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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
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)↗
DOE OSTI2019

Mathematical modeling in cancer nanomedicine: a review

Cancer continues to be among the leading healthcare problems worldwide, and efforts continue not just to find better drugs, but also better drug delivery methods. The need for delivering cytotoxic agents selectively to cancerous cells, for improved safety and efficacy, has triggered the application of nanotechnology in medicine. This effort has provided drug delivery systems that can potentially revolutionize cancer treatment. Nanocarriers, due to their capacity for targeted drug delivery, can shift the balance of cytotoxicity from healthy to cancerous cells. The field of cancer nanomedicine has made significant progress, but challenges remain that impede its clinical translation. Several biophysical barriers to the transport of nanocarriers to the tumor exist, and a much deeper understanding of nano-bio interactions is necessary to change the status quo. Mathematical modeling has been instrumental in improving our understanding of the physicochemical and physiological underpinnings of nanomaterial behavior in biological systems. Here, we present a comprehensive review of literature on mathematical modeling works that have been and are being employed towards a better understanding of nano-bio interactions for improved tumor delivery efficacy.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2018

A mathematical model of tree harvesting in age-structured forests subject to beetle infestations

In this paper, we investigate a mathematical model for age-structured forest–beetle interactions that includes harvesting of trees. The aim is to broaden the understanding of the synergistic effects of harvesting and insect infestation on the age structure of the forests and the harvesting benefit. In the first part of this study, we consider different scenarios of the forest infestation by beetles and observe that the quantitative age profile of the forest depends significantly on whether the beetle population is in its endemic or epidemic states. In the second part, we also include harvesting of the forest trees and analyze two different harvesting strategies: cutting all trees older than a certain age, and cutting a fixed proportion of trees older than a certain age. Numerical simulations are implemented to determine the optimal cutting age for both harvesting strategies. The numerical simulations reveal that, independent of the steady state of the beetle population (that is, no beetles, endemic or epidemic state) clear cutting all trees older than a given age provides a higher harvesting benefit. Our numerical simulations further indicate that to obtain a fixed harvesting yield, a forest under a beetle epidemic state has to be cut at a younger age than if the forest were at an endemic beetle state or a no-beetle state.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Qualitative properties of mathematical model for data flow

In this paper, properties of a recently proposed mathematical model for data flow in large-scale asynchronous computer systems are analyzed. In particular, the existence of special weak solutions based on propagating fronts is established. Qualitative properties of these solutions are investigated, both theoretically and numerically.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Mathematical Modeling of Nonstationary Separation Processes in a Cascade of Gas Centrifuges for Separation of Tungsten Isotopes

We have developed and program-realized a mathematical model of nonstationary separation processes proceeding in cascades of gas centrifuges for separation of multicomponent isotope mixtures. With the help of this model we have calculated the parameters of nonstationary separation processes proceeding in the cascades of gas centrifuges for tungsten isotope separation. It has been shown that the model adequately describes the nonstationary processes in the cascade and is suitable for calculating their parameters during separation of multicomponent isotope mixtures.

42 ENGINEERING↗
DOE OSTI2016

Development of Kinetics and Mathematical Models for High Pressure Gasification of Lignite-Switchgrass Blends

The overall objective of the current project was to investigate the high pressure gasification characteristics of a feed containing both coal and biomass. The two feed types differ in their ash contents and ash composition, particularly the alkali content. Gasification of a combined feed of coal and biomass has the potential for considerable synergies that might lead to a dramatic improvement in process economics and flexibility. The proposed study aimed to develop a detailed understanding of the chemistry, kinetics, and transport effects during high pressure gasification of coal-biomass blend feed. Specifically, we studied to develop: (a) an understanding of the catalytic effect of alkali and other inorganic species present in the biomass and coal, (b) an understanding of processing conditions under which synergistic effects of the blending of coal and biomass might be observed. This included the role of particle size, residence time, and proximity of the two feed types, (c) kinetics of high pressure gasification of individual feeds as well as the blends, and (d) development of mathematical models that incorporate kinetics and transport models to enable prediction of gasification rate at a given set of operating conditions, and (e) protocols to extend the results to other feed resources. The goal was to provide a fundamental understanding of the gasification process and guide in optimizing the configurations and design of the next generation of gasifiers. The approach undertaken was centered on two basic premises: (1) the gasification for small particles without internal mass transfer limitations can be treated as the sum of two processes in series (pyrolysis and char gasification) , and (2) the reactivity of the char generated during pyrolysis not only depends on the pressure and temperature but is also affected by the heating rates. Thus low heating rates (10-50 °C/min) typical of PTGA fail to produce char that would typically be formed at high heating rates (~10 4 °C/sec), encountered in entrained flow gasifiers. The char morphology, also a function of the heating rate, would influence the transport rates during the char gasification phase. Thus, heating rate plays a critical role through which both, pyrolysis and char gasification, are interconnected. We utilized two complementary gasification experiments: PEFR (pressurized entrained flow gasifier) and PTGA (pressurized thermo-gravimetric analyzer). The PEFR allowed us to study gasification at pressures, temperatures, and heating rates relevant for coal-biomass gasifiers. The PTGA work was useful in understanding the basic chemistry of the evolution of various gaseous species during pyrolysis. These results helped improved our understanding of the chemistry and chemical changes during pyrolysis. The role alkali metals and other inorganics in char gasification using steam and/or CO 2 was investigated. Finally, the mathematical models for char gasification without the transport effects were developed at commercial operating conditions.

