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At least 1,549 records · Page 86

Software Models Impact Stresses

Generalized Impact Stress Software designed to assist engineers in predicting stresses caused by variety of impacts. Program straightforward, simple to implement on personal computers, "user friendly", and handles variety of boundary conditions applied to struck body being analyzed. Applications include mathematical modeling of motions and transient stresses of spacecraft, analysis of slamming of piston, of fast valve shutoffs, and play of rotating bearing assembly. Provides fast and inexpensive analytical tool for analysis of stresses and reduces dependency on expensive impact tests. Written in FORTRAN 77. Requires use of commercial software package PLOT88.

Hanshaw, Timothy C.↗

Tests characterizing bioprocessor hardware for analytical modeling

The tests outlined in this paper were used to characterize the hardware components of the Salad Machine, a small NASA-developed bioprocessor. The data from these tests are presented, and the methods by which this data can be integrated into system mathematical models are briefly discussed. The subsystems and physical processes discussed include the lighting system, the air loop (condensing heat exchanger and the blower), heat transfer to the surroundings, and leakage. Through this effort it was learned that in the development of a test protocol, care should be taken to order the tests such that environmental parameters, particularly humidity, require as few large adjustments as possible. Sensor calibration and installation take a substantial amount of time, which should be built into the test schedule. Two properties were particularly hard to quantify: the air flow rate and the energy from the lighting system entering into the growth volume. Flow rate can be measured using the appropriate device for the system configuration and airflow. Lighting system radiation level was measured using three methods. The results of these methods varied substantially, putting off conclusive quantification of this value.

Gustavino, S.↗

Flexible Approximation Model Approach for Bi-Level Integrated System Synthesis

Bi-Level Integrated System Synthesis (BLISS) is an approach that allows design problems to be naturally decomposed into a set of subsystem optimizations and a single system optimization. In the BLISS approach, approximate mathematical models are used to transfer information from the subsystem optimizations to the system optimization. Accurate approximation models are therefore critical to the success of the BLISS procedure. In this paper, new capabilities that are being developed to generate accurate approximation models for BLISS procedure will be described. The benefits of using flexible approximation models such as Kriging will be demonstrated in terms of convergence characteristics and computational cost. An approach of dealing with cases where subsystem optimization cannot find a feasible design will be investigated by using the new flexible approximation models for the violated local constraints.

Sobieszczanski-Sobieski, Jaroslaw↗

Multiscale Modeling and Experimental Insights into High-Temperature Soil Biodegradation Dynamics of Semi-Crystalline Poly(Lactic Acid) Nonwoven Fabrics

This study investigates the biodegradation of semi-crystalline poly(lactic acid) (PLA) nonwovens (NWs) in soil at 58 °C using both experimental and mathematical modeling approaches. The model utilizes a system of parabolic diffusion-reaction partial differential equations (PDEs) to elucidate chemical transformations over time and in space. It accounts for phenomena such as the diffusion of water and lactic acid monomers through the polymer matrix and into the surrounding soil, along with their microbial breakdown. It also accounts for the initial PLA crystallinity and predicts its evolution in time. The model is solved numerically for a single filament, and the results were used to shed light on PLA NW transformations observed in soil over a 180-day incubation period. Various characterization techniques, including scanning electron microscopy (SEM), differential scanning calorimetry (DSC), and Raman spectroscopy, were employed to assess morphological changes, crystallinity, and molecular changes in the NWs throughout the experiment. By comparing the experimental data with the model predictions, the hydrolysis rate coefficient was found to be 3.37 × 10 -7 s -1 , while the rate of microbial degradation of lactic acid monomers was faster, of the order of 9.63 × 10 -7 s -1 . The findings highlight the significant role of crystallinity in the biodegradation process. The PLA degradation ceases when no amorphous material remains, and the crystallinity reaches 0.8, as observed in the experiments by day 120. Furthermore, this research contributes to a deeper understanding of PLA biodegradation dynamics and offers insights for effectively managing biodegradable materials in environmental settings.

Diffusion−reaction modeling↗

C-band radar pulse Doppler error: Its discovery, modeling, and elimination

The discovery of a C Band radar pulse Doppler error is discussed and use of the GEOS 3 satellite's coherent transponder to isolate the error source is described. An analysis of the pulse Doppler tracking loop is presented and a mathematical model for the error was developed. Error correction techniques were developed and are described including implementation details.

