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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Mathematical Modeling For Control Of A Flexible Manipulator

Improved method of mathematical modeling of dynamics of flexible robotic manipulators developed for use in controlling motions of manipulators. Involves accounting for effect, upon modes of vibration of manipulator, of changes in configuration of manipulator and manipulated payload(s). Flexible manipulator has one or more long, slender articulated link(s), like those used in outer space, method also applicable to terrestrial industrial robotic manipulators with relatively short, stiff links, or to such terrestrial machines as construction cranes.

Hu, Anren↗
NASA NTRS2007

Whole-body mathematical model for simulating intracranial pressure dynamics

A whole-body mathematical model (10) for simulating intracranial pressure dynamics. In one embodiment, model (10) includes 17 interacting compartments, of which nine lie entirely outside of intracranial vault (14). Compartments (F) and (T) are defined to distinguish ventricular from extraventricular CSF. The vasculature of the intracranial system within cranial vault (14) is also subdivided into five compartments (A, C, P, V, and S, respectively) representing the intracranial arteries, capillaries, choroid plexus, veins, and venous sinus. The body's extracranial systemic vasculature is divided into six compartments (I, J, O, Z, D, and X, respectively) representing the arteries, capillaries, and veins of the central body and the lower body. Compartments (G) and (B) include tissue and the associated interstitial fluid in the intracranial and lower regions. Compartment (Y) is a composite involving the tissues, organs, and pulmonary circulation of the central body and compartment (M) represents the external environment.

Lakin, William D.↗
DOE OSTI2013

Validation of mathematical models for the prediction of organs-at-risk dosimetric metrics in high-dose-rate gynecologic interstitial brachytherapy

Purpose: Given the complicated nature of an interstitial gynecologic brachytherapy treatment plan, the use of a quantitative tool to evaluate the quality of the achieved metrics compared to clinical practice would be advantageous. For this purpose, predictive mathematical models to predict the D{sub 2cc} of rectum and bladder in interstitial gynecologic brachytherapy are discussed and validated.Methods: Previous plans were used to establish the relationship between D2cc and the overlapping volume of the organ at risk with the targeted area (C0) or a 1-cm expansion of the target area (C1). Three mathematical models were evaluated: D{sub 2cc}=α*C{sub 1}+β (LIN); D{sub 2cc}=α– exp(–β*C{sub 0}) (EXP); and a mixed approach (MIX), where both C{sub 0} and C{sub 1} were inputs of the model. The parameters of the models were optimized on a training set of patient data, and the predictive error of each model (predicted D{sub 2cc}− real D{sub 2cc}) was calculated on a validation set of patient data. The data of 20 patients were used to perform a K-fold cross validation analysis, with K = 2, 4, 6, 8, 10, and 20.Results: MIX was associated with the smallest mean prediction error <6.4% for an 18-patient training set; LIN had an error <8.5%; EXP had an error <8.3%. Best case scenario analysis shows that an error ≤5% can be achieved for a ten-patient training set with MIX, an error ≤7.4% for LIN, and an error ≤6.9% for EXP. The error decreases with the increase in training set size, with the most marked decrease observed for MIX.Conclusions: The MIX model can predict the D{sub 2cc} of the organs at risk with an error lower than 5% with a training set of ten patients or greater. The model can be used in the development of quality assurance tools to identify treatment plans with suboptimal sparing of the organs at risk. It can also be used to improve preplanning and in the development of real-time intraoperative planning tools.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2014

Mathematical model of testing of pipeline integrity by thermal fields

Thermal fields testing at the ground surface above a pipeline are considered. One method to obtain and investigate an ideal thermal field in different environments is a direct numerical simulation of heat transfer processes taking into account the most important physical factors. In the paper a mathematical model of heat propagation from an underground source is described with accounting of physical factors such as filtration of water in soil and solar radiation. Thermal processes are considered in 3D origin where the heat source is a pipeline with constant temperature and non-uniform isolated shell (with 'damages'). This problem leads to solution of heat diffusivity equation with nonlinear boundary conditions. Approaches to analysis of thermal fields are considered to detect damages.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2019

Mathematical modeling in cancer nanomedicine: a review

Cancer continues to be among the leading healthcare problems worldwide, and efforts continue not just to find better drugs, but also better drug delivery methods. The need for delivering cytotoxic agents selectively to cancerous cells, for improved safety and efficacy, has triggered the application of nanotechnology in medicine. This effort has provided drug delivery systems that can potentially revolutionize cancer treatment. Nanocarriers, due to their capacity for targeted drug delivery, can shift the balance of cytotoxicity from healthy to cancerous cells. The field of cancer nanomedicine has made significant progress, but challenges remain that impede its clinical translation. Several biophysical barriers to the transport of nanocarriers to the tumor exist, and a much deeper understanding of nano-bio interactions is necessary to change the status quo. Mathematical modeling has been instrumental in improving our understanding of the physicochemical and physiological underpinnings of nanomaterial behavior in biological systems. Here, we present a comprehensive review of literature on mathematical modeling works that have been and are being employed towards a better understanding of nano-bio interactions for improved tumor delivery efficacy.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1989

