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Results for “Mathematical Model”

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 1,099 records · Page 61
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Model selection and parameter estimation in tumor growth models using approximate Bayesian computation-ABC

Cancer is one of the most fatal diseases in the world. Governments and researchers from various areas have continuously concentrated efforts to better understand the disease and propose diagnostic and treatment techniques. The use of mathematical models of tumor growth is of great importance for the development of such techniques. Due to the variety of models nowadays available in the literature, the problems of model selection and parameter estimation come into picture, aiming at suitably predicting the patient’s status of the disease. As the available data on dependent variables of existing models might not justify the use of common likelihood functions, approximate Bayesian computation (ABC) becomes a very attractive tool for model selection and model calibration (parameter estimation) in tumor growth models. In the present study, a Monte Carlo approximate Bayesian computation (ABC) algorithm is applied to select among competing models of tumor growth, with and without chemotherapy treatment. Simulated measurements are used in this work. The results obtained show that the algorithm correctly selects the model and estimates the parameters used to generate the simulated measurements.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Development and Evaluation of Occupancy-Aware Model Predictive Control for Residential Building Energy Efficiency and Occupant Comfort

The residential sector accounts for 25% of global primary energy consumption. Two methods have previously been proposed to reduce residential energy use associated with the provision of occupant thermal comfort: 1. Occupancy-based HVAC control, operating systems only during confirmed occupancy, and 2. model predictive control (MPC), harnessing a mathematical model and forecasts to find optimal operating strategies. Previous studies estimate the average energy savings of the two methods individually in the range of 21% and 16%, respectively. The research presented herein was carried out to evaluate the energy savings potential in residential buildings by combining both approaches across different climates, house vintages, and occupancy patterns. Occupancy and eight different physical modalities (e.g. CO2 and VOC) data were collected from five homes for time periods of 4–9 weeks. Collected data sets were used to train occupancy prediction models suggested by an extensive literature survey of occupancy model types. The trained prediction models were combined with MPC and detailed EnergyPlus building simulation models to evaluate residential building performance in terms of annual energy savings and thermal comfort, along with discomfort exceedance metrics. Multiple home types and regions were analyzed to understand regional and climate-dependent potential. Based on actual field data, the occupancy models had a prediction inaccuracy between 8% and 35% across the investigated homes. Average occupancy for the collected data ranged from 56% to 86%, a typical range reported in the literature. Building simulations were conducted for three control scenarios: conventional thermostatic control, occupancy-based, and occupancy-based MPC. The results indicate that all advanced strategies improve upon the conventional control, with some scenarios cutting energy use in half with only occasional incurrence of discomfort. The findings indicate that occupancy-aware model predictive residential building control has the potential to drastically reduce energy use and associated emissions while maintaining occupant comfort for both new and existing buildings.

ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION↗
DOE OSTI2023

Catalyst: Fast and flexible modeling of reaction networks

We introduce Catalyst.jl, a flexible and feature-filled Julia library for modeling and high-performance simulation of chemical reaction networks (CRNs). Catalyst supports simulating stochastic chemical kinetics (jump process), chemical Langevin equation (stochastic differential equation), and reaction rate equation (ordinary differential equation) representations for CRNs. Through comprehensive benchmarks, we demonstrate that Catalyst simulation runtimes are often one to two orders of magnitude faster than other popular tools. More broadly, Catalyst acts as both a domain-specific language and an intermediate representation for symbolically encoding CRN models as Julia-native objects. This enables a pipeline of symbolically specifying, analyzing, and modifying CRNs; converting Catalyst models to symbolic representations of concrete mathematical models; and generating compiled code for numerical solvers. Leveraging ModelingToolkit.jl and Symbolics.jl, Catalyst models can be analyzed, simplified, and compiled into optimized representations for use in numerical solvers. Finally, we demonstrate Catalyst’s broad extensibility and composability by highlighting how it can compose with a variety of Julia libraries, and how existing open-source biological modeling projects have extended its intermediate representation.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1984

Computer-Aided Geometry Modeling

Techniques in computer-aided geometry modeling and their application are addressed. Mathematical modeling, solid geometry models, management of geometric data, development of geometry standards, and interactive and graphic procedures are discussed. The applications include aeronautical and aerospace structures design, fluid flow modeling, and gas turbine design.

