AN ISOGEOMETRIC APPROACH TO STREAMLINING HIGH-END STRUCTURAL DYNAMICS SIMULATION FOR AUTOMOTIVE AND OTHER APPLICATIONS
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42 ENGINEERING↗
SEARCH · Engineering Papers
Results for “mathematical analysis”
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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Economic Parameter Uncertainty Quantification Demonstration
HERON has recently added uncertainty quantification capabilities for economic parameters. Users may now associate a distribution with certain cash flow parameters to simulate uncertainty in cost or other economic inputs. For example, a user may want to capture the uncertainty of capital expenditures of an advanced nuclear power plant because public data is hard to find or is not available yet. This new addition allows users to account for that uncertainty.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Theoretical Four Pressure Model Development: A Real Characteristic Formulation for RELAP5-3D
This presentation summarizes the development of the project called Theoretical Four Pressure Model Development : A Real Characteristic Formulation for RELAP5-3D, A “Well Posed” Equation System in 2-D. This has produced a well-posed system of equations for modeling nuclear power plants (and many other systems).
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
System Advisor Model (SAM) [Slides]
The System Advisor Model (SAM) is a free software that enables detailed performance and financial analysis for energy systems. • Conducts technoeconomic analysis of energy technologies to facilitate planning and decision making.
29 ENERGY PLANNING, POLICY, AND ECONOMY↗
Mixed-mode oscillations in a three-timescale coupled Morris–Lecar system
Mixed-mode oscillations (MMOs) are complex oscillatory behaviors of multiple-timescale dynamical systems in which there is an alternation of large-amplitude and small-amplitude oscillations. It is well known that MMOs in two-timescale systems can arise either from a canard mechanism associated with folded node singularities or a delayed Andronov–Hopf bifurcation (DHB) of the fast subsystem. While MMOs in two-timescale systems have been extensively studied, less is known regarding MMOs emerging in three-timescale systems. In this work, we examine the mechanisms of MMOs in coupled Morris–Lecar neurons with three distinct timescales. We investigate two kinds of MMOs occurring in the presence of a singularity known as canard-delayed-Hopf (CDH) and in cases where CDH is absent. In both cases, we examine how features and mechanisms of MMOs vary with respect to variations in timescales. Our analysis reveals that MMOs supported by CDH demonstrate significantly stronger robustness than those in its absence. Moreover, we show that the mere presence of CDH does not guarantee the occurrence of MMOs. This work yields important insights into conditions under which the two separate mechanisms in two-timescale context, canard and DHB, can interact in a three-timescale setting and produce more robust MMOs, particularly against timescale variations.
97 MATHEMATICS AND COMPUTING↗
Integrating tactical planning, operational planning and scheduling using data-driven feasibility analysis
Supply chain operations and scheduling are well-studied problems in the literature. Although these problems are related, they are often solved sequentially. This uncoordinated approach usually leads to sub-optimal solutions. Here this paper proposes a methodology for integrating scheduling operations into the supply chain network, motivated by the available enterprise data, and feasibility analysis. Existing literature on integrated models for addressing the supply chain is reviewed and classified. Then the mathematical model formulation for each level is discussed, after which the proposed data-driven integrated framework is described. The methodology is tested on two different case studies of varying dimensions. For each case study, the solution solves a multi-objective problem with the overall aim of an optimal solution that is robust towards achieving optimal cost while keeping customer satisfaction in mind.
