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Results for “Mathematical models”

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 OSTI2013

Analysis of laser remote fusion cutting based on a mathematical model

Laser remote fusion cutting is analyzed by the aid of a semi-analytical mathematical model of the processing front. By local calculation of the energy balance between the absorbed laser beam and the heat losses, the three-dimensional vaporization front can be calculated. Based on an empirical model for the melt flow field, from a mass balance, the melt film and the melting front can be derived, however only in a simplified manner and for quasi-steady state conditions. Front waviness and multiple reflections are not modelled. The model enables to compare the similarities, differences, and limits between laser remote fusion cutting, laser remote ablation cutting, and even laser keyhole welding. In contrast to the upper part of the vaporization front, the major part only slightly varies with respect to heat flux, laser power density, absorptivity, and angle of front inclination. Statistical analysis shows that for high cutting speed, the domains of high laser power density contribute much more to the formation of the front than for low speed. The semi-analytical modelling approach offers flexibility to simplify part of the process physics while, for example, sophisticated modelling of the complex focused fibre-guided laser beam is taken into account to enable deeper analysis of the beam interaction. Mechanisms like recast layer generation, absorptivity at a wavy processing front, and melt film formation are studied too.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Mathematical Model for Collision–Coalescence Among Inclusions in the Bloom Continuous Caster with M-EMS

Mathematical simulation is an effective tool to analyze the fluid flow and the inclusion behavior in the bloom continuous caster with mold electromagnetic stirring (M-EMS). The mathematical model is applied to the modeling of magnetic field, flow field, and inclusion field. Due to the introduction of Archimedes force, the collision mechanism and inclusion’s slipping velocity should be modified in the inclusion mass and population conservation model. Numerically predicted magnetic field, flow field, and the inclusion spatial distribution conform to the experimental results in the existing literature. Lorentz force plays an important role in the fluid flow, and Archimedes force plays an important role in the inclusion distribution in the continuous caster. Due to Brownian collision, Stokes collision, Archimedes collision, and turbulent collision, the coalescence among inclusions occurs in the bloom continuous caster with M-EMS. Among the four types of collisions, turbulent collision occurs most frequently, followed by Archimedes collision and Stokes collision. The frequency of Brownian collision is several orders of magnitudes smaller and is therefore negligible. The inclusion volume concentration, number density, and characteristic radius exhibit a U-shape in the continuous caster without M-EMS. However, with M-EMS, they exhibit an inverted U-shape.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Machine learning mathematical models for incidence estimation during pandemics

Accurate estimates of the incidence of infectious diseases are key for the control of epidemics. However, healthcare systems are often unable to test the population exhaustively, especially when asymptomatic and paucisymptomatic cases are widespread; this leads to significant and systematic under-reporting of the real incidence. Here, we propose a machine learning approach to estimate the incidence of a pandemic in real-time, using reported cases and the overall test rate. In particular, we use Bayesian symbolic regression to automatically learn the closed-form mathematical models that most parsimoniously describe incidence. We develop and validate our models using COVID-19 incidence values for nine different countries, confirming their ability to accurately predict daily incidence. Remarkably, despite the differences in epidemic trajectories and dynamics across countries, we find that a single model for all countries offers a more parsimonious description and is more predictive of actual incidence compared to separate models for each country. Our results show the potential to accurately model incidence in real-time using closed-form mathematical models, providing a valuable tool for public health decision-makers.

Fajardo-Fontiveros, Oscar (ORCID:0000000207058972)↗
NASA NTRS1997

Light, temperature, and leaf nitrogen distribution in the tropical rain forest of Biosphere 2 and their importance in the mathematical models for global environmental changes

As the environmental changes occur throughout the world in rapid rate, we need to have further understandings for our planet. Since the ecosystems are so complex, it is almost impossible for us to integrate every factor. However, mathematical models are powerful tools which can be used to simulate those ecosystems with limited data. In this project, I collected light intensity, canopy leaf temperature and Air Handler (AHU) temperature, and nitrogen concentration in the leaves for different profiles in the rainforest mesocosm. These data will later be put into mathematical models such as "big-leaf" and "sun/shade" models to determine how these factors will affect CO2 exchange in the rainforest. As rainforests are diminishing from our planet and their existence is very important for all living things on earth, it is necessary for us to learn more about the unique system of rainforests and how we can co-exist rather than destroy.

