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Sample records for quasilinear theory

  1. Reformulation of quasi-linear theory.

    NASA Technical Reports Server (NTRS)

    Kaufman, A. N.

    1972-01-01

    Standard plasma quasi-linear theory is reformulated on the basis of a classical quantum derivation proceeding from the Vlasov equation and dealing only with frequency, wavenumber, and velocity. The wave amplitudes are assumed to be weakly time-dependent, and no distinction is made between growing and decaying waves. The proposed method leads to no negative diffusivity of 'fake' diffusion. By appropraite treatment of nonresonant interaction, expressions are obtained for wave energy and momentum.

  2. Quasi-linear theory via the cumulant expansion approach

    NASA Technical Reports Server (NTRS)

    Jones, F. C.; Birmingham, T. J.

    1974-01-01

    The cumulant expansion technique of Kubo was used to derive an intergro-differential equation for f , the average one particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the f equation degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory for this limited class of fluctuations. For more physically realistic fluctuations, however, quasi-linear theory is at best approximate.

  3. Simulation and quasilinear theory of proton firehose instability

    SciTech Connect

    Seough, Jungjoon; Yoon, Peter H.; Hwang, Junga

    2015-01-15

    The electromagnetic proton firehose instability is driven by excessive parallel temperature anisotropy, T{sub ∥} > T{sub ⊥} (or more precisely, parallel pressure anisotropy, P{sub ∥} > P{sub ⊥}) in high-beta plasmas. Together with kinetic instabilities driven by excessive perpendicular temperature anisotropy, namely, electromagnetic proton cyclotron and mirror instabilities, its role in providing the upper limit for the temperature anisotropy in the solar wind is well-known. A recent Letter [Seough et al., Phys. Rev. Lett. 110, 071103 (2013)] employed quasilinear kinetic theory for these instabilities to explain the observed temperature anisotropy upper bound in the solar wind. However, the validity of quasilinear approach has not been rigorously tested until recently. In a recent paper [Seough et al., Phys. Plasmas 21, 062118 (2014)], a comparative study is carried out for the first time in which quasilinear theory of proton cyclotron instability is tested against results obtained from the particle-in-cell simulation method, and it was demonstrated that the agreement was rather excellent. The present paper addresses the same issue involving the proton firehose instability. Unlike the proton cyclotron instability, however, it is found that the quasilinear approximation enjoys only a limited range of validity, especially for the wave dynamics and for the relatively high-beta regime. Possible causes and mechanisms responsible for the discrepancies are speculated and discussed.

  4. Simulation and quasilinear theory of aperiodic ordinary mode instability

    SciTech Connect

    Seough, Jungjoon; Yoon, Peter H.; Hwang, Junga; Nariyuki, Yasuhiro

    2015-08-15

    The purely growing ordinary (O) mode instability driven by excessive parallel temperature anisotropy for high-beta plasmas was first discovered in the 1970s. This instability receives renewed attention because it may be applicable to the solar wind plasma. The electrons in the solar wind feature temperature anisotropies whose upper values are apparently limited by plasma instabilities. The O-mode instability may be important in this regard. Previous studies of O mode instability have been based on linear theory, but the actual solar wind electrons may be in saturated state. The present paper investigates the nonlinear saturation behavior of the O mode instability by means of one-dimensional particle-in-cell simulation and quasilinear theory. It is shown that the quasilinear method accurately reproduces the simulation results.

  5. Simulation and quasilinear theory of aperiodic ordinary mode instability

    NASA Astrophysics Data System (ADS)

    Seough, Jungjoon; Yoon, Peter H.; Hwang, Junga; Nariyuki, Yasuhiro

    2015-08-01

    The purely growing ordinary (O) mode instability driven by excessive parallel temperature anisotropy for high-beta plasmas was first discovered in the 1970s. This instability receives renewed attention because it may be applicable to the solar wind plasma. The electrons in the solar wind feature temperature anisotropies whose upper values are apparently limited by plasma instabilities. The O-mode instability may be important in this regard. Previous studies of O mode instability have been based on linear theory, but the actual solar wind electrons may be in saturated state. The present paper investigates the nonlinear saturation behavior of the O mode instability by means of one-dimensional particle-in-cell simulation and quasilinear theory. It is shown that the quasilinear method accurately reproduces the simulation results.

  6. Quasilinear theory and particle-in-cell simulation of proton cyclotron instability

    SciTech Connect

    Seough, Jungjoon E-mail: yoonp@umd.edu; Yoon, Peter H. E-mail: yoonp@umd.edu; Hwang, Junga E-mail: yoonp@umd.edu

    2014-06-15

    The electromagnetic ion (proton) cyclotron instability is important for regulating the excessive development of perpendicular temperature anisotropy in the solar wind, for instance, when it is compressed in the vicinity of the Earth's magnetosheath environment. A recent letter [Seough et al., Phys. Rev. Lett. 110, 071103 (2013)] successfully employed the quasilinear kinetic theory to explain the observed temperature anisotropy upper bound. The present paper rigorously examines the reliability of the quasilinear theory by making a direct comparison against results from the particle-in-cell simulation method. It is found that the quasilinear approach is indeed a valid first-cut theoretical tool in the study of proton cyclotron instability.

  7. Electromagnetic hot ion beam instabilities - Quasi-linear theory and simulation

    NASA Technical Reports Server (NTRS)

    Rogers, B.; Gary, S. P.; Winske, D.

    1985-01-01

    This paper considers the quasi-linear theory of the right- and left-hand resonant electromagnetic instabilities driven by a hot ion beam streaming parallel to a magnetic field in a homogeneous Vlasov plasma. Using the single-mode approximation, the time evolutions of important parameters are obtained to show that for the range of parameters considered, reduction of the beam speed and formation of temperature anisotropies are the most significant factors in the quasi-linear stabilization process. Combining both instabilities in a quasi-linear study is found to produce a roughly equal mixture of both polarizations and relatively isotropic conditions for tenuous beam densities and low initial beam drift speeds. Computer simulations are used to compare with the quasi-linear results. The simulations justify the single-mode assumption, verify that quasi-linear changes are the means of saturation for the parameter range of concern, and check the nonlinear evolution of the system when both modes are present.

  8. Anomalous energy exchange in the gBL and quasilinear theories

    SciTech Connect

    Mynick, H.E.

    1992-02-01

    The rate of turbulence-induced energy exchange {dot W}{sub o} between species is computed in the framework of the quasilinear and gBL transport theories, and the relationship between these two theories, and the relationship between these two similar theories is thereby elucidated. For both theories, general formal expressions for {dot W}{sub o} are developed, and then applied to the trapped electron mode for illustration. The general expressions for {dot W}{sub o} in the two theories are formally closely related, but can yield predictions of very different magnitude in concrete applications. The fact that quasilinear theory is not valid for saturated steady-state turbulence gives rise to certain peculiarities in its predictions for this normal experimental situation, such as permitting energy to flow from the cooler to the hotter species, even in the limit of thermal equilibrium, where real-space gradients vanish. The gBL theory may be viewed as a modification of quasilinear theory to be valid for steady-state turbulence, keeping extra terms due to the self-consistent back reaction of particles on the fluctuations, which are just such as to eliminate these peculiarities.

  9. Quasilinear theory of general electromagnetic fluctuations in unmagnetized plasmas

    SciTech Connect

    Schlickeiser, R. E-mail: yoonp@umd.edu; Yoon, P. H. E-mail: yoonp@umd.edu

    2014-09-15

    The general quasilinear Fokker-Planck kinetic equation for the plasma particle distribution functions in unmagnetized plasmas is derived, making no restrictions on the frequency of the electromagnetic fluctuations. The derived kinetic particle equation complements our earlier study of the general fluctuation's kinetic equation. For collective plasma eigenmodes and gyrotropic particle distribution functions, the two coupled kinetic equations describe the self-consistent dynamical evolution of the plasma. The limit of weakly damped collective modes correctly reproduces the well-known textbook kinetic particle equation with longitudinal Langmuir and ion-acoustic fluctuations, demonstrating, in particular, the resonant nature of parallel momentum diffusion of particles. In the limit of aperiodic modes, the Fokker-Planck equation contains the nonresonant diffusion of particles in momentum and the parallel and perpendicular momentum drag coefficients. As an application these drag and diffusion coefficients are calculated for extragalactic cosmic ray particles propagating in the unmagnetized intergalactic medium. Whereas for all cosmic rays, the perpendicular momentum diffusion in intergalactic aperiodic fluctuations is negligibly small; cosmic ray protons with energies below 10{sup 5 }GeV are affected by the plasma drag.

  10. Stochastic field-line wandering in magnetic turbulence with shear. I. Quasi-linear theory

    NASA Astrophysics Data System (ADS)

    Shalchi, A.; Negrea, M.; Petrisor, I.

    2016-07-01

    We investigate the random walk of magnetic field lines in magnetic turbulence with shear. In the first part of the series, we develop a quasi-linear theory in order to compute the diffusion coefficient of magnetic field lines. We derive general formulas for the diffusion coefficients in the different directions of space. We like to emphasize that we expect that quasi-linear theory is only valid if the so-called Kubo number is small. We consider two turbulence models as examples, namely, a noisy slab model as well as a Gaussian decorrelation model. For both models we compute the field line diffusion coefficients and we show how they depend on the aforementioned Kubo number as well as a shear parameter. It is demonstrated that the shear effect reduces all field line diffusion coefficients.

  11. A New Cosmic Ray Transport Theory in Partially Turbulent Space Plasmas: Extending the Quasilinear Approach

    NASA Astrophysics Data System (ADS)

    Schlickeiser, R.

    2011-05-01

    A new transport theory of cosmic rays in magnetized space plasmas with axisymmetric incompressible magnetic turbulence is developed extending the quasilinear approximation to the particle orbit. Arbitrary gyrophase deviations from the unperturbed spiral orbits in the uniform magnetic field are allowed. For quasi-stationary and spatially homogeneous magnetic turbulence, we derive the small Larmor radius approximation gyrophase-averaged cosmic ray Fokker-Planck coefficients. The generalized Fokker-Planck coefficients correctly reduce to their known quasilinear values in the corresponding limit. New forms of the quasilinear Fokker-Planck coefficients in axisymmetric turbulence are derived which no longer involve infinite sums of products of Bessel functions, which facilitate their numerical computation for specified turbulence field correlation tensors. The Fokker-Planck coefficients for arbitrary phase orbits of the cosmic ray particles provide strict upper limits for the perpendicular and pitch-angle Fokker-Planck coefficients, which in turn yield strict upper and lower limits for the perpendicular and parallel spatial diffusion coefficients, respectively, describing the spatial diffusion of the isotropic part of the cosmic ray phase space density. For the associated mean free paths, we find for this general case that the product of the minimum parallel mean free path with the sum of the maximum perpendicular mean free paths equals R 2 L , where RL denotes the cosmic ray gyroradius.

  12. Quasi-linear theory of electron density and temperature fluctuations with application to MHD generators and MPD arc thrusters

    NASA Technical Reports Server (NTRS)

    Smith, M.

    1972-01-01

    Fluctuations in electron density and temperature coupled through Ohm's law are studied for an ionizable medium. The nonlinear effects are considered in the limit of a third order quasi-linear treatment. Equations are derived for the amplitude of the fluctuation. Conditions under which a steady state can exist in the presence of the fluctuation are examined and effective transport properties are determined. A comparison is made to previously considered second order theory. The effect of third order terms indicates the possibility of fluctuations existing in regions predicted stable by previous analysis.

  13. Quasi-linear theory of electron density and temperature fluctuations with application to MHD generators and MPD arc thrusters.

    NASA Technical Reports Server (NTRS)

    Smith, J. M.

    1972-01-01

    Fluctuations in electron density and temperature coupled through Ohm's law are studied for an ionizable medium. The nonlinear effects are considered in the limit of a third order quasi-linear treatment. Equations are derived for the amplitude of the fluctuation. Conditions under which a steady state can exist in the presence of the fluctuation are examined and effective transport properties are determined. A comparison is made to previously considered second order theory. The effect of third order terms indicates the possibility of fluctuations existing in regions predicted stable by previous analysis.

  14. Electrothermal oscillations and the quasilinear theory of electron enthalpy fluctuations in magnetohydrodynamic generators and magnetoplasmadynamic arc thrusters

    NASA Technical Reports Server (NTRS)

    Smith, J. M.

    1972-01-01

    Flucturations in electron density and temperature coupled through OHM's Law are studied for MHD power generator and MPD arc thruster applications. The dispersion relation based on linear theory is derived, and the two limiting cases of infinite ionization rate and frozen flow are examined. The nonlinear effects of the frozen flow case are then studied in the quasilinear limit. Equations are derived for the amplitude of the fluctuation and its effect upon Ohm's Law and the electron temperature equation. Conditions under which a steady state can exist in the presence of the fluctuation are examined, and effective transport properties are determined.

  15. Quasi-linear theory and transport theory. [particle acceleration in interplanetary medium

    NASA Technical Reports Server (NTRS)

    Smith, Charles W.

    1992-01-01

    The theory of energetic particle scattering by magnetostatic fluctuations is reviewed in so far as it fails to produce the rigidity-independent mean-free-paths observed. Basic aspects of interplanetary magnetic field fluctuations are reviewed with emphasis placed on the existence of dissipation range spectra at high wavenumbers. These spectra are then incorporated into existing theories for resonant magnetostatic scattering and are shown to yield infinite mean-free-paths. Nonresonant scattering in the form of magnetic mirroring is examined and offered as a partial solution to the magnetostatic problem. In the process, mean-free-paths are obtained in good agreement with observations in the interplanetary medium at 1 AU and upstream of planetary bow shocks.

  16. Investigation of the validity of quasilinear theory for electron Landau damping in a tokamak using a broad-band wave effect

    SciTech Connect

    Lee, Jungpyo; Bonoli, Paul; Wright, John

    2011-01-15

    The quasilinear diffusion coefficient assuming a constant magnetic field along the electron orbit is widely used to describe electron Landau damping of waves in a tokamak where the magnitude of the magnetic field varies on a flux surface. To understand the impact of violating the constant magnetic field assumption, we introduce the effect of a broad-bandwidth wave spectrum which has been used in the past to validate quasilinear theory for the fast decorrelation process between resonances. By the reevaluation of the diffusion coefficient through the level of the phase integral for the tokamak geometry with the broad-band wave effect included, we identify the three acceptable errors for the use of the quasilinear diffusion coefficient.

  17. Investigation of the validity of quasilinear theory for electron Landau damping in a tokamak using a broad-band wave effect

    SciTech Connect

    Lee, Jungpyo; Bonoli, Paul; Wright, John

    2011-01-01

    The quasilinear diffusion coefficient assuming a constant magnetic field along the electron orbit is widely used to describe electron Landau damping of waves in a tokamak where the magnitude of the magnetic field varies on a flux surface. To understand the impact of violating the constant magnetic field assumption, we introduce the effect of a broad-bandwidth wave spectrum which has been used in the past to validate quasilinear theory for the fast decorrelation process between resonances. By the reevaluation of the diffusion coefficient through the level of the phase integral for the tokamak geometry with the broad-band wave effect included, we identify the three acceptable errors for the use of the quasilinear diffusion coefficient.

  18. Investigation of the validity of quasilinear theory for electron Landau damping in a tokamak using a broad-band wave effect

    DOE PAGESBeta

    Lee, Jungpyo; Bonoli, Paul; Wright, John

    2011-01-01

    The quasilinear diffusion coefficient assuming a constant magnetic field along the electron orbit is widely used to describe electron Landau damping of waves in a tokamak where the magnitude of the magnetic field varies on a flux surface. To understand the impact of violating the constant magnetic field assumption, we introduce the effect of a broad-bandwidth wave spectrum which has been used in the past to validate quasilinear theory for the fast decorrelation process between resonances. By the reevaluation of the diffusion coefficient through the level of the phase integral for the tokamak geometry with the broad-band wave effect included,more » we identify the three acceptable errors for the use of the quasilinear diffusion coefficient.« less

  19. Theory and simulation of quasilinear transport from external magnetic field perturbations in a DIII-D plasma

    NASA Astrophysics Data System (ADS)

    Waltz, R. E.; Ferraro, N. M.

    2015-04-01

    The linear response profiles for the 3D perturbed magnetic fields, currents, ion velocities, plasma density, pressures, and electric potential from low-n external resonant magnetic field perturbations (RMPs) are obtained from the collisional two-fluid M3D-C1 code [N. M. Ferraro and S. C. Jardin, J. Comput. Phys. 228, 7742 (2009)]. A newly developed post-processing RMPtran code computes the resulting quasilinear E×B and magnetic (J×B) radial transport flows with respect to the unperturbed flux surfaces in all channels. RMPtran simulations focus on ion (center of mass) particle and transient non-ambipolar current flows, as well as the toroidal angular momentum flow. The paper attempts to delineate the RMP transport mechanisms that might be responsible for the RMP density pump-out seen in DIII-D [M. A. Mahdavi and J. L. Luxon, Fusion Sci. Technol. 48, 2 (2005)]. Experimentally, the starting high toroidal rotation does not brake to a significantly lower rotation after the pump-out suggesting that convective and E×B transport mechanisms dominate. The direct J×B torque from the transient non-ambipolar radial current expected to accelerate plasma rotation is shown to cancel much of the Maxwell stress J×B torque expected to brake the plasma rotation. The dominant E×B Reynolds stress accelerates rotation at the top of the pedestal while braking rotation further down the pedestal.

  20. Enhancement of NUBEAM for the simulation of fast ion and RF-wave interaction based on the quasi-linear theory

    NASA Astrophysics Data System (ADS)

    Kwon, Jae-Min; McCune, Douglas; Chang, C. S.

    2007-11-01

    The Monte-Carlo package NUBEAM for time-dependent modeling of fast ions in a tokamak geometry has been upgraded to simulate the effects of ICRF heating on the fast ions. The RF-wave field data is provided by executing TORIC5 inside TRANSP and passed to NUBEAM. An iterative algorithm has been implemented to match the RF-power absorption value calculated by NUBEAM with the level predicted by TORIC5. The effects of RF-wave fields on the fast ions are modeled by evaluating Monte-Carlo kicks based on the quasi-linear theory. Because of the unique feature of NUBEAM, the so called ``goosing'' which enables an order of magnitude faster calculation, special care needs to be taken in the Monte-Carlo simulation. The modification of the goose algorithm in the presence of RF-wave fields will be presented. Also, the necessary features of NUBEAM for future application to self-consistent coupling with an ICRF full wave code will be discussed.

  1. An improved method to analyze the stress relaxation of ligaments following a finite ramp time based on the quasi-linear viscoelastic theory.

    PubMed

    Abramowitch, Steven D; Woo, Savio L

    2004-02-01

    The quasi-linear viscoelastic (QLV) theory proposed by Fung (1972) has been frequently used to model the nonlinear time- and history-dependent viscoelastic behavior of many soft tissues. It is common to use five constants to describe the instantaneous elastic response (constants A and B) and reduced relaxation function (constants C, tau 1, and tau 2) on experiments with finite ramp times followed by stress relaxation to equilibrium. However, a limitation is that the theory is based on a step change in strain which is not possible to perform experimentally. Accounting for this limitation may result in regression algorithms that converge poorly and yield nonunique solutions with highly variable constants, especially for long ramp times (Kwan et al. 1993). The goal of the present study was to introduce an improved approach to obtain the constants for QLV theory that converges to a unique solution with minimal variability. Six goat femur-medial collateral ligament-tibia complexes were subjected to a uniaxial tension test (ramp time of 18.4 s) followed by one hour of stress relaxation. The convoluted QLV constitutive equation was simultaneously curve-fit to the ramping and relaxation portions of the data (r2 > 0.99). Confidence intervals of the constants were generated from a bootstrapping analysis and revealed that constants were distributed within 1% of their median values. For validation, the determined constants were used to predict peak stresses from a separate cyclic stress relaxation test with averaged errors across all specimens measuring less than 6.3 +/- 6.0% of the experimental values. For comparison, an analysis that assumed an instantaneous ramp time was also performed and the constants obtained for the two approaches were compared. Significant differences were observed for constants B, C, tau 1, and tau 2, with tau 1 differing by an order of magnitude. By taking into account the ramping phase of the experiment, the approach allows for viscoelastic

  2. Mirror Instability: Quasi-linear Effects

    NASA Astrophysics Data System (ADS)

    Hellinger, P.; Travnicek, P. M.; Passot, T.; Sulem, P.; Kuznetsov, E. A.

    2008-12-01

    Nonlinear properties of the mirror instability are investigated by direct integration of the quasi-linear diffusion equation [Shapiro and Shevchenko, 1964] near threshold. The simulation results are compared to the results of standard hybrid simulations [Califano et al., 2008] and discussed in the context of the nonlinear dynamical model by Kuznetsov et al. [2007]. References: Califano, F., P. Hellinger, E. Kuznetsov, T. Passot, P. L. Sulem, and P. M. Travnicek (2008), Nonlinear mirror mode dynamics: Simulations and modeling, J. Geophys. Res., 113, A08219, doi:10.1029/2007JA012898. Kuznetsov, E., T. Passot and P. L. Sulem (2007), Dynamical model for nonlinear mirror modes near threshold, Phys. Rev. Lett., 98, 235003 . Shapiro, V. D., and V. I. Shevchenko (1964), Quasilinear theory of instability of a plasma with an anisotropic ion velocity distribution, Sov. JETP, 18, 1109.

  3. Generalized Quasilinear Approximation: Application to Zonal Jets

    NASA Astrophysics Data System (ADS)

    Marston, J. B.; Chini, G. P.; Tobias, S. M.

    2016-05-01

    Quasilinear theory is often utilized to approximate the dynamics of fluids exhibiting significant interactions between mean flows and eddies. We present a generalization of quasilinear theory to include dynamic mode interactions on the large scales. This generalized quasilinear (GQL) approximation is achieved by separating the state variables into large and small zonal scales via a spectral filter rather than by a decomposition into a formal mean and fluctuations. Nonlinear interactions involving only small zonal scales are then removed. The approximation is conservative and allows for scattering of energy between small-scale modes via the large scale (through nonlocal spectral interactions). We evaluate GQL for the paradigmatic problems of the driving of large-scale jets on a spherical surface and on the beta plane and show that it is accurate even for a small number of large-scale modes. As GQL is formally linear in the small zonal scales, it allows for the closure of the system and can be utilized in direct statistical simulation schemes that have proved an attractive alternative to direct numerical simulation for many geophysical and astrophysical problems.

  4. Quasilinear theory of terahertz free-electron lasers based on Compton scattering of incoherent pump wave by intense relativistic electron beam

    NASA Astrophysics Data System (ADS)

    Ginzburg, N. S.; Kocharovskaya, E. R.

    2016-08-01

    The use of incoherent broadband pump radiation for improving the electron efficiency in the free-electron lasers (FEL) based on stimulated backscattering is considered. On the basis of a quasilinear approach, it is shown that the efficiency increases in proportion to the width of the pump spectrum. The effect is owing to a broadening of the spectrum of synchronous combination waves and realization of a mechanism of stochastic particle deceleration. The injection of a monochromatic seed signal in a single pass FEL amplifier or the implementation of a selective high-Q resonator in an FEL oscillator makes the high-frequency scattered radiation be monochromatic in spite of an incoherent pumping. In the regime of stochastic particle deceleration, the efficiency only slightly depends on the spread of the beam parameters, which is beneficial for a terahertz FEL powered by intense relativistic electron beams.

  5. Reducing quasilinear systems to block triangular form

    SciTech Connect

    Tunitsky, Dmitry V

    2013-03-31

    The paper is concerned with systems of n quasilinear partial differential equations of the first order with 2 independent variables. Using a geometric formalism for such equations, which goes back to Riemann, it is possible to assign a field of linear operators on an appropriate vector bundle to this type of quasilinear system. Several tests for a quasilinear system to be reducible to triangular or block triangular form are obtained in terms of this field; they supplement well known results on diagonalization and block diagonalization due to Haantjes and Bogoyavlenskij. Bibliography: 10 titles.

  6. LBQ2D, Extending the Line Broadened Quasilinear Model to TAE-EP Interaction

    NASA Astrophysics Data System (ADS)

    Ghantous, Katy; Gorelenkov, Nikolai; Berk, Herbert

    2012-10-01

    The line broadened quasilinear model was proposed and tested on the one dimensional electrostatic case of the bump on tailfootnotetextH.L Berk, B. Breizman and J. Fitzpatrick, Nucl. Fusion, 35:1661, 1995 to study the wave particle interaction. In conventional quasilinear theory, the sea of overlapping modes evolve with time as the particle distribution function self consistently undergo diffusion in phase space. The line broadened quasilinear model is an extension to the conventional theory in a way that allows treatment of isolated modes as well as overlapping modes by broadening the resonant line in phase space. This makes it possible to treat the evolution of modes self consistently from onset to saturation in either case. We describe here the model denoted by LBQ2D which is an extension of the proposed one dimensional line broadened quasilinear model to the case of TAEs interacting with energetic particles in two dimensional phase space, energy as well as canonical angular momentum. We study the saturation of isolated modes in various regimes and present the analytical derivation and numerical results. Finally, we present, using ITER parameters, the case where multiple modes overlap and describe the techniques used for the numerical treatment.

  7. Quasi-linear equation for magnetoplasma oscillations in the weakly relativistic approximation

    NASA Astrophysics Data System (ADS)

    Rizzato, F. B.

    Some limitations which are present in the dynamical equations for collisionless plasmas are discussed. Some elementary corrections to the linear theories are obtained in a heuristic form, which directly lead to the so-called quasi-linear theories in its non-relativistic and relativistic forms. The effect of the relativistic variation of the gyrofrequency on the diffusion coefficient is examined in a typically perturbative approximation.

  8. Quasilinear saturation of the aperiodic ordinary mode streaming instability

    SciTech Connect

    Stockem Novo, A. Schlickeiser, R.; Yoon, P. H.; Lazar, M.; Poedts, S.; Seough, J.

    2015-09-15

    In collisionless plasmas, only kinetic instabilities and fluctuations are effective in reducing the free energy and scatter plasma particles, preventing an increase of their anisotropy. Solar energetic outflows into the interplanetary plasma give rise to important thermal anisotropies and counterstreaming motions of plasma shells, and the resulting instabilities are expected to regulate the expansion of the solar wind. The present paper combines quasilinear theory and kinetic particle-in-cell simulations in order to study the weakly nonlinear saturation of the ordinary mode in hot counter-streaming plasmas with a temperature anisotropy as a follow-up of the paper by Seough et al. [Phys. Plasmas 22, 082122 (2015)]. This instability provides a plausible mechanism for the origin of dominating, two-dimensional spectrum of transverse magnetic fluctuations observed in the solar wind. Stimulated by the differential motion of electron counterstreams the O mode instability may convert their free large-scale energy by nonlinear collisionless dissipation on plasma particles.

  9. Stellarator Turbulence: Subdominant Eigenmodes and Quasilinear Modeling

    NASA Astrophysics Data System (ADS)

    Pueschel, M. J.; Faber, B. J.; Citrin, J.; Hegna, C. C.; Terry, P. W.; Hatch, D. R.

    2016-02-01

    Owing to complex geometry, gyrokinetic simulations in stellarator geometry produce large numbers of subdominant unstable and stable, near-orthogonal eigenmodes. Here, results based on the full eigenmode spectrum in stellarator geometry are presented for the first time. In the nonlinear state of a low-magnetic-shear ion-temperature-gradient-driven case, a multitude of these modes are active and imprint the system. Turbulent frequency spectra are broadband as a consequence, in addition to a nonlinear, narrow signature at electron frequencies. It is shown that successful quasilinear, mixing-length transport modeling is possible in stellarators, where it is essential to account for all subdominant unstable modes.

  10. Quasilinearization method applied to multidimensional quantum tunneling

    NASA Astrophysics Data System (ADS)

    Razavy, M.; Cote, Vincent J.

