Brønsted acidity of protic ionic liquids: a modern ab initio valence bond theory perspective.

PubMed

Patil, Amol Baliram; Mahadeo Bhanage, Bhalchandra

2016-09-21

Room temperature ionic liquids (ILs), especially protic ionic liquids (PILs), are used in many areas of the chemical sciences. Ionicity, the extent of proton transfer, is a key parameter which determines many physicochemical properties and in turn the suitability of PILs for various applications. The spectrum of computational chemistry techniques applied to investigate ionic liquids includes classical molecular dynamics, Monte Carlo simulations, ab initio molecular dynamics, Density Functional Theory (DFT), CCSD(t) etc. At the other end of the spectrum is another computational approach: modern ab initio Valence Bond Theory (VBT). VBT differs from molecular orbital theory based methods in the expression of the molecular wave function. The molecular wave function in the valence bond ansatz is expressed as a linear combination of valence bond structures. These structures include covalent and ionic structures explicitly. Modern ab initio valence bond theory calculations of representative primary and tertiary ammonium protic ionic liquids indicate that modern ab initio valence bond theory can be employed to assess the acidity and ionicity of protic ionic liquids a priori.

Kinetic theory and Vlasov simulation of nonlinear ion-acoustic waves in multi-ion species plasmas.

PubMed

Chapman, T; Berger, R L; Brunner, S; Williams, E A

2013-05-10

The theory of damping and nonlinear frequency shifts from particles resonant with ion-acoustic waves (IAWs) is presented for multi-ion species plasma and compared to driven wave Vlasov simulations. Two distinct IAW modes may be supported in multi-ion species plasmas, broadly classified as fast and slow by their phase velocity relative to the constituent ion thermal velocities. In current fusion-relevant long pulse experiments, the ion to electron temperature ratio, T(i)/T(e), is expected to reach a level such that the least damped and thus more readily driven mode is the slow mode, with both linear and nonlinear properties that are shown to differ significantly from the fast mode. The lighter ion species of the slow mode is found to make no significant contribution to the IAW frequency shift despite typically being the dominant contributor to the Landau damping.

Application and Extension of an Analytical Model of the Confined Acoustic Beam Generated by a Transducer

DTIC Science & Technology

1990-01-01

1988. 12 K. T. Shu and J. H. Ginsberg, "Ray Solution for Finite Amplitude Two- Dimensional Waves in a Hard -Walled Rectangular Waveguide", 115th...the effect of nonlinearity on a hard -walled rectangular waveguide. The excitation would induce only the fundamental nonplanar symmetric mode if the...interacting waves. In linear the surface of the plate vanishes. Such lines are perpendicu- theory, a mode in a hard -walled waveguide may be con- lar to the

Special Course on Stability and Transition of Laminar Flow

DTIC Science & Technology

1984-06-01

10"^ ; the high values of T, such as those used by HALL and HISLOP , are achieved by installing grids just upstream of the test section. Figure 16...1979, Springer Verlag ( 1980 ) "On the secondary motion induced by oscillations in a shear flow Phys. Fluids, 3, (1960) 656-657 "A non linear theory...SCHLICHTING wave by a sound wave" lUTAM Symposium on Laminar-Turbulent Transition, SUTTGART 1979, Springer Verlag ( 1980 ) "The influence of sound upon

Wave-induced hydraulic forces on submerged aquatic plants in shallow lakes.

PubMed

Schutten, J; Dainty, J; Davy, A J

2004-03-01

Hydraulic pulling forces arising from wave action are likely to limit the presence of freshwater macrophytes in shallow lakes, particularly those with soft sediments. The aim of this study was to develop and test experimentally simple models, based on linear wave theory for deep water, to predict such forces on individual shoots. Models were derived theoretically from the action of the vertical component of the orbital velocity of the waves on shoot size. Alternative shoot-size descriptors (plan-form area or dry mass) and alternative distributions of the shoot material along its length (cylinder or inverted cone) were examined. Models were tested experimentally in a flume that generated sinusoidal waves which lasted 1 s and were up to 0.2 m high. Hydraulic pulling forces were measured on plastic replicas of Elodea sp. and on six species of real plants with varying morphology (Ceratophyllum demersum, Chara intermedia, Elodea canadensis, Myriophyllum spicatum, Potamogeton natans and Potamogeton obtusifolius). Measurements on the plastic replicas confirmed predicted relationships between force and wave phase, wave height and plant submergence depth. Predicted and measured forces were linearly related over all combinations of wave height and submergence depth. Measured forces on real plants were linearly related to theoretically derived predictors of the hydraulic forces (integrals of the products of the vertical orbital velocity raised to the power 1.5 and shoot size). The general applicability of the simplified wave equations used was confirmed. Overall, dry mass and plan-form area performed similarly well as shoot-size descriptors, as did the conical or cylindrical models of shoot distribution. The utility of the modelling approach in predicting hydraulic pulling forces from relatively simple plant and environmental measurements was validated over a wide range of forces, plant sizes and species.

Simulation of Nonlinear Instabilities in an Attachment-Line Boundary Layer

NASA Technical Reports Server (NTRS)

Joslin, Ronald D.

1996-01-01

The linear and the nonlinear stability of disturbances that propagate along the attachment line of a three-dimensional boundary layer is considered. The spatially evolving disturbances in the boundary layer are computed by direct numerical simulation (DNS) of the unsteady, incompressible Navier-Stokes equations. Disturbances are introduced either by forcing at the in ow or by applying suction and blowing at the wall. Quasi-parallel linear stability theory and a nonparallel theory yield notably different stability characteristics for disturbances near the critical Reynolds number; the DNS results con rm the latter theory. Previously, a weakly nonlinear theory and computations revealed a high wave-number region of subcritical disturbance growth. More recent computations have failed to achieve this subcritical growth. The present computational results indicate the presence of subcritically growing disturbances; the results support the weakly nonlinear theory. Furthermore, an explanation is provided for the previous theoretical and computational discrepancy. In addition, the present results demonstrate that steady suction can be used to stabilize disturbances that otherwise grow subcritically along the attachment line.

Limitations of quasilinear transport theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balescu, R.

1992-01-01

The anomalous fluxes are evaluated in the simplest possible geometric situation: drift waves in a shearless slab geometry, in the presence of density and temperature gradients. It is shown that, within the strict quasilinear framework, the linear transport equations relating the fluxes to the thermodynamic forces have serious limitations. Such a linear relation does not even exist for the ion energy flux. For all the fluxes, the first correction'' has a singularity whose location depends on the relative value of the density gradient and of the ion temperature gradient: its existence seriously restricts the domain of validity of the quasilinearmore » transport theory. The semiempirical quasilinear'' formulas used in the comparisons with experiments are also discussed.« less

Gyro-viscosity and linear dispersion relations in pair-ion magnetized plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kono, M.; Vranjes, J.; Departamento de Astrofisica, Universidad de La Laguna, Tenerife E38205

2015-11-15

A fluid theory has been developed by taking account of gyro-viscosity to study wave propagation characteristics in a homogeneous pair-ion magnetized plasma with a cylindrical symmetry. The exact dispersion relations derived by the Hankel-Fourier transformation are shown comparable with those observed in the experiment by Oohara and co-workers. The gyro-viscosity is responsible for the change in propagation characteristics of the ion cyclotron wave from forward to backward by suppressing the effect of the thermal pressure which normally causes the forward nature of dispersion. Although the experiment has been already explained by a kinetic theory by the present authors, the kineticmore » derivations are so involved because of exact particle orbits in phase space, finite Lamor radius effects, and higher order ion cyclotron resonances. The present fluid theory provides a simple and transparent structure to the dispersion relations since the gyro-viscosity is renormalized into the ion cyclotron frequency which itself indicates the backward nature of dispersion. The usual disadvantage of a fluid theory, which treats only fundamental modes of eigen-waves excited in a system and is not able to describe higher harmonics that a kinetic theory does, is compensated by simple derivations and clear picture based on the renormalization of the gyro-viscosity.« less

Renormalizability of the gradient flow in the 2D O(N) non-linear sigma model

NASA Astrophysics Data System (ADS)

Makino, Hiroki; Suzuki, Hiroshi

2015-03-01

It is known that the gauge field and its composite operators evolved by the Yang-Mills gradient flow are ultraviolet (UV) finite without any multiplicative wave function renormalization. In this paper, we prove that the gradient flow in the 2D O(N) non-linear sigma model possesses a similar property: The flowed N-vector field and its composite operators are UV finite without multiplicative wave function renormalization. Our proof in all orders of perturbation theory uses a (2+1)-dimensional field theoretical representation of the gradient flow, which possesses local gauge invariance without gauge field. As an application of the UV finiteness of the gradient flow, we construct the energy-momentum tensor in the lattice formulation of the O(N) non-linear sigma model that automatically restores the correct normalization and the conservation law in the continuum limit.

Nonlinear water waves: introduction and overview

NASA Astrophysics Data System (ADS)

Constantin, A.

2017-12-01

For more than two centuries progress in the study of water waves proved to be interdependent with innovative and deep developments in theoretical and experimental directions of investigation. In recent years, considerable progress has been achieved towards the understanding of waves of large amplitude. Within this setting one cannot rely on linear theory as nonlinearity becomes an essential feature. Various analytic methods have been developed and adapted to come to terms with the challenges encountered in settings where approximations (such as those provided by linear or weakly nonlinear theory) are ineffective. Without relying on simpler models, progress becomes contingent upon the discovery of structural properties, the exploitation of which requires a combination of creative ideas and state-of-the-art technical tools. The successful quest for structure often reveals unexpected patterns and confers aesthetic value on some of these studies. The topics covered in this issue are both multi-disciplinary and interdisciplinary: there is a strong interplay between mathematical analysis, numerical computation and experimental/field data, interacting with each other via mutual stimulation and feedback. This theme issue reflects some of the new important developments that were discussed during the programme `Nonlinear water waves' that took place at the Isaac Newton Institute for Mathematical Sciences (Cambridge, UK) from 31st July to 25th August 2017. A cross-section of the experts in the study of water waves who participated in the programme authored the collected papers. These papers illustrate the diversity, intensity and interconnectivity of the current research activity in this area. They offer new insight, present emerging theoretical methodologies and computational approaches, and describe sophisticated experimental results. This article is part of the theme issue 'Nonlinear water waves'.

Nonlinear water waves: introduction and overview.

PubMed

Constantin, A

2018-01-28

For more than two centuries progress in the study of water waves proved to be interdependent with innovative and deep developments in theoretical and experimental directions of investigation. In recent years, considerable progress has been achieved towards the understanding of waves of large amplitude. Within this setting one cannot rely on linear theory as nonlinearity becomes an essential feature. Various analytic methods have been developed and adapted to come to terms with the challenges encountered in settings where approximations (such as those provided by linear or weakly nonlinear theory) are ineffective. Without relying on simpler models, progress becomes contingent upon the discovery of structural properties, the exploitation of which requires a combination of creative ideas and state-of-the-art technical tools. The successful quest for structure often reveals unexpected patterns and confers aesthetic value on some of these studies. The topics covered in this issue are both multi-disciplinary and interdisciplinary: there is a strong interplay between mathematical analysis, numerical computation and experimental/field data, interacting with each other via mutual stimulation and feedback. This theme issue reflects some of the new important developments that were discussed during the programme 'Nonlinear water waves' that took place at the Isaac Newton Institute for Mathematical Sciences (Cambridge, UK) from 31st July to 25th August 2017. A cross-section of the experts in the study of water waves who participated in the programme authored the collected papers. These papers illustrate the diversity, intensity and interconnectivity of the current research activity in this area. They offer new insight, present emerging theoretical methodologies and computational approaches, and describe sophisticated experimental results.This article is part of the theme issue 'Nonlinear water waves'. © 2017 The Author(s).

Hydrodynamic and kinetic models for spin-1/2 electron-positron quantum plasmas: Annihilation interaction, helicity conservation, and wave dispersion in magnetized plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Andreev, Pavel A., E-mail: andreevpa@physics.msu.ru

2015-06-15

We discuss the complete theory of spin-1/2 electron-positron quantum plasmas, when electrons and positrons move with velocities mach smaller than the speed of light. We derive a set of two fluid quantum hydrodynamic equations consisting of the continuity, Euler, spin (magnetic moment) evolution equations for each species. We explicitly include the Coulomb, spin-spin, Darwin and annihilation interactions. The annihilation interaction is the main topic of the paper. We consider the contribution of the annihilation interaction in the quantum hydrodynamic equations and in the spectrum of waves in magnetized electron-positron plasmas. We consider the propagation of waves parallel and perpendicular tomore » an external magnetic field. We also consider the oblique propagation of longitudinal waves. We derive the set of quantum kinetic equations for electron-positron plasmas with the Darwin and annihilation interactions. We apply the kinetic theory to the linear wave behavior in absence of external fields. We calculate the contribution of the Darwin and annihilation interactions in the Landau damping of the Langmuir waves. We should mention that the annihilation interaction does not change number of particles in the system. It does not related to annihilation itself, but it exists as a result of interaction of an electron-positron pair via conversion of the pair into virtual photon. A pair of the non-linear Schrodinger equations for the electron-positron plasmas including the Darwin and annihilation interactions is derived. Existence of the conserving helicity in electron-positron quantum plasmas of spinning particles with the Darwin and annihilation interactions is demonstrated. We show that the annihilation interaction plays an important role in the quantum electron-positron plasmas giving the contribution of the same magnitude as the spin-spin interaction.« less

On the theory of the relativistic motion of a charged particle in the field of intense electromagnetic radiation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Milant'ev, V. P., E-mail: vmilantiev@sci.pfu.edu.ru; Castillo, A. J., E-mail: vmilant@mail.ru

2013-04-15

Averaged relativistic equations of motion of a charged particle in the field of intense electromagnetic radiation have been obtained in the geometrical optics approximation using the Bogoliubov method. Constraints are determined under which these equations are valid. Oscillating additions to the smoothed dynamical variables of the particle have been found; they are reduced to known expressions in the case of the circularly and linearly polarized plane waves. It has been shown that the expressions for the averaged relativistic force in both cases contain new additional small terms weakening its action. The known difference between the expressions for the ponderomotive forcemore » in the cases of circularly and linearly polarized waves has been confirmed.« less

Analysis of scattering by a linear chain of spherical inclusions in an optical fiber

NASA Astrophysics Data System (ADS)

Chremmos, Ioannis D.; Uzunoglu, Nikolaos K.

