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At least 613 records · Page 34

Eigenspace techniques for active flutter suppression

Mathematical models to be used in the control system design were developed. A computer program, which takes aerodynamic and structural data for the ARW-2 aircraft and converts these data into state space models suitable for use in modern control synthesis procedures, was developed. Reduced order models of inboard and outboard control surface actuator dynamics and a second order vertical wind gust model were developed. An analysis of the rigid body motion of the ARW-2 was conducted. The deletion of the aerodynamic lag states in the rigid body modes resulted in more accurate values for the eigenvalues associated with the plunge and pitch modes than were obtainable if the lag states were retained.

Garrard, W. L.↗

Learning energy-based representations of quantum many-body states

Efficient representation of quantum many-body states on classical computers is a problem of practical importance. An ideal representation of a quantum state combines a succinct characterization informed by the structure and symmetries of the system along with the ability to predict the physical observables of interest. Several machine-learning approaches have been recently used to construct such classical representations, which enable predictions of observables and account for physical symmetries. However, the structure of a quantum state typically gets lost unless a specialized is employed based on prior knowledge of the system. Moreover, most such approaches give no information about what states are easier to learn in comparison with others. Here, we propose a generative energy-based representation of quantum many-body states derived from Gibbs distributions used for modeling the thermal states of classical spin systems. Based on the prior information on a family of quantum states, the energy function can be specified by a small number of parameters using an explicit low-degree polynomial or a generic parametric family such as neural nets and can naturally include the known symmetries of the system. Our results show that such a representation can be efficiently learned from data using exact algorithms in a form that enables the prediction of expectation values of physical observables. Importantly, the structure of the learned energy function provides a natural explanation for the difficulty of learning an energy-based representation of a given class of quantum states when measured in a certain basis. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Dielectric constant of liquid alkanes and hydrocarbon mixtures

The complex dielectric constants of n-alkanes with two to seven carbon atoms have been measured. The measurements were conducted using a slotted-line technique at 1.2 GHz and at atmospheric pressure. The temperature was varied from the melting point to the boiling point of the respective alkanes. The real part of the dielectric constant was found to decrease with increasing temperature and correlate with the change in the molar volume. An upper limit to all the loss tangents was established at 0.001. The complex dielectric constants of a few mixtures of liquid alkanes were also measured at room temperature. For a pentane-octane mixture the real part of the dielectric constant could be explained by the Clausius-Mosotti theory. For the mixtures of n-hexane-ethylacetate and n-hexane-acetone the real part of the dielectric constants could be explained by the Onsager theory extended to mixtures. The dielectric constant of the n-hexane-acetone mixture displayed deviations from the Onsager theory at the highest fractions of acetone. The dipole moments of ethylacetate and acetone were determined for dilute mixtures using the Onsager theory and were found to be in agreement with their accepted gas-phase values. The loss tangents of the mixtures exhibited a linear relationship with the volume fraction for low concentrations of the polar liquids.

NASA Program Exobiology↗

Security Analysis of a Class of Spread Spectrum Systems Presentation

A method of adding physical layer security to a class of spread spectrum systems has been recently proposed. In this paper, we look into the rate at which an eavesdropper may gain information about the system to decipher the data symbols. The Shannon mutual information is used to measure the rate of information that may be gained by an eavesdropper. The k-nearest neighbors (k-NN) method is used to obtain estimates of relevant entropy values, which will then be used to quantify the rate of information recovery as more data is transmitted. It turns out that such information recovery requires the adoption of special methods that avoid any destructive bias in the estimates. Details of these methods are also presented.

97 - MATHEMATICS AND COMPUTING↗

Security Analysis of a Class of Secured Spread Spectrum Systems

Abstract—A method of adding physical layer security to a class of spread spectrum systems has been recently proposed. In this paper, we look into the rate at which an eavesdropper may gain information about the system to decipher the data symbols. The Shannon mutual information is used to measure the rate of information that may be gained by an eavesdropper. The k-nearest neighbors (k-NN) method is used to obtain the estimates of relevant entropy values which will be then used to quantify the rate of information recovery as more data are being transmitted. It turns out that such information recovery requires adoption of special methods that avoid any destructive bias in the estimates. Details of these methods are also presented.

