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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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At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Nonlinear control of safety factor gradient in tokamaks using spatially variable electron cyclotron current drives

Active control of plasma properties may be necessary to achieve stable operation of next-generation tokamaks over large time scales. Such control algorithms can regulate the plasma properties to avoid the onset of magnetohydrodynamic (MHD) instabilities. For instance, the global and local properties of the safety factor profile are linked to the onset of neoclassical tearing modes (NTMs). This work proposes a model-based control approach for deterring/delaying NTMs through active modulation of one of the safety factor properties - the gradient of the safety factor profile at a particular rational safety factor surface. In particular, a novel control-oriented model for the local safety factor gradient is developed. The nonlinear control model is governed by a nonautonomous ordinary differential equation that accounts for a given rational safety factor surface’s spatial variation over time. Further, to improve the controllability of the spatially evolving parameter, the control model treats ECH&CD positions, along with noninductive powers, as controllable variables. A nonlinear control algorithm based on feedback linearization with optimization is synthesized to achieve the objective of regulating the safety factor gradient around a given target. The proposed algorithm allocates optimal ECH&CD positions, in addition to auxiliary powers, at each time instant as the rational safety factor surface drifts to locations with a low control authority. Stability guarantees of the proposed control law are also discussed in this work. The proposed algorithm is tested for a DIII-D tokamak scenario in nonlinear simulations carried out using the Control Oriented Transport SIMulator (COTSIM). Both fixed and moving ECH&CD cases are studied, and their outcomes are compared. Simulation results demonstrate that enthusiastic regulation of the safety factor gradient can be achieved during the ramp-up and flat-top phases of tokamak operation in both fixed and moving ECH&CD cases. However, real-time updates of ECH&CD positions can prevent the saturation of auxiliary powers.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Modeling atmospheric data and identifying dynamics Temporal data-driven modeling of air pollutants

Atmospheric modelling has recently experienced a surge with the advent of deep learning. Most of these models, however, predict concentrations of pollutants following a data-driven approach in which the physical laws that govern their behaviors and relationships remain hidden. Furthermore, with the aid of real-world air quality data collected hourly in different stations throughout Madrid, we present a case study using a series of data-driven techniques with the following goals: (1) Find systems of ordinary differential equations that model the concentration of pollutants and their changes over time; (2) assess the performance and limitations of our model using stability analysis; (3) reconstruct the time series of chemical pollutants not measured in certain stations using delay coordinate embedding results.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

High-order partitioned spectral deferred correction solvers for multiphysics problems

We present an arbitrarily high-order, conditionally stable, partitioned spectral deferred correction (SDC) method for solving multiphysics problems using a sequence of pre-existing single-physics solvers. This method extends the work in [1], [2], which used implicit-explicit Runge-Kutta methods (IMEX) to build high-order, partitioned multiphysics solvers. We consider a generic multiphysics problem modeled as a system of coupled ordinary differential equations (ODEs), coupled through coupling terms that can depend on the state of each subsystem; therefore the method applies to both a semi-discretized system of partial differential equations (PDEs) or problems naturally modeled as coupled systems of ODEs. The sufficient conditions to build arbitrarily high-order partitioned SDC schemes are derived. Based on these conditions, various of partitioned SDC schemes are designed. The stability of the first-order partitioned SDC scheme is analyzed in detail on a coupled, linear model problem. We show that the scheme is conditionally stable, and under conditions on the coupling strength, the scheme can be unconditionally stable. We demonstrate the performance of the proposed partitioned solvers on several classes of multiphysics problems with moderate coupling strength. They include a stiff linear system of ODEs, advection-diffusion-reaction systems, and fluid-structure interaction problems with both incompressible and compressible flows, where we verify the design order of the SDC schemes and study various stability properties. We also directly compare the accuracy, stability, and cost of the proposed partitioned SDC solver with the partitioned IMEX method in [1], [2] on this suite of test problems. The results suggest that the high-order partitioned SDC solvers are more robust than the partitioned IMEX solvers for the numerical examples considered in this work, while the IMEX methods require fewer implicit solves.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A unified formulation of splitting-based implicit time integration schemes

