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 811 records · Page 45
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Highly sensitive SPR PCF biosensors based on Ag/TiN and Ag/ZrN configurations

We numerically present and analyze a surface plasmon resonance (SPR) bimetallic photonic crystal fiber (PCF) biosensor using full vectorial finite element method. The bimetallic configuration is based on Silver and (TiN or ZrN) as alternative plasmonic materials. The reported design relies on PCF with an external channel to house the analyte. The inner surface of the channel is coated by a silver layer followed by TiN or ZrN to protect the silver layer from oxidation. The proposed biosensor can be implemented to detect the unknown analytes, organic chemicals, biological analytes, and biomolecules via the sensitive resonant peaks to the analyte refractive index variations for both polarized modes with high linearity. In this study, a comparison is made between the Ag/TiN configuration and the Ag/ZrN counterpart in terms of sensitivity, losses, and linearity. The geometrical parameters are optimized to achieve high refractive index sensitivities of 7000 nm/RIU for quasi-transverse electric (TE) mode and 6900 nm/RIU for quasi-transverse magnetic (TM) mode, respectively for the Ag/TiN configuration. However, the quasi TE and quasi TM modes achieve high sensitivity of 5300 and 5400 nm/RIU, respectively using the Ag/ZrN configuration. The standard PCF fabrication technologies can be used to fabricate the proposed SPR PCF biosensors.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Pulsed laser interactions with space debris: Target shape effects

Among the approaches to the proposed mitigation and remediation of the space debris problem is the de-orbiting of objects in low Earth orbit through irradiation by ground-based high-intensity pulsed lasers. Laser ablation of a thin surface layer causes target recoil, resulting in the depletion of orbital angular momentum and accelerated atmospheric re-entry. However, both the magnitude and direction of the recoil are shape dependent, a feature of the laser-based remediation concept that has received little attention. Since the development of a predictive capability is desirable, we have investigated the dynamical response to ablation of objects comprising a variety of shapes. We derive and demonstrate a simple analytical technique for calculating the ablation-driven transfer of linear momentum, emphasizing cases for which the recoil is not exclusively parallel to the incident beam. For the purposes of comparison and contrast, we examine one case of momentum transfer in the low-intensity regime, where photon pressure is the dominant momentum transfer mechanism, showing that shape and orientation effects influence the target response in a similar, but not identical, manner. As a result, we address the related problem of target spin and, by way of a few simple examples, show how ablation can alter the spin state of a target, which often has a pronounced effect on the recoil dynamics.

42 ENGINEERING↗
DOE OSTI2020

Nonlinear sparse Bayesian learning for physics-based models

This paper addresses the issue of overfitting while calibrating unknown parameters of over-parameterized physics-based models with noisy and incomplete observations. Here, a semi-analytical Bayesian framework of nonlinear sparse Bayesian learning (NSBL) is proposed to identify sparsity among model parameters during Bayesian inversion. NSBL offers significant advantages over machine learning algorithm of sparse Bayesian learning (SBL) for physics-based models, such as 1) the likelihood function or the posterior parameter distribution is not required to be Gaussian, and 2) prior parameter knowledge is incorporated into sparse learning (i.e. not all parameters are treated as questionable). NSBL employs the concept of automatic relevance determination (ARD) to facilitate sparsity among questionable parameters through parameterized prior distributions. The analytical tractability of NSBL is enabled by employing Gaussian ARD priors and by building a Gaussian mixture-model approximation of the posterior parameter distribution that excludes the contribution of ARD priors. Subsequently, type-II maximum likelihood is executed using Newton's method whereby the evidence and its gradient and Hessian information are computed in a semi-analytical fashion. We show numerically and analytically that SBL is a special case of NSBL for linear regression models. Subsequently, a linear regression example involving multimodality in both parameter posterior pdf and model evidence is considered to demonstrate the performance of NSBL in cases where SBL is inapplicable. Next, NSBL is applied to identify sparsity among the damping coefficients of a mass-spring-damper model of a shear building frame. These numerical studies demonstrate the robustness and efficiency of NSBL in alleviating overfitting during Bayesian inversion of nonlinear physics-based models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Buoyancy instability of homologous implosions