97 - MATHEMATICS AND COMPUTING↗

Aerodynamic mathematical modeling - basic concepts

This lecture is a review of the basic concepts involved In the mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers. The review leads from Bryan's original formulation through the concepts of linear aerodynamic indicial functions and superposition to the extension of these concepts into the nonlinear regime. The nonlinear generalization yields a form for the aerodynamic response that can be built up from the responses to a limited number of well-defined characteristic motions, reproducible in principle either in wind-tunnel experiments or flow-field computations. A further generalization leads to a torn, accommodating the discontinuous and double-valued behavior characteristic of hysteresis in the steady-state aerodynamic response

Murray Tobak↗

Modeling the Activity of Single Genes

The central dogma of molecular biology states that information is stored in DNA, transcribed to messenger RNA (mRNA) and then translated into proteins. This picture is significantly augmentated when we consider the action of certain proteins in regulating transcription. These transcription factors provide a feedback pathway by which genes can regulate one another's expression as mRNA and then as protein. To review: DNA, RNA and proteins have different functions. DNA is the molecular storehouse of genetic information. When cells divide, the DNA is replicated, so that each daughter cell maintains the same genetic information as the mother cell. RNA acts as a go-between from DNA to proteins. Only a single copy of DNA is present, but multiple copies of the same piece of RNA may be present, allowing cells to make huge amounts of protein. In eukaryotes (organisms with a nucleus), DNA is found in the nucleus only. RNA is copied in the nucleus then translocates(moves) outside the nucleus, where it is transcribed into proteins. Along the way, the RNA may be spliced, i.e., may have pieces cut out. RNA then attaches to ribosomes and is translated to proteins. Proteins are the machinery of the cell other than DNA and RNA, all the complex molecules of the cell are proteins. Proteins are specialized machines, each of which fulfills its own task, which may be transporting oxygen, catalyzing reactions, or responding to extracellular signals, just to name a few. One of the more interesting functions a protein may have is binding directly or indirectly to DNA to perform transcriptional regulation, thus forming a closed feedback loop of gene regulation. The structure of DNA and the central dogma were understood in the 50s; in the early 80s it became possible to make arbitrary modifications to DNA and use cellular machinery to transcribe and translate the resulting genes; more recently, genomes (i.e., the complete DNA sequence) of many organisms have been sequenced. This large-scale sequencing began with simple organisms, viruses and bacteria, progressed to eukaryotes such as yeast, and more recently (1998) progressed to a multi-cellular animal, the nematode Caenorhabditis elegans. Sequencers have now moved on to the fruit fly Drosophila melanogaster, whose sequence is slated for completion by the end of 1999. The human genome project is expected to determine the complete sequence of all 3 billion bases of human DNA within the next five years. In the wake of genome-scale sequencing, further instrumentation is being developed to assay gene expression and function on a comparably large scale. Much of the work in computational biology focuses on computational tools used in sequencing, finding genes that are related to a particular gene, finding which parts of the DNA code for proteins and which do not, understanding what proteins will be formed from a given length of DNA, predicting how the proteins will fold from a one-dimensional structure into a three dimensional structure, and so on. Much less computational work has been done regarding the function of proteins. One reason for this is that different proteins function very differently, and so work on protein function is very specific to certain classes of proteins. There are, for example, proteins such enzymes that catalyze various intracellular reactions, receptors that respond to extracellular signals and ion channels that regulate the flow of charged particles into and out of the cell. In this chapter, we will consider a particular class of proteins called transcription factors(TFs), which are responsible for regulating when a certain gene is expressed in a certain cell, which cells it is express in, and how much is expressed. Understanding these processes will involve developing a deeper understanding of transcription, translation, and the cellular processes that control those processes. All of these elements fall under the aegis of gene regulation or more narrowly transcriptional regulation. Some of the key questions in gene regulation are: What genes are expressed in a certain cell at a certain time? How does gene expression differ from cell to cell in a multicellular organism? Which proteins act as transcription factors, i.e., are important in regulating gene expression? From questions like these, we hope to understand which genes are important for various macroscopic processes. Nearly all of the cells of a multicellular organism contain the same DNA. Yet this same genetic information yields a large number of different cell types. The fundamental difference between a neuron and a liver cell, for example, is which genes are expressed. Thus understanding gene regulation is an important step in understanding development. Furthermore, understanding the usual genes that are expressed in cells may give important clues about various diseases. Some diseases, such as sickle cell anemia and cystic fibrosis, are caused by defects in single, non-regulatory genes; others, such as certain cancers, are caused when the cellular control circuitry malfunctions - an understanding of these diseases will involve pathways of multiple interacting gene products. There are numerous challenges in the area of understanding and modeling gene regulation. First and foremost, biologists would like to develop a deeper understanding of the processes involved, including which genes and families of genes are important, how they interact, etc. From a computation point of view, there has been embarrassingly little work done. In this chapter there are many areas in which we can phrase meaningful, non-trivial computational questions, but questions that have not been addressed. Some of these are purely computational (what is a good algorithm for dealing with a model of type X) and others are more mathematical (given a system with certain characteristics, what sort of model can one use? How does one find biochemical parameters from system-level behavior using as few experiments as possible?). In addition to biological and algorithmic problems, there is also the ever-present issue of theoretical biology - what general principles can be derived from these systems, what can one do with models other than just simulate time-courses, what can be deduced about a class of systems without knowing all the details? The fundamental challenge to computationalists and theorists is to add value to the biology - to use models, modeling techniques and algorithms to understand the biology in new ways.

