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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 1,495 records · Page 83
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Experimental and analytical investigation of a fluidic power generator

A combined experimental and analytical investigation was performed to understand the various fluid processes associated with the conversion of flow energy into electric power in a fluidic generator. Experiments were performed under flight-simulated laboratory conditions and results were compared with those obtained in the free-flight conditions. It is concluded that the mean mass flow critically controlled the output of the fluidic generator. Cross-correlation of the outputs of transducer data indicate the presence of a standing wave in the tube; the mechanism of oscillation is an acoustic resonance tube phenomenon. A linearized model was constructed coupling the flow behavior of the jet, the jet-layer, the tube, the cavity, and the holes of the fluidic generator. The analytical results also show that the mode of the fluidic power generator is an acoustical resonance phenomenon with the frequency of operation given by f approx = a/4L, where f is the frequency of jet swallowing, a is the average speed of sound in the tube, and L is the length of the tube. Analytical results further indicated that oscillations in the fluidic generator are always damped and consequently there is a forcing of the system in operation.

Sarohia, V.↗
NASA NTRS1995

Cooling of solar flares plasmas. 1: Theoretical considerations

Theoretical models of the cooling of flare plasma are reexamined. By assuming that the cooling occurs in two separate phase where conduction and radiation, respectively, dominate, a simple analytic formula for the cooling time of a flare plasma is derived. Unlike earlier order-of-magnitude scalings, this result accounts for the effect of the evolution of the loop plasma parameters on the cooling time. When the conductive cooling leads to an 'evaporation' of chromospheric material, the cooling time scales L(exp 5/6)/p(exp 1/6), where the coronal phase (defined as the time maximum temperature). When the conductive cooling is static, the cooling time scales as L(exp 3/4)n(exp 1/4). In deriving these results, use was made of an important scaling law (T proportional to n(exp 2)) during the radiative cooling phase that was forst noted in one-dimensional hydrodynamic numerical simulations (Serio et al. 1991; Jakimiec et al. 1992). Our own simulations show that this result is restricted to approximately the radiative loss function of Rosner, Tucker, & Vaiana (1978). for different radiative loss functions, other scaling result, with T and n scaling almost linearly when the radiative loss falls off as T(exp -2). It is shown that these scaling laws are part of a class of analytic solutions developed by Antiocos (1980).

Cargill, Peter J.↗
DOE OSTI2014

Gaussian-type light bullet solutions of the (3+1)-dimensional Schrödinger equation with cubic and power-law nonlinearities in PT-symmetric potentials

Two kinds of Gaussian-type light bullet (LB) solutions of the (3+1)-dimensional Schrödinger equation with cubic and power-law nonlinearities in PT-symmetric potentials are analytically obtained. The phase switches, powers and transverse power-flow densities of these solutions in homogeneous media are studied. The linear stability analysis of these LB solutions and the direct numerical simulation indicate that LB solutions are stable below some thresholds for the imaginary part of PT-symmetric potentials in the defocusing cubic and focusing power-law nonlinear medium, while they are always unstable for all parameters in other media. Moreover, the broadened and compressed behaviors of LBs in the exponential periodic amplification system and diffraction decreasing system are discussed. Results indicate that LB is more stable for the sign-changing nonlinearity in the exponential periodic amplification system than for the non-sign-changing nonlinearity in the diffraction decreasing system at the same propagation distances.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Unitarity of quantum tunneling decay for an analytical exact non-Hermitian resonant-state approach

Highlights: • Foundations of quantum mechanics • Quantum decay • Non-Hermitian Hamiltonian • Unitarity • Resonant state By using an analytical exact non-Hermitian formalism for quantum tunneling decay that involves the expansion of the decaying wave function as a linear combination of resonant states and transient functions associated with the complex poles of the outgoing Green’s function to the problem, it is shown that the integrated decaying probability density in the whole space satisfies unitarity at each value of time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Data on erosion and hydrogen fuel retention in Beryllium plasma-facing materials

ITER will use beryllium as a plasma-facing material in the main chamber, covering a total surface area of about 620 m 2 . Given the importance of beryllium erosion and co-deposition for tritium retention in ITER, significant efforts have been made to understand the behaviour of beryllium under fusion-relevant conditions with high particle and heat loads. This paper provides a comprehensive report on the state of knowledge of beryllium behaviour under fusion-relevant conditions: the erosion mechanisms and their consequences, beryllium migration in JET, fuel retention and dust generation. The paper reviews basic laboratory studies, advanced computer simulations and experience from laboratory plasma experiments in linear simulators of plasma–wall interactions and in controlled fusion devices using beryllium plasma-facing components. A critical assessment of analytical methods and simulation codes used in beryllium studies is given. The overall objective is to review the existing set of data with a broad literature survey and to identify gaps and research needs to broaden the database for ITER.

