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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Mathematical analysis of laboratory microbial experiments demonstrating deterministic chaotic dynamics

Presented is a system of four ordinary differential equations and a mathematical analysis of microbiological experiments in a four-component chemostat—nutrient n, rods r, cocci c, and predators p. The analysis is consistent with the conclusion that previous experiments produced features of deterministic chaotic and classical dynamics depending on dilution rate. The surrogate model incorporates as much experimental detail as possible, but necessarily contains unmeasured parameters. The objective is to understand better the differences between model simulations and experimental results in complex microbial populations. The key methodology for simulation of chaotic dynamics, consistent with the measured dilution rate and microbial volume averages, was to cause the preference of p for r vs. c to vary with the r and c concentrations, to make r more competitive for nutrient than c, and to recycle some dying p biomass, leading to a modified version of the Monod kinetics model. Our mathematical model demonstrated that the occurrence of chaotic dynamics requires a predator, p, preference for r versus c to increase significantly with increases in r and c populations. Also included is a discussion of several generalizations of the existing model and a possible involvement of the minimum energy dissipation principle. This principle appears fundamental to thermodynamic systems including living systems. Several new experiments are suggested.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2016

The big contradiction between the perturbation theory and the chaotic state. A detailed mathematical analysis indicates when the plasma is stable or unstable

In the present manuscript enough observations and interpretations of three issues of Plasma Physics are presented. The first issue is linked to the common experimental confirmation of plasma waves which appear to be repeated in a standard way while there are also cases where plasma waves change to an unstable state or even to chaotic state. The second issue is associated with a mathematical analysis of the movement of a charged particle using the perturbation theory; which could be used as a guide for new researchers on similar issues. Finally, the suitability and applicability of the perturbation theory or the chaotic theory is presented. Although this study could be conducted on many plasma phenomena (e.g. plasma diffusion) or plasma quantities (e.g. plasma conductivity), here it was decided this study to be conducted on plasma waves and particularly on drift waves. This was because of the significance of waves on the plasmatic state and especially their negative impact on the thermonuclear fusion, but also due to the long-time experience of the plasma laboratory of Demokritos on drift waves.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A mathematical analysis of carbon fixing materials that grow, reinforce, and self-heal from atmospheric carbon dioxide

Carbon fixing materials are a new class of self-healing, self-reinforcing materials we have introduced that utilize ambient CO 2 to chemically add to an ever extending carbon backbone. This class of materials can utilize biological or non-biological photocatalysts and support a wide range of potential backbone chemistries. However, there is no analysis to date that describes their fundamental limits in terms of chemical kinetics and mass transfer. In this computational study, we employ a reaction engineering, and materials science analysis to answer basic questions about the maximum growth rate, photocatalytic requirements and limits of applicable materials. Our proposed mathematical framework envelops three main functions required for carbon fixing materials: (1) adsorption of CO 2 from air, (2) photocatalytic reduction of CO 2 into selected monomers, and (3) polymerization of CO 2 -derived monomers. First, by performing a Damköhler number analysis, we derive criteria for the cross over from kinetic control to mass transfer limited growth, setting upper limits on performance of a potential photocatalyst. Next, we analyze photocatalytic reduction of CO 2 to single carbon products, using known catalytic pathways and kinetic data. We identify formaldehyde as a C1 intermediate having unique potential for incorporation into the material backbone of carbon fixing materials. As an example, we find that a diamond-shaped reaction network graph for CO 2 reduction, passing through CO and HCOOH intermediates, accurately describes kinetic data for cobalt-promoted TiO 2 nanoparticles at room temperature and 1 atm CO 2 . Finally, as an applied case study, we consider and analyze the example of a carbon fixing poly(oxymethylene) system with embedded catalyst promoting the photocatalytic reduction of CO 2 to formaldehyde. The latter then trimerizes to a trioxane monomer which subsequently polymerizes to polyoxymethylene. This reaction engineering analysis introduces benchmarks for carbon fixing materials with respect to achievable rates of photocatalysis, adsorption, and polymerization. These results should prove valuable for the design, evaluation, and benchmarking of this emergent and new class of environmentally sustainable materials.