    1994-04-01

    We apply the quasilinearization method of Bellman and Kalaba [Quasilinearization and Nonlinear Boundary-Value Problems (Elsevier, New York, 1965)] to find approximate solutions for the multidimensional quantum tunneling for separable as well as nonseparable wave equations. By introducing the idea of the complex ``semiclassical trajectory'' which is valid for the motion over and under the barrier, and which, in the proper limit, reduces to the real classical trajectory in the allowed region, we obtain an eigenvalue equation for the characteristic wave numbers. This eigenvalue equation is similar to the corresponding equation obtained from the WKB approximation and yields complex eigenvalues with negative imaginary parts. When the barrier changes very rapidly as a function of the radial distance, we can replace the concept of the semiclassical trajectory, which may not be applicable in this case, by the concept of a complex ``quantum trajectory.'' The trajectory defined either way depends on a constant of integration, and by minimizing the action with respect to this constant we can obtain the minimum escape path. The case of two-dimensional tunneling is discussed as an example of this method.

  11. Testing quasilinear modified Newtonian dynamics in the Solar System

    NASA Astrophysics Data System (ADS)

    Galianni, Pasquale; Feix, Martin; Zhao, Hongsheng; Horne, Keith

    2012-08-01

    A unique signature of the modified Newtonian dynamics (MOND) paradigm is its peculiar behavior in the vicinity of the points where the total Newtonian acceleration exactly cancels. In the Solar System, these are the saddle points of the gravitational potential near the planets. Typically, such points are embedded into low-acceleration bubbles where modified gravity theories à la MOND predict significant deviations from Newton’s laws. As it has been pointed out recently, the Earth-Sun bubble may be visited by the LISA Pathfinder spacecraft in the near future, providing a unique occasion to put these theories to a direct test. In this work, we present a high-precision model of the Solar System’s gravitational potential to determine accurate positions and motions of these saddle points and study the predicted dynamical anomalies within the framework of quasilinear MOND. Considering the expected sensitivity of the LISA Pathfinder probe, we argue that interpolation functions which exhibit a “faster” transition between the two dynamical regimes have a good chance of surviving a null result. An example of such a function is the QMOND analog of the so-called simple interpolating function which agrees well with much of the extragalactic phenomenology. We have also discovered that several of Saturn’s outermost satellites periodically intersect the Saturn-Sun bubble, providing the first example of Solar System objects that regularly undergo the MOND regime.

  12. Three-dimensional forward modelling and inversion of complex resistivity based on the improved quasi-linear approximation

    NASA Astrophysics Data System (ADS)

    Liu, Y.; Li, T.; Zhu, C.; Zhang, R.; Wu, Y.

    2015-12-01

    Three-dimensional (3-D) electromagnetic (EM) forward modelling and inversion continues to be an important issue for the correct interpretation of EM data.To this end,approximate solutions have been developed that allow the construction of relatively fast forward modelling and inversion schemes.We have developed an improved quasi-linear approximation which is more appropriate in solving the linear equation for greatly shortening calculation time.We achieved this by using green's function properties.Then we introduced the improved quasi-linear approximation to spectral induced polarization (SIP) to tackle the problem of the resolution and the efficiency.The localized quasi-linear (LQL) approximation theory is appropriate for multisource array-type surveys assuming that the normal field is slowly varying within the inhomogeneity domain.However,the normal field of attenuates severely which dose not satisfy the assumption of the LQL approximation.As a consenquence,the imaginary part is not accurate when LQL approximation is adopted for the simulation.The improved quasi-linear approximation provide a new approach with the same resolution of QL approximation and much less calculation time.We have also constructed three-dimensional SIP forward modeling based on improved quasi-linear approximation method.It only takes 0.8s for forward modeling when inhomogeneity domain is divided into 2000 blocks.Beyond that, we have introduced the Cole-Cole model to the algorithm and complete the three-dimensional complex resistivity conjugate gradient inversion with parameter restraint.The model trial results show that this method can obtain good inversion results in physical parameters such as zero frequency resistivity, polarization.The results demonstrate the stability and the efficiency of the improved quasi-linear approximation and the method may be a practical solution for3-D EM forward modelling and inversion of SIP.

  13. A quasi-linear kinetic equation for cosmic rays in the interplanetary medium

    NASA Technical Reports Server (NTRS)

    Luhmann, J. G.

    1976-01-01

    A kinetic equation for interplanetary cosmic rays is set up with the aid of weak-plasma-turbulence theory for an idealized radially symmetric model of the interplanetary magnetic field. As a starting point, this treatment invokes the Vlasov equation instead of the traditional Fokker-Planck equation. Quasi-linear theory is applied to obtain a momentum diffusion equation for the heliocentric frame of reference which describes the interaction of cosmic rays with convecting magnetic irregularities in the solar-wind plasma. Under restricted conditions, the well-known equation of solar modulation can be obtained from this kinetic equation.

  14. Quasi-linear pitch angle and energy diffusion of pickup ions near Comet Halley

    NASA Technical Reports Server (NTRS)

    Huddleston, D. E.; Johnstone, A. D.; Coates, A. J.; Neubauer, F. M.

    1991-01-01

    The process of ion pickup in the environment of Halley's comet is studied in order to see if velocity diffusion driven by the observed level of turbulence can explain the observed development of the implanted ion distribution. The theoretical description used is based on a quasi-linear approach and considers the implantation and transport of cometary ions along solar wind flow lines. To make such a study requires some way of extrapolating the measurements on the Giotto trajectory into the upstream region; models for mass loading and turbulence are used. A simplified kinetic equation describing the source, convection, and quasi-linear velocity diffusion of the heavy cometary ions is solved numerically along flow lines parallel to the sun-comet line. Full two-dimensional (pitch angle and velocity) distributions are obtained at positions along the Giotto trajectory, which are compared with measurements. This study finds that quasi-linear theory, with the empirical model for the observed turbulence level, produces the right order of pitch angle diffusion.

  15. Nonlinear damping and quasi-linear modelling.

    PubMed

    Elliott, S J; Ghandchi Tehrani, M; Langley, R S

    2015-09-28

    The mechanism of energy dissipation in mechanical systems is often nonlinear. Even though there may be other forms of nonlinearity in the dynamics, nonlinear damping is the dominant source of nonlinearity in a number of practical systems. The analysis of such systems is simplified by the fact that they show no jump or bifurcation behaviour, and indeed can often be well represented by an equivalent linear system, whose damping parameters depend on the form and amplitude of the excitation, in a 'quasi-linear' model. The diverse sources of nonlinear damping are first reviewed in this paper, before some example systems are analysed, initially for sinusoidal and then for random excitation. For simplicity, it is assumed that the system is stable and that the nonlinear damping force depends on the nth power of the velocity. For sinusoidal excitation, it is shown that the response is often also almost sinusoidal, and methods for calculating the amplitude are described based on the harmonic balance method, which is closely related to the describing function method used in control engineering. For random excitation, several methods of analysis are shown to be equivalent. In general, iterative methods need to be used to calculate the equivalent linear damper, since its value depends on the system's response, which itself depends on the value of the equivalent linear damper. The power dissipation of the equivalent linear damper, for both sinusoidal and random cases, matches that dissipated by the nonlinear damper, providing both a firm theoretical basis for this modelling approach and clear physical insight. Finally, practical examples of nonlinear damping are discussed: in microspeakers, vibration isolation, energy harvesting and the mechanical response of the cochlea. PMID:26303921

  16. Classical analog of quasilinear Landau-Zener tunneling.

    PubMed

    Kovaleva, Agnessa; Manevitch, Leonid I

    2012-01-01

    In this paper we develop an analytical framework to study the effect of nonlinearity on irreversible energy transfer in a system of two weakly coupled oscillators with time-dependent parameters, with special attention to an analogy between classical energy transfer and nonadiabatic quantum tunneling. For preciseness, we suppose that a linear oscillator with constant parameters is excited by an initial impulse but a coupled quasilinear oscillator with slowly varying parameters is initially at rest. It is shown that the equations of the slow passage through resonance in this system are identical to quasilinear equations of nonadiabatic Landau-Zener tunneling. Due to revealed equivalence, a recently found analogy between irreversible energy transfer in a classical linear system and conventional linear Landau-Zener tunneling can be extended to quasilinear systems. An explicit analytical solution of the quasilinear problem is found with the help of an iteration procedure, wherein the linear solution is chosen as an initial approximation. Correctness of the constructed approximations is confirmed by numerical simulations. The results presented in this paper, in addition to providing an analytical framework for understanding the transient dynamics of coupled oscillators, suggest an approximate procedure for solving the quasilinear Landau-Zener equations with arbitrary initial conditions over a finite time interval. PMID:22400638

  17. Enhancement of residual stress by electromagnetic fluctuations: A quasi-linear study

    NASA Astrophysics Data System (ADS)

    Kaang, Helen H.; Jhang, Hogun; Singh, R.; Kim, Juhyung; Kim, S. S.

    2016-05-01

    A study is conducted on the impact of electromagnetic (EM) fluctuations on residual Reynolds stress in the context of the quasi-linear theory. We employ a fluid formulation describing EM ion temperature gradient turbulence. Analyses show that finite plasma β (=plasma thermal energy/magnetic energy) significantly increases the residual stress, potentially leading to the strong enhancement of flow generation in high β plasmas. We identify that this strong increase of residual stress originates from the reinforcement of radial ⟨ k ∥ ⟩ (=spectrally averaged parallel wavenumber) asymmetry due to the deformation of eigenfunctions near a rational surface.

  18. Multidimensional quasilinear first-order equations and multivalued solutions of the elliptic and hyperbolic equations

    NASA Astrophysics Data System (ADS)

    Zhuravlev, V. M.

    2016-03-01

    We discuss an extension of the theory of multidimensional second-order equations of the elliptic and hyperbolic types related to multidimensional quasilinear autonomous first-order partial differential equations. Calculating the general integrals of these equations allows constructing exact solutions in the form of implicit functions. We establish a connection with hydrodynamic equations. We calculate the number of free functional parameters of the constructed solutions. We especially construct and analyze implicit solutions of the Laplace and d'Alembert equations in a coordinate space of arbitrary finite dimension. In particular, we construct generalized Penrose-Rindler solutions of the d'Alembert equation in 3+1 dimensions.

  19. Multibump solutions for quasilinear elliptic equations with critical growth

    SciTech Connect

    Liu, Jiaquan; Wang, Zhi-Qiang; Wu, Xian

    2013-12-15

    The current paper is concerned with constructing multibump solutions for a class of quasilinear Schrödinger equations with critical growth. This extends the classical results of Coti Zelati and Rabinowitz [Commun. Pure Appl. Math. 45, 1217–1269 (1992)] for semilinear equations as well as recent work of Liu, Wang, and Guo [J. Funct. Anal. 262, 4040–4102 (2012)] for quasilinear problems with subcritical growth. The periodicity of the potentials is used to glue ground state solutions to construct multibump bound state solutions.

  20. Boundary control problems for quasilinear systems of hyperbolic equations

    NASA Astrophysics Data System (ADS)

    Alekseenko, A. E.; Kholodov, A. S.; Kholodov, Ya. A.

    2016-06-01

    For quasilinear systems of hyperbolic equations, the nonclassical boundary value problem of controlling solutions with the help of boundary conditions is considered. Previously, this problem was extensively studied in the case of the simplest hyperbolic equations, namely, the scalar wave equation and certain linear systems. The corresponding problem formulations and numerical solution algorithms are extended to nonlinear (quasilinear and conservative) systems of hyperbolic equations. Some numerical (grid-characteristic) methods are considered that were previously used to solve the above problems. They include explicit and implicit conservative difference schemes on compact stencils that are linearizations of Godunov's method. The numerical algorithms and methods are tested as applied to well-known linear examples.

  1. A quasi-linear control theory analysis of timesharing skills

    NASA Technical Reports Server (NTRS)

    Damos, D.; Wickens, C. D.

    1977-01-01

    Performance with practice on two dual-task combinations, dual-axis tracking and two discrete information processing tasks, is examined in an effort to identify the presence and development of specific time sharing skills, such as parallel information processing or rapid intertask switching. The generality of time sharing skills also is investigated by examining transfer of these skills between the two qualitatively different task combinations.

  2. A quasi-linear control theory analysis of timesharing skills

    NASA Technical Reports Server (NTRS)

    Agarwal, G. C.; Gottlieb, G. L.

    1977-01-01

    The compliance of the human ankle joint is measured by applying 0 to 50 Hz band-limited gaussian random torques to the foot of a seated human subject. These torques rotate the foot in a plantar-dorsal direction about a horizontal axis at a medial moleolus of the ankle. The applied torques and the resulting angular rotation of the foot are measured, digitized and recorded for off-line processing. Using such a best-fit, second-order model, the effective moment of inertia of the ankle joint, the angular viscosity and the stiffness are calculated. The ankle joint stiffness is shown to be a linear function of the level of tonic muscle contraction, increasing at a rate of 20 to 40 Nm/rad/Kg.m. of active torque. In terms of the muscle physiology, the more muscle fibers that are active, the greater the muscle stiffness. Joint viscosity also increases with activation. Joint stiffness is also a linear function of the joint angle, increasing at a rate of about 0.7 to 1.1 Nm/rad/deg from plantar flexion to dorsiflexion rotation.

  3. Two-pulse ionization injection into quasilinear laser wakefields.

    PubMed

    Bourgeois, N; Cowley, J; Hooker, S M

    2013-10-11

    We describe a scheme for controlling electron injection into the quasilinear wakefield driven by a guided drive pulse via ionization of a dopant species by a collinear injection laser pulse with a short Rayleigh range. The scheme is analyzed by particle-in-cell simulations which show controlled injection and acceleration of electrons to an energy of 370 MeV, a relative energy spread of 2%, and a normalized transverse emittance of 2.0 μm. PMID:24160608

  4. A quasilinear model for solute transport under unsaturated flow

    SciTech Connect

    Houseworth, J.E.; Leem, J.

    2009-05-15

    We developed an analytical solution for solute transport under steady-state, two-dimensional, unsaturated flow and transport conditions for the investigation of high-level radioactive waste disposal. The two-dimensional, unsaturated flow problem is treated using the quasilinear flow method for a system with homogeneous material properties. Dispersion is modeled as isotropic and is proportional to the effective hydraulic conductivity. This leads to a quasilinear form for the transport problem in terms of a scalar potential that is analogous to the Kirchhoff potential for quasilinear flow. The solutions for both flow and transport scalar potentials take the form of Fourier series. The particular solution given here is for two sources of flow, with one source containing a dissolved solute. The solution method may easily be extended, however, for any combination of flow and solute sources under steady-state conditions. The analytical results for multidimensional solute transport problems, which previously could only be solved numerically, also offer an additional way to benchmark numerical solutions. An analytical solution for two-dimensional, steady-state solute transport under unsaturated flow conditions is presented. A specific case with two sources is solved but may be generalized to any combination of sources. The analytical results complement numerical solutions, which were previously required to solve this class of problems.

  5. Quasilinear Carbon Transport In An Impurity Hole Plasma In LHD

    SciTech Connect

    Mikkelsen, David R.; Tanaka, K.; Nunami, M.; Watanabe, T-H.; Sugama, H.; Yoshinuma, M.; Suzuki, Y.; Goto, M.; Morita, S.; Wieland, B.; Yamada, I.; Yashura, R.; Akiyama, T.; Pablant, Novimir A.

    2014-04-01

    Comprehensive electrostatic gyrokinetic linear stability calculations for ion-scale microinstabilities in an LHD plasma with an ion-ITB and carbon "impurity hole" are used to make quasilinear estimates of particle flux to explore whether microturbulence can explain the observed outward carbon fluxes that flow "up" the impurity density gradient. The ion temperature is not stationary in the ion-ITB phase of the simulated discharge, during which the core carbon density decreases continuously. To fully sample these varying conditions the calculations are carried out at three radial locations and four times. The plasma parameter inputs are based on experimentally measured profiles of electron and ion temperature, as well as electron and carbon density. The spectroscopic line-average ratio of hydrogen and helium densities is used to set the density of these species. Three ion species (H,He,C) and the electrons are treated kinetically, including collisions. Electron instability drive does enhance the growth rate significantly, but the most unstable modes have characteristics of ion temperature gradient (ITG) modes in all cases. As the carbon density gradient is scanned between the measured value and zero, the quasilinear carbon flux is invariably inward when the carbon density profile is hollow, so turbulent transport due to the instabilities considered here does not explain the observed outward flux of impurities in impurity hole plasmas. The stiffness of the quasilinear ion heat flux is found to be 1.7-2.3, which is lower than several estimates in tokamaks.

  6. Global integral gradient bounds for quasilinear equations below or near the natural exponent

    NASA Astrophysics Data System (ADS)

    Phuc, Nguyen Cong

    2014-10-01

    We obtain sharp integral potential bounds for gradients of solutions to a wide class of quasilinear elliptic equations with measure data. Our estimates are global over bounded domains that satisfy a mild exterior capacitary density condition. They are obtained in Lorentz spaces whose degrees of integrability lie below or near the natural exponent of the operator involved. As a consequence, nonlinear Calderón-Zygmund type estimates below the natural exponent are also obtained for -superharmonic functions in the whole space ℝ n . This answers a question raised in our earlier work (On Calderón-Zygmund theory for p- and -superharmonic functions, to appear in Calc. Var. Partial Differential Equations, DOI 10.1007/s00526-011-0478-8) and thus greatly improves the result there.

  7. A quasi-linear analysis of the impurity effect on turbulent momentum transport and residual stress

    SciTech Connect

    Ko, S. H. Jhang, Hogun; Singh, R.

    2015-08-15

    We study the impact of impurities on turbulence driven intrinsic rotation (via residual stress) in the context of the quasi-linear theory. A two-fluid formulation for main and impurity ions is employed to study ion temperature gradient modes in sheared slab geometry modified by the presence of impurities. An effective form of the parallel Reynolds stress is derived in the center of mass frame of a coupled main ion-impurity system. Analyses show that the contents and the radial profile of impurities have a strong influence on the residual stress. In particular, an impurity profile aligned with that of main ions is shown to cause a considerable reduction of the residual stress, which may lead to the reduction of turbulence driven intrinsic rotation.

  8. A more general model equation of nonlinear Rayleigh waves and their quasilinear solutions

    NASA Astrophysics Data System (ADS)

    Zhang, Shuzeng; Li, Xiongbing; Jeong, Hyunjo

    2016-03-01

    A more general two-dimensional wave motion equation with consideration of attenuation and nonlinearity is proposed to describe propagating nonlinear Rayleigh waves of finite amplitude. Based on the quasilinear theory, the numerical solutions for the sound beams of fundamental and second harmonic waves are constructed with Green’s function method. Compared with solutions from the parabolic approximate equation, results from the general equation have more accuracy in both the near distance of the propagation direction and the far distance of the transverse direction, as quasiplane waves are used and non-paraxial Green’s functions are obtained. It is more effective to obtain the nonlinear Rayleigh sound beam distributions accurately with the proposed general equation and solutions. Brief consideration is given to the measurement of nonlinear parameter using nonlinear Rayleigh waves.

  9. Local Integral Estimates for Quasilinear Equations with Measure Data.

    PubMed

    Tian, Qiaoyu; Zhang, Shengzhi; Xu, Yonglin; Mu, Jia

    2016-01-01

    Local integral estimates as well as local nonexistence results for a class of quasilinear equations -Δ p u = σP(u) + ω for p > 1 and Hessian equations F k [-u] = σP(u) + ω were established, where σ is a nonnegative locally integrable function or, more generally, a locally finite measure, ω is a positive Radon measure, and P(u) ~ exp⁡αu (β) with α > 0 and β ≥ 1 or P(u) = u (p-1). PMID:27294190

  10. Local Integral Estimates for Quasilinear Equations with Measure Data

    PubMed Central

    Tian, Qiaoyu; Zhang, Shengzhi; Xu, Yonglin; Mu, Jia

    2016-01-01

    Local integral estimates as well as local nonexistence results for a class of quasilinear equations −Δpu = σP(u) + ω for p > 1 and Hessian equations Fk[−u] = σP(u) + ω were established, where σ is a nonnegative locally integrable function or, more generally, a locally finite measure, ω is a positive Radon measure, and P(u) ~ exp⁡αuβ with α > 0 and β ≥ 1 or P(u) = up−1. PMID:27294190

  11. Quasi-linear gyrokinetic predictions of the Coriolis momentum pinch in National Spherical Torus Experiment

    DOE PAGESBeta

    Guttenfelder, W.; Kaye, S. M.; Ren, Y.; Solomon, W.; Bell, R. E.; Candy, J.; Gerhardt, S. P.; LeBlanc, B. P.; Yuh, H.

    2016-05-11

    This paper presents quasi-linear gyrokinetic predictions of the Coriolis momentum pinch for low aspect-ratio National Spherical Torus Experiment (NSTX) H-modes where previous experimental measurements were focused. Local, linear calculations predict that in the region of interest (just outside the mid-radius) of these relatively high-beta plasmas, profiles are most unstable to microtearing modes that are only effective in transporting electron energy. However, sub-dominant electromagnetic and electrostaticballooning modes are also unstable, which are effective at transporting energy, particles, and momentum. The quasi-linear prediction of transport from these weaker ballooning modes, assuming they contribute transport in addition to that from microtearing modes inmore » a nonlinear turbulent state, leads to a very small or outward convection of momentum, inconsistent with the experimentally measured inward pinch, and opposite to predictions in conventional aspect ratio tokamaks. Additional predictions of a low beta L-mode plasma, unstable to more traditional electrostatic ion temperature gradient-trapped electron mode instability, show that the Coriolis pinch is inward but remains relatively weak and insensitive to many parameter variations. The weak or outward pinch predicted in NSTX plasmas appears to be at least partially correlated to changes in the parallel mode structure that occur at a finite beta and low aspect ratio, as discussed in previous theories. The only conditions identified where a stronger inward pinch is predicted occur either in the purely electrostatic limit or if the aspect ratio is increased. Lastly, as the Coriolis pinch cannot explain the measured momentum pinch, additional theoretical momentum transport mechanisms are discussed that may be potentially important.« less

  12. Quasi-linear gyrokinetic predictions of the Coriolis momentum pinch in National Spherical Torus Experiment

    NASA Astrophysics Data System (ADS)

    Guttenfelder, W.; Kaye, S. M.; Ren, Y.; Solomon, W.; Bell, R. E.; Candy, J.; Gerhardt, S. P.; LeBlanc, B. P.; Yuh, H.

    2016-05-01

    This paper presents quasi-linear gyrokinetic predictions of the Coriolis momentum pinch for low aspect-ratio National Spherical Torus Experiment (NSTX) H-modes where previous experimental measurements were focused. Local, linear calculations predict that in the region of interest (just outside the mid-radius) of these relatively high-beta plasmas, profiles are most unstable to microtearing modes that are only effective in transporting electron energy. However, sub-dominant electromagnetic and electrostatic ballooning modes are also unstable, which are effective at transporting energy, particles, and momentum. The quasi-linear prediction of transport from these weaker ballooning modes, assuming they contribute transport in addition to that from microtearing modes in a nonlinear turbulent state, leads to a very small or outward convection of momentum, inconsistent with the experimentally measured inward pinch, and opposite to predictions in conventional aspect ratio tokamaks. Additional predictions of a low beta L-mode plasma, unstable to more traditional electrostatic ion temperature gradient-trapped electron mode instability, show that the Coriolis pinch is inward but remains relatively weak and insensitive to many parameter variations. The weak or outward pinch predicted in NSTX plasmas appears to be at least partially correlated to changes in the parallel mode structure that occur at a finite beta and low aspect ratio, as discussed in previous theories. The only conditions identified where a stronger inward pinch is predicted occur either in the purely electrostatic limit or if the aspect ratio is increased. As the Coriolis pinch cannot explain the measured momentum pinch, additional theoretical momentum transport mechanisms are discussed that may be potentially important.

  13. Generalised quasilinear approximation of the helical magnetorotational instability

    NASA Astrophysics Data System (ADS)

    Child, Adam; Hollerbach, Rainer; Marston, Brad; Tobias, Steven

    2016-06-01

    > Motivated by recent advances in direct statistical simulation (DSS) of astrophysical phenomena such as out-of-equilibrium jets, we perform a direct numerical simulation (DNS) of the helical magnetorotational instability (HMRI) under the generalised quasilinear approximation (GQL). This approximation generalises the quasilinear approximation (QL) to include the self-consistent interaction of large-scale modes, interpolating between fully nonlinear DNS and QL DNS whilst still remaining formally linear in the small scales. In this paper we address whether GQL can more accurately describe low-order statistics of axisymmetric HMRI when compared with QL by performing DNS under various degrees of GQL approximation. We utilise various diagnostics, such as energy spectra in addition to first and second cumulants, for calculations performed for a range of Reynolds and Hartmann numbers (describing rotation and imposed magnetic field strength respectively). We find that GQL performs significantly better than QL in describing the statistics of the HMRI even when relatively few large-scale modes are kept in the formalism. We conclude that DSS based on GQL (GCE2) will be significantly more accurate than that based on QL (CE2).

  14. Quasi-linear viscoelastic characterization of human hip ligaments.

    PubMed

    Kemper, Andrew R; McNally, Craig; Smith, Byron; Duma, Stefan M

    2007-01-01

    The object of this study was to develop a quasi-linear viscoelastic model for the iliofemoral and ischiofemoral hip ligaments. In order to accomplish this, a total of 56 axial tension tests were performed on 8 bone-ligament-bone specimens prepared from 4 fresh frozen male cadavers. Each specimen went through a battery of 7 tests including a series of step-and-hold tests and load-and-unload ramp tests. The bone-ligament-bone specimens were situated so that the load from a servo-hydraulic Material Testing System would be applied on the long axis of each ligament. The reduced relaxation data was fit to a two exponential damping function while the instantaneous elastic response was fit to a power-law function. These two constituents were then combined to create a single constitutive equation for each ligament. The quasi-linear viscoelastic model presented in this study can be used to improve the biofidelity of computational models of the human hip. PMID:17487102

  15. Quasilinear simulations of interplanetary shocks and Earth's bow shock

    NASA Astrophysics Data System (ADS)

    Afanasiev, Alexandr; Battarbee, Markus; Ganse, Urs; Vainio, Rami; Palmroth, Minna; Pfau-Kempf, Yann; Hoilijoki, Sanni; von Alfthan, Sebastian

    2016-04-01

    We have developed a new self-consistent Monte Carlo simulation model for particle acceleration in shocks. The model includes a prescribed large-scale magnetic field and plasma density, temperature and velocity profiles and a self-consistently computed incompressible ULF foreshock under the quasilinear approximation. Unlike previous analytical treatments, our model is time dependent and takes full account of the anisotropic particle distributions and scattering in the wave-particle interaction process. We apply the model to the problem of particle acceleration at traveling interplanetary (IP) shocks and Earth's bow shock and compare the results with hybrid-Vlasov simulations and spacecraft observations. A qualitative agreement in terms of spectral shape of the magnetic fluctuations and the polarization of the unstable mode is found between the models and the observations. We will quantify the differences of the models and explore the region of validity of the quasilinear approach in terms of shock parameters. We will also compare the modeled IP shocks and the bow shock, identifying the similarities and differences in the spectrum of accelerated particles and waves in these scenarios. The work has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 637324 (HESPERIA). The Academy of Finland is thanked for financial support. We acknowledge the computational resources provided by CSC - IT Centre for Science Ltd., Espoo.

  16. Existence of solutions for quasilinear elliptic equations with Hardy potential

    NASA Astrophysics Data System (ADS)

    Deng, Yinbin; Guo, Yuxia; Liu, Jiaquan

    2016-03-01

    In this paper, we consider the following quasilinear elliptic equation with Hardy potential and Dirichlet boundary condition: - ∑ i , j = 1 N D j ( a i j ( x , u ) D i u ) + /1 2 ∑ i , j = 1 N D s a i , j ( x , u ) D i u D j u - λ | x | - 2 u = f ( x , u ) i n Ω , where Ω ⊂ ℝN(N ≥ 3) is a smooth bounded domain, D i = /∂ ∂ x i , D s a i j ( x , s ) = /∂ ∂ s a i j ( x , s ) , and 0 ≤ λ < λ ∗ : = ( /N - 2 2 ) 2 , and λ|x|-2 is called the Hardy potential. By using the perturbation method, we prove the existence of infinitely many solutions for the above problem.