Erosion–deposition↗
DOE OSTI2017

Analysis of current-driven oscillatory dynamics of single-layer homoepitaxial islands on crystalline conducting substrates

Here we report results of a systematic study on the complex oscillatory current-driven dynamics of single-layer homoepitaxial islands on crystalline substrate surfaces and the dependence of this driven dynamical behavior on important physical parameters, including island size, substrate surface orientation, and direction of externally applied electric field. The analysis is based on a nonlinear model of driven island edge morphological evolution that accounts for curvature-driven edge diffusion, edge electromigration, and edge diffusional anisotropy. Using a linear theory of island edge morphological stability, we calculate a critical island size at which the island’s equilibrium edge shape becomes unstable, which sets a lower bound for the onset of time-periodic oscillatory dynamical response. Using direct dynamical simulations, we study the edge morphological dynamics of current-driven single-layer islands at larger-than-critical size, and determine the actual island size at which the migrating islands undergo a transition from steady to time-periodic asymptotic states through a subcritical Hopf bifurcation. At the highest symmetry of diffusional anisotropy examined, on {111} surfaces of face-centered cubic crystalline substrates, we find that more complex stable oscillatory states can be reached through period-doubling bifurcation at island sizes larger than those at the Hopf points. We characterize in detail the island morphology and dynamical response at the stable time-periodic asymptotic states, determine the range of stability of these oscillatory states terminated by island breakup, and explain the morphological features of the stable oscillating islands on the basis of linear stability theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2011

Nonlinear waves and coherent structures in the quantum single-wave model

Starting from the von Neumann-Maxwell equations for the Wigner quasi-probability distribution and for the self-consistent electric field, the quantum analog of the classical single-wave model has been derived. The linear stability of the quantum single-wave model has been studied, and periodic in time patterns have been found both analytically and numerically. In addition, some features of quantum chaos have been detected in the unstable region in parameter space. Further, a class of standing-wave solutions of the quantum single-wave model has also been found, which have been observed to behave as stable solitary-wave structures. The analytical results have been finally compared to the exact system dynamics obtained by solving the corresponding equations in Schrodinger representation numerically.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Thermally activated switching of perpendicular magnet by spin-orbit spin torque

We theoretically investigate the threshold current for thermally activated switching of a perpendicular magnet by spin-orbit spin torque. Based on the Fokker-Planck equation, we obtain an analytic expression of the switching current, in agreement with numerical result. We find that thermal energy barrier exhibits a quasi-linear dependence on the current, resulting in an almost linear dependence of switching current on the log-scaled current pulse-width even below 10 ns. This is in stark contrast to standard spin torque switching, where thermal energy barrier has a quadratic dependence on the current and the switching current rapidly increases at short pulses. Our results will serve as a guideline to design and interpret switching experiments based on spin-orbit spin torque.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Contact kinematics of biomimetic scales

Dermal scales, prevalent across biological groups, considerably boost survival by providing multifunctional advantages. Here, we investigate the nonlinear mechanical effects of biomimetic scale like attachments on the behavior of an elastic substrate brought about by the contact interaction of scales in pure bending using qualitative experiments, analytical models, and detailed finite element (FE) analysis. Our results reveal the existence of three distinct kinematic phases of operation spanning linear, nonlinear, and rigid behavior driven by kinematic interactions of scales. The response of the modified elastic beam strongly depends on the size and spatial overlap of rigid scales. The nonlinearity is perceptible even in relatively small strain regime and without invoking material level complexities of either the scales or the substrate.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Polarizabilities and van der Waals C{sub 6} coefficients of fullerenes from an atomistic electrodynamics model: Anomalous scaling with number of carbon atoms

The van der Waals C{sub 6} coefficients of fullerenes are shown to exhibit an anomalous dependence on the number of carbon atoms N such that C{sub 6} ∝ N{sup 2.2} as predicted using state-of-the-art quantum mechanical calculations based on fullerenes with small sizes, and N{sup 2.75} as predicted using a classical-metallic spherical-shell approximation of the fullerenes. We use an atomistic electrodynamics model where each carbon atom is described by a polarizable object to extend the quantum mechanical calculations to larger fullerenes. The parameters of this model are optimized to describe accurately the static and complex polarizabilities of the fullerenes by fitting against accurate ab initio calculations. This model shows that C{sub 6} ∝ N{sup 2.8}, which is supportive of the classical-metallic spherical-shell approximation. Additionally, we show that the anomalous dependence of the polarizability on N is attributed to the electric charge term, while the dipole–dipole term scales almost linearly with the number of carbon atoms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Global geodesic acoustic mode in an ideal magnetohydrodynamic tokamak plasma