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

Mathematical Analysis of the Solidification Behavior of Plain Steel Based on Solute- and Heat-Transfer Equations in the Liquid–Solid Zone

An analytical approximate solution to non-linear solute- and heat-transfer equations in the unsteady-state mushy zone of Fe-C plain steel has been obtained, assuming a linear relationship between the solid fraction and the temperature of the mushy zone. The heat transfer equations for both the solid and liquid zone along with the boundary conditions have been linked with the equations to solve the whole equations. The model predictions (e.g., the solidification constants and the effective partition ratio) agree with the generally accepted values and with a separately performed numerical analysis. The solidus temperature predicted by the model is in the intermediate range of the reported formulas. The model and Neuman’s solution are consistent in the low carbon range. A conventional numerical heat analysis (i.e., an equivalent specific heat method using the solidus temperature predicted by the model) is consistent with the model predictions for Fe-C plain steels. The model presented herein simplifies the computations to solve the solute- and heat-transfer simultaneous equations while searching for a solidus temperature as a part of the solution. Thus, this model can reduce the complexity of analyses considering the heat- and solute-transfer phenomena in the mushy zone.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A Combined Computational and Mathematical Analysis of Interconnect Fatigue Potential in Photovoltaic Modules

A finite element model of a 60-cell monocrystalline silicon glass-polymer photovoltaic module was simulated with ±1.0 kPa and ±2.4 kPa loads applied to the glass to calculate the deformation under load. Cell-to-cell displacements were used to approximate interconnect strain and stress. A mathematical fatigue cycle life relation was fitted to data for the interconnect material (copper), to generate a life prediction at each interconnect location based on the local stress means, reversal extents, and amplitudes. Interconnect stress was found to be significantly asymmetric about zero despite symmetric positive and negative module loads due to laminate thickness offsets about the neutral plane and the effects of module framing. Cycle life results indicated that interconnect fatigue failure was unlikely to occur over a 30-year lifetime of conservative wind and snow load cycles since the typical cell design feature of leaving some unconstrained length between the cell edge and first solder pad increases the effective gauge length and decreases the stress levels below the material endurance limit. Follow-up analyses found that 3.6 mm and 6.4 mm were the minimum unconstrained lengths required to survive the assumed lifetime of wind and snow cycles, respectively, confirming that typical industrial module constructions with 8–15 mm unconstrained lengths should survive conservatively. Notably, large magnitude, low-cycle snow loading was consistently the limiting factor requiring a longer unconstrained interconnect length. Finally, insights and workflows from this study inform module interconnection design limits for survival against mechanical fatigue in deployment environments.

14 SOLAR ENERGY↗
DOE OSTI2023

Convergence analysis of single rate and multirate fixed stress split iterative coupling schemes in heterogeneous poroelastic media

Recently, the accurate modeling of flow–structure interactions has gained more attention and importance for both petroleum and environmental engineering applications. Of particular interest is the coupling between subsurface flow and reservoir geomechanics. Different single rate and multirate iterative and explicit coupling schemes have been proposed and analyzed in the past. In addition, Banach fixed point contraction results were obtained for iterative coupling schemes, and conditionally stable results were obtained for explicit coupling schemes. In this work, we will consider the mathematical analysis of the single rate and multirate fixed stress split iterative coupling schemes for spatially heterogeneous poroelastic media. We will re–establish the contractivity for both schemes in the localized case, and we will show that heterogeneities come at the expense of imposing more restricted conditions on the number of fine flow time steps that can be taken within one coarse mechanics time step in the multirate case. Our mathematical analysis is supplemented by numerical simulations validating our derived upper bounds. Finally, to the best of our knowledge, this is the first rigorous mathematical analysis of the multirate fixed–stress split iterative coupling scheme in heterogeneous poroelastic media.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Recovery Simulator and Analysis Formulation: Mathematical Framework for Enhanced Resilience and Resource Allocation