2006-12-01

The scattering by a linear chain of spherical dielectric inclusions, embedded along the axis of an optical fiber, is analyzed using a rigorous integral equation formulation, based on the dyadic Green's function theory. The coupled electric field integral equations are solved by applying the Galerkin technique with Mie-type expansion of the field inside the spheres in terms of spherical waves. The analysis extends the previously studied case of a single spherical inhomogeneity inside a fiber to the multisphere-scattering case, by utilizing the classic translational addition theorems for spherical waves in order to analytically extract the direct-intersphere-coupling coefficients. Results for the transmitted and reflected power, on incidence of the fundamental HE11 mode, are presented for several cases.

A test of the Hall-MHD model: Application to low-frequency upstream waves at Venus

NASA Technical Reports Server (NTRS)

Orlowski, D. S.; Russell, C. T.; Krauss-Varban, D.; Omidi, N.

1994-01-01

Early studies suggested that in the range of parameter space where the wave angular frequency is less than the proton gyrofrequency and the plasma beta, the ratio of the thermal to magnetic pressure, is less than 1 magnetohydrodynamics provides an adequate description of the propagating modes in a plasma. However, recently, Lacombe et al. (1992) have reported significant differences between basic wave characteristics of the specific propagation modes derived from linear Vlasov and Hall-magnetohydrodynamic (MHD) theories even when the waves are only weakly damped. In this paper we compare the magnetic polarization and normalization magnetic compression ratio of ultra low frequency (ULF) upstream waves at Venus with magnetic polarization and normalized magnetic compression ratio derived from both theories. We find that while the 'kinetic' approach gives magnetic polarization and normalized magnetic compression ratio consistent with the data in the analyzed range of beta (0.5 less than beta less than 5) for the fast magnetosonic mode, the same wave characteristics derived from the Hall-MHD model strongly depend on beta and are consistent with the data only at low beta for the fast mode and at high beta for the intermediate mode.

Fabric dependence of wave propagation in anisotropic porous media

PubMed Central

Cowin, Stephen C.; Cardoso, Luis

2012-01-01

Current diagnosis of bone loss and osteoporosis is based on the measurement of the Bone Mineral Density (BMD) or the apparent mass density. Unfortunately, in most clinical ultrasound densitometers: 1) measurements are often performed in a single anatomical direction, 2) only the first wave arriving to the ultrasound probe is characterized, and 3) the analysis of bone status is based on empirical relationships between measurable quantities such as Speed of Sound (SOS) and Broadband Ultrasound Attenuation (BUA) and the density of the porous medium. However, the existence of a second wave in cancellous bone has been reported, which is an unequivocal signature of poroelastic media, as predicted by Biot’s poroelastic wave propagation theory. In this paper the governing equations for wave motion in the linear theory of anisotropic poroelastic materials are developed and extended to include the dependence of the constitutive relations upon fabric - a quantitative stereological measure of the degree of structural anisotropy in the pore architecture of a porous medium. This fabric-dependent anisotropic poroelastic approach is a theoretical framework to describe the microarchitectural-dependent relationship between measurable wave properties and the elastic constants of trabecular bone, and thus represents an alternative for bone quality assessment beyond BMD alone. PMID:20461539

Role of structural anisotropy of biological tissues in poroelastic wave propagation

PubMed Central

Cardoso, Luis; Cowin, Stephen C.

2011-01-01

Ultrasound waves have a broad range of clinical applications as a non-destructive testing approach in imaging and in the diagnoses of medical conditions. Generally, biological tissues are modeled as an homogenized equivalent medium with an apparent density through which a single wave propagates. Only the first wave arriving at the ultrasound probe is used for the measurement of the speed of sound. However, the existence of a second wave in tissues such as cancellous bone has been reported and its existence is an unequivocal signature of Biot type poroelastic media. To account for the fact that ultrasound is sensitive to microarchitecture as well as density, a fabric-dependent anisotropic poroelastic ultrasound (PEU) propagation theory was recently developed. Key to this development was the inclusion of the fabric tensor - a quantitative stereological measure of the degree of structural anisotropy of bone - into the linear poroelasticity theory. In the present study, this framework is extended to the propagation of waves in several soft and hard tissues. It was found that collagen fibers in soft tissues and the mineralized matrix in hard tissues are responsible for the anisotropy of the solid tissue constituent through the fabric tensor in the model. PMID:22162897

Gravitational Wave in Linear General Relativity

NASA Astrophysics Data System (ADS)

Cubillos, D. J.

2017-07-01

General relativity is the best theory currently available to describe the interaction due to gravity. Within Albert Einstein's field equations this interaction is described by means of the spatiotemporal curvature generated by the matter-energy content in the universe. Weyl worked on the existence of perturbations of the curvature of space-time that propagate at the speed of light, which are known as Gravitational Waves, obtained to a first approximation through the linearization of the field equations of Einstein. Weyl's solution consists of taking the field equations in a vacuum and disturbing the metric, using the Minkowski metric slightly perturbed by a factor ɛ greater than zero but much smaller than one. If the feedback effect of the field is neglected, it can be considered as a weak field solution. After introducing the disturbed metric and ignoring ɛ terms of order greater than one, we can find the linearized field equations in terms of the perturbation, which can then be expressed in terms of the Dalambertian operator of the perturbation equalized to zero. This is analogous to the linear wave equation in classical mechanics, which can be interpreted by saying that gravitational effects propagate as waves at the speed of light. In addition to this, by studying the motion of a particle affected by this perturbation through the geodesic equation can show the transversal character of the gravitational wave and its two possible states of polarization. It can be shown that the energy carried by the wave is of the order of 1/c5 where c is the speed of light, which explains that its effects on matter are very small and very difficult to detect.

Rethinking wave-kinetic theory applied to zonal flows

NASA Astrophysics Data System (ADS)

Parker, Jeffrey

2017-10-01

Over the past two decades, a number of studies have employed a wave-kinetic theory to describe fluctuations interacting with zonal flows. Recent work has uncovered a defect in this wave-kinetic formulation: the system is dominated by the growth of (arbitrarily) small-scale zonal structures. Theoretical calculations of linear growth rates suggest, and nonlinear simulations confirm, that this system leads to the concentration of zonal flow energy in the smallest resolved scales, irrespective of the numerical resolution. This behavior results from the assumption that zonal flows are extremely long wavelength, leading to the neglect of key terms responsible for conservation of enstrophy. A corrected theory, CE2-GO, is presented; it is free of these errors yet preserves the intuitive phase-space mathematical structure. CE2-GO properly conserves enstrophy as well as energy, and yields accurate growth rates of zonal flow. Numerical simulations are shown to be well-behaved and not dependent on box size. The steady-state limit simplifies into an exact wave-kinetic form which offers the promise of deeper insight into the behavior of wavepackets. The CE2-GO theory takes its place in a hierarchy of models as the geometrical-optics reduction of the more complete cumulant-expansion statistical theory CE2. The new theory represents the minimal statistical description, enabling an intuitive phase-space formulation and an accurate description of turbulence-zonal flow dynamics. This work was supported by an NSF Graduate Research Fellowship, a US DOE Fusion Energy Sciences Fellowship, and US DOE Contract Nos. DE-AC52-07NA27344 and DE-AC02-09CH11466.

Perturbation method for the second-order nonlinear effect of focused acoustic field around a scatterer in an ideal fluid.

PubMed

Liu, Gang; Jayathilake, Pahala Gedara; Khoo, Boo Cheong

2014-02-01

Two nonlinear models are proposed to investigate the focused acoustic waves that the nonlinear effects will be important inside the liquid around the scatterer. Firstly, the one dimensional solutions for the widely used Westervelt equation with different coordinates are obtained based on the perturbation method with the second order nonlinear terms. Then, by introducing the small parameter (Mach number), a dimensionless formulation and asymptotic perturbation expansion via the compressible potential flow theory is applied. This model permits the decoupling between the velocity potential and enthalpy to second order, with the first potential solutions satisfying the linear wave equation (Helmholtz equation), whereas the second order solutions are associated with the linear non-homogeneous equation. Based on the model, the local nonlinear effects of focused acoustic waves on certain volume are studied in which the findings may have important implications for bubble cavitation/initiation via focused ultrasound called HIFU (High Intensity Focused Ultrasound). The calculated results show that for the domain encompassing less than ten times the radius away from the center of the scatterer, the non-linear effect exerts a significant influence on the focused high intensity acoustic wave. Moreover, at the comparatively higher frequencies, for the model of spherical wave, a lower Mach number may result in stronger nonlinear effects. Copyright © 2013 Elsevier B.V. All rights reserved.

Acoustic and Seismic Dispersion in Complex Fluids and Solids

NASA Astrophysics Data System (ADS)

Goddard, Joe

2017-04-01

The first part of the present paper is the continuation of a previous work [3] on the effects of higher spatial gradients and temporal relaxation on stress and heat flux in complex fluids. In particular, the general linear theory is applied to acoustic dispersion, extending a simpler model proposed by Davis and Brenner [2]. The theory is applied to a linearized version of the Chapman-Enskog fluid [1] valid to terms of Burnett order and including Maxwell-Cataneo relaxation of stress and heat flux on relaxation time scales τ. For this model, the dispersion relation k(ω) giving spatial wave number k as function of temporal frequency ω is a cubic in k2, in contrast to the quadratic in k2 given by the classical model and the recently proposed modification [2]. The cubic terms are shown to be important only for ωτ = O(1) where Maxwell-Cataneo relaxation is also important. As a second part of the present work, it is shown how the above model can also be applied to isotropic solids, where both shear and pressure waves are important. Finally, consideration is given to hyperstress in micro- polar continua, including both graded and micro-morphic varieties. [1]S. Chapman and T. Cowling. The mathematical theory of non-uniform gases. Cambridge University Press, [Cambridge, UK], 1960. [2]A. M.J. Davis and H. Brenner. Thermal and viscous effects on sound waves: revised classical theory. J. Acoust. Soc. Am., 132(5):2963-9, 2012. [3] J.D. Goddard. On material velocities and non-locality in the thermo-mechanics of continua. Int. J. Eng. Sci., 48(11):1279-88, 2010.

Quasi-linear diffusion coefficients for highly oblique whistler mode waves

NASA Astrophysics Data System (ADS)

Albert, J. M.

2017-05-01

Quasi-linear diffusion coefficients are considered for highly oblique whistler mode waves, which exhibit a singular "resonance cone" in cold plasma theory. The refractive index becomes both very large and rapidly varying as a function of wave parameters, making the diffusion coefficients difficult to calculate and to characterize. Since such waves have been repeatedly observed both outside and inside the plasmasphere, this problem has received renewed attention. Here the diffusion equations are analytically treated in the limit of large refractive index μ. It is shown that a common approximation to the refractive index allows the associated "normalization integral" to be evaluated in closed form and that this can be exploited in the numerical evaluation of the exact expression. The overall diffusion coefficient formulas for large μ are then reduced to a very simple form, and the remaining integral and sum over resonances are approximated analytically. These formulas are typically written for a modeled distribution of wave magnetic field intensity, but this may not be appropriate for highly oblique whistlers, which become quasi-electrostatic. Thus, the analysis is also presented in terms of wave electric field intensity. The final results depend strongly on the maximum μ (or μ∥) used to model the wave distribution, so realistic determination of these limiting values becomes paramount.

Wave friction factor rediscovered

NASA Astrophysics Data System (ADS)

Le Roux, J. P.

2012-02-01

The wave friction factor is commonly expressed as a function of the horizontal water particle semi-excursion ( A wb) at the top of the boundary layer. A wb, in turn, is normally derived from linear wave theory by {{U_{{wb}}/T_{{w}}}}{{2π }} , where U wb is the maximum water particle velocity measured at the top of the boundary layer and T w is the wave period. However, it is shown here that A wb determined in this way deviates drastically from its real value under both linear and non-linear waves. Three equations for smooth, transitional and rough boundary conditions, respectively, are proposed to solve this problem, all three being a function of U wb, T w, and δ, the thickness of the boundary layer. Because these variables can be determined theoretically for any bottom slope and water depth using the deepwater wave conditions, there is no need to physically measure them. Although differing substantially from many modern attempts to define the wave friction factor, the results coincide with equations proposed in the 1960s for either smooth or rough boundary conditions. The findings also confirm that the long-held notion of circular water particle motion down to the bottom in deepwater conditions is erroneous, the motion in fact being circular at the surface and elliptical at depth in both deep and shallow water conditions, with only horizontal motion at the top of the boundary layer. The new equations are incorporated in an updated version (WAVECALC II) of the Excel program published earlier in this journal by Le Roux et al. Geo-Mar Lett 30(5): 549-560, (2010).

Characteristics of finite amplitude stationary gravity waves in the atmosphere of Venus

NASA Technical Reports Server (NTRS)

Young, Richard E.; Walterscheid, Richard L.; Schubert, Gerald; Pfister, Leonhard; Houben, Howard; Bindschadler, Duane L.

