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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Investigations on a fuzzy process: effect of diffusion on calibration and particle identification in Liquid Argon Time Projection Chambers

Ionization electron diffusion in Liquid Argon Time Projection Chambers (LArTPCs) has typically been considered at the detector design stage, but little attention has been given to its effects on calibration and particle identification. We use a GEANT4-based simulation to study how diffusion impacts these techniques, and give consideration to how this effect is simulated. We find that diffusion can cause a drift-dependent bias to both the median and Most Probable Value (MPV) of dQ/dx distributions. The bias is estimated to be ~2.5% (median) and ~5.0% (MPV) for typical maximum drift times in currently running LArTPCs before adding detector specific considerations such as electric field non-uniformities. This information indicates that these metrics should not be used for calibration without care, contrary to the conventional wisdom. The impact of diffusion on the ability of LArTPCs to separate muons and protons is small, and not expected to pose any problems in future detectors. Diffusion may however be a significant source of systematic uncertainty when separating particles of more similar masses (muons and pions, kaons and protons). Separation of such populations may be improved by implementation of a drift-time dependent particle identification.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2018

Hermite analogs of the lowest order Raviart–Thomas mixed method for convection–diffusion equations

The Raviart–Thomas mixed finite-element method of the lowest order (Raviart and Thomas in mixed finite-element methods for second-order elliptic problems, Lecture Notes in mathematics, Springer, New York, 1977) commonly known as the RT{sub 0} method, is a well-established and popular numerical tool to solve diffusion-like problems providing flux continuity across inter-element boundaries. Douglas and Roberts extended the method to the case of more general second-order boundary-value problems including the convection–diffusion equations (cf. this journal Douglas in Comput Appl Math 1:91–103; 1982). The main drawback of these methods, however, is the poor representation of the primal variable by piecewise constant functions. The Hermite analog of the RT{sub 0} method for treating pure diffusion phenomena proposed in Ruas (J Comput Appl Math, 246:234–242; 2013) proved to be a valid alternative to attain higher order approximation of the primal variable while keeping intact the matrix structure and the quality of the discrete flux variable of the original RT{sub 0} method. Non-trivial extensions of this method are studied here that can be viewed as Hermite analogs of the two Douglas and Roberts’ versions of the RT{sub 0} method, to solve convection–diffusion equations. A detailed convergence study is carried out for one of the Hermite methods, and numerical results illustrate the performance of both of them, as compared to each other and to the corresponding mixed methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Post-processing interstitialcy diffusion from molecular dynamics simulations

An algorithm to rigorously trace the interstitialcy diffusion trajectory in crystals is developed. The algorithm incorporates unsupervised learning and graph optimization which obviate the need to input extra domain specific information depending on crystal or temperature of the simulation. The algorithm is implemented in a flexible framework as a post-processor to molecular dynamics (MD) simulations. We describe in detail the reduction of interstitialcy diffusion into known computational problems of unsupervised clustering and graph optimization. We also discuss the steps, computational efficiency and key components of the algorithm. Using the algorithm, thermal interstitialcy diffusion from low to near-melting point temperatures is studied. We encapsulate the algorithms in a modular framework with functionality to calculate diffusion coefficients, migration energies and other trajectory properties. The study validates the algorithm by establishing the conformity of output parameters with experimental values and provides detailed insights for the interstitialcy diffusion mechanism. The algorithm along with the help of supporting visualizations and analysis gives convincing details and a new approach to quantifying diffusion jumps, jump-lengths, time between jumps and to identify interstitials from lattice atoms. -- Graphical abstract:.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

A new approach for simulating inhomogeneous chemical kinetics

Abstract In this paper, inhomogeneous chemical kinetics are simulated by describing the concentrations of interacting chemical species by a linear expansion of basis functions in such a manner that the coupled reaction and diffusion processes are propagated through time efficiently by tailor-made numerical methods. The approach is illustrated through modelling $$\alpha$$ α - and $$\gamma$$ γ -radiolysis in thin layers of water and at their solid interfaces from the start of the chemical phase until equilibrium was established. The method’s efficiency is such that hundreds of such systems can be modelled in a few hours using a single core of a typical laptop, allowing the investigation of the effects of the underlying parameter space. Illustrative calculations showing the effects of changing dose-rate and water-layer thickness are presented. Other simulations are presented which show the approach’s capability to solve problems with spherical symmetry (an approximation to an isolated radiolytic spur), where the hollowing out of an initial Gaussian distribution is observed, in line with previous calculations. These illustrative simulations show the generality and the computational efficiency of this approach to solving reaction-diffusion problems. Furthermore, these example simulations illustrate the method’s suitability for simulating solid-fluid interfaces, which have received a lot of experimental attention in contrast to the lack of computational studies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Overset meshing coupled with hybridizable discontinuous Galerkin finite elements