  17. Collisionality dependence of the quasilinear particle flux due to microinstabilities

    SciTech Connect

    Fueloep, T.; Pusztai, I.; Helander, P.

    2008-07-15

    The collisionality dependence of the quasilinear particle flux due to the ion temperature gradient (ITG) and trapped electron mode (TEM) instabilities is studied by including electron collisions modeled by a pitch-angle scattering collision operator in the gyrokinetic equation. The inward transport due to ITG modes is caused mainly by magnetic curvature and thermodiffusion and can be reversed as electron collisions are introduced, if the plasma is far from marginal stability. However, if the plasma is close to marginal stability, collisions may even enhance the inward transport. The sign and the magnitude of the transport are sensitive to the form of the collision operator, to the magnetic drift normalized to the real frequency of the mode, and to the density and temperature scale lengths. These analytical results are in agreement with previously published gyrokinetic simulations. Unlike the ITG-driven flux, the TEM-driven flux is expected to be outwards for conditions far from marginal stability and inwards otherwise.

  18. Quasilinear Model for Energetic Particles Interacting with TAE Modes

    NASA Astrophysics Data System (ADS)

    Ghantous, Katy; Gorelenkov, Nikolai; Berk, Herbert

    2010-11-01

    TAE instabilities are thought to be a major source of Energetic Particle transport which could set limits on operational scenarios, especially for burning plasmas, and causes damage to the first wall. The quasilinear model proposed by Berk et al.ootnotetextH. L. Berk et al, Nucl. Fusion, 35:1661, 1995. relies on diffusion mechanisms for particle dynamics to captures the evolution of the energetic particle distribution function and the associated mode amplitude. Using the bump-on-tail as a paradigm, we analyze the dynamics near the resonances for accurate diffusion coefficient representation. We verify the model to get the predicted single mode saturation levels and benchmark the case of multimode overlap against particle codes. Using the TAE mode structures computed by the ideal MHD code NOVA, we generalize this method to relax energetic particles' profiles in the full 3D phase space.

  19. Quasilinear Line Broadened Model for Energetic Particle Transport

    NASA Astrophysics Data System (ADS)

    Ghantous, Katy; Gorelenkov, Nikolai; Berk, Herbert

    2011-10-01

    We present a self-consistent quasi-linear model that describes wave-particle interaction in toroidal geometry and computes fast ion transport during TAE mode evolution. The model bridges the gap between single mode resonances, where it predicts the analytically expected saturation levels, and the case of multiple modes overlapping, where particles diffuse across phase space. Results are presented in the large aspect ratio limit where analytic expressions are used for Fourier harmonics of the power exchange between waves and particles, . Implemention of a more realistic mode structure calculated by NOVAK code are also presented. This work is funded by DOE contract DE-AC02-09CH11466.

  20. Quasilinear perturbed equilibria of resistively unstable current carrying plasma

    NASA Astrophysics Data System (ADS)

    Hu, Di; Zakharov, Leonid E.

    2015-12-01

    > A formalism for consideration of island formation is presented using a model of a cylindrical resistively unstable plasma. Both current and pressure driven island formation at resonant surfaces are considered. The proposed formalism of perturbed equilibria avoids problems typical for linear analysis of resistive magneto-hydrodynamic instabilities related to extraction of the so-called small solution near the resonant surfaces. The matching technique of this paper is not sensitive to configuration parameters near the resonant surfaces. The comparison of the perturbed equilibrium method with the frequently used quasilinear mode analysis based on a perturbed averaged current density profile shows that the latter is limited in its applicability and underestimates the stability. Presented here for a cylindrical case, the perturbed equilibrium technique can be used in toroidal perturbed equilibrium codes with minor modifications.

  1. Comparing the line broadened quasilinear model to Vlasov code

    NASA Astrophysics Data System (ADS)

    Ghantous, K.; Berk, H. L.; Gorelenkov, N. N.

    2014-03-01

    The Line Broadened Quasilinear (LBQ) model is revisited to study its predicted saturation level as compared with predictions of a Vlasov solver BOT [Lilley et al., Phys. Rev. Lett. 102, 195003 (2009) and M. Lilley, BOT Manual. The parametric dependencies of the model are modified to achieve more accuracy compared to the results of the Vlasov solver both in regards to a mode amplitude's time evolution to a saturated state and its final steady state amplitude in the parameter space of the model's applicability. However, the regions of stability as predicted by LBQ model and BOT are found to significantly differ from each other. The solutions of the BOT simulations are found to have a larger region of instability than the LBQ simulations.

  2. Comparing the line broadened quasilinear model to Vlasov code

    SciTech Connect

    Ghantous, K.; Berk, H. L.; Gorelenkov, N. N.

    2014-03-15

    The Line Broadened Quasilinear (LBQ) model is revisited to study its predicted saturation level as compared with predictions of a Vlasov solver BOT [Lilley et al., Phys. Rev. Lett. 102, 195003 (2009) and M. Lilley, BOT Manual. The parametric dependencies of the model are modified to achieve more accuracy compared to the results of the Vlasov solver both in regards to a mode amplitude's time evolution to a saturated state and its final steady state amplitude in the parameter space of the model's applicability. However, the regions of stability as predicted by LBQ model and BOT are found to significantly differ from each other. The solutions of the BOT simulations are found to have a larger region of instability than the LBQ simulations.

  3. Quasi-linear regime of gravitational instability as a clue to understanding the large-scale structure in the Universe

    NASA Technical Reports Server (NTRS)

    Shandarin, Sergei F.

    1992-01-01

    In the late seventies, an image of the large-scale structure in the Universe began to emerge as a result of the accumulation of the galaxy redshifts. Most of the galaxies are found to concentrate in large filaments and perhaps sheets leaving most of the volume empty. Similar structures were predicted theoretically in the frame of the adiabatic theory of galaxy formation (Zeldovich) and later in the hot dark matter cosmology. However, both scenarios have been ruled out by the observations. With these scenarios the dynamical part of the scenario was also erroneously rejected by many as well. In this talk, I derive the Zeldovich approximation from the exact dynamic equations and show that it is always better than the standard linear approximation. The advantage of the Zeldovich approximation is the greatest in the quasi-linear regime when delta(sub rms) is less than 1 (delta identical to delta(rho)/rho), but the displacement of the matter is essential. The range of scales in the quasi-linear regime depends upon the slope of the initial spectrum and increases with decreasing n, where n is the exponent, if the initial spectrum is approximated by a simple power law P(k) varies as k(exp n).

  4. Simulation of the energy distribution of relativistic electron precipitation caused by quasi-linear interactions with EMIC waves

    PubMed Central

    Li, Zan; Millan, Robyn M; Hudson, Mary K

    2013-01-01

    [1]Previous studies on electromagnetic ion cyclotron (EMIC) waves as a possible cause of relativistic electron precipitation (REP) mainly focus on the time evolution of the trapped electron flux. However, directly measured by balloons and many satellites is the precipitating flux as well as its dependence on both time and energy. Therefore, to better understand whether pitch angle scattering by EMIC waves is an important radiation belt electron loss mechanism and whether quasi-linear theory is a sufficient theoretical treatment, we simulate the quasi-linear wave-particle interactions for a range of parameters and generate energy spectra, laying the foundation for modeling specific events that can be compared with balloon and spacecraft observations. We show that the REP energy spectrum has a peaked structure, with a lower cutoff at the minimum resonant energy. The peak moves with time toward higher energies and the spectrum flattens. The precipitating flux, on the other hand, first rapidly increases and then gradually decreases. We also show that increasing wave frequency can lead to the occurrence of a second peak. In both single- and double-peak cases, increasing wave frequency, cold plasma density or decreasing background magnetic field strength lowers the energies of the peak(s) and causes the precipitation to increase at low energies and decrease at high energies at the start of the precipitation. PMID:26167427

  5. Wave-Particle Interactions with Whistlers: Comparison Between Particle-in-Cell and Quasi-Linear Simulations

    NASA Astrophysics Data System (ADS)

    Camporeale, E.; Zimbardo, G.

    2015-12-01

    We study the wave-particle interactions between lower band chorus whistlers and an anisotropic tenuous population of relativistic electrons. We present the first direct comparison of first-principle particle-in-cell (PIC) simulations with a quasi-linear diffusion code. In the PIC approach, the waves are self-consistently generated by the temperature anisotropy instability that quickly saturates and relaxes the system toward marginal stability. We show that the quasi-linear diffusion and PIC results have significant quantitative mismatch in regions of energy/pitch angle where the resonance condition is not satisfied. Moreover, for pitch angles close to the loss cone the diffusion code overestimates the scattering, particularly at low energies. This suggests that higher-order nonlinear theories should be taken in consideration in order to capture non-resonant interactions, resonance broadening, and to account for scattering at angles close to 90 degree. Finally, we show that pitch angle diffusion is enhanced during the linear wave growth phase, and it rapidly saturates well before a single bounce period. We discuss how the saturation is related to the fact that the domain in which the particles pitch angle diffuse is bounded, and to the well-known problem of 90 degree diffusion barrier.

  6. On the quasi-linear diffusion in collisionless plasmas (to say nothing about Landau damping)

    SciTech Connect

    Hellinger, Petr; Travnicek, Pavel M.

    2012-06-15

    General quasi-linear diffusion coefficients for nonrelativistic collisionless plasmas are derived for unstable modes and analytically continued to damped modes. Properties of the resulting diffusion are investigated and discussed.

  7. Reduced quasilinear models for energetic particles interaction with Alfvenic eigenmodes

    NASA Astrophysics Data System (ADS)

    Ghantous, Katy

    The Line Broadened Quasilinear (LBQ) and the 1.5D reduced models are able to predict the effect of Alfvenic eigenmodes' interaction with energetic particles in burning plasmas. This interaction can result in energetic-particle losses that can damage the first wall, deteriorate the plasma performance, and even prevent ignition. The 1.5D model assumes a broad spectrum of overlapping modes and, based on analytic expressions for the growth and damping rates, calculates the pressure profiles that the energetic particles relax to upon interacting with the modes. 1.5D is validated with DIII-D experiments and predicted neutron losses consistent with observation. The model is employed to predict alpha-particle fusion-product losses in a large-scale operational parameter-space for burning plasmas. The LBQ model captures the interaction both in the regime of isolated modes as well as in the conventional regime of overlapping modes. Rules were established that allow quasilinear equations to replicate the expected steady-state saturation levels of isolated modes. The fitting formula is improved and the model is benchmarked with a Vlasov code, BOT. The saturation levels are accurately predicted and the mode evolution is well-replicated in the case of steady-state evolution where the collisions are high enough that coherent structures do not form. When the collisionality is low, oscillatory behavior can occur. LBQ can also exhibit non-steady behavior, but the onset of oscillations occurs for much higher collisional rates in BOT than in LBQ. For certain parameters of low collisionality, hole-clump creation and frequency chirping can occur which are not captured by the LBQ model. Also, there are cases of non-steady evolution without chirping which is possible for LBQ to study. However the results are inconclusive since the periods and amplitudes of the oscillations in the mode evolution are not well-replicated. If multiple modes exist, they can grow to the point of overlap which

  8. Quasilinear parabolic variational inequalities with multi-valued lower-order terms

    NASA Astrophysics Data System (ADS)

    Carl, Siegfried; Le, Vy K.

    2014-10-01

    In this paper, we provide an analytical frame work for the following multi-valued parabolic variational inequality in a cylindrical domain : Find and an such that where is some closed and convex subset, A is a time-dependent quasilinear elliptic operator, and the multi-valued function is assumed to be upper semicontinuous only, so that Clarke's generalized gradient is included as a special case. Thus, parabolic variational-hemivariational inequalities are special cases of the problem considered here. The extension of parabolic variational-hemivariational inequalities to the general class of multi-valued problems considered in this paper is not only of disciplinary interest, but is motivated by the need in applications. The main goals are as follows. First, we provide an existence theory for the above-stated problem under coercivity assumptions. Second, in the noncoercive case, we establish an appropriate sub-supersolution method that allows us to get existence, comparison, and enclosure results. Third, the order structure of the solution set enclosed by sub-supersolutions is revealed. In particular, it is shown that the solution set within the sector of sub-supersolutions is a directed set. As an application, a multi-valued parabolic obstacle problem is treated.

  9. Multiple solutions for a singular quasilinear elliptic system.

    PubMed

    Chen, Lin; Chen, Caisheng; Xiu, Zonghu

    2013-01-01

    We consider the multiplicity of nontrivial solutions of the following quasilinear elliptic system -div(|x|(-ap)|∇u|(p-2)∇u) + f₁(x)|u|(p-2) u = (α/(α + β))g(x)|u| (α-2) u|v| (β) + λh₁(x)|u| (γ-2) u + l₁(x), -div(|x|(-ap) |∇v| (p-2)∇v) + f₂(x)|v| (p-2) v = (β/(α + β))g(x)|v|(β-2) v|u|(α) + μh 2(x)|v|(γ-2)v + l 2(x), u(x) > 0, v(x) > 0, x ∈ ℝ(N), where λ, μ > 0, 1 < p < N, 1 < γ < p < α + β < p* = Np/(N-pd), 0 ≤ a < (N - p)/p, a ≤ b < a + 1, d = a + 1 - b > 0. The functions f₁(x), f₂(x), g(x), h₁(x), h₂(x), l₁(x), and l₂(x) satisfy some suitable conditions. We will prove that the problem has at least two nontrivial solutions by using Mountain Pass Theorem and Ekeland's variational principle. PMID:24282377

  10. Quasi-linear viscoelastic properties of the human medial patello-femoral ligament.

    PubMed

    Criscenti, G; De Maria, C; Sebastiani, E; Tei, M; Placella, G; Speziali, A; Vozzi, G; Cerulli, G

    2015-12-16

    The evaluation of viscoelastic properties of human medial patello-femoral ligament is fundamental to understand its physiological function and contribution as stabilizer for the selection of the methods of repair and reconstruction and for the development of scaffolds with adequate mechanical properties. In this work, 12 human specimens were tested to evaluate the time- and history-dependent non linear viscoelastic properties of human medial patello-femoral ligament using the quasi-linear viscoelastic (QLV) theory formulated by Fung et al. (1972) and modified by Abramowitch and Woo (2004). The five constant of the QLV theory, used to describe the instantaneous elastic response and the reduced relaxation function on stress relaxation experiments, were successfully evaluated. It was found that the constant A was 1.21±0.96MPa and the dimensionless constant B was 26.03±4.16. The magnitude of viscous response, the constant C, was 0.11±0.02 and the initial and late relaxation time constants τ1 and τ2 were 6.32±1.76s and 903.47±504.73s respectively. The total stress relaxation was 32.7±4.7%. To validate our results, the obtained constants were used to evaluate peak stresses from a cyclic stress relaxation test on three different specimens. The theoretically predicted values fit the experimental ones demonstrating that the QLV theory could be used to evaluate the viscoelastic properties of the human medial patello-femoral ligament. PMID:26573904

  11. Reduced order parameter estimation using quasilinearization and quadratic programming

    NASA Astrophysics Data System (ADS)

    Siade, Adam J.; Putti, Mario; Yeh, William W.-G.

    2012-06-01

    The ability of a particular model to accurately predict how a system responds to forcing is predicated on various model parameters that must be appropriately identified. There are many algorithms whose purpose is to solve this inverse problem, which is often computationally intensive. In this study, we propose a new algorithm that significantly reduces the computational burden associated with parameter identification. The algorithm is an extension of the quasilinearization approach where the governing system of differential equations is linearized with respect to the parameters. The resulting inverse problem therefore becomes a linear regression or quadratic programming problem (QP) for minimizing the sum of squared residuals; the solution becomes an update on the parameter set. This process of linearization and regression is repeated until convergence takes place. This algorithm has not received much attention, as the QPs can become quite large, often infeasible for real-world systems. To alleviate this drawback, proper orthogonal decomposition is applied to reduce the size of the linearized model, thereby reducing the computational burden of solving each QP. In fact, this study shows that the snapshots need only be calculated once at the very beginning of the algorithm, after which no further calculations of the reduced-model subspace are required. The proposed algorithm therefore only requires one linearized full-model run per parameter at the first iteration followed by a series of reduced-order QPs. The method is applied to a groundwater model with about 30,000 computation nodes where as many as 15 zones of hydraulic conductivity are estimated.

  12. Quasilinear Viscoelastic Behavior of Bovine Extraocular Muscle Tissue

    PubMed Central

    Yoo, Lawrence; Kim, Hansang; Gupta, Vijay; Demer, Joseph L.

    2009-01-01

    Purpose Until now, there has been no comprehensive mathematical model of the nonlinear viscoelastic stress-strain behavior of extraocular muscles (EOMs). The present study describes, with the use of a quasilinear viscoelastic (QLV) model, the nonlinear, history-dependent viscoelastic properties and elastic stress-strain relationship of EOMs. Methods Six oculorotary EOMs were obtained fresh from a local abattoir. Longitudinally oriented specimens were taken from different regions of the EOMs and subjected to uniaxial tensile, relaxation, and cyclic loading testing with the use of an automated load cell under temperature and humidity control. Twelve samples were subjected to uniaxial tensile loading with 1.7%/s strain rate until failure. Sixteen specimens were subjected to relaxation studies over 1500 seconds. Cyclic loading was performed to validate predictions of the QLV model characterized from uniaxial tensile loading and relaxation data. Results Uniform and highly repeatable stress-strain behavior was observed for 12 specimens extracted from various regions of all EOMs. Results from 16 different relaxation trials illustrated that most stress relaxation occurred during the first 30 to 60 seconds for 30% extension. Elastic and reduced relaxation functions were fit to the data, from which a QLV model was assembled and compared with cyclic loading data. Predictions of the QLV model agreed with observed peak cyclic loading stress values to within 8% for all specimens and conditions. Conclusions Close agreement between the QLV model and the relaxation and cyclic loading data validates model quantification of EOM mechanical properties and will permit the development of accurate overall models of mechanics of ocular motility and strabismus. PMID:19357357

  13. Numerical Tests of the Quasilinear Approximation of Mean-field Electrodynamics

    NASA Astrophysics Data System (ADS)

    Zsargo, J.; Petrovay, K.

    1995-05-01

    It is widely known that a sufficient condition for the applicability of quasilinear-type approximations (e.g. the second-order correlation approximation or SOCA) in mean-field electrodynamics is that Utau << min {l, H} where l, H, U and tau are characteristic horizontal and vertical scale lengths, velocity, and time, respectively. A necessary condition for their validity is however not known. In order to check the validity of the quasilinear results in cases where the above condition is not satisfied, as well as to study qualitative and quantitative differences between the quasilinear results and the actual solutions, we numerically solve the MHD induction equation for the kinematical case in a series of simplified "toy" model flows and then compare the results with the corresponding quasilinear solutions. Our model flows are two-dimensional two-component flows with simple (exponential or linear) stratifications. For conceptual clarity, in each model only one independent physical quantity (initial magnetic field, density, or velocity amplitude, respectively) has an inhomogeneous distribution. Solutions are computed for several widely differing values of the l/H horizontal/vertical scale length ratio. In all cases we find that the computed turbulent electromotive force does not differ from the quasilinear value by more than an order-of-unity factor, as long as Utau does not greatly exceed min {l, H}.

  14. Inference in dynamic systems using B-splines and quasilinearized ODE penalties.

    PubMed

    Frasso, Gianluca; Jaeger, Jonathan; Lambert, Philippe

    2016-05-01

    Nonlinear (systems of) ordinary differential equations (ODEs) are common tools in the analysis of complex one-dimensional dynamic systems. We propose a smoothing approach regularized by a quasilinearized ODE-based penalty. Within the quasilinearized spline-based framework, the estimation reduces to a conditionally linear problem for the optimization of the spline coefficients. Furthermore, standard ODE compliance parameter(s) selection criteria are applicable. We evaluate the performances of the proposed strategy through simulated and real data examples. Simulation studies suggest that the proposed procedure ensures more accurate estimates than standard nonlinear least squares approaches when the state (initial and/or boundary) conditions are not known. PMID:26602190

  15. 1.5D quasilinear model and its application on beams interacting with Alfven eigenmodes in DIII-D

    SciTech Connect

    Ghantous, K.; Gorelenkov, N. N.; Berk, H. L.; Heidbrink, W. W.; Van Zeeland, M. A.

    2012-09-15

    We propose a model, denoted here by 1.5D, to study energetic particle (EP) interaction with toroidal Alfvenic eigenmodes (TAE) in the case where the local EP drive for TAE exceeds the stability limit. Based on quasilinear theory, the proposed 1.5D model assumes that the particles diffuse in phase space, flattening the pressure profile until its gradient reaches a critical value where the modes stabilize. Using local theories and NOVA-K simulations of TAE damping and growth rates, the 1.5D model calculates the critical gradient and reconstructs the relaxed EP pressure profile. Local theory is improved from previous study by including more sophisticated damping and drive mechanisms such as the numerical computation of the effect of the EP finite orbit width on the growth rate. The 1.5D model is applied on the well-diagnosed DIII-D discharges no. 142111 [M. A. Van Zeeland et al., Phys. Plasmas 18, 135001 (2011)] and no. 127112 [W. W. Heidbrink et al., Nucl. Fusion. 48, 084001 (2008)]. We achieved a very satisfactory agreement with the experimental results on the EP pressure profiles redistribution and measured losses. This agreement of the 1.5D model with experimental results allows the use of this code as a guide for ITER plasma operation where it is desired to have no more than 5% loss of fusion alpha particles as limited by the design.

  16. Periodic solutions of the quasilinear equation of forced beam vibrations with homogeneous boundary conditions

    NASA Astrophysics Data System (ADS)

    Rudakov, I. A.

    2015-10-01

    We prove the existence of a countable family of time-periodic solutions of the quasilinear equation of beam vibrations with homogeneous boundary conditions and time-periodic right-hand side in the case when the non-linear term has power growth.

  17. Restrictions on the Quasi-Linear Description of Electron-Chorus Interaction in the Earth's Magnetosphere

    NASA Technical Reports Server (NTRS)

    Khazanov, George V.; Sibeck, David G.

    2013-01-01

    The interaction of electrons with coherent chorus waves in the random phase approximation can be described as quasi-linear diffusion for waves with amplitudes below some limit. The limit is calculated for relativistic and non-relativistic electrons. For stronger waves, the friction force should be taken into account.

  18. Renormalized entropy solutions of the Cauchy problem for a first-order inhomogeneous quasilinear equation

    SciTech Connect

    Panov, E Yu

    2013-10-31

    The concept of a renormalized entropy solution of the Cauchy problem for an inhomogeneous quasilinear equation of the first order is introduced. Existence and uniqueness theorems are proved, together with a comparison principle. Connections with generalized entropy solutions are investigated. Bibliography: 10 titles.

  19. Positive minimizers of the best constants and solutions to coupled critical quasilinear systems

    NASA Astrophysics Data System (ADS)

    Kang, Dongsheng

    2016-01-01

    In this paper, systems of quasilinear elliptic equations are investigated, which involve critical homogeneous nonlinearities and deferent Hardy-type terms. By variational methods and careful analysis, positive minimizers of the related best Sobolev constants are found and the existence of positive solutions to the systems is verified. The results are new even in the case p = 2.

  20. Multispecies Density and Temperature Gradient Dependence of Quasilinear Particle and Energy Fluxes

    SciTech Connect

    G. Rewoldt; R.V. Budny; W.M. Tang

    2004-08-09

    The variations of the normalized quasilinear particle and energy fluxes with artificial changes in the density and temperature gradients, as well as the variations of the linear growth rates and real frequencies, for ion temperature gradient and trapped-electron modes, are calculated. The quasilinear fluxes are normalized to the total energy flux, summed over all species. Here, realistic cases for tokamaks and spherical torii are considered which have two impurity species. For situations where there are substantial changes in the normalized fluxes, the ''diffusive approximation,'' in which the normalized fluxes are taken to be linear in the gradients, is seen to be inaccurate. Even in the case of small artificial changes in density or temperature gradients, changes in the fluxes of different species (''off-diagonal'') generally are significant, or even dominant, compared to those for the same species (''diagonal'').

  1. Quasilinear model for energetic particle diffusion in radial and velocity space

    SciTech Connect

    Waltz, R. E.; Staebler, G. M.; Bass, E. M.

    2013-04-15

    A quasilinear model for passive energetic particle (EP) turbulent diffusion in radial and velocity space is fitted and tested against nonlinear gyrokinetic tokamak simulations with the GYRO code [J. Candy and R. E. Waltz, Phys. Rev. Lett. 91, 045001 (2003)]. Off diagonal elements of a symmetric positive definite 2 Multiplication-Sign 2 EP diffusion matrix account for fluxes up radial (energy) gradients driven by energy (radial) gradients of the EP velocity space distribution function. The quasilinear ratio kernel of the model is provided by a simple analytic formula for the EP radial and velocity space EP diffusivity relative to radial thermal ion energy diffusivity at each linear mode of the turbulence driven by the thermal plasma. The TGLF [G. M. Staebler, J. E. Kinsey, and R. E. Waltz, Phys. Plasmas 14, 0055909 (2007); ibid. 15, 0055908 (2008)] tokamak transport model provides the linear mode frequency and growth rates to the kernel as well as the nonlinear spectral weight for each mode.

  2. Quasilinear model for energetic particle diffusion in radial and velocity space

    NASA Astrophysics Data System (ADS)

    Waltz, R. E.; Bass, E. M.; Staebler, G. M.

    2013-04-01

    A quasilinear model for passive energetic particle (EP) turbulent diffusion in radial and velocity space is fitted and tested against nonlinear gyrokinetic tokamak simulations with the GYRO code [J. Candy and R. E. Waltz, Phys. Rev. Lett. 91, 045001 (2003)]. Off diagonal elements of a symmetric positive definite 2×2 EP diffusion matrix account for fluxes up radial (energy) gradients driven by energy (radial) gradients of the EP velocity space distribution function. The quasilinear ratio kernel of the model is provided by a simple analytic formula for the EP radial and velocity space EP diffusivity relative to radial thermal ion energy diffusivity at each linear mode of the turbulence driven by the thermal plasma. The TGLF [G. M. Staebler, J. E. Kinsey, and R. E. Waltz, Phys. Plasmas 14, 0055909 (2007); ibid. 15, 0055908 (2008)] tokamak transport model provides the linear mode frequency and growth rates to the kernel as well as the nonlinear spectral weight for each mode.

  3. Collisional model of quasilinear transport driven by toroidal electrostatic ion temperature gradient modes

    SciTech Connect

    Pusztai, I.; Fueloep, T.; Candy, J.; Hastie, R. J.

    2009-07-15

    The stability of ion temperature gradient (ITG) modes and the quasilinear fluxes driven by them are analyzed in weakly collisional tokamak plasmas using a semianalytical model based on an approximate solution of the gyrokinetic equation, where collisions are modeled by a Lorentz operator. Although the frequencies and growth rates of ITG modes far from threshold are only very weakly sensitive to the collisionality, the a/L{sub Ti} threshold for stability is affected significantly by electron-ion collisions. The decrease in collisionality destabilizes the ITG mode driving an inward particle flux, which leads to the steepening of the density profile. Closed analytical expressions for the electron and ion density and temperature responses have been derived without expansion in the smallness of the magnetic drift frequencies. The results have been compared with gyrokinetic simulations with GYRO and illustrated by showing the scalings of the eigenvalues and quasilinear fluxes with collisionality, temperature scale length, and magnetic shear.

  4. PITCH-ANGLE SCATTERING: RESONANCE VERSUS NONRESONANCE, A BASIC TEST OF THE QUASILINEAR DIFFUSIVE RESULT

    SciTech Connect

    Ragot, B. R.