1994-01-01

This paper extends the study of stationary gravity waves generated near the surface of Venus reported previously by Young et al. to include finite amplitude effects associated with large amplitude waves. Waves are forced near the surface of Venus by periodic forcing. The height-dependent profiles of static stability and mean wind in the Venus atmosphere play a very important role in the evolution of the nonlinear behavior of the waves, just as they do in the linear wave solutions. Certain wave properties are qualitatively consistent with linear wave theory, such as wave trapping, resonance, and wave evanescence for short horizontal wavelenghts. However, the finite amplitude solutions also exhibit many other interesting features. In particular, for forcing amplitudes representative of those that could be expected in mountainous regions such as Aphrodite Terra, waves generated near the surface can reach large amplitudes at and above cloud levels, with clear signatures in the circulation pattern. At still higher levels, the waves can reach large enough amplitude to break, unless damping rates above the clouds are sufficient to limit wave amplitude growth. Well below cloud levels the waves develop complex flow patterns as the result of finite amplitude wave-wave interactions, and waves are generated having considerably shorter horizontal wavelenghts than that associated with the forcing near the surface. Nonlinear interactions can excite waves that are resonant with the background wind and static stability fields even when the primary surface forcing does not, and these waves can dominate the wave spectrum near cloud levels. A global map of Venus topographic slopes derived from Magellan altimetry data shows that slopes of magnitude comparable to or exceeding that used to force the model are ubiquitous over the surface.

Gravitational waves — A review on the theoretical foundations of gravitational radiation

NASA Astrophysics Data System (ADS)

Dirkes, Alain

2018-05-01

In this paper, we review the theoretical foundations of gravitational waves in the framework of Albert Einstein’s theory of general relativity. Following Einstein’s early efforts, we first derive the linearized Einstein field equations and work out the corresponding gravitational wave equation. Moreover, we present the gravitational potentials in the far away wave zone field point approximation obtained from the relaxed Einstein field equations. We close this review by taking a closer look on the radiative losses of gravitating n-body systems and present some aspects of the current interferometric gravitational waves detectors. Each section has a separate appendix contribution where further computational details are displayed. To conclude, we summarize the main results and present a brief outlook in terms of current ongoing efforts to build a spaced-based gravitational wave observatory.

The excitation of spiral density waves through turbulent fluctuations in accretion discs - II. Numerical simulations with MRI-driven turbulence

NASA Astrophysics Data System (ADS)

Heinemann, T.; Papaloizou, J. C. B.

2009-07-01

We present fully three-dimensional local simulations of compressible magneto-rotational instability (MRI) turbulence with the object of studying and elucidating the excitation of the non-axisymmetric spiral density waves that are observed to always be present in such simulations. They are potentially important for affecting protoplanetary migration through the action of associated stochastic gravitational forces and producing residual transport in MHD inactive regions through which they may propagate. The simulations we perform are with zero net flux and produce mean activity levels corresponding to the Shakura & Syunyaev α ~ 5 × 10-3, being at the lower end of the range usually considered in accretion disc modelling. We reveal the nature of the mechanism responsible for the excitation of these waves by determining the time-dependent evolution of the Fourier transforms of the participating state variables. The dominant waves are found to have no vertical structure and to be excited during periodically repeating swings in which they change from leading to trailing. The initial phase of the evolution of such a swing is found to be in excellent agreement with that expected from the WKBJ theory developed in a preceding paper by Heinemann & Papaloizou. However, shortly after the attainment of the expected maximum wave amplitude, the waves begin to be damped on account of the formation of weak shocks. As expected from the theory, the waves are seen to shorten in radial wavelength as they propagate. This feature enables non-linear dissipation to continue in spite of amplitude decrease. As a consequence, the waves are almost always seen to be in the non-linear regime. We demonstrate that the important source terms causing excitation of the waves are related to a quantity that reduces to the potential vorticity for small perturbations from the background state with no vertical dependence. We find that the root mean square density fluctuations associated with the waves are positively correlated with both this quantity and the general level of hydromagnetic turbulence. The mean angular momentum transport associated with spiral density waves generated in our simulations is estimated to be a significant fraction of that associated with the turbulent Reynolds stress.

Near-threshold NN→dπ reaction in chiral perturbation theory

NASA Astrophysics Data System (ADS)

Gårdestig, A.; Phillips, D. R.; Elster, Ch.

2006-02-01

The near-threshold np→dπ0 cross section is calculated in chiral perturbation theory to next-to-leading order in the expansion parameter √(Mmπ)/Λχ. At this order irreducible pion loops contribute to the relevant pion-production operator. Although their contribution to this operator is finite, considering initial- and final-state distortions produces a linear divergence in its matrix elements. We renormalize this divergence by introducing a counterterm, whose value we choose to reproduce the threshold np→dπ0 cross section measured at TRIUMF. The energy dependence of this cross section is then predicted in chiral perturbation theory, being determined by the production of p-wave pions, and also by energy dependence in the amplitude for the production of s-wave pions. With an appropriate choice of the counterterm, the chiral prediction for this energy dependence converges well.

Development of attenuation and diffraction corrections for linear and nonlinear Rayleigh surface waves radiating from a uniform line source

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jeong, Hyunjo, E-mail: hjjeong@wku.ac.kr; Cho, Sungjong; Zhang, Shuzeng

2016-04-15

In recent studies with nonlinear Rayleigh surface waves, harmonic generation measurements have been successfully employed to characterize material damage and microstructural changes, and found to be sensitive to early stages of damage process. A nonlinearity parameter of Rayleigh surface waves was derived and frequently measured to quantify the level of damage. The accurate measurement of the nonlinearity parameter generally requires making corrections for beam diffraction and medium attenuation. These effects are not generally known for nonlinear Rayleigh waves, and therefore not properly considered in most of previous studies. In this paper, the nonlinearity parameter for a Rayleigh surface wave ismore » defined from the plane wave displacement solutions. We explicitly define the attenuation and diffraction corrections for fundamental and second harmonic Rayleigh wave beams radiated from a uniform line source. Attenuation corrections are obtained from the quasilinear theory of plane Rayleigh wave equations. To obtain closed-form expressions for diffraction corrections, multi-Gaussian beam (MGB) models are employed to represent the integral solutions derived from the quasilinear theory of the full two-dimensional wave equation without parabolic approximation. Diffraction corrections are presented for a couple of transmitter-receiver geometries, and the effects of making attenuation and diffraction corrections are examined through the simulation of nonlinearity parameter determination in a solid sample.« less

A New Global Multi-fluid MHD Model of the Solar Corona

NASA Astrophysics Data System (ADS)

van der Holst, B.; Chandran, B. D. G.; Alterman, B. L.; Kasper, J. C.; Toth, G.

2017-12-01

We present a multi-fluid generalization of the AWSoM model, a global magnetohydrodynamic (MHD) solar corona model with low-frequency Alfven wave turbulence (van der Holst et al., 2014). This new extended model includes electron and multi-ion temperatures and velocities (protons and alpha particles). The coronal heating and acceleration is addressed via outward propagating low-frequency Alfven waves that are partially reflected by Alfven speed gradients. The nonlinear interaction of these counter-propagating waves results in turbulent energy cascade. To apportion the wave dissipation to the electron and ion temperatures, we employ the results of the theories of linear wave damping and nonlinear stochastic heating as described by Chandran et al. (2011, 2013). This heat partitioning results in a more than mass proportional heating among ions.

Phase-locked scroll waves defy turbulence induced by negative filament tension.

PubMed

Li, Teng-Chao; Gao, Xiang; Zheng, Fei-Fei; Cai, Mei-Chun; Li, Bing-Wei; Zhang, Hong; Dierckx, Hans

2016-01-01

Scroll waves in a three-dimensional media may develop into turbulence due to negative tension of the filament. Such negative tension-induced instability of scroll waves has been observed in the Belousov-Zhabotinsky reaction systems. Here we propose a method to restabilize scroll wave turbulence caused by negative tension in three-dimensional chemical excitable media using a circularly polarized (rotating) external field. The stabilization mechanism is analyzed in terms of phase-locking caused by the external field, which makes the effective filament tension positive. The phase-locked scroll waves that have positive tension and higher frequency defy the turbulence and finally restore order. A linear theory for the change of filament tension caused by a generic rotating external field is presented and its predictions closely agree with numerical simulations.

A study of hypersonic small-disturbance theory

NASA Technical Reports Server (NTRS)

Van Dyke, Milton D

1954-01-01

A systematic study is made of the approximate inviscid theory of thin bodies moving at such high supersonic speeds that nonlinearity is an essential feature of the equations of flow. The first-order small-disturbance equations are derived for three-dimensional motions involving shock waves, and estimates are obtained for the order of error involved in the approximation. The hypersonic similarity rule of Tsien and Hayes, and Hayes' unsteady analogy appear in the course of the development. It is shown that the hypersonic theory can be interpreted so that it applies also in the range of linearized supersonic flow theory. Several examples are solved according to the small-disturbance theory, and compared with the full solutions when available.

Enhancement of wave growth for warm plasmas with a high-energy tail distribution

NASA Technical Reports Server (NTRS)

Thorne, Richard M.; Summers, Danny

1991-01-01

The classical linear theory of electromagnetic wave growth in a warm plasma is considered for waves propagating parallel to a uniform ambient magnetic field. Wave-growth rates are calculated for ion-driven right-hand mode waves for Kappa and Maxwellian particle distribution functions and for various values of the spectral index, the temperature anisotropy, and the ratio of plasma pressure to magnetic pressure appropriate to the solar wind. When the anisotropy is low the wave growth is limited to frequencies below the proton gyrofrequency and the growth rate increases dramatically as the spectral index is reduced. The growth rate for any Kappa distribution greatly exceeds that for a Maxwellian with the same bulk properties. For large thermal anisotropy the growth rate from either distribution is greatly enhanced. The growth rates from a Kappa distribution are generally larger than for a Maxwellian distribution, and significant wave growth occurs over a broader range of frequencies.

Waves on radial film flows

NASA Astrophysics Data System (ADS)

Cholemari, Murali R.; Arakeri, Jaywant H.

2005-08-01

We study the stability of surface waves on the radial film flow created by a vertical cylindrical water jet striking a horizontal plate. In such flows, surface waves have been found to be unstable and can cause transition to turbulence. This surface-wave-induced transition is different from the well-known Tollmien-Schlichting wave-induced transition. The present study aims at understanding the instability and the transition process. We do a temporal stability analysis by assuming the flow to be locally two-dimensional but including spatial variations to first order in the basic flow. The waves are found to be dispersive, mostly unstable, and faster than the mean flow. Spatial variation is the major destabilizing factor. Experiments are done to test the results of the linear stability analysis and to document the wave breakup and transition. Comparison between theory and experiments is fairly good and indicates the adequacy of the model.

Composite rogue waves and modulation instability for the three-coupled Hirota system in an optical fiber

NASA Astrophysics Data System (ADS)

Chai, Han-Peng; Tian, Bo; Chai, Jun; Du, Zhong

2017-10-01

We investigate the three-coupled Hirota system, which is applied to model the long distance communication and ultrafast signal routing systems governing the propagation of light pulses. With the aid of the Darboux dressing transformation, composite rogue wave solutions are derived. Spatial-temporal structures, including the four-petaled structure for the three-coupled Hirota system, are exhibited. We find that the four-petaled rogue waves occur in two of the three components, whereas the eye-shaped rogue wave occurs in the other one. The composite rogue waves can split up into two or three single rogue waves. The corresponding conditions for the occurrence of such phenomena are discussed and presented. We find that the relative position of every single rogue wave is influenced by the ratios of certain parameters. Besides, the linear instability analysis is performed, and our results agree with those from the baseband modulation instability theory.

A three dimensional Dirichlet-to-Neumann map for surface waves over topography

NASA Astrophysics Data System (ADS)

Nachbin, Andre; Andrade, David

2016-11-01

We consider three dimensional surface water waves in the potential theory regime. The bottom topography can have a quite general profile. In the case of linear waves the Dirichlet-to-Neumann operator is formulated in a matrix decomposition form. Computational simulations illustrate the performance of the method. Two dimensional periodic bottom variations are considered in both the Bragg resonance regime as well as the rapidly varying (homogenized) regime. In the three-dimensional case we use the Luneburg lens-shaped submerged mound, which promotes the focusing of the underlying rays. FAPERJ Cientistas do Nosso Estado Grant 102917/2011 and ANP/PRH-32.

Simulation studies of plasma waves in the electron foreshock - The transition from reactive to kinetic instability

NASA Technical Reports Server (NTRS)

Dum, C. T.

1990-01-01

Particle simulation experiments were used to analyze the electron beam-plasma instability. It is shown that there is a transition from the reactive state of the electron beam-plasma instability to the kinetic instability of Langmuir waves. Quantitative tests, which include an evaluation of the dispersion relation for the evolving non-Maxwellian beam distribution, show that a quasi-linear theory describes the onset of this transition and applies again fully to the kinetic stage. This stage is practically identical to the late stage seen in simulations of plasma waves in the electron foreshock described by Dum (1990).

On the Wind Generation of Water Waves

NASA Astrophysics Data System (ADS)

Bühler, Oliver; Shatah, Jalal; Walsh, Samuel; Zeng, Chongchun

2016-11-01

In this work, we consider the mathematical theory of wind generated water waves. This entails determining the stability properties of the family of laminar flow solutions to the two-phase interface Euler equation. We present a rigorous derivation of the linearized evolution equations about an arbitrary steady solution, and, using this, we give a complete proof of the instability criterion of M iles [16]. Our analysis is valid even in the presence of surface tension and a vortex sheet (discontinuity in the tangential velocity across the air-sea interface). We are thus able to give a unified equation connecting the Kelvin-Helmholtz and quasi-laminar models of wave generation.

Wave theory in rotating systems: Schrödinger equations bridge the gaps between the equatorial β-plane and the spherical earth

NASA Astrophysics Data System (ADS)

Paldor, N.