A concise and transparent second order ordinary differential equation (ODE) describing the radial structure of the global geodesic acoustic mode (GAM) is analytically presented in a low-β tokamak plasma. The large-aspect-ratio and circular cross section are assumed to linearize the ideal magnetohydrodynamic equations. We show clearly how finite β-dependent terms affect the global GAM frequency and radial mode structure. Here, a typical Wentzel–Kramers–Brillouin form of solution is found for some reversed shear equilibria. For some other equilibria with lower β, even also in a reversed shear tokamak, the GAM continuum is upraised by the high order β-dependent terms so that its maximum is beyond ω G , where ω G is the classical local frequency of GAM. As a result, no self-consistent solution to the ODE can be found.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Sources of error and methods to improve accuracy in interface state density analysis using quasi-static capacitance–voltage measurements in wide bandgap semiconductors

Characterizing interface trap states in commercial wide bandgap devices using frequency-based measurements requires unconventionally high probing frequencies to account for both fast and slow traps associated with wide bandgap materials. The C - ψs technique has been suggested as a viable quasi-static method for determining the interface trap state densities in wide bandgap systems, but the results are shown to be susceptible to errors in the analysis procedure. Here this work explores the primary sources of errors present in the C - ψs technique using an analytical model that describes the apparent response for wide bandgap MOS capacitor devices. Measurement noise is shown to greatly impact the linear fitting routine of the 1/C$^{*2}_s$ vs Ψ s plot to calibrate the additive constant in the surface potential/gate voltage relationship, and an inexact knowledge of the oxide capacitance is also shown to impede interface trap state analysis near the band edge. In addition, a slight nonlinearity that is typically present throughout the 1/C$^{*2}_s$ vs Ψ s plot hinders the accurate estimation of interface trap densities, which is demonstrated for a fabricated n-SiC MOS capacitor device. Methods are suggested to improve quasi-static analysis, including a novel method to determine an approximate integration constant without relying on a linear fitting routine.

42 ENGINEERING↗
DOE OSTI2013

TOWARD A THEORY OF ASTROPHYSICAL PLASMA TURBULENCE AT SUBPROTON SCALES

We present an analytical study of subproton electromagnetic fluctuations in a collisionless plasma with a plasma beta of the order of unity. In the linear limit, a rigorous derivation from the kinetic equation is conducted focusing on the role and physical properties of kinetic-Alfvén and whistler waves. Then, nonlinear fluid-like equations for kinetic-Alfvén waves and whistler modes are derived, with special emphasis on the similarities and differences in the corresponding plasma dynamics. The kinetic-Alfvén modes exist in the lower-frequency region of phase space, ω << k v{sub Ti} , where they are described by the kinetic-Alfvén system. These modes exist both below and above the ion-cyclotron frequency. The whistler modes, which are qualitatively different from the kinetic-Alfvén modes, occupy a different region of phase space, k v{sub Ti} << ω << k{sub z}v{sub Te} , and they are described by the electron magnetohydrodynamics (MHD) system or the reduced electron MHD system if the propagation is oblique. Here, k{sub z} and k are the wavenumbers along and transverse to the background magnetic field, respectively, and v{sub Ti} and v{sub Te} are the ion and electron thermal velocities, respectively. The models of subproton plasma turbulence are discussed and the results of numerical simulations are presented. We also point out possible implications for solar-wind observations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Covariance matrices for galaxy cluster weak lensing: from virial regime to uncorrelated large-scale structure

Next-generation optical imaging surveys will revolutionize the observations of weak gravitational lensing by galaxy clusters and provide stringent constraints on growth of structure and cosmic acceleration. In these experiments, accurate modelling of covariance matrices of cluster weak lensing plays the key role in obtaining robust measurements of the mean mass of clusters and cosmological parameters. We use a combination of analytical calculations and high-resolution N -body simulations to derive accurate covariance matrices that span from the virial regime to linear scales of the cluster-matter cross-correlation. We validate this calculation using a public ray-tracing lensing simulation and provide a software package for calculating covariance matrices for a wide range of cluster and source sample choices. We discuss the relative importance of shape noise and density fluctuations, the impact of radial bin size, and the impact of off-diagonal elements. For a weak lensing source density n s = 10 arcmin -2 , shape noise typically dominates the variance on comoving scales $r_{\rm p}\lesssim 5\ h^{-1} \, \rm Mpc$. However, for n s = 60 arcmin -2 , potentially achievable with future weak lensing experiments, density fluctuations typically dominate the variance at $r_{\rm p}\gtrsim 1\ h^{-1} \, \rm Mpc$ and remain comparable to shape noise on smaller scales.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Magnetic susceptibility of the quark condensate and polarization from chiral models

