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DOE OSTI2023

Tuning Active Site Flexibility by Defect Engineering of Graphene Ribbon Edge–hosted Fe–N3 Sites

Nitrogen-doped, carbon-supported transition metal catalysts are excellent for several reactions. Structural engineering of metal-Nx sites to boost catalytic activity is rarely studied. Here, we demonstrate that the structural flexibility of Fe-N3 site is vital for tuning the electronic structure of Fe atoms and regulating the catalytic transfer hydrogenation (CTH) activity. By introducing carbon defects, we construct Fe-N3 sites with varying Fe-N bond lengths distinguishable by X-ray absorption spectroscopy. We investigate the CTH activity by density functional theory and microkinetic calculations and reveal that the vertical displacement of the Fe atom out of the plane of the support, induced by the Fe-N3 distortion, raises the Fe [[EQUATION]]orbital and strengthens binding. We propose that the activity is controlled by the relaxation of the reconstructed site, which is further affected by Fe-N bond length, an excellent activity descriptor. Furthermore, we elucidate the origin of the CTH activity and principles for high-performing Fe-N-C catalysts by defect engineering.

09 BIOMASS FUELS↗

NASA NTRS1984

Analytical characterization of AOTV perigee aerothermodynamic regime

In preliminary design studies of AOTV (Aeroassisted Orbital Transfer Vehicle) configurations, it is desirable to have a simple analytical method for characterizing the aerothermodynamic regime at skip trajectory perigee as a function of vehicle L/D and m/CDA (ballistic coefficient). The present study derives an approximate perigee solution from the generalized equations of motion. For a prescribed entry velocity vector, the solution determines a Zeta function (proportional to density divided by m/CDA) at perigee as a parametric function of the exit velocity vector and (constant) L/D. The perigee Zeta function then determines perigee density (or altitude) as a parametric function of m/CDA. The solution allows the following classic aerothermodynamic parameters to be determined at perigee as parametric functions of m/CDA, L/D, and the exit velocity vector: Reynolds Number (viscous effects), Mach Number (compressibility effects), Knudsen Number (rarefaction effects), sphere and disk bow shock standoff distance, Damkohler Number (relaxation effects), viscous correlation parameter (viscid-inviscid interactions), and Stanton Number (convective heat transfer). Results of the analysis are given for low L/D and mid L/D AOTV configurations on return from geosynchronous and L5 orbits. It is concluded the method successfully provides preliminary estimates of the aerothermodynamic parameters through the use of simple algebraic equations and plots.

Desautel, D.↗

NASA NTRS2013

The Force-Free Magnetosphere of a Rotating Black Hole

We revisit the Blandford-Znajek process and solve the fundamental equation that governs the structure of the steady-state force-free magnetosphere around a Kerr black hole. The solution depends on the distributions of the magnetic field angular velocity and the poloidal electric current. These are not arbitrary. They are determined self-consistently by requiring that magnetic field lines cross smoothly the two singular surfaces of the problem: the inner "light surface" located inside the ergosphere and the outer "light surface" which is the generalization of the pulsar light cylinder.We find the solution for the simplest possible magnetic field configuration, the split monopole, through a numerical iterative relaxation method analogous to the one that yields the structure of the steady-state axisymmetric force-free pulsar magnetosphere. We obtain the rate of electromagnetic extraction of energy and confirm the results of Blandford and Znajek and of previous time-dependent simulations. Furthermore, we discuss the physical applicability of magnetic field configurations that do not cross both "light surfaces."

Contopoulos, Ioannis↗

NASA NTRS1986

Implicit time-marching solution of the Navier-Stokes equations for thrust reversing and thrust vectoring nozzle flows

An implicit finite volume method is investigated for the solution of the compressible Navier-Stokes equations for flows within thrust reversing and thrust vectoring nozzles. Thrust reversing nozzles typically have sharp corners, and the rapid expansion and large turning angles near these corners are shown to cause unacceptable time step restrictions when conventional approximate factorization methods are used. In this investigation these limitations are overcome by using second-order upwind differencing and line Gauss-Siedel relaxation. This method is implemented with a zonal mesh so that flows through complex nozzle geometries may be efficiently calculated. Results are presented for five nozzle configurations including two with time varying geometries. Three cases are compared with available experimental data and the results are generally acceptable.