We introduce the use of hybridizable discontinuous Galerkin (HDG) finite element methods on overlapping (overset) meshes. Overset mesh methods are advantageous for solving problems on complex geometrical domains. We also combine geometric flexibility of overset methods with the advantages of HDG methods: arbitrarily high-order accuracy, reduced size of the global discrete problem, and the ability to solve elliptic, parabolic, and/or hyperbolic problems with a unified form of discretization. This approach to developing the ‘overset HDG’ method is to couple the global solution from one mesh to the local solution on the overset mesh. We present numerical examples for steady convection–diffusion and static elasticity problems. The examples demonstrate optimal order convergence in all primal fields for an arbitrary amount of overlap of the underlying meshes.

42 ENGINEERING↗
DOE OSTI2018

High-order, linearly stable, partitioned solvers for general multiphysics problems based on implicit–explicit Runge–Kutta schemes

This work introduces a general framework for constructing high-order, linearly stable, partitioned solvers for multiphysics problems from a monolithic implicit–explicit Runge–Kutta (IMEX-RK) discretization of the semi-discrete equations. The generic multiphysics problem is modeled as a system of n systems of partial differential equations where the i th subsystem is coupled to the other subsystems through a coupling term that can depend on the state of all the other subsystems. This coupled system of partial differential equations reduces to a coupled system of ordinary differential equations via the method of lines where an appropriate spatial discretization is applied to each subsystem. The coupled system of ordinary differential equations is taken as a monolithic system and discretized using an IMEX-RK discretization with a specific implicit–explicit decomposition that introduces the concept of a predictor for the coupling term. We propose four coupling predictors that enable the monolithic system to be solved in a partitioned manner, i.e., subsystem-by-subsystem, and preserve the IMEX-RK structure and therefore the design order of accuracy of the monolithic scheme. The four partitioned solvers that result from these predictors are high-order accurate, allow for maximum re-use of existing single-physics software, and two of the four solvers allow the subsystems to be solved in parallel at a given stage and time step. We also analyze the stability of a coupled, linear model problem with a specific coupling structure and show that one of the partitioned solvers achieves unconditional linear stability for this problem, while the others are unconditionally stable only for certain values of the coupling strength. We demonstrate the performance of the proposed partitioned solvers on several classes of multiphysics problems including a simple linear system of ODEs, advection–diffusion–reaction systems, fluid–structure interaction problems, and particle-laden flows, where we verify the design order of the IMEX schemes and study various stability properties.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Resolution of a Few Problems in the Application of Quasilinear Theory to Calculating Diffusion Coefficients in Heliophysics

A theory of quasilinear diffusion for obliquely propagating electromagnetic waves was developed in the 1960's and applied in the 1970's to model scattering of relativistic electrons by a prescribed distribution of waves. In the latter work, a transformation of variables, from wavevector space to the temporal frequency and tangent of the wave normal angle, was used so that simple Gaussian functions of frequency and tangent of the wave normal angle could be multiplied together to define the distribution of wave power, although arbitrary distributions of power in these two variables is also permitted. Finally, in 2005, previous work was consolidated and has been widely used in heliophysics studies that require computation of quasilinear diffusion coefficients. Here it is shown that this transformation is inppropriate when the precise wave vector distribution is known. The correct transformation is derived and used to produce diffusion coefficients that can differ by orders of magnitude from those computed using the inappropriate transformation. The differences are largest when the distribution of wave power extends to wave normal angles near the resonance cone. When the ratio of the plasma frequency to the gyrofrequency is large, only low energies (keV) are affected, but as the ratio decreases higher energies (MeV) also show differences. It is also shown that the derivation from the 1960's uses a notation that results in the diffusion coefficients depending on the distribution of wave power with respect to the wave azimuthal angle whereas there should be no such dependence.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