Krabill, W. B.↗

Pilot modeling, modal analysis, and control of large flexible aircraft

The issues to be addressed are threefold. The first deals with the question of whether dynamic aeroelastic effects can significantly impact piloted flight dynamics. For example, if one were to explore this problem experimentally, what mathematical model would be appropriate to use in the simulation? What modes, for example, should be included in the simulation, or what linear model should be used in the control synthesis? The second question deals with the appropriate design criteria or design objectives. In the case of active control, for example, what would be the design objectives for the control synthesis if aeroelastic effects are a problem? The outline of the topics includes a description of a model analysis methodology aimed at answering the question of the significance of higher order dynamics. Secondly, a pilot vehicle analysis of some experimental data addresses the question of ""What's important in the task?'' The experimental data will be presented briefly, followed by the results of an open-loop modal analysis of the generic vehicle configurations in question. Finally, one of the vehicles will be augmented via active control and the results presented.

Schmidt, D. K.↗

Some further developments in the dynamic modelling and control of the large angle magnetic suspension test fixture

A small-scale laboratory magnetic suspension system, the Large Angle Magnetic Suspension Test Fixture (LAMSTF) has been constructed at NASA Langley Research Center. This paper first presents some recent developments in the mathematical modelling of the system, particularly in the area of eddy current effects. It is shown that these effects are significant, but may be amenable to modelling and measurement. Next, a theoretical framework is presented, together with a comparison of computed and experimental data. Finally, some control aspects are discussed, together with illustration that the major design objective of LAMSTF - a controlled 360 deg rotation about the vertical axis, has been accomplished.

Britcher, Colin P.↗

An analytic study of near terminal area optimal sequencing and flow control techniques

Optimal flow control and sequencing of air traffic operations in the near terminal area are discussed. The near terminal area model is based on the assumptions that the aircraft enter the terminal area along precisely controlled approach paths and that the aircraft are segregated according to their near terminal area performance. Mathematical models are developed to support the optimal path generation, sequencing, and conflict resolution problems.

Park, S. K.↗

A fixed tilt solar collector employing reversible vee-trough reflectors and vacuum tube receivers for solar heating and cooling systems

The usefulness of vee-trough concentrators in improving the efficiency and reducing the cost of collectors assembled from evacuated tube receivers was studied in the vee-trough/vacuum tube collector (VTVTC) project. The VTVTC was analyzed rigorously and various mathematical models were developed to calculate the optical performance of the vee-trough concentrator and the thermal performance of the evacuated tube receiver. A test bed was constructed to verify the mathematical analyses and compare reflectors made out of glass, Alzak and aluminized FEP Teflon. Tests were run at temperatures ranging from 95 to 180 C. Vee-trough collector efficiencies of 35 to 40% were observed at an operating temperature of about 175 C. Test results compared well with the calculated values. Predicted daily useful heat collection and efficiency values are presented for a year's duration of operation temperatures ranging from 65 to 230 C. Estimated collector costs and resulting thermal energy costs are presented. Analytical and experimental results are discussed along with a complete economic evaluation.

Selcuk, M. K.↗

Analysis, development and testing of a fixed tilt solar collector employing reversible Vee-Trough reflectors and vacuum tube receivers

The Vee-Trough/Vacuum Tube Collector (VTVTC) aimed to improve the efficiency and reduce the cost of collectors assembled from evacuated tube receivers. The VTVTC was analyzed rigorously and a mathematical model was developed to calculate the optical performance of the vee-trough concentrator and the thermal performance of the evacuated tube receiver. A test bed was constructed to verify the mathematical analyses and compare reflectors made out of glass, Alzak and aluminized GEB Teflon. Tests were run at temperatures ranging from 95 to 180 C during the months of April, May, June, July and August 1977. Vee-trough collector efficiencies of 35-40 per cent were observed at an operating temperature of about 175 C. Test results compared well with the calculated values. Test data covering a complete day are presented for selected dates throughout the test season. Predicted daily useful heat collection and efficiency values are presented for a year's duration at operation temperatures ranging from 65 to 230 C. Estimated collector costs and resulting thermal energy costs are presented. Analytical and experimental results are discussed along with an economic evaluation.

