Search NASA⌕ Search

SEARCH · Search NASA

Results for “Analytic linearization”

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 1,207 records · Page 67
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Secondary metallicity in analytic models of chemical evolution of galaxies

Analytic models of the chemical evolution of galactic regions that grow in mass owing to the continuous infall of matter are characterized, emphasizing the solutions for secondary nuclei (defined as those nuclei whose stellar yields are proportional to the abundance of a primary seed nucleus) in the families of models described by Clayton (1984 and 1985). Wide variations in time dependence of both primary and secondary nuclei as well as in the ratio of secondary to primary are displayed by these model families, confirming again the usefulness of these families as interpretive guides if galaxies do in fact evolve with substantial infall. Additionally, analytic solutions are presented for two other possible interesting systems: the evolution of abundances if the primary metallicity in the infall is increasing in time, and the evolution of abundances if the primary yield changes linearly with time owing to continuous changes in the stellar mass function, the opacity, or other astrophysical agents. Finally, test evaluations of the instantaneous recycling approximation on which these analytic models rely are presented.

Clayton, D. D.↗
DOE OSTI2025

A theoretical study of the upper bound of surface elevation variance in the Phillips initial stage during wind-wave generation

The resonance mechanism in the initial of wind-wave generation proposed by Phillips is a foundation of wind-wave generation theory, but a precise theoretical quantification of wave energy growth in this initial stage has not been obtained yet after more than six decades of research. In this study, we aim to address this knowledge gap by developing an analytical approach based on a novel complex analysis method to theoretically investigate the temporal evolution of the wave energy in the Phillips initial stage. We quantitatively derive and analyse the growth behaviour of the surface wave energy and obtain an analytical solution for its upper bound. Our result highlights the crucial effects of surface tension. Because the phase velocity of gravity–capillary waves has a minimal value at a critical wavenumber, gravity–capillary waves and gravity waves (which neglect surface tension) exhibit distinct resonance curve properties and wave energy growth behaviours. For gravity waves, the resonance curve extends indefinitely; for gravity–capillary waves, it either forms a finite-length curve or does not exist, depending on the wind speed. The leading-order term of the upper-bound solution of the energy of gravity waves increases linearly over time, while for gravity–capillary waves, the term increases linearly over time under strong wind conditions but remains finite under weak wind conditions. This theoretical study provides an analytical framework for the generation of wind-waves in the Phillips initial stage, which may inspire further theoretical, numerical and experimental research.

58 GEOSCIENCES↗
DOE OSTI2010

Effects of radiation reaction in relativistic laser acceleration

The goal of this paper is twofold: to explore the response of classical charges to electromagnetic force at the level of unity in natural units and to establish a criterion that determines physical parameters for which the related radiation-reaction effects are detectable. In pursuit of this goal, the Landau-Lifshitz equation is solved analytically for an arbitrary (transverse) electromagnetic pulse. A comparative study of the radiation emission of an electron in a linearly polarized pulse for the Landau-Lifshitz equation and for the Lorentz force equation reveals the radiation-reaction-dominated regime, in which radiation-reaction effects overcome the influence of the external fields. The case of a relativistic electron that is slowed down by a counterpropagating electromagnetic wave is studied in detail. We further show that when the electron experiences acceleration of order unity, the dynamics of the Lorentz force equation, the Landau-Lifshitz equation and the Lorentz-Abraham-Dirac equation all result in different radiation emission that could be distinguished in experiment. Finally, our analytic and numerical results are compared with those appearing in the literature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Species-Selective Detection of Volatile Organic Compounds by Ionic Liquid-Based Electrolyte Using Electrochemical Methods