An optimization-based approach to parameter learning for fractional type nonlocal models

Nonlocal operators of fractional type are a popular modeling choice for applications that do not adhere to classical diffusive behavior; however, one major challenge in nonlocal simulations is the selection of model parameters. In this study we propose an optimization-based approach to parameter identification for fractional models with an optional truncation radius. We formulate the inference problem as an optimal control problem where the objective is to minimize the discrepancy between observed data and an approximate solution of the model, and the control variables are the fractional order and the truncation length. For the numerical solution of the minimization problem we propose a gradient-based approach, where we enhance the numerical performance by an approximation of the bilinear form of the state equation and its derivative with respect to the fractional order. Several numerical tests in one and two dimensions illustrate the theoretical results and show the robustness and applicability of our method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A model of thermal creep and annealing in finite domains based on coupled dislocation climb and vacancy diffusion

Here, we develop a framework to investigate thermal creep and annealing in finite domains, where the climb motion of discrete dislocations is coupled to the diffusion of a continuum vacancy field. The model is first formulated in a continuum finite-deformation setting. All governing equations and boundary conditions are obtained from a unified irreversible thermodynamics principle. The resulting model couples a mechanical boundary value problem (BVP), a vacancy diffusion BVP, and the climb and glide motion of the discrete dislocation network within the crystal. The framework is then linearized for implementation in three-dimensional (3D) discrete dislocation dynamics (DDD) simulations for arbitrary anisotropic crystals. A solution scheme is developed based on the superposition principle, which is imposed weakly on the dislocation network to obtain a Galerkin solution for the nodal climb velocities. The framework includes diffusional (Nabarro–Herring) creep deformation as well as dislocation creep by climb-assisted-glide. The method is applied to simulate the annealing of vacancy loops in Al, with good agreement to experimental measurements by Silcox and Hirsch. We further consider the effects of annealing under stress, and of the proximity of the vacancy loops to loaded and free boundaries Simulations in polycrystalline materials are carried out to highlight the effects of the grain size on dislocation climb and vacancy loop annealing. The method is also applied to estimate the creep rate due to climb-assisted glide of jogged-screw dislocations in γ-TiAl, and results are compared to experiments by Viswanathan et al. Finally, we discuss the effects of uniaxial and hydrostatic stresses on the two diffusive deformation pathways of the material, namely Nabarro–Herring creep and dislocation climb.

36 MATERIALS SCIENCE↗
DOE OSTI2020

An optimization-based approach to parameter learning for fractional type nonlocal models

Nonlocal operators of fractional type are a popular modeling choice for applications that do not adhere to classical diffusive behavior; however, one major challenge in nonlocal simulations is the selection of model parameters. In this work we propose an optimization-based approach to parameter identification for fractional models with an optional truncation radius. We formulate the inference problem as an optimal control problem where the objective is to minimize the discrepancy between observed data and an approximate solution of the model, and the control variables are the fractional order and the truncation length. For the numerical solution of the minimization problem we propose a gradient-based approach, where we enhance the numerical performance by an approximation of the bilinear form of the state equation and its derivative with respect to the fractional order. Several numerical tests in one and two dimensions illustrate the theoretical results and show the robustness and applicability of our method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Fractional diffusion on bounded domains

We found that the mathematically correct specification of a fractional differential equation on a bounded domain requires specification of appropriate boundary conditions, or their fractional analogue. In this paper we discuss the application of nonlocal diffusion theory to specify well-posed fractional diffusion equations on bounded domains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Hybrid Multiscale Finite Volume Method for Advection-Diffusion Equations Subject to Heterogeneous Reactive Boundary Conditions

