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DOE OSTI2020

Properties of Medium Nuclei from First Principles

During this project we have extended the Auxiliary Field Diffusion Monte Carlo (AFDMC) to calculate several properties of light/medium nuclei. In particular, we have included and tested several models of three-body forces and the associated approximations required, and the comparison with other exact calculations for simpler problems demonstrated the accuracy of the AFDMC method. In this project we have also developed new subroutines to solve for the ground-state of open shell nuclei. This case requires very complex wave function with respect to the case of closed-shell nuclei. We have used the AFDMC code to calculate many properties of nuclei up to the Oxygen, including energies, radii, spatial and momentum distributions and others.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2018

Collaborative Research: Multi-scale Dynamics of Kinetic Turbulence in Weakly Collisional, High-Beta Plasmas

The transport of energy and momentum and the heating of plasma particles by waves and turbulence are key ingredients in many problems at the frontiers of heliospheric and astrophysics research. This includes the heating and acceleration of the solar wind; the observational appearance of black-hole accretion flows on event-horizon scales; and the properties of the hot, diffuse plasmas that fill dark-matter halos. This work addressed the physics of plasma waves and turbulence in weakly collisional, weakly magnetized (high-beta) plasmas. In this regime, deviations from local thermodynamic equilibrium (i.e., pressure anisotropies) and the instabilities they excite can dramatically change the properties of waves and turbulence from those predicted by fluid (i.e., magnetohydrodynamic) and linear kinetic theories. Through a combination of analytic theory and first-principles kinetic simulations, we have shown that: (1) ion-acoustic waves of sufficient amplitude drive pressure anisotropies large enough to trigger kinetic Larmor-scale instabilities, which in turn interrupt the otherwise strong collisionless damping such waves suffer; (2) pressure anisotropies generated by fluctuating magnetic fields in strong Alfvénic turbulence produce a viscous scale comparable to the driving scale and a cascade with significant non-local interactions; (3) strong Alfvénic turbulence in an expanding high-beta plasma self-organizes to maintain critical balance, even as kinetic Larmor-scale instabilities regulate the plasma viscosity and reduce the elasticity of magnetic-field lines; (4) imbalanced Alfvénic turbulence leads to a "helicity barrier" that ultimately triggers the cyclotron heating of ions, in a manner consistent with spacecraft measurements taken in the solar wind; and (5) relativistic synchrotron-radiating plasmas develop kinetically unstable pressure anisotropy, which changes the nature of their cooling in a way that can couple the thermodynamics of ions and electrons.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Analysis of cell-based diffusion acceleration for the slice balance approach

In this work, we perform analysis on the use of cell-based diffusion acceleration methodologies to accelerate the convergence of transport solutions discretized with the slice balance approach (SBA) on unstructured polygonal grids.We investigated both linear diffusion synthetic acceleration (DSA) and non linear diffusion acceleration (NDA), including its partial-current variant (pNDA). DSA and NDA were both shown to diverge for intermediate ranges of mesh optical thicknesses. However, pNDA and Krylov methods like GMRES and Broyden stabilized the acceleration schemes, including problems with degenerate cells formed by mesh refinement. (author)

42 ENGINEERING↗

DOE OSTI2019

Modeling the Ex-core Detector Response into a Production Option in MPACT

In the past few years, the Consortium for Advanced Simulation of Light Water Reactors (CASL) has overseen a successful activity to extend the radiation transport capability from the reactor in-core geometry to the ex-core geometry by coupling the deterministic neutronics code MPACT, with the Monte Carlo code Shift. However, transient problems such as RIAs require an efficient prediction of the ex-core detector response to determine the timeframe for a reactor trip. Therefore, in addition to the high-fidelity MPACT-Shift coupled calculation, separate efforts have been made to explore simplified methods for ex-core detector response with MPACT standalone calculation. In a previous milestone L3_RTM.MCH.P17.06, several simplified methods for ex-core detector response were developed in MPACT. In particular, the double kernel method is based on the default MPACT core geometry, so extensive modeling or transport calculation with full reflector and ex-core details are not needed in this method. Since the 1-D diffusion and neutron streaming kernels are used for extended ex-core calculations, the extra computational efforts are very small. The work implemented in the current milestone provides a fully integrated option for MPACT to approximately calculate the ex-core detector response using the double kernel method. To overcome the difficulty of obtaining the consistent diffusion coefficients (these were obtained through separate CMFD calculation and edits), the 1-D diffusion solver is replaced by a 1-D Sn transport solver to compute the neutron flux at the vessel outer surface. The new VERA inputs for ex-core detector are processed in MPACT. The detector signals are linked to the SCRAM logic as an option to trip the core during transient calculation. Two sets of 3-D quarter core problems are run with MPACT standalone and VeraShift to verify the radial and axial effects on detector response by varying the moderator density and control rod position. For the cases with moderator density changes, the detector responses from MPACT are within 2 sigma error of VeraShift. For the cases at different control rod positions, the axial offsets computed from MPACT are within 2% error of VeraShift results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2018

