Search NASA⌕ Search

SEARCH · Search NASA

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Mathematical model of a personalized neoantigen cancer vaccine and the human immune system

Cancer vaccines are an important component of the cancer immunotherapy toolkit enhancing immune response to malignant cells by activating CD4 + and CD8 + T cells. Multiple successful clinical applications of cancer vaccines have shown good safety and efficacy. Despite the notable progress, significant challenges remain in obtaining consistent immune responses across heterogeneous patient populations, as well as various cancers. We present a mechanistic mathematical model describing key interactions of a personalized neoantigen cancer vaccine with an individual patient’s immune system. Specifically, the model considers the vaccine concentration of tumor-specific antigen peptides and adjuvant, the patient’s major histocompatibility complexes I and II copy numbers, tumor size, T cells, and antigen presenting cells. We parametrized the model using patient-specific data from a clinical study in which individualized cancer vaccines were used to treat six melanoma patients. Model simulations predicted both immune responses, represented by T cell counts, to the vaccine as well as clinical outcome (determined as change of tumor size). This model, although complex, can be used to describe, simulate, and predict the behavior of the human immune system to a personalized cancer vaccine.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Mathematical Model for Li-S Cell with Shuttling-Induced Capacity Loss Approximation

Lithium sulfur (Li-S) batteries have the potential to outperform the current lithium ion batteries and transform the technology of the future. However, dissolution, diffusion, and shuttling of the dissolved polysulfides result in parasitic reactions and substantial capacity loss. To provide a better understanding of the shuttling process, a 1D porous electrode mathematical model has been developed in this paper. An approximation method is used to account for the shuttling-induced capacity loss by adding an extra source/sink term in the material balance equations for the species involved in the parasitic reactions. Shuttling constants used in the source terms can be determined by fitting the model predictions to the experimental measurements. Here, the results showed that by including the approximation method, the model was able to predict the active material loss and the continuous decrease of volume fractions of Li 2 S on the cathode surface. The model sheds light on the capacity loss mechanism occurring inside the cell as a result of the shuttling of polysulfides.

25 ENERGY STORAGE↗
DOE OSTI2013

Empirical and physics based mathematical models of uranium hydride decomposition kinetics with quantified uncertainties.

Metal particle beds have recently become a major technique for hydrogen storage. In order to extract hydrogen from such beds, it is crucial to understand the decomposition kinetics of the metal hydride. We are interested in obtaining a a better understanding of the uranium hydride (UH3) decomposition kinetics. We first developed an empirical model by fitting data compiled from different experimental studies in the literature and quantified the uncertainty resulting from the scattered data. We found that the decomposition time range predicted by the obtained kinetics was in a good agreement with published experimental results. Secondly, we developed a physics based mathematical model to simulate the rate of hydrogen diffusion in a hydride particle during the decomposition. We used this model to simulate the decomposition of the particles for temperatures ranging from 300K to 1000K while propagating parametric uncertainty and evaluated the kinetics from the results. We compared the kinetics parameters derived from the empirical and physics based models and found that the uncertainty in the kinetics predicted by the physics based model covers the scattered experimental data. Finally, we used the physics-based kinetics parameters to simulate the effects of boundary resistances and powder morphological changes during decomposition in a continuum level model. We found that the species change within the bed occurring during the decomposition accelerates the hydrogen flow by increasing the bed permeability, while the pressure buildup and the thermal barrier forming at the wall significantly impede the hydrogen extraction.