With this study, I consider the hydrodynamic stability of imploding ideal gases as an idealized model for inertial confinement fusion capsules, sonoluminescent bubbles and the gravitational collapse of astrophysical gases. For oblate modes (short-wavelength incompressive modes elongated in the direction of the mean flow), a second-order ordinary differential equation is derived that can be used to assess the stability of any time-dependent flow with planar, cylindrical or spherical symmetry. Upon further restricting the analysis to homologous flows, it is shown that a monatomic gas is governed by the Schwarzschild criterion for buoyant stability. Under buoyantly unstable conditions, both entropy and vorticity fluctuations experience power-law growth in time, with a growth rate that depends upon mean flow gradients and, in the absence of dissipative effects, is independent of mode number. If the flow accelerates throughout the implosion, oblate modes amplify by a factor (2C) |N 0 |t i , where C is the convergence ratio of the implosion, N 0 is the initial buoyancy frequency and t i is the implosion time scale. If, instead, the implosion consists of a coasting phase followed by stagnation, oblate modes amplify by a factor exp(π|N 0 |t s ), where N 0 is the buoyancy frequency at stagnation and t s is the stagnation time scale. Even under stable conditions, vorticity fluctuations grow due to the conservation of angular momentum as the gas is compressed. For non-monatomic gases, this additional growth due to compression results in weak oscillatory growth under conditions that would otherwise be buoyantly stable; this over-stability is consistent with the conservation of wave action in the fluid frame. The above analytical results are verified by evolving the complete set of linear equations as an initial value problem, and it is demonstrated that oblate modes are the fastest-growing modes and that high mode numbers are required to reach this limit (Legendre mode ℓ ≳ 100 for spherical flows). Finally, comparisons are made with a Lagrangian hydrodynamics code, and it is found that a numerical resolution of ~30 zones per wavelength is required to capture these solutions accurately. This translates to an angular resolution of ~(12/ℓ)°, or ≲ 0.1° to resolve the fastest-growing modes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Faxén form of time-domain force on a sphere in unsteady spatially varying viscous compressible flows

An explicit expression for the time-dependent force on a stationary, finite-sized spherical particle located in an unsteady inhomogeneous ambient flow is presented. The force expression accounts for both viscous and compressible effects. Towards this end, a time-harmonic plane travelling wave of a given frequency propagating in a viscous compressible flow over a sphere is considered. Linearized compressible Navier–Stokes equations are solved to obtain an analytical expression for the force exerted on the particle in the frequency domain. The force obtained in the Laplace space due to a travelling wave of a given frequency and wavenumber is then generalized to any arbitrary incoming flow. This is achieved by relating the radial and tangential velocity components in the Laplace space to the surface-averaged radial velocity and volume-averaged velocity vectors respectively in the time space. Moreover an expression relating the surface-averaged radial velocity and volume-averaged velocity vector has been provided. The total force is written as a summation of the undisturbed and disturbed force (quasi-steady, inviscid-unsteady and viscous-unsteady) contributions. The force contributions thus obtained are expressed as comprising of two parts – that arising due to spatial variation in the ambient flow and the other arising due to temporal variation. The current formulation is applicable to inhomogeneous ambient flows, however in the limit of negligible Reynolds and Mach numbers. The results are applicable even for particles of sizes larger than the acoustic wavelength. The accuracy of the explicit time-domain force expression is first tested by computing the force on an 80 mm diameter particle due to a weak planar expansion fan. Extension of this formulation when nonlinear effects become important is also proposed and tested by considering strong expansion fans. The results thus obtained are compared against corresponding axisymmetric numerical simulations.

Mechanics↗
DOE OSTI2014

Quantitative estimation of the spin-wave features supported by a spin-torque-driven magnetic waveguide

The main features of the spin-waves excited at the threshold via spin-polarized currents in a one-dimensional normally-to-plane magnetized waveguide are quantitatively determined both analytically and numerically. In particular, the dependence of the threshold current, frequency, wavenumber, and decay length is investigated as a function of the size of the nanocontact area through which the electric current is injected. From the analytical viewpoint, such a goal has required to solve the linearized Landau-Lifshitz-Gilbert-Slonczewski equation together with boundary and matching conditions associated with the waveguide geometry. Owing to the complexity of the resulting transcendent system, particular solutions have been obtained in the cases of elongated and contracted nanocontacts. These results have been successfully compared with those arising from numerical integration of the abovementioned transcendent system and with micromagnetic simulations. This quantitative agreement has been achieved thanks to the model here considered which takes explicitly into account the diagonal demagnetizing factors of a rectangular prism as well as the dependence of the relaxation rate on the wavenumber. Our analysis confirmed that the spin-wave features supported by such a waveguide geometry are significantly different from the ones observed in classical two-dimensional nanocontact devices. Moreover, it has been proved that the characteristic parameters depend strongly on the material properties and on the modulus of external field, but they could be independent of the nanocontact length. Finally, it is shown that spin-transfer oscillators based on contracted nanocontacts have a better capability to transmit spin-waves over large distances.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Collisionless kinetic theory of oblique tearing instabilities

