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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Human–mouse comparison of the multistage nature of radiation carcinogenesis in a mathematical model

Abstract Mouse models are vital for assessing risk from environmental carcinogens, including ionizing radiation, yet the interspecies difference in the dose response precludes direct application of experimental evidence to humans. Herein, we take a mathematical approach to delineate the mechanism underlying the human–mouse difference in radiation‐related cancer risk. We used a multistage carcinogenesis model assuming a mutational action of radiation to analyze previous data on cancer mortality in the Japanese atomic bomb survivors and in lifespan mouse experiments. Theoretically, the model predicted that exposure will chronologically shift the age‐related increase in cancer risk forward by a period corresponding to the time in which the spontaneous mutational process generates the same mutational burden as that the exposure generates. This model appropriately fitted both human and mouse data and suggested a linear dose response for the time shift. The effect per dose decreased with increasing age at exposure similarly between humans and mice on a per‐lifespan basis (0.72‐ and 0.71‐fold, respectively, for every tenth lifetime). The time shift per dose was larger by two orders of magnitude in humans (7.8 and 0.046 years per Gy for humans and mice, respectively, when exposed at ~35% of their lifetime). The difference was mostly explained by the two orders of magnitude difference in spontaneous somatic mutation rates between the species plus the species‐independent radiation‐induced mutation rate. Thus, the findings delineate the mechanism underlying the interspecies difference in radiation‐associated cancer mortality and may lead to the use of experimental evidence for risk prediction in humans.

Oncology↗
DOE OSTI2026

Mathematical modelling of the concave front in the adjacent high explosive detonation problem

This study presents an analysis of the transition-zone in adjacent high explosive (HE) detonation problems which uses a $D, 𝜅, \dot{D}$ relationship, where $D$ is the detonation front-normal velocity, 𝜅 is the detonation front curvature and $\dot{D}$ is the time derivative of detonation front-normal velocity. Our approach extends the traditional $(D, 𝜅)$ model to accurately predict the behaviour of both diverging and converging detonation shock fronts. Our findings affirm that a hyperbolic type of front evolution equation, enhanced with wave acceleration, provides a robust framework for modelling complex shock front dynamics in HE materials. This approach not only captures the natural effects of straightness and boundary slope jumps in the transition-zone but also bridges the gap between mathematical predictions and experimental observations, offering insights into the behaviour of both diverging and converging detonation propagations in a homogeneous HE.

acceleration↗
DOE OSTI2016

Mathematical modelling of the beam under axial compression force applied at any point – the buckling problem

The study is devoted to stability of simply supported beam under axial compression. The beam is subjected to an axial load located at any point along the axis of the beam. The buckling problem has been desribed and solved mathematically. Critical loads have been calculated. In the particular case, the Euler’s buckling load is obtained. Explicit solutions are given. The values of critical loads are collected in tables and shown in figure. The relation between the point of the load application and the critical load is presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Multi-variable mathematical models for the air-cathode microbial fuel cell system

This research adopted the version control system into the model construction for the single chamber air-cathode microbial fuel cell (MFC) system, to understand the interrelation of biological, chemical, and electrochemical reactions. The anodic steady state model was used to consider the chemical species diffusion and electric migration influence to the MFC performance. In the cathodic steady state model, the mass transport and reactions in a multi-layer, abiotic cathode and multi-bacteria cathode biofilm were simulated. Transport of hydroxide was assumed for cathodic pH change. This assumption is an alternative to the typical notion of proton consumption during oxygen reduction to explain elevated cathode pH. The cathodic steady state model provided the power density and polarization curve performance results that can be compared to an experimental MFC system. Another aspect we considered was the relative contributions of platinum catalyst and microbes on the cathode to the oxygen reduction reaction (ORR). We found simulation results showed that the biocatalyst in a cathode that includes a Pt/C catalyst likely plays a minor role in ORR, contributing up to 8% of the total power calculated by the models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Mathematical Models and Numerical Methods for High-Fidelity Simulation of Ignition of Reactive Mixtures by Nanosecond Plasma Discharges in Realistic Configurations

We present a newly developed framework for the numerical simulation of ignition of reactive mixtures using single or repeated nanosecond discharge pulses. The framework builds upon the AMReX library, using the existing compressible solver PeleC and low-Mach solver PeleLMeX and allowing for adaptive mesh refinement, complex geometries, and execution on next-generation high-performance computing (HPC) systems. High-fidelity elementary models are adopted for weakly-ionised plasma discharges with significant energy deposition, consistent with nanosecond discharge pulses, and then implemented in the solver. The treatment of non-thermal electrons and charged species, thermodynamics of non-equilbrium species, plasma kinetics, limiting time scales, and boundary conditions for charged species are discussed and addressed for computational efficiency. The framework is demonstrated for three relevant applications: single and multi-pulse discharges in air, single pulse ignition of an ethylene/air mixture, and a three-dimensional plasma discharge in air with temperature stratification. The successful application of the framework demonstrates the feasibility of high-fidelity simulation of ignition of air/hydrocarbon mixtures in three-dimensions with multiple discharge pulses.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Development of mathematical model and simulation tool for the high capacity production of carbon fiber

