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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 73 records · Page 4
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DOE OSTI2024

On Properties of Adjoint Systems for Evolutionary PDEs

We investigate the geometric structure of adjoint systems associated with evolutionary partial differential equations at the fully continuous, semi-discrete, and fully discrete levels and the relations between these levels. We show that the adjoint system associated with an evolutionary partial differential equation has an infinite-dimensional Hamiltonian structure, which is useful for connecting the fully continuous, semi-discrete, and fully discrete levels. We subsequently address the question of discretize-then-optimize versus optimize-then-discrete for both semi-discretization and time integration, by characterizing the commutativity of discretize-then-optimize methods versus optimize-then-discretize methods uniquely in terms of an adjoint-variational quadratic conservation law. For Galerkin semi-discretizations and one-step time integration methods in particular, we explicitly construct these commuting methods by using structure-preserving discretization techniques.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A Type II Hamiltonian Variational Principle and Adjoint Systems for Lie Groups

We present a novel Type II variational principle on the cotangent bundle of a Lie group which enforces Type II boundary conditions, i.e., fixed initial position and final momentum. In general, such Type II variational principles are only globally defined on vector spaces or locally defined on general manifolds; however, by left translation, we are able to define this variational principle globally on cotangent bundles of Lie groups. Type II boundary conditions are particularly important for adjoint sensitivity analysis, which is our motivating application. As such, we additionally discuss adjoint systems on Lie groups, their properties, and how they can be used to solve optimization problems subject to dynamics on Lie groups.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Physics-based stabilized finite element approximations of the Poisson–Nernst–Planck equations

We present and analyze two stabilized finite element methods for solving numerically the Poisson–Nernst–Planck equations. The stabilization we consider is carried out by using a shock detector and a discrete graph Laplacian operator for the ion equations, whereas the discrete equation for the electric potential need not be stabilized. Discrete solutions stemmed from the first algorithm preserve both maximum and minimum discrete principles. For the second algorithm, its discrete solutions are conceived so that they hold discrete principles and obey an entropy law provided that an acuteness condition is imposed for meshes. Remarkably the latter is found to be unconditionally stable. We validate our methodology through transient numerical experiments that show convergence toward steady-state solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Improving the accuracy of discretisations of the vector transport equation on the lowest-order quadrilateral Raviart-Thomas finite elements

Within finite element models of fluids, vector-valued fields such as velocity or momentum variables are commonly discretised using the Raviart-Thomas elements. However, when using the lowest-order quadrilateral Raviart-Thomas elements, standard finite element discretisations of the vector transport equation typically have a low order of spatial accuracy. This paper describes two schemes that improve the accuracy of transporting such vector-valued fields on two-dimensional curved manifolds. The first scheme that is presented reconstructs the transported field in a higher-order function space, where the transport equation is then solved. The second scheme applies a mixed finite element formulation to the vector transport equation, simultaneously solving for the transported field and its vorticity. In this work, an approach to stabilising this mixed vector-vorticity formulation is presented that uses a Streamline Upwind Petrov-Galerkin (SUPG) method. These schemes are then demonstrated, along with their accuracy properties, through some numerical tests. Two new test cases are used to assess the transport of vector-valued fields on curved manifolds, solving the vector transport equation in isolation. The improvement of the schemes is also shown through two standard test cases for rotating shallow-water models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Structural conserved moiety splitting of a stoichiometric matrix

Characterising biochemical reaction network structure in mathematical terms enables the inference of functional biochemical consequences from network structure with existing mathematical techniques and spurs the development of new mathematics that exploits the peculiarities of biochemical network structure. The structure of a biochemical network may be specified by reaction stoichiometry, that is, the relative quantities of each molecule produced and consumed in each reaction of the network. A biochemical network may also be specified at a higher level of resolution in terms of the internal structure of each molecule and how molecular structures are transformed by each reaction in a network. The stoichiometry for a set of reactions can be compiled into a stoichiometric matrix N ϵ Z mxn where each row corresponds to a molecule and each column corresponds to a reaction. We demonstrate that a stoichiometric matrix may be split into the sum of m - rank(N) moiety transition matrices, each of which corresponds to a subnetwork accessible to a structurally identifiable conserved moiety. The existence of this moiety matrix splitting is a property that distinguishes a stoichiometric matrix from an arbitrary rectangular matrix.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Projective embedding of dynamical systems: Uniform mean field equations

Herein we study embeddings of continuous dynamical systems in larger dimensions via projector operators. We call this technique PEDS, projective embedding of dynamical systems, as the stable fixed point of the original system dynamics are recovered via projection from the higher dimensional space. In this paper we provide a general definition and prove that for a particular type of rank-1 projector operator, the uniform mean field projector, the equations of motion become a mean field approximation of the dynamical system. While in general the embedding depends on a specified variable ordering, the same is not true for the uniform mean field projector. We prove a variety of results on the relationship between the spectrum of the Jacobian for fixed points in the original and in the embedded system. Direct applications of PEDS can be non-convex optimization and machine learning.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Predicting stress response and improved protein overproduction in Bacillus subtilis