Variational multiscale element-free Galerkin method combined with the moving Kriging interpolation for solving some partial differential equations with discontinuous solutions

Solving partial differential equations with discontinuous solutions is an important challenging problem in numerical analysis. To this end, there are some methods such as finite volume method, discontinuous Galerkin approach and particle technique that are able to solve these problems. In the current paper, the moving Kriging element-free Galerkin method has been combined with the variational multiscale algorithm to obtain acceptable and high-resolution solutions. For testing this technique, we select some PDEs with discontinuous solution such as Burgers’, Sod’s shock tube, advection–reaction–diffusion, Kuramoto–Sivashinsky, Boussinesq and shallow water equations. First, we obtain a time-discrete scheme by approximating time derivative via finite difference technique. Then we introduce the moving Kriging interpolation and also obtain their shape functions. We use the element-free Galerkin method for approximating the spatial derivatives. This method uses a weak form of the considered equation that is similar to the finite element method with the difference that in the classical element-free Galerkin method test and trial functions are moving least squares approximation (MLS) shape functions. Since the shape functions of moving least squares (MLS) approximation do not have Kronecker delta property, we cannot implement the essential boundary condition, directly. Thus, we employ the shape functions of moving Kriging interpolation and radial point interpolation technique which have the mentioned property. Also, in the element-free Galekin method, we do not use any triangular, quadrangular or other type of meshes. The element-free Galerkin method is a global method while finite element method is a local one. This technique employs a background mesh for integration which makes it different from the truly mesh procedures. Several test problems are solved and numerical simulations are reported which confirm the efficiency of the proposed schemes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Code Coverage Status of ARC Code-DIF3D

The Argonne Reactor Code (ARC) software system supports users in their fast reactor design goals by providing neutronic, thermal-hydraulic, and structural analysis capabilities. DIF3D plays a pivotal role in the ARC system as the primary homogenized assembly neutronic calculation methodology for fast reactor problems. Over its 40 years history, ARC software usage with DIF3D has been applied to numerous fast and thermal spectrum reactor analysis projects with good to excellent comparison against experiments. With continued improvement of computation resources, many of the geometry modeling capabilities in DIF3D that were primarily used in low order schemes are not really needed anymore. Today, the diffusion and transport capabilities of DIF3D-VARIANT are primarily used in the reactor design process with some scattered usage of DIF3D-FD and DIF3D-Nodal. In recent work, the DIF3D software verification was completed for DIF3D-FD and DIF3D-VARIANT on the geometry options used in the Versatile Test Reactor project. While we can be confident that these capabilities of DIF3D are well used and thus trusted, it does not demonstrate that all possible input options of DIF3D are actually working, but just those that were tested as part of VTR are and that they are correct. Thus, the purpose of the present work is to identify a set of test problems for DIF3D and assess the code coverage of DIF3D for those test problems. The goal is to document what parts of the existing DIF3D code are touched by the set of test problems and which are not. Because the verification work done on DIF3D-VARIANT and DIF3D-FD was focused on the most common uses of DIF3D for fast reactor analysis, the code coverage assessment of those capabilities is the highest priority. This will ensure that nothing is being missed by the existing verification test problems that DIF3D relies upon. The DIF3D-Nodal capability will also be inspected for code coverage as part of this work to further ensure that regular regression testing of DIF3D will trap any likely errors the end user might experience with the DIF3D software. The code coverage analysis of DIF3D was performed with the Code Coverage Tool of the Intel Fortran compiler which requires modifications to the compilation of DIF3D. The detailed coverage tables are given for each submodule of DIF3D separately, and for the submodules which are primarily developed for DIF3D, most of the source files could be at least partially touched. Most of the uncovered parts/files could be easily ignored, because they are either for error message and debugging output or obviously not needed by DIF3D. Out of the entire source codes of DIF3D, only a few uncovered modules deserve further investigation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Code Coverage Status of the ARC Code DIF3D