Tohda, Motofumi↗
DOE OSTI2015

DaMoScope and its internet graphics for the visual control of adjusting mathematical models describing experimental data

The experience of using the dynamic atlas of the experimental data and mathematical models of their description in the problems of adjusting parametric models of observable values depending on kinematic variables is presented. The functional possibilities of an image of a large number of experimental data and the models describing them are shown by examples of data and models of observable values determined by the amplitudes of elastic scattering of hadrons. The Internet implementation of an interactive tool DaMoScope and its interface with the experimental data and codes of adjusted parametric models with the parameters of the best description of data are schematically shown. The DaMoScope codes are freely available.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2000

Mathematical Modeling of an Oscillating Droplet

Oscillating droplets are of interest in a number of disciplines. A practical application is the oscillating drop method, which is a technique for measuring surface tension and viscosity of liquid metals. It is especially suited to undercooled and highly reactive metals, because it is performed by electromagnetic levitation. The natural oscillation frequency of the droplets is related to the surface tension of the material, and the decay of oscillations is related to its viscosity. The fluid flow inside the droplet must be laminar in order for this technique to yield good results. Because no experimental method has yet been developed to visualize flow in electromagnetically-levitated oscillating metal droplets, mathematical modeling is required to determine whether or not turbulence occurs. Three mathematical models of the flow: (1) assuming laminar conditions, (2) using the k-epsilon turbulence model, and (3) using the RNG turbulence model, respectively, are compared and contrasted to determine the physical characteristics of the flow. It is concluded that the RNG model is the best suited for describing this problem. The goal of the presented work was to characterize internal flow in an oscillating droplet of liquid metal, and to verify the accuracy of the characterization by comparing calculated surface tension and viscosity.

Berry, S.↗
NASA NTRS1989

A mathematical model of physiological processes and its application to the study of aging

The behavior of a physiological system which, after displacement, returns by homeostatic mechanisms to its original condition can be described by a simple differential equation in which the "recovery time" is a parameter. Two such systems, which influence one another, can be linked mathematically by the use of "coupling" or "feedback" coefficients. These concepts are the basis for many mathematical models of physiological behavior, and we describe the general nature of such models. Next, we introduce the concept of a "fatal limit" for the displacement of a physiological system, and show how measures of such limits can be included in mathematical models. We show how the numerical values of such limits depend on the values of other system parameters, i.e., recovery times and coupling coefficients, and suggest ways of measuring all these parameters experimentally, for example by monitoring changes induced by X-irradiation. Next, we discuss age-related changes in these parameters, and show how the parameters of mortality statistics, such as the famous Gompertz parameters, can be derived from experimentally measurable changes. Concepts of onset-of-aging, critical or fatal limits, equilibrium value (homeostasis), recovery times and coupling constants are involved. Illustrations are given using published data from mouse and rat populations. We believe that this method of deriving survival patterns from model that is experimentally testable is unique.

Aging/physiology↗
NASA NTRS1970

A mathematical model of the effect of a predator on species diversity

Mathematical model determines reaction between new predator and microbe competitor when the competitor is the predator's sole nutrient resource. The model utilizes differential equations to describe the interactions with the specific growth rates, and analyzes these growth rates as they are affected by population density and nutrient concentration.

Weston, C. R.↗
NASA NTRS1980

Propulsion system mathematical model for a lift/cruise fan V/STOL aircraft

A propulsion system mathematical model is documented that allows calculation of internal engine parameters during transient operation. A non-realtime digital computer simulation of the model is presented. It is used to investigate thrust response and modulation requirements as well as the impact of duty cycle on engine life and design criteria. Comparison of simulation results with steady-state cycle deck calculations showed good agreement. The model was developed for a specific 3-fan subsonic V/STOL aircraft application, but it can be adapted for use with any similar lift/cruise V/STOL configuration.

Cole, G. L.↗
NASA NTRS1987

A mathematical model of a lithium/thionyl chloride primary cell

A 1-D mathematical model for the lithium/thionyl chloride primary cell was developed to investigate methods of improving its performance and safety. The model includes many of the components of a typical lithium/thionyl chloride cell such as the porous lithium chloride film which forms on the lithium anode surface. The governing equations are formulated from fundamental conservation laws using porous electrode theory and concentrated solution theory. The model is used to predict 1-D, time dependent profiles of concentration, porosity, current, and potential as well as cell temperature and voltage. When a certain discharge rate is required, the model can be used to determine the design criteria and operating variables which yield high cell capacities. Model predictions can be used to establish operational and design limits within which the thermal runaway problem, inherent in these cells, can be avoided.

Evans, T. I.↗
NASA NTRS1994

Mathematical modeling of a class of multibody flexible spacecraft structures

A mathematical model for a general multibody flexible spacecraft is obtained. The generic spacecraft considered consists of a flexible central body to which a number of flexible multibody structures are attached. The coordinate systems used in the derivation allow effective decoupling of the translational motion of the entire spacecraft from its rotational motion about its center of mass. The derivation assumes that the deformations in the bodies are only due to elastic motions. The dynamic model derived is a closed-form vector-matrix differential equation. The model developed can be used for analysis and simulation of many realistic spacecraft configurations.

Kelkar, Atul, G.↗