The linear dispersion relation for collisionless kinetic tearing instabilities is calculated for the Harris equilibrium. In contrast to the conventional 2D geometry, which considers only modes at the center of the current sheet, modes can span the current sheet in 3D. Modes at each resonant surface have a unique angle with respect to the guide field direction. Both kinetic simulations and numerical eigenmode solutions of the linearized Vlasov-Maxwell equations have recently revealed that standard analytic theories vastly overestimate the growth rate of oblique modes. In this paper, we find that this stabilization is associated with the density-gradient-driven diamagnetic drift. The analytic theories miss this drift stabilization because the inner tearing layer broadens at oblique angles sufficiently far that the assumption of scale separation between the inner and outer regions of boundary-layer theory breaks down. The dispersion relation obtained by numerically solving a single second order differential equation is found to approximately capture the drift stabilization predicted by solutions of the full integro-differential eigenvalue problem. Finally, a simple analytic estimate for the stability criterion is provided.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Core and filament formation in magnetized, self-gravitating isothermal layers

We examine the role of the gravitational instability in an isothermal, self-gravitating layer threaded by magnetic fields on the formation of filaments and dense cores. Using a numerical simulation, we follow the non-linear evolution of a perturbed equilibrium layer. The linear evolution of such a layer is described in the analytic work of Nagai et al. We find that filaments and dense cores form simultaneously. Depending on the initial magnetic field, the resulting filaments form either a spiderweb-like network (for weak magnetic fields) or a network of parallel filaments aligned perpendicular to the magnetic field lines (for strong magnetic fields). Although the filaments are radially collapsing, the density profile of their central region (up to the thermal scale height) can be approximated by a hydrodynamical equilibrium density structure. Thus, the magnetic field does not play a significant role in setting the density distribution of the filaments. The density distribution outside of the central region deviates from the equilibrium. The radial column density distribution is then flatter than the expected power law of r {sup –4} and similar to filament profiles observed with Herschel. Our results do not explain the near constant filament width of ∼0.1pc. However, our model does not include turbulent motions. It is expected that the accretion-driven amplification of these turbulent motions provides additional support within the filaments against gravitational collapse. Finally, we interpret the filamentary network of the massive star forming complex G14.225-0.506 in terms of the gravitational instability model and find that the properties of the complex are consistent with being formed out of an unstable layer threaded by a strong, parallel magnetic field.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

Constraining primordial magnetic fields with future cosmic shear surveys

The origin of astrophysical magnetic fields observed in galaxies and clusters of galaxies is still unclear. One possibility is that primordial magnetic fields generated in the early Universe provide seeds that grow through compression and turbulence during structure formation. A cosmological magnetic field present prior to recombination would produce substantial matter clustering at intermediate/small scales, on top of the standard inflationary power spectrum. In this work we study the effect of this alteration on one particular cosmological observable, cosmic shear. We adopt the semi-analytic halo model in order to describe the non-linear clustering of matter, and feed it with the altered mass variance induced by primordial magnetic fields. We find that the convergence power spectrum is, as expected, substantially enhanced at intermediate/small angular scales, with the exact amplitude of the enhancement depending on the magnitude and power-law index of the magnetic field power spectrum. Specifically, for a fixed amplitude, the effect of magnetic fields is larger for larger spectral indices. We use the predicted statistical errors for a future wide-field cosmic shear survey, on the model of the ESA Cosmic Vision mission Euclid, in order to forecast constraints on the amplitude of primordial magnetic fields as a function of the spectral index. We find that the amplitude will be constrained at the level of ∼ 0.1 nG for n{sub B} ∼ −3, and at the level of ∼ 10{sup −7} nG for n{sub B} ∼ 3. The latter is at the same level of lower bounds coming from the secondary emission of gamma-ray sources, implying that for high spectral indices Euclid will certainly be able to detect primordial magnetic fields, if they exist. The present study shows how large-scale structure surveys can be used for both understanding the origins of astrophysical magnetic fields and shedding new light on the physics of the pre-recombination Universe.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Black holes in a cubic Galileon universe