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

An Efficient High-Order Solver for Diffusion Equations with Strong Anisotropy on Non-Anisotropy-Aligned Meshes

This paper concerns numerical solution of the diffusion equation with strong anisotropy on meshes not aligned with the anisotropic vector field. In order to resolve the numerical pollution for simulations on a non-anisotropy-aligned mesh and reduce the associated high computational cost we propose an effective preconditioner, extending our previous work. Similar to the anisotropy-aligned mesh case, we apply the auxiliary space preconditioning framework to design a preconditioner where a continuous finite element space is used as the auxiliary space for the discontinuous finite element space. The key component is an effective line smoother that can mitigate the high-frequency errors perpendicular to the magnetic field. We design a graph-based approach to find such a line smoother that is approximately perpendicular to the vector fields when the mesh does not align with the anisotropy. Finally, numerical experiments for several benchmark problems are presented, demonstrating the effectiveness and robustness of the proposed preconditioner when applied to Krylov iterative methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Implicit-explicit Runge-Kutta for radiation hydrodynamics I: Gray diffusion

Radiation hydrodynamics are a challenging multiscale and multiphysics set of equations. To capture the relevant physics of interest, one typically must time step on the hydrodynamics timescale, making explicit integration the obvious choice. On the other hand, the coupled radiation equations have a scaling such that implicit integration is effectively necessary in non-relativistic regimes. A first-order Lie-Trotter-like operator split is the most common time integration scheme used in practice, alternating between an explicit hydrodynamics step and an implicit radiation solve and energy deposition step. However, such a scheme is limited to first-order accuracy, and nonlinear coupling between the radiation and hydrodynamics equations makes a more general additive partitioning of the equations non-trivial. Here, we develop a new formulation and partitioning of radiation hydrodynamics with gray diffusion that allows us to apply (linearly) implicit-explicit Runge-Kutta time integration schemes. In conclusion, we prove conservation of total energy in the new framework, and demonstrate 2nd-order convergence in time on multiple radiative shock problems, achieving error 3–5 orders of magnitude smaller than the first-order Lie-Trotter operator split at the hydrodynamic CFL, even when Lie-Trotter applies a 3rd-order TVD Runge-Kutta scheme to the hydrodynamics equations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2016

Engineering on-chip nanoporous gold material libraries via precision photothermal treatment [Precision Photothermal Annealing of Nanoporous Gold Thin Films for the Microfabrication of a Single-ship Material Libraries]

Single-chip material libraries of thin films of nanostructured materials are a promising approach for high throughput studies of structure-property relationship in the fields of physics and biology. Nanoporous gold (np-Au), produced by an alloy corrosion process, is a nanostructured material of specific interest in both these fields. One attractive property of np-Au is its self-similar coarsening behavior by thermally induced surface diffusion. However, traditional heat application techniques for the modification of np-Au are bulk processes that cannot be used to generate a library of different pore sizes on a single chip. Laser micromachining offers an attractive solution to this problem by providing a means to apply energy with high spatial and temporal resolution. In our present study we use finite element multiphysics simulations to predict the effects of laser mode (continuous-wave vs. pulsed) and supporting substrate thermal conductivity on the local np-Au film temperatures during photothermal annealing and subsequently investigate the mechanisms by which the np-Au network is coarsening. Our simulations predict that continuous-wave mode laser irradiation on a silicon supporting substrate supports the widest range of morphologies that can be created through the photothermal annealing of thin film np-Au. Using this result we successfully fabricate a single-chip material library consisting of 81 np-Au samples of 9 different morphologies for use in increased throughput material interaction studies.