09 BIOMASS FUELS↗
DOE OSTI2019

Mathematical Modeling of Fracture Processes in Plates with Systems of Cracks Under the Action of Long-Term Loads, High Temperatures, and Corrosive Media

We formulate mathematical models for the evaluation of the lifetime of plates with systems of cracks under the action of long-term force loads in the presence of high temperatures and corrosive media. These models are based on the use of the well-known main mechanisms of propagation of creep cracks, corrosion fracture, and the first law of thermodynamics (balance of energy components and rates of their changes) for a metal plate containing a system of macrocracks and subjected to the action of long-term tension and corrosive media at high temperatures. We consider the case of a double-periodic system of cracks.

42 ENGINEERING↗
DOE OSTI2021

Mathematical modeling and parameter estimation of MFI membranes for para/ortho‐xylene separation

Abstract A mathematical model of a membrane with a thin, oriented, and selective MFI layer, which also includes contributions from defects, pore blockages, support layer, and external mass transfer, was formulated based on the Maxwell‐Stefan equations. It was validated using reported (Kim et al., Angew Chemie Int Ed, 2018, 57:480–485; Jeon et al., Nature, 2017, 543:690–694) para/ortho‐xylene separation data from five MFI membranes. The diffusivities of the xylenes were considered to be the same for all membranes, while the thickness and the density of defects and pore blockage were treated as unique properties of each membrane, and their contributions were estimated by fitting the model to the corresponding separation data. The effects of these properties and the role of permeate pressure on the separation performance were subsequently analyzed. The proposed modeling, parameter estimation, and analysis framework allow one to quantitatively interpret the variation of separation performance, to understand separation bottlenecks, and to provide guidance for designing membranes with desired performance.

Liu, Jingjun↗
DOE OSTI2018

Bistability analysis in mathematical model of M-phase control in Xenopus oocyte extracts

To gain more insight into the molecular mechanism that regulates eukaryotic cell cycle, we propose a modification to an existing Mathematical model of mitosis-promoting factor control in Xenopus oocyte extract. To achieve this, we redirect how cell exits from mitosis using ubiquitin ligase enzyme APCP:Cdc20 which is acting as a modifier in cyclin degradation. We present a modified wiring map using combination of mass action kinetics and Michaelis–Menten kinetics to represent the biochemical processes. This results in a system of non-linear ordinary differential equations. The equilibria of the system were analyzed analytically. Using MPF as a bifurcation parameter, we analytically derived conditions under which bistability can occur in the MPF activation module. We find that for bistability to occur, it is necessary that the rate of phosphorylation of Wee1 must be greater than the rate of its dephosphorylation and that the concentration of MPF must lie in certain range of parameter values. Numerical simulations conducted show that the time taken to exit the cell cycle is shorter than those published in some reports and the sensitivity analysis results suggest that the rate of synthesis of cyclin is the most sensitive parameter in the dynamics of cell cycle. Through numerical experiments, we found new parameter sets that will give rise to bistability in the MPF activation module.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Mathematical Model of ATM Activation and Chromatin Relaxation by Ionizing Radiation

We propose a comprehensive mathematical model to study the dynamics of ionizing radiation induced Ataxia-telangiectasia mutated (ATM) activation that consists of ATM activation through dual mechanisms: the initiative activation pathway triggered by the DNA damage-induced local chromatin relaxation and the primary activation pathway consisting of a self-activation loop by interplay with chromatin relaxation. The model is expressed as a series of biochemical reactions, governed by a system of differential equations and analyzed by dynamical systems techniques. Radiation induced double strand breaks (DSBs) cause rapid local chromatin relaxation, which is independent of ATM but initiates ATM activation at damage sites. Key to the model description is how chromatin relaxation follows when active ATM phosphorylates KAP-1, which subsequently spreads throughout the chromatin and induces global chromatin relaxation. Additionally, the model describes how oxidative stress activation of ATM triggers a self-activation loop in which PP2A and ATF2 are released so that ATM can undergo autophosphorylation and acetylation for full activation in relaxed chromatin. In contrast, oxidative stress alone can partially activate ATM because phosphorylated ATM remains as a dimer. The model leads to predictions on ATM mediated responses to DSBs, oxidative stress, or both that can be tested by experiments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