The detection of volatile organic compounds (VOCs) is an important topic for environmental safety and public health. However, the current commercial VOC detectors suffer from cross-sensitivity and low reproducibility. In this work, we present species-selective detection for VOCs using an electrochemical cell based on ionic liquid (IL) electrolytes with features of high selectivity and reliability. The voltammograms measured with the IL-based electrolyte absorbing different VOCs exhibited species-selective features that were extracted and classified by linear discriminant analysis (LDA). The detection system could identify as many as four types of VOCs, including methanol, ethanol, acetone, formaldehyde, and additional water. A mixture of methanol and formaldehyde was detected as well. The sample required for the VOCs classification system was 50 μL, or 1.164 mmol, on average. The response time for each VOC measurement is as fast as 24 s. The volume of VOCs such as formaldehyde in solution could also be quantified by LDA and electrochemical impedance spectroscopy techniques, respectively. The system showed a tunable detection range for 1.6 and 16% (w/v) CH 2 O solution by adjusting the composition of the electrolyte. The limit of detection was as low as 1 μL. For the 1.6% CH 2 O solution, the linearity calibration range was determined to be from 5.30 to 53.00 μmol with a limit of detection at 0.53 μmol. The mechanisms for VOCs determination and quantification are also thoroughly discussed. Finally, it is expected that this work could provide a new insight into the concept of electrochemical detection of VOCs with machine learning analysis and be applied to both VOCs gas monitoring and fluid detection.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Full-Field Strain Measurement Integrated with Two Dimension Regression Analysis to Evaluate the Bi-Modulus Elastic Properties of Isotropic and Transversely Isotropic Materials

Background: Measuring the physical properties of shale is critical for optimizing engineering activities such as geothermal energy generation and hydraulic fracturing. Shale is a transversely isotropic material. Furthermore, this material can also include micro and macro cracks at different locations and orientations that cause it to behave differently under tensile or compressive loading. Objective: In this work, a combined experimental–numerical approach is proposed to evaluate the bi-modulus elastic properties of isotropic and transversely isotropic materials. Methods: Full-field strain measurements for a circular disk under diametral compression are integrated with a regression analysis technique to evaluate the elastic properties of bi-modulus materials subjected to tensile and compressive loads using two loading configurations on the same specimen. Digital Image Correlation (DIC) is used to measure the full-field strains. Subsequently, in the case of an isotropic material, a linear least-squares approach is utilized to process the experimentally determined strains in conjunction with analytical expressions of the stress fields (in terms of far-field loading) to determine the elastic modulus E, the shear modulus G, and the Poisson’s ratio $v$. In the case of a transversely isotopic material, such as shale, a finite element model is implemented to determine the stress fields (again in terms of far-field loading), which is followed by repeating the previous regression analysis in an iterative process to estimate the elastic parameters. Results: The results show that the proposed technique successfully provides a complete set of elastic properties as a function of both the loading condition and the principal material directions. The technique is validated by measurements on a known isotropic material and then applied to determine the properties of shale. Conclusion: In this work, the proposed approach is successfully used to calculate the bi-modulus elastic response of poly(methyl meth- acrylate) (PMMA) and shale. As expected, PMMA exhibits an isotropic response with no bi-modulus effect, however, shale exhibits both transverse isotropy and a bi-modulus effect. Therefore, this approach holds promise for investigating the elastic properties of materials like rocks and fiber-reinforced composite laminates as functions of the principal material directions and the loading conditions.

42 ENGINEERING↗
DOE OSTI2018

Relative Fisher information in some central potentials

Highlights: • Relative Fisher information in both r and p spaces is calculated analytically. • In case of central potentials, circular state of a given l, is selected as reference. • In hydrogenic system IR provides better result than that of I. • In case of oscillator potentials IR comments about change of bond strength with n{sub r}. - Abstract: Relative Fisher information (IR) was pursued for 1D quantum harmonic oscillator (QHO), 3D isotropic QHO, hydrogen atom and pseudoharmonic potential (PHP) in both r and p spaces. In 1D case, the n=0 state is chosen as reference, whereas for a central potential, the respective circular (corresponding to lowest radial quantum number n{sub r}) state of a given l quantum number, is selected. Starting from their exact wave functions, expressions of IR in both r and p spaces are obtained in closed analytical forms in all these systems. For the 1D QHO, IR in r,p spaces increases linearly with n. For 3D QHO and PHP, it varies with single power of n{sub r} in both spaces. But, in H atom they depend on both principal (n) and azimuthal (l) quantum numbers. However, at a fixed l, IR initially advances with rise of n and then falls off; also for a given n, it always decreases with l.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Survival probabilities in the Sisyphus random walk model with absorbing traps

