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Results for “Mathematical Modeling”

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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Mathematical model of massive dynamics in the neighborhood of disturbance focus

We consider a model problem for the research of Earth’s surface state caused by discharge of tectonic stress on the deep cracks in the earth’s crust. Using the numerical method of bicharacteristics, algorithm is developed and solution of the problem of non-stationary dynamics of a homogeneous isotropic elastic half-space is built under plane strain when one resets the vertical stress on crack. Diffraction of waves on the surface is studied, pictures of wave fields and stress-strain state of the medium and the surface for different moments of time are built.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Systematically Improving Espresso: Insights from Mathematical Modeling and Experiment

Espresso is a beverage brewed using hot, high-pressure water forced through a bed of roasted coffee. Despite being one of the most widely consumed coffee formats, it is also the most susceptible to variation. Here, we report a novel model, complimented by experiment, that is able to isolate the contributions of several brewing variables, thereby disentangling some of the sources of variation in espresso extraction. Under the key assumption of homogeneous flow through the coffee bed, a monotonic decrease in extraction yield with increasingly coarse grind settings is predicted. However, experimental measurements show a peak in the extraction yield versus grind setting relationship, with lower extraction yields at both very coarse and fine settings. This result strongly suggests that inhomogeneous flow is operative at fine grind settings, resulting in poor reproducibility and wasted raw material. With instruction from our model, we outline a procedure to eliminate these shortcomings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Mathematical modeling of positron emission tomography (PET) data to assess radiofluoride transport in living plants following petiolar administration

Background: Ion transport is a fundamental physiological process that can be studied non-invasively in living plants with radiotracer imaging methods. Fluoride is a known phytotoxic pollutant and understanding its transport in plants after leaf absorption is of interest to those in agricultural areas near industrial sources of airborne fluoride. Here we report the novel use of a commercial, high-resolution, animal positron emission tomography (PET) scanner to trace a bolus of [¹⁸F]fluoride administered via bisected petioles of Brassica oleracea , an established model species, to simulate whole plant uptake of atmospheric fluoride. This methodology allows for the first time mathematical compartmental modeling of fluoride transport in the living plant. Radiotracer kinetics in the stem were described with a single-parameter free- and trapped-compartment model and mean arrival times at different stem positions were calculated from the free-compartment time-activity curves. Results: After initiation of administration at the bisected leaf stalk, [¹⁸F] radioactivity climbed for approximately 10 minutes followed by rapid washout from the stem and equilibration within leaves. Kinetic modeling of transport in the stem yielded a trapping rate of 1.5 +/- 0.3%/min (mean +/- s.d., n = 3), velocity of 2.2 +/- 1.1 cm/min, and trapping fraction of 0.8 +/- 0.5%/cm. Conclusion: Quantitative assessment of physiologically meaningful transport parameters of fluoride in living plants is possible using standard positron emission tomography in combination with petiolar radiotracer administration. Movement of free fluoride was observed to be consistent with bulk flow in xylem, namely a rapid and linear change in position with respect to time. Trapping, likely in the apoplast, was observed. Future applications of the methods described here include studies of transport of other ions and molecules of interest in plant physiology.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Data-Driven Mathematical Modeling of the Effect of Particle Size Distribution on the Transitory Reaction Kinetics of Hot Metal Desulfurization

The aim of this work was to develop a prediction model for hot metal desulfurization. More specifically, the study aimed at finding a set of explanatory variables that are mandatory in prediction of the kinetics of the lime-based transitory desulfurization reaction and evolution of the sulfur content in the hot metal. The prediction models were built through multivariable analysis of process data and phenomena-based simulations. The model parameters for the suggested model types are identified by solving multivariable least-squares cost functions with suitable solution strategies. One conclusion we arrived at was that in order to accurately predict the rate of desulfurization, it is necessary to know the particle size distribution of the desulfurization reagent. It was also observed that a genetic algorithm can be successfully applied in numerical parameter identification of the proposed model type. It was found that even a very simplistic parameterized expression for the first-order rate constant provides more accurate prediction for the end content of sulfur compared to more complex models, if the data set applied for the modeling contains the adequate information.

