Search NASA⌕ Search

SEARCH · Search NASA

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,261 records · Page 70

Fano resonances based on plasmonic square resonator with high figure of merits and its application in glucose concentrations sensing

A compact plasmonic structure is proposed employing symmetrical metal–insulator-metal (MIM) waveguides coupled to the square resonator for nano-sensing applications, especially for water glucose sensing. Finite difference time domain method is chosen to derivate the output characteristics and magnetic-field distributions. Outcomes illustrate the Fano resonance in the output characteristics can be simply managed by varying the inner and outer lengths and the refractive index of the square cavity. Also, between Fano resonance wavelength and resonator length, a linear behavior exists. These features suggest that physical parameters provide flexibility to propose the structure. Our plasmonic device produces a sensitivity and figure of merit of about 6400 nm/RIU and 1 × 10{sup 4}, respectively. By utilizing the mathematical model for water refractive index, we aim to develop a sensor structure to detect the glucose concentration in water. This designed sensor may discover significant applications in future nanosensing domain.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DC Microgrids Under Denial of Service Attacks: Feasibility and Stability Issues

Distributed control has been extensively studied for a DC microgrid to coordinate multiple grid assets where each asset can generate its own control decisions based on communications within its neighborhood. Nevertheless, such a control strategy usually has a strong dependence on active information exchange and needs to always maintain a pre-determined communication graph. This makes it vulnerable to cyber attacks, especially denial of service (DoS) attacks that block communication channels that effectively change the communication graph. In this paper, we study two potential impacts of DoS attacks: the inability to maintain steady-state and dynamical generation-demand balance, i.e. the feasibility and stability issues. We develop a mathematical model to describe the cyber-induced system steady-state and dynamical performance. The model reveals the impacts of DoS attacks and enables formal analysis. Case studies are shown to verify the proposed work.

41 EE - Solar Energy Technologies Office (EE-4S)↗

Consideration of the Impact of the Environmental Conditions when Designing Heat-Receiving Systems of the Solar Cylindrical Parabolic Modules

The aerohydrodynamic and heat exchange characteristics in the cylindrical heat receiver of a solar cylindrical parabolic concentrating module are investigated. The mathematical model is based on the Navier- Stokes equation system for a laminar flow in a channel. The model is implemented using the control volume method. The created computer algorithm allows carrying out parametric studies and revealing the most rational geometric, dynamic, and power parameters of the process. The proposed model describes the general physical outlines of the heat exchange in a cylindrical heat receiver which allows estimating the influence of the environment—wind velocity, ambient temperature, etc.—on it.

14 SOLAR ENERGY↗

An efficient computational method for characterizing the effects of random surface errors on the average power pattern of reflectors

Based on the works of Ruze (1966) and Vu (1969), a novel mathematical model has been developed to determine efficiently the average power pattern degradations caused by random surface errors. In this model, both nonuniform root mean square (rms) surface errors and nonuniform illumination functions are employed. In addition, the model incorporates the dependence on F/D in the construction of the solution. The mathematical foundation of the model rests on the assumption that in each prescribed annular region of the antenna, the geometrical rms surface value is known. It is shown that closed-form expressions can then be derived, which result in a very efficient computational method for the average power pattern. Detailed parametric studies are performed with these expressions to determine the effects of different random errors and illumination tapers on parameters such as gain loss and sidelobe levels. The results clearly demonstrate that as sidelobe levels decrease, their dependence on the surface rms/wavelength becomes much stronger and, for a specified tolerance level, a considerably smaller rms/wavelength is required to maintain the low sidelobes within the required bounds.

Rahmat-Samii, Y.↗

Generation of Droplet Bessel Beams Using a Semiconductor Laser

In this paper, we studied Bessel beams obtained using an axicon with a substantially rounded apex. A study of the interference of two wave fronts arising from the refraction of the generating beam on an imperfect axicon showed that rounding its apex results in periodic pulsations of intensity in the resultant quasi-Bessel beam resembling visually the “droplets” of light. The proposed mathematical model demonstrates excellent agreement with the experiment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quadrupole Radiation of an Uncharged Droplet That Oscillates in the Presence of Uniform Electric Field

Capillary oscillations of an uncharged spheroid droplet of nonviscous conducting uncompressible liquid in the presence of uniform electric field are analyzed in the first order of smallness with respect to the ratio of the oscillation amplitude to a linear size of the droplet and in the second order of smallness with respect to the squared ratio of the linear size to the radiation wavelength. It is shown that the electric quadrupole moment of the droplet is time-dependent due to surface oscillations, which lead to the emission of quadrupole electromagnetic waves. A mathematical model of the quadrupole electromagnetic radiation of an uncharged droplet that oscillates in the presence of electrostatic field is constructed, and the radiation intensity and frequency are estimated.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Energy-Efficient Actuator for the Control System of Promising Vehicles

A mathematical model is developed to describe the energy-efficient actuator of control systems for promising autonomous vehicles (drones, torpedoes, etc.) with different current sources. The energy and dynamic characteristics of control systems with different power supplies are compared.