We analyze the dynamics of the Sisyphus random walk model, a discrete Markov chain in which the walkers may randomly return to their initial position x{sub 0}. In particular, we present a remarkably compact derivation of the time-dependent survival probability function S(t;x{sub 0}) which characterizes the random walkers in the presence of an absorbing trap at the origin. The survival probabilities are expressed in a compact mathematical form in terms of the x{sub 0}-generalized Fibonacci-like numbers G{sub t}{sup (x{sub 0})}. Interestingly, it is proved that, as opposed to the standard random walk model in which the survival probabilities depend linearly on the initial distance x{sub 0} of the walkers from the trap and decay asymptotically as an inverse power of the time, in the Sisyphus random walk model the asymptotic survival probabilities decay exponentially in time and are characterized by a non-trivial (non-linear) dependence on the initial gap x{sub 0} from the absorbing trap. We use the analytically derived results in order to analyze the underlying dynamics of the ‘survival-game’, a highly risky investment strategy in which non-absorbed agents receive a reward P(t) which gradually increases in time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

A novel Lagrangian approach for the stable numerical simulation of fault and fracture mechanics

The simulation of the mechanics of geological faults and fractures is of paramount importance in several applications, such as ensuring the safety of the underground storage of wastes and hydrocarbons or predicting the possible seismicity triggered by the production and injection of subsurface fluids. However, the stable numerical modeling of ground ruptures is still an open issue. The present work introduces a novel formulation based on the use of the Lagrange multipliers to prescribe the constraints on the contact surfaces. The variational formulation is modified in order to take into account the frictional work along the activated fault portion according to the principle of maximum plastic dissipation. The numerical model, developed in the framework of the Finite Element method, provides stable solutions with a fast convergence of the non-linear problem. The stabilizing properties of the proposed model are emphasized with the aid of a realistic numerical example dealing with the generation of ground fractures due to groundwater withdrawal in arid regions. - Highlights: • A numerical model is developed for the simulation of fault and fracture mechanics. • The model is implemented in the framework of the Finite Element method and with the aid of Lagrange multipliers. • The proposed formulation introduces a new contribution due to the frictional work on the portion of activated fault. • The resulting algorithm is highly non-linear as the portion of activated fault is itself unknown. • The numerical solution is validated against analytical results and proves to be stable also in realistic applications.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

Machine-learning predictions of the shale wells’ performance

The ultra-low permeability nature of shale reservoirs leads to an extended linear flow and necessitates horizontal wells with multi-stage engineered fractures to efficiently extract hydrocarbons resources. These artificially-generated and naturally-occurring fractures form complex networks that create complex flow regimes which control oil production. These fractures are neither identical nor equally-spaced, which leads to a production profile with a masked onset of the boundary-dominated flow. The combination of the extended linear flow with the indeterminate onset of the boundary-dominated flow challenges the current deterministic analytic approaches to forecast the estimated ultimate recovery (EUR). In this work, we propose a novel machine-learning approach which overcomes these challenges and provides reliable EUR estimates based on field-wide analyses. We implement a novel unsupervised machine learning (ML) methodology, which allows for automatic identification of the optimal number of features (signals) present in the data based on non-negative matrix/tensor factorization coupled with k-means clustering incorporating regularization and physics constraints. In the presented analyses, the input data to the ML algorithm is the available (public) production history from the field collected at existing unconventional reservoirs. We validate our approach through hindcasting of the production data, where we achieved an excellent agreement. In addition, our approach is able to identify the poorly-performing wells, which could benefit from early refracing. Our approach provides fast and accurate estimations of the well performance without presumptions about the state of the well or the flow regime.