    2012-01-01

    Due to the very broad range of the scales available for the development of turbulence in space and astrophysical plasmas, the energy at the resonant scales of wave-particle interaction often constitutes only a tiny fraction of the total magnetic turbulent energy. Despite the high efficiency of resonant wave-particle interaction, one may therefore question whether resonant interaction really is the determining interaction process between particles and turbulent fields. By evaluating and comparing resonant and nonresonant effects in the frame of a quasilinear calculation, the dominance of resonance is here put to the test. By doing so, a basic test of the classical resonant quasilinear diffusive result for the pitch-angle scattering of charged energetic particles is also performed.

  5. The small data solutions of general 3-D quasilinear wave equations. II

    NASA Astrophysics Data System (ADS)

    Ding, Bingbing; Witt, Ingo; Yin, Huicheng

    2016-07-01

    This paper is a continuation of the work in [8], where the authors established the global existence of smooth small data solutions to the general 3-D quasilinear wave equation ∑ i , j = 0 3 gij (u , ∂ u) ∂ij2 u = 0 when the weak null condition holds. In the present paper, we show that the smooth small data solutions of equation ∑ i , j = 0 3 gij (u , ∂ u) ∂ij2 u = 0 will blow up in finite time when the weak null condition does not hold and a generic nondegenerate condition on the initial data is satisfied, moreover, a precise blowup time is completely determined. Therefore, collecting the main results in this paper and [8], we have given a basically complete study on the blowup or global existence of small data solutions to the 3-D quasilinear wave equation ∑ i , j = 0 3 gij (u , ∂ u) ∂ij2 u = 0.

  6. Quasi-linear H2/H∞/LTR Control of Vertical Parallel Flexible Structures Connected by a Spring

    NASA Astrophysics Data System (ADS)

    Han, Seong Ik; Kim, Jong Shik

    The quasi-linear H2/H∞/LTR control method is presented for the robust control of hardnonlinear multivariable systems. The hard nonlinear elements such as Coulomb friction, dead-zone and backlash are replaced by their random input describing functions (RIDF) to develop a quasi-linear model for designing a quasi-linear H2/H∞ controller. However, a nonlinear correction term appears in the coupled Riccati equations when the quasi-linear H2/H∞ method is applied for a quasi-linear model. It is shown that a nonlinear correction term can be ignored using the loop transfer recovery (LTR) under the appropriate condition. Thus, the quasi-linear H2/H∞ controller can be synthesized by introducing the inverse random input describing function (IRIDF). To show the effectiveness of the proposed control method, it will be applied to a flexible parallel inverted pendulum with Coulomb friction. The results of simulation show that the proposed control method is robust to nonlinear effects and the vibration of end tip.

  7. Non-Existence of Global Solutions For a Quasilinear Benney System

    NASA Astrophysics Data System (ADS)

    Antontsev, S.; Dias, J. P.; Figueira, M.; Oliveira, F.

    2011-06-01

    Benney introduced in 1977 (cf. Stud Appl Math 56:81-94, 1977) a general strategy for deriving systems of nonlinear PDEs describing the interaction between long and short waves. In Dias et al. (CR Acad Sci Paris I 344:493-496, 2007) we have studied the local existence and unicity of solutions to a quasilinear version of these systems. In the present paper we prove that in some important cases global strong solutions do not exist.

  8. Quasi-Linear Evolution of the Modulational Instability in the Presence of Partial Incoherence

    NASA Astrophysics Data System (ADS)

    Lisak, M.; Anderson, D.; Helczynski-Wolf, L.; Berczynski, P.; Fedele, R.; Semenov, V.

    2004-01-01

    A basic system of model equations describing the quasi-linear development of the modulational instability in the presence of partial incoherence is derived. This system can be interpreted as balance equations for the number of quasi-particles in the Wigner spectrum where the basic processes which are active are emission and absorption of quasi-particles by quasi-particles with different wave vectors.

  9. Uniqueness of a high-order accurate bicompact scheme for quasilinear hyperbolic equations

    NASA Astrophysics Data System (ADS)

    Bragin, M. D.; Rogov, B. V.

    2014-05-01

    The possibility of constructing new third- and fourth-order accurate differential-difference bicompact schemes is explored. The schemes are constructed for the one-dimensional quasilinear advection equation on a symmetric three-point spatial stencil. It is proved that this family of schemes consists of a single fourth-order accurate bicompact scheme. The result is extended to the case of an asymmetric three-point stencil.

  10. Nodal soliton solutions for generalized quasilinear Schrödinger equations

    SciTech Connect

    Deng, Yinbin Peng, Shuangjie; Wang, Jixiu

    2014-05-15

    This paper is concerned with constructing nodal radial solutions for generalized quasilinear Schrödinger equations in R{sup N} which arise from plasma physics, fluid mechanics, as well as high-power ultashort laser in matter. For any given integer k ⩾ 0, by using a change of variables and minimization argument, we obtain a sign-changing minimizer with k nodes of a minimization problem.

  11. Quasi-linear heating and acceleration in bi-Maxwellian plasmas

    SciTech Connect

    Hellinger, Petr; Trávníček, Pavel M.

    2013-12-15

    Quasi-linear acceleration and heating rates are derived for drifting bi-Maxwellian distribution functions in a general nonrelativistic case for arbitrary wave vectors, propagation angles, and growth/damping rates. The heating rates in a proton-electron plasma due to ion-cyclotron/kinetic Alfvén and mirror waves for a wide range of wavelengths, directions of propagation, and growth or damping rates are explicitly computed.

  12. Quasilinear simulation of auroral kilometric radiation by a relativistic Fokker-Planck code

    SciTech Connect

    Matsuda, Y.

    1991-01-01

    An intense terrestrial radiation called the auroral kilometric radiation (AKR) is believed to be generated by cyclotron maser instability. We study a quasilinear evolution of this instability by means of a two-dimensional relativistic Fokker-Planck code which treats waves and distributions self-consistently, including radiation loss and electron source and sink. We compare the distributions and wave amplitude with spacecraft observations to elucidate physical processes involved. 3 refs., 1 fig.

  13. EVIDENCE OF QUASI-LINEAR SUPER-STRUCTURES IN THE COSMIC MICROWAVE BACKGROUND AND GALAXY DISTRIBUTION

    SciTech Connect

    Inoue, Kaiki Taro; Sakai, Nobuyuki; Tomita, Kenji

    2010-11-20

    Recent measurements of hot and cold spots on the cosmic microwave background (CMB) sky suggest the presence of super-structures on (>100 h {sup -1} Mpc) scales. We develop a new formalism to estimate the expected amplitude of temperature fluctuations due to the integrated Sachs-Wolfe (ISW) effect from prominent quasi-linear structures. Applying the developed tools to the observed ISW signals from voids and clusters in catalogs of galaxies at redshifts z < 1, we find that they indeed imply a presence of quasi-linear super-structures with a comoving radius of 100 {approx} 300 h {sup -1} Mpc and a density contrast |{delta}| {approx} O(0.1). We also find that the observed ISW signals are at odds with the concordant {Lambda} cold dark matter model that predicts Gaussian primordial perturbations at {approx}>3{sigma} level. We confirm that the mean temperature around the CMB cold spot in the southern Galactic hemisphere filtered by a compensating top-hat filter deviates from the mean value at {approx}3{sigma} level, implying that a quasi-linear supervoid or an underdensity region surrounded by a massive wall may reside at low redshifts z < 0.3 and the actual angular size (16{sup 0}-17{sup 0}) may be larger than the apparent size (4{sup 0}-10{sup 0}) discussed in literature. Possible solutions are briefly discussed.

  14. Computing quasi-linear diffusion coefficients using the delta-f particle-in-cell method

    SciTech Connect

    Austin, T. M.; Smithe, D. N.; Ranjbar, V.

    2009-11-26

    Linear wave codes AORSA and TORIC couple to the bounce-averaged nonlinear Fokker-Planck code CQL3D through quasi-linear diffusion coefficients. Both linear wave codes rely on the quasi-local approximation that includes only first-order parallel and perpendicular gradient variations of cyclotron frequency and ignores field line curvature along with temperature and density gradient effects. The delta-f particle-in-cell (DFPIC) method has been successfully used for simulating ion-cyclotron fast wave behavior. This method also permits particle behavior such as multiple pass resonance, banana orbits, and superadiabaticity. We present new work on generating quasi-linear diffusion coefficients using the DFPIC method that will permit the electromagnetic particle-in-cell (EMPIC) code, VORPAL, to couple to CQL3D and to compare to AORSA and TORIC. A new multiple weight delta-f approach will be presented that converts velocity derivatives to action derivatives and yields a full tensor quasi-linear diffusion coefficient.

  15. The quasi-linear relaxation of thick-target electron beams in solar flares

    NASA Technical Reports Server (NTRS)

    Mcclements, K. G.; Brown, J. C.; Emslie, A. G.

    1986-01-01

    The effects of quasi-linear interactions on thick-target electron beams in the solar corona are investigated. Coulomb collisions produce regions of positive gradient in electron distributions which are initially monotonic decreasing functions of energy. In the resulting two-stream instability, energy and momentum are transferred from electrons to Langmuir waves and the region of positive slope in the electron distribution is replaced by a plateau. In the corona, the timescale for this quasi-linear relaxation is very short compared to the collision time. It is therefore possible to model the effects of quasi-linear relaxation by replacing any region of positive slop in the distribution by a plateau at each time step, in such a way as to conserve particle number. The X-ray bremsstrahlung and collisional heating rate produced by a relaxed beam are evaluated. Although the analysis is strictly steady state, it is relevant to the theoretical interpretation of hard X-ray bursts with durations of the order of a few seconds (i.e., the majority of such bursts).

  16. Quasi-Linear Cochlear Responses to Noise Can Result from Instantaneous Nonlinearities

    NASA Astrophysics Data System (ADS)

    Liu, Yi-Wen; Neely, Stephen T.

    2011-11-01

    Responses to acoustic stimuli in the cochlea are known to be nonlinear. Many existing models of cochlear mechanics were built upon three basic assumptions: traveling-wave amplification is provided by active mechanisms in the outer hair cells (OHCs). Second, as the stimulus level increases, the gain decreases due to saturation nonlinearity in the OHCs. Finally, the saturation non-linearity is "instantaneous"; its input-output relation does not possess memory. These assumptions were recently challenged by reports that basilar-membrane (BM) responses to noise can be predicted well by level-dependent Wiener filters and are thus quasi-linear. It was argued that the quasi-linear responses could not result from instantaneous nonlinearity. In this paper, we present a model of cochlear mechanics which has instantaneous OHC saturation nonlinearity but produces quasi-linear responses to noise. Correlation coefficients were consistently greater than 0.9 between simulated noise responses and the responses predicted by equivalent Wiener filters. Further, Gaussianity in the acoustic stimuli was preserved on the BM. We conclude that the results support the common understandings and assumptions of cochlear mechanics.

  17. Positive solution for a quasilinear elliptic equation involving critical or supercritical exponent

    NASA Astrophysics Data System (ADS)

    Liu, Haidong

    2016-04-01

    This paper concerns the quasilinear elliptic equation - Δ u + u - Δ ( u 2 ) u = |" separators=" u | p - 2 u + μ |" separators=" u | q - 2 u in R N , where N ≥ 3, 2 < p < 2 ṡ 2∗ = 4N/(N - 2) ≤ q, and μ is a positive parameter. For μ > 0 sufficiently small, existence of a positive solution will be proved via variational methods together with truncation technique and L∞-estimate. The main novelty is that no growth condition is required for the nonlinearity.

  18. Reduction of nonlinear phase noise using optical phase conjugation in quasi-linear optical transmission systems.

    PubMed

    Kumar, Shiva; Liu, Ling

    2007-03-01

    An analytical expression for the variance of nonlinear phase noise for a quasi-linear system using the midpoint optical phase conjugation (OPC) is obtained. It is shown that the the system with OPC and dispersion inversion (DI) can exactly cancel the nonlinear phase noise up to the first order in nonlinear coefficient if the amplifier and the end point of the system are equidistant from the OPC. It is found that the nonlinear phase noise variance of the midpoint phase-conjugated optical transmission system with DI is smaller than that of the system without DI. PMID:19532453

  19. Analytic solutions of the time-dependent quasilinear diffusion equation with source and loss terms

    SciTech Connect

    Hassan, M.H.A. ); Hamza, E.A. )

    1993-08-01

    A simplified one-dimensional quasilinear diffusion equation describing the time evolution of collisionless ions in the presence of ion-cyclotron-resonance heating, sources, and losses is solved analytically for all harmonics of the ion cyclotron frequency. Simple time-dependent distribution functions which are initially Maxwellian and vanish at high energies are obtained and calculated numerically for the first four harmonics of resonance heating. It is found that the strongest ion tail of the resulting anisotropic distribution function is driven by heating at the second harmonic followed by heating at the fundamental frequency.

  20. Solution of second order quasi-linear boundary value problems by a wavelet method

    SciTech Connect

    Zhang, Lei; Zhou, Youhe; Wang, Jizeng

    2015-03-10

    A wavelet Galerkin method based on expansions of Coiflet-like scaling function bases is applied to solve second order quasi-linear boundary value problems which represent a class of typical nonlinear differential equations. Two types of typical engineering problems are selected as test examples: one is about nonlinear heat conduction and the other is on bending of elastic beams. Numerical results are obtained by the proposed wavelet method. Through comparing to relevant analytical solutions as well as solutions obtained by other methods, we find that the method shows better efficiency and accuracy than several others, and the rate of convergence can even reach orders of 5.8.

  1. Tension control of space tether via online quasi-linearization iterations

    NASA Astrophysics Data System (ADS)

    Wen, Hao; Zhu, Zheng H.; Jin, Dongping; Hu, Haiyan

    2016-02-01

    The paper presents how to stabilize the deployment and retrieval processes of a space tether system via the tension control, where the model predictive control is exploited to optimize the control performance while the nonlinear dynamics and tension constraint are explicitly taken into account. A new scheme of online quasi-linearization iteration is proposed to transfer the nonlinear optimal control problem into a series of linear optimal control problems that can be solved in sequence at a series of sampling instants. Consequently, it avoids the complete solution of the nonlinear optimal control problem at each sampling interval such that the computational load can be greatly alleviated. Furthermore, the scheme extends the conventional quasi-linearization schemes by distributing the iterative process across sampling instants and online updating the initial condition of the linear optimal control problem. The problems of linear optimal control are discretized using a pseudo-spectral algorithm and then solved by a solver of linear quadratic programming. Numerical case studies indicate that successful deployment and retrieval of the system can be achieved using the proposed control scheme without violating the positive tension constraint. The time cost for each online optimization in the proposed scheme is on the order of 10 ms and far below the sampling interval under consideration.

  2. Control of nonlinear systems represented in quasilinear form. Ph.D. Thesis, 1994 Final Report

    NASA Technical Reports Server (NTRS)

    Coetsee, Josef A.

    1993-01-01

    Methods to synthesize controllers for nonlinear systems are developed by exploiting the fact that under mild differentiability conditions, systems of the form: x-dot = f(x) + G(x)u can be represented in quasilinear form, viz: x-dot = A(x)x + B(x)u. Two classes of control methods are investigated. The first is zero-look-ahead control, where the control input depends only on the current values of A(x) and B(x). For this case the control input is computed by continuously solving a matrix Riccati equation as the system progresses along a trajectory. The second is controllers with look-ahead, where the control input depends on the future behavior of A(x) and B(x). These controllers use the similarity between quasilinear systems and linear time varying systems to find approximate solutions to optimal control type problems. The methods that are developed are not guaranteed to be globally stable. However in simulation studies they were found to be useful alternatives for synthesizing control laws for a general class of nonlinear systems.

  3. One-dimensional energetic particle quasilinear diffusion for realistic TAE instabilities

    NASA Astrophysics Data System (ADS)

    Duarte, Vinicius; Ghantous, Katy; Berk, Herbert; Gorelenkov, Nikolai

    2014-10-01

    Owing to the proximity of the characteristic phase (Alfvén) velocity and typical energetic particle (EP) superthermal velocities, toroidicity-induced Alfvén eigenmodes (TAEs) can be resonantly destabilized endangering the plasma performance. Thus, it is of ultimate importance to understand the deleterious effects on the confinement resulting from fast ion driven instabilities expected in fusion-grade plasmas. We propose to study the interaction of EPs and TAEs using a line broadened quasilinear model, which captures the interaction in both regimes of isolated and overlapping modes. The resonance particles diffuse in the phase space where the problem essentially reduces to one dimension with constant kinetic energy and the diffusion mainly along the canonical toroidal angular momentum. Mode structure and wave particle resonances are computed by the NOVA code and are used in a quasilinear diffusion code that is being written to study the evolution of the distribution function, under the assumption that they can be considered virtually unalterable during the diffusion. A new scheme for the resonant particle diffusion is being proposed that builds on the 1-D nature of the diffusion from a single mode, which leads to a momentum conserving difference scheme even when there is mode overlap.

  4. 1.5D quasilinear model and its application on beams interacting with Alfvén eigenmodes in DIII-D

    NASA Astrophysics Data System (ADS)

    Ghantous, K.; Gorelenkov, N. N.; Berk, H. L.; Heidbrink, W. W.; Van Zeeland, M. A.

    2012-09-01

    We propose a model, denoted here by 1.5D, to study energetic particle (EP) interaction with toroidal Alfvenic eigenmodes (TAE) in the case where the local EP drive for TAE exceeds the stability limit. Based on quasilinear theory, the proposed 1.5D model assumes that the particles diffuse in phase space, flattening the pressure profile until its gradient reaches a critical value where the modes stabilize. Using local theories and NOVA-K simulations of TAE damping and growth rates, the 1.5D model calculates the critical gradient and reconstructs the relaxed EP pressure profile. Local theory is improved from previous study by including more sophisticated damping and drive mechanisms such as the numerical computation of the effect of the EP finite orbit width on the growth rate. The 1.5D model is applied on the well-diagnosed DIII-D discharges #142111 [M. A. Van Zeeland et al., Phys. Plasmas 18, 135001 (2011)] and #127112 [W. W. Heidbrink et al., Nucl. Fusion. 48, 084001 (2008)]. We achieved a very satisfactory agreement with the experimental results on the EP pressure profiles redistribution and measured losses. This agreement of the 1.5D model with experimental results allows the use of this code as a guide for ITER plasma operation where it is desired to have no more than 5% loss of fusion alpha particles as limited by the design.

  5. Global structure stability of Riemann solutions of quasilinear hyperbolic systems of conservation laws: shocks and contact discontinuities

    NASA Astrophysics Data System (ADS)

    Kong, De-Xing

    In this paper, the author proves the global structure stability of the Lax's Riemann solution u=U( {x}/{t}) , containing only shocks and contact discontinuities, of general n× n quasilinear hyperbolic system of conservation laws. More precisely, the author proves the global existence and uniqueness of the piecewise C1 solution u= u( t, x) of a class of generalized Riemann problem, which can be regarded as a perturbation of the corresponding Riemann problem, for the quasilinear hyperbolic system of conservation laws; moreover, this solution has a global structure similar to that of the solution u=U( {x}/{t}) . Combining the results in Kong (Global structure instability of Riemann solutions of quasilinear hyperbolic systems of conservation laws: rarefaction waves, to appear), the author proves that the Lax's Riemann solution of general n× n quasilinear hyperbolic system of conservation laws is globally structurally stable if and only if it contains only non-degenerate shocks and contact discontinuities, but no rarefaction waves and other weak discontinuities.

  6. Deviations from early-time quasilinear behavior for the atom-optics kicked rotor near the classical limit

    NASA Astrophysics Data System (ADS)

    Sadgrove, Mark; Mullins, Terry; Parkins, Scott; Leonhardt, Rainer

    2005-02-01

    We present experimental measurements of the mean energy for the atom-optics kicked rotor after just two kicks. The energy is found to deviate from the quasilinear value for small kicking periods. The observed deviation is explained by recent theoretical results which include the effect of a nonuniform initial momentum distribution, previously applied only to systems using much colder atoms than ours.

  7. Quasi-linear vacancy dynamics modeling and circuit analysis of the bipolar memristor.

    PubMed

    Abraham, Isaac

    2014-01-01

    The quasi-linear transport equation is investigated for modeling the bipolar memory resistor. The solution accommodates vacancy and circuit level perspectives on memristance. For the first time in literature the component resistors that constitute the contemporary dual variable resistor circuit model are quantified using vacancy parameters and derived from a governing partial differential equation. The model describes known memristor dynamics even as it generates new insight about vacancy migration, bottlenecks to switching speed and elucidates subtle relationships between switching resistance range and device parameters. The model is shown to comply with Chua's generalized equations for the memristor. Independent experimental results are used throughout, to validate the insights obtained from the model. The paper concludes by implementing a memristor-capacitor filter and compares its performance to a reference resistor-capacitor filter to demonstrate that the model is usable for practical circuit analysis. PMID:25390634

  8. Quasi-linear analysis of the extraordinary electron wave destabilized by runaway electrons

    SciTech Connect

    Pokol, G. I.; Kómár, A.; Budai, A.; Stahl, A.; Fülöp, T.

    2014-10-15

    Runaway electrons with strongly anisotropic distributions present in post-disruption tokamak plasmas can destabilize the extraordinary electron (EXEL) wave. The present work investigates the dynamics of the quasi-linear evolution of the EXEL instability for a range of different plasma parameters using a model runaway distribution function valid for highly relativistic runaway electron beams produced primarily by the avalanche process. Simulations show a rapid pitch-angle scattering of the runaway electrons in the high energy tail on the 100–1000 μs time scale. Due to the wave-particle interaction, a modification to the synchrotron radiation spectrum emitted by the runaway electron population is foreseen, exposing a possible experimental detection method for such an interaction.

  9. A physically-based, quasilinear viscoelasticity model for the dynamic response of polyurea

    NASA Astrophysics Data System (ADS)

    Clifton, Rodney J.; Wang, Xinjie; Jiao, Tong

    2016-08-01

    Polyurea, a promising material for damage mitigation in impact scenarios, has been investigated through plane-wave, pressure-shear plate impact (PSPI) experiments to obtain its mechanical response at high pressures and high strain rates. Based on these experimental results, a physically-based, quasi-linear, viscoelasticity model is introduced to capture the observed nonlinear pressure-volume behavior, the strong dependence of shearing resistance on pressure, and the strong relaxation of deviatoric stresses. This model has been implemented in finite element software ABAQUS to simulate the response of polyurea P1000 under the impact conditions of a variety of PSPI experiments. Simulation results agree reasonably well with those of the experiments.

  10. Quasi-Linear Vacancy Dynamics Modeling and Circuit Analysis of the Bipolar Memristor

    PubMed Central

    Abraham, Isaac

    2014-01-01

    The quasi-linear transport equation is investigated for modeling the bipolar memory resistor. The solution accommodates vacancy and circuit level perspectives on memristance. For the first time in literature the component resistors that constitute the contemporary dual variable resistor circuit model are quantified using vacancy parameters and derived from a governing partial differential equation. The model describes known memristor dynamics even as it generates new insight about vacancy migration, bottlenecks to switching speed and elucidates subtle relationships between switching resistance range and device parameters. The model is shown to comply with Chua's generalized equations for the memristor. Independent experimental results are used throughout, to validate the insights obtained from the model. The paper concludes by implementing a memristor-capacitor filter and compares its performance to a reference resistor-capacitor filter to demonstrate that the model is usable for practical circuit analysis. PMID:25390634

  11. On nonlinear viscoelastic deformations: a reappraisal of Fung's quasi-linear viscoelastic model

    PubMed Central

    De Pascalis, Riccardo; Abrahams, I. David; Parnell, William J.

    2014-01-01

    This paper offers a reappraisal of Fung's model for quasi-linear viscoelasticity. It is shown that a number of negative features exhibited in other works, commonly attributed to the Fung approach, are merely a consequence of the way it has been applied. The approach outlined herein is shown to yield improved behaviour and offers a straightforward scheme for solving a wide range of models. Results from the new model are contrasted with those in the literature for the case of uniaxial elongation of a bar: for an imposed stretch of an incompressible bar and for an imposed load. In the latter case, a numerical solution to a Volterra integral equation is required to obtain the results. This is achieved by a high-order discretization scheme. Finally, the stretch of a compressible viscoelastic bar is determined for two distinct materials: Horgan–Murphy and Gent. PMID:24910527

  12. Numerical quasi-linear study of the critical ionization velocity phenomenon

    NASA Technical Reports Server (NTRS)

    Moghaddam-Taaheri, E.; Goertz, C. K.

    1993-01-01

    The critical ionization velocity (CIV) for a neutral barium (Ba) gas cloud moving across the static magnetic field is studied numerically using quasi-linear equations and a parameter range which is typical for the shaped-charge Ba gas release experiments in space. For consistency the charge exchange between the background oxygen ions and neutral atoms and its reverse process, as well as the excitation of the neutral Ba atoms, are included. The numerical results indicate that when the ionization rate due to CIV becomes comparable to the charge exchange rate the energy lost to the ionization and excitation collisions by the superthermal electrons exceeds the energy gain from the waves that are excited by the ion beam. This results in a CIV yield less than the yield by the charge exchange process.

  13. Numerical quasi-linear study of the critical ionization velocity phenomenon

    SciTech Connect

    Moghaddam-Taaheri, E.; Goertz, C.K. )

    1993-02-01

    The critical ionization velocity, (CIV) for a neutral barium (Ba) gas cloud moving across the static magnetic field is studied numerically using quasi-linear equations and a parameter range which is typical for the shaped-charge Ba gas release experiments in space. For consistency the charge exchange between the background oxygen ions and neutral atoms and its reverse process, as well as the excitation of the neutral Ba atoms, are included. The numerical results indicate that when the ionization rate due to CIV becomes comparable to the charge exchange rate the energy lost to the ionization and excitation collisions by the superthermal electrons exceeds the energy gain from the waves that are excited by the ion beam. This results in a CIV yield less than the yield by the charge exchange process. 75 refs., 18 figs., 3 tabs.

  14. Conjugate quasilinear Dirichlet and Neumann problems and a posteriori error bounds

    NASA Technical Reports Server (NTRS)

    Lavery, J. E.

    1976-01-01

    Quasilinear Dirichlet and Neumann problems on a rectangle D with boundary D prime are considered. Using these concepts, conjugate problems, that is, a pair of one Dirichlet and one Neumann problem, the minima of the energies of which add to zero, are introduced. From the concept of conjugate problems, two-sided bounds for the energy of the exact solution of any given Dirichlet or Neumann problem are constructed. These two-sided bounds for the energy at the exact solution are in turn used to obtain a posteriori error bounds for the norm of the difference of the approximate and exact solutions of the problem. These bounds do not involve the unknown exact solution and are easily constructed numerically.

  15. A nodal inverse problem for a quasi-linear ordinary differential equation in the half-line

    NASA Astrophysics Data System (ADS)

    Pinasco, Juan P.; Scarola, Cristian

    2016-07-01

    In this paper we study an inverse problem for a quasi-linear ordinary differential equation with a monotonic weight in the half-line. First, we find the asymptotic behavior of the singular eigenvalues, and we obtain a Weyl-type asymptotics imposing an appropriate integrability condition on the weight. Then, we investigate the inverse problem of recovering the coefficients from nodal data. We show that any dense subset of nodes of the eigenfunctions is enough to recover the weight.

  16. Asymptotic uniqueness of ground states for a class of quasilinear Schrödinger equations with H1-supercritical exponent

    NASA Astrophysics Data System (ADS)

    Adachi, Shinji; Watanabe, Tatsuya

    2016-02-01

    In this paper, we obtain the asymptotic uniqueness of ground states for a class of quasilinear Schrödinger equations with H1-supercritical exponent. To this aim, the uniqueness and the non-degeneracy of positive solutions of the corresponding limit equation, which is a zero mass problem, play important roles. Thus we also show the uniqueness and non-degeneracy result for a class of zero mass problems by applying ODE techniques.