This report introduces recovery simulator and analysis (RSA), a framework aimed at enhancing the resilience of electrical grids post-disruption. The RSA model leverages an optimization problem formulation that focuses on maximizing the load served (or optionally customers served) through a coordinated and cooptimized recovery of non-black start generation, transmission lines, feeders and substations subject to labor budget constraints. By integrating advanced linear programming techniques, the simulator selects efficient reocovery pathways, optimizing both short-term and long-term grid recovery strategies. The mathematical framework guides decision-making through a comprehensive evaluation of potential recovery actions, factoring in the trade-offs between labor constraints and load (or optionally customer) restoration efficacy. This enables grid operators to simulate diverse outage scenarios and delineate optimal recovery pathways, thereby prioritizing critical repair tasks and ensuring resource allocation is both economical and effective. The intended use case of RSA is to allow planners to explore many recovery scenarios quickly and determine assets most critical across a wide range of scenarios, and therefore strong candidates for hardening or additional investment. RSA might also be used in an operational setting, following a single event, for exploring efficient recovery pathways.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

Direct Effect of Solvent Viscosity on the Physical Mass Transfer for Wavy Film Flow in a Packed Column

ABSTRACT Post-combustion carbon capture via solvent absorption in a packed column can be a promising technology for mitigating greenhouse gas emissions. The mass transfer between gas and liquid solvent phases plays a critical role in determining the packing height of the packed column. Recent experiments [1] involving physical mass transfer for aqueous amine in a packed column have distinguished the direct and indirect impacts of viscosity (µ_L) on the mass transfer coefficient ?( k?_L). The direct impact of viscosity on the mass transfer coefficient has been found to be significantly higher for a packed column ?(k?_L~µ_L^(-0.38)) than a wetted wall column (WWC) ?(k?_L~µ_L^(-0.17)). To explain the deviation from the well-controlled uniform film flow in a WWC, we propose a mechanism involving the unavoidable wavy film flow and eddy-enhanced mass transfer in a packed column. A mathematical analysis based on fundamental flow and mass transfer equations is presented to quantify this deviation. The correlation for mass transfer coefficient derived from the mathematical analysis is found to match the corresponding one derived from the experiments for a packed column. Multiphase flow simulations using the Volume of Fluid method also are conducted to verify the direct impact of viscosity on the mass transfer coefficient for both uniform and wavy film flows. The mass transfer coefficient calculated from simulations shows steeper variation with viscosity for wavy film compared to the uniform film, further confirming our proposed theory. A similar relation ?(k?_L~µ^(-0.38)) for wavy film flow in a packed column is observed for aqueous solvent from both theory, experiment, and computer simulations.

Mass transfer, viscosity, eddy diffusion↗
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 OSTI2019

Energy Saving by Insulating a Cooking Pot

Sandia National Laboratories is one of the most technologically advanced and resourceful national laboratories in the United States. Their mission is to use science and technology, innovative research, and global engagement to counter threats, reduce dangers, and respond to disasters. To achieve this mission, Sandia is divided into ten divisions that are overlooked by Dr. Stephen Younger, the Laboratories Director. Amongst the ten divisions, the internship will take place in Division 8000, which is Integrated Security Solutions. Inside this division, the internship will be a Structural and Thermal Analysis R&D. Apart from being strictly focused on security, the division performs research for small companies that do not count with the resources to perform it themselves. During the summer internship, one of these cases is being attended. A small company invented an insulating cover that is supposed to be placed over the top of a cooking pot lid. They claim that the insulating cover helps in the saving of energy. As an intern and researcher, the task is to determine how much energy is effectively saved by placing the insulating cover over the cooking pot. To achieve the goal, mathematical analyses, experiments and simulations will be done. Then, if appropriate, a better design will be made to increase the energy saved by the insulating cover. For the mathematical analysis, the thermal resistance method was used, resulting in energy saved at a rate of 14.2795 W. After the mathematical analysis was done, a test plan was developed and presented to the supervisor for approval. After some recommendations, the test plan will be modified accordingly.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2017