36 MATERIALS SCIENCE↗

DOE OSTI2015

PLASMA INSTABILITIES IN THE CONTEXT OF CURRENT HELIUM SEDIMENTATION MODELS: DYNAMICAL IMPLICATIONS FOR THE ICM IN GALAXY CLUSTERS

Understanding whether Helium can sediment to the core of galaxy clusters is important for a number of problems in cosmology and astrophysics. All current models addressing this question are one-dimensional and do not account for the fact that magnetic fields can effectively channel ions and electrons, leading to anisotropic transport of momentum, heat, and particle diffusion in the weakly collisional intracluster medium (ICM). This anisotropy can lead to a wide variety of instabilities, which could be relevant for understanding the dynamics of heterogeneous media. In this paper, we consider the radial temperature and composition profiles as obtained from a state-of-the-art Helium sedimentation model and analyze its stability properties. We find that the associated radial profiles are unstable to different kinds of instabilities depending on the magnetic field orientation at all radii. The fastest growing modes are usually related to generalizations of the magnetothermal instability (MTI) and the heat-flux-driven buoyancy instability which operate in heterogeneous media. We find that the effect of sedimentation is to increase (decrease) the predicted growth rates in the inner (outer) cluster region. The unstable modes grow quickly compared to the sedimentation timescale. This suggests that the composition gradients as inferred from sedimentation models, which do not fully account for the anisotropic character of the weakly collisional environment, might not be very robust. Our results emphasize the subtleties involved in understanding the gas dynamics of the ICM and argue for the need of a comprehensive approach to address the issue of Helium sedimentation beyond current models.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Ensemble Simulation Techniques and Fast Randomized Algorithms

The major goals of the project were to develop and analyze new ensemble simulation techniques, including trajectory stratification and preconditioned MCMC techniques, as well as develop fast numerical linear algebra techniques closely related to ensemble simulation ideas. The trajectory stratification techniques involve simulating in parallel short trajectory fragments of a Markov process confined to a specific region of space‐time and then patching together the statistics gathered to assemble estimates of very general dynamical properties. We have also developed this approach for rare event simulation and extended the techniques to applications requiring a more general framework (such as electronic structure calculations). The preconditioned MCMC techniques involve simulating multiple Markov chains in parallel and then using information from the ensemble to speed the mixing of each individual chain. The fast randomized linear algebra methods are motivated by the diffusion Monte Carlo technique, but are applicable to finding the dominant eigenvalue of (almost) general matrices. For most non‐negative matrices, the schemes result in an error (compared to the power method) that is constant in the dimension of the problem. For more general matrices, we see a very clear sublinear cost trend in computational tests.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

VARI3D & PERSENT: Perturbation and Sensitivity Analysis

The nodal diffusion method is one of the most widely used approaches in modern reactor analysis. In the nodal diffusion method, a coarse multi-group set of “homogenized” parameters is constructed such that the complex geometry of a reactor core along with the energy dependence of neutron and gamma ray cross sections in a nuclear reactor are conserved in the simpler geometry. The homogenization is typically done on a fuel assembly level as is the case in the DIF3D code developed at Argonne National Laboratory. The nodal methodology is used primarily to predict fuel cycle behavior of nuclear systems of which there is a substantial amount of validation in the literature. Another use of the nodal method is to obtain reactivity coefficients and kinetics parameters for use in a safety analysis of a given nuclear reactor. While there are many ways to obtain reactivity worth and kinetics parameters, the work presented in this manuscript is unique as it provides the user with the ability to compute reactivity worths, kinetics parameters, and cross section sensitivities with a Cartesian and hexagonal geometry based transport code. This manuscript serves as a single manual for two separate codes: VARI3D and PERSENT. The VARI3D code (VARIational 3D) is based upon the classic finite difference diffusion theory solver available in DIF3D. The PERSENT code (PERturbation and SENitivity for Transport) is based upon the variational nodal method employed in DIF3D termed VARIANT. The VARIANT solver was added to DIF3D in 1995 and has seen continued development and use for the last 18 years. Because VARI3D primarily uses deprecated coding practices, rather than incorporating the perturbation and sensitivity treatments for transport within VARI3D, a new coding development was built using modern Fortran coding. The primary purpose of this manual is to describe the theory behind PERSENT (and by convenience, that of VARI3D) and discuss the input and output of PERSENT along with giving potential users an idea of how to use it. While this manuscript does describe the input and output of VARI3D, the PERSENT code is intended to be the replacement capability of VARI3D as PERSENT can generate nearly identical (if not superior) diffusion theory results. In this manuscript, the relevant aspects of generalized perturbation theory and exact perturbation theory that apply to both VARI3D and PERSENT are covered. The input and output of VARI3D is displayed by excerpting several of the example problems. Similarly, the input and output of PERSENT is displayed along with tips on how best to use the code. Note that the input and output of the inhomogeneous solver wrapped around DIF3D (DIF3D_IFS) is also discussed as it is needed to carry out some of the sensitivities in PERSENT such as reaction rate ratios. This manuscript describes several perturbation and sensitivity problems, and the results computed using PERSENT. From these sections, potential users should find that PERSENT provides not only the typical tables of numbers desired in perturbation and sensitivity analysis work, but also can visually plot the result for a more thorough understanding of the space and energy distribution (Section 5). Overall, PERSENT is observed to produce accurate reactivity worths and sensitivities for the displayed set of test problems and clearly demonstrates the need to have a transport-based sensitivity capability as evident from the thousands of percent errors observed in the 21-group hexagonal fast reactor problem (covered in Section 7). The uncertainty calculation capability is described in Section 3 and demonstrated in Section 7.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2026