03 NATURAL GAS↗
DOE OSTI2022

Modeling and implementation of vertical excursion FFA in the Zgoubi ray-tracing code

Vertical Fixed Field Accelerators (vFFAs) feature complex and highly non-linear magnetic fields, which require simulation codes allowing step-wise particle tracking. Methods to model the 3D magnetic field of scaling vFFAs have been developed in the ray-tracing code Zgoubi. The field modeling and particle tracking methods include the field non-linearities, the fringe fields, and the field superposition of neighboring magnets. The procedure implements the vFFA analytical field expressions, allowing design studies and parameter optimizations using the Zgoubi built-in fit method. The vFFA procedure has been applied to a ten-fold symmetry ring with a triplet focusing structure designed to accelerate protons from 3 MeV to 12 MeV and studied under the ISIS-II proton driver prototype project. Results from particle tracking in externally generated 3D semi-analytical field maps and the developed vFFA analytical model are shown to be in excellent agreement.

43 PARTICLE ACCELERATORS↗
DOE OSTI2010

How to Solve Schroedinger Problems by Approximating the Potential Function

We give a survey over the efforts in the direction of solving the Schroedinger equation by using piecewise approximations of the potential function. Two types of approximating potentials have been considered in the literature, that is piecewise constant and piecewise linear functions. For polynomials of higher degree the approximating problem is not so easy to integrate analytically. This obstacle can be circumvented by using a perturbative approach to construct the solution of the approximating problem, leading to the so-called piecewise perturbation methods (PPM). We discuss the construction of a PPM in its most convenient form for applications and show that different PPM versions (CPM,LPM) are in fact equivalent.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Adiabatic nonlinear waves with trapped particles. II. Wave dispersion

A general nonlinear dispersion relation is derived in a nondifferential form for an adiabatic sinusoidal Langmuir wave in collisionless plasma, allowing for an arbitrary distribution of trapped electrons. The linear dielectric function is generalized, and the nonlinear kinetic frequency shift {omega}{sub NL} is found analytically as a function of the wave amplitude a. Smooth distributions yield {omega}{sub NL}{proportional_to}{radical}(a), as usual. However, beam-like distributions of trapped electrons result in different power laws, or even a logarithmic nonlinearity, which are derived as asymptotic limits of the same dispersion relation. Such beams are formed whenever the phase velocity changes, because the trapped distribution is in autoresonance and thus evolves differently from the passing distribution. Hence, even adiabatic {omega}{sub NL}(a) is generally nonlocal.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

On the multistream approach of relativistic Weibel instability. I. Linear analysis and specific illustrations

A one-dimensional multistream formalism is extended for the study of temperature anisotropy driven Weibel-type instabilities in collisionless and relativistic plasma. The formulation is based on a Hamiltonian reduction technique using the invariance of generalized canonical momentum in transverse direction. The Vlasov-Maxwell model is expressed in terms of an ensemble of one-dimensional Vlasov-type equations, coupled together with the Maxwell equations in a self-consistent way. Although the model is fundamentally nonlinear, this first of three companion papers focuses on the linear aspect. Dispersion relations of the Weibel instability are derived in the linear regime for different kinds of polarization of the electromagnetic potential vector. The model allows new unexpected insights on the instability: enhanced growth rates for the Weibel instability are predicted when a dissymmetric distribution is considered in p{sub ⊥}. In the case of a circular polarization, a simplification of the linear analysis can be obtained by the introduction of the “multiring” approach allowing to extend the analytical model of Yoon and Davidson [Phys. Rev. A 35, 2718 (1987)]. Applications of this model are left to the other two papers of the series where specific problems are addressed pertaining to the nonlinear and relativistic dynamics of magnetically trapped particles met in the saturation regime of the Weibel instability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Plasmoid instability in double current sheets