36 MATERIALS SCIENCE↗
DOE OSTI2017

A Mathematical Model for the Multiphase Transport and Reaction Kinetics in a Ladle with Bottom Powder Injection

A computation fluid dynamics-population balance model-simultaneous reaction model (CFD-PBM-SRM) coupled model has been proposed to study the multiphase flow behavior and refining reaction kinetics in a ladle with bottom powder injection, and some new and important phenomena and mechanisms are presented. For the multiphase flow behavior, the effects of bubbly plume flow, powder particle motion, particle-particle collision and growth, particle-bubble collision and adhesion, and powder particle removal into top slag are considered. For the reaction kinetics, the mechanisms of multicomponent simultaneous reactions, including Al, S, Si, Mn, Fe, and O, at the multi-interface, including top slag-liquid steel interface, air-liquid steel interface, powder droplet-liquid steel interface, and bubble-liquid steel interface, are presented, and the effect of sulfur solubility in the powder droplet on the desulfurization is also taken into account. Model validation is carried out using hot tests in a 2-t induction furnace with bottom powder injection. The result shows that the powder particles gradually disperse in the entire furnace; in the vicinity of the bottom slot plugs, the desulfurization product CaS is liquid phase, while in the upper region of the furnace, the desulfurization product CaS is solid phase. The predicted sulfur contents by the present model agree well with the measured data in the 2-t furnace with bottom powder injection.

36 MATERIALS SCIENCE↗
DOE OSTI2016

A new mathematical model for the equation of state of an asymmetric infinite nuclear matter

In this paper, the average energy variation with respect to the density of a system of nucleons is studied. A new formula is presented for the nuclear equation of state. This formula is related to an infinite system of protons and neutrons with relatively small thermal excitations. It is shown that the proposed formulation for the nuclear equation of state reproduces the results obtained in the Skyrme-Hartree-Fock (SHF) and Relativistic Mean-Field (RMF) models of nuclear matter. It should be realized that the consistency of the obtained results for nuclear matter with the predictions of well-known SHF and RMF models for symmetric and asymmetric system of nucleons indicates the reliability of this formulation for different types of nuclear matter in large scales such as neutron stars.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Mathematical modeling of cold cap: Effect of bubbling on melting rate

The rate of melting is a primary concern in the vitrification of radioactive wastes because it directly influences the life cycle of nuclear waste cleanup efforts. To increase glass melting performance, experimental and industrial all-electric waste glass melters employ various melt-rate enhancement techniques, the most prominent being the application of bubblers submerged into molten glass. This study investigates various ways in which bubbling affects melting rate in a waste glass melter. Using the recently developed cold cap model, we suggest that forced convection of molten glass, which increases the cold cap bottom temperature, is the main factor. Other effects, such as stirring the feed into molten glass or reducing the insulating effect of foaming, also play a role.

bubbling↗
DOE OSTI2018

Mathematical Model of Transfer and Deposition of Finely Dispersed Particles in a Turbulent Flow of Emulsions and Suspensions

The problem of modeling turbulent transfer of finely dispersed particles in liquids has been considered. An approach is used where the transport of particles is represented in the form of a variety of the diffusion process with the coefficient of turbulent transfer to the wall. Differential equations of transfer are written for different cases, and a solution of the cell model is obtained for calculating the efficiency of separation in a channel. Based on the theory of turbulent transfer of particles and of the boundary layer model, an expression has been obtained for calculating the rate of turbulent deposition of finely dispersed particles. The application of this expression in determining the efficiency of physical coagulation of emulsions in different channels and on the surface of chaotic packings is shown.

42 ENGINEERING↗
DOE OSTI2016

Mathematical model for self-propelled droplets driven by interfacial tension

We propose a model for the spontaneous motion of a droplet induced by inhomogeneity in interfacial tension. The model is derived from a variation of the Lagrangian of the system and we use a time-discretized Morse flow scheme to perform its numerical simulations. Our model can naturally simulate the dynamics of a single droplet, as well as that of multiple droplets, where the volume of each droplet is conserved. We reproduced the ballistic motion and fission of a droplet, and the collision of two droplets was also examined numerically.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Mathematical model of unmanned aerial vehicle used for endurance autonomous monitoring

The paper purpose is to present some aspects regarding the control system of unmanned aerial vehicle - UAV, used to local observations, surveillance and monitoring interest area. The calculus methodology allows a numerical simulation of UAV evolution in bad atmospheric conditions by using nonlinear model, as well as a linear one for obtaining guidance command. The UAV model which will be presented has six DOF (degrees of freedom), and autonomous control system. This theoretical development allows us to build stability matrix, command matrix and control matrix and finally to analyse the stability of autonomous UAV flight. A robust guidance system, based on uncoupled state will be evaluated for different fly conditions and the results will be presented. The flight parameters and guidance will be analysed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Mathematical modeling of gas-dynamic and radiative processes in experiments with the use of laser and heavy-ion beams

Results are presented from theoretical and experimental studies of gas-dynamic and radiative processes in the plasma that is planned to be used in future experiments on the stopping of fast heavy-ion beams. These experiments are aimed at measuring the enhanced (as compared to cold substance) plasma stopping power. To reliably interpret the experimental results, it is necessary to create a hydrodynamically stable homogeneous plasma with a uniform temperature and a lifetime exceeding the transit time of the heavy-ion beam (3–5 ns). The method for calculating plasma gas-dynamic characteristics with allowance for radiative heat transfer is described. The specific features of the so-called ion model of plasma, which is used to calculate plasma radiative characteristics, are discussed. The emission spectrum formed as a result of conversion of laser radiation into X-rays and the subsequent passing through a triacetate cellulose (C{sub 12}H{sub 16}O{sub 8}) target is calculated. The simulated spectrum of transmitted radiation satisfactorily agrees with experimental data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Three-Dimensional Mathematical Model of Oxygen Transport Behavior in Electroslag Remelting Process