Mjolsness, Eric↗

The Role of Margin in Link Design and Optimization

Link analysis is a system engineering process in the design, development, and operation of communication systems and networks. Link models that are mathematical abstractions representing the useful signal power and the undesirable noise and attenuation effects (including weather effects if the signal path transverses through the atmosphere) that are integrated into the link budget calculation that provides the estimates of signal power and noise power at the receiver. Then the link margin is applied which attempts to counteract the fluctuations of the signal and noise power to ensure reliable data delivery from transmitter to receiver. (Link margin is dictated by the link margin policy or requirements.) A simple link budgeting approach assumes link parameters to be deterministic values typically adopted a rule-of-thumb policy of 3 dB link margin. This policy works for most S- and X-band links due to their insensitivity to weather effects. But for higher frequency links like Ka-band, Ku-band, and optical communication links, it is unclear if a 3 dB link margin would guarantee link closure. Statistical link analysis that adopted the 2-sigma or 3-sigma link margin incorporates link uncertainties in the sigma calculation. (The Deep Space Network (DSN) link margin policies are 2-sigma for downlink and 3-sigma for uplink.) The link reliability can therefore be quantified statistically even for higher frequency links. However in the current statistical link analysis approach, link reliability is only expressed as the likelihood of exceeding the signal-to-noise ratio (SNR) threshold that corresponds to a given bit-error-rate (BER) or frame-error-rate (FER) requirement. The method does not provide the true BER or FER estimate of the link with margin, or the required signalto-noise ratio (SNR) that would meet the BER or FER requirement in the statistical sense. In this paper, we perform in-depth analysis on the relationship between BER/FER requirement, operating SNR, and coding performance curve, in the case when the channel coherence time of link fluctuation is comparable or larger than the time duration of a codeword. We compute the "true" SNR design point that would meet the BER/FER requirement by taking into account the fluctuation of signal power and noise power at the receiver, and the shape of the coding performance curve. This analysis yields a number of valuable insights on the design choices of coding scheme and link margin for the reliable data delivery of a communication system - space and ground. We illustrate the aforementioned analysis using a number of standard NASA error-correcting codes.

Cheung, K.↗

Vibration attenuation of the NASA Langley evolutionary structure experiment using H(sub infinity) and structured singular value (micron) robust multivariable control techniques

The use is studied of active control to attenuate structural vibrations of the NASA Langley Phase Zero Evolutionary Structure due to external disturbance excitations. H sub infinity and structured singular value (mu) based control techniques are used to analyze and synthesize control laws for the NASA Langley Controls Structures Interaction (CSI) Evolutionary Model (CEM). The CEM structure experiment provides an excellent test bed to address control design issues for large space structures. Specifically, control design for structures with numerous lightly damped, coupled flexible modes, collocated and noncollocated sensors and actuators and stringent performance specifications. The performance objectives are to attenuate the vibration of the structure due to external disturbances, and minimize the actuator control force. The control design problem formulation for the CEM Structure uses a mathematical model developed with finite element techniques. A reduced order state space model for the control design is formulated from the finite element model. It is noted that there are significant variations between the design model and the experimentally derived transfer function data.

