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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.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Linear corotation torques in non-barotropic disks

A fully analytic expression for the linear corotation torque to first order in eccentricity for planets in non-barotropic protoplanetary disks is derived, taking into account the effect of disk entropy gradients. This torque formula is applicable to both the co-orbital, corotation torques and the non-co-orbital, corotation torques—for planets in orbits with non-zero eccentricity—in disks where the thermal diffusivity and viscosity are sufficient to maintain the linearity of these interactions. While the co-orbital, corotation torque is important for migration of planets in Type I migration, the non-co-orbital, corotation torque plays an important role in the eccentricity evolution of giant planets that have opened gaps in the disk. The presence of an entropy gradient in the disk can significantly modify the corotation torque in both these cases.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Nonlinear beam deflection in photonic lattices with negative defects

We demonstrate both theoretically and experimentally that a nonlinear beam can be reflected by a negative defect in a photonic lattice if the incident angle is below a threshold value. Above this threshold angle, the beam simply passes through the defect. This phenomenon occurs in both one- and two-dimensional photonic lattices, and it provides a way to use the incident angle to control beam propagation in a lattice network. If the defect is absent or positive, no evident transition from reflection to transmission occurs. These nonlinear phenomena are also compared with linear nondiffracting-beam propagation in a photonic lattice with a defect, and both similarities and differences are observed. In addition, some important features in linear and nonlinear beam propagations are explained analytically by using a linear model with a delta-function defect.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

An analytic approach to quasinormal modes for coupled linear systems

Quasinormal modes describe the ringdown of compact objects deformed by small perturbations. In generic theories of gravity that extend General Relativity, the linearized dynamics of these perturbations is described by a system of coupled linear differential equations of second order. We first show, under general assumptions, that such a system can be brought to a Schrödinger-like form. We then devise an analytic approximation scheme to compute the spectrum of quasinormal modes. We validate our approach using a toy model with a controllable mixing parameter ε and showing that the analytic approximation for the fundamental mode agrees with the numerical computation when the approximation is justified. The accuracy of the analytic approximation is at the (sub-) percent level for the real part and at the level of a few percent for the imaginary part, even when ε is of order one. Our approximation scheme can be seen as an extension of the approach of Schutz and Will [1] to the case of coupled systems of equations, although our approach is not phrased in terms of a WKB analysis, and offers a new viewpoint even in the case of a single equation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

A fluid pressure and deformation analysis for geological sequestration of carbon dioxide

We present a hydro-mechanical model and deformation analysis for geological sequestration of carbon dioxide. The model considers the poroelastic effects by taking into account the two-way coupling between the geomechanical response and the fluid flow process in greater detail. In order for analytical solutions, the simplified hydro-mechanical model includes the geomechanical part that relies on the theory of linear elasticity, while the fluid flow is based on the Darcy’s law. The model was derived through coupling the two parts using the standard linear poroelasticity theory. Analytical solutions for fluid pressure field were obtained for a typical geological sequestration scenario and the solutions for ground deformation were obtained using the method of Green’s function. Solutions predict the temporal and spatial variation of fluid pressure, the effect of permeability and elastic modulus on the fluid pressure, the ground surface uplift, and the radial deformation during the entire injection period.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2012

PHURBAS: AN ADAPTIVE, LAGRANGIAN, MESHLESS, MAGNETOHYDRODYNAMICS CODE. II. IMPLEMENTATION AND TESTS

We present an algorithm for simulating the equations of ideal magnetohydrodynamics and other systems of differential equations on an unstructured set of points represented by sample particles. The particles move with the fluid, so the time step is not limited by the Eulerian Courant-Friedrichs-Lewy condition. Full spatial adaptivity is required to ensure the particles fill the computational volume and gives the algorithm substantial flexibility and power. A target resolution is specified for each point in space, with particles being added and deleted as needed to meet this target. We have parallelized the code by adapting the framework provided by GADGET-2. A set of standard test problems, including 10{sup -6} amplitude linear magnetohydrodynamics waves, magnetized shock tubes, and Kelvin-Helmholtz instabilities is presented. Finally, we demonstrate good agreement with analytic predictions of linear growth rates for magnetorotational instability in a cylindrical geometry. This paper documents the Phurbas algorithm as implemented in Phurbas version 1.1.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Commissioning of Photon Beams of a Flattening Filter-Free Linear Accelerator and the Accuracy of Beam Modeling Using an Anisotropic Analytical Algorithm;TrueBeam; Flattening filter free; Commissioning; Anisotropic analytical algorithm