Weight reduction in the transportation is the most effective way for reducing fuel consumption. Carbon fiber composites have been increasingly used by automotive manufacturers in vehicle nonstructural and structural parts. Larger penetration of carbon fiber-based materials requires very large quantities of fiber at a low price, and of consistently high quality. The advancements in carbon fiber technology that are required to achieve this production scale-up and cost reduction, are very challenging. The most expensive production step is the conversion of textile-grade polyacrylonitrile (PAN) precursor to carbon fiber. The conversion takes place in three main stages: stabilization, low and high temperature carbonization. Most of the research to date has focused on the stabilization of the PAN precursors and oxidized PAN fibers. Comparingly little effort has been dedicated to the investigation of processing conditions during low temperature (LT) carbonization. During this stage of fiber conversion, the largest fiber mass loss occurs, and the fundamental carbon fiber structure and material properties are established. The understanding of the conversion processes in the LT furnace, and the effects of spatial and temporal variations of the LT process parameters on the carbon fiber properties are necessary to identify possible process improvements and cost savings. The objective of this research was to develop computational models for gas flow and energy transport in the gas and fiber phases of the LT furnace, and to couple them with the fiber conversion process models. The model is implemented in the three-dimensional framework that enables analysis of process condition variations in all directions. The formulation is based on modified transport equation to simulate steady state conditions and thus significantly reduce computational effort associated with transient methods. The model is implemented in open source computational fluid dynamics (CFD) code OpenFOAM. The model has been demonstrated on a prototype carbon fiber LT furnace and can be extended to other geometries and process conditions. Extensions to other physical effects, such as accounting evolution of multiple gas species, and fiber tensioning are straightforward. The model uses High Performance Computing (HPC) capabilities of OpenFOAM and can be implemented on multi-processor workstations or mid-size computer clusters common in the industrial setting.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Analysis of tumor-immune functional responses in a mathematical model of neoantigen cancer vaccines

Cancer neoantigen vaccines have emerged as a promising approach to stimulating the immune system to fight cancer. We propose a simple model including key elements of cancer-immune interactions and conduct a phase plane analysis to understand the immunological mechanisms of cancer neoantigen vaccines. Analytical results are obtained for two widely used functional forms that represent the killing rate of tumor cells by immune cells: the law of mass action (LMA) and the dePillis-Radunskaya Law (LPR). Using the LMA, our results reveal that a slowly growing tumor can escape the immune surveillance and that there is a unique periodic solution. The LPR offers richer dynamics, in which tumor elimination and uncontrolled tumor growth are both present. We show that tumor elimination requires sufficient number of initial activated T cells in relationship to the malignant cells, which lends support to using the neoantigen cancer vaccine as an adjuvant therapy after the primary tumor is surgically removed or treated using radiotherapy. We also derive a sufficient condition for uncontrolled tumor growth under the assumption of the LPR. Here, the juxtaposition of analyses with these two different choices for the killing rate function highlights their importance on model behavior and biological implications, by which we hope to spur further theoretical and experimental work to understand mechanisms underlying different functional forms for the killing rate.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

Mathematical Modelling of Arctic Polygonal Tundra with Ecosys : 1. Microtopography Determines How Active Layer Depths Respond to Changes in Temperature and Precipitation

Microtopographic variation that develops among features (troughs, rims, and centers) within polygonal landforms of coastal arctic tundra strongly affects movement of surface water and snow and thereby affects soil water contents (θ) and active layer depth (ALD). Spatial variation in ALD among these features may exceed interannual variation in ALD caused by changes in climate and so needs to be represented in projections of changes in arctic ALD. For this study, increases in near-surface θ with decreasing surface elevation among polygon features at the Barrow Experimental Observatory (BEO) were modeled from topographic effects on redistribution of surface water and snow and from lateral water exchange with a subsurface water table during a model run from 1981 to 2015. These increases in θ caused increases in thermal conductivity that in turn caused increases in soil heat fluxes and hence in ALD of up to 15 cm with lower versus higher surface elevation which were consistent with increases measured at BEO. The modeled effects of θ caused interannual variation in maximum ALD that compared well with measurements from 1985 to 2015 at the Barrow Circumpolar Active Layer Monitoring (CALM) site (R 2 = 0.61, RMSE = 0.03 m). For higher polygon features, interannual variation in ALD was more closely associated with annual precipitation than mean annual temperature, indicating that soil wetting from increases in precipitation may hasten permafrost degradation beyond that caused by soil warming from increases in air temperature. This degradation may be more rapid if increases in precipitation cause sustained wetting in higher features.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Mathematical Modelling of Arctic Polygonal Tundra with Ecosys: 2. Microtopography Determines How CO 2 and CH 4 Exchange Responds to Changes in Temperature and Precipitation