We compute the magnetic susceptibility of the quark condensate and the polarization of quarks at zero temperature and in a uniform magnetic background. Our theoretical framework consists of two chiral models that allow us to treat self-consistently the spontaneous breaking of chiral symmetry: the linear {sigma}-model coupled to quarks, dubbed quark-meson model, and the Nambu-Jona-Lasinio model. We also perform analytic estimates of the same quantities within the renormalized quark-meson model, both in the regimes of weak and strong fields. Our numerical results are in agreement with the recent literature; moreover, we confirm previous attice findings, related to the saturation of the polarization at large fields.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Effect of non-Gaussian lensing deflections on CMB lensing measurements

We investigate the impact of non-Gaussian lensing deflections on measurements of the CMB lensing power spectrum. We find that the false assumption of their Gaussianity significantly biases these measurements in current and future experiments at the percent level. The bias is detected by comparing CMB lensing reconstructions from simulated CMB data lensed with Gaussian deflection fields to reconstructions from simulations lensed with fully non-Gaussian deflection fields. The non-Gaussian deflections are produced by ray-tracing through snapshots of an N-body simulation and capture both the non-Gaussianity induced by non-linear structure formation and by multiple correlated deflections. We find that the amplitude of the measured bias is in agreement with analytical predictions by Bohm et al. 2016. The bias is largest in temperature-based measurements and we do not find evidence for it in measurements from a combination of polarization fields (EB;EB). We argue that the non-Gaussian bias should be even more important for measurements of cross-correlations of CMB lensing with low-redshift tracers of large-scale structure.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

WE-EF-207-01: FEATURED PRESENTATION and BEST IN PHYSICS (IMAGING): Task-Driven Imaging for Cone-Beam CT in Interventional Guidance

Purpose: This work introduces a task-driven imaging framework that utilizes a patient-specific anatomical model, mathematical definition of the imaging task, and a model of the imaging system to prospectively design acquisition and reconstruction techniques that maximize task-based imaging performance. Utility of the framework is demonstrated in the joint optimization of tube current modulation and view-dependent reconstruction kernel in filtered-backprojection reconstruction and non-circular orbit design in model-based reconstruction. Methods: The system model is based on a cascaded systems analysis of cone-beam CT capable of predicting the spatially varying noise and resolution characteristics as a function of the anatomical model and a wide range of imaging parameters. Detectability index for a non-prewhitening observer model is used as the objective function in a task-driven optimization. The combination of tube current and reconstruction kernel modulation profiles were identified through an alternating optimization algorithm where tube current was updated analytically followed by a gradient-based optimization of reconstruction kernel. The non-circular orbit is first parameterized as a linear combination of bases functions and the coefficients were then optimized using an evolutionary algorithm. The task-driven strategy was compared with conventional acquisitions without modulation, using automatic exposure control, and in a circular orbit. Results: The task-driven strategy outperformed conventional techniques in all tasks investigated, improving the detectability of a spherical lesion detection task by an average of 50% in the interior of a pelvis phantom. The non-circular orbit design successfully mitigated photon starvation effects arising from a dense embolization coil in a head phantom, improving the conspicuity of an intracranial hemorrhage proximal to the coil. Conclusion: The task-driven imaging framework leverages a knowledge of the imaging task within a patient-specific anatomical model to optimize image acquisition and reconstruction techniques, thereby improving imaging performance beyond that achievable with conventional approaches. 2R01-CA-112163; R01-EB-017226; U01-EB-018758; Siemens Healthcare (Forcheim, Germany)

60 APPLIED LIFE SCIENCES↗
DOE OSTI2010

Asymptotics of the S-matrix and unitarisation

The manner in which the elastic scattering amplitude obeys unitarity, how it enters the circle of unitarity, and what its asymptotic limit is, remains a problem for models which include terms that rise fast with s. We have checked that the features of cross sections which come from unitarisation are present for most unitarisation schemes, e.g. those that saturate the profile function or those that describe multiple exchanges via an analytic formula. We have also obtained a scheme which interpolates between different classes of the unitarisation and found corresponding non-linear equations. Considering different forms of energy dependence of the scattering amplitude, and a variety of unitarisation schemes, we show that, in order to reproduce the data, the fits choose an amplitude that corresponds to an asymptotic value S = 0.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