Splitting-based time integration approaches such as fractional step, alternating direction implicit, operator splitting, and locally one dimensional methods partition the system of interest into components, and solve individual components implicitly in a cost-effective way. Here this work proposes a unified formulation of splitting time integration schemes in the framework of general-structure additive Runge–Kutta (GARK) methods. Specifically, we develop implicit-implicit (IMIM) GARK schemes, provide the order conditions for this class, and explain their application to partitioned systems of ordinary differential equations. We show that classical splitting methods belong to the IMIM GARK family, and therefore can be studied in this unified framework. New IMIM-GARK splitting methods are developed and tested using parabolic systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Towards sharp error analysis of extended Lagrangian molecular dynamics

The extended Lagrangian molecular dynamics (XLMD) method provides a useful framework for reducing the computational cost of a class of molecular dynamics simulations with constrained latent variables. The XLMD method relaxes the constraints by introducing a fictitious mass ε for the latent variables and solving a set of singularly perturbed ordinary differential equations. While favorable numerical performance of XLMD has been demonstrated in several different contexts in the past decade, mathematical analysis of the method remains scarce. Here, we propose the first error analysis of the XLMD method in the context of a classical polarizable force field model. While the dynamics with respect to the atomic degrees of freedom are general and nonlinear, the key mathematical simplification of the polarizable force field model is that the constraints on the latent variables are given by a linear system of equations. We prove that when the initial value of the latent variables is compatible in a sense that we define, XLMD converges as the fictitious mass ε is made small with $\mathscr{O}$(ε) error for the atomic degrees of freedom and with $\mathscr{O}$($\sqrt{ε}$) error for the latent variables, when the dimension of the latent variable d' is 1. Furthermore, when the initial value of the latent variables is improved to be optimally compatible in a certain sense, we prove that the convergence rate can be improved to $\mathscr{O}$(ε) for the latent variables as well. Numerical results verify that both estimates are sharp not only for d'=1, but also for arbitrary d'. In the setting of general d', we do obtain convergence, but with the non-sharp rate of $\mathscr{O}$($\sqrt{ε}$) for both the atomic and latent variables.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Liouville operators over the Hardy space

The role of Liouville operators in the study of dynamical systems through the use of occupation measures has been an active area of research in control theory over the past decade. This article investigates Liouville operators over the Hardy space, which encode complex ordinary differential equations in an operator over a reproducing kernel Hilbert space.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Combined selection of the dynamic model and modeling error in nonlinear aeroelastic systems using Bayesian Inference

Here, we report a Bayesian framework for concurrent selection of physics-based models and (modeling) error models. We investigate the use of colored noise to capture the mismatch between the predictions of calibrated models and observational data that cannot be explained by measurement error alone within the context of Bayesian estimation for stochastic ordinary differential equations. Proposed models are characterized by the average data-fit, a measure of how well a model fits the measurements, and the model complexity measured using the Kullback–Leibler divergence. The use of a more complex error models increases the average data-fit but also increases the complexity of the combined model, possibly over-fitting the data. Bayesian model selection is used to find the optimal physical model as well as the optimal error model. The optimal model is defined using the evidence, where the average data-fit is balanced by the complexity of the model. The effect of colored noise process is illustrated using a nonlinear aeroelastic oscillator representing a rigid NACA0012 airfoil undergoing limit cycle oscillations due to complex fluid–structure interactions. Several quasi-steady and unsteady aerodynamic models are proposed with colored noise or white noise for the model error. The use of colored noise improves the predictive capabilities of simpler models.