Differences of surface elevation in arctic polygonal landforms cause spatial variation in soil water contents (θ), active layer depths (ALD), and thereby in CO 2 and CH 4 exchange. In this paper, we test hypotheses in ecosys for topographic controls on CO 2 and CH 4 exchange in trough, rim, and center features of low- and flat-centered polygons (LCP and FCP) against chamber and eddy covariance (EC) measurements during 2013 at Barrow, Alaska. Larger CO 2 influxes and CH 4 effluxes were measured with chambers and modeled with ecosys in LCPs than in FCPs and in lower features (troughs) than in higher (rims) within LCPs and FCPs. Spatially aggregated CO 2 and CH 4 fluxes from ecosys were significantly correlated with EC flux measurements. Lower features were modeled as C sinks (52–56 g C m -2 yr -1 ) and CH 4 sources (4–6 g C m -2 yr -1 ), and higher features as near C neutral (-2–15 g C m -2 yr -1 ) and CH 4 neutral (0.0–0.1 g C m -2 yr -1 ). Much of the spatial and temporal variations in CO 2 and CH 4 fluxes were modeled from topographic effects on water and snow movement and thereby on θ, ALD, and soil O 2 concentrations. Model results forced with meteorological data from 1981 to 2015 indicated increasing net primary productivity in higher features and CH 4 emissions in some lower and higher features since 2008, attributed mostly to recent rises in precipitation. Finally, small-scale variation in surface elevation causes large spatial variation of greenhouse gas (GHG) exchanges and therefore should be considered in estimates of GHG exchange in polygonal landscapes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

MATHEMATICAL MODELING OF EXTRACELLULAR ELECTRON TRANSFER IN BIOFILMS

Electrochemically active biofilms have a unique form of respiration in which they utilize solid external materials as terminal electron acceptors for their metabolism. Currently, two primary mechanisms have been identified for long-range extracellular electron transfer (EET): a diffusion- and a conduction-based mechanism. Evidence in the literature suggests that some biofilms, particularly Shewanella oneidensis, produce the requisite components for both mechanisms. In this study, a generic model is presented that incorporates the diffusion- and the conduction-based mechanisms and allows electrochemically active biofilms to utilize both simultaneously. The model was applied to S. oneidensis and Geobacter sulfurreducens biofilms using experimentally generated data found in the literature. Our simulation results show that 1) biofilms having both mechanisms available, especially if they can interact, may have a metabolic advantage over biofilms that can use only a single mechanism; 2) the thickness of G. sulfurreducens biofilms is likely not limited by conductivity; 3) accurate intrabiofilm diffusion coefficient values are critical for current generation predictions; and 4) the local biofilm potential and redox potential are two distinct parameters and cannot be assumed to have identical values. Finally, we determined that simulated cyclic and squarewave voltammetry based on our model are currently not capable of determining the specific percentages of extracellular electron transfer mechanisms in a biofilm. The developed model will be a critical tool for designing experiments to explain EET mechanisms.

Environmental Molecular Sciences Laboratory↗
DOE OSTI2021

Evaluation of the rheological and electrical percolation of high‐density polyethylene/carbon black composites using mathematical models

Abstract In this work, conductive polymer composites (CPCs) of bio‐based polyethylene (BioPe) containing different concentrations of carbon black (CB) were developed. By using oscillatory rheology analysis, a Newtonian plateau was observed in BioPe, and all BioPe/CB composites had a behavior of a pseudo‐solid and that composites with volume fractions ranging from 0.24 to 0.56 presented higher viscosity, storage, and loss modulus. This suggests the formation of a percolated network and by using the power‐law models, it was observed that the electrical percolation threshold was higher than the rheological percolation threshold. The electrical conductivity was measured using the four‐point probe method and a sigmoid model was used to predict the CPCs' electrical conductivity percolation threshold. The results indicated that the four‐point probe method presented satisfactory results according to the calculated standard deviations and voltage–current characteristics for each round of measurements considering the same ranging as used in rheology analysis. The analytical model used showed a coefficient of determination ( R 2 ) higher than 95%, allowing the prediction of the electrical conductivity of the CPC and the percolation threshold as a function of the volumetric fraction of the CB.