We find and study the properties of black hole solutions for a subclass of Horndeski theory including the cubic Galileon term. The theory under study has shift symmetry but not reflection symmetry for the scalar field. The Galileon is assumed to have linear time dependence characterized by a velocity parameter. We give analytic 3-dimensional solutions that are akin to the BTZ solutions but with a non-trivial scalar field that modifies the effective cosmological constant. We then study the 4-dimensional asymptotically flat and de Sitter solutions. The latter present three different branches according to their effective cosmological constant. For two of these branches, we find families of black hole solutions, parametrized by the velocity of the scalar field. These spherically symmetric solutions, obtained numerically, are different from GR solutions close to the black hole event horizon, while they have the same de-Sitter asymptotic behavior. The velocity parameter represents black hole primary hair.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

“Ripples” on a relativistically expanding fluid

Recent studies have shown that fluctuations of various types play important roles in the evolution of the fireball created in relativistic heavy ion collisions and bear many phenomenological consequences for experimental observables. In addition, the bulk dynamics of the fireball is well described by relativistic hydrodynamic expansion and the fluctuations on top of such expanding background can be studied within the linearized hydrodynamic framework. In this paper we present complete and analytic sound wave solutions on top of both Bjorken flow and Hubble flow backgrounds.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Source-free integration method for black hole perturbations and self-force computation: Radial fall

Perturbations of Schwarzschild-Droste black holes in the Regge-Wheeler gauge benefit from the availability of a wave equation and from the gauge invariance of the wave function, but lack smoothness. Nevertheless, the even perturbations belong to the C{sup 0} continuity class, if the wave function and its derivatives satisfy specific conditions on the discontinuities, known as jump conditions, at the particle position. These conditions suggest a new way for dealing with finite element integration in the time domain. The forward time value in the upper node of the (t,r*) grid cell is obtained by the linear combination of the three preceding node values and of analytic expressions based on the jump conditions. The numerical integration does not deal directly with the source term, the associated singularities and the potential. This amounts to an indirect integration of the wave equation. The known wave forms at infinity are recovered and the wave function at the particle position is shown. In this series of papers, the radial trajectory is dealt with first, being this method of integration applicable to generic orbits of EMRI (Extreme Mass Ratio Inspiral).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Three-dimensional particle-in-cell modeling of parametric instabilities near the quarter-critical density in plasmas

The nonlinear regime of laser-plasma interactions including both two-plasmon decay (TPD) and stimulated Raman scattering (SRS) instabilities has been studied in three-dimensional (3D) particle-in-cell simulations with parameters relevant to the inertial confinement fusion (ICF) experiments. SRS and TPD develop in the same region in plasmas, and the generation of fast electrons can be described accurately with only the full model including both SRS and TPD. The growth of instabilities in the linear stage is found to be in good agreement with analytical theories. In the saturation stage the low-frequency density perturbations driven by the daughter waves of the SRS side scattering can saturate the TPD and consequently inhibit the fast-electron generation. As a result, the fast-electron flux in 3D modeling is up to an order of magnitude smaller than previously reported in 2D TPD simulations, bringing it close to the results of ICF experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

SU-E-T-508: Internal Organ Motion Effect On Radiation Dose to a Point Under Half-Beam Block Match Line

Purpose Half-beam block is a field matching technique frequently used in radiotherapy. With no setup error, a well calibrated linac, and no internal organ motion, two photon fields can be matched seamlessly dosimetry-wise with their central axes passing the match line. However, in actual clinical situations, internal organ motion is often inevitable. This study was conducted to investigate its influence on radiation dose to patient internal points directly under the matching line. Methods A clinical setting is modeled as two half-space (x<0 and x<0) radiation fields that are turned on sequentially with a time gap of integer times of the patient internal organ motion period (T{sub 0}). Our point of interest moves with patient internal organs periodically and evenly in and out of the radiation fields, resulting in an average location at x=0. When the fields are delivered without any motion management, the initial phase of the point’s movement is unknown. Statistical methods are used to compute the expected value ( ) and variance (σ) of the point dose given the uncertainty. Results Analytical solutions are obtained for and s of dose received by a point directly under the match line. is proportional to the total beam-on time (T1), and σ demonstrates previously unknown periodic behavior. /<Dσ has local maximums (minimums) when T{sub 1} is 2n*T{sub 0} ((2n+1)*T{sub 0}) (n is an integer) with an upper envelope scales as 1/T{sub 1}. Worst case scenario the point dose can be zero or double of the expected value. Conclusion We have analytically analyzed the internal organ motion effect on radiation dose received by a patient internal point directly under a half-beam block match line. Our results help us to better understand this phenomenon and facilitate the reduction of point dosimetric uncertainties in our clinical practice.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