Multi-physics Preconditioning for Thermally Activated Batteries

Thermal batteries, also known as molten-salt batteries, are single-use reserve power systems activated by pyrotechnic heat generation, which transitions the solid electrolyte into a molten state. The simulation of these batteries relies on multiphysics modeling to evaluate performance and behavior under various conditions. This paper presents advancements in scalable preconditioning strategies for the Thermally Activated Battery Simulator (TABS) tool, enabling efficient solutions to the coupled electrochemical systems that dominate computational costs in thermal battery simulations. We propose a hierarchical block Gauss-Seidel preconditioner implemented through the Teko package in Trilinos, which effectively addresses the challenges posed by tightly coupled physics, including charge transport, porous flow, and species diffusion. The preconditioner leverages scalable subblock solvers, including smoothed aggregation algebraic multigrid (SA-AMG) methods and domain-decomposition techniques, to achieve robust convergence and parallel scalability. Strong and weak scaling studies demonstrate the solver’s ability to handle problem sizes up to 51.3 million degrees of freedom on 2048 processors, achieving near sub-second setup and solve times for the end-to-end electrochemical solve. These advancements significantly improve the computational efficiency and turnaround time of thermal battery simulations, paving the way for higher-resolution models and enabling the transition from 2D axisymmetric to full 3D simulations.

25 ENERGY STORAGE↗

DOE OSTI2015

Second-order adjoint sensitivity analysis methodology (2ND-ASAM) for computing exactly and efficiently first- and second-order sensitivities in large-scale systems - 14356

This work presents the second-order adjoint sensitivity analysis methodology (2.-ASAM) for computing exactly and efficiently the second-order functional derivatives ('sensitivities') of system responses to the system's model parameters. For a physical system comprising N{sub α} parameters and N{sub r} responses, forward methods require a total of at least (N{sup 2}{sub α}/2+3N{sub α}/2) large-scale computations for obtaining all of the first- and second-order sensitivities, for all N{sub r} system responses. On the other hand, for one functional-type system response, the 2.-ASAM requires one large-scale computation using the first-level adjoint sensitivity system (1.-LASS) for obtaining all of the first-order sensitivities, followed by at most (2N{sub α}+1) large-scale computations using the second-level adjoint sensitivity systems (2.-LASS) for obtaining all of the second-order sensitivities. The second-order sensitivities contribute decisively to causing asymmetries in the response distribution, since they are the leading contributors to the third-order response correlations (skewness). They also cause the 'expected value of the response' to differ from the 'computed nominal value of the response'. The implementation of the 2.-ASAM requires very little additional effort beyond the construction of the adjoint sensitivity system needed for computing the first-order sensitivities. Only the sources on the right-sides of the diffusion (differential) operator needed to be modified; the left-side of the differential equations (and hence the 'solver' in large-scale practical applications) remain unchanged. The application of the 2.-ASAM is illustrated on a benchmark heat conduction/convection problem, which makes transparent the underlying mathematical derivations. For this illustrative problem, 4 'large-scale' adjoint computations suffice for computing exactly all of the 6 first- and 21 distinct second-order derivatives. The 2.-ASAM presented in this work should enable the hitherto very difficult, if not intractable, exact computation of all of the second-order response sensitivities for large-systems involving many parameters, which is expected to affect significantly other fields that need efficiently computed second-order response sensitivities, such as optimization, data assimilation/adjustment, model calibration, and predictive modeling. (author)