08 HYDROGEN↗
DOE OSTI2020

Mathematical model of broadly reactive plasma cell production

Strain-specific plasma cells are capable of producing neutralizing antibodies that are essential for clearance of challenging pathogens. These neutralizing antibodies also function as a main defense against disease establishment in a host. However, when a rapidly mutating pathogen infects a host, successful control of the invasion requires shifting the production of plasma cells from strain-specific to broadly reactive. In this study, we develop a mathematical model of germinal center dynamics and use it to predict the events that lead to improved breadth of the plasma cell response. We examine scenarios that lead to germinal centers that are composed of B-cells that come from a single strain-specific clone, a single broadly reactive clone or both clones. We find that the initial B-cell clonal composition, T-follicular helper cell signaling, increased rounds of productive somatic hypermutation, and B-cell selection strength are among the mechanisms differentiating between strain-specific and broadly reactive plasma cell production during infections. Understanding the contribution of these factors to emergence of breadth may assist in boosting broadly reactive plasma cells production.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2015

TU-CD-304-05: 4Ï€ Non-Coplanar Radiotherapy: From Mathematical Modeling to Clinical Implementation

Purpose: To develop and clinically implement 4π radiotherapy, an inverse optimization platform that maximally utilizes non-coplanar intensity modulated radiotherapy (IMRT) beams to significantly improve critical organ sparing. Methods: A 3D scanner was used to digitize the human and phantom subject surfaces, which were positioned in the computer assisted design (CAD) model of a TrueBeam machine to create a virtual geometrical model, based on which, the feasible beam space was calculated for different tumor locations. Beamlets were computed for all feasible beams using convolution/superposition. A column generation algorithm was employed to optimize patient specific beam orientations and fluence maps. Optimal routing through all selected beams were calculated by a level set method. The resultant plans were converted to XML files and delivered to phantoms in the TrueBeam developer mode. Finally, 4π plans were recomputed in Eclipse and manually delivered to recurrent GBM patients. Results: Compared to IMRT utilizing manually selected beams and volumetric modulated arc therapy plans, markedly improved dosimetry was observed using 4π for the brain, head and neck, liver, lung, and prostate patients. The improvements were due to significantly improved conformality and reduced high dose spillage to organs mediolateral to the PTV. The virtual geometrical model was experimentally validated. Safety margins with 99.9% confidence in collision avoidance were included to the model based model accuracy estimates determined via 300 physical machine to phantom distance measurements. Automated delivery in the developer mode was completed in 10 minutes and collision free. Manual 4 π treatment on the GBM cases resulted in significant brainstem sparing and took 35–45 minutes including multiple images, which showed submillimeter cranial intrafractional motion. Conclusion: The mathematical modeling utilized in 4π is accurate to create and guide highly complex non-coplanar IMRT treatments that consistently and significantly outperform human-operator-created plans. Deliverability of such plans is clinically demonstrated. This work is funded by Varian Medical Systems and the NSF Graduate Research Fellowship DGE-1144087.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2018

Mathematical modeling of a proton-conducting solid oxide fuel cell with current leakage

Here, a framework of charge transports in proton-conducting solid oxide fuel cells (H-SOFCs) with considering current leakage is developed by assuming four electrode reactions. Current leakage happens when electron holes pass through the electrolyte and combine with electrons at the anode side. An analytical solution of leakage currents is proposed depending on the Nernst-Planck equation. On the basis of the analysis expression, a mathematical model of H-SOFCs is proposed, which can provide the information about current-voltage characteristics, leakage current density, Faraday and energy efficiencies. Moreover, H-SOFCs with the BaZr 0.8 Y 0.2 O 3 electrolyte are fabricated and tested, and the proposed model well reproduces the experimental data. The simulation results indicate that current leakage primarily affects the H-SOFC performance when the output voltage is close to the OCV. Both Faraday efficiencies and energy efficiencies decrease with increasing operating temperatures due to the existence of current leakage.