  17. An iterative ensemble quasi-linear data assimilation approach for integrated reservoir monitoring

    NASA Astrophysics Data System (ADS)

    Li, J. Y.; Kitanidis, P. K.

    2013-12-01

    Reservoir forecasting and management are increasingly relying on an integrated reservoir monitoring approach, which involves data assimilation to calibrate the complex process of multi-phase flow and transport in the porous medium. The numbers of unknowns and measurements arising in such joint inversion problems are usually very large. The ensemble Kalman filter and other ensemble-based techniques are popular because they circumvent the computational barriers of computing Jacobian matrices and covariance matrices explicitly and allow nonlinear error propagation. These algorithms are very useful but their performance is not well understood and it is not clear how many realizations are needed for satisfactory results. In this presentation we introduce an iterative ensemble quasi-linear data assimilation approach for integrated reservoir monitoring. It is intended for problems for which the posterior or conditional probability density function is not too different from a Gaussian, despite nonlinearity in the state transition and observation equations. The algorithm generates realizations that have the potential to adequately represent the conditional probability density function (pdf). Theoretical analysis sheds light on the conditions under which this algorithm should work well and explains why some applications require very few realizations while others require many. This algorithm is compared with the classical ensemble Kalman filter (Evensen, 2003) and with Gu and Oliver's (2007) iterative ensemble Kalman filter on a synthetic problem of monitoring a reservoir using wellbore pressure and flux data.

  18. Quasi-linear modeling of lower hybrid current drive in ITER and DEMO

    NASA Astrophysics Data System (ADS)

    Cardinali, A.; Cesario, R.; Panaccione, L.; Santini, F.; Amicucci, L.; Castaldo, C.; Ceccuzzi, S.; Mirizzi, F.; Tuccillo, A. A.

    2015-12-01

    First pass absorption of the Lower Hybrid waves in thermonuclear devices like ITER and DEMO is modeled by coupling the ray tracing equations with the quasi-linear evolution of the electron distribution function in 2D velocity space. As usually assumed, the Lower Hybrid Current Drive is not effective in a plasma of a tokamak fusion reactor, owing to the accessibility condition which, depending on the density, restricts the parallel wavenumber to values greater than n∥crit and, at the same time, to the high electron temperature that would enhance the wave absorption and then restricts the RF power deposition to the very periphery of the plasma column (near the separatrix). In this work, by extensively using the "raystar" code, a parametric study of the propagation and absorption of the LH wave as function of the coupled wave spectrum (as its width, and peak value), has been performed very accurately. Such a careful investigation aims at controlling the power deposition layer possibly in the external half radius of the plasma, thus providing a valuable aid to the solution of how to control the plasma current profile in a toroidal magnetic configuration, and how to help the suppression of MHD mode that can develop in the outer part of the plasma. This analysis is useful not only for exploring the possibility of profile control of a pulsed operation reactor as well as the tearing mode stabilization, but also in order to reconsider the feasibility of steady state regime for DEMO.

  19. Multi-Party Privacy-Preserving Set Intersection with Quasi-Linear Complexity

    NASA Astrophysics Data System (ADS)

    Cheon, Jung Hee; Jarecki, Stanislaw; Seo, Jae Hong

    Secure computation of the set intersection functionality allows n parties to find the intersection between their datasets without revealing anything else about them. An efficient protocol for such a task could have multiple potential applications in commerce, health care, and security. However, all currently known secure set intersection protocols for n>2 parties have computational costs that are quadratic in the (maximum) number of entries in the dataset contributed by each party, making secure computation of the set intersection only practical for small datasets. In this paper, we describe the first multi-party protocol for securely computing the set intersection functionality with both the communication and the computation costs that are quasi-linear in the size of the datasets. For a fixed security parameter, our protocols require O(n2k) bits of communication and Õ(n2k) group multiplications per player in the malicious adversary setting, where k is the size of each dataset. Our protocol follows the basic idea of the protocol proposed by Kissner and Song, but we gain efficiency by using different representations of the polynomials associated with users' datasets and careful employment of algorithms that interpolate or evaluate polynomials on multiple points more efficiently. Moreover, the proposed protocol is robust. This means that the protocol outputs the desired result even if some corrupted players leave during the execution of the protocol.

  20. Analytical estimates of electron quasi-linear diffusion by fast magnetosonic waves

    NASA Astrophysics Data System (ADS)

    Mourenas, D.; Artemyev, A. V.; Agapitov, O. V.; Krasnoselskikh, V.

    2013-06-01

    Quantifying the loss of relativistic electrons from the Earth's radiation belts requires to estimate the effects of many kinds of observed waves, ranging from ULF to VLF. Analytical estimates of electron quasi-linear diffusion coefficients for whistler-mode chorus and hiss waves of arbitrary obliquity have been recently derived, allowing useful analytical approximations for lifetimes. We examine here the influence of much lower frequency and highly oblique, fast magnetosonic waves (also called ELF equatorial noise) by means of both approximate analytical formulations of the corresponding diffusion coefficients and full numerical simulations. Further analytical developments allow us to identify the most critical wave and plasma parameters necessary for a strong impact of fast magnetosonic waves on electron lifetimes and acceleration in the simultaneous presence of chorus, hiss, or lightning-generated waves, both inside and outside the plasmasphere. In this respect, a relatively small frequency over ion gyrofrequency ratio appears more favorable, and other propitious circumstances are characterized. This study should be useful for a comprehensive appraisal of the potential effect of fast magnetosonic waves throughout the magnetosphere.

  1. Global existence and boundedness in a higher-dimensional quasilinear chemotaxis system

    NASA Astrophysics Data System (ADS)

    Wang, Yilong; Xiang, Zhaoyin

    2015-12-01

    This paper deals with the boundedness of global solutions to the quasilinear Keller-Segel system u_t=nabla\\cdotbig(D(u)nabla u-unabla vbig), &quad xinΩ, t>0, v_t=Δ v-uf(v),&quad xinΩ, t>0, nabla u\\cdot ν=0, nabla v\\cdotν=0,&quad xin partialΩ, t>0 in a bounded domain {Ωsubset Rn(n≥ 3)} with smooth boundary, where D( u) is supposed to satisfy D( u) ≥ D 0 u m-1 with some positive constant D 0. It is proved that when {m>2-n+2/2n}, the system possesses global bounded weak solutions for any sufficiently smooth nonnegative initial data. In particular, we improved the recent result by Wang et al. (Z Angew Math Phys, 2015. doi: 10.1007/s00033-014-0491-9 ) in the sense that we established the global boundedness of weak solutions. We also removed the convexity assumption on the domain used by Wang et al. (Z Angew Math Phys 65:1137-1152, 2014, 2015).

  2. Simulation of quasi-linear mesoscale convective systems in northern China: Lightning activities and storm structure

    NASA Astrophysics Data System (ADS)

    Li, Wanli; Qie, Xiushu; Fu, Shenming; Su, Debin; Shen, Yonghai

    2016-01-01

    Two intense quasi-linear mesoscale convective systems (QLMCSs) in northern China were simulated using the WRF (Weather Research and Forecasting) model and the 3D-Var (three-dimensional variational) analysis system of the ARPS (Advanced Regional Prediction System) model. A new method in which the lightning density is calculated using both the precipitation and non-precipitation ice mass was developed to reveal the relationship between the lightning activities and QLMCS structures. Results indicate that, compared with calculating the results using two previous methods, the lightning density calculated using the new method presented in this study is in better accordance with observations. Based on the calculated lightning densities using the new method, it was found that most lightning activity was initiated on the right side and at the front of the QLMCSs, where the surface wind field converged intensely. The CAPE was much stronger ahead of the southeastward progressing QLMCS than to the back it, and their lightning events mainly occurred in regions with a large gradient of CAPE. Comparisons between lightning and non-lightning regions indicated that lightning regions featured more intense ascending motion than non-lightning regions; the vertical ranges of maximum reflectivity between lightning and non-lightning regions were very different; and the ice mixing ratio featured no significant differences between the lightning and non-lightning regions.

  3. Kinetic Model of Coronal Hole Protons Undergoing Turbulent Stochastic Heating and Quasilinear Wave Generation

    NASA Astrophysics Data System (ADS)

    Isenberg, P. A.; Vasquez, B. J.

    2015-12-01

    We have constructed a kinetic model of coronal hole protons heated in the directions perpendicular to the magnetic field according to the turbulent stochastic heating mechanism of Chandran et al. The kinetic heating is modeled by a proton diffusion in v_perp. The protons additionally respond to the coronal hole forces of gravity, charge-separation electric field, and the mirror force as described in our previous kinetic guiding-center models. We have further extended this kinetic model to include wave growth and damping by the anisotropic protons through the quasilinear cyclotron-resonant interaction. We solve the coupled equations for the kinetic proton behavior and for the self-consistent development of ion-cyclotron wave spectra propagating within 60˚ of the magnetic field direction. We seek to obtain a steady-state solution, showing the evolution of the proton distribution and the wave spectra with increasing heliocentric radial position due to the combined effects of heating, resonant scattering coupled to the wave generation, and the kinetic response to the large-scale forces of the inhomogeneous coronal hole. We will report on our results and the implications for the measurements to be made by the Solar Probe Plus mission.

  4. Theory and simulation of the beam cyclotron instability.

    NASA Technical Reports Server (NTRS)

    Lampe, M.; Manheimer, W. M.; Mcbride, J. B.; Orens, J. H.; Papadopoulos, K.; Shanny, R.; Sudan, R. N.

    1972-01-01

    A theory of plasma beam cyclotron instability is developed on the basis of computer simulation experiments. The theory holds that at certain turbulence levels, electron cross-field diffusion which supresses the electron gyroresonances is created by turbulent wave-particle interactions in a plasma beam after a period of quasi-linear exponential development of turbulence. The stabilizing effect of Landau ion damping is noted. The behavior of cold and hot ions is discussed.

  5. Generalized Jeans' Escape of Pick-Up Ions in Quasi-Linear Relaxation

    NASA Technical Reports Server (NTRS)

    Moore, T. E.; Khazanov, G. V.

    2011-01-01

    Jeans escape is a well-validated formulation of upper atmospheric escape that we have generalized to estimate plasma escape from ionospheres. It involves the computation of the parts of particle velocity space that are unbound by the gravitational potential at the exobase, followed by a calculation of the flux carried by such unbound particles as they escape from the potential well. To generalize this approach for ions, we superposed an electrostatic ambipolar potential and a centrifugal potential, for motions across and along a divergent magnetic field. We then considered how the presence of superthermal electrons, produced by precipitating auroral primary electrons, controls the ambipolar potential. We also showed that the centrifugal potential plays a small role in controlling the mass escape flux from the terrestrial ionosphere. We then applied the transverse ion velocity distribution produced when ions, picked up by supersonic (i.e., auroral) ionospheric convection, relax via quasi-linear diffusion, as estimated for cometary comas [1]. The results provide a theoretical basis for observed ion escape response to electromagnetic and kinetic energy sources. They also suggest that super-sonic but sub-Alfvenic flow, with ion pick-up, is a unique and important regime of ion-neutral coupling, in which plasma wave-particle interactions are driven by ion-neutral collisions at densities for which the collision frequency falls near or below the gyro-frequency. As another possible illustration of this process, the heliopause ribbon discovered by the IBEX mission involves interactions between the solar wind ions and the interstellar neutral gas, in a regime that may be analogous [2].

  6. Boundedness in a quasilinear chemotaxis-haptotaxis system with logistic source

    NASA Astrophysics Data System (ADS)

    Liu, Ji; Zheng, Jiashan; Wang, Yifu

    2016-04-01

    In this paper, we consider the quasilinear chemotaxis-haptotaxis system u_t=nabla\\cdot(D(u)nabla u)-nabla\\cdot(S_1(u)nabla v)-nabla\\cdot(S_2(u)nabla w)+uf(u,w),quad xinΩ, t > 0,v_t=Δ v-v+u,quad xinΩ, t > 0,w_t=-vw,quad xinΩ, t > 0 in a bounded smooth domain {Ωsubset R^n (n≥1)} under zero-flux boundary conditions, where the nonlinearities {D, S_1} and {S_2} are assumed to generalize the prototypes D(u)=CD(u+1)^{m-1}, S_1(u)=C_{S_1}u(u+1)^{q_1-1} quad {and} quad S_2(u)=C_{S_2}u(u+1)^{q_2-1} with {C_D,C_{S_1},C_{S_2} > 0, m,q_1,q_2in R} and {f(u,w)in C^1([0,+infty)×[0,+∞))} fulfills f(u,w)≤ r-buquad {for all} ~u≥ 0quad {and} quad w≥ 0, where {r > 0, b > 0.} Assuming nonnegative initial data {u_0(x)in W^{1,∞}(Ω),v_0(x)in W^{1,∞}(Ω)} and {w_0(x)in C^{2,α}(barΩ)} for some {αin(0,1),} we prove that (i) for {n≤2,} if q_1,q_2\\ < m+2/n-1,} then {(star)} has a unique nonnegative classical solution which is globally bounded, (ii) for {n > 2,} if {max{q_1,q_2} < m+2/n-1} and {m > 2-2/n} or {max{q_1,q_2} < m+2/n-1} and {m≤ 1,} then {(star)} has a unique nonnegative classical solution which is globally bounded.

  7. Quasi-linear modeling of lower hybrid current drive in ITER and DEMO

    SciTech Connect

    Cardinali, A. Cesario, R.; Panaccione, L.; Santini, F.; Amicucci, L.; Castaldo, C.; Ceccuzzi, S.; Mirizzi, F.; Tuccillo, A. A.

    2015-12-10

    First pass absorption of the Lower Hybrid waves in thermonuclear devices like ITER and DEMO is modeled by coupling the ray tracing equations with the quasi-linear evolution of the electron distribution function in 2D velocity space. As usually assumed, the Lower Hybrid Current Drive is not effective in a plasma of a tokamak fusion reactor, owing to the accessibility condition which, depending on the density, restricts the parallel wavenumber to values greater than n{sub ∥crit} and, at the same time, to the high electron temperature that would enhance the wave absorption and then restricts the RF power deposition to the very periphery of the plasma column (near the separatrix). In this work, by extensively using the “ray{sup star}” code, a parametric study of the propagation and absorption of the LH wave as function of the coupled wave spectrum (as its width, and peak value), has been performed very accurately. Such a careful investigation aims at controlling the power deposition layer possibly in the external half radius of the plasma, thus providing a valuable aid to the solution of how to control the plasma current profile in a toroidal magnetic configuration, and how to help the suppression of MHD mode that can develop in the outer part of the plasma. This analysis is useful not only for exploring the possibility of profile control of a pulsed operation reactor as well as the tearing mode stabilization, but also in order to reconsider the feasibility of steady state regime for DEMO.

  8. Hydromagnetic waves and cosmic ray diffusion theory

    NASA Technical Reports Server (NTRS)

    Lee, M. A.; Voelk, H. J.

    1975-01-01

    Pitch angle diffusion of cosmic rays in hydromagnetic wave fields is considered strictly within the quasilinear approximation. It is shown that the popular assumption of an isotropic power spectrum tensor of magnetic fluctuations requires in this case equal forms and magnitudes of Alfven and magnetosonic wave spectra - a situation which is generally unlikely. The relative contributions to the pitch angle diffusion coefficient from the cyclotron resonances and Landau resonance due to the different types of waves are evaluated for a typical situation in the solar wind. Since in this approximation also the Landau resonance does not lead to particle reflections a proper consideration of the nonlinear particle orbits is indeed necessary to overcome the well known difficulties of quasilinear scattering theory for cosmic rays near 90 degrees pitch angle.

  9. A synthesis theory for self-oscillating adaptive systems /SOAS/

    NASA Technical Reports Server (NTRS)

    Horowitz, I.; Smay, J.; Shapiro, A.

    1974-01-01

    A quantitative synthesis theory is presented for the Self-Oscillating Adaptive System (SOAS), whose nonlinear element has a static, odd character with hard saturation. The synthesis theory is based upon the quasilinear properties of the SOAS to forced inputs, which permits the extension of quantitative linear feedback theory to the SOAS. A reasonable definition of optimum design is shown to be the minimization of the limit cycle frequency. The great advantages of the SOAS is its zero sensitivity to pure gain changes. However, quasilinearity and control of the limit cycle amplitude at the system output, impose additional constraints which partially or completely cancel this advantage, depending on the numerical values of the design parameters. By means of narrow-band filtering, an additional factor is introduced which permits trade-off between filter complexity and limit cycle frequency minimization.

  10. Why is the force-velocity relationship in leg press tasks quasi-linear rather than hyperbolic?

    PubMed

    Bobbert, Maarten F

    2012-06-01

    Force-velocity relationships reported in the literature for functional tasks involving a combination of joint rotations tend to be quasi-linear. The purpose of this study was to explain why they are not hyperbolic, like Hill's relationship. For this purpose, a leg press task was simulated with a musculoskeletal model of the human leg, which had stimulation of knee extensor muscles as only independent input. In the task the ankles moved linearly, away from the hips, against an imposed external force that was reduced over contractions from 95 to 5% of the maximum isometric value. Contractions started at 70% of leg length, and force and velocity values were extracted when 80% of leg length was reached. It was shown that the relationship between leg extension velocity and external force was quasi-linear, while the relationship between leg extension velocity and muscle force was hyperbolic. The discrepancy was explained by the fact that segmental dynamics canceled more and more of the muscle force as the external force was further reduced and velocity became higher. External power output peaked when the imposed external force was ∼50% of maximum, while muscle power output peaked when the imposed force was only ∼15% of maximum; in the latter case ∼70% of muscle power was buffered by the leg segments. According to the results of this study, there is no need to appeal to neural mechanisms to explain why, in leg press tasks, the force-velocity relationship is quasi-linear rather than hyperbolic. PMID:22442026

  11. Global existence of weak solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type

    NASA Astrophysics Data System (ADS)

    Ishida, Sachiko; Yokota, Tomomi

    This paper deals with the quasilinear degenerate Keller-Segel system (KS) of parabolic-parabolic type. The global existence of weak solutions to (KS) is established when q

  12. On the existence of a solution to a quasilinear elliptic system of the Lane, Emden and Fowler type

    NASA Astrophysics Data System (ADS)

    Covei, Dragoş-Pǎtru

    2012-11-01

    In this article, we give an algorithm to obtain the existence of a solution for a quasilinear elliptic system. Our result is new and is based on a recent work of [R.J. Biezuner, J. Brown, G. Ercole and E.M. Martins, Computing the first eigenpair of the p-Laplacian via inverse iteration of sublinear supersolutions, J. Sci. Computation, 2011]. Such problems appear in boundary layer phenomena for viscous fluids, the equilibrium configuration of mass in a spherical cloud of gas, thermal explosion as well as in others applications.

  13. 1.5D Quasilinear Model for Alpha Particle-TAE Interaction in ARIES ACT-I

    SciTech Connect

    K. Ghantous, N.N. Gorelenkov, C. Kessel, F. Poli

    2013-01-30

    We study the TAE interaction with alpha particle fusion products in ARIES ACT-I using the 1.5D quasilinear model. 1.5D uses linear analytic expressions for growth and damping rates of TAE modes evaluated using TRANSP pro les to calculates the relaxation of pressure pro les. NOVA- K simulations are conducted to validate the analytic dependancies of the rates, and to normalize their absolute value. The low dimensionality of the model permits calculating loss diagrams in large parameter spaces.

  14. Anomalous resistivity at the field null of the FRC: a quasi-linear expression based upon flute-type modes

    SciTech Connect

    Gerwin, R.

    1983-10-01

    In the Field-Reversed Theta Pinch (FRC) experiment, the poloidal flux is observed to be lost at a rate several times greater than classical resistivity would allow. Thus, there must be anomalous resistivity at the field null. Assuming that an electromagnetic microinstability of the flute mode type is responsible for this, we derived a general expression for the anomalous resistivity at the field null based upon a quasi-linear model of the microturbulence. This general expression does not depend upon the details of the ion-species model, for example, whether the ions are fluid or kinetic.

  15. New critical exponents in a fully parabolic quasilinear Keller-Segel system and applications to volume filling models

    NASA Astrophysics Data System (ADS)

    Cieślak, Tomasz; Stinner, Christian

    2015-03-01

    We carry on our studies related to the fully parabolic quasilinear Keller-Segel system started in [6] and continued in [7]. In the above mentioned papers we proved finite-time blowup of some radially symmetric solutions to the quasilinear Keller-Segel system if the nonlinear chemosensitivity is strong enough and an adequate relation between nonlinear diffusion and chemosensitivity holds. On the other hand we proved that once chemosensitivity is weak enough solutions exist globally in time. The present paper is devoted to looking for critical exponents distinguishing between those two behaviors. Moreover, we apply our results to the so-called volume filling models with a power-type jump probability function. The most important consequence of our investigations of the latter is a critical mass phenomenon found in dimension 2. Namely we find a value m* such that when the solution to the two-dimensional volume filling Keller-Segel system starts with mass smaller than m*, then it is bounded, while for some initial data with mass exceeding m* solutions are unbounded, though being defined for any time t > 0.

  16. Global existence of weak solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type with small data

    NASA Astrophysics Data System (ADS)

    Ishida, Sachiko; Yokota, Tomomi

    This paper deals with the quasilinear degenerate Keller-Segel system (KS) of "parabolic-parabolic" type. The global existence of weak solutions to (KS) with small initial data is established when q⩾m+2/N ( m denotes the intensity of diffusion and q denotes the nonlinearity). In the system of "parabolic-elliptic" type, Sugiyama and Kunii (2006) [13, Theorem 3] and Sugiyama (2007) [12, Theorem 2] state the similar result; note that q=m+2/N corresponds to generalized Fujita's critical exponent. However, the super-critical case where q⩾m+2/N has been unsolved for "parabolic-parabolic" type. Therefore this paper gives an answer to the unsolved problem.

  17. Response analysis of a class of quasi-linear systems with fractional derivative excited by Poisson white noise.

    PubMed

    Yang, Yongge; Xu, Wei; Yang, Guidong; Jia, Wantao

    2016-08-01

    The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative. PMID:27586619

  18. Hydromagnetic waves and cosmic-ray diffusion theory

    NASA Technical Reports Server (NTRS)

    Lee, M. A.; Voelk, H. J.

    1975-01-01

    Pitch-angle (and energy) diffusion of cosmic rays in hydromagnetic wave fields is considered. The treatment remains strictly within the quasi-linear approximation. It is shown that the popular assumption of an isotropic power spectrum tensor of magnetic fluctuations requires in this case equal forms and magnitudes of Alfven and magnetosonic wave spectra - a situation which is generally unlikely. The relative contributions to the pitch-angle diffusion coefficient from the cyclotron resonances and Landau resonance due to the different types of waves are evaluated for a typical situation in the solar wind. Since the Landau resonance in this approximation also does not lead to particle reflections, a proper consideration of the nonlinear particle orbits is indeed necessary to overcome the well-known difficulties of quasi-linear scattering theory for cosmic rays near 90 deg pitch angle.

  19. The influence of a prediction display on the quasi-linear describing function and remnant measured with an adaptive analog-pilot in a closed loop

    NASA Technical Reports Server (NTRS)

    Dey, D.

    1972-01-01

    The effect of a prediction display on the human transfer characteristics is explained with the aid of a quasi-linear model. The prediction display causes an increase of the gain factor and the lead factor, a diminishing of the lag factor and a decrease of the remnant. Altogether, these factors yield a smaller mean square value of the control deviation and a simultaneous decrease of the mean square value of the stick signal.

  20. A New Discretization Method of Order Four for the Numerical Solution of One-Space Dimensional Second-Order Quasi-Linear Hyperbolic Equation

    ERIC Educational Resources Information Center

    Mohanty, R. K.; Arora, Urvashi

    2002-01-01

    Three level-implicit finite difference methods of order four are discussed for the numerical solution of the mildly quasi-linear second-order hyperbolic equation A(x, t, u)u[subscript xx] + 2B(x, t, u)u[subscript xt] + C(x, t, u)u[subscript tt] = f(x, t, u, u[subscript x], u[subscript t]), 0 less than x less than 1, t greater than 0 subject to…

  1. The electron beam instability and turbulence theories

    NASA Technical Reports Server (NTRS)

    Dum, C. T.

    1990-01-01

    Extensions and practical applications of recent observations of electron beam-plasma interactions are investigated for the range of turbulence theories, extending from quasi-linear to strong turbulence theory, which have been developed on the basis of the Langmuir-wave excitation model. Electron foreshock observations have indicated that linear instability theory must encompass the excitation of waves whose frequencies are substantially different from those of the plasma frequency; the point of departure for such extensions should be a quantitative test of existing theories, and particle simulations conducive to such testing are presented. A step-by-step addition of physical considerations is used in such simulation studies to differentiate among nonlinear turbulence effects.

  2. The formation of shocks and fundamental solution of a fourth-order quasilinear Boussinesq-type equation

    NASA Astrophysics Data System (ADS)

    Galaktionov, Victor A.

    2009-02-01

    As a basic higher-order model, the fourth-order Boussinesq-type quasilinear wave equation (the QWE-4) \\[ \\begin{equation*}\\fl u_{tt} = -(|u|^n u)_{xxxx} \\tqs in\\ \\mathbb{R} \\times \\mathbb{R}_+, \\quad with\\ exponent\\ n > 0,\\end{equation*} \\] is considered. Self-similar blow-up solutions \\[ \\begin{eqnarray*}\\tqs\\tqs u_-(x,t)=g(z), \\quad\\, z=\\frac x{\\sqrt{T-t}},\\\\ where\\ g\\ solved\\ the\\ ODE\\ \\frac 14 g'' z^2 + \\frac 34 g'z = -(|g|^n g)^{(4)},\\end{eqnarray*} \\] are shown to exist that generate as t → T- discontinuous shock waves. The QWE-4 is also shown to admit a smooth (for t > 0) global 'fundamental solution' \\[ \\begin{eqnarray*}\\fl b_n(x,t)= t^{\\frac{2}{n+4}} F_n(y),\\ y = x/t^{\\frac{n+2}{n+4}},\\ such\\ that\\ b_{n}(x,0)= 0,\\ b_{nt}(x,0)= {\\delta}(x),\\end{eqnarray*} \\] i.e. having a measure as initial data. A 'homotopic' limit n → 0 is used to get b_0(x,t)= \\sqrt t \\, F_0(x/\\sqrt t) being the classic fundamental solution of the 1D linear beam equation \\[ \\begin{equation*}u_{tt} = -u_{xxxx} \\tqs in\\ \\mathbb{R} \\times \\mathbb{R}_+.\\end{equation*} \\

  3. Infinitely many solutions for quasilinear Schrödinger systems with finite and sign-changing potentials

    NASA Astrophysics Data System (ADS)

    Guo, Yuxia; Nie, Jianjun

    2016-04-01

    We consider the following quasilinear Schrödinger system in R^N with {N≥3}: sum_{i,j=1}ND_j(a_{ij}(u)D_i u)-1/2 sum_{i,j=1}ND_s a_{ij}(u) D_i u D_j u-A(x) u+F_u(u,v)=0 sum_{i,j=1}ND_j(a_{ij}(v)D_iv)-1/2 sum_{i,j=1}ND_s a_{ij}(v) D_i v D_j v-B(x)v+F_v(u,v)=0, where {D_i=partial/partial x_i, D_s a_{ij}(s)=d/dsa_{ij}(s)}, {F(u,v)} is the coupling term, {A(x)} and {B(x)} are finite and sign-changing potential functions. Using an approximation scheme and {q}-Laplacian regularization, we prove the existence of infinitely many solutions for system {(P)}.

  4. Approximate analytical solutions for the trapped electron distribution due to quasi-linear diffusion by whistler mode waves

    NASA Astrophysics Data System (ADS)

    Mourenas, D.; Artemyev, A. V.; Agapitov, O. V.; Krasnoselskikh, V.; Li, W.

