogeneous coupled lattice-gas (HCLG) simulations of spatiotemporal behavior. In addition, msLG + HCLG modeling can describe coverage variations across polycrystalline catalysts surfaces, pressure variations across catalyst surfaces in microreactors, and could be incorporated into a multiphysics framework to describe mass and heat transfer limitations for high-pressure catalysis. (C) 2013 Elsevier Ltd. All rights reserved.
36 MATERIALS SCIENCE↗
Influence of deep levels on the electrical transport properties of CdZnTeSe detectors
Here, we investigated the influence of deep levels on the electrical transport properties of CdZnTeSe radiation detectors by comparing experimental data with numerical simulations based on the simultaneous solution of drift-diffusion and Posisson equations, including the Shockley-Read-Hall model of the carrier trapping. We determined the Schottky barrier heights and the Fermi level position from I-V measurements. We measured the time evolution of the electric field and the electrical current after the application of a voltage bias. We observed that the electrical properties of CZTS are fundamentally governed by two deep levels close to the mid-bandgap - one recombination and one hole trap. We show that the hole trap indirectly increases the mobility-lifetime product of electrons. We conclude that the structure of deep levels in CZTS are favorable for high electrical charge transport.
36 MATERIALS SCIENCE↗
Correlations of conserved quantities at finite baryon density
Correlations involving the seven conserved quantities, namely energy, baryon number, electric charge, strangeness, and the three components of momentum, give rise to correlations in heavy-ion collisions. Through the utilization of a simple one-dimensional hydrodynamic model, we calculate the evolution of the entire 7×7 matrix of correlations as a function of relative spatial rapidity. This comprehensive analysis accounts for finite baryon density, which results in off-diagonal correlations between the charge-related quantities and the energy-momentum quantities. These correlations in coordinate space are subsequently transformed into correlations in momentum space using statistical weighting. As a result, the entire matrix of correlations is revealed to be highly sensitive to the equation of state, viscosity, and diffusivity.
Equations of state of nuclear matter↗
Two-dimensional equations of the surface harmonics method for solving problems of spatial neutron kinetics in square-lattice reactors
Two-dimensional time-dependent finite-difference equations of the surface harmonics method (SHM) for the description of the neutron transport are derived for square-lattice reactors. These equations are implemented in the SUHAM-TD code. Verification of the derived equations and the developed code are performed by the example of known test problems, and the potential and efficiency of the SHM as applied to the solution of the time-dependent neutron transport equation in the diffusion approximation in two-dimensional geometry are demonstrated. These results show the substantial advantage of SHM over direct finite-difference modeling in computational costs.
74 ATOMIC AND MOLECULAR PHYSICS↗
Predictive Integrated Modeling of Heated Tokamak Plasmas (Final Technical Report)
The research carried out by the Lehigh University fusion group during this reporting period: (1) Self-consistent predictive core-pedestal ITER scenario modeling; (2) Microtearing instabilities and electron thermal transport in standard and spherical tokamak discharges; (3) Neural network model of the Multi-Mode anomalous transport module; (4) Anomalous transport in KSTAR, JET, EAST, Alcator C-Mod and DIII-D discharges; (5) Theory for transport in magnetized plasmas; (6) Control-oriented modeling of the q-profile dynamic response in preparation for advanced scenario control in KSTAR and in EAST; (7) Modeling of edge harmonic oscillation in DIII-D QH mode discharges; (8) Elucidating plasma dynamics in Hasegawa-Wakatani turbulence by information geometry; (9) Non-linear Langevin and Fractional Fokker–Planck equations for anomalous diffusion by Levy stable processes; and (10) Investigation of the plasma shaping effects on the H-mode pedestal structure.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Integration of Electromagnetic Geophysics Forward Simulation in Coupled Flow and Geomechanics for Monitoring a Gas Hydrate Deposit Located in the Ulleung Basin, East Sea, Korea
We investigate the feasibility of electromagnetic (EM) geophysics methods to detect the dissociation of gas hydrate specifically from a gas hydrate deposit located in the Ulleung Basin, East Sea, Korea via an integrated flow-geomechanics-EM geophysics simulation. To this end, coupled flow and geomechanics simulation is first performed with the multiple porosity model employed, where a mixed formulation with the finite volume (FV) and finite element (FE) methods are taken for the flow and geomechanics, respectively. From the saturation and porosity fields obtained from the coupled flow and geomechanics, the electrical conductivity model is established for the EM simulation. Solving the partial differential equation of electrical diffusion which is linearized using the 3D finite element method (FEM), the EM fields are then computed. For numerical experiments, particularly two approaches in the configuration for the EM methods are compared in this contribution: the surface-to-surface and the surface-to-borehole methods. When the surface-to-surface EM method is employed, the EM is found to be less sensitive, implying low detectability. Especially for the short term of production, the low detectability is attributed to the similarity of electrical resistivity between the dissociated gas (CH4) and hydrate as well as the specific dissociation pattern within the intercalated composites of the field. On the other hand, when the surface-to-borehole EM method is employed, its sensitivity to capture the produced gas flow is improved, confirming its detectability in monitoring gas flow. Hence, the EM geophysics simulation integrated with coupled flow and geomechanics can be a potential tool for monitoring gas hydrate deposits.
