Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “mathematics computing”

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 1,531 records · Page 85
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Memcomputing the Spectrum of Correlated Quantum Systems

The goals and objectives of the grant DE‐SC0020892 were to apply a new computing paradigm, MemComputing, to efficiently simulate properties of correlated quantum systems. The method has been applied to a wide set of problems ranging from quantum state tomography to finding the ground state of correlated systems. In all cases, substantial advantages compared to state-of-the-art approaches have been obtained. The project has also led to the suggestion of the transformer architecture (used nowadays in large-language models) as an efficient quantum state representation, and a better understanding of the role of memory in the generation of long-range order in neural networks. This grant has supported the work of a PhD student, inspired a new class on unconventional computing taught at the University of California, San Diego and has generated several peer-reviewed papers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Gravitational Contact Interactions -- Does the Jordan Frame Exist?

Scalar--tensor theories, with Einstein Hilbert and non-minimal interactions, $\sim M^2R/2 -\alpha\phi^2R/12 $, have graviton exchange induced contact interactions. These always pull the theory back into a formal Einstein frame in which $\alpha$ does not exist. In the Einstein frame, contact terms are induced, that are then absorbed back into other couplings to define the effective potential (or equivalently, the renormalization group). We show how these effects manifest themselves in a simple model by computing the effective potential in both frames displaying the discrepancy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

A machine-learning framework for the simulation of nuclear deflection of Planet-Killer-Asteroids

Here, as detection capabilities in astronomy have dramatically improved over the last two decades, concerns over Planet-Killer-Asteroids (PKAs) have become widespread, with nuclear weapons being proposed to destroy or deflect asteroids that are on a short-term projected collision course with Earth. Two main mitigation strategies have been proposed: • Case 1: Break up an incoming asteroid into smaller pieces that will disperse widely, resulting in smaller-scale, less detrimental, Earth-impacts or • Case 2: Deflect an incoming asteroid trajectory to avoid collision altogether. While the two strategies are not mutually exclusive, deflection is a safer strategy, ideally by harnessing all of the released energy from a nuclear device to move the asteroid as a rigid body. However, this case may not be always possible, since the strength of the energy release may break up the asteroid. In this work, the dynamical response of a PKA to a series of ultra-high energy impulses, such as those generated by nuclear devices, is formulated. A rapid iterative Discrete Element Method (DEM) method is developed to describe the deflection and potential breakup of the PKA as a function of a material bonding strength parameter within the asteroid and the magnitude of the applied impulse. The use of DEM allows for fragmentation of the PKA and the ability to compute the trajectories and distribution of the resulting debris field. Finally, a machine-learning algorithm is then developed and combined with the DEM approach to optimize the pulsation strategy for maximum possible safety and success.

42 ENGINEERING↗
DOE OSTI2021

Stiff neural ordinary differential equations

Neural Ordinary Differential Equations (ODEs) are a promising approach to learn dynamical models from time-series data in science and engineering applications. This work aims at learning neural ODEs for stiff systems, which are usually raised from chemical kinetic modeling in chemical and biological systems. We first show the challenges of learning neural ODEs in the classical stiff ODE systems of Robertson’s problem and propose techniques to mitigate the challenges associated with scale separations in stiff systems. We then present successful demonstrations in stiff systems of Robertson’s problem and an air pollution problem. The demonstrations show that the usage of deep networks with rectified activations, proper scaling of the network outputs as well as loss functions, and stabilized gradient calculations are the key techniques enabling the learning of stiff neural ODEs. The success of learning stiff neural ODEs opens up possibilities of using neural ODEs in applications with widely varying time-scales, such as chemical dynamics in energy conversion, environmental engineering, and life sciences.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Brochure on the 2024 ASCR Workshop on Analog Computing for Science

Analog computing fundamentally differs from digital by representing data with fully continuous physical quantities, such as voltages, probabilities, chemical concentrations, or light intensities, rather than encoding values in discrete binary states. While digital computing has historically excelled in precision, scalability, and noise resistance, newer analog approaches are gaining interest for their potential to dramatically improve energy efficiency and processing speed. Analog systems can inherently solve mathematical problems through their physical behavior and offer distinct advantages in scenarios where continuous operations are more effective than Boolean logic.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Celeritas Midterm SciDAC Report