Purpose: To investigate dosimetric characteristics of a new linear accelerator designed to deliver flattened, as well as flattening filter-free (FFF), beams. To evaluate the accuracy of beam modeling under physical conditions using an anisotropic analytical algorithm. Methods and Materials: Dosimetric data including depth dose curves, profiles, surface dose, penumbra, out-of-field dose, output, total and scatter factors were examined for four beams (X6, X6FFF, X10, and X10FFF) of Varian's TrueBeam machine. Beams modeled by anisotropic analytical algorithm were compared with measured dataset. Results: FFF beams have lower mean energy (tissue-phantom ratio at the depths of 20 and 10 cm (TPR 20/10): X6, 0.667; X6FFF, 0.631; X10, 0.738; X10FFF, 0.692); maximum dose is located closer to the surface; and surface dose increases by 10%. FFF profiles have sharper but faster diverging penumbra. For small fields and shallow depths, dose outside a field is lower for FFF beams; however, the advantage fades with increasing phantom scatter. Output increases 2.26 times for X6FFF and 4.03 times for X10FFF and is less variable with field size; collimator exchange effect is reduced. A good agreement between modeled and measured data is observed. Criteria of 2% depth-dose and 2-mm distance-to-agreement are always met. Conclusion: Reference dosimetric characteristics of TrueBeam photon bundles were obtained, and successful modeling of the beams was achieved.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2024

Analytic Nuclear Gradients for Complete Active Space Linearized Pair-Density Functional Theory

Accurately modeling photochemical reactions is difficult due to the presence of conical intersections and locally avoided crossings, as well as the inherently multiconfigurational character of excited states. As such, one needs a multistate method that incorporates state interaction in order to accurately model the potential energy surface at all nuclear coordinates. The recently developed linearized pair-density functional theory (L-PDFT) is a multistate extension of multiconfiguration PDFT, and it has been shown to be a cost-effective post-MCSCF method (as compared to more traditional and expensive multireference many-body perturbation methods or multireference configuration interaction methods) that can accurately model potential energy surfaces in regions of strong nuclear–electronic coupling in addition to accurately predicting Franck–Condon vertical excitations. Here, in this paper, we report the derivation of analytic gradients for L-PDFT and their implementation in the PySCF-forge software, and we illustrate the utility of these gradients for predicting ground- and excited-state equilibrium geometries and adiabatic excitation energies for formaldehyde, s-trans-butadiene, phenol, and cytosine.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2010

Discrimination of the effects of saturation and optical pumping in velocity-dependent pump-probe spectroscopy of rubidium: A simple analytical study

This paper presents a simple analytical theory for the velocity-dependent pump-probe laser spectroscopy of {sup 87}Rb and {sup 85}Rb atoms where the pump and the probe beams are circularly or linearly polarized. The analytical solutions of the line shapes of the velocity-selective optical pumping spectroscopy [G. Moon and H. R. Noh, Phys. Rev. A 78, 032506 (2008)] and saturated absorption spectroscopy [G. Moon and H. R. Noh, J. Opt. Soc. Am. B 25, 701 (2008); 27, 1741 (2010)] obtained in the previous reports, expressed as a sum of several Lorentzian functions, could be approximated as one (or in some cases, two) Lorentzian function(s). In particular, the contributions of the saturation and optical pumping effects could be discriminated explicitly in these simple analytical solutions, which is not possible in existing theories such as Nakayama's model. The simple analytical results for the saturation spectroscopy were compared with experimental results, and good agreement between them was observed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2011

Quantum interference in laser-assisted photoionization and analytical methods for the measurement of an attosecond xuv pulse

Investigations of the quantum interference in laser-assisted photoionization by an attosecond extreme ultraviolet (xuv) pulse shows an approximately constant value for the total photoionizations for different laser intensities. The square of the full width at half maximum of a photoelectron energy spectrum (PES) linearly depends on the laser intensity. By determining the laser-related phase of each streaked electron and using a transfer equation with linear corrections, an analytically quick method is proposed for precisely reconstructing the xuv pulse intensity (chirp) from one (two) measured PES(s) with a theoretical root-mean-square temporal (energy) difference of less than 1 attosecond (0.1 eV).