42 ENGINEERING↗
DOE OSTI2020

Time-series learning of latent-space dynamics for reduced-order model closure

In this work, we study the performance of long short-term memory networks (LSTMs) and neural ordinary differential equations (NODEs) in learning latent-space representations of dynamical equations for an advection-dominated problem given by the viscous Burgers equation. Our formulation is devised in a nonintrusive manner with an equation-free evolution of dynamics in a reduced space with the latter being obtained through a proper orthogonal decomposition. In addition, we leverage the sequential nature of learning for both LSTMs and NODEs to demonstrate their capability for closure in systems that are not completely resolved in the reduced space. We assess our hypothesis for two advection-dominated problems given by the viscous Burgers equation. We observe that both LSTMs and NODEs are able to reproduce the effects of the absent scales for our test cases more effectively than does intrusive dynamics evolution through a Galerkin projection. This result empirically suggests that time-series learning techniques implicitly leverage a memory kernel for coarse-grained system closure as is suggested through the Mori–Zwanzig formalism.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Building predictive signaling models by perturbing yeast cells with time-varying stimulations resulting in distinct signaling responses

This protocol provides a step-by-step approach to perturb single cells with time-varying stimulation profiles, collect distinct signaling responses, and use these to infer a system of ordinary differential equations to capture and predict dynamics of protein-protein regulation in signal transduction pathways. The models are validated by predicting the signaling activation upon new cell stimulation conditions. In comparison to using standard step-like stimulations, application of diverse time-varying cell stimulations results in better inference of model parameters and substantially improves model predictions. For complete details on the use and results of this protocol, please refer to Jashnsaz et al. (2020).

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

An extension of Thwaites’ method for turbulent boundary layers

Thwaites developed an approximate method for determining the evolution of laminar boundary layers. The approximation follows from an assumption that the growth of a laminar boundary layer in the presence of pressure gradients could be parameterized solely as a function of the Holstein–Bohlen flow parameter, thus reducing the von Kármán momentum integral to a first-order ordinary differential equation. This method is useful for the analysis of laminar flows, and in computational potential flow solvers to account for the viscous effects. In this work, an approximate method for determining the momentum thickness of a two-dimensional, turbulent boundary layer is proposed following Thwaites’ work. It is shown that the method provides good estimates of the momentum thickness for multiple boundary layers, including both favourable and adverse pressure gradient effects, up to the point of separation. In the limit of high Reynolds numbers, it is possible to derive a criterion for the onset of separation from the proposed model, which is shown to be in agreement with prior empirical observations. The sensitivity of the separation location with respect to upstream perturbations is also analysed through this model for the NASA/Boeing speed bump and the transonic Bachalo–Johnson bump.

17 WIND ENERGY↗
DOE OSTI2023

Near-wall model for compressible turbulent boundary layers based on an inverse velocity transformation

In this work, a near-wall model, which couples the inverse of a recently developed compressible velocity transformation (Griffin et al., Proc. Natl Acad. Sci., vol. 118, 2021, p. 34) and an algebraic temperature–velocity relation, is developed for high-speed turbulent boundary layers. As input, the model requires the mean flow state at one wall-normal height in the inner layer of the boundary layer and at the boundary-layer edge. As output, the model can predict mean temperature and velocity profiles across the entire inner layer, as well as the wall shear stress and heat flux. The model is tested in an a priori sense using a wide database of direct numerical simulation high-Mach-number turbulent channel flows, pipe flows and boundary layers (48 cases, with edge Mach numbers in the range 0.77–11, and semi-local friction Reynolds numbers in the range 170–5700). The present model is significantly more accurate than the classical ordinary differential equation (ODE) model for all cases tested. The model is deployed as a wall model for large-eddy simulations in channel flows with bulk Mach numbers in the range 0.7–4 and friction Reynolds numbers in the range 320–1800. When compared to the classical framework, in the a posteriori sense, the present method greatly improves the predicted heat flux, wall stress, and temperature and velocity profiles, especially in cases with strong heat transfer. In addition, the present model solves one ODE instead of two, and has a computational cost and implementation complexity similar to that of the commonly used ODE model.