da SiIva, Moacy P.↗
DOE OSTI2018

Mathematical Model of Heat Transfer in the Catalyst Granule with Point Reaction Centers

This paper considers a catalyst granule with a porous ceramic chemically inert base and active point centers, at which an exothermic reaction of synthesis takes place. The rate of a chemical reaction depends on temperature by the Arrhenius law. The heat is removed from the catalyst granule surface to the synthesis products by heat transfer. Based on the idea of self-consistent field, a closed system of equations is constructed for calculating the temperatures of the active centers. As an example, a catalyst granule of the Fischer–Tropsch synthesis with active metallic cobalt particles is considered. The stationary temperatures of the active centers are calculated by the timedependent technique by solving a system of ordinary differential equations. The temperature distribution inside the granule has been found for the local centers located on one diameter of the granule and distributed randomly in the granule’s volume. The existence of the critical temperature inside the reactor has been established, the excess of which leads to substantial superheating of local centers. The temperature distribution with local reaction centers differs qualitatively from the granule temperature calculated in the homogeneous approximation. The results of calculations are given.

42 ENGINEERING↗
DOE OSTI2018

Mathematical Modeling of Decarburization in Levitated Fe-Cr-C Droplets

Using carbon dioxide to replace oxygen as an alternative oxidant gas has proven to be a viable solution in the decarburization process, with potential for industrial applications. In a recent study, the transport phenomena governing the carbon dioxide decarburization process through the use of electromagnetic levitation (EML) was examined. CO{sub 2}/CO mass transfer was found to be the principal reaction rate control step, as a result gas diffusion has gained significant attention. In the present study, gas diffusion during decarburization process was investigated using computational fluid dynamics (CFD) modeling coupled with chemical reactions. The resulting model was verified through experimental data in a published paper, and employed to provide insights on phenomena typically unobservable through experiments. Based on the results, a new correction of the Frössling equation was presented which better represents the mass transfer phenomena at the metal-gas interface within the range of this research.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Mathematical Modelling of Gas–Liquid, Two-Phase Flows in a Ladle Shroud

Differential and macroscopic models of argon–steel flows in ladle shroud have been developed. In this, argon–steel, two-phase flow phenomena have been formulated via a transient, three dimensional, turbulent flow model, based on the volume of fluid (VOF) calculation procedure. While realizable k–ε turbulence model has been applied to map turbulence, commercial, CFD software ANSYS-Fluent™ (Version 18), has been applied to carry out numerical calculations. Predictions from the model have been directly assessed against experimental measurements across the range of shroud dimensions and volumetric flow rates typically practiced in the industry. It is demonstrated that the two-phase turbulent flow model captures the general features of gas–liquid flows in ladle shroud providing estimates of free jet length and threshold gas flow rates (required to halt air ingression) which are in agreement with corresponding experimental measurements. In the absence of differential solutions, a macroscopic model has been worked out through dimensional analysis embodying multiple non-linear regression. It is shown that dimensionless free jet length in bloom and slab casting shrouds can be estimated reasonably accurately from the following correlation (in SI unit), viz., ((L{sub jet})/(D{sub CN}))=2.8×10{sup −2}(((Q{sub G})/(Q{sub L}))){sup 1.14}(((gD{sub CN}{sup 5})/(Q{sub L}{sup 2}))){sup 0.8}(((σD{sub CN}{sup 3})/(ρ{sub L}Q{sub L}{sup 2}))){sup −0.9}(((D{sub sh})/(D{sub CN}))){sup 2.0}(((ρ{sub G})/(ρ{sub L}))){sup −0.30}in which, L{sub jet} is the free liquid jet length (m), Q{sub G} is the gas flow rate (m{sup 3}/s), Q{sub L} is the liquid flow rate (m{sup 3}/s), D{sub sh} is shroud diameter (m), D{sub CN} is the collector nozzle diameter (m), σ is the interfacial tension (N/m), and ρ{sub G} as well as ρ{sub L} are respectively density of gas and liquid (kg/m{sup 3}). It is demonstrated that the proposed correlation is consistent with the laws of physical modeling and leads to estimates that are in good agreement with predictions from the differential models, for both air-water as well as argon–steel systems. Numerical simulations as well as macroscopic modeling have indicated that thermo-physical properties of the gas–liquid system are important and exert some influences on the gas–liquid, two-phase, flow in ladle shrouds, albeit not to a large extent. Despite dissimilar thermo-physical properties, full scale water modeling appears to be sufficiently predictive and provides reasonable macroscopic descriptions of the two-phase flow phenomena in industrial ladle shroud systems.

42 ENGINEERING↗