2017-12-01

The concise and elegant wave theory developed on the equatorial β-plane by Matsuno (1966, M66 hereafter) is based on the formulation of a Schrödinger equation associated with the governing Linear Rotating Shallow Water Equations (LRSWE). The theory yields explicit expressions for the dispersion relations and meridional amplitude structures of all zonally propagating waves - Rossby, Inertia-Gravity, Kelvin and Yanai. In contrast, the spherical wave theory of Longuet-Higgins (1968) is a collection of asymptotic expansions in many sub-ranges e.g. large, small (and even negative) Lamb Number; high and low frequency; low-latitudes, etc. that rests upon extensive numerical solutions of several Ordinary Differential Equations. The difference between the two theories is highlighted by their lengths. The essential elements of the former planar study are completely revealed in just 3-4 pages including the derivation of explicit formulae for the phase speeds and amplitude meridional structures. In comtrast, the latter spherical theory contains 97 pages and the results of the numerical calculations are summarized in 30 pages of tables filled with numerical values and about 31 figures, each of which containing many separate curves! In my talk I will re-visit the wave problem on a sphere by developing several Schrödinger equations that approximate the governing eigenvalue equation associated with zonally propagating waves. Each of the Schrödinger equations approximates the original second order Ordinary Differential Equation in a different range of the 3 parameters: Lamb-Number, frequency and zonal wavenumber. As in M66, each of the Schrödinger equations yields explicit expressions for the dispersion relations and meridional amplitude structure of Rossby and Inertia-Gravity waves. In addition, the analysis shows that Yanai wave exists on a sphere even tough the zonal velocity is regular everywhere there (in contrast to the β-plane where the zonal velocity is singular everywhere) and that Kelvin waves do not exist as a separate mode (but the eastward propagating n=0 Inertia-Gravity is nearly non-dispersive). References Longuet-Higgins, M. S. Phil. Trans. Roy. Soc. London; 262, 511-607; 1968 Matsuno, T.; J. Met. Soc. Japan. 44(1), 25-43; 1966

Power loss of a single electron charge distribution confined in a quantum plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mehramiz, A.; Department of Physics, Faculty of Science, I. K. Int'l University, Qazvin 34149-16818; Mahmoodi, J.

2011-05-15

The dielectric tensor for a quantum plasma is derived by using a linearized quantum hydrodynamic theory. The wave functions for a nanostructure bound system have been investigated. Finally, the power loss for an oscillating charge distribution of a mixed state will be calculated, using the dielectric function formalism.

In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part I: Linear Theory

NASA Technical Reports Server (NTRS)

Goldman, Benjamin D.; Dowell, Earl H.; Scott, Robert C.

2014-01-01

Conical shell theory and piston theory aerodynamics are used to study the aeroelastic stability of the thermal protection system (TPS) on the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). Structural models of the TPS consist of single or multiple orthotropic conical shell systems resting on several circumferential linear elastic supports. The shells in each model may have pinned (simply-supported) or elastically-supported edges. The Lagrangian is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the equations of motion. The natural modes of vibration and aeroelastic stability boundaries are found by calculating the eigenvalues and eigenvectors of a large coefficient matrix. When the in-flight configuration of the TPS is approximated as a single shell without elastic supports, asymmetric flutter in many circumferential waves is observed. When the elastic supports are included, the shell flutters symmetrically in zero circumferential waves. Structural damping is found to be important in this case. Aeroelastic models that consider the individual TPS layers as separate shells tend to flutter asymmetrically at high dynamic pressures relative to the single shell models. Several parameter studies also examine the effects of tension, orthotropicity, and elastic support stiffness.

Oscillation of satellite droplets in an Oldroyd-B viscoelastic liquid jet

NASA Astrophysics Data System (ADS)

Li, Fang; Yin, Xie-Yuan; Yin, Xie-Zhen

2017-01-01

A one-dimensional numerical simulation is carried out to study the oscillation characteristics of satellite droplets in the beads-on-a-string structure of an Oldroyd-B viscoelastic liquid jet. The oscillation of satellite droplets is compared with the linear oscillation of a single viscoelastic droplet. It is found that, contrary to the predictions of linear theory, the period of oscillation of satellite droplets decreases with time, despite the increase in droplet volume. The mechanism may lie in the existence of the filament, which exerts an extra resistance on droplets. On the other hand, the oscillation of droplets does not influence very much the thinning of the filament. The influence of the axial wave number, viscosity, and elasticity on the oscillation of satellite droplets is examined. Increasing the wave number may result in the decrease in the period and the increase in the decay rate of oscillation, while increasing viscosity may lead to the increase in both the period and the decay rate of oscillation. Elasticity is shown to suppress the oscillation at large wave numbers, but its influence is limited at small wave numbers.

Novel modeling technique for the stator of traveling wave ultrasonic motors.

PubMed

Pons, José L; Rodríguez, Humberto; Ceres, Ramón; Calderón, Leopoldo

2003-11-01

Traveling wave ultrasonic motors (TWUM) are a promising type of piezoelectric transducers, which are based on the friction transmission of mechanical propagating waves. These waves are excited on the stator by using high Q piezoelectric ceramics. This article presents a modeling strategy, which allows for a quick and precise modal and forced analysis of the stator of TWUM. First-order shear deformation laminated plate theory is applied to annular subdomains (super-elements) of the stator. In addition to shear deformations, the model takes into account the effect of rotary inertia, the stiffness contribution of the teeth, and the linear varying thickness of the stator. Moreover, the formulation considers a more realistic function for the electric field inside the piezoelectric ceramic, i.e., a linear function, instead of the generally assumed constant electric field. The Ritz method is used to find an approximated solution for the dynamic equations. Finally, the modal response is obtained and compared against the results from classical simplified models and the finite element method. Thus, the high accuracy and short computation times of the novel strategy were demonstrated.

Green's function and Bloch theory for the analysis of the dynamic response of a periodically supported beam to a moving load

NASA Astrophysics Data System (ADS)

Lassoued, R.; Lecheheb, M.; Bonnet, G.

2012-08-01

This paper describes an analytical method for the wave field induced by a moving load on a periodically supported beam. The Green's function for an Euler beam without support is evaluated by using the direct integration. Afterwards, it introduces the supports into the model established by using the superposition principle which states that the response from all the sleeper points and from the external point force add up linearly to give a total response. The periodicity of the supports is described by Bloch's theorem. The homogeneous system thus obtained represents a linear differential equation which governs rail response. It is initially solved in the homogeneous case, and it admits a no null solution if its determinant is null, this permits the establishment the dispersion equation to Bloch waves and wave bands. The Bloch waves and dispersion curves contain all the physics of the dynamic problem and the wave field induced by a dynamic load applied to the system is finally obtained by decomposition into Bloch waves, similarly to the usual decomposition into dynamic modes on a finite structure. The method is applied to obtain the field induced by a load moving at constant velocity on a thin beam supported by periodic elastic supports.

Observation of wave celerity evolution in the nearshore using digital video imagery

NASA Astrophysics Data System (ADS)

Yoo, J.; Fritz, H. M.; Haas, K. A.; Work, P. A.; Barnes, C. F.; Cho, Y.

2008-12-01

Celerity of incident waves in the nearshore is observed from oblique video imagery collected at Myrtle Beach, S.C.. The video camera covers the field view of length scales O(100) m. Celerity of waves propagating in shallow water including the surf zone is estimated by applying advanced image processing and analysis methods to the individual video images sampled at 3 Hz. Original image sequences are processed through video image frame differencing, directional low-pass image filtering to reduce the noise arising from foam in the surf zone. The breaking wave celerity is computed along a cross-shore transect from the wave crest tracks extracted by a Radon transform-based line detection method. The observed celerity from the nearshore video imagery is larger than the linear wave celerity computed from the measured water depths over the entire surf zone. Compared to the nonlinear shallow water wave equation (NSWE)-based celerity computed using the measured depths and wave heights, in general, the video-based celerity shows good agreements over the surf zone except the regions across the incipient wave breaking locations. In the regions across the breaker points, the observed wave celerity is even larger than the NSWE-based celerity due to the transition of wave crest shapes. The observed celerity using the video imagery can be used to monitor the nearshore geometry through depth inversion based on the nonlinear wave celerity theories. For this purpose, the exceeding celerity across the breaker points needs to be corrected accordingly compared to a nonlinear wave celerity theory applied.

Effect of Random Circuit Fabrication Errors on Small Signal Gain and Phase in Helix Traveling Wave Tubes

NASA Astrophysics Data System (ADS)

Pengvanich, P.; Chernin, D. P.; Lau, Y. Y.; Luginsland, J. W.; Gilgenbach, R. M.

2007-11-01

Motivated by the current interest in mm-wave and THz sources, which use miniature, difficult-to-fabricate circuit components, we evaluate the statistical effects of random fabrication errors on a helix traveling wave tube amplifier's small signal characteristics. The small signal theory is treated in a continuum model in which the electron beam is assumed to be monoenergetic, and axially symmetric about the helix axis. Perturbations that vary randomly along the beam axis are introduced in the dimensionless Pierce parameters b, the beam-wave velocity mismatch, C, the gain parameter, and d, the cold tube circuit loss. Our study shows, as expected, that perturbation in b dominates the other two. The extensive numerical data have been confirmed by our analytic theory. They show in particular that the standard deviation of the output phase is linearly proportional to standard deviation of the individual perturbations in b, C, and d. Simple formulas have been derived which yield the output phase variations in terms of the statistical random manufacturing errors. This work was supported by AFOSR and by ONR.

High frequency poroelastic waves in hydrogels.

PubMed

Chiarelli, Piero; Lanatà, Antonio; Carbone, Marina; Domenici, Claudio

2010-03-01

In this work a continuum model for high frequency poroelastic longitudinal waves in hydrogels is presented. A viscoelastic force describing the interaction between the polymer network and the bounded water present in such materials is introduced. The model is tested by means of ultrasound wave speed and attenuation measurements in polyvinylalcohol hydrogel samples. The theory and experiments show that ultrasound attenuation decreases linearly with the increase in the water volume fraction beta of the hydrogel. The introduction of the viscoelastic force between the bounded water and the polymer network leads to a bi-phasic theory, showing an ultrasonic fast wave attenuation that can vary as a function of the frequency with a non-integer exponent in agreement with the experimental data in literature. When beta tends to 1 (100% of interstitial water) due to the presence of bounded water in the hydrogel, the ultrasound phase velocity acquires higher value than that of pure water. The ultrasound speed gap at beta=1 is confirmed by the experimental results, showing that it increases in less cross-linked gel samples which own a higher concentration of bounded water.

On the tidal effects in the motion of artificial satellites.

NASA Technical Reports Server (NTRS)

Musen, P.; Estes, R.

1972-01-01

The general perturbations in the elliptic and vectorial elements of a satellite as caused by the tidal deformations of the non-spherical Earth are developed into trigonometric series in the standard ecliptical arguments of Hill-Brown lunar theory and in the equatorial elements of the satellite. The integration of the differential equations for variation of elements of the satellite in this theory is easy because all arguments are linear or nearly linear in time. The trigonometrical expansion permits a judgment about the relative significance of the amplitudes and periods of different tidal 'waves' over a long period of time. Graphs are presented of the tidal perturbations in the elliptic elements of the BE-C satellite which illustrate long term periodic behavior. The tidal effects are clearly noticeable in the observations and their comparison with the theory permits improvement of the 'global' Love numbers for the Earth.

Effect of observed micropolar motions on wave propagation in deep Earth minerals

NASA Astrophysics Data System (ADS)

Abreu, Rafael; Thomas, Christine; Durand, Stephanie

2018-03-01

We provide a method to compute the Cosserat couple modulus for a bridgmanite (MgSiO3 silicate perovskite) solid from frequency gaps observed in Raman experiments. To this aim, we apply micropolar theory which is a generalization of the classical linear elastic theory, where each particle has an intrinsic rotational degree of freedom, called micro-rotation and/or spin, and which depends on the so-called Cosserat couple modulus μc that characterizes the micropolar medium. We investigate both wave propagation and dispersion. The wave propagation simulations in both potassium nitrate (KNO3) and bridgmanite crystal leads to a faster elastic wave propagation as well as to an independent rotational field of motion, called optic mode, which is smaller in amplitude compared to the conventional rotational field. The dispersion analysis predicts that the optic mode only appears above a cutoff frequency, ωr , which has been observed in Raman experiments done at high pressures and temperatures on bridgmanite crystal. The comparison of the cutoff frequency observed in experiments and the micropolar theory enables us to compute for the first time the temperature and pressure dependency of the Cosserat couple modulus μc of bridgmanite. This study thus shows that the micropolar theory can explain particle motions observed in laboratory experiments that were before neglected and that can now be used to constrain the micropolar elastic constants of Earth's mantle like material. This pioneer work aims at encouraging the use of micropolar theory in future works on deep Earth's mantle material by providing Cosserat couple modulus that were not available before.

On the Scaling Law for Broadband Shock Noise Intensity in Supersonic Jets

NASA Technical Reports Server (NTRS)

Kanudula, Max

2009-01-01

A theoretical model for the scaling of broadband shock noise intensity in supersonic jets was formulated on the basis of linear shock-shear wave interaction. An hypothesis has been postulated that the peak angle of incidence (closer to the critical angle) for the shear wave primarily governs the generation of sound in the interaction process rather than the noise generation contribution from off-peak incident angles. The proposed theory satisfactorily explains the well-known scaling law for the broadband shock -associated noise in supersonic jets.

NMR shieldings from density functional perturbation theory: GIPAW versus all-electron calculations

NASA Astrophysics Data System (ADS)

de Wijs, G. A.; Laskowski, R.; Blaha, P.; Havenith, R. W. A.; Kresse, G.; Marsman, M.

2017-02-01

We present a benchmark of the density functional linear response calculation of NMR shieldings within the gauge-including projector-augmented-wave method against all-electron augmented-plane-wave+local-orbital and uncontracted Gaussian basis set results for NMR shieldings in molecular and solid state systems. In general, excellent agreement between the aforementioned methods is obtained. Scalar relativistic effects are shown to be quite large for nuclei in molecules in the deshielded limit. The small component makes up a substantial part of the relativistic corrections.

NMR shieldings from density functional perturbation theory: GIPAW versus all-electron calculations.