Imlay, S. T.↗

DOE OSTI2022

Dissociation-induced depletion of high-energy reactant molecules as a mechanism for pressure-dependent rate constants for bimolecular reactions

In 1922, Lindemann proposed the now-well-known mechanism for pressure-dependent rate constants for unimolecular reactions: reactant molecules with sufficiently high energies dissociate more quickly than collisions can reestablish the Boltzmann distribution of the internal energies of the molecule during its dissociation at low pressures – yielding pressure-dependent rate constants for unimolecular reactions due to the preferential depletion of the high energy states capable of dissociation. In the last century, incredible progress has been made in achieving a far greater understanding of and quantitative predictions for unimolecular and association reactions. In the modern era, pressure-dependent phenomenological rate constants are now nearly universally used to describe the rates of unimolecular and associative reactions in phenomenological kinetic modeling. However, there is a second, more indirect, implication of Lindemann’s mechanism that relates to how these dissociation-induced non-equilibrium distributions impact bimolecular reactions, including non-associative bimolecular reactions – which are generally not considered to have pressure-dependent rate constants. Yet, as we show herein, the same high energy states depleted due to dissociation would otherwise react most rapidly in high-activation-energy bimolecular reactions – yielding a mechanism for pressure-dependent rate constants for bimolecular reactions (including non-associative reactions). Here, we present results from a case study for CH 2 O dissociation, isomerization, and bimolecular reaction with O2 to explore this question. Results from our master equation calculations indicate that the effect of dissociation-induced non-equilibrium distributions on bimolecular reactions can be substantial – even when chemical timescales are well separated from internal energy relaxational timescales (i.e. when the traditional rate constant description would be thought to apply). This effect is found to be more pronounced – and more complex – for bimolecular reactions involving molecular entities whose chemical timescales are merged with the internal energy relaxational timescales. Lastly, we present some ideas for discussion regarding what should be considered as “chemical species” in phenomenological kinetic models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Triboplasma assisted chemical conversion in granular systems: a semi-analytic model

We present a semi-analytic model for a novel plasma-assisted chemical conversion pathway using triboplasmas generated in granular flows. Triboelectric charge relaxation is a well known phenomena where the potential generated from contact charging of particles exceeds the breakdown voltage of the background gas. In this work, we extend the triboelectric charge relaxation theory to include non equilibrium plasma energy and particle balance equations to predict the formation of dissociated and excited species that act as precursors to chemical conversion, for example in plasma-assisted ammonia synthesis. Our example case study with nitrogen background gas and teflon/aluminum tribomaterial system yielded high excited nitrogen species densities per collision that are comparable to current plasma-assisted conversion pathways. We also present a regime diagram for various gases where Paschen breakdown parameters are used to determine whether triboplasmas can be formed for a given effective work-function difference between two materials. Our sensitivity studies indicate particle velocity, particle radius, solids fraction and space charge effects play a critical role in overall plasma densities and excited species production.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1983

A Unified Constitutive Relationship for the Time-dependent Behavior of Fast Breeder Alloys

Constitutive equations based on classical concepts of creep and plasticity generally rest on the assumption that the inelastic strain can be decomposed into two distinct and additive contributions, one time dependent (creep) and the other time dependent (plastic). It is suggested that an approach is to adopt a unified representation in which creep and plasticity are characterized as occurring simultaneously and interactively and time is an essential ingredient throughout. Examples of the inherent time dependency exhibited by some fast breeder alloys at elevated temperature are rate dependency under monotonic and cyclic straining, thermal recovery and strong creep-elasticity interaction. The stron influence of the recent history of plastic straining on stress relaxation is shown.

Robinson, D. N.↗

NASA NTRS2000

Theory of the lattice Boltzmann Method: Dispersion, Dissipation, Isotropy, Galilean Invariance, and Stability