Abstract Bacillus subtilis is a well-characterized microorganism and a model for the study of Gram-positive bacteria. The bacterium can produce proteins at high densities and yields, which has made it valuable for industrial bioproduction. Like other cell factories, metabolic modeling of B. subtilis has discovered ways to optimize its metabolism toward various applications. The first genome-scale metabolic model (M-model) of B. subtilis was published more than a decade ago and has been applied extensively to understand metabolism, to predict growth phenotypes, and served as a template to reconstruct models for other Gram-positive bacteria. However, M-models are ill-suited to simulate the production and secretion of proteins as well as their proteomic response to stress. Thus, a new generation of metabolic models, known as metabolism and gene expression models (ME-models), has been initiated. Here, we describe the reconstruction and validation of a ME model of B. subtilis , i JT964-ME. This model achieved higher performance scores on the prediction of gene essentiality as compared to the M-model. We successfully validated the model by integrating physiological and omics data associated with gene expression responses to ethanol and salt stress. The model further identified the mechanism by which tryptophan synthesis is upregulated under ethanol stress. Further, we employed i JT964-ME to predict amylase production rates under two different growth conditions. We analyzed these flux distributions and identified key metabolic pathways that permitted the increase in amylase production. Models like i JT964-ME enable the study of proteomic response to stress and the illustrate the potential for optimizing protein production in bacteria.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Optimization of nutrient utilization efficiency and productivity for algal cultures under light and dark cycles using genome-scale model process control

Abstract Algal cultivations are strongly influenced by light and dark cycles. In this study, genome-scale metabolic models were applied to optimize nutrient supply during alternating light and dark cycles of Chlorella vulgaris . This approach lowered the glucose requirement by 75% and nitrate requirement by 23%, respectively, while maintaining high final biomass densities that were more than 80% of glucose-fed heterotrophic culture. Furthermore, by strictly controlling glucose feeding during the alternating cycles based on model-input, yields of biomass, lutein, and fatty acids per gram of glucose were more than threefold higher with cycling compared to heterotrophic cultivation. Next, the model was incorporated into open-loop and closed-loop control systems and compared with traditional fed-batch systems. Closed-loop systems which incorporated a feed-optimizing algorithm increased biomass yield on glucose more than twofold compared to standard fed-batch cultures for cycling cultures. Finally, the performance was compared to conventional proportional-integral-derivative (PID) controllers. Both simulation and experimental results exhibited superior performance for genome-scale model process control (GMPC) compared to traditional PID systems, reducing the overall measured value and setpoint error by 80% over 8 h. Overall, this approach provides researchers with the capability to enhance nutrient utilization and productivity of cell factories systematically by combining genome-scale models and controllers into an integrated platform with superior performance to conventional fed-batch and PID methodologies.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Leveraging public AI tools to explore systems biology resources in mathematical modeling

Predictive mathematical modeling is an essential part of systems biology and is interconnected with information management. Systems biology information is often stored in specialized formats to facilitate data storage and analysis. These formats are not designed for easy human readability and thus require specialized software to visualize and interpret results. Therefore, comprehending modeling and underlying networks and pathways is contingent on mastering systems biology tools, which is particularly challenging for users with no or little background in data science or system biology. To address this challenge, we investigated the usage of public Artificial Intelligence (AI) tools in exploring systems biology resources in mathematical modeling. We tested public AI’s understanding of mathematics in models, related systems biology data, and the complexity of model structures. Our approach can enhance the accessibility of systems biology for non-system biologists and help them understand systems biology without a deep learning curve.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Kibble-Zurek mechanism for nonequilibrium phase transitions in driven systems with quenched disorder

Abstract We show that the Kibble-Zurek mechanism applies to nonequilibrium phase transitions found in driven assemblies of superconducting vortices and colloids moving over quenched disorder where a transition occurs from a plastic disordered flowing state to a moving anisotropic crystal. We measure the density of topological defects as a function of quench rate through the nonequilibrium phase transition, and find that on the ordered side of the transition, the topological defect density ρ d scales as a power law, $${\rho }_{{{{{{{{\rm{d}}}}}}}}}\propto 1/{t}_{{{{{{{{\rm{q}}}}}}}}}^{\beta }$$ ρ d ∝ 1 / t q β , where t q is the quench time duration, consistent with the Kibble-Zurek mechanism. We show that scaling with the same exponent holds for varied strengths of quenched disorder and that the exponents fall in the directed percolation universality class. Our results suggest that the Kibble-Zurek mechanism can be applied to the broader class of systems that exhibit absorbing phase transitions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks

We employ and adapt the image-to-image translation concept based on conditional generative adversarial networks (cGAN) for learning a forward and an inverse solution operator of partial differential equations (PDEs). We focus on steady-state solutions of coupled hydromechanical processes in heterogeneous porous media and present the parameterization of the spatially heterogeneous coefficients, which is exceedingly difficult using standard reduced-order modeling techniques. We show that our framework provides a speed-up of at least 2,000 times compared to a finite-element solver and achieves a relative root-mean-square error (r.m.s.e.) of less than 2% for forward modeling. For inverse modeling, the framework estimates the heterogeneous coefficients, given an input of pressure and/or displacement fields, with a relative r.m.s.e. of less than 7%, even for cases where the input data are incomplete and contaminated by noise. The framework also provides a speed-up of 120,000 times compared to a Gaussian prior-based inverse modeling approach while also delivering more accurate results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Dynamical commensuration effect in a two-dimensional Yukawa solid modulated by periodic substrates

Transverse depinning dynamics of a periodic-square-substrate modulated two-dimensional dusty plasma solid driven by a constant force in the longitudinal direction are investigated using Langevin dynamical simulations. When the commensuration ratio (the number ratio of particles to substrate potential wells) is increased, there is a nonmonotonic variation of the critical transverse depinning force, and the local maxima and minima of the critical transverse depinning force precisely correspond to the dynamical commensurate and incommensurate conditions, respectively. Here, the dynamical commensuration effect is also clearly visible in the stable one-dimensional channel particle trajectories and the highly ordered structure, while both the particle trajectories and the structure are more disordered under the incommensurate conditions. The nonmonotonic variation of the critical transverse depinning force is attributed to the stability of the lattice structure at specific commensuration ratios.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Where did the tumor start? An inverse solver with sparse localization for tumor growth models

In this work, we present a numerical scheme for solving an inverse problem for parameter estimation in tumor growth models for glioblastomas, a form of aggressive primary brain tumor. The growth model is a reaction–diffusion partial differential equation (PDE) for the tumor concentration. We use a PDE-constrained optimization formulation for the inverse problem. The unknown parameters are the reaction coefficient (proliferation), the diffusion coefficient (infiltration), and the initial condition field for the tumor PDE. Segmentation of magnetic resonance imaging (MRI) scans drive the inverse problem where segmented tumor regions serve as partial observations of the tumor concentration. Like most cases in clinical practice, we use data from a single time snapshot. Moreover, the precise time relative to the initiation of the tumor is unknown, which poses an additional difficulty for inversion. We perform a frozen-coefficient spectral analysis and show that the inverse problem is severely ill-posed. We introduce a biophysically motivated regularization on the structure and magnitude of the tumor initial condition. In particular, we assume that the tumor starts at a few locations (enforced with a sparsity constraint on the initial condition of the tumor) and that the initial condition magnitude in the maximum norm is equal to one. We solve the resulting optimization problem using an inexact quasi-Newton method combined with a compressive sampling algorithm for the sparsity constraint. Our implementation uses PETSc and AccFFT libraries. We conduct numerical experiments on synthetic and clinical images to highlight the improved performance of our solver over a previously existing solver that uses standard two-norm regularization for the calibration parameters. The existing solver is unable to localize the initial condition. Our new solver can localize the initial condition and recover infiltration and proliferation. In clinical datasets (for which the ground truth is unknown), our solver results in qualitatively different solutions compared to the two-norm regularized solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Wide class of logarithmic potentials with power-tower kink tails

We present a wide class of potentials which admit kinks and corresponding mirror kinks with either a power law or an exponential tail at the two extreme ends and a power-tower form of tails at the two neighbouring ends. We analyse kink stability equation in all these cases and show that there is no gap between the zero mode and the beginning of the continuum. Finally, we provide a recipe for obtaining logarithmic potentials with power-tower kink tails and estimate kink–kink interaction strength.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Behavior of solitary waves of coupled nonlinear Schrödinger equations subjected to complex external periodic potentials with odd-$\mathcal{PT}$ symmetry

In this work, we discuss the response of both moving and trapped solitary wave solutions of a two-component nonlinear Schrödinger system in 1 + 1 dimensions to an odd-$\mathcal{PT}$ external periodic complex potential. The dynamical behavior of perturbed solitary waves is explored by conducting numerical simulations of the nonlinear system and using a collective coordinate variational approximation. We present case examples corresponding to choices of parameter values and initial conditions involved therein. The results of the collective coordinate approximation are compared against numerical simulations where we observe qualitatively good agreement between the two. Unlike the case for a single-component solitary wave in a complex periodic $\mathcal{PT}$-symmetric potential, the collective coordinate equations do not have a small oscillation regime, and initially the height of the two components changes in opposite directions often causing instability. We find that the dynamic stability criteria we have used in the one-component case are a good indicator for the onset of dynamic instabilities in the present setup.

97 MATHEMATICS AND COMPUTING↗