depressurization↗
Rosseland and Flux Mean Opacities for Compton Scattering
Rosseland mean opacity plays an important role in theories of stellar evolution and X-ray burst models. In the high-temperature regime, when most of the gas is completely ionized, the opacity is dominated by Compton scattering. Our aim here is to critically evaluate previous works on this subject and to compute the exact Rosseland mean opacity for Compton scattering over a broad range of temperature and electron degeneracy parameter. We use relativistic kinetic equations for Compton scattering and compute the photon mean free path as a function of photon energy by solving the corresponding integral equation in the diffusion limit. As a byproduct we also demonstrate the way to compute photon redistribution functions in the case of degenerate electrons. We then compute the Rosseland mean opacity as a function of temperature and electron degeneracy and present useful approximate expressions. We compare our results to previous calculations and find a significant difference in the low-temperature regime and strong degeneracy. We then proceed to compute the flux mean opacity in both free-streaming and diffusion approximations, and show that the latter is nearly identical to the Rosseland mean opacity. We also provide a simple way to account for the true absorption in evaluating the Rosseland and flux mean opacities.
79 ASTRONOMY AND ASTROPHYSICS↗
Propagation of Solar Energetic Particles in Three-dimensional Interplanetary Magnetic Fields: Radial Dependence of Peak Intensities
A functional form I{sub max}(R)=kR{sup −α}, where R is the radial distance of a spacecraft, was usually used to model the radial dependence of peak intensities I{sub max}(R) of solar energetic particles (SEPs). In this work, the five-dimensional Fokker–Planck transport equation incorporating perpendicular diffusion is numerically solved to investigate the radial dependence of SEP peak intensities. We consider two different scenarios for the distribution of a spacecraft fleet: (1) along the radial direction line and (2) along the Parker magnetic field line. We find that the index α in the above expression varies in a wide range, primarily depending on the properties (e.g., location and coverage) of SEP sources and on the longitudinal and latitudinal separations between the sources and the magnetic foot points of the observers. Particularly, whether the magnetic foot point of the observer is located inside or outside the SEP source is a crucial factor determining the values of index α. A two-phase phenomenon is found in the radial dependence of peak intensities. The “position” of the break point (transition point/critical point) is determined by the magnetic connection status of the observers. This finding suggests that a very careful examination of the magnetic connection between the SEP source and each spacecraft should be taken in the observational studies. We obtain a lower limit of R{sup −1.7±0.1} for empirically modeling the radial dependence of SEP peak intensities. Our findings in this work can be used to explain the majority of the previous multispacecraft survey results, and especially to reconcile the different or conflicting empirical values of the index α in the literature.
79 ASTRONOMY AND ASTROPHYSICS↗
The Acceleration of Energetic Particles at Coronal Shocks and Emergence of a Double Power-law Feature in Particle Energy Spectra
We present numerical modeling of particle acceleration at coronal shocks propagating through a streamer-like magnetic field by solving the Parker transport equation with spatial diffusion both along and across the magnetic field. We show that the location on the shock where the high-energy particle intensity is the largest, depends on the energy of the particles and on time. The acceleration of particles to more than 100 MeV mainly occurs in the shock-streamer interaction region, due to perpendicular shock geometry and the trapping effect of closed magnetic fields. A comparison of the particle spectra to that in a radial magnetic field shows that the intensity at 100 MeV (200 MeV) is enhanced by more than one order (two orders) of magnitude. This indicates that the streamer-like magnetic field can be an important factor in producing large solar energetic particle events. We also show that the energy spectrum integrated over the simulation domain consists of two different power laws. Further analysis suggests that it may be a mixture of two distinct populations accelerated in the streamer and open field regions, where the acceleration rate differs substantially. Our calculations also show that the particle spectra are affected considerably by a number of parameters, such as the streamer tilt angle, particle spatial diffusion coefficient, and shock compression ratio. While the low-energy spectra agree well with standard diffusive shock acceleration theory, the break energy ranges from ~1 MeV to ~90 MeV and the high-energy spectra can extend to ~1 GeV with a slope of ~2–3.
97 MATHEMATICS AND COMPUTING↗
A Semi-Algebraic Two Level Solver
We develop a simple semi-algebraic 2-level solver built on traditional multigrid ideas. It is designed to be easily incorporated into existing simulation software. It exhibits good convergence for many classes of challenging problems including discontinuous diffusion, convection- diffusion, and Helmholtz equations. It has built-in structure that makes it simple to generalize in several interesting directions.
97 MATHEMATICS AND COMPUTING↗