Selcuk, M. K.↗

Aircraft geometry verification with enhanced computer-generated displays

A method for visual verification of aerodynamic geometries using computer-generated, color-shaded images is described. The mathematical models representing aircraft geometries are created for use in theoretical aerodynamic analyses and in computer-aided manufacturing. The aerodynamic shapes are defined using parametric bi-cubic splined patches. This mathematical representation is then used as input to an algorithm that generates a color-shaded image of the geometry. A discussion of the techniques used in the mathematical representation of the geometry and in the rendering of the color-shaded display is presented. The results include examples of color-shaded displays, which are contrasted with wire-frame-type displays. The examples also show the use of mapped surface pressures in terms of color-shaded images of V/STOL fighter/attack aircraft and advanced turboprop aircraft.

Cozzolongo, J. V.↗

Finite Element Analysis of a Deployable Space Structure

The dynamic characteristics of the Solar Array Flight Experiment (SAFE) structure during deployment and retraction are investigated. The SAFE structure consists of a deployable mast with an attached solar blanket designed with accordion type folds to permit packaging in a small volume. The planar form of the blanket geometry during deployment is maintained by a blanket tension/guidewire system. Structurally, the mast is modeled as an Euler beam column with inplane and out of plane bending and finite torsional stiffness. For out of plane motion, the blanket is modeled as a distributed mass uniformly supported by the three guidewires. For inplane motion the blanket displacements are assumed to vary linearly from the mast base to the mast tip. The mathematical model uses a virtual work formulation, required because the axial loading on the mast is nonconservative, combined with assumed beam modes to derive the differential equations of motion. Consideration of the time dependent boundary conditions results in an infinite set of ODE with time dependent coefficients. Finally, correlation of mast tip accelerations to mast base bending moments for specified modal motions are indicated.

Weeks, G. E.↗

Manual of phosphoric acid fuel cell power plant optimization model and computer program

An optimized cost and performance model for a phosphoric acid fuel cell power plant system was derived and developed into a modular FORTRAN computer code. Cost, energy, mass, and electrochemical analyses were combined to develop a mathematical model for optimizing the steam to methane ratio in the reformer, hydrogen utilization in the PAFC plates per stack. The nonlinear programming code, COMPUTE, was used to solve this model, in which the method of mixed penalty function combined with Hooke and Jeeves pattern search was chosen to evaluate this specific optimization problem.

Lu, C. Y.↗

Model description document for a computer program for the emulation/simulation of a space station environmental control and life support system (ESCM)

Emulation/Simulation Computer Model (ESCM) computes the transient performance of a Space Station air revitalization subsystem with carbon dioxide removal provided by a solid amine water desorbed subsystem called SAWD. This manual describes the mathematical modeling and equations used in the ESCM. For the system as a whole and for each individual component, the fundamental physical and chemical laws which govern their operations are presented. Assumptions are stated, and when necessary, data is presented to support empirically developed relationships.