Transient dynamics of terrestrial carbon storage: Mathematical foundation and its applications

Terrestrial ecosystems have absorbed roughly 30% of anthropogenic CO 2 emissions over the past decades, but it is unclear whether this carbon (C) sink will endure into the future. Despite extensive modeling and experimental and observational studies, what fundamentally determines transient dynamics of terrestrial C storage under global change is still not very clear. Here we develop a new framework for understanding transient dynamics of terrestrial C storage through mathematical analysis and numerical experiments. Our analysis indicates that the ultimate force driving ecosystem C storage change is the C storage capacity, which is jointly determined by ecosystem C input (e.g., net primary production, NPP) and residence time. Since both C input and residence time vary with time, the C storage capacity is time-dependent and acts as a moving attractor that actual C storage chases. The rate of change in C storage is proportional to the C storage potential, which is the difference between the current storage and the storage capacity. The C storage capacity represents instantaneous responses of the land C cycle to external forcing, whereas the C storage potential represents the internal capability of the land C cycle to influence the C change trajectory in the next time step. The influence happens through redistribution of net C pool changes in a network of pools with different residence times. Moreover, this and our other studies have demonstrated that one matrix equation can replicate simulations of most land C cycle models (i.e., physical emulators). As a result, simulation outputs of those models can be placed into a three-dimensional (3-D) parameter space to measure their differences. The latter can be decomposed into traceable components to track the origins of model uncertainty. In addition, the physical emulators make data assimilation computationally feasible so that both C flux- and pool-related datasets can be used to better constrain model predictions of land C sequestration. Altogether, this new mathematical framework offers new approaches to understanding, evaluating, diagnosing, and improving land C cycle models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Searching for fat tails in CRISPR-Cas systems: Data analysis and mathematical modeling

Understanding CRISPR-Cas systems—the adaptive defence mechanism that about half of bacterial species and most of archaea use to neutralise viral attacks—is important for explaining the biodiversity observed in the microbial world as well as for editing animal and plant genomes effectively. The CRISPR-Cas system learns from previous viral infections and integrates small pieces from phage genomes called spacers into the microbial genome. The resulting library of spacers collected in CRISPR arrays is then compared with the DNA of potential invaders. One of the most intriguing and least well understood questions about CRISPR-Cas systems is the distribution of spacers across the microbial population. Here, using empirical data, we show that the global distribution of spacer numbers in CRISPR arrays across multiple biomes worldwide typically exhibits scale-invariant power law behaviour, and the standard deviation is greater than the sample mean. We develop a mathematical model of spacer loss and acquisition dynamics which fits observed data from almost four thousand metagenomes well. In analogy to the classical ‘rich-get-richer’ mechanism of power law emergence, the rate of spacer acquisition is proportional to the CRISPR array size, which allows a small proportion of CRISPRs within the population to possess a significant number of spacers. Our study provides an alternative explanation for the rarity of all-resistant super microbes in nature and why proliferation of phages can be highly successful despite the effectiveness of CRISPR-Cas systems.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2016

Is the Multigrid Method Fault Tolerant? The Two-Grid Case

The predicted reduced resiliency of next-generation high performance computers means that it will become necessary to take into account the effects of randomly occurring faults on numerical methods. Further, in the event of a hard fault occurring, a decision has to be made as to what remedial action should be taken in order to resume the execution of the algorithm. The action that is chosen can have a dramatic effect on the performance and characteristics of the scheme. Ideally, the resulting algorithm should be subjected to the same kind of mathematical analysis that was applied to the original, deterministic variant. The purpose of this work is to provide an analysis of the behaviour of the multigrid algorithm in the presence of faults. Multigrid is arguably the method of choice for the solution of large-scale linear algebra problems arising from discretization of partial differential equations and it is of considerable importance to anticipate its behaviour on an exascale machine. The analysis of resilience of algorithms is in its infancy and the current work is perhaps the first to provide a mathematical model for faults and analyse the behaviour of a state-of-the-art algorithm under the model. It is shown that the Two Grid Method fails to be resilient to faults. Attention is then turned to identifying the minimal necessary remedial action required to restore the rate of convergence to that enjoyed by the ideal fault-free method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Is the Multigrid Method Fault Tolerant? The Two-Grid Case