Balas, Gary J.↗

A Singular Value Decomposition Framework for Retrievals with Vertical Distribution Information from Greenhouse Gas Column Absorption Spectroscopy Measurements

We describe a variation of the Optimal Estimation (OE) method for greenhouse gas remote sensing retrievals using a singular value decomposition (SVD) and an uninformative prior. The SVD method is capable of discerning vertical information in column integrated absorption measurements. While traditional Bayesian optimal estimation (OE) assumes a prior distribution in order to regularize the inversion problem, the SVD approach identifies principal components that can be retrieved from the measurement without explicitly specifying a prior mean and prior covariance matrix. We discuss the method, illustrate its use on an integrated path differential absorption CO2 lidar measurement model, and compare it to traditional optimal estimation using numerical simulations. In the absence of forward model error, the mathematics behind the SVD method guarantee it to be bias-free, which is confirmed by the numerical simulations. In contrast, traditional OE retrievals exhibit bias when the prior mean used in the retrieval differs from the true mean. While the SVD approach can be used for most trace gas retrievals, it is particularly useful for situations where prior knowledge of the trace gas profile is poor. The SVD analysis is also useful in illustrating how vertical information is treated by the traditional OE approach.

Ramanathan, Anand K.↗

Computational Modeling for Non-Equilibrium Shock Tube Flows

Time accurate simulation of non-equilibrium flows inside shock tube facilities presents several challenges from both physical and mathematical aspects. Furthermore, the large computational cost makes it impractical to support a real-time experimental test campaign. In this work, we explore other methods for modeling the shock tube problem with the main focus on the post-shock region and the absolute radiation emanating from it. The proposed alternative approach is several orders of magnitude less computationally expensive while still accurate enough with regards to the quantities of interest. Excellent agreement is found with the established stagnation-line approach. Comparison with time-accurate simulations shows good agreement close to the peak values and disagreement of the temperatures relaxation and radiance profiles toward equilibrium.

Bensassi, Khalil↗

Launch window definition for sky target experiments.

This paper is a brief report on the computer program developed for the Extraterrestrial Physics Barium Ion Cloud (BIC) Project. The mathematical analysis developed for the program along with its programing characteristics are pointed out to show that this program is adaptable to similar sky target projects. Definite viewing constraints are specified so that the chosen ground tracking stations can photograph the behavior of the sky target after its release. Viewing factors include the illumination of the target by the sun, the relative elevation look angle to the target from each tracking station, the solar and lunar depression angles at each tracking station, and the total sky background brightness of the target relative to each tracking station. Numeric values are assigned to each factor through program input. The program output is flexible so that the results of the window calculations can be studied to the depth required.

Michaud, N. H.↗

New Secondary Batteries Utilizing Electronically Conductive Polypyrrole Cathode

To gain a better understanding of the dynamic behavior in electronically conducting polypyrroles and to provide guidance toward designs of new secondary batteries based on these polymers, two mathematical models are developed; one for the potentiostatically controlled switching behavior of polypyrrole film, and one for the galvanostatically controlled charge/discharge behavior of lithium/polypyrrole secondary battery cell. The first model is used to predict the profiles of electrolyte concentrations, charge states, and electrochemical potentials within the thin polypyrrole film during switching process as functions of applied potential and position. Thus, the detailed mechanisms of charge transport and electrochemical reaction can be understood. Sensitivity analysis is performed for independent parameters, describing the physical and electrochemical characteristic of polypyrrole film, to verify their influences on the model performance. The values of independent parameters are estimated by comparing model predictions with experimental data obtained from identical conditions. The second model is used to predict the profiles of electrolyte concentrations, charge state, and electrochemical potentials within the battery system during charge and discharge processes as functions of time and position. Energy and power densities are estimated from model predictions and compared with existing battery systems. The independent design criteria on the charge and discharge performance of the cell are provided by studying the effects of design parameters.

Yeu, Taewhan↗

Gravitational influences on the behavior of confined diffusion flames

Closed form, mathematical representations for the shapes of laminar diffusion flames stabilized on two-dimensional slot burners are derived for arbitrary gravitational levels. The solution technique employs the Schvab-Zeldovich conserved species variable. Effects of gravity on the velocity field are incorporated through the momentum equation; these effects, in turn, influence the species field. The results reduce smoothly to the classical Burke-Schumann solution as gravity approaches zero. It is shown that both flame height and width increase with decreasing gravity levels. Several interesting cases are considered explicitly; these include effects of negative and extremely high values of gravity. In the latter case, it is shown that the flame collapses onto the burner surface. The analysis finds application in the modeling of steady and unsteady gas and solid propellant diffusion flames.