The generalized hydrodynamics (the wave vector dependence of the transport coefficients) of a generalized lattice Boltzmann equation (LBE) is studied in detail. The generalized lattice Boltzmann equation is constructed in moment space rather than in discrete velocity space. The generalized hydrodynamics of the model is obtained by solving the dispersion equation of the linearized LBE either analytically by using perturbation technique or numerically. The proposed LBE model has a maximum number of adjustable parameters for the given set of discrete velocities. Generalized hydrodynamics characterizes dispersion, dissipation (hyper-viscosities), anisotropy, and lack of Galilean invariance of the model, and can be applied to select the values of the adjustable parameters which optimize the properties of the model. The proposed generalized hydrodynamic analysis also provides some insights into stability and proper initial conditions for LBE simulations. The stability properties of some 2D LBE models are analyzed and compared with each other in the parameter space of the mean streaming velocity and the viscous relaxation time. The procedure described in this work can be applied to analyze other LBE models. As examples, LBE models with various interpolation schemes are analyzed. Numerical results on shear flow with an initially discontinuous velocity profile (shock) with or without a constant streaming velocity are shown to demonstrate the dispersion effects in the LBE model; the results compare favorably with our theoretical analysis. We also show that whereas linear analysis of the LBE evolution operator is equivalent to Chapman-Enskog analysis in the long wave-length limit (wave vector k = 0), it can also provide results for large values of k. Such results are important for the stability and other hydrodynamic properties of the LBE method and cannot be obtained through Chapman-Enskog analysis.

Lallemand, Pierre↗

DOE OSTI2021

Theory of Plasmonic Hot-Carrier Generation and Relaxation

Hot-carrier (HC) generation from (localized) surface plasmon decay has recently attracted much attention due to its promising applications in physical, chemical, materials, and energy science. However, the detailed mechanisms of plasmonic HC generation, relaxation, and trapping are less studied. In this work, we developed and applied a quantum-mechanical model and coupled master equation method to study the generation of HCs from plasmon decay and their following relaxation processes with different mechanisms treated on equal footing. First, a quantum-mechanical model for HC generation is developed. Its connection to existing semiclassical models and time-dependent density functional theory (TDDFT) is discussed. Second, the relaxation and lifetimes of HCs are investigated in the presence of electron–electron and electron–phonon interactions. A GW-like approximation is introduced to account for the electron–electron scattering. The numerical simulations on the Jellium nanoparticles with a size up to 1.6 nm demonstrate the electron–electron scattering and electron–phonon scattering dominate different time scale in the relaxation dynamics. We also generalize the model to study the extraction of HCs to attached molecules. The quantum yield of extracting HCs for other applications is found to be size-dependent. In general, the smaller size of NP improves the quantum yield, which is in agreement with recent experimental measurements. Even though we demonstrate this newly developed theoretical formalism with Jellium model, the theory applies to any other atomistic models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Convergence of sum-up rounding schemes for cloaking problems governed by the Helmholtz equation

In this work, we consider the problem of designing a cloak for waves described by the Helmholtz equation from an integer programming point of view. The problem can be modeled as a PDE-constrained optimization problem with integer-valued control inputs that are distributed in the computational domain. A first-discretize-then-optimize approach results in a large-scale mixed-integer nonlinear program that is in general intractable because of the large number of integer variables that arise from the discretization of the domain. Instead, we propose an efficient algorithm that is able to approximate the local infima of the underlying nonconvex infinite-dimensional problem arbitrarily close without the need to solve the discretized finite-dimensional integer programs to optimality. We optimize only the continuous relaxations of the approximations for local minima and then apply the sum-up rounding methodology to obtain integer-valued controls. If the solutions of the discretized continuous relaxations converge to a local minimizer of the continuous relaxation, then the resulting discrete-valued control sequence converges weakly \(^*\) in \(L^\infty\) to the same local minimizer. These approximation properties follow under suitable refinements of the involved discretization grids. Our results use familiar concepts arising from the analytical properties of the underlying PDE and complement previous results, derived from a topology optimization point of view.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Parallel Algebraic Multigrid for Fusion and Higher-Order PDEs

Multigrid methods play a key role in large-scale scientific simulation because they are among the fastest and most scalable approaches for solving the underlying sparse linear systems of equations that arise from a wide array of Partial Differential Equation (PDE) discretizations. Algebraic multigrid (AMG) is a special type of multigrid method that depends only on the description of the linear system, giving it better portability and broader applicability than geometric multigrid, as it requires no explicit knowledge of the problem geometry. Even though these methods are widely used today, there are still applications where further development is needed. In this report, we focus on PDEs with higher-order terms (e.g., fourth order), concentrating on a PDE that arises in tokamak edge plasma simulations (a tokamak is a machine that confines a plasma using magnetic fields and is believed to be the leading plasma confinement concept for future fusion power plants). General multigrid relaxes a linear system on coarser grids and reverses this process with interpolation, but standard AMG methods struggle with the aforementioned higher-order PDEs. We investigate cyclic coarsening and interpolation heuristics, as well as new iterative approximation methods of refining the solution at each grid to improve the existing multigrid approach. To this end, we ensure that these techniques are transferable to a parallelized setting with LLNL’s supercomputers.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Extended molecular eigenmodes treatment of dipole–dipole NMR relaxation in real fluids