PubMed

de Wijs, G A; Laskowski, R; Blaha, P; Havenith, R W A; Kresse, G; Marsman, M

2017-02-14

We present a benchmark of the density functional linear response calculation of NMR shieldings within the gauge-including projector-augmented-wave method against all-electron augmented-plane-wave+local-orbital and uncontracted Gaussian basis set results for NMR shieldings in molecular and solid state systems. In general, excellent agreement between the aforementioned methods is obtained. Scalar relativistic effects are shown to be quite large for nuclei in molecules in the deshielded limit. The small component makes up a substantial part of the relativistic corrections.

Gravitational waves from non-Abelian gauge fields at a tachyonic transition

NASA Astrophysics Data System (ADS)

Tranberg, Anders; Tähtinen, Sara; Weir, David J.

2018-04-01

We compute the gravitational wave spectrum from a tachyonic preheating transition of a Standard Model-like SU(2)-Higgs system. Tachyonic preheating involves exponentially growing IR modes, at scales as large as the horizon. Such a transition at the electroweak scale could be detectable by LISA, if these non-perturbatively large modes translate into non-linear dynamics sourcing gravitational waves. Through large-scale numerical simulations, we find that the spectrum of gravitational waves does not exhibit such IR features. Instead, we find two peaks corresponding to the Higgs and gauge field mass, respectively. We find that the gravitational wave production is reduced when adding non-Abelian gauge fields to a scalar-only theory, but increases when adding Abelian gauge fields. In particular, gauge fields suppress the gravitational wave spectrum in the IR. A tachyonic transition in the early Universe will therefore not be detectable by LISA, even if it involves non-Abelian gauge fields.

Black Hole Scrambling from Hydrodynamics.

PubMed

Grozdanov, Sašo; Schalm, Koenraad; Scopelliti, Vincenzo

2018-06-08

We argue that the gravitational shock wave computation used to extract the scrambling rate in strongly coupled quantum theories with a holographic dual is directly related to probing the system's hydrodynamic sound modes. The information recovered from the shock wave can be reconstructed in terms of purely diffusionlike, linearized gravitational waves at the horizon of a single-sided black hole with specific regularity-enforced imaginary values of frequency and momentum. In two-derivative bulk theories, this horizon "diffusion" can be related to late-time momentum diffusion via a simple relation, which ceases to hold in higher-derivative theories. We then show that the same values of imaginary frequency and momentum follow from a dispersion relation of a hydrodynamic sound mode. The frequency, momentum, and group velocity give the holographic Lyapunov exponent and the butterfly velocity. Moreover, at this special point along the sound dispersion relation curve, the residue of the retarded longitudinal stress-energy tensor two-point function vanishes. This establishes a direct link between a hydrodynamic sound mode at an analytically continued, imaginary momentum and the holographic butterfly effect. Furthermore, our results imply that infinitely strongly coupled, large-N_{c} holographic theories exhibit properties similar to classical dilute gases; there, late-time equilibration and early-time scrambling are also controlled by the same dynamics.

Black Hole Scrambling from Hydrodynamics

NASA Astrophysics Data System (ADS)

Grozdanov, Sašo; Schalm, Koenraad; Scopelliti, Vincenzo

2018-06-01

We argue that the gravitational shock wave computation used to extract the scrambling rate in strongly coupled quantum theories with a holographic dual is directly related to probing the system's hydrodynamic sound modes. The information recovered from the shock wave can be reconstructed in terms of purely diffusionlike, linearized gravitational waves at the horizon of a single-sided black hole with specific regularity-enforced imaginary values of frequency and momentum. In two-derivative bulk theories, this horizon "diffusion" can be related to late-time momentum diffusion via a simple relation, which ceases to hold in higher-derivative theories. We then show that the same values of imaginary frequency and momentum follow from a dispersion relation of a hydrodynamic sound mode. The frequency, momentum, and group velocity give the holographic Lyapunov exponent and the butterfly velocity. Moreover, at this special point along the sound dispersion relation curve, the residue of the retarded longitudinal stress-energy tensor two-point function vanishes. This establishes a direct link between a hydrodynamic sound mode at an analytically continued, imaginary momentum and the holographic butterfly effect. Furthermore, our results imply that infinitely strongly coupled, large-Nc holographic theories exhibit properties similar to classical dilute gases; there, late-time equilibration and early-time scrambling are also controlled by the same dynamics.

An improved understanding of the natural resonances of moonpools contained within floating rigid-bodies: Theory and application to oscillating water column devices

DOE PAGES

Bull, Diana L.

2015-09-23

The fundamental interactions between waves, a floating rigid-body, and a moonpool that is selectively open to atmosphere or enclosed to purposefully induce pressure fluctuations are investigated. The moonpool hydrodynamic characteristics and the hydrodynamic coupling to the rigid-body are derived implicitly through reciprocity relations on an array of field points. By modeling the free surface of the moonpool in this manner, an explicit hydrodynamic coupling term is included in the equations of motion. This coupling results in the migration of the moonpool's natural resonance frequency from the piston frequency to a new frequency when enclosed in a floating rigid-body. Two geometriesmore » that highlight distinct aspects of marine vessels and oscillating water column (OWC) renewable energy devices are analyzed to reveal the coupled natural resonance migration. The power performance of these two OWCs in regular waves is also investigated. The air chamber is enclosed and a three-dimensional, linear, frequency domain performance model that links the rigid-body to the moonpool through a linear resistive control strategy is detailed. Furthermore, an analytic expression for the optimal linear resistive control values in regular waves is presented.« less

An improved understanding of the natural resonances of moonpools contained within floating rigid-bodies: Theory and application to oscillating water column devices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bull, Diana L.

The fundamental interactions between waves, a floating rigid-body, and a moonpool that is selectively open to atmosphere or enclosed to purposefully induce pressure fluctuations are investigated. The moonpool hydrodynamic characteristics and the hydrodynamic coupling to the rigid-body are derived implicitly through reciprocity relations on an array of field points. By modeling the free surface of the moonpool in this manner, an explicit hydrodynamic coupling term is included in the equations of motion. This coupling results in the migration of the moonpool's natural resonance frequency from the piston frequency to a new frequency when enclosed in a floating rigid-body. Two geometriesmore » that highlight distinct aspects of marine vessels and oscillating water column (OWC) renewable energy devices are analyzed to reveal the coupled natural resonance migration. The power performance of these two OWCs in regular waves is also investigated. The air chamber is enclosed and a three-dimensional, linear, frequency domain performance model that links the rigid-body to the moonpool through a linear resistive control strategy is detailed. Furthermore, an analytic expression for the optimal linear resistive control values in regular waves is presented.« less

Canards in a minimal piecewise-linear square-wave burster

DOE Office of Scientific and Technical Information (OSTI.GOV)

Desroches, M.; Krupa, M.; Fernández-García, S., E-mail: soledad@us.es

We construct a piecewise-linear (PWL) approximation of the Hindmarsh-Rose (HR) neuron model that is minimal, in the sense that the vector field has the least number of linearity zones, in order to reproduce all the dynamics present in the original HR model with classical parameter values. This includes square-wave bursting and also special trajectories called canards, which possess long repelling segments and organise the transitions between stable bursting patterns with n and n + 1 spikes, also referred to as spike-adding canard explosions. We propose a first approximation of the smooth HR model, using a continuous PWL system, and show that itsmore » fast subsystem cannot possess a homoclinic bifurcation, which is necessary to obtain proper square-wave bursting. We then relax the assumption of continuity of the vector field across all zones, and we show that we can obtain a homoclinic bifurcation in the fast subsystem. We use the recently developed canard theory for PWL systems in order to reproduce the spike-adding canard explosion feature of the HR model as studied, e.g., in Desroches et al., Chaos 23(4), 046106 (2013).« less

Heavy and Heavy-Light Mesons in the Covariant Spectator Theory

NASA Astrophysics Data System (ADS)

Stadler, Alfred; Leitão, Sofia; Peña, M. T.; Biernat, Elmar P.

2018-05-01

The masses and vertex functions of heavy and heavy-light mesons, described as quark-antiquark bound states, are calculated with the Covariant Spectator Theory (CST). We use a kernel with an adjustable mixture of Lorentz scalar, pseudoscalar, and vector linear confining interaction, together with a one-gluon-exchange kernel. A series of fits to the heavy and heavy-light meson spectrum were calculated, and we discuss what conclusions can be drawn from it, especially about the Lorentz structure of the kernel. We also apply the Brodsky-Huang-Lepage prescription to express the CST wave functions for heavy quarkonia in terms of light-front variables. They agree remarkably well with light-front wave functions obtained in the Hamiltonian basis light-front quantization approach, even in excited states.

Quantum theory of the far-off-resonance continuous-wave Raman laser: Heisenberg-Langevin approach

NASA Astrophysics Data System (ADS)

Roos, P. A.; Murphy, S. K.; Meng, L. S.; Carlsten, J. L.; Ralph, T. C.; White, A. G.; Brasseur, J. K.

2003-07-01

We present the quantum theory of the far-off-resonance continuous-wave Raman laser using the Heisenberg-Langevin approach. We show that the simplified quantum Langevin equations for this system are mathematically identical to those of the nondegenerate optical parametric oscillator in the time domain with the following associations: pump ↔ pump, Stokes ↔ signal, and Raman coherence ↔ idler. We derive analytical results for both the steady-state behavior and the time-dependent noise spectra, using standard linearization procedures. In the semiclassical limit, these results match with previous purely semiclassical treatments, which yield excellent agreement with experimental observations. The analytical time-dependent results predict perfect photon statistics conversion from the pump to the Stokes and nonclassical behavior under certain operational conditions.

Wave Propagation Analysis of Edge Cracked Circular Beams under Impact Force

PubMed Central

Akbaş, Şeref Doğuşcan

2014-01-01

This paper presents responses of an edge circular cantilever beam under the effect of an impact force. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. The Kelvin–Voigt model for the material of the beam is used. The cracked beam is modelled as an assembly of two sub-beams connected through a massless elastic rotational spring. The considered problem is investigated within the Bernoulli-Euler beam theory by using energy based finite element method. The system of equations of motion is derived by using Lagrange's equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. In the study, the effects of the location of crack, the depth of the crack, on the characteristics of the reflected waves are investigated in detail. Also, the positions of the cracks are calculated by using reflected waves. PMID:24972050

Nonlinear Gyro-Landau-Fluid Equations

NASA Astrophysics Data System (ADS)

Raskolnikov, I.; Mattor, Nathan; Parker, Scott E.

1996-11-01

We present fluid equations which describe the effects of both linear and nonlinear Landau damping (wave-particle-wave effects). These are derived using a recently developed analytical method similar to renormalization group theory. (Scott E. Parker and Daniele Carati, Phys. Rev. Lett. 75), 441 (1995). In this technique, the phase space structure inherent in Landau damping is treated analytically by building a ``renormalized collisionality'' onto a bare collisionality (which may be taken as vanishingly small). Here we apply this technique to the nonlinear ion gyrokinetic equation in slab geometry, obtaining nonlinear fluid equations for density, parallel momentum and heat. Wave-particle resonances are described by two functions appearing in the heat equation: a renormalized ``collisionality'' and a renormalized nonlinear coupling coeffient. It will be shown that these new equations may correct a deficiency in existing gyrofluid equations, (G. W. Hammett and F. W. Perkins, Phys. Rev. Lett. 64,) 3019 (1990). which can severely underestimate the strength of nonlinear interaction in regimes where linear resonance is strong. (N. Mattor, Phys. Fluids B 4,) 3952 (1992).

2D Heisenberg Triangular Antiferromagnet in Ba3CoSb2O9

NASA Astrophysics Data System (ADS)

Biffin, Alun; Demmel, Franz; Walker, Helen; Hayward, Michael; Coldea, Radu

We present inelastic neutron scattering (INS) experiments on the triangular antiferromagnet (TAF) Ba3CoSb2O9. High energy INS measurements allowed the crystal field levels of Co2+ ions to be resolved, and subsequently the terms relevant to its single ion Hamiltonian to be derived with the conclusion that the ions have a Jeff = 1 / 2 doublet as their groundstate with relatively weak local trigonal distortion of CoO6 octahedra. The result is a system which is a rare realisation of the canonical spin 1/2 Heisenberg TAF. Following this, low energy, high-resolution INS experiments have been performed which reveal the spin wave excitations emanating from the 120° ordered phase below TN = 3 . 8 K. However, as will be seen, linear spin wave calculations are not sufficient to describe all the features of the data, and these anomalies hint at quantum dynamics beyond linear spin wave theory within this realisation of the canonical S=1/2 TAF system.

Effects of orography on planetary scale flow

NASA Technical Reports Server (NTRS)

Smith, R. B.

1986-01-01

The earth's orography is composed of a wide variety of scales, each contributing to the spectrum of atmospheric motions. A well studied subject (originating with Charney and Eliassen) is the direct forcing of planetary scale waves by the planetary scale orography: primarily the Tibetan plateau and the Rockies. However, because of the non-linear terms in the equations of dynamic meteorology, even the smallest scales of mountain induced flow can contribute to the planetary scale if the amplitude of the small scale disturbance is sufficintly large. Two possible mechanisms for this are illustrated. First, preferentially located lee cyclones can force planetary waves by their meridional transport of heat and momentum (Hansen and Chen). Recent theories are helping to explain the phenomena of lee cyclogenesis (e.g., Smith, 1984, J.A.S.). Second, mesoscale mountain wave and severe downslope wind phenomena produce such a large local drag, that planetary scale waves can be produced. The mechanism of upscale transfer is easy to understand in this case as the standing planetary scale wave has a wavelength which depends on the mean structure of the atmosphere, and not on the width of the mountain (just as in small scale lee wave theory). An example of a theoretical description of a severe wind flow with very large drag is shown.

Amplitude variations of whistler-mode signals caused by their interaction with energetic electrons of the magnetosphere

NASA Technical Reports Server (NTRS)

Bernard, L. C.