Hegde, U.↗

Impact of Increased Monte Carlo Parameters on Sensitivity Calculations with SCALE [Slides]

For both models and tests, NPG and NSK parameters have only small effects on calculated sensitivity coefficients. Outside of NPG=100, only differences in CFP affected sensitivity coefficient values. Fission reactions ( 235 U) require more NPG values than scattering ( 238 U) reactions – more particles are needed to locate fission sources in the model more accurately. This work confirms the previous results with the IFP method where the CFP parameter has the greatest impact on calculated sensitivity coefficients. While immediate work focuses on fast systems, other model specifications may require a different set of MC parameters.

97 MATHEMATICS AND COMPUTING↗

Business Case Analysis for Artificial Intelligence-Large Language Model Technology Integration

AI-assisted processes are expected to enhance operational efficiency and improve decision-making, supporting the long-term economic viability of nuclear power plants. However, detailed business analyses of AI-generated cost savings are rarely performed. Given the recent industry interest in Large Language Model (LLM), the U.S. Department of Energy (DOE) Light Water Reactor Sustainability (LWRS) Program has conducted a comprehensive business case analysis of LLM Artificial Intelligence (AI) implementation in nuclear plant engineering workflows. The research employed three complementary business case approaches to evaluate impact of an LLM, using three representative engineering processes as use-cases: Boric Acid Corrosion (BAC) Evaluations, Maintenance Rule Evaluations, and 10 CFR 50.59 Screenings. Through detailed workload analyses and structured interviews, the study quantified significant efficiency improvements ranging from 11% to 59% across these processes. The research further considers how these efficiency gains could translate into tangible reliability improvements through enhanced engineering capacity. Analysis of historical plant trip data indicates that enabling engineers to focus on proactive reliability activities could provide substantial financial benefits through avoided outages, potentially generating greater value than the direct efficiency improvements alone. By documenting successful applications, implementation challenges, and strategic opportunities, this research provides nuclear utilities with a practical framework for evaluating the value of AI technology to support long-term operations through advanced digital technologies.

97 MATHEMATICS AND COMPUTING↗

Modeling of Bulk Evaporation and Condensation

This report describes the modeling and mathematical formulation of the bulk evaporation and condensation involved in liquid-vapor phase change processes. An internal energy formulation, for these phase change processes that occur under the constraint of constant volume, was studied. Compared to the enthalpy formulation, the internal energy formulation has a more concise and compact form. The velocity and time scales of the interface movement were obtained through scaling analysis and verified by performing detailed numerical experiments. The convection effect induced by the density change was analyzed and found to be negligible compared to the conduction effect. Two iterative methods for updating the value of the vapor phase fraction, the energy based (E-based) and temperature based (T-based) methods, were investigated. Numerical experiments revealed that for the evaporation and condensation problems the E-based method is superior to the T-based method in terms of computational efficiency. The internal energy formulation and the E-based method were used to compute the bulk evaporation and condensation processes under different conditions. The evolution of the phase change processes was investigated. This work provided a basis for the modeling of thermal performance of multi-phase nuclear fuel elements under variable gravity conditions, in which the buoyancy convection due to gravity effects and internal heating are involved.

Anghaie, S.↗

Parameter identification of material constants in a composite shell structure

One of the basic requirements in engineering analysis is the development of a mathematical model describing the system. Frequently comparisons with test data are used as a measurement of the adequacy of the model. An attempt is typically made to update or improve the model to provide a test verified analysis tool. System identification provides a systematic procedure for accomplishing this task. The terms system identification, parameter estimation, and model correlation all refer to techniques that use test information to update or verify mathematical models. The goal of system identification is to improve the correlation of model predictions with measured test data, and produce accurate, predictive models. For nonmetallic structures the modeling task is often difficult due to uncertainties in the elastic constants. A finite element model of the shell was created, which included uncertain orthotropic elastic constants. A modal survey test was then performed on the shell. The resulting modal data, along with the finite element model of the shell, were used in a Bayes estimation algorithm. This permitted the use of covariance matrices to weight the confidence in the initial parameter values as well as confidence in the measured test data. The estimation procedure also employed the concept of successive linearization to obtain an approximate solution to the original nonlinear estimation problem.

Martinez, David R.↗