Traditional models of NMR relaxation fail to account for the complex, multi-exponential behavior of the autocorrelation function in realistic systems characterized by soft-interactions and molecules that are chemically and physically complex. Here, in this study, we describe the relative diffusion of the spin dipoles by means of a Fokker–Planck equation that includes an interaction potential of mean force to account for the response of the physical/chemical environment around the dipoles. By numerically solving the Fokker–Planck equation for the diffusion propagator, we estimate dipole–dipole NMR relaxation for like- and unlike-spin systems via its eigenmode solution. We test the model against molecular simulations of diffusing dipoles with harmonic potentials and also validate using experimental longitudinal relaxation data from real systems, including Gd(III)–aqua and Gd(III)–DO3A–butrol complexes, the latter being an important MRI contrast agent. Using this novel approach, we predict both the inner- and outer-shell contributions to the relaxivity rates with excellent accuracy at frequencies relevant to MRI. We also show that, under the appropriate assumptions, our framework naturally recovers the Bloembergen–Purcell–Pound, the Solomon–Bloembergen–Morgan, and the Hwang–Freed models. Our implementation is general and publicly available for application to a broad range of systems.

Pinheiro dos Santos, Thiago J. [Rice Univ., Housto↗

NASA NTRS1976

Electrostatic analysis of charge-coupled structures

An analysis is presented which is based upon a numerical solution of Gauss's law for the multiple dielectric semiconductor and electrode structure. The formulation resulted in a large set of equations, usually nonlinear, which were solved by an iterative scheme based upon the Gauss-Seidel method employing a relaxation parameter. Proper consideration of the nonlinearity of the space-charge in the semiconductor allowed convergent solutions which can give reasonable approximations to the channel potential profiles though not as good for estimating the space charge itself. The results of this work, which are three computer programs, are listed. None of the programs give the electric field explicitly as output data. However, when this information is desired, the programs can be expanded to include field estimations based on a polynominal fit to the potential field, or they may serve as subprograms for main programs dealing with general aspects of charge transfer.

Gassaway, J. D.↗

NASA NTRS1988

Domain decomposition methods for the parallel computation of reacting flows

Domain decomposition is a natural route to parallel computing for partial differential equation solvers. Subdomains of which the original domain of definition is comprised are assigned to independent processors at the price of periodic coordination between processors to compute global parameters and maintain the requisite degree of continuity of the solution at the subdomain interfaces. In the domain-decomposed solution of steady multidimensional systems of PDEs by finite difference methods using a pseudo-transient version of Newton iteration, the only portion of the computation which generally stands in the way of efficient parallelization is the solution of the large, sparse linear systems arising at each Newton step. For some Jacobian matrices drawn from an actual two-dimensional reacting flow problem, comparisons are made between relaxation-based linear solvers and also preconditioned iterative methods of Conjugate Gradient and Chebyshev type, focusing attention on both iteration count and global inner product count. The generalized minimum residual method with block-ILU preconditioning is judged the best serial method among those considered, and parallel numerical experiments on the Encore Multimax demonstrate for it approximately 10-fold speedup on 16 processors.

Keyes, David E.↗

DOE OSTI2021

Distributed deep reinforcement learning for simulation control

Abstract Several applications in the scientific simulation of physical systems can be formulated as control/optimization problems. The computational models for such systems generally contain hyperparameters, which control solution fidelity and computational expense. The tuning of these parameters is non-trivial and the general approach is to manually ‘spot-check’ for good combinations. This is because optimal hyperparameter configuration search becomes intractable when the parameter space is large and when they may vary dynamically. To address this issue, we present a framework based on deep reinforcement learning (RL) to train a deep neural network agent that controls a model solve by varying parameters dynamically. First, we validate our RL framework for the problem of controlling chaos in chaotic systems by dynamically changing the parameters of the system. Subsequently, we illustrate the capabilities of our framework for accelerating the convergence of a steady-state computational fluid dynamics solver by automatically adjusting the relaxation factors of the discretized Navier–Stokes equations during run-time. The results indicate that the run-time control of the relaxation factors by the learned policy leads to a significant reduction in the number of iterations for convergence compared to the random selection of the relaxation factors. Our results point to potential benefits for learning adaptive hyperparameter learning strategies across different geometries and boundary conditions with implications for reduced computational campaign expenses 4 4 Data and codes available at https://github.com/Romit-Maulik/PAR-RL . .

