Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Numerical differentiation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

A mathematical model of asynchronous data flow in parallel computers *

Abstract We present a simplified model of data flow on processors in a high-performance computing framework involving computations necessitating inter-processor communications. From this ordinary differential model, we take its asymptotic limit, resulting in a model which treats the computer as a continuum of processors and data flow as an Eulerian fluid governed by a conservation law. We derive a Hamilton–Jacobi equation associated with this conservation law for which the existence and uniqueness of solutions can be proven. We then present the results of numerical experiments for both discrete and continuum models; these show a qualitative agreement between the two and the effect of variations in the computing environment’s processing capabilities on the progress of the modelled computation.

Barnard, Richard C.↗
DOE OSTI2024

Proteogenomic characterization of difficult-to-treat breast cancer with tumor cells enriched through laser microdissection

Abstract Background Breast cancer (BC) is the most commonly diagnosed cancer and the leading cause of cancer death among women globally. Despite advances, there is considerable variation in clinical outcomes for patients with non-luminal A tumors, classified as difficult-to-treat breast cancers (DTBC). This study aims to delineate the proteogenomic landscape of DTBC tumors compared to luminal A (LumA) tumors. Methods We retrospectively collected a total of 117 untreated primary breast tumor specimens, focusing on DTBC subtypes. Breast tumors were processed by laser microdissection (LMD) to enrich tumor cells. DNA, RNA, and protein were simultaneously extracted from each tumor preparation, followed by whole genome sequencing, paired-end RNA sequencing, global proteomics and phosphoproteomics. Differential feature analysis, pathway analysis and survival analysis were performed to better understand DTBC and investigate biomarkers. Results We observed distinct variations in gene mutations, structural variations, and chromosomal alterations between DTBC and LumA breast tumors. DTBC tumors predominantly had more mutations inTP53,PLXNB3, Zinc finger genes, and fewer mutations inSDC2,CDH1,PIK3CA,SVIL, andPTEN. Notably, Cytoband 1q21, which contains numerous cell proliferation-related genes, was significantly amplified in the DTBC tumors. LMD successfully minimized stromal components and increased RNA–protein concordance, as evidenced by stromal score comparisons and proteomic analysis. Distinct DTBC and LumA-enriched clusters were observed by proteomic and phosphoproteomic clustering analysis, some with survival differences. Phosphoproteomics identified two distinct phosphoproteomic profiles for high relapse-risk and low relapse-risk basal-like tumors, involving several genes known to be associated with breast cancer oncogenesis and progression, includingKIAA1522,DCK,FOXO3,MYO9B,ARID1A,EPRS,ZC3HAV1, andRBM14. Lastly, an integrated pathway analysis of multi-omics data highlighted a robust enrichment of proliferation pathways in DTBC tumors. Conclusions This study provides an integrated proteogenomic characterization of DTBC vs LumA with tumor cells enriched through laser microdissection. We identified many common features of DTBC tumors and the phosphopeptides that could serve as potential biomarkers for high/low relapse-risk basal-like BC and possibly guide treatment selections.

Oncology↗
DOE OSTI2023

Higher-Order Corrections to Optimisers based on Newton's Method

The Newton, Gauss–Newton and Levenberg–Marquardt methods all use the first derivative of a vector function (the Jacobian) to minimise its sum of squares. When the Jacobian matrix is ill-conditioned, the function varies much faster in some directions than others and the space of possible improvement in sum of squares becomes a long narrow ellipsoid in the linear model. This means that even a small amount of nonlinearity in the problem parameters can cause a proposed point far down the long axis of the ellipsoid to fall outside of the actual curved valley of improved values, even though it is quite nearby. This paper presents a differential equation that ‘follows’ these valleys, based on the technique of geodesic acceleration, which itself provides a 2 nd order improvement to the Levenberg–Marquardt iteration step. Higher derivatives of this equation are computed that allow n th order improvements to the optimisation methods to be derived. These higher-order accelerated methods up to 4 th order are tested numerically and shown to provide substantial reduction of both number of steps and computation time.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