1973-01-01

Whistler mode waves that propagate through the magnetosphere exchange energy with energetic electrons by wave-particle interaction mechanisms. Using linear theory, a detailed investigation is presented of the resulting amplitude variations of the wave as it propagates. Arbitrary wave frequency and direction of propagation are considered. A general class of electron distributions that are nonseparable in particle energy and pitch-angle is proposed. It is found that the proposed distribution model is consistent with available whistler and particle observations. This model yields insignificant amplitude variation over a large frequency band, a feature commonly observed in whistler data. This feature implies a certain equilibrium between waves and particles in the magnetosphere over a wide spread of particle energy, and is relevant to plasma injection experiments and to monitoring the distribution of energetic electrons in the magnetosphere.

Upstream-advancing waves generated by a current over a sinusoidal bed

NASA Astrophysics Data System (ADS)

Kyotoh, Harumichi; Fukushima, Masaki

1997-07-01

Upstream-advancing waves are observed in open channel flows over a fixed sinusoidal bed with large amplitude, when the Froude number is less than the resonant value, at which stream velocity is equal to the celerity of the wave with wavelength equal to that of the bottom surface. Their wavelength is about 3-6 times as long as the bottom wavelength and the celerity is close to that obtained from potential flow theory. Therefore, the wavelength of upstream-advancing waves is determined by linear stability analyses assuming that they are induced by the Benjamin-Feir-type instability of steady flow. Here, two formulas for the wavelength with different scaling are introduced and compared with experiment. In addition, the mechanisms of upstream-advancing waves are investigated qualitatively using the forced Schrödinger equation.

Stability properties of solitary waves for fractional KdV and BBM equations

NASA Astrophysics Data System (ADS)

Angulo Pava, Jaime

2018-03-01

This paper sheds new light on the stability properties of solitary wave solutions associated with Korteweg-de Vries-type models when the dispersion is very low. Using a compact, analytic approach and asymptotic perturbation theory, we establish sufficient conditions for the existence of exponentially growing solutions to the linearized problem and so a criterium of spectral instability of solitary waves is obtained for both models. Moreover, the nonlinear stability and spectral instability of the ground state solutions for both models is obtained for some specific regimen of parameters. Via a Lyapunov strategy and a variational analysis, we obtain the stability of the blow-up of solitary waves for the critical fractional KdV equation. The arguments presented in this investigation show promise for use in the study of the instability of traveling wave solutions of other nonlinear evolution equations.

Spin-Wave Chirality and Its Manifestations in Antiferromagnets

NASA Astrophysics Data System (ADS)

Proskurin, Igor; Stamps, Robert L.; Ovchinnikov, Alexander S.; Kishine, Jun-ichiro

2017-10-01

As first demonstrated by Tang and Cohen in chiral optics, the asymmetry in the rate of electromagnetic energy absorption between left and right enantiomers is determined by an optical chirality density. Here, we demonstrate that this effect can exist in magnetic spin systems. By constructing a formal analogy with electrodynamics, we show that in antiferromagnets with broken chiral symmetry, the asymmetry in local spin-wave energy absorption is proportional to a spin-wave chirality density, which is a direct counterpart of optical zilch. We propose that injection of a pure spin current into an antiferromagnet may serve as a chiral symmetry breaking mechanism, since its effect in the spin-wave approximation can be expressed in terms of additional Lifshitz invariants. We use linear response theory to show that the spin current induces a nonequilibrium spin-wave chirality density.

The dynamics of magnetic Rossby waves in spherical dynamo simulations: A signature of strong-field dynamos?

NASA Astrophysics Data System (ADS)

Hori, K.; Teed, R. J.; Jones, C. A.

2018-03-01

We investigate slow magnetic Rossby waves in convection-driven dynamos in rotating spherical shells. Quasi-geostrophic waves riding on a mean zonal flow may account for some of the geomagnetic westward drifts and have the potential to allow the toroidal field strength within the planetary fluid core to be estimated. We extend the work of Hori et al. (2015) to include a wider range of models, and perform a detailed analysis of the results. We find that a predicted dispersion relation matches well with the longitudinal drifts observed in our strong-field dynamos. We discuss the validity of our linear theory, since we also find that the nonlinear Lorentz terms influence the observed waveforms. These wave motions are excited by convective instability, which determines the preferred azimuthal wavenumbers. Studies of linear rotating magnetoconvection have suggested that slow magnetic Rossby modes emerge in the magnetostrophic regime, in which the Lorentz and Coriolis forces are in balance in the vorticity equation. We confirm this to be predominant balance for the slow waves we have detected in nonlinear dynamo systems. We also show that a completely different wave regime emerges if the magnetic field is not present. Finally we report the corresponding radial magnetic field variations observed at the surface of the shell in our simulations and discuss the detectability of these waves in the geomagnetic secular variation.

A Weakly Nonlinear Model for the Damping of Resonantly Forced Density Waves in Dense Planetary Rings

NASA Astrophysics Data System (ADS)

Lehmann, Marius; Schmidt, Jürgen; Salo, Heikki

2016-10-01

In this paper, we address the stability of resonantly forced density waves in dense planetary rings. Goldreich & Tremaine have already argued that density waves might be unstable, depending on the relationship between the ring’s viscosity and the surface mass density. In the recent paper Schmidt et al., we have pointed out that when—within a fluid description of the ring dynamics—the criterion for viscous overstability is satisfied, forced spiral density waves become unstable as well. In this case, linear theory fails to describe the damping, but nonlinearity of the underlying equations guarantees a finite amplitude and eventually a damping of the wave. We apply the multiple scale formalism to derive a weakly nonlinear damping relation from a hydrodynamical model. This relation describes the resonant excitation and nonlinear viscous damping of spiral density waves in a vertically integrated fluid disk with density dependent transport coefficients. The model consistently predicts density waves to be (linearly) unstable in a ring region where the conditions for viscous overstability are met. Sufficiently far away from the Lindblad resonance, the surface mass density perturbation is predicted to saturate to a constant value due to nonlinear viscous damping. The wave’s damping lengths of the model depend on certain input parameters, such as the distance to the threshold for viscous overstability in parameter space and the ground state surface mass density.

Perturbations of the Richardson number field by gravity waves

NASA Technical Reports Server (NTRS)

Wurtele, M. G.; Sharman, R. D.

1985-01-01

An analytic solution is presented for a stratified fluid of arbitrary constant Richardson number. By computer aided analysis the perturbation fields, including that of the Richardson number can be calculated. The results of the linear analytic model were compared with nonlinear simulations, leading to the following conclusions: (1) the perturbations in the Richardson number field, when small, are produced primarily by the perturbations of the shear; (2) perturbations of in the Richardson number field, even when small, are not symmetric, the increase being significantly larger than the decrease (the linear analytic solution and the nonlinear simulations both confirm this result); (3) as the perturbations grow, this asymmetry increases, but more so in the nonlinear simulations than in the linear analysis; (4) for large perturbations of the shear flow, the static stability, as represented by N2, is the dominating mechanism, becoming zero or negative, and producing convective overturning; and (5) the convectional measure of linearity in lee wave theory, NH/U, is no longer the critical parameter (it is suggested that (H/u sub 0) (du sub 0/dz) takes on this role in a shearing flow).

Modeling Elastic Wave Propagation from an Underground Chemical Explosion Using Higher Order Finite Difference Approximation: Theory, Validation and Application to SPE

NASA Astrophysics Data System (ADS)

Hirakawa, E. T.; Ezzedine, S. M.; Petersson, A.; Sjogreen, B.; Vorobiev, O.; Pitarka, A.; Antoun, T.; Walter, W. R.

2016-12-01

Motions from underground explosions are governed by non-linear hydrodynamic response of material. However, the numerical calculation of this non-linear constitutive behavior is computationally intensive in contrast to the elastic and acoustic linear wave propagation solvers. Here, we develop a hybrid modeling approach with one-way hydrodynamic-to-elastic coupling in three dimensions in order to propagate explosion generated ground motions from the non-linear near-source region to the far-field. Near source motions are computed using GEODYN-L, a Lagrangian hydrodynamics code for high-energy loading of earth materials. Motions on a dense grid of points sampled on two nested shells located beyond the non-linear damaged zone are saved, and then passed to SW4, an anelastic anisotropic fourth order finite difference code for seismic wave modeling. Our coupling strategy is based on the decomposition and uniqueness theorems where motions are introduced into SW4 as a boundary source and continue to propagate as elastic waves at a much lower computational cost than by using GEODYN-L to cover the entire near- and the far-field domain. The accuracy of the numerical calculations and the coupling strategy is demonstrated in cases with a purely elastic medium as well as non-linear medium. Our hybrid modeling approach is applied to SPE-4' and SPE-5 which are the most recent underground chemical explosions conducted at the Nevada National Security Site (NNSS) where the Source Physics Experiments (SPE) are performed. Our strategy by design is capable of incorporating complex non-linear effects near the source as well as volumetric and topographic material heterogeneity along the propagation path to receiver, and provides new prospects for modeling and understanding explosion generated seismic waveforms. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-ABS-698608.

Oblique wave trapping by vertical permeable membrane barriers located near a wall

NASA Astrophysics Data System (ADS)

Koley, Santanu; Sahoo, Trilochan

2017-12-01

The effectiveness of a vertical partial flexible porous membrane wave barrier located near a rigid vertical impermeable seawall for trapping obliquely incident surface gravity waves are analyzed in water of uniform depth under the assumption of linear water wave theory and small amplitude membrane barrier response. From the general formulation of the submerged membrane barrier, results for bottom-standing and surface-piercing barriers are computed and analyzed in special cases. Using the eigenfunction expansion method, the boundary-value problems are converted into series relations and then the required unknowns are obtained using the least squares approximation method. Various physical quantities of interests like reflection coefficient, wave energy dissipation, wave forces acting on the membrane barrier and the seawall are computed and analyzed for different values of the wave and structural parameters. The study will be useful in the design of the membrane wave barrier for the creation of tranquility zone in the lee side of the barrier to protect the seawall.

The second-order theory of electromagnetic hot ion beam instabilities. [in interplanetary magnetic field

NASA Technical Reports Server (NTRS)

Gary, S. P.; Tokar, R. L.

1985-01-01

The present investigation is concerned with the application of a second-order theory for electromagnetic instabilities in a collisionless plasma to two modes which resonate with hot ion beams. The application of the theory is strictly limited to the linear growth phase. However, the application of the theory may be extended to obtain a description of the beam at postsaturation if the wave-beam resonance is sufficiently broad in velocity space. Under the considered limitations, it is shown that, as in the cold beam case, the fluctuating fields do not gain appreciable momentum and that the primary exchange of momentum is between the beam and main component.

Bounded Error Schemes for the Wave Equation on Complex Domains

NASA Technical Reports Server (NTRS)

Abarbanel, Saul; Ditkowski, Adi; Yefet, Amir

1998-01-01

This paper considers the application of the method of boundary penalty terms ("SAT") to the numerical solution of the wave equation on complex shapes with Dirichlet boundary conditions. A theory is developed, in a semi-discrete setting, that allows the use of a Cartesian grid on complex geometries, yet maintains the order of accuracy with only a linear temporal error-bound. A numerical example, involving the solution of Maxwell's equations inside a 2-D circular wave-guide demonstrates the efficacy of this method in comparison to others (e.g. the staggered Yee scheme) - we achieve a decrease of two orders of magnitude in the level of the L2-error.

Properties of Nonlinear Dynamo Waves

NASA Technical Reports Server (NTRS)

Tobias, S. M.

1997-01-01

Dynamo theory offers the most promising explanation of the generation of the sun's magnetic cycle. Mean field electrodynamics has provided the platform for linear and nonlinear models of solar dynamos. However, the nonlinearities included are (necessarily) arbitrarily imposed in these models. This paper conducts a systematic survey of the role of nonlinearities in the dynamo process, by considering the behaviour of dynamo waves in the nonlinear regime. It is demonstrated that only by considering realistic nonlinearities that are non-local in space and time can modulation of the basic dynamo wave he achieved. Moreover, this modulation is greatest when there is a large separation of timescales provided by including a low magnetic Prandtl number in the equation for the velocity perturbations.

Generalized radially self-accelerating helicon beams.

PubMed

Vetter, Christian; Eichelkraut, Toni; Ornigotti, Marco; Szameit, Alexander

2014-10-31

We report, in theory and experiment, on a new class of optical beams that are radially self-accelerating and nondiffracting. These beams continuously evolve on spiraling trajectories while maintaining their amplitude and phase distribution in their rotating rest frame. We provide a detailed insight into the theoretical origin and characteristics of radial self-acceleration and prove our findings experimentally. As radially self-accelerating beams are nonparaxial and a solution to the full scalar Helmholtz equation, they can be implemented in many linear wave systems beyond optics, from acoustic and elastic waves to surface waves in fluids and soft matter. Our work generalized the study of classical helicon beams to a complete set of solutions for rotating complex fields.

Shallow Water Quasi-Geostrophic Theory on the Sphere

NASA Astrophysics Data System (ADS)

Schubert, Wayne H.; Taft, Richard K.; Silvers, Levi G.