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Evaluation of Graph Analytics Frameworks Using the GAP Benchmark Suite

The analysis of connected data is an increasingly important application in high-performance computing. Such analyses can reveal fraudulent patterns in financial transactions, optimize telecommunications networks, predict information flow in social networks, etc. However, the landscape of graph analytics is highly diverse. Graph algorithms stress processor architectures differently, and no one graph can represent all topologies. Consequently, no single approach or framework is expected to be optimal for all graph analytics problems. To help make sense of this diverse landscape, we evaluated four approaches to graph analytics: GraphBLAS, Galois, BGL17, GraphIt; and compare them against hand-tuned implementations that take advantage of hardware features on our test platform. Graph- BLAS formulates graph analytics as sparse linear algebra. Galois provides syntactic constructs for data parallelism over irregular data structures. BGL17 is a generic C++ template library for implementing graph algorithms. GraphIt provides a domain- specific language to describe and optimize graph algorithms. We use the GAP Benchmark Suite to establish baseline performance and guide the side-by-side evaluation of each framework. GAP consists of 30 tests: six graph analytics algorithms (breadth- first search, single-source shortest path, PageRank, betweenness centrality, connected components, and triangle counting) run on five graphs, each with different topological characteristics (e.g., high diameter, skewed degree distribution, high average degree). High-performance reference implementations are included for each benchmark algorithm. Because a graph can be loaded into memory a number of ways (e.g., flat file on disk, compressed sparse format, data frames, retrieved from SQL or NoSQL databases), our evaluation focused on computational performance rather than I/O. Our results show the relative strengths of each framework.

Graph algorithms, Benchmarking, shared-memory prog↗
DOE OSTI2024

Linear response of molecular polaritons

In this article, we show that the collective light–matter strong coupling regime where N molecular emitters couple to the photon mode of an optical cavity can be mapped to a quantum impurity model where the photon is the impurity that is coupled to a bath of anharmonic transitions. In the thermodynamic limit where N ≫ 1, we argue that the bath can be replaced with an effective harmonic bath, leading to a dramatic simplification of the problem into one of the coupled harmonic oscillators. We derive simple analytical expressions for linear optical spectra (transmission, reflection, and absorption) where the only molecular input required is the molecular linear susceptibility. This formalism is applied to a series of illustrative examples, showing the role of temperature, disorder, vibronic coupling, and optical saturation of the molecular ensemble, explaining that it is useful even when describing an important class of nonlinear optical experiments. For completeness, we provide Appendixes A–C that include a self-contained derivation of the relevant spectroscopic observables for arbitrary anharmonic systems (for both large and small N) within the rotating-wave approximation. While some of the presented results herein have already been reported in the literature, we provide a unified presentation of the results as well as new interpretations that connect powerful concepts in open quantum systems and linear response theory with molecular polaritonics.

Chemistry↗
DOE OSTI2016

Effects of linear trends on estimation of noise in GNSS position time-series

A thorough understanding of time-dependent noise in Global Navigation Satellite System (GNSS) position time-series is necessary for computing uncertainties in any signals found in the data. However, estimation of time-correlated noise is a challenging task and is complicated by the difficulty in separating noise from signal, the features of greatest interest in the time-series. In this study, we investigate how linear trends affect the estimation of noise in daily GNSS position time-series. We use synthetic time-series to study the relationship between linear trends and estimates of time-correlated noise for the six most commonly cited noise models. We find that the effects of added linear trends, or conversely de-trending, vary depending on the noise model. The commonly adopted model of random walk (RW), flicker noise (FN) and white noise (WN) is the most severely affected by de-trending, with estimates of low-amplitude RW most severely biased. FN plus WN is least affected by adding or removing trends. Non-integer power-law noise estimates are also less affected by de-trending, but are very sensitive to the addition of trend when the spectral index is less than one. We derive an analytical relationship between linear trends and the estimated RW variance for the special case of pure RW noise. Finally, overall, we find that to ascertain the correct noise model for GNSS position time-series and to estimate the correct noise parameters, it is important to have independent constraints on the actual trends in the data.

58 GEOSCIENCES↗
DOE OSTI2022

A symbolic framework to obtain mid-fidelity models of flexible multibody systems with application to horizontal-axis wind turbines

Abstract. The article presents a symbolic framework (also called computer algebra program) that is used to obtain, in symbolic mathematical form, the linear and nonlinear equations of motion of a mid-fidelity multibody system including rigid and flexible bodies. Our approach is based on Kane's method and a nonlinear shape function representation for flexible bodies. The shape function approach does not represent the state of the art for flexible multibody dynamics but is an effective trade-off to obtain mid-fidelity models with few degrees of freedom, taking advantage of the separation of space and time. The method yields compact symbolic equations of motion with implicit account of the constraints. The general and automatic framework facilitates the creation and manipulation of models with various levels of complexity by adding or removing degrees of freedom. The symbolic treatment allows for analytical gradients and linearized equations of motion. The linear and nonlinear equations can be exported to Python code or dedicated software. There are multiple applications, such as time domain simulation, stability analyses, frequency domain analyses, advanced controller design, state observers, and digital twins. In this article, we describe the method we used to systematically generate the equations of motion of multibody systems and present the implementation of the framework using the Python package SymPy. We apply the framework to generate illustrative land-based and offshore wind turbine models. We compare our results with OpenFAST simulations and discuss the advantages and limitations of the method. The Python implementation is provided as an open-source project.

