Stability of attitude control systems acted upon by random perturbations
Mathematical models on stability of attitude control systems acted upon by random perturbation processes
MATHEMATICAL MODEL↗
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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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Optimal control of anthropogenic carbon dioxide emissions through technological options: a modeling study
The anthropogenic emission of carbon dioxide (CO{sub 2}) is the prime culprit for the menace of global warming. To achieve the goal of mitigation of global warming, it is crucial to curb the anthropogenic carbon dioxide emissions. The prime anthropogenic source of CO{sub 2} is fossil fuel burning. In this paper, we propose a nonlinear mathematical model to study the impact of technological options, used for the reduction of CO{sub 2} emissions from fossil fuel burning and industrial processes, on the control of atmospheric CO{sub 2}. In the modeling process, it is assumed that the technological options are implemented to curb the CO{sub 2} emissions from the source at a rate proportional to the anthropogenic CO{sub 2} emissions. Model analysis reveals that the atmospheric level of CO{sub 2} can be effectively reduced by increasing the implementation rate of technological options and their efficiency. The strategies which optimally reduce atmospheric CO{sub 2} levels while minimizing the cost associated with the implementation of technological options are identified using optimal control theory. Numerical simulation has been carried out to illustrate theoretical results.
54 ENVIRONMENTAL SCIENCES↗
A model for closing the inviscid form of the average-passage equation system
A mathematical model is proposed for closing or mathematically completing the system of equations which describes the time average flow field through the blade passages of multistage turbomachinery. These equations referred to as the average passage equation system govern a conceptual model which has proven useful in turbomachinery aerodynamic design and analysis. The closure model is developed so as to insure a consistency between these equations and the axisymmetric through flow equations. The closure model was incorporated into a computer code for use in simulating the flow field about a high speed counter rotating propeller and a high speed fan stage. Results from these simulations are presented.
Adamczyk, J. J.↗
A model for closing the inviscid form of the average-passage equation system
A mathematical model is proposed for closing or mathematically completing the system of equations which describes the time average flow field through the blade passages of multistage turbomachinery. These equations referred to as the average passage equation system govern a conceptual model which has proven useful in turbomachinery aerodynamic design and analysis. The closure model is developed so as to insure a consistency between these equations and the axisymmetric through flow equations. The closure model was incorporated into a computer code for use in simulating the flow field about a high speed counter rotating propeller and a high speed fan stage. Results from these simulations are presented.
Adamczyk, J. J.↗
Ergodic Lagrangian dynamics in a superhero universe
We present a fictional scenario that, while undeniably whimsical, provides the foundation for a unique exercise in extended problem solving, physics analysis, and quantitative model development. Starting with the foundational premise of the Wild Cards shared-world superhero universe, we demonstrate how a variety of concepts appropriate to the advanced undergraduate level—ergodicity, functional analysis, Lagrangian mechanics, and the ever-important simplifying approximation—can be combined into a rich, coherent mathematical model. The goal of this case study is to develop a useful pedagogical exercise in exploring an open-ended research question that presents, at first glance, no clear path forward. Being both eclectic and lengthy, this exercise offers a unique way for students to apply their core physics and mathematics education. It is perhaps best used within a senior honors seminar or within a brief (e.g., January term) elective class.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Optimal Tool Design for Grinding Operations
An algorithm is outlined for the design of abrasive tools of optimal structure for a specific grinding operation, ensuring maximum productivity and minimum cost. Systems analysis is employed. Mathematical models for the design calculation are presented, and an example is given to illustrate the optimization of grinding tools.
42 ENGINEERING↗
A maximum principle re-entry study
Mathematical model of maximum principle of Pontryagin used to find point-to-point reentry trajectory of space vehicle
REENTRY TRAJECTORY↗
Modeling suggests SARS-CoV-2 rebound after nirmatrelvir-ritonavir treatment is driven by target cell preservation coupled with incomplete viral clearance
In a subset of SARS-CoV-2-infected individuals treated with the antiviral nirmatrelvir-ritonavir, the virus rebounds following treatment. The mechanisms driving this rebound are not well understood. We used a mathematical model to describe the longitudinal viral load dynamics of 51 individuals treated with nirmatrelvir-ritonavir, 20 of whom rebounded. Target cell preservation, either by a robust innate immune response or initiation of N-R near the time of symptom onset, coupled with incomplete viral clearance, appears to be the main factor leading to viral rebound. Moreover, the occurrence of viral rebound is likely influenced by the time of treatment initiation relative to the progression of the infection, with earlier treatments leading to a higher chance of rebound. A comparison with an untreated cohort suggests that early treatments with nirmatrelvir-ritonavir may be associated with a delay in the onset of an adaptive immune response. Nevertheless, our model demonstrates that extending the course of nirmatrelvir-ritonavir treatment to a 10-day regimen may greatly diminish the chance of rebound in people with mild-to-moderate COVID-19 and who are at high risk of progression to severe disease. Altogether, our results suggest that in some individuals, a standard 5-day course of nirmatrelvir-ritonavir starting around the time of symptom onset may not completely eliminate the virus. Thus, after treatment ends, the virus can rebound if an effective adaptive immune response has not fully developed. These findings on the role of target cell preservation and incomplete viral clearance also offer a possible explanation for viral rebounds following other antiviral treatments for SARS-CoV-2.
