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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
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 OSTI2016

The arbitrary order mixed mimetic finite difference method for the diffusion equation

Here, we propose an arbitrary-order accurate mimetic finite difference (MFD) method for the approximation of diffusion problems in mixed form on unstructured polygonal and polyhedral meshes. As usual in the mimetic numerical technology, the method satisfies local consistency and stability conditions, which determines the accuracy and the well-posedness of the resulting approximation. The method also requires the definition of a high-order discrete divergence operator that is the discrete analog of the divergence operator and is acting on the degrees of freedom. The new family of mimetic methods is proved theoretically to be convergent and optimal error estimates for flux and scalar variable are derived from the convergence analysis. A numerical experiment confirms the high-order accuracy of the method in solving diffusion problems with variable diffusion tensor. It is worth mentioning that the approximation of the scalar variable presents a superconvergence effect.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

The nonconforming Virtual Element Method for eigenvalue problems

In this work, we analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allows to treat in the same formulation the two- and three-dimensional case. We present two possible formulations of the discrete problem, derived respectively by the nonstabilized and stabilized approximation of the $L^2$-inner product, and we study the convergence properties of the corresponding discrete eigenvalue problem. The proposed schemes provide a correct approximation of the spectrum, in particular we prove optimal-order error estimates for the eigenfunctions and the usual double order of convergence of the eigenvalues. Finally we show a large set of numerical tests supporting the theoretical results, including a comparison with the conforming Virtual Element choice.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Orthogonality preserving infinite dimensional quadratic stochastic operators

In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Stability of entrainment of a continuum of coupled oscillators

Complex natural and engineered systems are ubiquitous, and their behavior is challenging to characterize and control. Here, we examine the design of the entrainment process for an uncountably infinite collection of coupled phase oscillators that are all subject to the same periodic driving signal. In the absence of coupling, an appropriately designed input can result in each oscillator attaining the frequency of the driving signal, with a phase offset determined by its natural frequency. We also consider a special case of interacting oscillators in which the coupling tends to destabilize the phase configuration to which the driving signal would send the collection in the absence of coupling. In this setting, we derive stability results that characterize the trade-off between the effects of driving and coupling, and compare these results to the well-known Kuramoto model of a collection of free-running coupled oscillators.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Practical rare event sampling for extreme mesoscale weather

Extreme mesoscale weather, including tropical cyclones, squall lines, and floods, can be enormously damaging and yet challenging to simulate; hence, there is a pressing need for more efficient simulation strategies. Here, we present a new rare event sampling algorithm called quantile diffusion Monte Carlo (quantile DMC). Quantile DMC is a simple-to-use algorithm that can sample extreme tail behavior for a wide class of processes. We demonstrate the advantages of quantile DMC compared to other sampling methods and discuss practical aspects of implementing quantile DMC. To test the feasibility of quantile DMC for extreme mesoscale weather, we sample extremely intense realizations of two historical tropical cyclones, 2010 Hurricane Earl and 2015 Hurricane Joaquin. Our results demonstrate quantile DMC’s potential to provide low-variance extreme weather statistics while highlighting the work that is necessary for quantile DMC to attain greater efficiency in future applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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 OSTI2013

Reducing quasilinear systems to block triangular form

The paper is concerned with systems of n quasilinear partial differential equations of the first order with 2 independent variables. Using a geometric formalism for such equations, which goes back to Riemann, it is possible to assign a field of linear operators on an appropriate vector bundle to this type of quasilinear system. Several tests for a quasilinear system to be reducible to triangular or block triangular form are obtained in terms of this field; they supplement well known results on diagonalization and block diagonalization due to Haantjes and Bogoyavlenskij. Bibliography: 10 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Mechanical systems with closed orbits on manifolds of revolution

We study natural mechanical systems describing the motion of a particle on a two-dimensional Riemannian manifold of revolution in the field of a central smooth potential. We obtain a classification of Riemannian manifolds of revolution and central potentials on them that have the strong Bertrand property: any nonsingular (that is, not contained in a meridian) orbit is closed. We also obtain a classification of manifolds of revolution and central potentials on them that have the 'stable' Bertrand property: every parallel is an 'almost stable' circular orbit, and any nonsingular bounded orbit is closed. Bibliography: 14 titles.

97 MATHEMATICS AND COMPUTING↗