25 ENERGY STORAGE↗
DOE OSTI2014

Experimental Investigation and Mathematical Modeling of Cold Cap Behavior in High-Level-Waste Glass Melter

The cold cap is a layer of reacting melter feed floating on the surface of molten glass in a glass-melting furnace. The cold cap consists of two distinct portions, of which the upper allows the reaction gases to escape through open pores, whereas the lower portion traps the gases within the continuous glass-forming melt, creating foam. The temperature span over the cold cap is ~1000 K. Data needed to simulate the cold cap mathematically include the kinetics of multiple reactions, reaction enthalpies, heat capacity, density, porosity, and heat conductivity as functions of both the temperature and the rate of heating. These data were produced via crucible experiments. The mathematical model has been completed. It relates the cold cap thickness, the rate of melting, the temperature field, and cold cap structure (foaming, dissolution of quartz particles, and formation and subsequent dissolution of crystalline phases, such as spinel) to the cold cap bottom temperature, the fraction of heat flow to the upper cold cap surface, the melt foaminess, and the chemical and physical nature of melter feed materials. To verify the model, cold caps were produced in a laboratory-scale melter and their structure is currently investigated.

Hrma, Pavel R.↗
DOE OSTI2014

Effect of Antigen Shedding on Targeted Delivery of Immunotoxins in Solid Tumors from a Mathematical Model

Most cancer-specific antigens used as targets of antibody-drug conjugates and immunotoxins are shed from the cell surface (Zhang & Pastan (2008) Clin. Cancer Res. 14: 7981-7986), although at widely varying rates and by different mechanisms (Dello Sbarba & Rovida (2002) Biol. Chem. 383: 69–83). Why many cancer-specific antigens are shed and how the shedding affects delivery efficiency of antibody-based protein drugs are poorly understood questions at present. Before a detailed numerical study, it was assumed that antigen shedding would reduce the efficacy of antibody-drug conjugates and immunotoxins. However, our previous study using a comprehensive mathematical model showed that antigen shedding can significantly improve the efficacy of the mesothelin-binding immunotoxin, SS1P (anti-mesothelin-Fv-PE38), and suggested that receptor shedding can be a general mechanism for enhancing the effect of inter-cellular signaling molecules. Here, we improved this model and applied it to both SS1P and another recombinant immunotoxin, LMB-2, which targets CD25. We show that the effect of antigen shedding is influenced by a number of factors including the number of antigen molecules on the cell surface and the endocytosis rate. The high shedding rate of mesothelin is beneficial for SS1P, for which the antigen is large in number and endocytosed rapidly. On the other hand, the slow shedding of CD25 is beneficial for LMB-2, for which the antigen is small in number and endocytosed slowly.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2018

A mathematical model to systematically align superconducting radio frequency cavities employing the serial robot kinematic theory

In Superconducting Radio Frequency (SRF) cryomodules, precise alignment of cavities is necessary to ensure high beam quality and to increase the overall energetic efficiency. In the SSR1 (Single Spoke Resonator 1) cryomodule, the cavities are aligned using a system of seven screws which allows to control five Degree of Freedoms (DOFs). The relation between the rotation of each screw and the movement of the cavity is non-linear, thus the aligning process, currently based on a trial-and-error procedure, can be time consuming and affected by human error. In this paper the design of an alignment mathematical model, based on the serial robot kinematic, is described and tested on a SSR1 cavity. Furthermore, the goal of the proposed model is to give a step by step operational procedure that bring the SSR1 cavity to a desired location reducing the uncertainties related to the current operator-driven alignment process.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

(Invited) Continuum Mathematical Modeling of Water Electrolysis: A Tutorial

Widespread use of hydrogen energy is contingent on the development of reliable and economical sources of hydrogen. Electrolysis from renewably-derived low-carbon electricity is a potentially viable method of hydrogen generation. Prime among the electrolysis technologies are those utilizing ion-conducting polymers (ionomers) including proton-exchange-membrane water electrolyzer (PEMWE). However, these technologies need to exhibit increased efficiency, performance, and durability to become commercially viable. Like most electrochemical devices, PEMWEs involve multiple components (e.g., catalyst, ionomer, transport layers, membrane, plates) and multiple phases, with phenomena occurring across different time and length scales. Furthermore, it is difficult to experimentally probe many of the species and phenomena during operation. Thus, mathematical modeling at the continuum level has been an invaluable aid in exploring, understanding, and optimizing PEMWE cell and components. Furthermore, this is especially true in the highly coupled and complex physics and chemistries that occur with the membrane-electrode assembly (MEA). The physics in a typical volume-averaged non-isothermal model include multiphase transport in porous media, concentrated-solution theory, Ohm's Law, and Butler-Volmer kinetics, and ion, gas, and water transport in the ionomer.