42 ENGINEERING↗
COMPLEX NETWORK ANALYSIS AND INTELLIGENT PLAFORM
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97 MATHEMATICS AND COMPUTING↗
Modern chemical graph theory
Abstract Graph theory has a long history in chemistry. Yet as the breadth and variety of chemical data is rapidly changing, so too do graph encoding methods and analyses that yield qualitative and quantitative insights. Using illustrative cases within a basic mathematical framework, we showcase modern chemical graph theory's utility in Chemists' analysis and model development toolkit. The encoding of both experimental and simulation data is discussed at various levels of granularity of information. This is followed by a discussion of the two major classes of graph theoretical analyses: identifying connectivity patterns and partitioning methods. Measures, metrics, descriptors, and topological indices are then introduced with an emphasis upon enhancing interpretability and incorporation into physical models. Challenging data cases are described that include strategies for studying time dependence. Throughout, we incorporate recent advancements in computer science and applied mathematics that are propelling chemical graph theory into new domains of chemical study. This article is categorized under: Molecular and Statistical Mechanics > Molecular Dynamics and Monte‐Carlo Methods Structure and Mechanism > Computational Materials Science Structure and Mechanism > Molecular Structures
Leite, Leonardo S. G.↗
Lectures on Lie Group Analysis: Solving Differential Equations Using Symmetries
These notes are meant to be a supplemental reference for the beginner Lie Group Analyst. It is assumed that the reader has a basic concept of the fundamentals of Lie Group Theory (LGT), e.g. has seen the derivation of the infinitesimal generator and understands the mathematical meaning behind invariance. An excellent reference is Albright et al., “Symmetry Analysis of Differential Equations: A Primer,”. The reader is urged to read at least the first three chapters of that document to be able to follow the outset of Chapter 2 of this document. The reader should also have a general understanding of calculus, ordinary differential equations, and partial differential equations.
97 MATHEMATICS AND COMPUTING↗
Performing Bayesian Analyses With AZURE2 Using BRICK: An Application to the 7 Be System
Phenomenological R-matrix has been a standard framework for the evaluation of resolved resonance cross section data in nuclear physics for many years. It is a powerful method for comparing different types of experimental nuclear data and combining the results of many different experimental measurements in order to gain a better estimation of the true underlying cross sections. Yet a practical challenge has always been the estimation of the uncertainty on both the cross sections at the energies of interest and the fit parameters, which can take the form of standard level parameters. Frequentist (χ 2 -based) estimation has been the norm. In this work, a Markov Chain Monte Carlo sampler, emcee, has been implemented for the R-matrix code AZURE2, creating the Bayesian R-matrix Inference Code Kit (BRICK). Bayesian uncertainty estimation has then been carried out for a simultaneous R-matrix fit of the 3 He (α,γ) 7 Be and 3 He (α,α) 3 He reactions in order to gain further insight into the fitting of capture and scattering data. Both data sets constrain the values of the bound state α-particle asymptotic normalization coefficients in 7 Be. The analysis highlights the need for low-energy scattering data with well-documented uncertainty information and shows how misleading results can be obtained in its absence.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Bounding uncertainty in functional data: A case study
Functional data are fast becoming a preeminent source of information across a wide range of industries. A particularly challenging aspect of functional data is bounding uncertainty. In this unique case study, we present our attempts at creating bounding functions for selected applications at Sandia National Laboratories (SNL). The first attempt involved a simple extension of functional principal component analysis (fPCA) to incorporate covariates. Though this method was straightforward, the extension was plagued by poor coverage accuracy for the bounding curve. This led to a second attempt utilizing elastic methodology which yielded more accurate coverage at the cost of more complexity.
97 MATHEMATICS AND COMPUTING↗
FLASSH 1.0: Thermal Scattering Law Evaluation and Cross Section Generation
The Full Law Analysis Scattering System Hub ( FLASSH ) is an advanced code which evaluates the thermal scattering law (i.e. TSL, S(α,β)) for thermal scattering cross sections and resonance Doppler broadening. The ability to accurately capture these two key cross section features is dependent on accurate, high fidelity TSL evaluations. FLASSH 1.0 provides advanced physics capabilities resulting in an improved, generalized TSL to most accurately represent the lattice dynamics within any material. This improved TSL will allow for consistent analysis in both the thermal and epithermal energy ranges. The features for TSL analysis are packaged within the FLASSH GUI for easy user interface along with data output in many file formats including ENDF File 7 and ACE files.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
User-Centered Software Design in the All Hazards Analysis Application
To design good software, you must always keep the end user in mind. Some benefits of incorporating the user-centered design process include saving users time and effort and helping them to utilize all capabilites of an application. In my work on the All Hazards Analysis (AHA) application, I employed principles of user-centered design to make the application easier for new users to navigate. This poster describes user-centered software design in general and showcases some of my user-centered design work on the AHA application.