BPS spectra and 3-manifold invariants

We provide a physical definition of new homological invariants H a (M 3 ) of 3-manifolds (possibly, with knots) labeled by abelian flat connections. The physical system in question involves a 6d fivebrane theory on M 3 times a 2-disk, D 2 , whose Hilbert space of BPS states plays the role of a basic building block in categorification of various partition functions of 3d N = 2 theory T[M 3 ]: D 2 × S 1 half-index, S 2 × S 1 superconformal index, and S 2 × S 1 topologically twisted index. The first partition function is labeled by a choice of boundary condition and provides a refinement of Chern–Simons (WRT) invariant. A linear combination of them in the unrefined limit gives the analytically continued WRT invariant of M 3 . The last two can be factorized into the product of half-indices. Here, we show how this works explicitly for many examples, including Lens spaces, circle fibrations over Riemann surfaces, and plumbed 3-manifolds.

3-manifold↗
DOE OSTI2022

Stochastic Vector Techniques in Ground-State Electronic Structure

Herein we review a suite of stochastic vector computational approaches for studying the electronic structure of extended condensed matter systems. These techniques help reduce algorithmic complexity, facilitate efficient parallelization, simplify computational tasks, accelerate calculations, and diminish memory requirements. While their scope is vast, we limit our study to ground-state and finite temperature density functional theory (DFT) and second-order many-body perturbation theory. More advanced topics, such as quasiparticle (charge) and optical (neutral) excitations and higher-order processes, are covered elsewhere. We start by explaining how to use stochastic vectors in computations, characterizing the associated statistical errors. Next, we show how to estimate the electron density in DFT and discuss effective techniques to reduce statistical errors. Finally, we review the use of stochastic vectors for calculating correlation energies within the second-order Møller-Plesset perturbation theory and its finite temperature variational form. Example calculation results are presented and used to demonstrate the efficacy of the methods.

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

The Optical Signatures of Stochastic Processes in Many-Body Exciton Scattering

We review our recent quantum stochastic model for spectroscopic lineshapes in the presence of a coevolving and nonstationary background population of excitations. Starting from a field theory description for interacting bosonic excitons, we derive a reduced model whereby optical excitons are coupled to an incoherent background via scattering as mediated by their screened Coulomb coupling. The Heisenberg equations of motion for the optical excitons are then driven by an auxiliary stochastic population variable, which we take to be the solution of an Ornstein–Uhlenbeck process. Here, we present an overview of the theoretical techniques we have developed as applied to predicting coherent nonlinear spectroscopic signals. We show how direct (Coulomb) and exchange coupling to the bath give rise to distinct spectral signatures and discuss mathematical limits on inverting spectral signatures to extract the background density of states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Aberration compensation in a Skew parametric-resonance ionization cooling channel

Skew Parametric-resonance Ionization Cooling (Skew PIC) represents a novel method for focusing of highly divergent particle beams, as in the final 6D cooling stage of a high-luminosity muon collider. In the muon collider concept, the resultant equilibrium transverse emittances from cooling with Skew PIC are an order of magnitude smaller than in conventional ionization cooling. The concept makes use of coupling of the transverse dynamic behavior, and the linear dynamics are well-behaved with good agreement between analytic solutions and simulation results. Compared to the uncoupled system, coupling of the transverse dynamic behavior purports to reduce the number of multipoles required for aberration compensation while also avoiding unwanted resonances. Aberration compensation is more complicated in the coupled case, especially in the high-luminosity muon collider application where equilibrium angular spreads in the cooling channel are on the order of 200 mrad. We present recent progress on aberration compensation for control of highly divergent muon beams in the coupled correlated optics channel, and a simple cooling model to test the transverse acceptance of the channel.

Sy, Amy V.↗