The linear behavior of plasmoid instability in double current sheet configurations, namely, double plasmoid mode (DPM), is analytically and numerically investigated within the framework of a reduced magnetohydrodynamic model. Analytical analysis shows that if the separation of double current sheets is sufficiently small [κx{sub s}≪κ{sup 2/9}S{sub L}{sup 1/3}], the growth rate of DPMs scales as κ{sup 2/3}S{sub L}{sup 0} in the non-constant-ψ regime, where κ=kL{sub CS}/2 is the wave vector measured by the half length of the system L{sub CS}/2, 2x{sub s} is the separation between two resonant surfaces, and S{sub L}=L{sub CS}V{sub A}/2η is Lundquist number with V{sub A} and η being Alfven velocity and resistivity, respectively. If the separation is very large [κx{sub s}≫κ{sup 2/9}S{sub L}{sup 1/3}], the growth rate scales as κ{sup −2/5}S{sub L}{sup 2/5} in the constant-ψ regime. Furthermore, it is also analytically found that the maximum wave number scales as x{sub s}{sup −9/7}S{sub L}{sup 3/7} at the transition position between these two regimes, and the corresponding maximum growth rate scales as x{sub s}{sup −6/7}S{sub L}{sup 2/7} there. The analytically predicted scalings are verified in some limits through direct numerical calculations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Dynamics retrieval from stochastically weighted incomplete data by low-pass spectral analysis

Time-resolved serial femtosecond crystallography (TR-SFX) provides access to protein dynamics on sub-picosecond timescales, and with atomic resolution. Due to the nature of the experiment, these datasets are often highly incomplete and the measured diffracted intensities are affected by partiality. To tackle these issues, one established procedure is that of splitting the data into time bins, and averaging the multiple measurements of equivalent reflections within each bin. This binning and averaging often involve a loss of information. Here, we propose an alternative approach, which we call low-pass spectral analysis (LPSA). In this method, the data are projected onto the subspace defined by a set of trigonometric functions, with frequencies up to a certain cutoff. This approach attenuates undesirable high-frequency features and facilitates retrieving the underlying dynamics. A time-lagged embedding step can be included prior to subspace projection to improve the stability of the results with respect to the parameters involved. Subsequent modal decomposition allows to produce a low-rank description of the system's evolution. Using a synthetic time-evolving model with incomplete and partial observations, we analyze the LPSA results in terms of quality of the retrieved signal, as a function of the parameters involved. We compare the performance of LPSA to that of a range of other sophisticated data analysis techniques. We show that LPSA allows to achieve excellent dynamics reconstruction at modest computational cost. Finally, we demonstrate the superiority of dynamics retrieval by LPSA compared to time binning and merging, which is, to date, the most commonly used method to extract dynamical information from TR-SFX data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

On the molecular correlations that result in field-dependent conductivities in electrolyte solutions

Employing recent advances in response theory and nonequilibrium ensemble reweighting, we study the dynamic and static correlations that give rise to an electric field-dependent ionic conductivity in electrolyte solutions. We consider solutions modeled with both implicit and explicit solvents, with different dielectric properties, and at multiple concentrations. Implicit solvent models at low concentrations and small dielectric constants exhibit strongly field-dependent conductivities. We compare these results to Onsager-Wilson theory of the Wien effect, which provides a qualitatively consistent prediction at low concentrations and high static dielectric constants but is inconsistent away from these regimes. The origin of the discrepancy is found to be increased ion correlations under these conditions. Explicit solvent effects act to suppress nonlinear responses, yielding a weakly field-dependent conductivity over the range of physically realizable field strengths. By decomposing the relevant time correlation functions, we find that the insensitivity of the conductivity to the field results from the persistent frictional forces on the ions from the solvent. Our findings illustrate the utility of nonequilibrium response theory in rationalizing nonlinear transport behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