2009-02-01

Quasi-geostrophic theory forms the basis for much of our understanding of mid-latitude atmospheric dynamics. The theory is typically presented in either its f-plane form or its β-plane form. However, for many applications, including diagnostic use in global climate modeling, a fully spherical version would be most useful. Such a global theory does in fact exist and has for many years, but few in the scientific community seem to have ever been aware of it. In the context of shallow water dynamics, it is shown that the spherical version of quasigeostrophic theory is easily derived (re-derived) based on a partitioning of the flow between nondivergent and irrotational components, as opposed to a partitioning between geostrophic and ageostrophic components. In this way, the invertibility principle is expressed as a relation between the streamfunction and the potential vorticity, rather than between the geopotential and the potential vorticity. This global theory is then extended by showing that the invertibility principle can be solved analytically using spheroidal harmonic transforms, an advancement that greatly improves the usefulness of this "forgotten" theory. When the governing equation for the time evolution of the potential vorticity is linearized about a state of rest, a simple Rossby-Haurwitz wave dispersion relation is derived and examined. These waves have a horizontal structure described by spheroidal harmonics, and the Rossby-Haurwitz wave frequencies are given in terms of the eigenvalues of the spheroidal harmonic operator. Except for sectoral harmonics with low zonal wavenumber, the quasi-geostrophic Rossby-Haurwitz frequencies agree very well with those calculated from the primitive equations. One of the many possible applications of spherical quasi-geostrophic theory is to the study of quasi-geostrophic turbulence on the sphere. In this context, the theory is used to derive an anisotropic Rhines barrier in three-dimensional wavenumber space.

Mode-coupling and wave-particle interactions for unstable ion-acoustic waves.

NASA Technical Reports Server (NTRS)

Martin, P.; Fried, B. D.

1972-01-01

A theory for the spatial development of linearly unstable, coupled waves is presented in which both quasilinear and mode-coupling effects are treated in a self-consistent manner. Steady-state excitation of two waves is assumed at the boundary x = 0, the plasma being homogeneous in the y and z directions. Coupled equations are derived for the x dependence of the amplitudes of the primary waves and the secondary waves, correct through terms of second order in the wave amplitude, but without the usual approximation of small growth rates. This general formalism is then applied to the case of coupled ion-acoustic waves driven unstable by an ion beam streaming in the direction of the x axis. If the modifications of the ion beam by the waves (quasilinear effects) are ignored, explosive instabilities (singularities in all of the amplitudes at finite x) are found even when all of the waves have positive energy. If these wave-particle interactions are included, the solutions are no longer singular, and all of the amplitudes have finite maxima.

EXPERIMENTAL DETERMINATION OF WHISTLER WAVE DISPERSION RELATION IN THE SOLAR WIND

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stansby, D.; Horbury, T. S.; Chen, C. H. K.

2016-09-20

The origins and properties of large-amplitude whistler wavepackets in the solar wind are still unclear. In this Letter, we utilize single spacecraft electric and magnetic field waveform measurements from the ARTEMIS mission to calculate the plasma frame frequency and wavevector of individual wavepackets over multiple intervals. This allows direct comparison of experimental measurements with theoretical dispersion relations to identify the observed waves as whistler waves. The whistlers are right-hand circularly polarized, travel anti-sunward, and are aligned with the background magnetic field. Their dispersion is strongly affected by the local electron parallel beta in agreement with linear theory. The properties measuredmore » are consistent with the electron heat flux instability acting in the solar wind to generate these waves.« less

Influence of mean radial electric field on particle transport induced by RMPs in tokamak plasmas

NASA Astrophysics Data System (ADS)

Chen, Dunqiang; Xu, Yingfeng; Wang, Shaojie

2018-06-01

The quasi-linear theory of the particle diffusion coefficient including the finite Larmor radius effect and the mean radial electric field ( E r without shear) in a stochastic magnetic field is derived. The theory has been verified by comparing with test particle simulations and previous theory. It is found that E r can shift the wave-particle resonance position. The Er-shift effect mainly modifies the ion diffusion coefficients and leads to the modification of ion particle flux. By using the ambipolar condition, we obtained the balanced flux at the edge of a tokamak plasma and found good agreement with recent experimental observations.

A simple derivation of the exact quasiparticle theory and its extension to arbitrary initial excited eigenstates.

PubMed

Ohno, Kaoru; Ono, Shota; Isobe, Tomoharu

2017-02-28

The quasiparticle (QP) energies, which are minus of the energies required by removing or produced by adding one electron from/to the system, corresponding to the photoemission or inverse photoemission (PE/IPE) spectra, are determined together with the QP wave functions, which are not orthonormal and even not linearly independent but somewhat similar to the normal spin orbitals in the theory of the configuration interaction, by self-consistently solving the QP equation coupled with the equation for the self-energy. The electron density, kinetic, and all interaction energies can be calculated using the QP wave functions. We prove in a simple way that the PE/IPE spectroscopy and therefore this QP theory can be applied to an arbitrary initial excited eigenstate. In this proof, we show that the energy-dependence of the self-energy is not an essential difficulty, and the QP picture holds exactly if there is no relaxation mechanism in the system. The validity of the present theory for some initial excited eigenstates is tested using the one-shot GW approximation for several atoms and molecules.

Microhartree precision in density functional theory calculations

NASA Astrophysics Data System (ADS)

Gulans, Andris; Kozhevnikov, Anton; Draxl, Claudia

2018-04-01

To address ultimate precision in density functional theory calculations we employ the full-potential linearized augmented plane-wave + local-orbital (LAPW + lo) method and justify its usage as a benchmark method. LAPW + lo and two completely unrelated numerical approaches, the multiresolution analysis (MRA) and the linear combination of atomic orbitals, yield total energies of atoms with mean deviations of 0.9 and 0.2 μ Ha , respectively. Spectacular agreement with the MRA is reached also for total and atomization energies of the G2-1 set consisting of 55 molecules. With the example of α iron we demonstrate the capability of LAPW + lo to reach μ Ha /atom precision also for periodic systems, which allows also for the distinction between the numerical precision and the accuracy of a given functional.

The effect of shear stress on solitary waves in arteries.

PubMed

Demiray, H

1997-09-01

In the present work, we study the propagation of solitary waves in a prestressed thick walled elastic tube filled with an incompressible inviscid fluid. In order to include the geometric dispersion in the analysis the wall inertia and shear deformation effects are taken into account for the inner pressure-cross-sectional area relation. Using the reductive perturbation technique, the propagation of weakly non-linear waves in the long-wave approximation is examined. It is shown that, contrary to thin tube theories, the present approach makes it possible to have solitary waves even for a Mooney-Rivlin (M-R) material. Due to dependence of the coefficients of the governing Korteweg-deVries equation on initial deformation, the solution profile changes with inner pressure and the axial stretch. The variation of wave profiles for a class of elastic materials are depicted in graphic forms. As might be seen from these illustrations, with increasing thickness ratio, the profile of solitary wave is steepened for a M-R material but it is broadened for biological tissue.

Theory of Gyrotron Traveling Wave Amplifiers at Harmonics of the Gyration Frequency

NASA Astrophysics Data System (ADS)

Li, Qiangfa

In developing gyrotrons at millimeter and submillimeter wavelengths, a means of operation at lower applied magnetic fields is desirable because of the size and weight of convetional magnets, and the expense and complexity of cryogenic magnets. This requirement can be met by operating the devices at higher harmonics of the electron gyration frequency. In the present work, a unified theory is developed for the gyrotron traveling wave amplifers (gyro-TWA) at harmonics of the gyration frequency, both in the nonlinear regime and in the linear regime. This theory can be applied to a wide class of waveguide cross sections, arbitrary harmonic number, any waveguide mode, and generalized electron beam model. The fields in the beam-field interaction region in the waveguide are expressed in the form of an infinite series of multipoles expanded around the guiding center of the electrons. A set of equations governing the nonlinear behavior of the gyro-TWA is derived. A general dispersion equation is derived both from that set of nonlinear equations by an iteration method and from plasma kinetic theory. The latter is employed to analyze gyro-TWA devices in a systematic and generalized manner. The Laplace transformation is introduced to allow inclusion of the initial values at the input end of the waveguide. From the linear theory it is found that for a gyrotron working at s-th gyration harmonic the electrons can interact only with the 2s-th order multipole field component. It is also found that a higher order waveguide mode is not always better than a lower order mode for the gyro-TWA working at higher harmonics. A novel out-ridged waveguide is proposed and analyzed for the use in gyrotrons. The prominent features of this new waveguide include simplicity of manufacture, freedom from local modes, good separation of lower order modes, high power handling ability, and high gain per unit length at higher gyration harmonics. A comparison of the gyro-TWAs with several different waveguide structures, such as the out-ridged, magnetron-type, rectangular and circular waveguides, is made through numerical examples of the gain-frequency curves computed from the linear kinetic theory.

Space-time properties of wind-waves: a new look at directional wave distributions

NASA Astrophysics Data System (ADS)

Leckler, Fabien; Ardhuin, Fabrice; Benetazzo, Alvise; Fedele, Francesco; Bergamasco, Filippo; Dulov, Vladimir

2014-05-01

Few accurate observed directional wave spectra are available in the literature at spatial scales ranging between 0.5 and 5.0 m. These intermediate wave scales, relevant for air-sea fluxes and remote sensing are also expected to feed back on the dominant wave properties through wave generation. These wave scales can be prolifically investigated using the well-known optical stereo methods that provides, from a couple of synchronized images, instantaneous representation of wave elevations over a given sea surface. Thus, two stereo systems (the so-called Wave Acquisition Stereo Systems, WASS) were deployed on top of the deep-water platform at Katsiveli, in the Black Sea, in September 2011 and 2013. From image pairs taken by the couple of synchronized high-resolution cameras, ocean surfaces have been reconstructed by stereo-triangulation. Here we analyze sea states corresponding to mean wind speeds of 11 to 14 m/s, and young wave ages of 0.35 to 0.42, associated to significant wave heights of 0.3 to 0.55m. As a result, four 12 Hz time evolutions of sea surface elevation maps with areas about 10 x 10 m2 have been obtained for sequence durations ranging between 15 and 30 minutes, and carefully validated with nearby capacitance wave gauges. The evolving free surfaces elevations were processed into frequency-wavenumber-direction 3D spectra. We found that wave energy chiefly follows the dispersion relation up to frequency of 1.6Hz and wavenumber of 10 rad/m, corresponding to wavelength of about 0.5 m. These spectra also depict well the energy contribution from non-linear waves, which is quantified and compared to theory. A strong bi-modality of the linear spectra was also observed, with the angle of the two maxima separated by about 160 degrees. Furthermore, spectra also exhibit the bimodality of the non-linear part. Integrated over positive frequencies to obtain wavenumber spectra unambiguous in direction, the bimodality of the spectra is partially hidden by the energy from second order waves, in particular from wave harmonics of the peak waves. However, the obtained spreading functions and integrals question the isotropy of the spectrum at high frequencies, generally assumed to explain deep water pressure measurement.

Many-body problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Parry, W.E.

1973-01-01

An introduction is given to techniques used in the many-body problem, and a reference book is given for those techniques. Sevcral different formulations of the techniques, and their interrelations, are discussed, to prepare the reader for the published literature. Examples are taken mostly from the physics of solids, fluids and plasmas. Second quantization, perturbation theory, Green functions and correlation functions, examples in the use of diagrammatic perturbation theory, the equation of motion method, magnetism (the drone-fermion representation), linear response and transport processes, niany- body systems at zero temperature, the variational principle and pair-wave approximation. (UK)

Electronic, thermoelectric and transport properties of cesium cadmium trifluoride: A DFT study

NASA Astrophysics Data System (ADS)

Abraham, Jisha Annie; Pagare, G.; Sanyal, Sankar P.

2018-04-01

The full potential linearized augmented plane wave method based on density functional theory is employed to investigate the electronic structure of CsCdF3. The electronic properties of this compound have been studied from the band structure plot and density of states. The presence of indirect energy gap reveals its insulating nature. Using constant relaxation time, the electrical conductivity, electronic thermal conductivity, Seebeck coefficient and figure of merit are calculated by using Boltzmann transport theory. We have also studied the temperature dependence of thermoelectric properties of this compound.

Acoustic and elastic multiple scattering and radiation from cylindrical structures

NASA Astrophysics Data System (ADS)

Amirkulova, Feruza Abdukadirovna

Multiple scattering (MS) and radiation of waves by a system of scatterers is of great theoretical and practical importance and is required in a wide variety of physical contexts such as the implementation of "invisibility" cloaks, the effective parameter characterization, and the fabrication of dynamically tunable structures, etc. The dissertation develops fast, rapidly convergent iterative techniques to expedite the solution of MS problems. The formulation of MS problems reduces to a system of linear algebraic equations using Graf's theorem and separation of variables. The iterative techniques are developed using Neumann expansion and Block Toeplitz structure of the linear system; they are very general, and suitable for parallel computations and a large number of MS problems, i.e. acoustic, elastic, electromagnetic, etc., and used for the first time to solve MS problems. The theory is implemented in Matlab and FORTRAN, and the theoretical predictions are compared to computations obtained by COMSOL. To formulate the MS problem, the transition matrix is obtained by analyzing an acoustic and an elastic single scattering of incident waves by elastic isotropic and anisotropic solids. The mathematical model of wave scattering from multilayered cylindrical and spherical structures is developed by means of an exact solution of dynamic 3D elasticity theory. The recursive impedance matrix algorithm is derived for radially heterogeneous anisotropic solids. An explicit method for finding the impedance in piecewise uniform, transverse-isotropic material is proposed; the solution is compared to elasticity theory solutions involving Buchwald potentials. Furthermore, active exterior cloaking devices are modeled for acoustic and elastic media using multipole sources. A cloaking device can render an object invisible to some incident waves as seen by some external observer. The active cloak is generated by a discrete set of multipole sources that destructively interfere with an incident wave to produce zero total field over a finite spatial region. The approach precisely determines the necessary source amplitudes and enables a cloaked region to be determined using Graf's theorem. To apply the approach, the infinite series of multipole expansions are truncated, and the accuracy of cloaking is studied by modifying the truncation parameter.

Collisional damping rates for electron plasma waves reassessed

DOE Office of Scientific and Technical Information (OSTI.GOV)

Banks, J. W.; Brunner, S.; Berger, R. L.