A Multi-scale Mathematical Model of Growth and Coalescence of Bubbles Beneath the Anode in an Aluminum Reduction Cell

Modeling of bubble shapes is challenging because of the wide range of length scales in aluminum reduction cells. A 3D multi-scale mathematical model was developed to understand the nucleation, growth and coalescence of bubbles beneath the anode and to investigate the transition of bubbles from the micro- to macro level. The motion of micro-bubbles is examined using the discrete bubble model (DBM) within a Lagrangian reference. An algorithm for the transition from discrete micro-bubbles to large bubbles, which are fully resolved by the volume of fluid (VOF) approach, is achieved using a user-defined function. The two-way coupling between discrete bubbles and continuous fluids is achieved by inter-phase momentum exchange. The model involves three kinds of bubble coalescence: micro-bubble coalescence is taken into account by the DBM; large bubbles swallowing up micro-bubbles are solved by the discrete-continuum transition model; the coalescence between large bubbles is handled by the VOF method. Numerical results show that the coverage and thickness of bubbles agree well with the experimental data in the literature. Bubble thickness stops increasing when the bubble elongates with the anode bottom, which is 4.0 to 4.5 mm. Meanwhile, two asymmetrical thick heads can be observed under the anode. Bubble release frequency increases with increasing current density.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Patient-Specific Mathematical Model of the Clear Cell Renal Cell Carcinoma Microenvironment

The interactions between cells and molecules in the tumor microenvironment can give insight into the initiation and progression of tumors and their optimal treatment options. In this paper, we developed an ordinary differential equation (ODE) mathematical model of the interaction network of key players in the clear cell renal cell carcinoma (ccRCC) microenvironment. We then performed a global gradient-based sensitivity analysis to investigate the effects of the most sensitive parameters of the model on the number of cancer cells. The results indicate that parameters related to IL-6 have high a impact on cancer cell growth, such that decreasing the level of IL-6 can remarkably slow the tumor’s growth.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

Mathematical Modeling in Systems for Operational Evaluation of the Stress-Strain State of the Arch-Gravity Dam at the Sayano-Shushenskaya Hydroelectric Power Plant

Current studies of the stress-strain state of the dam at the Sayano-Shushenskaya Hydroelectric Power Plant at VNIIG based on mathematical modeling including full scale and experimental data are described. Applications and programs intended for automatic operational evaluation of the stress-strain state of the dam for optimizing control of the upper race level in the course of the annual filling-drawdown cycle and during seismic events are examined. Improvements in systems for monitoring the stress-strain state of concrete dams are proposed.

42 ENGINEERING↗
DOE OSTI2018

Mathematical Model for Evaluating the Technical Condition and Predicting Collapse of Protective Barriers on Flooded Radiation-Hazardous Sites

The possible consequences of flooding of nuclear and radiation-hazardous sites and objects should be included among the environmental risks arising during the rapid development of the infrastructure in the Arctic. A mathematical model, algorithms, and software codes for evaluating the condition and predicting the collapse of the protective barriers, and determining the emission rate of radionuclides and the possible radioactive contamination of the environment, including long-term prediction and situation analysis, have been developed. The software codes have been accepted into the government registry at Rospatent.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

A Mathematical Model of Breast Tumor Progression Based on Immune Infiltration

Breast cancer is the most prominent type of cancer among women. Understanding the microenvironment of breast cancer and the interactions between cells and cytokines will lead to better treatment approaches for patients. In this study, we developed a data-driven mathematical model to investigate the dynamics of key cells and cytokines involved in breast cancer development. We used gene expression profiles of tumors to estimate the relative abundance of each immune cell and group patients based on their immune patterns. Dynamical results show the complex interplay between cells and molecules, and sensitivity analysis emphasizes the direct effects of macrophages and adipocytes on cancer cell growth. In addition, we observed the dual effect of IFN-γ on cancer proliferation, either through direct inhibition of cancer cells or by increasing the cytotoxicity of CD8+ T-cells.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Mathematical Modelling of Fault Reactivation Induced by Water Injection

Faults in the host rock that might exist in the vicinity of deep geological repositories for radioactive waste, constitute potential enhanced pathways for radionuclide migration. Several processes might trigger pore pressure increases in the faults leading to fault failure and induced seismicity, and increase the faults’ permeability. In this research, we developed a mathematical model to simulate fault activation during an experiment of controlled water injection in a fault at the Mont-Terri Underground Research Laboratory in Switzerland. The effects of in-situ stress, fault shear strength parameters and heterogeneity are assessed. It was shown that the above factors are critical and need to be adequately characterized in order to predict the faults’ hydro-mechanical behaviour.

58 GEOSCIENCES↗