Incorporation of measured photosynthetic rate in a mathematical model for calculation of non-structural saccharide concentration

A simple mathematical model for calculating the concentration of mobile carbon skeletons in the shoot of soya bean plants [Glycine max (L.) Merrill cv. Ransom] was built to examine the suitability of measured net photosynthetic rates (PN) for calculation of saccharide flux into the plant. The results suggest that either measurement of instantaneous PN overestimated saccharide influx or respiration rates utilized in the model were underestimated. If neither of these is the case, end-product inhibition of photosynthesis or waste respiration through the alternative pathway should be included in modelling of CH2O influx or efflux; and even if either of these is the case, the model output at a low coefficient of leaf activity indicates that PN still may be controlled by either end-product inhibition or alternative respiration.

NASA Program CELSS↗
NASA NTRS1989

An investigation of a mathematical model of an optically pumped Ti(3+):Al2O3 laser system

During the last several years, solid state lasers were developed that have the potential for meeting rigorous performance requirements for space-based remote sensing of the atmosphere. In order to design a stable and efficient laser and to understand the effect on laser output of changes in the physical and design parameters, an understanding of the development of the dynamical processes of the laser is necessary. Typically, the dynamical processes in a laser system are investigated via rate equations describing the evolution of the occupancy in the electronic levels and of the photon density in the laser cavity. There are two approaches to this type of study. Most often, for the sake of simplicity, the spatial variations of the dynamic variables in the laser system are disregarded and the mathematical model consists of a system of first order nonlinear ordinary differential equations (ODE). The second approach is to take into account both spatial and temporal variations in the dynamic variables in the laser cavity. The resulting model consists of a first order semilinear system of partial differential equations (PDE). The model which was studied was studied was generic in the sense that it was a four-level laser system, but the parameters used in the numerical study were specific to Titanium-doped sapphire. For simplicity, a constant, spatially uniform pumping scheme was considered. In addition, a simplification of the model was made so that it treats a single lasing wavelength with a narrow bandwidth. The purpose was to investigate both versions of the mathematical model and to determine whether the numerical solutions are similar both qualitatively and quantitatively. The systems of ordinary differential equations were solved numerically using a Runge-Kutta-Fehlberg algorithm which was very efficient for typical values of the physical parameters. A numerical scheme, based on the Modified Euler method, for computing solutions to the system of partial differential equations was developed and implemented. The PDE model was solved numerically at the expense of greatly increased computer time.

Roberts, Lila F.↗
DOE OSTI2018

A mathematical model of tree harvesting in age-structured forests subject to beetle infestations

In this paper, we investigate a mathematical model for age-structured forest–beetle interactions that includes harvesting of trees. The aim is to broaden the understanding of the synergistic effects of harvesting and insect infestation on the age structure of the forests and the harvesting benefit. In the first part of this study, we consider different scenarios of the forest infestation by beetles and observe that the quantitative age profile of the forest depends significantly on whether the beetle population is in its endemic or epidemic states. In the second part, we also include harvesting of the forest trees and analyze two different harvesting strategies: cutting all trees older than a certain age, and cutting a fixed proportion of trees older than a certain age. Numerical simulations are implemented to determine the optimal cutting age for both harvesting strategies. The numerical simulations reveal that, independent of the steady state of the beetle population (that is, no beetles, endemic or epidemic state) clear cutting all trees older than a given age provides a higher harvesting benefit. Our numerical simulations further indicate that to obtain a fixed harvesting yield, a forest under a beetle epidemic state has to be cut at a younger age than if the forest were at an endemic beetle state or a no-beetle state.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1971

Mathematical models of the open magnetosphere - Application to dayside auroras.

Two static mathematical models of the open or Dungey model of the magnetosphere are constructed. The process of construction is similar to that for early closed magnetosphere models, such as the Taylor-Hones model. The first model in fact is simply an addition of an interplanetary field in arbitrary direction to a Taylor-Hones image dipole model. In order to preserve the shape of the magnetosphere at high latitudes, and to partially exclude the exterior field, another model is constructed with the magnetopause approximated by a diamagnetic sphere. We find that there are some interplanetary field lines connected to the earth for all orientations of the interplanetary field other than strictly northward, and that the maximum number of connected field lines occurs with a due southward field. For an average spiral hose angle of the interplanetary field, the dayside neutral point occurs on the magnetopause at about 10 o'clock local time. Dayside auroras, convection patterns, and other phenomena may exhibit symmetry about this local time. For a positive (negative) interplanetary field sector, energetic, anisotropic particle fluxes should have direct access to the northern (southern) polar caps, as is supported by many recent observations.