Dizon, Arthur↗
DOE OSTI2020

Mathematical Modeling of Hydroxide-Exchange-Membrane Water Electrolyzer

Water electrolyzers can transform intermittent renewable energy like solar energy and wind energy into the chemical energy of hydrogen with zero greenhouse-gas emissions. The hydroxide-exchange membrane electrolyzer (HEME) combines the capability to produce pressurized hydrogen with the advantage of being able to use low or non-platinum group metal (PGM) electrocatalysts in the alkaline environment.1 Hydroxide salts, for example, KOH, are added to the HEME water feed on both anode and cathode to improve its performance. However, the specific mechanism of performance improvement still needs to be further understood. In addition, at high current densities, bubble evolution can result in mass-transport limitations, a less well studied phenomena. Mathematical modeling is ideal to explore these issues as it is cost and time efficient and can deconvolute the physics, processes, and observed phenomena and study the applied-voltage breakdown. In this work, we extend our previously developed 1D two-phase continuum model2 to study the varies processes in the HEME and provide insights on performance optimizations. First, the oxygen evolution reaction (OER) and hydrogen evolution reaction (HER) kinetics at different hydroxide concentrations have been studied by rotating disk electrodes (RDE) and implemented in the model. Then, the model is calibrated and validated against experimental HEME polarization curves for different KOH concentrations as a liquid electrolyte. The model clearly shows a performance increase with increasing KOH concentrations, which is consistent with the experimental results. The reduced ohmic resistance and increased electrochemical active surface area (ECSA) are the two main reasons for performance increase. The large amount of hydroxide in the liquid electrolyte not only helps to distribute the reactant hydroxide throughout the catalyst layer (CL), which reduces ohmic loss, but also enables reaction at the interface between the liquid electrolyte and electrocatalyst, which increases the ECSA. Applied-voltage breakdown demonstrates that the electrolyzer performance is dominated by anode kinetics and ohmic loss. A comparison with the DI water feed shows a more uniform current distribution in the anode CL when KOH is added, which indicates a higher utilization of the CL. Second, we present modeling on the effects of bubble coverage. As gas evolves, part of the ECSA is minimized due to bubble coverage. To account for this effect, an empirical relationship between the fractional bubble coverage and the current density is implemented in the model.3 The model shows this bubble coverage effect is more pronounced at large current densities with DI water feed. Acknowledgements This work was funded under the HydroGEN Consortium by the Energy Efficiency and Renewable Energy, Hydrogen and Fuel Cell Technologies Office, of the U. S. Department of Energy under contract number DE-AC02-05CH11231. References R. Abbasi, B. P. Setzler, S. Lin, J. Wang, Y. Zhao, H. Xu, B. Pivovar, B. Tian, X. Chen, G. Wu and Y. Yan, 31, 1805876 (2019). L. N. Stanislaw, M. R. Gerhardt and A. Z. Weber, ECS Transactions, 92, 767 (2019). H. Vogt and R. J. Balzer, Electrochimica Acta, 50, 2073 (2005).