We present a hybrid scheme for the coupling of macro and microscale continuum models for reactive contaminant transport in fractured and porous media. The transport model considered is the advection-dispersion equation, subject to linear heterogeneous reactive boundary conditions. The Multiscale Finite Volume method (MsFV) is employed to define an approximation to the microscale concentration field defined in terms of macroscopic or \emph{global} degrees of freedom, together with local interpolator and corrector functions capturing microscopic spatial variability. The macroscopic mass balance relations for the MsFV global degrees of freedom are coupled with the macroscopic model, resulting in a global problem for the simultaneous time-stepping of all macroscopic degrees of freedom throughout the domain. In order to perform the hybrid coupling, the micro and macroscale models are applied over overlapping subdomains of the simulation domain, with the overlap denoted as the handshake subdomain $\Omega^{hs}$, over which continuity of concentration and transport fluxes between models is enforced. Continuity of concentration is enforced by posing a restriction relation between models over $\Omega^{hs}$. Continuity of fluxes is enforced by prolongating the macroscopic model fluxes across the boundary of $\Omega^{hs}$ to microscopic resolution. The microscopic interpolator and corrector functions are solutions to local microscopic advection-diffusion problems decoupled from the global degrees of freedom and from each other by virtue of the MsFV decoupling ansatz. The error introduced by the decoupling ansatz is reduced iteratively by the preconditioned GMRES algorithm, with the hybrid MsFV operator serving as the preconditioner.

Barajas-Solano, David A.↗
DOE OSTI2018

Fluctuating hydrodynamics of reactive liquid mixtures

Fluctuating hydrodynamics (FHD) provides a framework for modeling microscopic fluctuations in a manner consistent with statistical mechanics and nonequilibrium thermodynamics. This paper presents an FHD formulation for isothermal reactive incompressible liquid mixtures with stochastic chemistry. Fluctuating multispecies mass diffusion is formulated using a Maxwell-Stefan description without assuming a dilute solution, and momentum dynamics is described by a stochastic Navier-Stokes equation for the fluid velocity. We consider a thermodynamically consistent generalization for the law of mass action for non-dilute mixtures and use it in the chemical master equation (CME) to model reactions as a Poisson process. The FHD approach provides remarkable computational efficiency over traditional reaction-diffusion master equation methods when the number of reactive molecules is large, while also retaining accuracy even when there are as few as ten reactive molecules per hydrodynamic cell. We present a numerical algorithm to solve the coupled FHD and CME equations and validate it on both equilibrium and nonequilibrium problems. We simulate a diffusively driven gravitational instability in the presence of an acid-base neutralization reaction, starting from a perfectly flat interface. We demonstrate that the coupling between velocity and concentration fluctuations dominates the initial growth of the instability.

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

Evaluation of a nonlinear variational multiscale method for fluid transport problems

Diverse transport problems, especially those based on fluid flow models, are intrinsically multiscale and nonlinear, characteristics that often lead to intricate dynamics such as the development of instabilities and turbulence. Computational simulations that resolve all scales in these problems are often unfeasible, prompting to coarse-grained simulation strategies in which small-scale features are modeled instead of resolved. Variational Multiscale (VMS) methods, and particularly residual-based Large-Eddy Simulation (LES) approaches, have proven effective and robust for the coarse-grained simulation of complex transport problems. VMS methods avoid the assumption of separable nonlinearity and the reliance on empirical small-scale models by using a variational decomposition of scales together with a residual-based approximation of the small-scales. Evaluation of a nonlinear VMS approach, denoted as VMS n , is presented for the coarse-grained simulation of transient-advective-diffusive-reactive (TADR) transport problems arising from fluid flow models. In contrast to classical VMS approaches that neglect the effect of the small scales on the transport operator, VMS n treats the inter-dependence between large- and small-scales upfront. The treatment of inter-scale coupling involves the solution of a local algebraic nonlinear system describing the evolution of the small-scales. The VMS n approach is complemented with two algebraic approximations of the small-scales: one based on the main diagonal of the transport matrices and another that preserves transport fluxes and is suitable for generic TADR systems. The suitability of the VMS n approach for handling general TADR problems and regimes is evaluated with benchmark incompressible, compressible, and magnetohydrodynamic laminar flow problems, the incompressible Taylor-Green vortex flow, the turbulent free jet, and the two-temperature arc in crossflow. Furthermore, simulation results show that VMS n leads to minor improvements in accuracy with respect to the classical VMS for the laminar flow problems, but to significantly greater accuracy for the turbulent flows and the unsteady plasma flow problems, while using the same cohesive numerical formulation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Multilevel Convergence Analysis of Multigrid-Reduction-in-Time