Forbes, T. G.↗
NASA NTRS1972

Mathematical model of a flexible space shuttle vehicle

The development of a mathematical model of the lateral motion of a flexible space shuttle vehicle during ascent is described. The model was developed to perform control system synthesis using stochastic constrained optimization techniques. The goals of the control system synthesis are to demonstrate the applicability of the techniques and to discover any problems peculiar to the flexible nature of a shuttle vehicle. The equations of motion are derived. A brief description of the generation of numerical data is given. Explicit definitions and numerical values of trajectory data and coefficients appearing in the equations of motion are included.

Harvey, C. A.↗
NASA NTRS1982

A mathematical model of a single main rotor helicopter for piloted simulation

A mathematical model, suitable for piloted simulation of the flying qualities of helicopters, is a nonlinear, total force and moment model of a single main rotor helicopter. The model has ten degrees of freedom: six rigid body, three rotor flapping, and the rotor rotational degrees of freedom. The rotor model assumes rigid blades with rotor forces and moments radially integrated and summed about the azimuth. The fuselage aerodynamic model uses a detailed representation over a nominal angle of attack and sideslip range of + or - 15 deg., as well as a simplified curve fit at large angles of attack or sideslip. Stabilizing surface aerodynamics are modeled with a lift curve slope between stall limits and a general curve fit for large angles of attack. A generalized stability and control augmentation system is described. Additional computer subroutines provide options for a simplified engine/governor model, atmospheric turbulence, and a linearized six degree of freedom dynamic model for stability and control analysis.

Talbot, P. D.↗
NASA NTRS1990

A flight-dynamic helicopter mathematical model with a single flap-lag-torsion main rotor

A mathematical model of a helicopter system with a single main rotor that includes rigid, hinge-restrained rotor blades with flap, lag, and torsion degrees of freedom is described. The model allows several hinge sequences and two offsets in the hinges. Quasi-steady Greenberg theory is used to calculate the blade-section aerodynamic forces, and inflow effects are accounted for by using three-state nonlinear dynamic inflow model. The motion of the rigid fuselage is defined by six degrees of freedom, and an optional rotor rpm degree of freedom is available. Empennage surfaces and the tail rotor are modeled, and the effect of main-rotor downwash on these elements is included. Model trim linearization, and time-integration operations are described and can be applied to a subset of the model in the rotating or nonrotating coordinate frame. A preliminary validation of the model is made by comparing its results with those of other analytical and experimental studies. This publication presents the results of research compiled in November 1989.

Takahashi, Marc D.↗
NASA NTRS1992

A mathematical model of a tilt-wing aircraft for piloted simulation

A mathematical model of a tilt-wing aircraft that was used in a piloted, six-degree-of-freedom flight simulation application is described. Two types of control systems developed for the math model are discussed: a conventional, programmed-flap wing-tilt control system and a geared-flap wing-tilt control system. The primary objective was to develop the capability to study tilt-wing aircraft. Experienced Tilt-wing pilots subjectively evaluated the model using programmed-flap control to assess the quality of the simulation. The math model was then applied to study geared-flap control to investigate the possibility of eliminating the need for auxilary pitch-control devices (such as the horizontal tail rotor or tail jet used in earlier tilt-wing designs). This investigation was performed in the moving-base simulation environment, and the vehicle responses with programmed-flap and geared-flap control were compared. The results of the evaluation of the math model are discussed.

Totah, Joseph J.↗
DOE OSTI2013

Is Dynamic Autocrine Insulin Signaling Possible? A Mathematical Model Predicts Picomolar Concentrations of Extracellular Monomeric Insulin within Human Pancreatic Islets

Insulin signaling is essential for β-cell survival and proliferation in vivo. Insulin also has potent mitogenic and anti-apoptotic actions on cultured β-cells, with maximum effect in the high picomolar range and diminishing effect at high nanomolar doses. In order to understand whether these effects of insulin are constitutive or can be subjected to physiological modulation, it is essential to estimate the extracellular concentration of monomeric insulin within an intact islet. Unfortunately, the in vivo concentration of insulin monomers within the islet cannot be measured directly with current technology. Here, we present the first mathematical model designed to estimate the levels of monomeric insulin within the islet extracellular space. Insulin is released as insoluble crystals that exhibit a delayed dissociation into hexamers, dimers, and eventually monomers, which only then can act as signaling ligands. The rates at which different forms of insulin dissolve in vivo have been estimated from studies of peripheral insulin injection sites. We used this and other information to formulate a mathematical model to estimate the local insulin concentration within a single islet as a function of glucose. Model parameters were estimated from existing literature. Components of the model were validated using experimental data, if available. Model analysis predicted that the majority of monomeric insulin in the islet is that which has been returned from the periphery, and the concentration of intra-islet monomeric insulin varies from β50–300 pM when glucose is in the physiological range. Thus, our results suggest that the local concentration of monomeric insulin within the islet is in the picomolar ‘sweet spot’ range of insulin doses that activate the insulin receptor and have the most potent effects on β-cells in vitro. Together with experimental data, these estimations support the concept that autocrine/paracrine insulin signalling within the islet is dynamic, rather than constitutive and saturated.

59 BASIC BIOLOGICAL SCIENCES↗