Branlard, Emmanuel (ORCID:0000000277506128)↗
DOE OSTI2019

Assessing the structure of classical molecular optimal control landscapes

Here we consider laser-driven optimal control landscape of a molecule from a classical mechanical perspective. The goal of optimal control in the present work is to steer the molecule from an initial state to a target state, denoted by two distinct points in phase space. Thus, a particular control objective is given as the difference between the final achieved phase space point and the target. The corresponding control landscape is defined as the latter control objective as a functional of the control field. While previous examination of the landscape critical points (i.e., a suboptimal point on the landscape where there is a zero gradient) has shown that the landscape topology is generally trap-free, the structure of the landscape away from these critical points is not well understood. We explore the landscape structure by examining an underlying metric defined as the ratio R of the gradient-based optimization path length of the control field evolution to the Euclidean distance between a given initial control field and the resultant optimal control field, where the latter field corresponds to a point at the top of the landscape. We analyze the path length-to-distance ratio R analytically for a linear forced harmonic oscillator and numerically for a nonlinear forced Morse oscillator. For the linear forced harmonic oscillator, we find that R ≤ $\sqrt{2}$ and reaches its minimum value of 1 (i.e., corresponding to “a straight shot” through control space) in the large target time limit, as well as at special finite target times. The ratio R is similarly small for Morse oscillator simulations when following a steepest-ascent path to the top of the landscape, implying that the landscape is quite smooth and devoid of gnarled features. This conclusion is exemplified for a path discovered with R≃ 1.0 where simply following the initial gradient direction takes the climb very close to the top of the landscape. These findings are consistent with a variety of previous like simulations examining R in quantum control scenarios.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

Electron cloud considerations for HIF drivers

Here, we review some previous results on electron-cloud dynamics and accumulation and the impact of electron clouds on ion beam dynamics, and assess these in the context of a magnetic-quadrupole-based heavy-ion fusion driver. We present a new analysis which exploits analytic solution of linearized envelope equations between accelerating gaps to derive a set of mapping equations which we use to extrapolate from previously obtained particle-simulation results for a beam transport system to an HIF driver.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2011

Diffraction-controlled backscattering threshold and application to Raman gap

In most classic analytical models of linear stimulated scatter, light diffraction is omitted, a priori. However, modern laser optic typically includes a variant of the random phase plate [Y. Kato et al., Phys. Rev. Lett. 53, 1057 (1984)], resulting in diffraction limited laser intensity fluctuations - or localized speckles - which may result in explosive reflectivity growth as the average laser intensity approaches a critical value [H. A. Rose and D. F. DuBois, Phys. Rev. Lett. 72, 2883 (1994)]. Among the differences between stimulated Raman scatter (SRS) and stimulated Brillouin scatter is that the SRS scattered light diffracts more strongly than the laser light with increase of electron density. This weakens the tendency of the SRS light to closely follow the most amplified paths, diminishing gain. Let G{sub 0} be the one-dimensional power gain exponent of the stimulated scatter. In this paper we show that differential diffraction gives rise to an increase of G{sub 0} at the SRS physical threshold with increase of electron density up to a drastic disruption of SRS as electron density approaches one fourth of its critical value from below. For three wave interaction lengths not small compared to a speckle length, this is a physically robust Raman gap mechanism.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Tsunami and acoustic-gravity waves in water of constant depth

A study of wave radiation by a rather general bottom displacement, in a compressible ocean of otherwise constant depth, is carried out within the framework of a three-dimensional linear theory. Simple analytic expressions for the flow field, at large distance from the disturbance, are derived. Realistic numerical examples indicate that the Acoustic-Gravity waves, which significantly precede the Tsunami, are expected to leave a measurable signature on bottom-pressure records that should be considered for early detection of Tsunami.

58 GEOSCIENCES↗
DOE OSTI2014

Dissipative solitons in pair-ion plasmas

The effects of ion-neutral collisions on the dynamics of the nonlinear ion acoustic wave in pair-ion plasma are investigated. The standard perturbative approach leads to a Korteweg-de Vries equation with a linear damping term for the dynamics of the finite amplitude wave. The ion-neutral collision induced dissipation is responsible for the linear damping. The analytical solution and numerical simulation reveal that the nonlinear wave propagates in the form of a weakly dissipative compressive solitons. Furthermore, the width of the soliton is proportional to the amplitude of the wave for fixed soliton velocity. Results are discussed in the context of the fullerene pair-ion plasma experiment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