The predicted reduced resiliency of next-generation high performance computers means that it will become necessary to take into account the effects of randomly occurring faults on numerical methods. Further, in the event of a hard fault occurring, a decision has to be made as to what remedial action should be taken in order to resume the execution of the algorithm. The action that is chosen can have a dramatic effect on the performance and characteristics of the scheme. Ideally, the resulting algorithm should be subjected to the same kind of mathematical analysis that was applied to the original, deterministic variant. The purpose of this work is to provide the first rigorous analysis of the behavior of the multigrid algorithm in the presence of faults. Specifically, we prove estimates on the behavior of the Two Grid Method similar to the classical asymptotic results. Multigrid is arguably the method of choice for the solution of large-scale linear algebra problems arising from discretization of partial differential equations, and it is of considerable importance to anticipate its behavior on an exascale machine. The analysis of resilience of algorithms is in its infancy, and the current work is perhaps the first to provide a mathematical model for faults and analyze the behavior of a state-of-the-art algorithm under the model. It is shown that the Two Grid Method fails to be resilient to faults. Attention is then turned to identifying the minimal necessary remedial action required to restore the rate of convergence to that enjoyed by the ideal fault-free method.

Mathematics↗
DOE OSTI2018

In Situ Monitoring of the Growth of Nickel, Manganese, and Cobalt Hydroxide Precursors during Co-Precipitation Synthesis of Li-Ion Cathode Materials

The electrochemical performance of cathode materials for Li-ion batteries depends on the morphology of the material, which, in turn, depends on the synthesis conditions. Very few studies have focused on the impact of process conditions on the final morphology of the cathode particles and analyzed the growth during synthesis. In this paper, the evolution of nickel, manganese, and cobalt hydroxide precursor, Ni 1/3 Mn 1/3 Co 1/3 (OH) 2 , is investigated using a combination of in situ and ex situ techniques during the commonly-used coprecipitation process. These include in situ wide angle X-ray scattering, in-situ ultra-small angle X-ray scattering and ex situ particle size analysis. The growth rate of crystalline Ni 1/3 Mn 1/3 Co 1/3 (OH) 2 primary particle is found to be almost constant, consistent with a mathematical analysis of process. The growth of the Ni 1/3 Mn 1/3 Co 1/3 (OH) 2 secondary particle and its particle size distribution revealed different growth stages for samples prepared at different pH. These techniques are complimented with scanning electron microscopy and electrochemical testing to track the morphology and performance of the hydroxide particle and the subsequent calcined LiNi 1/3 Mn 1/3 Co 1/3 O 2 cathode active material. This study presents insights into the synthesis process and provides a deeper understanding to aid in process optimization.

Cathode precursor↗
DOE OSTI2016

A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties

Calibration parameters in deterministic computer experiments are those attributes that cannot be measured or available in physical experiments. Here, an approach to estimate them by using data from physical experiments and computer simulations. A theoretical framework is given which allows us to study the issues of parameter identifiability and estimation. We define the L 2 -consistency for calibration as a justification for calibration methods. It is shown that a simplified version of the original KO method leads to asymptotically L 2 -inconsistent calibration. This L 2 -inconsistency can be remedied by modifying the original estimation procedure. A novel calibration method, called the L 2 calibration, is proposed and proven to be L 2 -consistent and enjoys optimal convergence rate. Furthermore a numerical example and some mathematical analysis are used to illustrate the source of the L 2 -inconsistency problem.

97 MATHEMATICS AND COMPUTING↗