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At least 883 records · Page 49

Mathematical modeling of the impedance of single and multi-tube AMTEC units

AMTEC power systems are designed for use on extended space missions. During the lifetime of such missions the power available for the spacecraft will depend on the degradation of the system performance. Development of a tool that allows monitoring of the system degradation will provide an aid in dtermining the condition of the power source.

AMTEC modeling↗

General Mission Analysis Tool (GMAT) Mathematical Specifications

The General Mission Analysis Tool (GMAT) is a space trajectory optimization and mission analysis system developed by NASA and private industry in the spirit of the NASA Mission. GMAT contains new technology and is a testbed for future technology development.

Hughes, Steve↗

Mathematical circulatory system model

A system and method of modeling a circulatory system including a regulatory mechanism parameter. In one embodiment, a regulatory mechanism parameter in a lumped parameter model is represented as a logistic function. In another embodiment, the circulatory system model includes a compliant vessel, the model having a parameter representing a change in pressure due to contraction of smooth muscles of a wall of the vessel.

Lakin, William D.↗

Vibration Propagation of Gear Dynamics in a Gear-Bearing-Housing System Using Mathematical Modeling and Finite Element Analysis

Vibration and noise caused by gear dynamics at the meshing teeth propagate through power transmission components to the surrounding environment. This study is devoted to developing computational tools to investigate the vibro-acoustic propagation of gear dynamics through a gearbox using different bearings. Detailed finite element/contact mechanics and boundary element models of the gear/bearing/housing system are established to compute the system vibration and noise propagation. Both vibration and acoustic models are validated by experiments including the vibration modal testing and sound field measurements. The effectiveness of each bearing type to disrupt vibration propagation is speed-dependent. Housing plays an important role in noise radiation .It, however, has limited effects on gear dynamics. Bearings are critical components in drivetrains. Accurate modeling of rolling element bearings is essential to assess vibration and noise of drivetrain systems. This study also seeks to fully describe the vibro-acoustic propagation of gear dynamics through a power-transmission system using rolling element and fluid film wave bearings. Fluid film wave bearings, which have higher damping than rolling element bearings, could offer an energy dissipation mechanism that reduces the gearbox noise. The effectiveness of each bearing type to disrupt vibration propagation in explored using multi-body computational models. These models include gears, shafts, rolling element and fluid film wave bearings, and the housing. Radiated noise is mapped from the gearbox surface to surrounding environment. The effectiveness of rolling element and fluid film wave bearings in breaking the vibro-acoustic propagation path from the gear to the housing is investigated.

Parker, Robert G.↗

Free-Energy Calculations. A Mathematical Perspective

Ion channels are pore-forming assemblies of transmembrane proteins that mediate and regulate ion transport through cell walls. They are ubiquitous to all life forms. In humans and other higher organisms they play the central role in conducting nerve impulses. They are also essential to cardiac processes, muscle contraction and epithelial transport. Ion channels from lower organisms can act as toxins or antimicrobial agents, and in a number of cases are involved in infectious diseases. Because of their important and diverse biological functions they are frequent targets of drug action. Also, simple natural or synthetic channels find numerous applications in biotechnology. For these reasons, studies of ion channels are at the forefront of biophysics, structural biology and cellular biology. In the last decade, the increased availability of X-ray structures has greatly advanced our understanding of ion channels. However, their mechanism of action remains elusive. This is because, in order to assist controlled ion transport, ion channels are dynamic by nature, but X-ray crystallography captures the channel in a single, sometimes non-native state. To explain how ion channels work, X-ray structures have to be supplemented with dynamic information. In principle, molecular dynamics (MD) simulations can aid in providing this information, as this is precisely what MD has been designed to do. However, MD simulations suffer from their own problems, such as inability to access sufficiently long time scales or limited accuracy of force fields. To assess the reliability of MD simulations it is only natural to turn to the main function of channels - conducting ions - and compare calculated ionic conductance with electrophysiological data, mainly single channel recordings, obtained under similar conditions. If this comparison is satisfactory it would greatly increase our confidence that both the structures and our computational methodologies are sufficiently accurate. Channel conductance, defined as the ratio of ionic current through the channel to applied voltage, can be calculated in MD simulations by way of applying an external electric field to the system and counting the number of ions that traverse the channel per unit time. If the current is small, a voltage significantly higher than the experimental one needs to be applied to collect sufficient statistics of ion crossing events. Then, the calculated conductance has to be extrapolated to the experimental voltage using procedures of unknown accuracy. Instead, we propose an alternative approach that applies if ion transport through channels can be described with sufficient accuracy by the one-dimensional diffusion equation in the potential given by the free energy profile and applied voltage. Then, it is possible to test the assumptions of the equation, recover the full voltage/current dependence, determine the reliability of the calculated conductance and reconstruct the underlying (equilibrium) free energy profile, all from MD simulations at a single voltage. We will present the underlying theory, model calculations that test this theory and simulations on ion conductance through a channel that has been extensively studied experimentally. To our knowledge this is the first case in which the complete, experimentally measured dependence of the current on applied voltage has been reconstructed from MD simulations.

free energy↗

Theoretical Aeroacoustics: Compiled Mathematical Derivations of Fereidoun 'Feri' Farassat

Dr. Fereidoun 'Feri' Farassat was a theoretical aero-acoustician at the National Aeronautics and Space Administration (NASA) Langley Research Center. This book contains technical derivations, notes, and classes that Dr. Farassat produced during his professional career. The layout of the book has been carefully crafted so that foundational ideas through advanced theories, which altered the technical discipline of aeroacoustics, build upon one another. The book can be used to understand the theories of acoustics and learn one contemporary aeroacoustic prediction approach made popular by Dr. Farassat. Most importantly, this book gives the general reader insight into how one of NASA's best aeroacoustics theoreticians thought, constructed, and solved problems throughout his career.