John N. Shoosmith↗
NASA NTRS2008

Measuring Positions of Objects using Two or More Cameras

An improved method of computing positions of objects from digitized images acquired by two or more cameras (see figure) has been developed for use in tracking debris shed by a spacecraft during and shortly after launch. The method is also readily adaptable to such applications as (1) tracking moving and possibly interacting objects in other settings in order to determine causes of accidents and (2) measuring positions of stationary objects, as in surveying. Images acquired by cameras fixed to the ground and/or cameras mounted on tracking telescopes can be used in this method. In this method, processing of image data starts with creation of detailed computer- aided design (CAD) models of the objects to be tracked. By rotating, translating, resizing, and overlaying the models with digitized camera images, parameters that characterize the position and orientation of the camera can be determined. The final position error depends on how well the centroids of the objects in the images are measured; how accurately the centroids are interpolated for synchronization of cameras; and how effectively matches are made to determine rotation, scaling, and translation parameters. The method involves use of the perspective camera model (also denoted the point camera model), which is one of several mathematical models developed over the years to represent the relationships between external coordinates of objects and the coordinates of the objects as they appear on the image plane in a camera. The method also involves extensive use of the affine camera model, in which the distance from the camera to an object (or to a small feature on an object) is assumed to be much greater than the size of the object (or feature), resulting in a truly two-dimensional image. The affine camera model does not require advance knowledge of the positions and orientations of the cameras. This is because ultimately, positions and orientations of the cameras and of all objects are computed in a coordinate system attached to one object as defined in its CAD model.

Klinko, Steve↗
DOE OSTI2017

A Gibbs Energy Minimization Approach for Modeling of Chemical Reactions in a Basic Oxygen Furnace

In modern steelmaking, the decarburization of hot metal is converted into steel primarily in converter processes, such as the basic oxygen furnace. The objective of this work was to develop a new mathematical model for top blown steel converter, which accounts for the complex reaction equilibria in the impact zone, also known as the hot spot, as well as the associated mass and heat transport. An in-house computer code of the model has been developed in Matlab. The main assumption of the model is that all reactions take place in a specified reaction zone. The mass transfer between the reaction volume, bulk slag, and metal determine the reaction rates for the species. The thermodynamic equilibrium is calculated using the partitioning of Gibbs energy (PGE) method. The activity model for the liquid metal is the unified interaction parameter model and for the liquid slag the modified quasichemical model (MQM). The MQM was validated by calculating iso-activity lines for the liquid slag components. The PGE method together with the MQM was validated by calculating liquidus lines for solid components. The results were compared with measurements from literature. The full chemical reaction model was validated by comparing the metal and slag compositions to measurements from industrial scale converter. The predictions were found to be in good agreement with the measured values. Furthermore, the accuracy of the model was found to compare favorably with the models proposed in the literature. The real-time capability of the proposed model was confirmed in test calculations.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Rich Dynamics of a General Producer–Grazer Interaction Model under Shared Multiple Resource Limitations

Organism growth is often determined by multiple resources interdependently. However, growth models based on the Droop cell quota framework have historically been built using threshold formulations, which means they intrinsically involve single-resource limitations. In addition, it is a daunting task to study the global dynamics of these models mathematically, since they employ minimum functions that are non-smooth (not differentiable). To provide an approach to encompass interactions of multiple resources, we propose a multiple-resource limitation growth function based on the Droop cell quota concept and incorporate it into an existing producer–grazer model. The formulation of the producer’s growth rate is based on cell growth process time-tracking, while the grazer’s growth rate is constructed based on optimal limiting nutrient allocation in cell transcription and translation phases. We show that the proposed model captures a wide range of experimental observations, such as the paradox of enrichment, the paradox of energy enrichment, and the paradox of nutrient enrichment. Together, our proposed formulation and the existing threshold formulation provide bounds on the expected growth of an organism. Moreover, the proposed model is mathematically more tractable, since it does not use the minimum functions as in other stoichiometric models.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2018

Determining the Force Exerted by a Stepped Punch

The relative pressure in the cold extrusion of hollow cylindrical aluminum- and copper-alloy parts by a stepped punch is determined experimentally. A mathematical model of the process is derived.

42 ENGINEERING↗