    2014-12-01

    The distribution of trapped energetic electrons inside the Earth's radiation belts is the focus of intense studies aiming at better describing the evolution of the space environment in the presence of various disturbances induced by the solar wind or by an enhanced lightning activity. Such studies are usually performed by means of comparisons with full numerical simulations solving the Fokker-Planck quasi-linear diffusion equation for the particle distribution function. Here we present for the first time approximate but realistic analytical solutions for the electron distribution, which are shown to be in good agreement with exact numerical solutions in situations where resonant scattering of energetic electrons by whistler mode hiss, lightning-generated or chorus waves, is the dominant process. Quiet time distributions are well recovered, as well as the evolution of energized relativistic electron distributions during disturbed geomagnetic conditions. It is further shown that careful comparisons between the analytical solutions and measured distributions may allow to infer important bounce- and drift-averaged wave characteristics (such as wave amplitude). It could also help to improve the global understanding of underlying physical phenomena.

  5. A kinetic approach to some quasi-linear laws of macroeconomics

    NASA Astrophysics Data System (ADS)

    Gligor, M.; Ignat, M.

    2002-11-01

    Some previous works have presented the data on wealth and income distributions in developed countries and have found that the great majority of population is described by an exponential distribution, which results in idea that the kinetic approach could be adequate to describe this empirical evidence. The aim of our paper is to extend this framework by developing a systematic kinetic approach of the socio-economic systems and to explain how linear laws, modelling correlations between macroeconomic variables, may arise in this context. Firstly we construct the Boltzmann kinetic equation for an idealised system composed by many individuals (workers, officers, business men, etc.), each of them getting a certain income and spending money for their needs. To each individual a certain time variable amount of money is associated this meaning him/her phase space coordinate. In this way the exponential distribution of money in a closed economy is explicitly found. The extension of this result, including states near the equilibrium, give us the possibility to take into account the regular increase of the total amount of money, according to the modern economic theories. The Kubo-Green-Onsager linear response theory leads us to a set of linear equations between some macroeconomic variables. Finally, the validity of such laws is discussed in relation with the time reversal symmetry and is tested empirically using some macroeconomic time series.

  6. A Quasi-Linear Behavioral Model and an Application to Self-Directed Learning

    NASA Technical Reports Server (NTRS)

    Ponton, Michael K.; Carr, Paul B.

    1999-01-01

    A model is presented that describes the relationship between one's knowledge of the world and the concomitant personal behaviors that serve as a mechanism to obtain desired outcomes. Integrated within this model are the differing roles that outcomes serve as motivators and as modifiers to one's worldview. The model is dichotomized between general and contextual applications. Because learner self-directedness (a personal characteristic) involves cognition and affection while self-directed learning (a pedagogic process) encompasses conation, behavior and introspection, the model can be dichotomized again in another direction. Presented also are the roles that cognitive motivation theories play in moving an individual through this behavioral model and the roles of wishes, self-efficacy, opportunity and self-influence.

  7. Spectral Quasi-linearization Method for Homogeneous-Heterogeneous Reactions on Nonlinear Convection Flow of Micropolar Fluid Saturated Porous Medium with Convective Boundary Condition

    NASA Astrophysics Data System (ADS)

    RamReddy, Chetteti; Pradeepa, Teegala

    2016-05-01

    Based on the nonlinear variation of density with temperature (NDT) in the buoyancy term, the mixed convection flow along a vertical plate of a micropolar fluid saturated porous medium is considered. In addition, the effect of homogeneous-heterogeneous reaction and convective boundary condition has been taken into account. Using lie scaling group transformations, the similarity representation is attained for the system of partial differential equations, prior to being solved by a spectral quasilinearization method. The results show that in the presence of aiding and opposing flow situations, both the species concentration and mass transfer rate decreases when the strength of homogeneous and heterogeneous reaction parameters are enhanced.

  8. A Thermodynamic Theory of Solid Viscoelasticity. Part II:; Nonlinear Thermo-viscoelasticity

    NASA Technical Reports Server (NTRS)

    Freed, Alan D.; Leonov, Arkady I.; Gray, Hugh R. (Technical Monitor)

    2002-01-01

    This paper, second in the series of three papers, develops a general, nonlinear, non-isothermal, compressible theory for finite rubber viscoelasticity and specifies it in a form convenient for solving problems important to the rubber, tire, automobile, and air-space industries, among others. Based on the quasi-linear approach of non-equilibrium thermodynamics, a general nonlinear theory of differential type has been developed for arbitrary non-isothermal deformations of viscoelastic solids. In this theory, the constitutive equations were presented as the sum of a rubber elastic (equilibrium) and a liquid type viscoelastic (non-equilibrium) terms. These equations have then been simplified using several modeling and simplicity arguments.

  9. A review of developments in the theory of elasto-plastic flow

    NASA Technical Reports Server (NTRS)

    Swedlow, J. L.

    1973-01-01

    The theory of elasto-plastic flow is developed so that it may accommodate features such as work-hardening, anisotropy, plastic compressibility, non-continuous loading including local or global unloading, and others. A complete theory is given in quasi-linear form; as a result, many useful attributes are accessible. Several integral theorems may be written, finite deformations may be incorporated, and efficient methods for solving problems may be developed; these and other aspects are described in some detail. The theory is reduced to special forms for 2-space, and extensive experience in solving such problems is cited.

  10. Quasi-Linear Circuit

    NASA Technical Reports Server (NTRS)

    Bradley, William; Bird, Ross; Eldred, Dennis; Zook, Jon; Knowles, Gareth

    2013-01-01

    This work involved developing spacequalifiable switch mode DC/DC power supplies that improve performance with fewer components, and result in elimination of digital components and reduction in magnetics. This design is for missions where systems may be operating under extreme conditions, especially at elevated temperature levels from 200 to 300 degC. Prior art for radiation-tolerant DC/DC converters has been accomplished utilizing classical magnetic-based switch mode converter topologies; however, this requires specific shielding and component de-rating to meet the high-reliability specifications. It requires complex measurement and feedback components, and will not enable automatic re-optimization for larger changes in voltage supply or electrical loading condition. The innovation is a switch mode DC/DC power supply that eliminates the need for processors and most magnetics. It can provide a well-regulated voltage supply with a gain of 1:100 step-up to 8:1 step down, tolerating an up to 30% fluctuation of the voltage supply parameters. The circuit incorporates a ceramic core transformer in a manner that enables it to provide a well-regulated voltage output without use of any processor components or magnetic transformers. The circuit adjusts its internal parameters to re-optimize its performance for changes in supply voltage, environmental conditions, or electrical loading at the output

  11. Global Structure Stability of Riemann Solution of Quasilinear Hyperbolic System of Conservation Law in Presence of Boundary: Shocks and Contact Discontinuities

    NASA Astrophysics Data System (ADS)

    Jin, Cui-Lian

    2008-11-01

    In this paper, we investigate a class of mixed initial-boundary value problems for a kind of n × n quasilinear hyperbolic systems of conservation laws on the quarter plan. We show that the structure of the piecewise C1 solution u = u(t, x) of the problem, which can be regarded as a perturbation of the corresponding Riemann problem, is globally similar to that of the solution u = U(x/t) of the corresponding Riemann problem. The piecewise C1 solution u = u(t, x) to this kind of problems is globally structure-stable if and only if it contains only non-degenerate shocks and contact discontinuities, but no rarefaction waves and other weak discontinuities.

  12. Summary of papers presented in the Theory and Modelling session

    NASA Astrophysics Data System (ADS)

    Lin-Liu, Y. R.; Westerhof, E.

    2012-09-01

    A total of 14 contributions were presented in the Theory and Modelling sessions at EC-17. One Theory and Modelling paper was included in the ITER ECRH and ECE sessions each. Three papers were in the area of nonlinear physics discussing parametric processes accompanying ECRH. Eight papers were based on the quasi-linear theory of wave heating and current drive. Three of these addressed the application of ECCD for NTM stabilization. Two papers considered scattering of EC waves by edge density fluctuations and related phenomena. In this summary, we briefly describe the highlights of these contributions. Finally, the three papers concerning modelling of various aspects of ECE are reported in the ECE session.

  13. A synthesis theory for the externally excited adaptive system /EEAS/

    NASA Technical Reports Server (NTRS)

    Horowitz, I. M.; Smay, J. W.; Shapiro, A.

    1974-01-01

    The externally excited adaptive system (EEAS) is a two-degree-of-freedom feedback system with a nonlinearity which is saturated hard by an external periodic signal. Under certain conditions, the EEAS responds quasi-linearly to command and plant disturbance signals, permitting the development of a quantitative synthesis theory for satisfying system tolerances despite large plant uncertainty. The great advantage of the EEAS is its zero sensitivity to plant gain variations, a property it shares with the self-oscillating adaptive system (SOAS). The EEAS is, however, more flexible than the SOAS in satisfying the quasi-linearity constraints. The essential difference is that in the EEAS the loop transmission bandwidth is not rigorously tied to the 'carrier' signal, as it is in the SOAS. There is a class of problems for which the EEAS is superior to the purely linear system, which in turn is superior to the SOAS. The superiority of the EEAS over the SOAS is especially marked in the case of significant plant disturbances, which generally vitiate a SOAS design.

  14. Kinetic theory of instability-enhanced collisional effects

    SciTech Connect

    Baalrud, S. D.; Callen, J. D.; Hegna, C. C.

    2010-05-15

    The Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy is used to derive a generalization of the Lenard-Balescu plasma kinetic equation that accounts for wave-particle scattering due to instabilities that originate from discrete particle motion. Application to convective instabilities is emphasized for which the growing waves either propagate out of the domain of interest or modify the particle distribution to reduce the instability amplitude before nonlinear amplitudes are reached. Two such applications are discussed: Langmuir's paradox and determining the Bohm criterion for multiple ion species plasmas. In these applications, collisions are enhanced by ion-acoustic and ion-ion two-stream instabilities, respectively. The relationship between this kinetic theory and quasilinear theory is discussed.

  15. Quasi-linear magnetoresistance and the violation of Kohler's rule in the quasi-one-dimensional Ta₄Pd₃Te₁₆ superconductor.

    PubMed

    Xu, Xiaofeng; Jiao, W H; Zhou, N; Guo, Y; Li, Y K; Dai, Jianhui; Lin, Z Q; Liu, Y J; Zhu, Zengwei; Lu, Xin; Yuan, H Q; Cao, Guanghan

    2015-08-26

    We report on the quasi-linear in field intrachain magnetoresistance in the normal state of a quasi-one-dimensional superconductor Ta4Pd3Te16 (Tc ~ 4.6 K). Both the longitudinal and transverse in-chain magnetoresistance shows a power-law dependence, Δρ∝B(α) with the exponent α close to 1 over a wide temperature and field range. The magnetoresistance shows no sign of saturation up to 50 T studied. The linear magnetoresistance observed in Ta4Pd3Te16 is found to be overall inconsistent with the interpretations based on the Dirac fermions in the quantum limit, charge conductivity fluctuations as well as quantum electron-electron interference. Moreover, it is observed that the Kohler's rule, regardless of the field orientations, is violated in its normal state. This result suggests the loss of charge carriers in the normal state of this chain-containing compound, due presumably to the charge-density-wave fluctuations. PMID:26222182

  16. Quasi-linear magnetoresistance and the violation of Kohler’s rule in the quasi-one-dimensional Ta4Pd3Te16 superconductor

    NASA Astrophysics Data System (ADS)

    Xu, Xiaofeng; Jiao, W. H.; Zhou, N.; Guo, Y.; Li, Y. K.; Dai, Jianhui; Lin, Z. Q.; Liu, Y. J.; Zhu, Zengwei; Lu, Xin; Yuan, H. Q.; Cao, Guanghan

    2015-08-01

    We report on the quasi-linear in field intrachain magnetoresistance in the normal state of a quasi-one-dimensional superconductor Ta4Pd3Te16 ({{T}\\text{c}}˜ 4.6 K). Both the longitudinal and transverse in-chain magnetoresistance shows a power-law dependence, Δ ρ \\propto Bα , with the exponent α close to 1 over a wide temperature and field range. The magnetoresistance shows no sign of saturation up to 50 T studied. The linear magnetoresistance observed in Ta4Pd3Te16 is found to be overall inconsistent with the interpretations based on the Dirac fermions in the quantum limit, charge conductivity fluctuations as well as quantum electron-electron interference. Moreover, it is observed that the Kohler’s rule, regardless of the field orientations, is violated in its normal state. This result suggests the loss of charge carriers in the normal state of this chain-containing compound, due presumably to the charge-density-wave fluctuations.

  17. Nonlinear stochastic biasing of halos: Analysis of cosmological N-body simulations and perturbation theories

    NASA Astrophysics Data System (ADS)

    Sato, Masanori; Matsubara, Takahiko

    2013-06-01

    It is crucial to understand and model a behavior of galaxy biasing for future ambitious galaxy redshift surveys. Using 40 large cosmological N-body simulations for a standard ΛCDM cosmology, we study the cross-correlation coefficient between matter and the halo density field, which is an indicator of the stochasticity of bias, over a wide redshift range 0≤z≤3. The cross-correlation coefficient is important to extract information on the matter density field, e.g., by combining galaxy clustering and galaxy-galaxy lensing measurements. We compare the simulation results with integrated perturbation theory (iPT) proposed by one of the present authors and standard perturbation theory combined with a phenomenological model of local bias. The cross-correlation coefficient derived from the iPT agrees with N-body simulation results down to r˜15(10)h-1Mpc within 0.5 (1.0)% for all redshifts and halo masses we consider. The standard perturbation theory with local bias does not explain complicated behaviors on quasilinear scales at low redshifts, while roughly reproduces the general behavior of the cross-correlation coefficient on fully nonlinear scales. The iPT is powerful to predict the cross-correlation coefficient down to quasilinear regimes with a high precision.

  18. An approximation theory for the identification of nonlinear distributed parameter systems

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Reich, Simeon; Rosen, I. G.

    1990-01-01

    An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato appproximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.

  19. An approximation theory for the identification of nonlinear distributed parameter systems

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Reich, Simeon; Rosen, I. G.

    1988-01-01

    An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.

  20. Theory and modeling of atmospheric turbulence, part 2

    NASA Technical Reports Server (NTRS)

    Chen, C. M.

    1984-01-01

    Two dimensional geostrophic turbulence driven by a random force is investigated. Based on the Liouville equation, which simulates the primitive hydrodynamical equations, a group-kinetic theory of turbulence is developed and the kinetic equation of the scaled singlet distribution is derived. The kinetic equation is transformed into an equation of spectral balance in the equilibrium and non-equilibrium states. Comparison is made between the propagators and the Green's functions in the case of the non-asymptotic quasi-linear equation to prove the equivalence of both kinds of approximations used to describe perturbed trajectories of plasma turbulence. The microdynamical state of fluid turbulence is described by a hydrodynamical system and transformed into a master equation analogous to the Vlasov equation for plasma turbulence. The spectral balance for the velocity fluctuations of individual components shows that the scaled pressure strain correlation and the cascade transfer are two transport functions that play the most important roles.

  1. Resonance zones and quasi-linear diffusion coefficients for radiation belt energetic electron interaction with oblique chorus waves in the Dungey magnetosphere

    SciTech Connect

    Shi Run; Ni, Binbin; Gu Xudong; Zhao Zhengyu; Zhou Chen

    2012-07-15

    The resonance regions for resonant interactions of radiation belt electrons with obliquely propagating whistler-mode chorus waves are investigated in detail in the Dungey magnetic fields that are parameterized by the intensity of uniform southward interplanetary magnetic field (IMF) Bz or, equivalently, by the values of D=(M/B{sub z,0}){sup 1/3} (where M is the magnetic moment of the dipole and B{sub z,0} is the uniform southward IMF normal to the dipole's equatorial plane). Adoption of background magnetic field model can considerably modify the determination of resonance regions. Compared to the results for the case of D = 50 (very close to the dipole field), the latitudinal coverage of resonance regions for 200 keV electrons interacting with chorus waves tends to become narrower for smaller D-values, regardless of equatorial pitch angle, resonance harmonics, and wave normal angle. In contrast, resonance regions for 1 MeV electrons tend to have very similar spatial lengths along the field line for various Dungey magnetic field models but cover different magnetic field intervals, indicative of a strong dependence on electron energy. For any given magnetic field line, the resonance regions where chorus-electron resonant interactions can take place rely closely on equatorial pitch angle, resonance harmonics, and kinetic energy. The resonance regions tend to cover broader latitudinal ranges for smaller equatorial pitch angles, higher resonance harmonics, and lower electron energies, consistent with the results in Ni and Summers [Phys. Plasmas 17, 042902, 042903 (2010)]. Calculations of quasi-linear bounce-averaged diffusion coefficients for radiation belt electrons due to nightside chorus waves indicate that the resultant scattering rates differ from using different Dungey magnetic field models, demonstrating a strong dependence of wave-induced electron scattering effect on the adoption of magnetic field model. Our results suggest that resonant wave

  2. String Theory and Gauge Theories

    SciTech Connect

    Maldacena, Juan

    2009-02-20

    We will see how gauge theories, in the limit that the number of colors is large, give string theories. We will discuss some examples of particular gauge theories where the corresponding string theory is known precisely, starting with the case of the maximally supersymmetric theory in four dimensions which corresponds to ten dimensional string theory. We will discuss recent developments in this area.

  3. Old and new results in regularity theory for diagonal elliptic systems via blowup techniques

    NASA Astrophysics Data System (ADS)

    Beck, Lisa; Bulíček, Miroslav; Frehse, Jens

    2015-12-01

    We consider quasilinear diagonal elliptic systems in bounded domains subject to Dirichlet, Neumann or mixed boundary conditions. The leading elliptic operator is assumed to have only measurable coefficients, and the nonlinearities (Hamiltonians) are allowed to be of quadratic (critical) growth in the gradient variable of the unknown. These systems appear in many applications, in particular in differential geometry and stochastic differential game theory. We impose on the Hamiltonians structural conditions developed between 1972-2002 and also a new condition (sum coerciveness) introduced in recent years (in the context of the pay off functional in stochastic game theory). We establish existence, Hölder continuity, Liouville properties, W 2, q estimates, etc. for solutions, via a unified approach through the blow-up method. The main novelty of the paper is the introduction of a completely new technique, which in particular leads to smoothness of the solution also for dimensions d ≥ 3.

  4. Gravitational slip as a test of alternative gravity theories

    NASA Astrophysics Data System (ADS)

    Daniel, Scott Foster

    Cosmic acceleration could be an effect of a "dark energy" fluid pervading the Universe. It could also be an indication that general relativity is not the correct theory of gravity at cosmological length scales. Unfortunately, observations of the cosmic acceleration alone provide insufficient data to allow us to distinguish between these two possibilities. Cosmic perturbation theory may be able to relieve this uncertainty. Without positing a specific alternative gravity theory, we parametrize departures from general relativity in terms of a redshift-dependent, scale-independent gravitational slip between the Newtonian and longitudinal potentials appearing in the perturbed Robertson- Walker metric. We calculate the effects of non-zero values of this new parameter on linear and quasi-linear order cosmological perturbation theory. We find that existing data sets are consistent with unmodified general relativity with a cosmological constant at the ~10% level. We discuss the ability of future work, both in the form of more precise experiments and more detailed theoretical calculations, to either refine or refute this observation.

  5. Packaging Theory.

    ERIC Educational Resources Information Center

    Williams, Jeffrey

    1994-01-01

    Considers the recent flood of anthologies of literary criticism and theory as exemplifications of the confluence of pedagogical concerns, economics of publishing, and other historical factors. Looks specifically at how these anthologies present theory. Cites problems with their formatting theory and proposes alternative ways of organizing theory…

  6. The three-point correlation function in an ensemble of three-dimensional simulations. [in gravitational perturbation theory

    NASA Technical Reports Server (NTRS)

    Fry, J. N.; Melott, A. L.; Shandarin, S. F.

    1993-01-01

    We evaluate the three-point function in Fourier space for an ensemble of three-dimensional 128 exp 3 numerical simulations with initial power spectra characterized by spectral index n = +1, 0, -1, -2, -3, with no high-frequency cutoff and with cutoff k(c) = 16 or k(c) = 4. To remove dependences on scale and on time, we present results as the reduced amplitude Q in the hierarchical model as a function of the dimensionless variable kd(rms), where d(rms) is the mean square displacement of a particle from its initial position. For scale-free initial conditions, there is no evolution in Q. For initial conditions with a cutoff, Q evolves until the scale of the cutoff is in the nonlinear regime; the results afterwards are no different from those with no initial cutoff. The transition from quasi-linear to nonlinear regimes is followed. In the quasi-linear regime, our results agree well with gravitational perturbation theory predictions, including a marked dependence on the shape of the configuration. In the nonlinear regime, the value of Q for scale-invariant initial conditions is remarkably independent of evolution epoch, of scale, and of configuration shape, and depends on spectral index roughly as Q = 3/(3 + n).

  7. COSMIC-RAY TRANSPORT THEORY IN PARTIALLY TURBULENT SPACE PLASMAS WITH COMPRESSIBLE MAGNETIC TURBULENCE

    SciTech Connect

    Casanova, S.; Schlickeiser, R.

    2012-02-01

    Recently, a new transport theory of cosmic rays in magnetized space plasmas extending the quasilinear approximation to the particle orbit has been developed for the case of an axisymmetric incompressible magnetic turbulence. Here, we generalize the approach to the important physical case of a compressible plasma. As previously obtained in the case of an incompressible plasma, we allow arbitrary gyrophase deviations from the unperturbed spiral orbits in the uniform magnetic field. For the case of quasi-stationary and spatially homogeneous magnetic turbulence we derive, in the small Larmor radius approximation, gyrophase-averaged cosmic-ray Fokker-Planck coefficients. Upper limits for the perpendicular and pitch-angle Fokker-Planck coefficients and for the perpendicular and parallel spatial diffusion coefficients are presented.

  8. Graph Theory

    SciTech Connect

    Sanfilippo, Antonio P.

    2005-12-27

    Graph theory is a branch of discrete combinatorial mathematics that studies the properties of graphs. The theory was pioneered by the Swiss mathematician Leonhard Euler in the 18th century, commenced its formal development during the second half of the 19th century, and has witnessed substantial growth during the last seventy years, with applications in areas as diverse as engineering, computer science, physics, sociology, chemistry and biology. Graph theory has also had a strong impact in computational linguistics by providing the foundations for the theory of features structures that has emerged as one of the most widely used frameworks for the representation of grammar formalisms.

  9. Confabulation Theory

    NASA Astrophysics Data System (ADS)

    Solari, Soren; Smith, Andrew; Minnett, Rupert; Hecht-Nielsen, Robert

    2008-06-01

    Confabulation Theory [Hecht-Nielsen R. Confabulation theory. Springer-Verlag; 2007] is the first comprehensive theory of human and animal cognition. Here, we briefly describe Confabulation Theory and discuss experimental results that suggest the theory is correct. Simply put, Confabulation Theory proposes that thinking is like moving. In humans, the theory postulates that there are roughly 4000 thalamocortical modules, the “muscles of thought”. Each module performs an internal competition ( confabulation) between its symbols, influenced by inputs delivered via learned axonal associations with symbols in other modules. In each module, this competition is controlled, as in an individual muscle, by a single graded (i.e., analog) thought control signal. The final result of this confabulation process is a single active symbol, the expression of which also results in launching of action commands that trigger and control subsequent movements and/or thought processes. Modules are manipulated in groups under coordinated, event-contingent control, in a similar manner to our 700 muscles. Confabulation Theory hypothesizes that the control of thinking is a direct evolutionary outgrowth of the control of movement. Establishing a complete understanding of Confabulation Theory will require launching and sustaining a massive new phalanx of confabulation neuroscience research.

  10. On the Quasi-linear Elliptic PDE {-nabla \\cdot ( nabla{u}/ sqrt{1-| nabla{u} |^2}) = 4 π sum_k a_k δ_{s_k}} in Physics and Geometry

    NASA Astrophysics Data System (ADS)

    Kiessling, Michael K.-H.

    2012-09-01

    It is shown that for each finite number N of Dirac measures {δ_{s_n}} supported at points {s_n in {R}^3} with given amplitudes {a_n in {R} backslash\\{0\\}} there exists a unique real-valued function {u in C^{0, 1}({R}^3)}, vanishing at infinity, which distributionally solves the quasi-linear elliptic partial differential equation of divergence form {-nabla \\cdot ( nabla{u}/ sqrt{1-| nabla{u} |^2}) = 4 π sum_{n=1}^N a_n δ_{s_n}}. Moreover, {u in C^{ω}({R}^3backslash \\{s_n\\}_{n=1}^N)}. The result can be interpreted in at least two ways: (a) for any number N of point charges of arbitrary magnitude and sign at prescribed locations s n in three-dimensional Euclidean space there exists a unique electrostatic field which satisfies the Maxwell-Born-Infeld field equations smoothly away from the point charges and vanishes as | s| → ∞; (b) for any number N of integral mean curvatures assigned to locations {s_n in {R}^3 subset{R}^{1, 3}} there exists a unique asymptotically flat, almost everywhere space-like maximal slice with point defects of Minkowski spacetime {{R}^{1, 3}}, having lightcone singularities over the s n but being smooth otherwise, and whose height function vanishes as | s| → ∞. No struts between the point singularities ever occur.

  11. String Theory

    NASA Astrophysics Data System (ADS)

    Susskind, Leonard

    2013-01-01

    After reviewing the original motivation for the formulation of string theory and what we learned from it, I discuss some of the implications of the holographic principle and of string dualities for the question of the building blocks of nature.

  12. Quantum Theory

    NASA Astrophysics Data System (ADS)

    Murdin, P.

    2000-11-01

    A theory based on the premise that, on the microscopic scale, physical quantities have discrete, rather than a continuous range of, values. The theory was devised in the early part of the twentieth century to account for certain phenomena that could not be explained by classical physics. In 1900, the German physicist, Max Planck (1858-1947), was able precisely to describe the previously unexplaine...

  13. Effective theories of universal theories

    NASA Astrophysics Data System (ADS)

    Wells, James D.; Zhang, Zhengkang

    2016-01-01

    It is well-known but sometimes overlooked that constraints on the oblique parameters (most notably S and T parameters) are generally speaking only applicable to a special class of new physics scenarios known as universal theories. In the effective field theory (EFT) framework, the oblique parameters should not be associated with Wilson coefficients in a particular operator basis, unless restrictions have been imposed on the EFT so that it describes universal theories. We work out these restrictions, and present a detailed EFT analysis of universal theories. We find that at the dimension-6 level, universal theories are completely characterized by 16 parameters. They are conveniently chosen to be: 5 oblique parameters that agree with the commonly-adopted ones, 4 anomalous triple-gauge couplings, 3 rescaling factors for the h 3, hf f , hV V vertices, 3 parameters for hV V vertices absent in the Standard Model, and 1 four-fermion coupling of order y f 2 . All these parameters are defined in an unambiguous and basis-independent way, allowing for consistent constraints on the universal theories parameter space from precision electroweak and Higgs data.

  14. The influence of sources terms on the boundary behavior of the large solutions of quasilinear elliptic equations: the power like case

    NASA Astrophysics Data System (ADS)

    Alarcón, S.; Díaz, G.; Rey, J. M.

    2013-06-01

    We study the explosive expansion near the boundary of the large solutions of the equation -Δpu+um=f quadin Ω where {Ω} is an open bounded set of {{R}N} , N > 1, with adequately smooth boundary, m > p-1 > 0, and f is a continuous nonnegative function in {Ω} . Roughly speaking, we show that the number of explosive terms in the asymptotic boundary expansion of the solution is finite, but it goes to infinity as m goes to p-1. For illustrative choices of the sources, we prove that the expansion consists of two possible geometrical and nongeometrical parts. For low explosive sources, the nongeometrical part does not exist, and all coefficients depend on the diffusion and the geometry of the domain. For high explosive sources, there are coefficients, relative to the nongeometrical part, independent on {Ω} and the diffusion. In this case, the geometrical part cannot exist, and we say then that the source is very high explosive. We emphasize that low or high explosive sources can cause different geometrical properties in the expansion for a given interior structure of the differential operator. This paper is strongly motivated by the applications, in particular by the non-Newtonian fluid theory where p ≠ 2 involves rheological properties of the medium.