Celeritas is a new Monte Carlo (MC) code that helps satisfy the increasing demand for high energy physics (HEP) detector simulation, using Graphics Processing Unit (GPU) hardware on high performance computing (HPC) systems to model Large Hadron Collider (LHC) experiments and beyond. This report details the project’s progress midway through its SciDAC funding period, highlighting the first complete implementation of standard electromagnetic (EM) physics on GPUs, initial results for performance and scalability on Leadership Computing Facilities (LCFs), and preliminary integration into the CMS and ATLAS experiments. By integrating HEP domain knowledge with expertise in MC transport, Celeritas has catalyzed a shift in the HEP community’s perception of GPU platforms as the future for HPC simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

CONNECT Neutronics Initial Report

This report represents the first status update from the Creation of Next-generation Nuclear Energy Computational Technology (CONNECT) effort within the Nuclear Energy Advanced Modeling and Simulation (NEAMS) Program and is intended to satisfy the reporting requirements of the following milestones: • M3MS-24OR0101321: Assess needs, requirements and opportunities for high-fidelity neutronics and transport as used in DOE-NE program. • M3MS-24AN0101301: Generate a community report on the needs, requirements, and opportunities for high-fidelity neutronics and transport as used in DOE-NE programs and industry. • M3MS-24OR0202433: Implement and assess numerical strategies leveraging Monte Carlo neutron transport on GPUs for production analysis. In particular, Sections 1, 2, and 3 detail the assessment of the current state of practice and the landscape of the broader advanced computing world to meet the objectives of M3MS-24OR0101321 and M3MS-24AN0101301, while Sections 4 and 5 describe new work during FY24 to extend current GPU Monte Carlo capabilities in areas relevant to active NEAMS development to satisfy M3MS-24OR0202433. Section 6 offers some thoughts about the potential future impact of Monte Carlo neutronics on NEAMS and the nuclear industry.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Nuclear-Renewable-Storage Systems: Enhancing Planning and Operations of Integrated Energy Systems

Nuclear-renewable-storage integrated energy systems (IES) are multi-carrier energy systems that include not only electricity but also other forms of demands. Because individual IES components must observe their thermo-physical limits, including ramp rates, start-up, and shut-down time, we formulate operations of the IES as an optimization model by minimizing the total operations costs subject to physical limits of all constituent components. In addition, we develop a data-driven approach to improve the computational performance of the economic dispatch model by using reinforcement learning, where an agent is rewarded by meeting demands and penalized otherwise when shifting to the next state.

25 ENERGY STORAGE↗
NASA NTRS1996

Finding New Math Identities by Computer

Recently a number of interesting new mathematical identities have been discovered by means of numerical searches on high performance computers, using some newly discovered algorithms. These include the following: pi = ((sup oo)(sub k=0))(Sigma) (1 / 16) (sup k) ((4 / 8k+1) - (2 / 8k+4) - (1 / 8k+5) - (1 / 8k+6)) and ((17 pi(exp 4)) / 360) = ((sup oo)(sub k=1))(Sigma) (1 + (1/2) + (1/3) + ... + (1/k))(exp 2) k(exp -2), zeta(3, 1, 3, 1, ..., 3, 1) = (2 pi(exp 4m) / (4m+2)! where m = number of (3,1) pairs. and where zeta(n1,n2,...,nr) = (sub k1 (is greater than) k2 (is greater than) ... (is greater than) kr)(Sigma) (1 / (k1 (sup n1) k2 (sup n2) ... kr (sup nr). The first identity is remarkable in that it permits one to compute the n-th binary or hexadecimal digit of pu directly, without computing any of the previous digits, and without using multiple precision arithmetic. Recently the ten billionth hexadecimal digit of pi was computed using this formula. The third identity has connections to quantum field theory. (The first and second of these been formally established; the third is affirmed by numerical evidence only.) The background and results of this work will be described, including an overview of the algorithms and computer techniques used in these studies.