Numerical assessment of triply periodic minimal surfaces for direct air capture of carbon dioxide

Direct air capture (DAC) systems often consist of packing material wetted by a capture fluid that reacts with CO 2 in the airstream. The efficiency of the contactor is determined by a complex relationship of fluid dynamics, heat and mass transfer, contactor geometry, and chemical properties. The efficiency of the contactor must be balanced with other factors, primarily pressure drop through the system. Triply periodic minimal surfaces (TPMS) are a class of differential surfaces that have been explored in multiple engineering applications and have been shown to exhibit excellent performance when used in heat exchangers. Their tortuous path provides a high surface-to-volume ratio and favorable trade-off between contact area and pressure drop. In this work, a gyroid-type TPMS contactor was evaluated using computational fluid dynamics for a variety of geometric parameters to explore the potential benefit of TPMS shapes for DAC applications. A thin-film model was employed to model the flow and distribution of the capture solvent, allowing efficient simulations of TPMS structures at scale by eliminating the need for a computationally intensive interface capturing method. A liquid-gas mass transfer model was implemented in the commercial software STAR-CCM+ and used to predict the CO 2 capture efficiency and study the trade-off between capture performance and pressure drop through analysis of capture rates, mass transfer coefficients, and other relevant variables. TPMS contactors with a variety of geometric parameters and two capture solvent options were investigated to determine the effect of design choices on the operational performance of DAC systems. In conclusion, results showed that while contactor geometry is the dominant factor in efficiency and pressure drop, the physiochemical properties of the solvent are an important secondary influence on the contactor performance.

CFD↗
DOE OSTI2025

Convex relaxation for Fokker–Planck equation

We propose an approach to directly estimate the moments or marginals for a high-dimensional equilibrium distribution in statistical mechanics by solving the high-dimensional Fokker–Planck equation in terms of low-order cluster moments or marginals. With this approach, we bypass the exponential complexity of estimating the full high-dimensional distribution and directly solve the simplified partial differential equations for low-order moments/marginals. Moreover, the proposed moment/marginal relaxation is fully convex and can be solved via off-the-shelf solvers. We further propose a time-dependent version of the convex programs to study non-equilibrium dynamics. In a specific setting, we show the proposed method can recover a mean-field-type equilibrium density. Numerical results are provided to demonstrate the performance of the proposed algorithm for high-dimensional systems.

Chen, Yian↗
DOE OSTI2020

Affine Approximation of Parametrized Kernels and Model Order Reduction for Nonlocal and Fractional Laplace Models

In this work, we consider parametrized problems driven by spatially nonlocal integral operators with parameter-dependent kernels. In particular, kernels with varying nonlocal interaction radius $\delta > 0$ and fractional Laplace kernels, parametrized by the fractional power $s\in(0,1)$, are studied. Furthermore, in order to provide an efficient and reliable approximation of the solution for different values of the parameters, we develop the reduced basis method as a parametric model order reduction approach. Major difficulties arise since the kernels are not affine in the parameters, singular, and discontinuous. Moreover, the spatial regularity of the solutions depends on the varying fractional power $s$. To address this, we derive regularity and differentiability results with respect to $\delta$ and $s$, which are of independent interest for other applications such as optimization and parameter identification. We then use these results to construct affine approximations of the kernels by local polynomials. Finally, we certify the method by providing reliable a posteriori error estimators, which account for all approximation errors, and support the theoretical findings by numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Fluidization of Group A Glass Particles: Experiments and Preliminary Validation