Miller, Steven A. E.↗

Science, Technology, Engineering, Mathematics Poster

This is a simple poster for Community Day at the Visitor Center. It describes, as an overview, an example of the use of GPS and LiDAR data to determine the loss of scrubjay habitat due to a change in water table.

STEM↗

A Taxonomy-Based Approach to Shed Light on the Babel of Mathematical Models for Rice Simulation

For most biophysical domains, differences in model structures are seldom quantified. Here, we used a taxonomy-based approach to characterise thirteen rice models. Classification keys and binary attributes for each key were identified, and models were categorised into five clusters using a binary similarity measure and the unweighted pair-group method with arithmetic mean. Principal component analysis was performed on model outputs at four sites. Results indicated that (i) differences in structure often resulted in similar predictions and (ii) similar structures can lead to large differences in model outputs. User subjectivity during calibration may have hidden expected relationships between model structure and behaviour. This explanation, if confirmed, highlights the need for shared protocols to reduce the degrees of freedom during calibration, and to limit, in turn, the risk that user subjectivity influences model performance.

model parameterisation↗

New Mathematical Functions for Vacuum System Analysis

A new bivariate function has been found that provides solutions of integrals having the form u (sup minus eta) e (sup u) du which arise when developing predictions for the behavior of pressure within a rigid volume under high vacuum conditions in the presence of venting as well as sources characterized by power law transient decay over the range [0,1] for eta and for u greater than or equal to 0. A few properties of the new function are explored in this work. For instance the eta equals 1/2 case reproduces the Dawson function. In addition, a slight variation of the solution technique reproduces the exponential integral for eta equals 1. The technique used to generate these functions leads to an approach for solving a more general class of nonlinear ordinary differential equations, with the potential for identifying other new functions that solve other integrals.

Dawson Function↗

Advanced Mathematics for Control System Design: Guidance, Navigation, and Control (GN&C) Studies

The study and control of inverted pendulum dynamics is of interest to NASA to better control the stability of a rocket. The different compartments of a rocket can move within a rocket during launch (i.e., rocket fuel slosh) and can affect its overall trajectory. Focusing on the inverted pendulum robot, PENNY, the dynamics are reduced to a simpler model which can prove to be more insightful for deriving more complex models and control laws. From the inverted pendulum bot, we can incorporate complexity into our physical model and approximate to the dynamics of a rocket (i.e., flexible inverted pendulum, multistage pendulum).

Autonomy↗

Calibrating a 3-Axis Accelerometer Instrument with a Less Accurate Calibration Device Part 1: Mathematical Methodology

A three-axis accelerometer instrument (3xAI) can provide the angular attitude of a 3D object using the gravity vector (g) as the sole reference. Calibrating such an instrument requires placing it at known (to some accuracy plus uncertainty) angular articulations with respect to g. This paper will show a potential process for calibrating a 3xAI by using a 2-axis rotary system (calibration device) to provide these articulations. Any calibration device (CD) with such capacity will contain internal misalignments. These misalignments, even if made relatively small or approximated to zero in the kinematics model (KM), can be detrimental to the calibration of the instrument when high measurement accuracy is required. This is especially true if the selected set of articulations chosen for calibration do not include their symmetrical counterpoints (a point where the misalignment has equal magnitude but is opposite in direction to a point chosen). The consequence of not including the combination, point and counterpoint, for any misalignment involved in the calibration, results in a biased instrument. This paper will demonstrate a calibration of the instrument using symbolic math resulting in a closed-form solution of the instrument coefficients. The main objective is to show the impact of all the CD misalignments to the instrument coefficients. This process is the basis for a more sophisticated method (shown in a future paper) for obtaining the instrument coefficients while simultaneously obtaining an estimate of the calibration device internal misalignments.

Angle↗

A Study of the Pope-Osborne Angular Momentum Synthesis Theory (POAMS) Including a Mathematical Reformulation and Validation Experiment

This Technical Memorandum records the results of research performed by NASA MSFC under a Space Act Agreement with Quantum Machines, LLC. (SAA8-1519855), signed July 1, 2015. The Pope-Osborne Angular Momentum Synthesis theory (POAMS) was evaluated and reformulated into a form which predicted a non-Newtonian spin-coupled force used to conceive and perform experiments. Rudimentary and preliminary data appears consistent with the predictions of a spin-coupled force based on the alignment of nucleons, but additional research on the theory and experiments with careful methodologies and measurements needs to be conducted. Experiments with better measurements may be realized if effective methods for inducing nuclear alignment in spin active materials can be devised.

POAMS↗