42 ENGINEERING↗

DOE OSTI2024

Ensemble variational Fokker-Planck methods for data assimilation

Particle flow filters solve Bayesian inference problems by smoothly transforming a set of particles into samples from the posterior distribution. Particles move in state space under the flow of an McKean-Vlasov-Itˆo process. This work introduces the Variational Fokker-Planck (VFP) framework for data assimilation, a general approach that includes previously known particle flow filters as special cases. The McKean-Vlasov-Itˆo process that transforms particles is defined via an optimal drift that depends on the selected diffusion term. It is established that the underlying probability density - sampled by the ensemble of particles - converges to the Bayesian posterior probability density. For a finite number of particles the optimal drift contains a regularization term that nudges particles toward becoming independent random variables. Based on this analysis, we derive computationally-feasible approximate regularization approaches that penalize the mutual information between pairs of particles, and avoid particle collapse. Moreover, the diffusion plays a role akin to a particle rejuvenation approach that aims to alleviate particle collapse. The VFP framework is very flexible. Different assumptions on prior and intermediate probability distributions can be used to implement the optimal drift, and localization and covariance shrinkage can be applied to alleviate the curse of dimensionality. A robust implicit-explicit method is discussed for the efficient integration of stiff McKean- Vlasov-Itˆo processes. Here, the effectiveness of the VFP framework is demonstrated on three progressively more challenging test problems, namely the Lorenz ’63, Lorenz ’96 and the quasi-geostrophic equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Fast penetration of megagauss fields into metallic conductors

Megagauss magnetic-field penetration into a conducting material is studied via a simplified but representative model, wherein the magnetic-diffusion equation is coupled with a thermal-energy balance. The specific scenario considered is that of a prescribed magnetic field rising (in proportion to an arbitrary power r of time) at the surface of a conducting half-space whose electric conductivity is assumed proportional to an arbitrary inverse power γ of temperature. We employ a systematic asymptotic scheme in which the case of a strong surface field corresponds to a singular asymptotic limit. In this limit, the highly magnetized and hot “skin” terminates at a distinct propagating wave-front. Employing the method of matched asymptotic expansions, we find self-similar solutions of the magnetized region which match a narrow boundary-layer region about the advancing wave front. The rapidly decaying magnetic-field profile in the latter region is also self similar; when scaled by the instantaneous propagation speed, its shape is time-invariant, depending only on the parameter γ. The analysis furnishes a simple asymptotic formula for the skin-depth (i.e., the wave-front position), which substantially generalizes existing approximations. It scales with the power γr + 1∕2 of time and the power γ of field strength, and is much larger than the field-independent skin depth predicted by an athermal model. The formula further involves a dimensionless O(1) pre-factor which depends on r and γ. It is determined by solving a nonlinear eigenvalue problem governing the magnetized region. Another main result of the analysis, apparently unprecedented, is an asymptotic formula for the magnitude of the current-density peak characterizing the wave-front region. Complementary to these systematic results, we provide a closed-form but ad hoc generalization of the theory approximately applicable to arbitrary monotonically rising surface fields. Our results are in excellent agreement with numerical simulations of the model, and compare favourably with detailed magnetohydrodynamic simulations reported in the literature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

A chain-of-states acceleration method for the efficient location of minimum energy paths

We describe a robust and efficient chain-of-states method for computing Minimum Energy Paths (MEPs) associated to barrier-crossing events in poly-atomic systems, which we call the acceleration method. The path is parametrized in terms of a continuous variable t ∈ [0, 1] that plays the role of time. In contrast to previous chain-of-states algorithms such as the nudged elastic band or string methods, where the positions of the states in the chain are taken as variational parameters in the search for the MEP, our strategy is to formulate the problem in terms of the second derivatives of the coordinates with respect to t, i.e., the state accelerations. We show this to result in a very simple and efficient method for determining the MEP. We describe the application of the method to a series of test cases, including two low-dimensional problems and the Stone-Wales transformation in C{sub 60}.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