This study presents a multilevel convergence framework for multigrid-reduction-in-time (MGRIT) as a generalization of previous two-grid estimates. The framework provides a priori upper bounds on the convergence of MGRIT V- and F-cycles, with different relaxation schemes, by deriving the respective residual and error propagation operators. The residual and error operators are functions of the time-stepping operator, analyzed directly and bounded in the norm, both numerically and analytically. We present various upper bounds of different computational cost and varying sharpness. These upper bounds are complemented by proposing analytic formulae for the approximate convergence factor of V-cycle algorithms that take the number of fine grid time points, the temporal coarsening factors, and the eigenvalues of the time-stepping operator as parameters. The paper concludes with supporting numerical investigations of parabolic (anisotropic diffusion) and hyperbolic (wave equation) model problems. We assess the sharpness of the bounds and the quality of the approximate convergence factors. Observations from these numerical investigations demonstrate the value of the proposed multilevel convergence framework for estimating MGRIT convergence a priori and for the design of a convergent algorithm. We further highlight that observations in the literature are captured by the theory, including that two-level Parareal and multilevel MGRIT with F-relaxation do not yield scalable algorithms and the benefit of a stronger relaxation scheme. An important observation is that with increasing numbers of levels MGRIT convergence deteriorates for the hyperbolic model problem, while constant convergence factors can be achieved for the diffusion equation. The theory also indicates that L-stable Runge--Kutta schemes are more amendable to multilevel parallel-in-time integration with MGRIT than A-stable Runge--Kutta schemes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Multigrid Reduction in Time for Nonlinear Parabolic Problems: A Case Study

The need for parallelism in the time dimension is being driven by changes in computer architectures, where performance increases are now provided through greater concurrency, not faster clock speeds. This creates a bottleneck for sequential time marching schemes because they lack parallelism in the time dimension. Multigrid reduction in time (MGRIT) is an iterative procedure that allows for temporal parallelism by utilizing multigrid reduction techniques and a multilevel hierarchy of coarse time grids. MGRIT has been shown to be effective for linear problems, with speedups of up to 50 times. The goal of this work is the efficient solution of nonlinear problems with MGRIT, where efficiency is defined as achieving similar performance when compared to an equivalent linear problem. The benchmark nonlinear problem is the p-Laplacian, where p=4 corresponds to a well-known nonlinear diffusion equation and p=2 corresponds to the standard linear diffusion operator, our benchmark linear problem. The key difficulty encountered is that the nonlinear time-step solver becomes progressively more expensive on coarser time levels as the time-step size increases. To overcome such difficulties, multigrid research has historically targeted an accumulated body of experience regarding how to choose an appropriate solver for a specific problem type. To that end, this paper develops a library of MGRIT optimizations and modifications, most important an alternate initial guess for the nonlinear time-step solver and delayed spatial coarsening, that will allow many nonlinear parabolic problems to be solved with parallel scaling behavior comparable to the corresponding linear problem.

parareal↗
DOE OSTI2016

Suppressing spectral diffusion of emitted photons with optical pulses

In many quantum architectures the solid-state qubits, such as quantum dots or color centers, are interfaced via emitted photons. However, the frequency of photons emitted by solid-state systems exhibits slow uncontrollable fluctuations over time (spectral diffusion), creating a serious problem for implementation of the photon-mediated protocols. Here we show that a sequence of optical pulses applied to the solid-state emitter can stabilize the emission line at the desired frequency. We demonstrate efficiency, robustness, and feasibility of the method analytically and numerically. Taking nitrogen-vacancy center in diamond as an example, we show that only several pulses, with the width of 1 ns, separated by few ns (which is not difficult to achieve) can suppress spectral diffusion. As a result, our method provides a simple and robust way to greatly improve the efficiency of photon-mediated entanglement and/or coupling to photonic cavities for solid-state qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Nonstationary Problem of Complex Heat Transfer in a System of Semitransparent Bodies with Boundary-Value Conditions of Diffuse Reflection and Refraction of Radiation

We consider a nonstationary initial boundary-value problem describing complex (radiative-conductive) heat transfer in a system of semitransparent bodies. To describe radiation propagation, we use the radiation transfer equation with boundary-value conditions of diffuse reflection and refraction of radiation. We take into account that the radiation intensity and optical properties of bodies depend on the radiation frequency. The unique solvability of a weak solution is established. The comparison theorem is proved. A priori estimates of a weak solution as well as its regularity are obtained.

97 MATHEMATICS AND COMPUTING↗