A transient three-dimensional model has been proposed to investigate the oxygen transport behavior in electroslag remelting process. The electromagnetism, heat transfer, multiphase flow, and species transport were calculated simultaneously by finite volume method. The volume of fluid approach was adopted to trace the metal–slag–air three-phase flow. Based on the necessary thermodynamics of oxygen transport behavior, a kinetic model was established to predict the mass source terms in species transport equation. The kinetic correction factor was proposed to account for the effect of the oxide scale formed on the electrode on the FeO content in slag. Finally, the effect of applied current on the oxygen transfer was studied. The predicted result agrees well with the measured data when the kinetic correction factor is set to be 0.5. The temperature distribution that affects the thermodynamics differs at the interfaces. The oxygen in air is absorbed into slag due to the oxidation at the slag/air interface. The Fe{sub 2}O{sub 3} in slag and the oxide scale contribute to the increase of FeO content in slag, and the latter one plays the leading role. The oxygen transfer from slag to metal mainly occurs during the formation of the droplet at the slag/metal droplet interface. With the current increasing from 1200 to 1800 A, the oxygen content increases from 76.4 to 89.8 ppm, and then slightly declines to 89.2 ppm when the current increases to 2100 A.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Mathematical Modeling on the Influence of Casting Parameters on Initial Solidification at the Meniscus of Slab Continuous Casting

In the current study, the two-dimensional mold model was applied to investigate the influence of different casting parameters on the initial solidification at the meniscus of the continuous casting mold. The profile of the meniscus and the slag rim, and the heat flux on the hot face of the copper plate, were compared with different locations of the mold and different casting parameters. The depth of the oscillation marks and solidified meniscus through simulation was measured with different casting parameters. With the mold oscillating downward from the peak to the valley, the maximum heat flux on the hot face of the copper plate near the meniscus increased from 4.3 to 5.5 MW/m{sup 2}, the thickness of the slag rim decreased from 4.7 to 4.2 mm, and the height of the curved meniscus also decreased. With the increase of casting speed from 1.2 to 1.45 m/min, the maximum speed of the upper backflow increased from 0.6 to 0.8 m/s, and the lowest location of the meniscus at approximately 310 mm from the copper plate decreased from 22 to 12 mm below the meniscus near the nozzle, where the slag entrapment easily occurred. With the increase of the casting speed, casting superheat, and oscillation frequency, and the decrease of the water flow rate in the mold and oscillation amplitude, the thickness of the slag rim decreased. With the increase of casting speed and superheat, and the decrease of the water flow rate in the mold, oscillation frequency, and oscillation amplitude, the depth of the solidified meniscus decreased. The regression equation was fitted to estimate the depth of hooks at the subsurface of slabs.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Modeling Mathematical Programs with Equilibrium Constraints in Pyomo

We describe new capabilities for modeling MPEC problems within the Pyomo modeling software. These capabilities include new modeling components that represent complementarity conditions, modeling transformations for re-expressing models with complementarity conditions in other forms, and meta-solvers that apply transformations and numeric optimization solvers to optimize MPEC problems. We illustrate the breadth of Pyomo's modeling capabilities for MPEC problems, and we describe how Pyomo's meta-solvers can perform local and global optimization of MPEC problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

A Long-Term Mathematical Model for Mining Industries

A parcimonious long term model is proposed for a mining industry. Knowing the dynamics of the global reserve, the strategy of each production unit consists of an optimal control problem with two controls, first the flux invested into prospection and the building of new extraction facilities, second the production rate. In turn, the dynamics of the global reserve depends on the individual strategies of the producers, so the models leads to an equilibrium, which is described by low dimensional systems of partial differential equations. The dimensionality depends on the number of technologies that a mining producer can choose. In some cases, the systems may be reduced to a Hamilton–Jacobi equation which is degenerate at the boundary and whose right hand side may blow up at the boundary. A mathematical analysis is supplied. Then numerical simulations for models with one or two technologies are described. In particular, a numerical calibration of the model in order to fit the historical data is carried out.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Mathematical Models for Adaptive Multi-modal Sensing

Project Proposal for Graduate Student Program - This is a project proposal for a group of graduate students in the Institute for Mathematics and Its Applications Math-to-Industry Bootcamp.

97 MATHEMATICS AND COMPUTING↗