60 APPLIED LIFE SCIENCES↗
Optimization of Tensile and Corrosion Properties of Dissimilar Friction Stir Welded AA2024-7075 Joints
In this work, we performed some joining experiments of dissimilar aluminum alloys AA2024-T351 and AA7075-T651 using friction stir welding (FSW) technique with different process parameters (rotational speed, welding speed and plunge depth). Response surface methodology based on a central composite rotatable design was used to establish the mathematical models predicting the tensile properties and corrosion rate of dissimilar FSW joints with some high confidence level. Analysis of variance method was employed to verify the developed models. Besides, the influences of FSW process parameters on tensile and corrosion properties of joints were analyzed. In order to obtain a desirable combination property of the dissimilar FSW joints, the optimum process parameters after experimental verification were proposed as: rotational speed 1495 rev/min, welding speed 187 mm/min and plunge depth 0.03 mm. This verification illustrated that the developed models are appropriate for the modeling and optimization of process.
36 MATERIALS SCIENCE↗
The prediction of large rocket nozzle material performance using a semi-empirical technique.
Prediction of large rocket nozzle material performance using semiempirical technique, noting mathematical models for internal and external heat and mass transfer
MASS TRANSFER↗
Axial pump rotordynamic study Final report
Mathematical model for predicting rotor dynamic motion phenomena associated with rotor whirl using computer simulation
COMPUTER SIMULATION↗
Parsimonious models of in-host viral dynamics and immune response
Mathematical models of in-host viral dynamics and immune response are a vital tool for patient-specific estimation of the initial viral load, prediction of the course of an infection, etc. The COVID-19 pandemics has given impetus to the development of models with an ever-increasing degree of complexity. We show that one of the most popular models---the Target Cell Limited model---fails the identifiability test, i.e., its parameters cannot be uniquely inferred from readily available data such as viral load measurements. Here, we present a model that is both identifiable and parsimonious according to information criteria. Our model's predictions match both reported observations of COVID-19 patients and predictions of its more complex counterparts.
60 APPLIED LIFE SCIENCES↗
Modal analysis and control of flexible manipulator arms
The possibility of modeling and controlling flexible manipulator arms was examined. A modal approach was used for obtaining the mathematical model and control techniques. The arm model was represented mathematically by a state space description defined in terms of joint angles and mode amplitudes obtained from truncation on the distributed systems, and included the motion of a two link two joint arm. Three basic techniques were used for controlling the system: pole allocation with gains obtained from the rigid system with interjoint feedbacks, Simon-Mitter algorithm for pole allocation, and sensitivity analysis with respect to parameter variations. An improvement in arm bandwidth was obtained. Optimization of some geometric parameters was undertaken to maximize bandwidth for various payload sizes and programmed tasks. The controlled system is examined under constant gains and using the nonlinear model for simulations following a time varying state trajectory.
Neto, O. M.↗
Minimum fuel trajectories for round trip lunar missions
In this work, a study about minimum fuel trajectories in a round trip journey to the Moon is presented. It is assumed that the velocity changes are instantaneous, that is, the propulsion system is capable of delivering impulses such that the fuel consumption is represented by the total velocity increment applied to the space vehicle. It is also assumed that the velocity increments are applied tangentially to the terminal orbits, and, the outgoing trip and the return trip are analyzed separately such that the whole mission is performed with four impulses (two impulses in each trip). The mathematical models used to describe the motion of the space vehicle are three: the lunar patched-conic approximation; the classic planar circular restricted three-body problem, and, the planar bi-circular restricted four-body problem (PBR4BP). For computing the optimal trajectories, the Sequential Gradient-Restoration Algorithm with constraints is used. The influence of the Sun on round trip lunar missions is analyzed through the PBR4BP model. For all models, the trajectories studied are direct ascent maneuvers, and, both the outgoing and return trips are considered. The results obtained through the different models are compared with each other. The optimal results for the PBR4BP model show that a small reduction of the fuel consumption can be achieved if the initial phase angle of the Sun is chosen properly.
79 ASTRONOMY AND ASTROPHYSICS↗
Posiva's Onkalo{sup R} FST (Full-Scale In Situ System Test) - 20051
The FST - Full-scale In Situ System Test - is a unique full-scale demonstration of disposal system in crystalline host rock. The FST was constructed in ONKALO{sup R} demonstration area at the disposal depth of 420 metres, in Posiva's actual final disposal facility at Olkiluoto, Finland. The demonstration has included design, manufacture, installation and comprehensive instrumentation for monitoring the evolution of the disposal system and its components. The demonstration tunnel and experimental deposition holes were excavated in 2010 in ONKALO to address that they can be excavated to meet the requirements set for them. Two experimental deposition holes, bored in the floor of the tunnel, host each a canister surrounded by bentonite clay buffer rings/segments in the holes. Inside the canisters are heating elements to simulate decay heat emitted by spent fuel. The tunnel part used for the test is about 50 m long and it was filled with bentonite clay backfill after the installation of the canisters and buffer components. The tunnel is closed with a steel-reinforced concrete plug. The test is equipped with 500 sensors to monitor early evolution of the system. To forecast the evolution of the system, a mathematical model has been created. (authors)
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
Dynamic behavior of porous electrode systems final report
Mathematical model of flooded porous electrodes under dynamic and static conditions - Methods for measuring porous electrode reaction distribution
MATHEMATICAL MODEL↗
Thermal and chemi-ionization processes in afterburning rocket exhausts.
Mathematical model for thermal and chemi- ionization processes in turbulent nonequilibrium afterburning rocket exhausts plume, studying neutral and charged species distribution
DENSITY DISTRIBUTION↗
Behavior of Titanium Alloys in Aerodynamic Heating of Hypersonic Airplanes
The requirements on the use of titanium alloys used as thermal protection in hypersonic airplanes are considered. The ignition of titanium alloys in aerodynamic heating is analyzed. A mathematical model is proposed for the surface oxidation of the alloys in a high-temperature air flux.
42 ENGINEERING↗