42 ENGINEERING↗

Treatment with integrase inhibitor suggests a new interpretation of HIV RNA decay curves that reveals a subset of cells with slow integration

The kinetics of HIV-1 decay under treatment depends on the class of antiretrovirals used. Mathematical models are useful to interpret the different profiles, providing quantitative information about the kinetics of virus replication and the cell populations contributing to viral decay. We modeled proviral integration in short- and long-lived infected cells to compare viral kinetics under treatment with and without the integrase inhibitor raltegravir (RAL). We fitted the model to data obtained from participants treated with RAL-containing regimes or with a four-drug regimen of protease and reverse transcriptase inhibitors. Our model explains the existence and quantifies the three phases of HIV-1 RNA decay in RAL-based regimens vs. the two phases observed in therapies without RAL. Our findings indicate that HIV-1 infection is mostly sustained by short-lived infected cells with fast integration and a short viral production period, and by long-lived infected cells with slow integration but an equally short viral production period. We propose that these cells represent activated and resting infected CD4+ T-cells, respectively, and estimate that infection of resting cells represent ~4% of productive reverse transcription events in chronic infection. RAL reveals the kinetics of proviral integration, showing that in short-lived cells the pre-integration population has a half-life of ~7 hours, whereas in long-lived cells this half-life is ~6 weeks. We also show that the efficacy of RAL can be estimated by the difference in viral load at the start of the second phase in protocols with and without RAL. Altogether, we provide a mechanistic model of viral infection that parsimoniously explains the kinetics of viral load decline under multiple classes of antiretrovirals.

59 BASIC BIOLOGICAL SCIENCES↗

Refined Dynamic Calculation of a Diesel-Engine Crank Mechanism

A mathematical model is proposed for the connecting rod of a diesel engine as a deformable component of a crank mechanism. VisSim 6.0 software is used for dynamic simulation of the connecting rod. Vibration is observed when the force exerted by the gas pressure is a maximum.

42 ENGINEERING↗

Quantitative and Predictive Genetic Parts for Plant Synthetic Biology

Plant synthetic biology aims to harness the natural abilities of plants and to turn them to new purposes. A primary goal of plant synthetic biology is to produce predictable and programmable genetic circuits from simple regulatory elements and well-characterized genetic components. The number of available DNA parts for plants is increasing, and the methods for rapid quantitative characterization are being developed, but the field of plant synthetic biology is still in its early stages. We here describe methods used to describe the quantitative properties of genetic components needed for plant synthetic biology. Once the quantitative properties and transfer function of a variety of genetic parts are known, computers can select the optimal components to assemble into functional devices, such as toggle switches and positive feedback circuits. However, while the variety of circuits and traits that can be put into plants are limitless, doing synthetic biology in plants poses unique challenges. Plants are composed of differentiated cells and tissues, each representing potentially unique regulatory or developmental contexts to introduced synthetic genetic circuits. Further, plants have evolved to be highly sensitive to environmental influences, such as light or temperature, any of which can affect the quantitative function of individual parts or whole circuits. Measuring the function of plant components within the context of a plant cell and, ideally, in a living plant, will be essential to using these components in gene circuits with predictable function. Mathematical modeling will be needed to account for the variety of contexts a genetic part will experience in different plant tissues or environments. With such understanding in hand, it may be possible to redesign plant traits to serve human and environmental needs.

59 BASIC BIOLOGICAL SCIENCES↗

Composite Heat Shields in Intense Energy Fluxes with Diffusion

A method is proposed for bench testing of reusable composite samples under intense thermal and ionizing radiation. Tests are conducted under intense energy fluxes. As a result of the tests, the temperature field and the displacement field at the surface of heat-shielding composite and in its depth are determined at different times. The proposed mathematical model adequately determines describes the temperature distribution in the composite shield under the action of intense energy and radiation fluxes. The influence of diffusion and the temperature field on the displacement field in the composite is studied. The theoretical results are compared with experimental data.