Liu, Jiangjin↗
DOE OSTI2018

Special Issue “Mathematical Modeling of Viral Infections”

How an infection will progress in the body is dependent on myriad factors: the rate of spread of the agent, the immune response, what treatment may be applied, .... Clinically following the progression of the disease is limited to snapshots at discrete time points (longitudinally in an individual or in an in vitro/animal model if that is available, but most often from cross-sectional data over cohorts of individuals), and in many cases the data obtained are from a body compartment that is not the site of replication of the disease. We then infer disease progression by putting these discrete data together based on our biological knowledge of the systems involved. However, based on these snapshots, it is not straightforward to work out important disease properties, such as the rate of progression, pathogenicity, and treatment and immune response effects. Mathematical modelling provides a scientifically sound, reproducible method to describe the underlying dynamics that produce these data, as well as a means to investigate new scenarios, such as the effect of a new drug. Its impact has been demonstrated on a number of diseases, for example, contributing to a better understanding of the speed with which human immunodeficiency virus (HIV) replicates [1,2], the dynamics of different drug classes for HIV [3], the main mode of action of interferon in hepatitis C virus (HCV) [4], the effects of direct-acting antivirals in HCV [5], potential effects of the immune response [6], and many others [7–11].

Murray, John↗
DOE OSTI2022

Minimum reflux calculation for multicomponent distillation in multi‐feed, multi‐product columns: Mathematical model

Abstract Multi‐feed, multi‐product distillation columns are ubiquitous in multicomponent distillation systems. The minimum reflux ratio of a distillation column is directly related to its energy consumption and capital cost. Thus, it is a key parameter for distillation systems design, operation, and comparison. In this series, we present the first accurate shortcut based algorithmic method to determine the minimum reflux condition for any general multi‐feed, multi‐product (MFMP) distillation column separating any ideal multicomponent mixture. The classic McCabe‐Thiele or Underwood method is a special case of this general approach. Compared with existing techniques, this method does not involve any rigorous tray‐by‐tray calculation, nor does it require guessing of key components. In this first part of the series, we present the mathematical model for a general MFMP column, derive constraints for feasible separation and minimum reflux condition, discuss their geometric interpretations, and present an illustrative example to demonstrate the effectiveness of our approach.

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

Mathematical modelling for the drying method and smoothing drying rate using cubic spline for seaweed Kappaphycus Striatum variety Durian in a solar dryer

The solar drying experiment of seaweed using Green V-Roof Hybrid Solar Drier (GVRHSD) was conducted in Semporna, Sabah under the metrological condition in Malaysia. Drying of sample seaweed in GVRHSD reduced the moisture content from about 93.4% to 8.2% in 4 days at average solar radiation of about 600W/m{sup 2} and mass flow rate about 0.5 kg/s. Generally the plots of drying rate need more smoothing compared moisture content data. Special cares is needed at low drying rates and moisture contents. It is shown the cubic spline (CS) have been found to be effective for moisture-time curves. The idea of this method consists of an approximation of data by a CS regression having first and second derivatives. The analytical differentiation of the spline regression permits the determination of instantaneous rate. The method of minimization of the functional of average risk was used successfully to solve the problem. This method permits to obtain the instantaneous rate to be obtained directly from the experimental data. The drying kinetics was fitted with six published exponential thin layer drying models. The models were fitted using the coefficient of determination (R{sup 2}), and root mean square error (RMSE). The modeling of models using raw data tested with the possible of exponential drying method. The result showed that the model from Two Term was found to be the best models describe the drying behavior. Besides that, the drying rate smoothed using CS shows to be effective method for moisture-time curves good estimators as well as for the missing moisture content data of seaweed Kappaphycus Striatum Variety Durian in Solar Dryer under the condition tested.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Mathematical modeling of gas desorption from a metal–organic supercontainer cavity filled with stored N 2 gas at critical limits

Metal–organic supercontainer (MOSC) molecules are ideal candidates for gas storage applications due to their construction with customizable ligands and tunable cavity and window sizes, which are found to be elastic in nature. Force field molecular dynamics (MD) are used to evaluate the utilization of MOSCs as nanoporous structures for gas storage. A MOSC, with nitrogen gas molecules filling the cavity, progresses through MD and releases gas molecules by applying temperature to the MOSC. It is the MOSC's elasticity which is responsible for the desorption of guests at elevated temperatures. Data obtained from MD serves as a guide for the derivation of analytical equations that can be used to describe and explain the mechanism of gas desorption from within the cavity. Mathematical modeling of gas desorption from the center cavity can provide a method of predicting MOSC behavior for a broader range of pressures and temperatures, which is challenging for direct atomistic modeling. The utilization of MD can provide data for a wide variety of properties and processes in various materials under different conditions for a broad range of technology-related applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Mathematical modeling of plus-strand RNA virus replication to identify broad-spectrum antiviral treatment strategies