Yanosy, James L.↗

Spiking Neurons for Analysis of Patterns

Artificial neural networks comprising spiking neurons of a novel type have been conceived as improved pattern-analysis and pattern-recognition computational systems. These neurons are represented by a mathematical model denoted the state-variable model (SVM), which among other things, exploits a computational parallelism inherent in spiking-neuron geometry. Networks of SVM neurons offer advantages of speed and computational efficiency, relative to traditional artificial neural networks. The SVM also overcomes some of the limitations of prior spiking-neuron models. There are numerous potential pattern-recognition, tracking, and data-reduction (data preprocessing) applications for these SVM neural networks on Earth and in exploration of remote planets. Spiking neurons imitate biological neurons more closely than do the neurons of traditional artificial neural networks. A spiking neuron includes a central cell body (soma) surrounded by a tree-like interconnection network (dendrites). Spiking neurons are so named because they generate trains of output pulses (spikes) in response to inputs received from sensors or from other neurons. They gain their speed advantage over traditional neural networks by using the timing of individual spikes for computation, whereas traditional artificial neurons use averages of activity levels over time. Moreover, spiking neurons use the delays inherent in dendritic processing in order to efficiently encode the information content of incoming signals. Because traditional artificial neurons fail to capture this encoding, they have less processing capability, and so it is necessary to use more gates when implementing traditional artificial neurons in electronic circuitry. Such higher-order functions as dynamic tasking are effected by use of pools (collections) of spiking neurons interconnected by spike-transmitting fibers. The SVM includes adaptive thresholds and submodels of transport of ions (in imitation of such transport in biological neurons). These features enable the neurons to adapt their responses to high-rate inputs from sensors, and to adapt their firing thresholds to mitigate noise or effects of potential sensor failure. The mathematical derivation of the SVM starts from a prior model, known in the art as the point soma model, which captures all of the salient properties of neuronal response while keeping the computational cost low. The point-soma latency time is modified to be an exponentially decaying function of the strength of the applied potential. Choosing computational efficiency over biological fidelity, the dendrites surrounding a neuron are represented by simplified compartmental submodels and there are no dendritic spines. Updates to the dendritic potential, calcium-ion concentrations and conductances, and potassium-ion conductances are done by use of equations similar to those of the point soma. Diffusion processes in dendrites are modeled by averaging among nearest-neighbor compartments. Inputs to each of the dendritic compartments come from sensors. Alternatively or in addition, when an affected neuron is part of a pool, inputs can come from other spiking neurons. At present, SVM neural networks are implemented by computational simulation, using algorithms that encode the SVM and its submodels. However, it should be possible to implement these neural networks in hardware: The differential equations for the dendritic and cellular processes in the SVM model of spiking neurons map to equivalent circuits that can be implemented directly in analog very-large-scale integrated (VLSI) circuits.

Huntsberger, Terrance↗

The Differential Equations That Model Diseases

In this brief tutorial, I will describe the simplest way of modeling a deadly infectious disease, such as COVID-19. I will show that at early times, the disease grows exponentially, but at late times, falls off like a Bell curve. I will solve the equations numerically with Python. A common mathematical model is the so-called compartmental model, where diseases can move people between "categories" such as healthy, infectious, or truly sick. This is a large, well established field and there are many good resources on this topic. I started with the SIAM review article The mathematics of infectious diseases. However, there are many excellent textbooks and more modern reviews as well.

60 APPLIED LIFE SCIENCES↗

Ion exchange behavior of astatine and bismuth

Astatine and bismuth sorption on several ion exchange resins from nitric acid media has been studied. This work covers commercially available resins Dowex 50 × 4, MP thiol, Dowex 1 × 8, and TEVA. One of the main advantages of using ion exchangers for astatine separation and purification is the absence of any organic media in the effluent in comparison with extraction chromatography resins. The behavior of the above-mentioned metals was investigated in up to 4 M HNO 3 solutions. The determined distribution coefficients are greater than 1 for all the resins studied, reaching 10 4 for MP thiol and TEVA resins. The interaction of nitric acid with an anion exchanger in Cl-form results in an exchange reaction, where AtO + chloro complexes can form. To understand the astatine behavior under these conditions, stability constants of AtOCl and AtOCl 2 – complexes have been reevaluated and discrepancy in the literature values has been eliminated. For each resin a thermodynamic model has been developed to suggest a possible mechanism of astatine sorption. Literature and new experimental data on bismuth sorption by studying resins in nitric acid media have been reviewed and a mathematical model to describe its behavior has been suggested. Furthermore, a ratio of corresponding fit functions of At and Bi assigned to the same resin and acidity has been used to estimate the separation factors of these elements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ocean modelling on the CYBER 205 at GFDL

At the Geophysical Fluid Dynamics Laboratory, research is carried out for the purpose of understanding various aspects of climate, such as its variability, predictability, stability and sensitivity. The atmosphere and oceans are modelled mathematically and their phenomenology studied by computer simulation methods. The present state-of-the-art in the computer simulation of large scale oceans on the CYBER 205 is discussed. While atmospheric modelling differs in some aspects, the basic approach used is similar. The equations of the ocean model are presented along with a short description of the numerical techniques used to find their solution. Computational considerations and a typical solution are presented in section 4.

Cox, M.↗