This work is aimed at providing reliable high-quality data from fluidization experiments. Geldart Group A glass beads are used as bed material. The fluidizing medium is air at atmospheric pressure which enters the system at 40% relative humidity. The air inlet velocity is varied over a broad range from 2 U mf to 26 U mf , where the minimum fluidization velocity, U mf , is 0.608 cm/s. There is not a significant change in the mean values of differential pressure; however, there are noticeable trends in their standard deviation values. Preliminary validation studies are performed using the open-source software Multiphase Flow with Interphase eXchanges (MFiX) developed by the National Energy Technology Laboratory (NETL). The results from Eulerian-Eulerian (MFiX-TFM, two-fluid model) and Eulerian-Lagrangian (MFiX-PIC, particle-in-cell) formulations are compared. The work presented in this report highlights the applicability of MFiX-PIC for large-scale applications, and reveals that PIC simulation offers a suitable alternative to TFM simulation when effects due to multiple components or polydispersity are significant. PIC modeling provides a readily extendible framework for such systems. However, PIC models do rely on an empirical closure for inter-particle stress. Some solution discrepancies were evident in MFiX-PIC predictions which require further analysis. As such, the study underlines the need for a systematic approach to quantify the sources of numerical uncertainty within the PIC model. However, even with known empiricism, MFiX-PIC has demonstrated considerable potential in analyzing gas-solid systems. The results obtained are encouraging and warrant further investigation to improve the predictive capability of MFiX-PIC.

36 MATERIALS SCIENCE↗
DOE OSTI2023

A unified hp-HDG framework for Friedrichs' PDE systems

Here, this work proposes a unified hp-adaptivity framework for hybridized discontinuous Galerkin (HDG) method for a large class of partial differential equations (PDEs) of Friedrichs' type. In particular, we present unified hp-HDG formulations for abstract one-field and two-field structures and prove their well-posedness. In order to handle non-conforming interfaces we simply take advantage of HDG built-in mortar structures. With split-type mortars and the approximation space of trace, a numerical flux can be derived via Godunov approach and be naturally employed without any additional treatment. As a consequence, the proposed formulations are parameter-free. We perform several numerical experiments for time-independent and linear PDEs including elliptic, hyperbolic, and mixed-type to verify the proposed unified hp-formulations and demonstrate the effectiveness of hp-adaptation. Two adaptivity criteria are considered: one is based on a simple and fast error indicator, while the other is rigorous but more expensive using an adjoint-based error estimate. The numerical results show that these two approaches are comparable in terms of convergence rate even for problems with strong gradients, discontinuities, and singularities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Taylor–Couette flow for astrophysical purposes

A concise review is given of astrophysically motivated experimental and theoretical research on Taylor–Couette flow. The flows of interest rotate differentially with the inner cylinder faster than the outer, but are linearly stable against Rayleigh’s inviscid centrifugal instability. At shear Reynolds numbers as large as 10 6 , hydrodynamic flows of this type (quasi-Keplerian) appear to be nonlinearly stable: no turbulence is seen that cannot be attributed to interaction with the axial boundaries, rather than the radial shear itself. Direct numerical simulations agree, although they cannot yet reach such high Reynolds numbers. This result indicates that accretion-disc turbulence is not purely hydrodynamic in origin, at least insofar as it is driven by radial shear. Theory, however, predicts linear magnetohydrodynamic (MHD) instabilities in astrophysical discs: in particular, the standard magnetorotational instability (SMRI). MHD Taylor–Couette experiments aimed at SMRI are challenged by the low magnetic Prandtl numbers of liquid metals. High fluid Reynolds numbers and careful control of the axial boundaries are required. The quest for laboratory SMRI has been rewarded with the discovery of some interesting inductionless cousins of SMRI, and with the recently reported success in demonstrating SMRI itself using conducting axial boundaries. Some outstanding questions and near-future prospects are discussed, especially in connection with astrophysics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems

In this work, we present Lift & Learn, a physics-informed method for learning low-dimensional models for large-scale dynamical systems. The method exploits knowledge of a system’s governing equations to identify a coordinate transformation in which the system dynamics have quadratic structure. This transformation is called a lifting map because it often adds auxiliary variables to the system state. The lifting map is applied to data obtained by evaluating a model for the original nonlinear system. This lifted data is projected onto its leading principal components, and low-dimensional linear and quadratic matrix operators are fit to the lifted reduced data using a least-squares operator inference procedure. Analysis of our method shows that the Lift & Learn models are able to capture the system physics in the lifted coordinates at least as accurately as traditional intrusive model reduction approaches. This preservation of system physics makes the Lift & Learn models robust to changes in inputs. Numerical experiments on the FitzHugh–Nagumo neuron activation model and the compressible Euler equations demonstrate the generalizability of our model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Differentiable stochastic halo occupation distribution