58 GEOSCIENCES↗
Exabiome: Advancing Microbial Science through Exascale Computing
The Exabiome project seeks to improve the understanding of microbiomes through the development of methods for accelerating metagenomic science using exascale computing. This article gives an overview of scientific impact of the three components of the project: metagenome assembly, protein family detection, and comparative analysis of metagenomes. Exabiome developed MetaHipMer, the only metagenome assembler capable of scaling to full exascale systems. MetaHipMer has enabled ground-breaking assemblies on the Frontier supercomputer, with many scientific benefits, such as the discovery of rare species and viral genomes. To investigate protein families, Exabiome developed two exascale tools, PASTIS and HipMCL. Together, these can utilize exascale resources to understand the functional diversity of billions of dark matter proteins and novel protein families. For comparative analysis, Exabiome developed kmerprof, a tool that can be used to compare huge metagenomes for many different scientific purposes, for example, grouping human microbiomes according to body location.
59 BASIC BIOLOGICAL SCIENCES↗
X-ray scattering based scanning tomography for imaging and structural characterization of cellulose in plants
X-ray and neutron scattering have long been used for structural characterization of cellulose in plants. Due to averaging over the illuminated sample volume, these measurements traditionally overlooked the compositional and morphological heterogeneity within the sample. Here, a scanning tomographic imaging method is described, using contrast derived from the X-ray scattering intensity, for virtually sectioning the sample to reveal its internal structure at a resolution of a few micrometres. This method provides a means for retrieving the local scattering signal that corresponds to any voxel within the virtual section, enabling characterization of the local structure using traditional data-analysis methods. This is accomplished through tomographic reconstruction of the spatial distribution of a handful of mathematical components identified by non-negative matrix factorization from the large dataset of X-ray scattering intensity. Joint analysis of multiple datasets, to find similarity between voxels by clustering of the decomposed data, could help elucidate systematic differences between samples, such as those expected from genetic modifications, chemical treatments or fungal decay. The spatial distribution of the microfibril angle can also be analyzed, based on the tomographically reconstructed scattering intensity as a function of the azimuthal angle.
36 MATERIALS SCIENCE↗
Tuning Multigrid Methods with Robust Optimization and Local Fourier Analysis
Local Fourier analysis is a useful tool for predicting and analyzing the performance of many efficient algorithms for the solution of discretized PDEs, such as multigrid and domain decomposition methods. The crucial aspect of local Fourier analysis is that it can be used to minimize an estimate of the spectral radius of a stationary iteration, or the condition number of a preconditioned system, in terms of a symbol representation of the algorithm. In practice, this is a “minimax” problem, minimizing with respect to solver parameters the appropriate measure of work, which involves maximizing over the Fourier frequency. Often, several algorithmic parameters may be determined by local Fourier analysis in order to obtain efficient algorithms. Analytical solutions to minimax problems are rarely possible beyond simple problems; the status quo in local Fourier analysis involves grid sampling, which is prohibitively expensive in high dimensions. In this paper, we propose and explore optimization algorithms to solve these problems efficiently. Finally, several examples, with known and unknown analytical solutions, are presented to show the effectiveness of these approaches.
97 MATHEMATICS AND COMPUTING↗
Implicit Multirate GARK Methods
This article considers multirate generalized-structure additively partitioned Runge–Kutta methods for solving stiff systems of ordinary differential equations with multiple time scales. These methods treat different partitions of the system with different timesteps for a more targeted and efficient solution compared to monolithic single rate approaches. With implicit methods used across all partitions, methods must find a balance between stability and the cost of solving nonlinear equations for the stages. In order to characterize this important trade-off, we explore multirate coupling strategies, problems for assessing linear stability, and techniques to efficiently implement Newton iterations for stage equations. Unlike much of the existing multirate stability analysis which is limited in scope to particular methods, we present general statements on stability and describe fundamental limitations for certain types of multirate schemes. New implicit multirate methods up to fourth order are derived, and their accuracy and efficiency properties are verified with numerical tests.
97 MATHEMATICS AND COMPUTING↗