42 ENGINEERING↗
DOE OSTI2023

Motion of a viscous slug on heterogeneous surfaces: crossover from stick–slip to steady sliding

We present a theoretical study of viscous slug motion inside a microscopically rough capillary tube, where pronounced stick–slip motion can emerge at slow displacement rates. The mathematical description of this intermittent motion can be reduced to a system of ordinary differential equations, which also describe the motion of a pendulum inside a fluid-filled rotating drum. We use this analogy to show that the stick–slip motion transitions to steady sliding at high displacement rates. We characterize this crossover with a simple scaling relation and show that the crossover is accompanied by a shift in the dominant energy dissipation mechanisms within the system.

Mechanics↗
DOE OSTI2024

Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNs

The molten sand that is a mixture of calcia, magnesia, alumina and silicate, known as CMAS, is characterized by its high viscosity, density and surface tension. The unique properties of CMAS make it a challenging material to deal with in high-temperature applications, requiring innovative solutions and materials to prevent its buildup and damage to critical equipment. Here, we use multiphase many-body dissipative particle dynamics simulations to study the wetting dynamics of highly viscous molten CMAS droplets. The simulations are performed in three dimensions, with varying initial droplet sizes and equilibrium contact angles. We propose a parametric ordinary differential equation (ODE) that captures the spreading radius behaviour of the CMAS droplets. The ODE parameters are then identified based on the physics-informed neural network (PINN) framework. Subsequently, the closed-form dependency of parameter values found by the PINN on the initial radii and contact angles are given using symbolic regression. Finally, we employ Bayesian PINNs (B-PINNs) to assess and quantify the uncertainty associated with the discovered parameters. In brief, this study provides insight into spreading dynamics of CMAS droplets by fusing simple parametric ODE modelling and state-of-the-art machine-learning techniques.

Mechanics↗
DOE OSTI2023

Theory of an Automatic Seepage Meter and Ramifications for Applications

A new approach for measuring fluxes across surface water—groundwater interfaces was recently proposed. The Automatic Seepage Meter (ASM) is equipped with a precise water level sensor and digital memory that analyzes water level time series in a vertical tube inserted into a streambed. The ability to infer flux values with high temporal resolution relies on an accurate interpretation of water level dynamics inside the tube. Here, we reduce the three-dimensional hydrodynamic problem that describes the ASM water level in a variety of field conditions to a single ordinary differential equation. This novel general analytical solution for estimating ASM responses is more comprehensive and flexible than previous approaches and is applicable to the entire range of field conditions, including steady or transient stream stages, evaporation, rainfall, and noise. For example, our analysis determines the timing of the nonmonotonic ASM response to a monotonic linear stream stage variation and explains previously used empirical parabolic approximation for estimating fluxes. We present algorithms for simultaneous inference of vertical interface flux and hydraulic conductivity values together with an example code. We quantify how the accuracy of parameter estimation depends on test duration and noise amplitude and propose how our analysis can be used to optimize field test protocols. On this basis, changing the ASM geometry by increasing the radius and decreasing tube insertion depth may enable ASM field test protocols that estimate interface flux and hydraulic conductivity faster while maintaining desired accuracy. Potential applications of joint parameter estimation are suggested.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Application of physiologically based pharmacokinetic modeling for sertraline dosing recommendations in pregnancy