42 ENGINEERING↗

NASA NTRS2002

A Thermodynamic Theory Of Solid Viscoelasticity. Part 1: Linear Viscoelasticity.

The present series of three consecutive papers develops a general theory for linear and finite solid viscoelasticity. Because the most important object for nonlinear studies are rubber-like materials, the general approach is specified in a form convenient for solving problems important for many industries that involve rubber-like materials. General linear and nonlinear theories for non-isothermal deformations of viscoelastic solids are developed based on the quasi-linear approach of non-equilibrium thermodynamics. In this, the first paper of the series, we analyze non-isothermal linear viscoelasticity, which is applicable in a range of small strains not only to all synthetic polymers and bio-polymers but also to some non-polymeric materials. Although the linear case seems to be well developed, there still are some reasons to implement a thermodynamic derivation of constitutive equations for solid-like, non-isothermal, linear viscoelasticity. The most important is the thermodynamic modeling of thermo-rheological complexity , i.e. different temperature dependences of relaxation parameters in various parts of relaxation spectrum. A special structure of interaction matrices is established for different physical mechanisms contributed to the normal relaxation modes. This structure seems to be in accord with observations, and creates a simple mathematical framework for both continuum and molecular theories of the thermo-rheological complex relaxation phenomena. Finally, a unified approach is briefly discussed that, in principle, allows combining both the long time (discrete) and short time (continuous) descriptions of relaxation behaviors for polymers in the rubbery and glassy regions.

Freed, Alan D.↗

DOE OSTI2022

Photoluminescence of Cis-Polyacetylene Semiconductor Material

Photoluminescence (PL) is one of the key experimental characterizations of optoelectronic materials, including conjugated polymers (CPs). In this study, a simplified model of an undoped cis-polyacetylene (cis-PA) oligomer was selected and used to explain the mechanism of photoluminescence (PL) of the CPs. Using a combination of the ab initio electronic structure and a time-dependent density matrix methodology, the photo-induced time-dependent excited state dynamics were computed. We explored the phonon-induced relaxation of the photoexcited state for a single oligomer of cis-PA. Here, the dissipative Redfield equation of the motion was used to compute the dissipative excited state dynamics of electronic degrees of freedom. This equation used the nonadiabatic couplings as parameters. The computed excited state dynamics showed that the relaxation rate of the electron is faster than the relaxation rate of the hole. The dissipative excited-state dynamics were combined with radiative recombination channels to predict the PL spectrum. The simulated results showed that the absorption and emission spectra both have a similar transition. The main result is that the computed PL spectrum demonstrates two mechanisms of light emission originating from (i) the inter-band transitions, corresponding to the same range of transition energies as the absorption spectrum and (ii) intra-band transitions not available in the absorption spectra. However, the dissipative Redfield equation of the motion was used to compute the electronic degrees of freedom of the nonadiabatic couplings, which helped to process the time propagation of the excited dynamic state. This excited dynamic state shows that the relaxation rate of the electron is faster than the relaxation rate of the hole, which can be used for improving organic semiconductor materials for photovoltaic and LED applications.

36 MATERIALS SCIENCE↗

NASA NTRS1981

Numerical algorithms for finite element computations on arrays of microprocessors

The development of a multicolored successive over relaxation (SOR) program for the finite element machine is discussed. The multicolored SOR method uses a generalization of the classical Red/Black grid point ordering for the SOR method. These multicolored orderings have the advantage of allowing the SOR method to be implemented as a Jacobi method, which is ideal for arrays of processors, but still enjoy the greater rate of convergence of the SOR method. The program solves a general second order self adjoint elliptic problem on a square region with Dirichlet boundary conditions, discretized by quadratic elements on triangular regions. For this general problem and discretization, six colors are necessary for the multicolored method to operate efficiently. The specific problem that was solved using the six color program was Poisson's equation; for Poisson's equation, three colors are necessary but six may be used. In general, the number of colors needed is a function of the differential equation, the region and boundary conditions, and the particular finite element used for the discretization.

Ortega, J. M.↗