  15. Orbital-free density functional theory at the nanoscale and beyond: Algorithms and applications

    NASA Astrophysics Data System (ADS)

    Hung, Linda

    Orbital-free density functional theory (OFDFT) is a quantum mechanical theory where the total energy of a system depends only on the electron density and an external potential. While not as well-known as its relative, the wavefunction-based Kohn-Sham density functional theory (KSDFT), OFDFT has been established as a fast yet accurate theory for modeling materials -- like aluminum -- where the valence electron density is nearly homogeneous. In this thesis, we describe improvements to the implementation of OFDFT that allow the study of materials at the nanoscale and beyond. We approximate the structure factor that appears in ion-electron and ion-ion terms with B-splines, so that the scaling of their computations is reduced from quadratic to quasilinear ( O(N log(N)), where N is some measure of system size). We also review the treatment of optimization variables, implement a norm-conserving line search, and use preconditioners to improve optimization algorithms. These preconditioners have limited success for simulation cells with regions of low electron density, but can speed up optimization 3-4 times in other cells. Many of these improvements are included in a new version of the PRinceton Orbital-Free Electronic Structure Software (PROFESS). With all energy, potential, force, and stress computations now parallelized and scaling quasilinearly, more than a million Al atoms can be explicitly simulated on 192 cores. Using this PROFESS 2.0 code, we study Al crack tips using a quasi-two-dimensional setup with ~20 nm x 20 nm samples. Although both the embedded-atom method (EAM) and OFDFT can reproduce KSDFT material properties, the mechanism of plasticity at crack tips in simulation can occur through different slip planes, depending on the choice of OFDFT or the EAM. We also model [111]-oriented Al nanowires with 1-8 nm diameter and length up to ~20 nm. During tensile loading from equilibrium, the iv axial displacements of surface atoms (not noticed in past nanowire

  16. Elasticity theory

    NASA Astrophysics Data System (ADS)

    Moraru, Gheorghe; Mursa, Condrat

    2006-12-01

    In this book we present the basic concepts of the theory of elasticity: stress and deformation states (plane and three-dimensional) and generalized Hooke's law. We present a number of problems which have applications in strength analysis. The book includes a synthesis of the theory of elasticity and modern methods of applied mathematics. This book is designed for students, post graduate students and specialists in strength analysis. the book contains a number of appendixes which includes: elements of matrix-calculation, concepts of tensorial calculation, the Fourier transform, the notion of improper integrals,singular and hypersingular integrals, generalized functions, the Dirac Delta function

  17. Theory of High Power Electron Cyclotron Resonance Heating.

    NASA Astrophysics Data System (ADS)

    Taylor, Allan Watson

    1987-09-01

    Available from UMI in association with The British Library. Electron cyclotron resonance heating has been successfully used on a series of experiments in an attempt to raise plasma temperatures beyond the constraints of the resistive dissipation which occurs with ohmic heating. Recently progress in gyrotron design has allowed for significant increases in applied microwave power and for the first time a free electron laser will generate high power pulsed radio-frequency waves in the MTX experiment at Lawrence Livermore Laboratory in 1987. Classically the theory of ECRH has been considered by a Fokker-Planck approach and by a quasilinear approach. Both lead to a diffusion equation in velocity space for the distribution function but as the applied power increases the approximations made in these approaches are likely to become unsatisfactory. Adopting a test particle approach we firstly consider modifications to the velocity space diffusion co-efficient at high powers and then dispense with the diffusion equation completely. We begin by deriving averaged particle equations from a Lagrangian formulation which require less computer processor time to integrate than the exact Lorentz-force equations. These have been incorporated in a particle code to simulate ECRH in a tokamak. The results for this code are compared with analytic expressions derived for a modified diffusion coefficient and a probability function P(v,Deltav). We show that for low fields the diffusive form is correct but for higher fields nonlinear effects become important.

  18. Theory Queries.

    ERIC Educational Resources Information Center

    Moorman, Thomas

    1992-01-01

    Students experience the distinction between observable fact and scientific theory by taking a critical look at how spaghetti can be sucked up into the mouth. A demonstration shows that air is needed to suck up the spaghetti but that the scientific explanation is not as simple. (MDH)

  19. Control Theory.

    ERIC Educational Resources Information Center

    Toso, Robert B.

    2000-01-01

    Inspired by William Glasser's Reality Therapy ideas, Control Theory (CT) is a disciplinary approach that stresses people's ability to control only their own behavior, based on internal motivations to satisfy five basic needs. At one North Dakota high school, CT-trained teachers are the program's best recruiters. (MLH)

  20. Electroweak Theory

    NASA Astrophysics Data System (ADS)

    Paschos, E. A.

    2005-01-01

    The electroweak theory unifies two basic forces of nature: the weak force and electromagnetism. This book is a concise introduction to the structure of the electroweak theory and its applications. It describes the structure and properties of field theories with global and local symmetries, leading to the construction of the standard model. It describes the new particles and processes predicted by the theory, and compares them with experimental results. It also covers neutral currents, the properties of W and Z bosons, the properties of quarks and mesons containing heavy quarks, neutrino oscillations, CP-asymmetries in K, D, and B meson decays, and the search for Higgs particles. Each chapter contains problems, stemming from the long teaching experience of the author, to supplement the text. This will be of great interest to graduate students and researchers in elementary particle physics. Password protected solutions are available to lecturers at www.cambridge.org/9780521860987. Each chapter has an introduction highlighting its contents and giving a historical perspective. Chapters are cross-referenced, interrelating concepts and sections of the book. Contains 49 exercises

  1. A quasi-linear structure of the southern margin of Eurasia prior to the India-Asia collision: First paleomagnetic constraints from Upper Cretaceous volcanic rocks near the western syntaxis of Tibet

    NASA Astrophysics Data System (ADS)

    Yi, Zhiyu; Huang, Baochun; Yang, Liekun; Tang, Xiangde; Yan, Yonggang; Qiao, Qingqing; Zhao, Jie; Chen, Liwei

    2015-07-01

    We report the first combined geochronologic and paleomagnetic study of volcanic rocks from the Shiquanhe and Yare Basins at the westernmost Lhasa Terrane, which aims to provide an accurate constraint on the shape and paleoposition of the southern margin of Asia prior to the India-Asia collision. Three new 40Ar/39Ar ages of 92.5 ± 2.9 Ma, 92.4 ± 0.9 Ma, and 79.6 ± 0.7 Ma determined by fresh matrix or feldspar from lava flows suggest a Late Cretaceous age for the investigated units. Characteristic remanent magnetizations have been successfully isolated from 38 sites which pass positive fold and/or reversal, conglomerate tests and are hence interpreted as primary in origin. The two paleopoles obtained from Yare and Shiquanhe yield consistent paleolatitudes of 13.6°N ± 9.6°N and 14.2°N ± 2.7°N, respectively (for a reference site of 31.5°N, 80°E), indicating that the southern margin of Asia near the western syntaxis was located far south during the Late Cretaceous time. A reconstruction of the Lhasa Terrane in the frame of Eurasia with paleomagnetic data obtained from its western and eastern parts indicates that the southern margin of Eurasia probably had a quasi-linear orientation prior to the collision formerly trending approximately 315°E. This is compatible with the shape of the Neo-Tethys slab observed from seismic tomographic studies. Our findings provide a solid basis for evaluating Cenozoic crustal shortening in the Asian interior and the size of Greater India near the western syntaxis.

  2. A Thermodynamic Theory Of Solid Viscoelasticity. Part 1: Linear Viscoelasticity.

    NASA Technical Reports Server (NTRS)

    Freed, Alan D.; Leonov, Arkady I.

    2002-01-01

    The present series of three consecutive papers develops a general theory for linear and finite solid viscoelasticity. Because the most important object for nonlinear studies are rubber-like materials, the general approach is specified in a form convenient for solving problems important for many industries that involve rubber-like materials. General linear and nonlinear theories for non-isothermal deformations of viscoelastic solids are developed based on the quasi-linear approach of non-equilibrium thermodynamics. In this, the first paper of the series, we analyze non-isothermal linear viscoelasticity, which is applicable in a range of small strains not only to all synthetic polymers and bio-polymers but also to some non-polymeric materials. Although the linear case seems to be well developed, there still are some reasons to implement a thermodynamic derivation of constitutive equations for solid-like, non-isothermal, linear viscoelasticity. The most important is the thermodynamic modeling of thermo-rheological complexity , i.e. different temperature dependences of relaxation parameters in various parts of relaxation spectrum. A special structure of interaction matrices is established for different physical mechanisms contributed to the normal relaxation modes. This structure seems to be in accord with observations, and creates a simple mathematical framework for both continuum and molecular theories of the thermo-rheological complex relaxation phenomena. Finally, a unified approach is briefly discussed that, in principle, allows combining both the long time (discrete) and short time (continuous) descriptions of relaxation behaviors for polymers in the rubbery and glassy regions.

  3. Theory Survey or Survey Theory?

    ERIC Educational Resources Information Center

    Dean, Jodi

    2010-01-01

    Matthew Moore's survey of political theorists in U.S. American colleges and universities is an impressive contribution to political science (Moore 2010). It is the first such survey of political theory as a subfield, the response rate is very high, and the answers to the survey questions provide new information about how political theorists look…

  4. Helicopter theory

    NASA Technical Reports Server (NTRS)

    Johnson, W.

    1980-01-01

    A comprehensive presentation is made of the engineering analysis methods used in the design, development and evaluation of helicopters. After an introduction covering the fundamentals of helicopter rotors, configuration and operation, rotary wing history, and the analytical notation used in the text, the following topics are discussed: (1) vertical flight, including momentum, blade element and vortex theories, induced power, vertical drag and ground effect; (2) forward flight, including in addition to momentum and vortex theory for this mode such phenomena as rotor flapping and its higher harmonics, tip loss and root cutout, compressibility and pitch-flap coupling; (3) hover and forward flight performance assessment; (4) helicopter rotor design; (5) rotary wing aerodynamics; (6) rotary wing structural dynamics, including flutter, flap-lag dynamics ground resonance and vibration and loads; (7) helicopter aeroelasticity; (8) stability and control (flying qualities); (9) stall; and (10) noise.

  5. The unified ballooning theory with weak up-down asymmetric mode structure and the numerical studies

    NASA Astrophysics Data System (ADS)

    Xie, T.; Qin, H.; Zhang, Y. Z.; Mahajan, S. M.

    2016-04-01

    A unified ballooning theory, constructed on the basis of two special theories [Zhang et al., Phys. Fluids B 4, 2729 (1992); Y. Z. Zhang and T. Xie, Nucl. Fusion Plasma Phys. 33, 193 (2013)], shows that a weak up-down asymmetric mode structure is normally formed in an up-down symmetric equilibrium; the weak up-down asymmetry in mode structure is the manifestation of non-trivial higher order effects beyond the standard ballooning equation. It is shown that the asymmetric mode may have even higher growth rate than symmetric modes. The salient features of the theory are illustrated by investigating a fluid model for the ion temperature gradient (ITG) mode. The two dimensional (2D) analytical form of the ITG mode, solved in ballooning representation, is then converted into the radial-poloidal space to provide the natural boundary condition for solving the 2D mathematical local eigenmode problem. We find that the analytical expression of the mode structure is in a good agreement with finite difference solution. This sets a reliable framework for quasi-linear computation.

  6. A quasilinear formulation of turbulence driven current

    NASA Astrophysics Data System (ADS)

    McDevitt, C. J.; Tang, Xian-Zhu; Guo, Zehua

    2014-02-01

    Non-inductive current drive mechanisms, such as the familiar neoclassical bootstrap current correspond to an essential component to the realization of steady state tokamak operation. In this work, we discuss a novel collisionless mechanism through which a mean plasma current may be driven in the presence of microturbulence. In analogy with the traditional neoclassical bootstrap current drive mechanism, in which the collisional equilibrium established between trapped and passing electrons results in the formation of a steady state plasma current, here we show that resonant scattering of electrons by drift wave microturbulence provides an additional means of determining the equilibrium between trapped and passing electrons. The resulting collisionless equilibrium is shown to result in the formation of an equilibrium current whose magnitude is a function of the thermodynamic forces. A mean field formulation is utilized to incorporate the above components into a unified framework through which both collisional as well as collisionless current drive mechanisms may be self-consistently treated. Utilizing a linearized Fokker-Planck collision operator, the plasma current in the presence of both collisions as well as turbulent stresses is computed, allowing for the relative strength of these two mechanisms to be quantified as a function of collisionality and fluctuation amplitude.

  7. A Quasilinear Formulation of Turbulence Driven Current

    NASA Astrophysics Data System (ADS)

    McDevitt, C. J.; Tang, X. Z.; Guo, Z. H.

    2012-10-01

    Non-inductive current drive mechanisms such as the familiar bootstrap current correspond to an essential component to the realization of steady state tokamak operation. In this work we discuss a novel collisionless mechanism through which a mean plasma current may be driven in the presence of microturbulence (as seen in [1]). In analogy with the traditional bootstrap current drive mechanism, in which the collisional equilibrium established between trapped and passing particles results in the formation of a steady state plasma current, here we show that velocity space scattering by drift wave microturbulence is capable of modifying the equilibrium between trapped and passing particles leading to the generation of a mean plasma current. In the collisionless limit, this current drive mechanism can in turn be balanced either by turbulence mediated electron-ion momentum exchange or radial electron momentum transport. A mean field formulation is utilized to incorporate the above components into a unified framework through which both collisional as well as collisionless current drive mechanisms may be self-consistently treated. [4pt] [1] W. X. Wang et al., 53rd APS-DPP, Salt Lake City, Utah, 2011

  8. A quasilinear formulation of turbulence driven current

    SciTech Connect

    McDevitt, C. J.; Tang, Xian-Zhu; Guo, Zehua

    2014-02-15

    Non-inductive current drive mechanisms, such as the familiar neoclassical bootstrap current correspond to an essential component to the realization of steady state tokamak operation. In this work, we discuss a novel collisionless mechanism through which a mean plasma current may be driven in the presence of microturbulence. In analogy with the traditional neoclassical bootstrap current drive mechanism, in which the collisional equilibrium established between trapped and passing electrons results in the formation of a steady state plasma current, here we show that resonant scattering of electrons by drift wave microturbulence provides an additional means of determining the equilibrium between trapped and passing electrons. The resulting collisionless equilibrium is shown to result in the formation of an equilibrium current whose magnitude is a function of the thermodynamic forces. A mean field formulation is utilized to incorporate the above components into a unified framework through which both collisional as well as collisionless current drive mechanisms may be self-consistently treated. Utilizing a linearized Fokker-Planck collision operator, the plasma current in the presence of both collisions as well as turbulent stresses is computed, allowing for the relative strength of these two mechanisms to be quantified as a function of collisionality and fluctuation amplitude.

  9. Quasilinear Elliptic Equations Involving Variable Exponents

    NASA Astrophysics Data System (ADS)

    Mihǎilescu, Mihai; Moroşanu, Gheorghe

    2008-09-01

    Consider the boundary value problem -Σi = N∂xi(|∂xiu|pi(x)-2∂xiu) = λ(x)|u|q(x)-2u in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in RN with smooth boundary ∂Ω, while p1,…,pN,q are continuous functions and q(x)>1,pi(x)⩾2 for all x∈Ω¯, i = 1,⋯,N. Combining the mountain pass theorem of Ambrosetti and Rabinowitz [1] and Ekeland's variational principle [7] we show that under suitable conditions the above problem has two nontrivial weak solutions. We also consider the eigenvalue problem corresponding to the case when λ in the above equation is a positive constant. We assume that there exist j,k∈{1,…,N} with j≠k such that pj ≡ q in Ω¯, and q is independent of xj with maxΩ¯q

  10. Orbital-free density functional theory study of crystalline Li-Si alloys

    NASA Astrophysics Data System (ADS)

    Xia, Junchao; Carter, Emily A.

    2014-05-01

    Li-Si interactions are of great interest currently due to the potential use of silicon anodes in Li-ion batteries. As a first step toward eventual nanoscale characterization of lithiation of silicon, here we study the crystalline Li-Si alloys LiSi, Li12Si7, Li7Si3, Li13Si4, Li15Si4, and Li22Si5 using orbital-free density functional theory (OFDFT). The recently proposed Wang-Govind-Carter decomposition (WGCD) and Huang-Carter (HC) kinetic energy density functionals (KEDFs) are used to evaluate the electron kinetic energy. Both KEDFs predict accurate cell lattice vectors, equilibrium volumes, bulk moduli, and ground-state densities when compared to Kohn-Sham density functional theory (KSDFT) benchmarks. Elastic constants and alloy formation energies calculated with the WGCD KEDF also agree reasonably well with KSDFT. Finally, Li atom adsorption energies on the Si(100) - 2 × 1 surface are calculated as a simple initial test of the Li-Si mixing process during lithiation of silicon. The OFDFT adsorption energies again are fairly close to KSDFT values. The results in this work demonstrate the accuracy of the WGCD and HC KEDFs for materials with mixed covalent-metallic character and their considerable transferability under different chemical environments. Because of its quasilinear scaling, coupled with the level of accuracy shown here, OFDFT appears quite promising for large-scale simulation of such materials phenomena.

  11. Theory and Vocational Education.

    ERIC Educational Resources Information Center

    Swanson, Gordon I.

    1988-01-01

    The search for an explanation of day-to-day problems is the appropriate framework for describing theory. Theory and research have reciprocal relationships: Theory gives direction to research and research refines theory. Vocational education occurs in the context of many theoretical frames. Understanding this theory relatedness is important to…

  12. Decidability of formal theories and hyperincursivity theory

    NASA Astrophysics Data System (ADS)

    Grappone, Arturo G.

    2000-05-01

    This paper shows the limits of the Proof Standard Theory (briefly, PST) and gives some ideas of how to build a proof anticipatory theory (briefly, PAT) that has no such limits. Also, this paper considers that Gödel's proof of the undecidability of Principia Mathematica formal theory is not valid for axiomatic theories that use a PAT to build their proofs because the (hyper)incursive functions are self-representable.

  13. String Theory and M-Theory

    NASA Astrophysics Data System (ADS)

    Becker, Katrin; Becker, Melanie; Schwarz, John H.

    String theory is one of the most exciting and challenging areas of modern theoretical physics. This book guides the reader from the basics of string theory to recent developments. It introduces the basics of perturbative string theory, world-sheet supersymmetry, space-time supersymmetry, conformal field theory and the heterotic string, before describing modern developments, including D-branes, string dualities and M-theory. It then covers string geometry and flux compactifications, applications to cosmology and particle physics, black holes in string theory and M-theory, and the microscopic origin of black-hole entropy. It concludes with Matrix theory, the AdS/CFT duality and its generalizations. This book is ideal for graduate students and researchers in modern string theory, and will make an excellent textbook for a one-year course on string theory. It contains over 120 exercises with solutions, and over 200 homework problems with solutions available on a password protected website for lecturers at www.cambridge.org/9780521860697. Comprehensive coverage of topics from basics of string theory to recent developments Ideal textbook for a one-year course in string theory Includes over 100 exercises with solutions Contains over 200 homework problems with solutions available to lecturers on-line

  14. Foundations for a theory of gravitation theories

    NASA Technical Reports Server (NTRS)

    Thorne, K. S.; Lee, D. L.; Lightman, A. P.

    1972-01-01

    A foundation is laid for future analyses of gravitation theories. This foundation is applicable to any theory formulated in terms of geometric objects defined on a 4-dimensional spacetime manifold. The foundation consists of (1) a glossary of fundamental concepts; (2) a theorem that delineates the overlap between Lagrangian-based theories and metric theories; (3) a conjecture (due to Schiff) that the Weak Equivalence Principle implies the Einstein Equivalence Principle; and (4) a plausibility argument supporting this conjecture for the special case of relativistic, Lagrangian-based theories.

  15. A Theory for Emergence of Equatorial Deep Jets from Turbulence based on Statistical Mean State Dynamics

    NASA Astrophysics Data System (ADS)

    Fitzgerald, J.; Farrell, B.

    2013-12-01

    Equatorial deep jets (EDJs) are persistent, zonally-coherent jets found within one degree of the equator in all ocean basins (Luyten and Swallow, 1976). The jets are characterized by a vertically oscillating ('stacked') structure between ~500-2000m depth, with jet amplitudes on the order of 10 cm/s superimposed upon a large-scale background shear flow. EDJs are a striking feature of the equatorial climate system and play an important role in equatorial ocean transport. However, the physical mechanism responsible for the presence of EDJs remains uncertain. Previous theoretical models for EDJs have suggested mechanisms involving the reflection and constructive interference of equatorially trapped waves (Wunsch 1977, McCreary 1984) and the instability of mixed Rossby-gravity waves with EDJs as the fastest-growing eigenfunction (Hua et al. 2008, Eden et al. 2008). In this work we explore the jet formation mechanism and the parameter dependence of EDJ structure in the idealized theoretical model of the stochastically-driven equatorial beta plane. The model is formulated in three ways: 1) Fully nonlinear equations of motion 2) Quasilinear (or mean-field) dynamics 3) Statistical state dynamics employing a second order closure method (stochastic structural stability theory). Results from the three models are compared, and the implications for both the jet formation and equilibration mechanisms, as well as the role of eddy-eddy nonlinearity in the EDJ system, are discussed.

  16. Theories and Modes

    ERIC Educational Resources Information Center

    Apsche, Jack A.

    2005-01-01

    In his work on the Theory of Modes, Beck (1996) suggested that there were flaws with his cognitive theory. He suggested that though there are shortcomings to his cognitive theory, there were not similar shortcomings to the practice of Cognitive Therapy. The author suggests that if there are shortcomings to cognitive theory the same shortcomings…

  17. The Offence of Theory

    ERIC Educational Resources Information Center

    MacLure, Maggie

    2010-01-01

    Theory frequently offends. The paper argues that this is its strength: the value of theory lies in its power to get in the way. Theory is needed to block the reproduction of banality, and thereby, hopefully, open new possibilities for thinking and doing. However, I also note that theory has become somewhat disengaged from its objects, diminishing…

  18. Quantum Theory is an Information Theory

    NASA Astrophysics Data System (ADS)

    D'Ariano, Giacomo M.; Perinotti, Paolo

    2016-03-01

    In this paper we review the general framework of operational probabilistic theories (OPT), along with the six axioms from which quantum theory can be derived. We argue that the OPT framework along with a relaxed version of five of the axioms, define a general information theory. We close the paper with considerations about the role of the observer in an OPT, and the interpretation of the von Neumann postulate and the Schrödinger-cat paradox.

  19. Nonrelativistic superstring theories

    SciTech Connect

    Kim, Bom Soo

    2007-12-15

    We construct a supersymmetric version of the critical nonrelativistic bosonic string theory [B. S. Kim, Phys. Rev. D 76, 106007 (2007).] with its manifest global symmetry. We introduce the anticommuting bc conformal field theory (CFT) which is the super partner of the {beta}{gamma} CFT. The conformal weights of the b and c fields are both 1/2. The action of the fermionic sector can be transformed into that of the relativistic superstring theory. We explicitly quantize the theory with manifest SO(8) symmetry and find that the spectrum is similar to that of type IIB superstring theory. There is one notable difference: the fermions are nonchiral. We further consider noncritical generalizations of the supersymmetric theory using the superspace formulation. There is an infinite range of possible string theories similar to the supercritical string theories. We comment on the connection between the critical nonrelativistic string theory and the lightlike linear dilaton theory.

  20. Renormalized theory of ion temperature gradient instability of the magnetic-field-aligned plasma shear flow with hot ions

    SciTech Connect

    Mikhailenko, V. V. Mikhailenko, V. S.; Lee, Hae June

    2015-10-15

    The developed kinetic theory for the stability of a magnetic-field-aligned (parallel) shear flow with inhomogeneous ion temperature [Mikhailenko et al., Phys. Plasmas 21, 072117 (2014)] predicted that a kinetic instability arises from the coupled reinforcing action of the flow velocity shear and ion temperature gradient in the cases where comparable ion and electron temperatures exist. In the present paper, the nonlinear theory was developed for the instability caused by the combined effects of ion-temperature-gradient and shear-flow (ITG–SF). The level of the electrostatic turbulence is determined for the saturation state of the instability on the basis of the nonlinear dispersion equation, which accounts for a nonlinear scattering of ions by the developed turbulence in a sheared flow. The renormalized quasilinear equation for the ion distribution function, which accounts for the turbulent scattering of ions by ITG–SF driven turbulence, was derived and employed for the estimation of the turbulent ion viscosity, the anomalous ion thermal conductivity, and anomalous ion heating rate at the saturation state of the instability.

  1. Spontaneous Rotation as a Recoil Process--Novel Experimental Evidences and Consistency with the Tenets of the Accretion Theory

    NASA Astrophysics Data System (ADS)

    Basu, B.; Coppi, B.; Zhou, T.

    2012-10-01

    The Accretion Theory [1] of the spontaneous (a.k.a. intrinsic) rotation phenomenon observed on axisymmetric toroidal plasmas was based on the idea that angular momentum is ejected by collective modes from the plasma column and therefore the plasma rotates in the opposite direction. Until recently, the entire plasma column was observed to rotate unidirectionally and the ejection was directed to the plasma chamber, which can not be seen to counter-rotate. According to recent experiments [2], pairs of adjacent regions rotating in opposite directions can emerge within a given plasma column. Thus we argue that, if the prevalent modes are excited in the narrow region within the plasma column where the radial gradients of relevant plasma parameters are significant, angular momentum can be expelled toward the outer region. Then the inner region rotates as a recoil from this expulsion, in the direction opposite to that of the rotation of the outer region. The linear and quasi-linear theories of the modes involved in the relevant transport processes are given.[4pt] [1] B. Coppi, Nucl. Fusion 42,1 (1966).[0pt] [2] J. Rice et al., Nucl. Fusion 51, 083005 (2011).

  2. Teaching Theory X and Theory Y in Organizational Communication

    ERIC Educational Resources Information Center

    Noland, Carey

    2014-01-01

    The purpose of the activity described here is to integrate McGregor's Theory X and Theory Y into a group application: design a syllabus that embodies either Theory X or Theory Y tenets. Students should be able to differentiate between Theory X and Theory Y, create a syllabus based on Theory X or Theory Y tenets, evaluate the different syllabi…

  3. The Effective Field Theory of Large Scale Structures at two loops

    SciTech Connect

    Carrasco, John Joseph M.; Foreman, Simon; Green, Daniel; Senatore, Leonardo E-mail: sfore@stanford.edu E-mail: senatore@stanford.edu

    2014-07-01

    Large scale structure surveys promise to be the next leading probe of cosmological information. It is therefore crucial to reliably predict their observables. The Effective Field Theory of Large Scale Structures (EFTofLSS) provides a manifestly convergent perturbation theory for the weakly non-linear regime of dark matter, where correlation functions are computed in an expansion of the wavenumber k of a mode over the wavenumber associated with the non-linear scale k{sub NL}. Since most of the information is contained at high wavenumbers, it is necessary to compute higher order corrections to correlation functions. After the one-loop correction to the matter power spectrum, we estimate that the next leading one is the two-loop contribution, which we compute here. At this order in k/k{sub NL}, there is only one counterterm in the EFTofLSS that must be included, though this term contributes both at tree-level and in several one-loop diagrams. We also discuss correlation functions involving the velocity and momentum fields. We find that the EFTofLSS prediction at two loops matches to percent accuracy the non-linear matter power spectrum at redshift zero up to k∼ 0.6 h Mpc{sup −1}, requiring just one unknown coefficient that needs to be fit to observations. Given that Standard Perturbation Theory stops converging at redshift zero at k∼ 0.1 h Mpc{sup −1}, our results demonstrate the possibility of accessing a factor of order 200 more dark matter quasi-linear modes than naively expected. If the remaining observational challenges to accessing these modes can be addressed with similar success, our results show that there is tremendous potential for large scale structure surveys to explore the primordial universe.