42 ENGINEERING↗

The quantum mechanics of high-order kinematic values

In this paper, within the framework of a unified mathematical model, the new formulation of quantum mechanics – quantum mechanics of higher order kinematic values – is proposed. In contrast to the well-known formulations of quantum mechanics in the new formulation, the wave function has not only a coordinate or momentum representation, but also representations through acceleration and accelerations of higher orders. The representations of the wave function in terms of higher order kinematic values make it possible to consider the dissipative systems problem and the variable entropy systems one within a single mathematical apparatus. The new formulation is not built phenomenologically, but from first principles and in a particular case contains the formulation of the de Broglie–Bohm ⟨wave-pilot⟩ quantum mechanics. The new formulation is based on the Vlasov equations chain. This approach allows us to obtain a natural connection between classical and quantum systems. Examples of such systems are considered in this paper.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Zika virus dynamics: Effects of inoculum dose, the innate immune response and viral interference

Experimental Zika virus infection in non-human primates results in acute viral load dynamics that can be well-described by mathematical models. The inoculum dose that would be received in a natural infection setting is likely lower than the experimental infections and how this difference affects the viral dynamics and immune response is unclear. Here we study a dataset of experimental infection of non-human primates with a range of doses of Zika virus. We develop new models of infection incorporating both an innate immune response and viral interference with that response. We find that such a model explains the data better than models with no interaction between virus and the immune response. We also find that larger inoculum doses lead to faster dynamics of infection, but approximately the same total amount of viral production.

59 BASIC BIOLOGICAL SCIENCES↗

<general dynamics of physical-chemical systems in mammals< fourth quarterly progress report, may 21 - aug. 20, 1965

Work is continuing on the mathematical modelling of the hydrodynamics of the arterial system. Discussion with Dr. McDonald has raised some questions relative to the geometric model of the arterial system. This area is considered important to provide a suitable base for consideration of the actual events taking place in the arteries. Attempts are being made to develop a model which will describe the geometry in terms of diameters against length, changes in cross-sectional area with division, and number of levels of arteries according to diameter. This work will be described in some detail in a technical report which is being prepared and will be submitted during the next quarter.

ARTERY↗

A new bi-objective periodic vehicle routing problem with maximization market share in an uncertain competitive environment

This paper presents a new variant of periodic vehicle routing problem in which the reaching time to the customers affects market share. Thus, there is a competition between distributors to achieve more market share by reaching the customers earlier than others; moreover, travel time between each two pairs of customers is uncertain. This situation is called an uncertain competitive environment. For the given problem, a new bi-objective mathematical model including minimization of total traveled time and maximization of the market share is presented. In order to solve this model, a multi-objective particle swarm (MOPSO) and local MOPSO algorithms are applied; and to evaluate the algorithm performance, some samples are generated; and the results of algorithms are compared based on some comparison metrics. The results demonstrate that the proposed LMOPSO algorithm leads to a better performance compared to the MOPSO in most comparison metrics.

97 MATHEMATICS AND COMPUTING↗

Transducerless time domain reflectance measurement of semiconductor thermal properties

The dominant techniques for laser-based thermal measurement, time-domain thermoreflectance (TDTR) and frequency-domain thermoreflectance, generally require that samples be coated with a metal transducer layer. The properties of the transducer and its interface to the sample are then important to the interpretation of results, and heat conduction in the transducer layer can limit measurements of ultra-thin samples or in-plane conductivity. Here, we demonstrate the feasibility of measuring semiconductor samples using standard TDTR instrumentation, without the use of a metal transducer. A mathematical model accounting for non-zero laser penetration depth as well as both thermal and charge carrier effects is presented, and the ability of the model to describe and fit to experimental data for silicon and germanium samples is demonstrated. Though at this stage measurement uncertainties are larger than for traditional TDTR, we anticipate that the use of this technique will expand the range of samples that can be measured with existing TDTR setups.

36 MATERIALS SCIENCE↗

Radar Measurements of the Vibration Amplitude

We propose a method for measuring the harmonic vibration amplitude of a reflector using a coherent radar station. A mathematical model describing the dependence of the Doppler spectrum of the reflected radio signal on the ratio of the vibration amplitude to the radiation wavelength is constructed. The vibration amplitude is calculated from the amplitude ratio of the third to first or fourth to second harmonics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Linear models to perform treaty verification tasks for enhanced information security

Linear mathematical models were applied to binary-discrimination tasks relevant to arms control verification measurements in which a host party wishes to convince a monitoring party that an item is or is not treaty accountable. These models process data in list-mode format and can compensate for the presence of variability in the source, such as uncertain object orientation and location. The Hotelling observer applies an optimal set of weights to binned detector data, yielding a test statistic that is thresholded to make a decision. The channelized Hotelling observer applies a channelizing matrix to the vectorized data, resulting in a lower dimensional vector available to the monitor to make decisions. We demonstrate how incorporating additional terms in this channelizing-matrix optimization offers benefits for treaty verification. We present two methods to increase shared information and trust between the host and monitor. The first method penalizes individual channel performance in order to maximize the information available to the monitor while maintaining optimal performance. Second, we present a method that penalizes predefined sensitive information while maintaining the capability to discriminate between binary choices. Data used in this study was generated using Monte Carlo simulations for fission neutrons, accomplished with the GEANT4 toolkit. Custom models for plutonium inspection objects were measured in simulation by a radiation imaging system. Model performance was evaluated and presented using the area under the receiver operating characteristic curve.

97 MATHEMATICS AND COMPUTING↗