ABSTRACT In this work, we demonstrate how differentiable stochastic sampling techniques developed in the context of deep reinforcement learning can be used to perform efficient parameter inference over stochastic, simulation-based, forward models. As a particular example, we focus on the problem of estimating parameters of halo occupation distribution (HOD) models that are used to connect galaxies with their dark matter haloes. Using a combination of continuous relaxation and gradient re-parametrization techniques, we can obtain well-defined gradients with respect to HOD parameters through discrete galaxy catalogue realizations. Having access to these gradients allows us to leverage efficient sampling schemes, such as Hamiltonian Monte Carlo, and greatly speed up parameter inference. We demonstrate our technique on a mock galaxy catalogue generated from the Bolshoi simulation using a standard HOD model and find near-identical posteriors as standard Markov chain Monte Carlo techniques with an increase of ∼8× in convergence efficiency. Our differentiable HOD model also has broad applications in full forward model approaches to cosmic structure and cosmological analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Local adaptation of both plant and pathogen: an arms‐race compromise in switchgrass rust

In coevolving species, parasites locally adapt to host populations as hosts locally adapt to resist parasites. Parasites often outpace host local adaptation since they have rapid life cycles, but host diversity, the strength of selection, and external environmental influence can result in complex outcomes. To better understand local adaptation in host–parasite systems, we examined locally adapted switchgrass (Panicum virgatum), and its leaf rust pathogen (Puccinia novopanici) across a latitudinal range in North America. We grew switchgrass genotypes in 10 replicated multiyear common gardens, measuring rust severity from natural infection in a ‘host reciprocal transplant’ framework for testing local adaptation. We conducted genome-wide association mapping to identify genetic loci associated with rust severity. Genetically differentiated rust populations were locally adapted to northern and southern switchgrass, despite host local adaptation to environmental conditions in the same regions. Rust resistance was polygenic, and distinct loci were associated with rust severity in the north and south. We narrowed a previously identified large-effect quantitative trait locus for rust severity to a candidate YELLOW STRIPE-LIKE gene and linked numerous other loci to defense-related genes. Overall, our results suggest that both hosts and parasites can be simultaneously locally adapted, especially when parasites impose less selection than other environmental factors.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Marmot V2

MARMOT is a robust numerical tool for mesoscale modeling of fuel performance developed under the NEAMS Fuels technical area to predict the coevolution of microstructure and properties in fuel and cladding materials. MARMOT accomplishes this using the phase field method coupled with finite strain mechanics and heat conduction. MARMOT is based on the open source Multiphysics Object-Oriented Simulation Environment (MOOSE) and solves the coupled partial differential equations defining the physics using the finite element method. MARMOT is being developed in order to facilitate the development of improved materials models for fuel performance, but it is also being developed as a powerful tool in and of itself for the simulation of mesoscale fuel performance.

Aagesen, LarryK.↗
DOE OSTI2021

Implicit-Explicit Multirate Infinitesimal GARK Methods

This work focuses on the development of a new class of high-order accurate methods for multirate time integration of systems of ordinary differential equations. Unlike other recent work in this area, the proposed methods support mixed implicit-explicit (IMEX) treatment of the slow time scale. In addition to allowing this slow time scale flexibility, the proposed methods utilize a so-called infinitesimal formulation for the fast time scale through definition of a sequence of modified “fast" initial-value problems that may be solved using any viable algorithm. We name the proposed class as implicit-explicit multirate infinitesimal generalized-structure additive Runge--Kutta (IMEX-MRI-GARK) methods. In addition to defining these methods, we prove that they may be viewed as specific instances of GARK methods and derive a set of order conditions on the IMEX-MRI-GARK coefficients to guarantee both third and fourth order accuracy for the overall multirate method. Additionally, we provide three specific IMEX-MRI-GARK methods, two of order three and one of order four. We conclude with numerical simulations on two multirate test problems, demonstrating the methods' predicted convergence rates and comparing their efficiency against both legacy IMEX multirate schemes and recent third and fourth order implicit MRI-GARK methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A domain decomposition preconditioning for an inverse volume scattering problem