Plus-strand RNA viruses are the largest group of viruses. Many are human pathogens that inflict a socio-economic burden. Interestingly, plus-strand RNA viruses share remarkable similarities in their replication. A hallmark of plus-strand RNA viruses is the remodeling of intracellular membranes to establish replication organelles (so-called “replication factories”), which provide a protected environment for the replicase complex, consisting of the viral genome and proteins necessary for viral RNA synthesis. In the current study, we investigate pan-viral similarities and virus-specific differences in the life cycle of this highly relevant group of viruses. We first measured the kinetics of viral RNA, viral protein, and infectious virus particle production of hepatitis C virus (HCV), dengue virus (DENV), and coxsackievirus B3 (CVB3) in the immuno-compromised Huh7 cell line and thus without perturbations by an intrinsic immune response. Based on these measurements, we developed a detailed mathematical model of the replication of HCV, DENV, and CVB3 and showed that only small virus-specific changes in the model were necessary to describe the in vitro dynamics of the different viruses. Our model correctly predicted virus-specific mechanisms such as host cell translation shut off and different kinetics of replication organelles. Further, our model suggests that the ability to suppress or shut down host cell mRNA translation may be a key factor for in vitro replication efficiency, which may determine acute self-limited or chronic infection. We further analyzed potential broad-spectrum antiviral treatment options in silico and found that targeting viral RNA translation, such as polyprotein cleavage and viral RNA synthesis, may be the most promising drug targets for all plus-strand RNA viruses. Moreover, we found that targeting only the formation of replicase complexes did not stop the in vitro viral replication early in infection, while inhibiting intracellular trafficking processes may even lead to amplified viral growth.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

R-Functions Method in the Mathematical Modeling of Convective Heat Exchange in an Octahedral Fuel Assembly with 37 Fuel Elements

We consider conjugate boundary-value problems of heat exchange for the cases where a viscous incompressible liquid moves through channels with noncanonical cross section flowing around a bundle of rods. The influence of the type of packing on the velocity and temperature distributions is investigated. For the solution, we use the R-functions method in combination with the Ritz variational method. We consider the cases of cyclic, staggered, and rectangular packing of fuel elements.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Conversion of Nuclear Waste into Nuclear Waste Glass: Experimental Investigation and Mathematical Modeling

The melter feed, slurry, or calcine charged on the top of a pool of molten glass forms a floating layer of reacting material called the cold cap. Between the cold-cap top, which is covered with boiling slurry, and its bottom, where bubbles separate it from molten glass, the temperature changes by up to 1000 K. The processes that occur over this temperature interval within the cold cap include liberation of gases, conduction and consumption of heat, dissolution of quartz particles, formation and dissolution of intermediate crystalline phases, and generation of foam and gas cavities. These processes have been investigated using thermal analyses, optical and electronic microscopies, x-ray diffraction, as well as other techniques. Properties of the reacting feed, such as heat conductivity and density, were measured as functions of temperature. Investigating the structure of quenched cold caps produced in a laboratory-scale melter complemented the crucible studies. The cold cap consists of two main layers. The top layer contains solid particles dissolving in the glass-forming melt and open pores through which gases are escaping. The bottom layer contains bubbly melt or foam where bubbles coalesce into larger cavities that move sideways and release the gas to the atmosphere. The feed-to-glass conversion became sufficiently understood for representing the cold-cap processes via mathematical models. These models, which comprise heat transfer, mass transfer, and reaction kinetics models, have been developed with the final goal to relate feed parameters to the rate of glass melting.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