  4. Generalizability Theory and Classical Test Theory

    ERIC Educational Resources Information Center

    Brennan, Robert L.

    2011-01-01

    Broadly conceived, reliability involves quantifying the consistencies and inconsistencies in observed scores. Generalizability theory, or G theory, is particularly well suited to addressing such matters in that it enables an investigator to quantify and distinguish the sources of inconsistencies in observed scores that arise, or could arise, over…

  5. Separation-individuation theory and attachment theory.

    PubMed

    Blum, Harold P

    2004-01-01

    Separation-individuation and attachment theories are compared and assessed in the context of psychoanalytic developmental theory and their application to clinical work. As introduced by Margaret Mahler and John Bowlby, respectively, both theories were initially regarded as diverging from traditional views. Separation-individuation theory, though it has had to be corrected in important respects, and attachment theory, despite certain limitations, have nonetheless enriched psychoanalytic thought. Without attachment an infant would die, and with severely insecure attachment is at greater risk for serious disorders. Development depends on continued attachment to a responsive and responsible caregiver. Continued attachment to the primary object was regarded by Mahler as as intrinsic to the process of separation-individuation. Attachment theory does not account for the essential development of separateness, and separation-individuation is important for the promotion of autonomy, independence, and identity. Salient historical and theoretical issues are addressed, including the renewed interest in attachment theory and the related decline of interest in separation-individuation theory. PMID:15222460

  6. Equivalency Theory and Distance Education.

    ERIC Educational Resources Information Center

    Simonson, Michael

    1999-01-01

    Discusses distance education and the need for an accepted theory. Highlights include theories of independent study; theory of industrialization of teaching; theory of interaction and communication; and equivalency theory that is based on local control, personalized instruction, and telecommunications. (LRW)

  7. Dissipative Field Theory

    SciTech Connect

    Kheirandish, F.; Amooshahi, M.

    2008-11-18

    Quantum field theory of a damped vibrating string as the simplest dissipative scalar field theory is investigated by introducing a minimal coupling method. The rate of energy flowing between the system and its environment is obtained.

  8. [Mathematics and string theory

    SciTech Connect

    Jaffe, A.; Yau, Shing-Tung.

    1993-01-01

    Work on this grant was centered on connections between non- commutative geometry and physics. Topics covered included: cyclic cohomology, non-commutative manifolds, index theory, reflection positivity, space quantization, quantum groups, number theory, etc.

  9. Theories of Career Development. A Comparison of the Theories.

    ERIC Educational Resources Information Center

    Osipow, Samuel H.

    These seven theories of career development are examined in previous chapters: (1) Roe's personality theory, (2) Holland's career typology theory, (3) the Ginzberg, Ginsburg, Axelrod, and Herma Theory, (4) psychoanalytic conceptions, (5) Super's developmental self-concept theory, (6) other personality theories, and (7) social systems theories.…

  10. Whither Social Theory?

    ERIC Educational Resources Information Center

    Pais, Alexandre; Valero, Paola

    2014-01-01

    What is the place of social theory in mathematics education research, and what is it for? This special issue of "Educational Studies in Mathematics" offers insights on what could be the role of some sociological theories in a field that has historically privileged learning theories coming from psychology and mathematics as the main…

  11. Comparing Measurement Theories.

    ERIC Educational Resources Information Center

    Schumacker, Randall E.

    In comparing measurement theories, it is evident that the awareness of the concept of measurement error during the time of Galileo has lead to the formulation of observed scores comprising a true score and error (classical theory), universe score and various random error components (generalizability theory), or individual latent ability and error…

  12. Modern Theories of Language.

    ERIC Educational Resources Information Center

    Davis, Philip W.

    This volume explores objectively the essential characteristic of nine twentieth-century linguistic theories with the theoretical variant for discussion based on one closely representative of work within a given approach or usually associated with the name of the theory. First, the theory of Ferdinand de Saussure is discussed based on his book,…

  13. Constructor theory of probability

    PubMed Central

    2016-01-01

    Unitary quantum theory, having no Born Rule, is non-probabilistic. Hence the notorious problem of reconciling it with the unpredictability and appearance of stochasticity in quantum measurements. Generalizing and improving upon the so-called ‘decision-theoretic approach’, I shall recast that problem in the recently proposed constructor theory of information—where quantum theory is represented as one of a class of superinformation theories, which are local, non-probabilistic theories conforming to certain constructor-theoretic conditions. I prove that the unpredictability of measurement outcomes (to which constructor theory gives an exact meaning) necessarily arises in superinformation theories. Then I explain how the appearance of stochasticity in (finitely many) repeated measurements can arise under superinformation theories. And I establish sufficient conditions for a superinformation theory to inform decisions (made under it) as if it were probabilistic, via a Deutsch–Wallace-type argument—thus defining a class of decision-supporting superinformation theories. This broadens the domain of applicability of that argument to cover constructor-theory compliant theories. In addition, in this version some of the argument's assumptions, previously construed as merely decision-theoretic, follow from physical properties expressed by constructor-theoretic principles. PMID:27616914

  14. Testing Theory through Theatrics.

    ERIC Educational Resources Information Center

    Sellers, Sandra Courtney

    2002-01-01

    In a nursing theory course, the final exam consists of a role play in which students assume the identity of a theorist they have studied and answer questions in the context of that role. Questions are designed demonstrate their knowledge of major nursing theories and models and the relevance of theory to practice. (SK)

  15. Frankl's Theory and Therapy.

    ERIC Educational Resources Information Center

    Missinne, Leo E.; Wilcox, Victoria

    This paper discusses the life, theories, and therapeutic techniques of psychotherapist, Viktor E. Frankl. A brief biography of Frankl is included discussing the relationship of his early experiences as a physician to his theory of personality. Frankl's theory focusing on man's need for meaning and emphasizing the spiritual dimension in each human…

  16. Reflections on Activity Theory

    ERIC Educational Resources Information Center

    Bakhurst, David

    2009-01-01

    It is sometimes suggested that activity theory represents the most important legacy of Soviet philosophy and psychology. But what exactly "is" activity theory? The canonical account in the West is given by Engestrom, who identifies three stages in the theory's development: from Vygotsky's insights, through Leontiev's articulation of the…

  17. Activity Theory and Ontology

    ERIC Educational Resources Information Center

    Peim, Nick

    2009-01-01

    This paper seeks to re-examine Yrio Engestrom's activity theory as a technology of knowledge designed to enable positive transformations of specific practices. The paper focuses on a key paper where Engestrom defines the nature and present state of activity theory. Beginning with a brief account of the relations between activity theory and…

  18. La theorie autrement (Theory in Another Light).

    ERIC Educational Resources Information Center

    Bertocchini, Paola; Costanzo, Edwige

    1985-01-01

    Outlines a technique using articles from "Le Francais dans le Monde" to teach reading comprehension and theory simultaneously to teachers of French as a second language. Describes a program in Italy using this approach. (MSE)

  19. Theory Interpretations in PVS

    NASA Technical Reports Server (NTRS)

    Owre, Sam; Shankar, Natarajan; Butler, Ricky W. (Technical Monitor)

    2001-01-01

    The purpose of this task was to provide a mechanism for theory interpretations in a prototype verification system (PVS) so that it is possible to demonstrate the consistency of a theory by exhibiting an interpretation that validates the axioms. The mechanization makes it possible to show that one collection of theories is correctly interpreted by another collection of theories under a user-specified interpretation for the uninterpreted types and constants. A theory instance is generated and imported, while the axiom instances are generated as proof obligations to ensure that the interpretation is valid. Interpretations can be used to show that an implementation is a correct refinement of a specification, that an axiomatically defined specification is consistent, or that a axiomatically defined specification captures its intended models. In addition, the theory parameter mechanism has been extended with a notion of theory as parameter so that a theory instance can be given as an actual parameter to an imported theory. Theory interpretations can thus be used to refine an abstract specification or to demonstrate the consistency of an axiomatic theory. In this report we describe the mechanism in detail. This extension is a part of PVS version 3.0, which will be publicly released in mid-2001.

  20. Rate theories for biologists

    PubMed Central

    Zhou, Huan-Xiang

    2012-01-01

    Some of the rate theories that are most useful for modeling biological processes are reviewed. By delving into some of the details and subtleties in the development of the theories, the review will hopefully help the reader gain a more than superficial perspective. Examples are presented to illustrate how rate theories can be used to generate insight at the microscopic level into biomolecular behaviors. Attempt is made to clear up a number of misconceptions in the literature regarding popular rate theories, including the appearance of Planck’s constant in the transition-state theory and the Smoluchowski result as an upper limit for protein-protein and protein-DNA association rate constants. Future work in combining the implementation of rate theories through computer simulations with experimental probes of rate processes, and in modeling effects of intracellular environments so theories can be used for generating rate constants for systems biology studies is particularly exciting. PMID:20691138

  1. Testing higher-order Lagrangian perturbation theory against numerical simulations. 2: Hierarchical models

    NASA Technical Reports Server (NTRS)

    Melott, A. L.; Buchert, T.; Weib, A. G.

    1995-01-01

    We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of scales. The Lagrangian theory of gravitational instability of Friedmann-Lemaitre cosmogonies is compared with numerical simulations. We study the dynamics of hierarchical models as a second step. In the first step we analyzed the performance of the Lagrangian schemes for pancake models, the difference being that in the latter models the initial power spectrum is truncated. This work probed the quasi-linear and weakly non-linear regimes. We here explore whether the results found for pancake models carry over to hierarchical models which are evolved deeply into the non-linear regime. We smooth the initial data by using a variety of filter types and filter scales in order to determine the optimal performance of the analytical models, as has been done for the 'Zel'dovich-approximation' - hereafter TZA - in previous work. We find that for spectra with negative power-index the second-order scheme performs considerably better than TZA in terms of statistics which probe the dynamics, and slightly better in terms of low-order statistics like the power-spectrum. However, in contrast to the results found for pancake models, where the higher-order schemes get worse than TZA at late non-linear stages and on small scales, we here find that the second-order model is as robust as TZA, retaining the improvement at later stages and on smaller scales. In view of these results we expect that the second-order truncated Lagrangian model is especially useful for the modelling of standard dark matter models such as Hot-, Cold-, and Mixed-Dark-Matter.

  2. Supersymmetry and String Theory

    NASA Astrophysics Data System (ADS)

    Dine, Michael

    2016-01-01

    Preface to the first edition; Preface to the second edition; A note on choice of metric; Text website; Part I. Effective Field Theory: The Standard Model, Supersymmetry, Unification: 1. Before the Standard Model; 2. The Standard Model; 3. Phenomenology of the Standard Model; 4. The Standard Model as an effective field theory; 5. Anomalies, instantons and the strong CP problem; 6. Grand unification; 7. Magnetic monopoles and solitons; 8. Technicolor: a first attempt to explain hierarchies; Part II. Supersymmetry: 9. Supersymmetry; 10. A first look at supersymmetry breaking; 11. The Minimal Supersymmetric Standard Model; 12. Supersymmetric grand unification; 13. Supersymmetric dynamics; 14. Dynamical supersymmetry breaking; 15. Theories with more than four conserved supercharges; 16. More supersymmetric dynamics; 17. An introduction to general relativity; 18. Cosmology; 19. Astroparticle physics and inflation; Part III. String Theory: 20. Introduction; 21. The bosonic string; 22. The superstring; 23. The heterotic string; 24. Effective actions in ten dimensions; 25. Compactification of string theory I. Tori and orbifolds; 26. Compactification of string theory II. Calabi–Yau compactifications; 27. Dynamics of string theory at weak coupling; 28. Beyond weak coupling: non-perturbative string theory; 29. Large and warped extra dimensions; 30. The landscape: a challenge to the naturalness principle; 31. Coda: where are we headed?; Part IV. The Appendices: Appendix A. Two-component spinors; Appendix B. Goldstone's theorem and the pi mesons; Appendix C. Some practice with the path integral in field theory; Appendix D. The beta function in supersymmetric Yang–Mills theory; References; Index.

  3. Generalized higher gauge theory

    NASA Astrophysics Data System (ADS)

    Ritter, Patricia; Sämann, Christian; Schmidt, Lennart

    2016-04-01

    We study a generalization of higher gauge theory which makes use of generalized geometry and seems to be closely related to double field theory. The local kinematical data of this theory is captured by morphisms of graded manifolds between the canonical exact Courant Lie 2-algebroid T M ⊕ T ∗ M over some manifold M and a semistrict gauge Lie 2-algebra. We discuss generalized curvatures and infinitesimal gauge transformations. Finite gauge transformation as well as global kinematical data are then obtained from principal 2-bundles over 2-spaces. As dynamical principle, we consider first the canonical Chern-Simons action for such a gauge theory. We then show that a previously proposed 3-Lie algebra model for the six-dimensional (2,0) theory is very naturally interpreted as a generalized higher gauge theory.

  4. Domains and Naive Theories

    PubMed Central

    Gelman, Susan A.; Noles, Nicholaus S.

    2013-01-01

    Human cognition entails domain-specific cognitive processes that influence memory, attention, categorization, problem-solving, reasoning, and knowledge organization. This review examines domain-specific causal theories, which are of particular interest for permitting an examination of how knowledge structures change over time. We first describe the properties of commonsense theories, and how commonsense theories differ from scientific theories, illustrating with children’s classification of biological and non-biological kinds. We next consider the implications of domain-specificity for broader issues regarding cognitive development and conceptual change. We then examine the extent to which domain-specific theories interact, and how people reconcile competing causal frameworks. Future directions for research include examining how different content domains interact, the nature of theory change, the role of context (including culture, language, and social interaction) in inducing different frameworks, and the neural bases for domain-specific reasoning. PMID:24187603

  5. Galileo's tidal theory.

    PubMed

    Naylor, Ron

    2007-03-01

    The aim of Galileo's tidal theory was to show that the tides were produced entirely by the earth's motion and thereby to demonstrate the physical truth of Copernicanism. However, in the Dialogue Concerning the Two Chief World Systems Galileo did not explain some of the most significant aspects of the theory completely. As a consequence, the way the theory works has long been disputed. Though there exist a number of interpretations in the literature, the most widely accepted are based on ideas that are not explicitly articulated by Galileo in the Dialogue. This essay attempts to understand the way the theory functions in terms of Galilean physics. It is an interpretation of the theory based solely on Galileo's arguments--and one that reveals it to have had some unrecognized consequences. This interpretation indicates that Galileo's theory would not have worked in the manner he described in the Dialogue. PMID:17539198

  6. A comparison of neutral and charged species of one- and two-dimensional models of graphene nanoribbons using multireference theory

    SciTech Connect

    Horn, Shawn; Lischka, Hans

    2015-02-07

    This study examines the dependence of the polyradical character of charged quasi-linear n-acenes and two-dimensional periacenes used as models for graphene nanoribbons in comparison to the corresponding neutral compounds. For this purpose, high-level ab initio calculations have been performed using the multireference averaged quadratic coupled cluster theory. Vertical ionization energies and electron affinities have been computed. Systematic tests show that the dependence on chain length of these quantities can be obtained from a consideration of the π system only and that remaining contributions coming from the σ orbitals or extended basis sets remain fairly constant. Using best estimate values, the experimental values for the ionization energy of the acene series can be reproduced within 0.1 eV and the experimental electron affinities within 0.4 V. The analysis of the natural orbital occupations and related unpaired electron densities shows that the ionic species exhibit a significant decrease in polyradical character and thus an increased chemical stability as compared to the neutral state.

  7. A comparison of neutral and charged species of one- and two-dimensional models of graphene nanoribbons using multireference theory.

    PubMed

    Horn, Shawn; Lischka, Hans

    2015-02-01

    This study examines the dependence of the polyradical character of charged quasi-linear n-acenes and two-dimensional periacenes used as models for graphene nanoribbons in comparison to the corresponding neutral compounds. For this purpose, high-level ab initio calculations have been performed using the multireference averaged quadratic coupled cluster theory. Vertical ionization energies and electron affinities have been computed. Systematic tests show that the dependence on chain length of these quantities can be obtained from a consideration of the π system only and that remaining contributions coming from the σ orbitals or extended basis sets remain fairly constant. Using best estimate values, the experimental values for the ionization energy of the acene series can be reproduced within 0.1 eV and the experimental electron affinities within 0.4 V. The analysis of the natural orbital occupations and related unpaired electron densities shows that the ionic species exhibit a significant decrease in polyradical character and thus an increased chemical stability as compared to the neutral state. PMID:25662640

  8. Automated Lattice Perturbation Theory

    SciTech Connect

    Monahan, Christopher

    2014-11-01

    I review recent developments in automated lattice perturbation theory. Starting with an overview of lattice perturbation theory, I focus on the three automation packages currently "on the market": HiPPy/HPsrc, Pastor and PhySyCAl. I highlight some recent applications of these methods, particularly in B physics. In the final section I briefly discuss the related, but distinct, approach of numerical stochastic perturbation theory.

  9. Extended theories of gravitation

    NASA Astrophysics Data System (ADS)

    Fatibene, Lorenzo; Garruto, Simon

    2016-04-01

    In this paper, we shall review the equivalence between Palatini-f(ℛ) theories and Brans-Dicke (BD) theories at the level of action principles. We shall define the Helmholtz Lagrangian associated to Palatini-f(ℛ) theory and we will define some transformations which will be useful to recover Einstein frame and BD frame. We shall see an explicit example of matter field and we will discuss how the conformal factor affects the physical quantities.

  10. Theory Modeling and Simulation

    SciTech Connect

    Shlachter, Jack

    2012-08-23

    Los Alamos has a long history in theory, modeling and simulation. We focus on multidisciplinary teams that tackle complex problems. Theory, modeling and simulation are tools to solve problems just like an NMR spectrometer, a gas chromatograph or an electron microscope. Problems should be used to define the theoretical tools needed and not the other way around. Best results occur when theory and experiments are working together in a team.

  11. The theory of flotation

    NASA Technical Reports Server (NTRS)

    Ostwald, Wolfgang

    1988-01-01

    A brief summary of the fundamentals of the Linear theory of flotation is given. The theory by no means contradicts the previous Laminar theory or even the thermodynamics (Wark-Siedler), rather it is a refinement of the known Hardy-Langmuir-Harkin conceptions for the case when there are not two phases and phase boundaries, but rather three phases and corresponding phase boundary edges. The appearance of such three-phase boundaries (ore, water, air) is characteristic for modern flotation methods.

  12. The Big Bang Theory

    SciTech Connect

    Lincoln, Don

    2014-09-30

    The Big Bang is the name of the most respected theory of the creation of the universe. Basically, the theory says that the universe was once smaller and denser and has been expending for eons. One common misconception is that the Big Bang theory says something about the instant that set the expansion into motion, however this isn’t true. In this video, Fermilab’s Dr. Don Lincoln tells about the Big Bang theory and sketches some speculative ideas about what caused the universe to come into existence.

  13. Between Theory and Observations

    NASA Astrophysics Data System (ADS)

    Wepster, Steven

    Three great mathematicians dominate the history of lunar theory in the middle of the eighteenth century: Leonhard Euler, Alexis Clairaut, and Jean le Rond d’Alembert. Each of them made a lasting contribution to the theory of celestial mechanics and their results had a broader impact than on lunar theory alone. To name but a few examples, Euler codified the trigonometric functions and pioneered the method of variation of orbital constants; Clairaut solved the arduous problem of the motion of the lunar apogee, thereby dealing a decisive blow to the sceptics of Newton’s law of gravitation; and d’Alembert worked out an accurate theory of precession and nutation.

  14. Ostwald ripening theory

    NASA Technical Reports Server (NTRS)

    Baird, J. K.

    1986-01-01

    The Ostwald-ripening theory is deduced and discussed starting from the fundamental principles such as Ising model concept, Mayer cluster expansion, Langer condensation point theory, Ginzburg-Landau free energy, Stillinger cutoff-pair potential, LSW-theory and MLSW-theory. Mathematical intricacies are reduced to an understanding version. Comparison of selected works, from 1949 to 1984, on solution of diffusion equation with and without sink/sources term(s) is presented. Kahlweit's 1980 work and Marqusee-Ross' 1954 work are more emphasized. Odijk and Lekkerkerker's 1985 work on rodlike macromolecules is introduced in order to simulate interested investigators.

  15. Why Do We Have Theories?

    ERIC Educational Resources Information Center

    Costley, Kevin C.

    2006-01-01

    University professors teaching pre-service teachers base much of their philosophies on theories. Students often ask "Why do we have theories?" "What is the purpose of theories?" "If we like a theory, do we have to use all of the theory?" The most frequent controversial issue is how to use a particular theory in a practical way. In the quest for…

  16. Testing higher-order Lagrangian perturbation theory against numerical simulation. 1: Pancake models

    NASA Technical Reports Server (NTRS)

    Buchert, T.; Melott, A. L.; Weiss, A. G.

    1993-01-01

    We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the

  17. Greek atomic theory

    NASA Astrophysics Data System (ADS)

    Roller, Duane H. D.

    1981-03-01

    Physics began about 600 B.C. with the Ionian Greeks and reached full development within three centuries. The creation of the concept of the atom is understandable within the context of Greek physical theory; so is the rejection of the atomic theory by the Greek physicists.

  18. Theory is personal.

    PubMed

    Siegel, Allen M

    2009-04-01

    In "Theory Is Personal," Allen Siegel MD, a Chicago psychoanalyst and Assistant Professor of Clinical Psychiatry at Rush University Medical Center, shares the very personal story of how he came to his theory. Sometimes we find our theory. Other times, Siegel argues, it is our theory that finds us. In this article Siegel catalogues his early encounters with figures--contemporary and real--from Sigmund Freud to influential department chairs to an analyst who would become legendary for introducing a bold new theory into the psychoanalytic canon. Charting key experiences that shaped his adoption of this new approach--a depression in response to his first patient, a clinical treatment with Heinz Kohut, and exposure to others who dared to challenge Freud--Siegel describes the theory that brought both himself and his patients to life. After outlining the principles that guide the new theory and practice known as self psychology, Siegel tells of the empathic ambiance that can now emerge in the consulting room. Finally, he shows how this new theory of human motivation provides not merely a rationale for psychotherapy but an explanatory apparatus for understanding human action in the world beyond the consulting room. He turns to a brief study of aggression and war, as expressed in a 1932 correspondence between Albert Einstein and Sigmund Freud, to illustrate how the understanding of aggression and war changes significantly when empathy is the field's data collecting instrument. PMID:19379249

  19. Evolution: Theory or Dogma?

    ERIC Educational Resources Information Center

    Mayer, William V.

    In this paper the author examines the question of whether evolution is a theory or a dogma. He refutes the contention that there is a monolithic scientific conspiracy to present evolution as dogma and suggests that his own presentation might be more appropriately entitled "Creationism: Theory or Dogma." (PEB)

  20. Greek Atomic Theory.

    ERIC Educational Resources Information Center

    Roller, Duane H. D.

    1981-01-01

    Focusing on history of physics, which began about 600 B.C. with the Ionian Greeks and reaching full development within three centuries, suggests that the creation of the concept of the atom is understandable within the context of Greek physical theory; so is the rejection of the atomic theory by the Greek physicists. (Author/SK)

  1. French Theory's American Adventures

    ERIC Educational Resources Information Center

    Cusset, Francois

    2008-01-01

    In this article, the author discusses how it is simply too late to be still speaking about French theory and its role in the intellectual life of the United States today. It seems to many observers that the gap between real-life politics and theory's guerrillas is much too wide already, after 30 years of academic fever, for the two worlds to even…

  2. Reimagining Critical Theory

    ERIC Educational Resources Information Center

    Rexhepi, Jevdet; Torres, Carlos Alberto

    2011-01-01

    This paper discusses Critical Theory, a model of theorizing in the field of the political sociology of education. We argue for a "reimagined" Critical Theory to herald an empowering, liberatory education that fosters curiosity and critical thinking, and a means for successful bottom-up, top-down political engagement. We present arguments at a…

  3. Evolution - A Theory Evolving

    ERIC Educational Resources Information Center

    Weinberg, Janet H.

    1975-01-01

    Presented is an explanation of a non-Darwinian theory of evolution based on the premise that functional differences are the result of many small mutations such as the substitution of one amino acid for another in a large protein molecule. A brief overview of Darwinian evolution and other theories are presented. (EB)

  4. Evaluating Conceptual Metaphor Theory

    ERIC Educational Resources Information Center

    Gibbs, Raymond W., Jr.

    2011-01-01

    A major revolution in the study of metaphor occurred 30 years ago with the introduction of "conceptual metaphor theory" (CMT). Unlike previous theories of metaphor and metaphorical meaning, CMT proposed that metaphor is not just an aspect of language, but a fundamental part of human thought. Indeed, most metaphorical language arises from…

  5. Theories and Methodologies.

    ERIC Educational Resources Information Center

    Skemp, Richard R.

    Provided is an examination of the methodology used to study the problems of learning addition and subtraction skills used by developmental researchers. The report has sections on categories of theory and their methodologies, which review: (1) Behaviorist, Neo-Behaviorist and Piagetian Theories; (2) the Behaviorist and Piagetian Paradigms; (3)…

  6. Universality and string theory

    NASA Astrophysics Data System (ADS)

    Bachlechner, Thomas Christian

    The first run at the Large Hadron Collider has deeply challenged conventional notions of naturalness, and CMB polarization experiments are about to open a new window to early universe cosmology. As a compelling candidate for the ultraviolet completion of the standard model, string theory provides a prime opportunity to study both early universe cosmology and particle physics. However, relating low energy observations to ultraviolet physics requires knowledge of the metastable states of string theory through the study of vacua. While it is difficult to directly obtain infrared data from explicit string theory constructions, string theory imposes constraints on low energy physics. The study of ensembles of low energy theories consistent with ultra-violet constraints provides insight on generic features we might expect to occur in string compactifications. In this thesis we present a statistical treatment of vacuum stability and vacuum properties in the context of random supergravity theories motivated by string theory. Early universe cosmology provides another avenue to high energy physics. From the low energy perspective large field inflation is typically considered highly unnatural: the scale relevant for the diameter of flat regions in moduli space is sub-Planckian in regions of perturbative control. To approach this problem, we consider generic Calabi-Yau compactifications of string theory and find that super-Planckian diameters of axion fundamental domains in fact arise generically. We further demonstrate that such super-Planckian flat regions are plausibly consistent with theWeak Gravity Conjecture.

  7. Organization Theory as Ideology.

    ERIC Educational Resources Information Center

    Greenfield, Thomas B.

    The theory that organizations are ideological inventions of the human mind is discussed. Organizational science is described as an ideology which is based upon social concepts and experiences. The main justification for organizational theory is that it attempts to answer why we behave as we do in social organizations. Ways in which ideas and…

  8. Put Theory into Practice

    ERIC Educational Resources Information Center

    Jaeger, Audrey J.; Dunstan, Stephany; Thornton, Courtney; Rockenbach, Alyssa B.; Gayles, Joy G.; Haley, Karen J.

    2013-01-01

    When making decisions that impact student learning, college educators often consider previous experiences, precedent, common sense, and advice from colleagues. But how often do they consider theory? At a recent state-level educators' meeting, the authors of this article asked 50 student affairs educators about the use of theory in their practice.…

  9. Sexual Murderers' Implicit Theories

    ERIC Educational Resources Information Center

    Beech, Anthony; Fisher, Dawn; Ward, Tony

    2005-01-01

    Interviews with 28 sexual murderers were subjected to grounded theory analysis. Five implicit theories (ITs) were identified: dangerous world, male sex drive is uncontrollable, entitlement, women as sexual objects, and women as unknowable. These ITs were found to be identical to those identified in the literature as being present in rapists. The…

  10. Game Theory .net.

    ERIC Educational Resources Information Center

    Shor, Mikhael

    2003-01-01

    States making game theory relevant and accessible to students is challenging. Describes the primary goal of GameTheory.net is to provide interactive teaching tools. Indicates the site strives to unite educators from economics, political and computer science, and ecology by providing a repository of lecture notes and tests for courses using…