In this work, we propose domain decomposition preconditioners for the solution of an integral equation formulation of the acoustic forward and inverse scattering problems. We study both forward and inverse volume problems and propose preconditioning techniques to accelerate the iterative solvers. For the forward scattering problem, we extend the domain decomposition based preconditioning techniques presented for partial differential equations in Cai and Sarkis (1999 SIAM J. Sci. Comput. 21 792–797), to integral equations. We combine this domain decomposition preconditioner with a low-rank correction, which is easy to construct, forming a new preconditioner. For the inverse scattering problem, we use the forward problem preconditioner as a building block for constructing a preconditioner for the Gauss–Newton Hessian. We present numerical results that demonstrate the performance of both preconditioning strategies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Ultra-Wideband Microwave Imaging System for Root Phenotyping

The roots are a vital organ for plant growth and health. The opaque surrounding environment of the roots and the complicated growth process means that in situ and non-destructive root phenotyping face great challenges, which thus spur great research interests. The existing methods for root phenotyping are either unable to provide high-precision and high accuracy in situ detection, or they change the surrounding root environment and are destructive to root growth and health. Thus,we propose and develop an ultra-wideband microwave scanning method that uses time reversal to achieve in situ root phenotyping nondestructively. To verify the method’s feasibility, we studied an electromagnetic numerical model that simulates the transmission signal of two ultra-wideband microwave antennas. The simulated signal of roots with different shapes shows the proposed system’s capability to measure the root size in the soil. Experimental validations were conducted considering three sets of measurements with different sizes, numbers and locations, and the experimental results indicate that the developed imaging system was able to differentiate root sizes and numbers with high contrast. The reconstruction from both simulations and experimental measurements provided accurate size estimation of the carrots in the soil, which indicates the system’s potential for root imaging.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

An analytic approach to quasinormal modes for coupled linear systems

Quasinormal modes describe the ringdown of compact objects deformed by small perturbations. In generic theories of gravity that extend General Relativity, the linearized dynamics of these perturbations is described by a system of coupled linear differential equations of second order. We first show, under general assumptions, that such a system can be brought to a Schrödinger-like form. We then devise an analytic approximation scheme to compute the spectrum of quasinormal modes. We validate our approach using a toy model with a controllable mixing parameter ε and showing that the analytic approximation for the fundamental mode agrees with the numerical computation when the approximation is justified. The accuracy of the analytic approximation is at the (sub-) percent level for the real part and at the level of a few percent for the imaginary part, even when ε is of order one. Our approximation scheme can be seen as an extension of the approach of Schutz and Will [1] to the case of coupled systems of equations, although our approach is not phrased in terms of a WKB analysis, and offers a new viewpoint even in the case of a single equation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Magnetic droplet soliton pairs

We demonstrate magnetic droplet soliton pairs in all-perpendicular spin-torque nano-oscillators (STNOs), where one droplet resides in the STNO free layer (FL) and the other in the reference layer (RL). Typically, theoretical, numerical, and experimental droplet studies have focused on the FL, with any additional dynamics in the RL entirely ignored. Here we show that there is not only significant magnetodynamics in the RL, but the RL itself can host a droplet driven by, and coexisting with, the FL droplet. Both single droplets and pairs are observed experimentally as stepwise changes and sharp peaks in the dc and differential resistance, respectively. While the single FL droplet is highly stable, the coexistence state exhibits high-power broadband microwave noise. Furthermore, micromagnetic simulations reveal that the pair dynamics display periodic, quasi-periodic, and chaotic signatures controlled by applied field and current. The strongly interacting and closely spaced droplet pair offers a unique platform for fundamental studies of highly non-linear soliton pair dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