Pregnancy is a period of significant change that impacts physiological and metabolic status leading to alterations in the disposition of drugs. Uncertainty in drug dosing in pregnancy can lead to suboptimal therapy, which can contribute to disease exacerbation. A few studies show there are increased dosing requirements for antidepressants in late pregnancy; however, the quantitative data to guide dose adjustments are sparse. We aimed to develop a physiologically based pharmacokinetic (PBPK) model that allows gestational-age dependent prediction of sertraline dosing in pregnancy. A minimal physiological model with defined gut, liver, plasma, and lumped placental-fetal compartments was constructed using the ordinary differential equation solver package, ‘mrgsolve’, in R. We extracted data from the literature to parameterize the model, including sertraline physicochemical properties, in vitro metabolism studies, disposition in nonpregnant women, and physiological changes during pregnancy. The model predicted the pharmacokinetic parameters from a clinical study with eight subjects for the second trimester and six subjects for the third trimester. Based on the model, gestational-dependent changes in physiology and metabolism account for increased clearance of sertraline (up to 143% at 40 weeks gestational age), potentially leading to under-dosing of pregnant women when nonpregnancy doses are used. The PBPK model was converted to a prototype web-based interactive dosing tool to demonstrate how the output of a PBPK model may translate into optimal sertraline dosing in pregnancy. Quantitative prediction of drug exposure using PBPK modeling in pregnancy will support clinically appropriate dosing and increase the therapeutic benefit for pregnant women.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2026

Energy-efficient scientific computing using chemical reservoirs

The rapid growth of computing demands driven by scientific computing, data analytics, and artificial intelligence (AI) advancements has exposed the limitations of traditional digital processing systems. These systems are nearing physical energy barriers, making significant gains in energy efficiency increasingly unattainable. As we advance toward post-exascale computing, disruptive approaches are critical to overcoming these limitations. Among emerging analog solutions, biochemical computing offers a transformative path for achieving orders-of-magnitude improvements in energy efficiency. By leveraging the natural optimization capabilities of chemical reaction networks (CRNs), biochemical systems have the potential to meet high-performance computing needs through natural scalability. However, numerous challenges remain, including theoretical limitations in mapping computational problems to CRNs and practical barriers in implementing biochemical computing devices. In this paper, we present a framework for chemical computation using biochemical systems and introduce key components of our approach for energy-efficient scientific computing. We showcase the feasibility of this framework by solving a system of ordinary differential equations by emulating a chemical reservoir device, demonstrating its potential for addressing modern computing challenges. This work lays a foundational step toward harnessing the computational power of chemistry to design energy-efficient, scalable, high-performance next-generation computing systems.

Johnson, Connah G. M. [Pacific Northwest National ↗
DOE OSTI2026

A mathematical framework for thermodynamic computing with applications to chemical reaction networks

The widespread adoption of energy-intensive computing applications has led to a growing need for energy-efficient computing approaches. Thermodynamic computing offers a promising approach for low-energy computation by leveraging the intrinsic computational capabilities of physical, chemical, or biological systems. However, the mathematical foundations of thermodynamic computing require further development to fully realize the potential energy efficiencies, as well as to assess factors like noise and operational speed. In this paper, we establish a mathematical framework for utilizing thermodynamic processes to perform fundamental operations, including addition, subtraction, multiplication, and division. We highlight the use of chemical reactions as potential computational units and explore synthetic chemical and biochemical systems as practical implementations. Additionally, we demonstrate how these principles can be applied to solving complex mathematical problems, such as ordinary differential equations (ODEs) and suggest the necessary components to implement the thermodynamic computing framework using chemical reactions based in a microfluidic device. This work enhances our understanding of thermodynamic processes for natural computing as a basis for scalable, energy-efficient computation in paradigm disruptive next-generation systems.

Cannon, William R. [Pacific Northwest National Lab↗
DOE OSTI2020

Global geodesic acoustic mode in an ideal magnetohydrodynamic tokamak plasma

A concise and transparent second order ordinary differential equation (ODE) describing the radial structure of the global geodesic acoustic mode (GAM) is analytically presented in a low-β tokamak plasma. The large-aspect-ratio and circular cross section are assumed to linearize the ideal magnetohydrodynamic equations. We show clearly how finite β-dependent terms affect the global GAM frequency and radial mode structure. Here, a typical Wentzel–Kramers–Brillouin form of solution is found for some reversed shear equilibria. For some other equilibria with lower β, even also in a reversed shear tokamak, the GAM continuum is upraised by the high order β-dependent terms so that its maximum is beyond ω G , where ω G is the classical local frequency of GAM. As a result, no self-consistent solution to the ODE can be found.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