Bailey, David H.↗
DOE OSTI2021

A Poisson equation method for prescribing fully developed non-Newtonian inlet conditions for computational fluid dynamics simulations in models of arbitrary cross-section

Prescribing inlet boundary conditions for computational fluid dynamics (CFD) simulations of internal flow in complex geometries such as anatomical vascular models is challenging. In the absence of patient-specific inlet velocity data, a common approach for long blood vessels is to assume that the inlet flow is fully developed. In vessels of irregular cross section, however, prescribing fully developed conditions is complicated due to the lack of a general closed-form analytical solution. In this study, we develop a simple Poisson equation method for prescribing fully developed inlet conditions for the flow of either Newtonian or non-Newtonian fluids in CFD models of arbitrary cross-section. We first derive the generalized Poisson equation for fully developed flow of a non-Newtonian fluid and we then develop and verify a methodology for numerically computing the solution on any planar boundary domain. In addition, we develop a simple extension of the method for prescribing a non-orthogonal inlet velocity that represents fully developed flow from an upstream tube that is connected to the CFD inlet at a non-orthogonal angle. This may be used to investigate a common source of uncertainty in CFD simulations of internal flow that is due to a lack of information concerning the exact streamwise flow direction at the inlets. Comparison to several Newtonian and non-Newtonian benchmark verification solutions shows the method to be extremely accurate. As a practical demonstration case, we use the method to prescribe fully developed conditions on multiple non-circular inlets for the non-Newtonian flow of blood in a patient-specific model of the inferior vena cava (IVC). Finally, we further demonstrate the utility of the method by performing a sensitivity study using the patient-specific IVC model, wherein we investigate the influence of inlet velocity flow direction on the non-Newtonian IVC hemodynamics. Given its simplicity and computational efficiency, the method is shown to be far superior to alternative approaches for prescribing fully developed inlet conditions in such complicated geometries. In conclusion, to facilitate the adoption of our Poisson equation method, we have distributed our OpenFOAM source code and the associated test cases from this study as open-source software.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Generalized moving least squares vs. radial basis function finite difference methods for approximating surface derivatives

Approximating differential operators defined on two-dimensional surfaces is an important problem that arises in many areas of science and engineering. Over the past ten years, localized meshfree methods based on generalized moving least squares (GMLS) and radial basis function finite differences (RBF-FD) have been shown to be effective for this task as they can give high orders of accuracy at low computational cost, and they can be applied to surfaces defined only by point clouds. However, there have yet to be any studies that perform a direct comparison of these methods for approximating surface differential operators (SDOs). The first purpose of this work is to fill that gap. For this comparison, we focus on an RBF-FD method based on polyharmonic spline kernels and polynomials (PHS+Poly) since they are most closely related to the GMLS method. Additionally, we use a relatively new technique for approximating SDOs with RBF-FD called the tangent plane method since it is simpler than previous techniques and natural to use with PHS+Poly RBF-FD. Further, the second purpose of this work is to relate the tangent plane formulation of SDOs to the local coordinate formulation used in GMLS and to show that they are equivalent when the tangent space to the surface is known exactly. The final purpose is to use ideas from the GMLS SDO formulation to derive a new RBF-FD method for approximating the tangent space for a point cloud surface when it is unknown. For the numerical comparisons of the methods, we examine their convergence rates for approximating the surface gradient, divergence, and Laplacian as the point clouds are refined for various parameter choices. We also compare their efficiency in terms of accuracy per computational cost, both when including and excluding setup costs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Jas4pp — A data-analysis framework for physics and detector studies

This paper describes the Jas4pp framework for exploring physics cases and for detector-performance studies of future particle collision experiments. Jas4pp is a multi-platform Java program for numeric calculations, scientific visualization in 2D and 3D, storing data in various file formats and displaying collision events and detector geometries. It also includes complex data-analysis algorithms for function minimization, regression analysis, event reconstruction (such as jet reconstruction), limit settings and other libraries widely used in particle physics. The framework can be used with several scripting languages, such as Python/Jython, Groovy and JShell. Several benchmark tests discussed in the paper illustrate significant improvements in the performance of the Groovy and JShell scripting languages compared to the standard Python implementation in C. Furthermore, the improvements for numeric computations in Java are attributed to recent enhancements in the Java Virtual Machine.

97 MATHEMATICS AND COMPUTING↗