Collisional damping of electron plasma waves, the primary damping for high phase velocity waves, is proportional to the electron-ion collision rate, ν ei,th. Here in this work, it is shown that the damping rate normalized to ν ei,th depends on the charge state, Z, on the magnitude of ν ei,th and the wave number k in contrast with the commonly used damping rate in plasma wave research. Only for weak collision rates in low-Z plasmas for which the electron self-collision rate is comparable to the electron-ion collision rate is the damping rate given by the commonly accepted value. The resultmore » presented here corrects the result presented in textbooks at least as early as 1973. Lastly, the complete linear theory requires the inclusion of both electron-ion pitch-angle and electron-electron scattering, which itself contains contributions to both pitch-angle scattering and thermalization.« less

Predicting electromagnetic ion cyclotron wave amplitude from unstable ring current plasma conditions

DOE PAGES

Fu, Xiangrong; Cowee, Misa M.; Jordanova, Vania K.; ...

2016-11-01

Electromagnetic ion cyclotron (EMIC) waves in the Earth's inner magnetosphere are enhanced fluctuations driven unstable by ring current ion temperature anisotropy. EMIC waves can resonate with relativistic electrons and play an important role in precipitation of MeV radiation belt electrons. In this study, we investigate the excitation and saturation of EMIC instability in a homogeneous plasma using both linear theory and nonlinear hybrid simulations. We have explored a four-dimensional parameter space, carried out a large number of simulations, and derived a scaling formula that relates the saturation EMIC wave amplitude to initial plasma conditions. Finally, such scaling can be usedmore » in conjunction with ring current models like ring current-atmosphere interactions model with self-consistent magnetic field to provide global dynamic EMIC wave maps that will be more accurate inputs for radiation belt modeling than statistical models.« less

Collisional damping rates for electron plasma waves reassessed

DOE PAGES

Banks, J. W.; Brunner, S.; Berger, R. L.; ...

2017-10-13

Collisional damping of electron plasma waves, the primary damping for high phase velocity waves, is proportional to the electron-ion collision rate, ν ei,th. Here in this work, it is shown that the damping rate normalized to ν ei,th depends on the charge state, Z, on the magnitude of ν ei,th and the wave number k in contrast with the commonly used damping rate in plasma wave research. Only for weak collision rates in low-Z plasmas for which the electron self-collision rate is comparable to the electron-ion collision rate is the damping rate given by the commonly accepted value. The resultmore » presented here corrects the result presented in textbooks at least as early as 1973. Lastly, the complete linear theory requires the inclusion of both electron-ion pitch-angle and electron-electron scattering, which itself contains contributions to both pitch-angle scattering and thermalization.« less

Rarefaction-driven Rayleigh–Taylor instability. Part 1. Diffuse-interface linear stability measurements and theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Morgan, R. V.; Likhachev, O. A.; Jacobs, J. W.

Theory and experiments are reported that explore the behaviour of the Rayleigh–Taylor instability initiated with a diffuse interface. Experiments are performed in which an interface between two gases of differing density is made unstable by acceleration generated by a rarefaction wave. Well-controlled, diffuse, two-dimensional and three-dimensional, single-mode perturbations are generated by oscillating the gases either side to side, or vertically for the three-dimensional perturbations. The puncturing of a diaphragm separating a vacuum tank beneath the test section generates a rarefaction wave that travels upwards and accelerates the interface downwards. This rarefaction wave generates a large, but non-constant, acceleration of the order ofmore » $$1000g_{0}$$, where$$g_{0}$$is the acceleration due to gravity. Initial interface thicknesses are measured using a Rayleigh scattering diagnostic and the instability is visualized using planar laser-induced Mie scattering. Growth rates agree well with theoretical values, and with the inviscid, dynamic diffusion model of Duffet al. (Phys. Fluids, vol. 5, 1962, pp. 417–425) when diffusion thickness is accounted for, and the acceleration is weighted using inviscid Rayleigh–Taylor theory. The linear stability formulation of Chandrasekhar (Proc. Camb. Phil. Soc., vol. 51, 1955, pp. 162–178) is solved numerically with an error function diffusion profile using the Riccati method. This technique exhibits good agreement with the dynamic diffusion model of Duffet al. for small wavenumbers, but produces larger growth rates for large-wavenumber perturbations. Asymptotic analysis shows a$$1/k^{2}$$decay in growth rates as$$k\\rightarrow \\infty$$for large-wavenumber perturbations.« less

Rarefaction-driven Rayleigh–Taylor instability. Part 1. Diffuse-interface linear stability measurements and theory

DOE PAGES

Morgan, R. V.; Likhachev, O. A.; Jacobs, J. W.

2016-02-15

Theory and experiments are reported that explore the behaviour of the Rayleigh–Taylor instability initiated with a diffuse interface. Experiments are performed in which an interface between two gases of differing density is made unstable by acceleration generated by a rarefaction wave. Well-controlled, diffuse, two-dimensional and three-dimensional, single-mode perturbations are generated by oscillating the gases either side to side, or vertically for the three-dimensional perturbations. The puncturing of a diaphragm separating a vacuum tank beneath the test section generates a rarefaction wave that travels upwards and accelerates the interface downwards. This rarefaction wave generates a large, but non-constant, acceleration of the order ofmore » $$1000g_{0}$$, where$$g_{0}$$is the acceleration due to gravity. Initial interface thicknesses are measured using a Rayleigh scattering diagnostic and the instability is visualized using planar laser-induced Mie scattering. Growth rates agree well with theoretical values, and with the inviscid, dynamic diffusion model of Duffet al. (Phys. Fluids, vol. 5, 1962, pp. 417–425) when diffusion thickness is accounted for, and the acceleration is weighted using inviscid Rayleigh–Taylor theory. The linear stability formulation of Chandrasekhar (Proc. Camb. Phil. Soc., vol. 51, 1955, pp. 162–178) is solved numerically with an error function diffusion profile using the Riccati method. This technique exhibits good agreement with the dynamic diffusion model of Duffet al. for small wavenumbers, but produces larger growth rates for large-wavenumber perturbations. Asymptotic analysis shows a$$1/k^{2}$$decay in growth rates as$$k\\rightarrow \\infty$$for large-wavenumber perturbations.« less

Physical uniqueness of higher-order Korteweg-de Vries theory for continuously stratified fluids without background shear

NASA Astrophysics Data System (ADS)

Shimizu, Kenji

2017-10-01

The 2nd-order Korteweg-de Vries (KdV) equation and the Gardner (or extended KdV) equation are often used to investigate internal solitary waves, commonly observed in oceans and lakes. However, application of these KdV-type equations for continuously stratified fluids to geophysical problems is hindered by nonuniqueness of the higher-order coefficients and the associated correction functions to the wave fields. This study proposes to reduce arbitrariness of the higher-order KdV theory by considering its uniqueness in the following three physical senses: (i) consistency of the nonlinear higher-order coefficients and correction functions with the corresponding phase speeds, (ii) wavenumber-independence of the vertically integrated available potential energy, and (iii) its positive definiteness. The spectral (or generalized Fourier) approach based on vertical modes in the isopycnal coordinate is shown to enable an alternative derivation of the 2nd-order KdV equation, without encountering nonuniqueness. Comparison with previous theories shows that Parseval's theorem naturally yields a unique set of special conditions for (ii) and (iii). Hydrostatic fully nonlinear solutions, derived by combining the spectral approach and simple-wave analysis, reveal that both proposed and previous 2nd-order theories satisfy (i), provided that consistent definitions are used for the wave amplitude and the nonlinear correction. This condition reduces the arbitrariness when higher-order KdV-type theories are compared with observations or numerical simulations. The coefficients and correction functions that satisfy (i)-(iii) are given by explicit formulae to 2nd order and by algebraic recurrence relationships to arbitrary order for hydrostatic fully nonlinear and linear fully nonhydrostatic effects.

A fractional Fourier transform analysis of the scattering of ultrasonic waves.

PubMed

Tant, Katherine M M; Mulholland, Anthony J; Langer, Matthias; Gachagan, Anthony

2015-03-08

Many safety critical structures, such as those found in nuclear plants, oil pipelines and in the aerospace industry, rely on key components that are constructed from heterogeneous materials. Ultrasonic non-destructive testing (NDT) uses high-frequency mechanical waves to inspect these parts, ensuring they operate reliably without compromising their integrity. It is possible to employ mathematical models to develop a deeper understanding of the acquired ultrasonic data and enhance defect imaging algorithms. In this paper, a model for the scattering of ultrasonic waves by a crack is derived in the time-frequency domain. The fractional Fourier transform (FrFT) is applied to an inhomogeneous wave equation where the forcing function is prescribed as a linear chirp, modulated by a Gaussian envelope. The homogeneous solution is found via the Born approximation which encapsulates information regarding the flaw geometry. The inhomogeneous solution is obtained via the inverse Fourier transform of a Gaussian-windowed linear chirp excitation. It is observed that, although the scattering profile of the flaw does not change, it is amplified. Thus, the theory demonstrates the enhanced signal-to-noise ratio permitted by the use of coded excitation, as well as establishing a time-frequency domain framework to assist in flaw identification and classification.

A source mechanism producing HF-induced plasma lines (HFPLS) with up-shifted frequencies

NASA Technical Reports Server (NTRS)

Kuo, S. P.; Lee, M. C.

1992-01-01

Attention is given to a nonlinear scattering process analyzed as a source mechanism producing the frequency up-shifted HFPLs observed in the Arecibo ionospheric heating experiments. A physical picture is offered to explain how Langmuir waves with frequencies greater than the HF heater wave frequency can be produced in the heating experiments and be detected by incoherent radars as frequency up-shifted HFPLs. Since the considered scattering process occurs in a region near the reflection height, it explains why the frequency up-shifted HFPLs should originate from the altitude near the reflection height as observed. The theory also shows that the amount of frequency up-shift is inversely proportional to the frequency of the HF heater and increases linearly with the electron temperature. The quantitative analysis of the theory shows a good agreement with the experimental results.

Polar-Tropical Coupling in the Winter Stratosphere

NASA Astrophysics Data System (ADS)

Scott, R.

2017-12-01

A distinct pattern of enhanced equatorial potential vorticitygradients during QBO westerly anomalies, enhanced subtropicalgradients during QBO easterlies, is used to motivate a new formulationof dynamical coupling between the tropics and winter polar vortexbased on remote transfer of finite amplitude wave activity defined interms of lateral potential vorticity displacements. While the weakpotential vorticity gradients in the surf zone imply laterallyevanescent Rossby waves, transfer of wave activity from the polarvortex edge to the subtropical barrier or to the QBO westerly phaseequatorial gradients arises from nonlocality of potential vorticityinversion and the large horizontal displacements of the vortex edge.Our approach goes beyond the traditional description of the effect ofQBO wind anomalies on linear wave propagation through the stratospherevia wave reflection at the zero wind line; linear wave theory isappealing but neglects the long horizontal and vertical wavelengthsinvolved and the inhomogeneous background potential vorticity. Aparticular issue of outstanding interest is whether and how therelatively shallow QBO anomalies can influence the deep verticallypropagating waves on the edge of the winter stratospheric polarvortex. Process studies with a mechanistic model with prescribed QBOand carefully controlled high-latitude wave forcing are analyzed,guided by a reexamination of meteorological reanalysis, to address howsuch a dynamical linkage may influence in particular the resonantexcitation of the winter vortex, and the occurrence ofvortex-splitting sudden warming events. We quantify the associatedtransfer of wave activity from vortex edge to the tropics, considerunder what conditions this becomes a significant source of easterlymomentum in the driving of the QBO itself, and how the structure ofthe Brewer-Dobson circulation varies in response to the location ofthe QBO westerly winds in any given winter.

Spatial Holmboe instability

NASA Astrophysics Data System (ADS)

Ortiz, Sabine; Chomaz, Jean-Marc; Loiseleux, Thomas

2002-08-01

In mixing-layers between two parallel streams of different densities, shear and gravity effects interplay; buoyancy acts as a restoring force and the Kelvin-Helmholtz mode is known to be stabilized by the stratification. If the density interface is sharp enough, two new instability modes, known as Holmboe modes, appear, propagating in opposite directions. This mechanism has been studied in the temporal instability framework. The present paper analyzes the associated spatial instability problem. It considers, in the Boussinesq approximation, two immiscible inviscid fluids with a piecewise linear broken-line velocity profile. We show how the classical scenario for transition between absolute and convective instability should be modified due to the presence of propagating waves. In the convective region, the spatial theory is relevant and the slowest propagating wave is shown to be the most spatially amplified, as suggested by intuition. Predictions of spatial linear theory are compared with mixing-layer [C. G. Koop and F. K. Browand, J. Fluid Mech. 93, 135 (1979)] and exchange flow [G. Pawlak and L. Armi, J. Fluid Mech. 376, 1 (1999)] experiments. The physical mechanism for Holmboe mode destabilization is analyzed via an asymptotic expansion that predicts the absolute instability domain at large Richardson number.

Experimental characterization and modeling of non-linear coupling of the LHCD power on Tore Supra

DOE Office of Scientific and Technical Information (OSTI.GOV)

Preynas, M.; Goniche, M.; Hillairet, J.

2014-02-12

To achieve steady state operation on future tokamaks, in particular on ITER, the unique capability of a LHCD system to efficiently drive off-axis non-inductive current is needed. In this context, it is of prime importance to study and master the coupling of LH wave to the core plasma at high power density (tens of MW/m{sup 2}). In some specific conditions, deleterious effects on the LHCD coupling are sometimes observed on Tore Supra. At high power the waves may modify the edge parameters that change the wave coupling properties in a non-linear manner. In this way, dedicated LHCD experiments have beenmore » performed using the LHCD system of Tore Supra, composed of two different conceptual designs of launcher: the Fully Active Multijunction (FAM) and the new Passive Active Multijunction (PAM) antennas. A nonlinear interaction between the electron density and the electric field has been characterized in a thin plasma layer in front of the two LHCD antennas. The resulting dependence of the power reflection coefficient with the LHCD power, leading occasionally to trips in the output power, is not predicted by the standard linear theory of the LH wave coupling. Therefore, it is important to investigate and understand the possible origin of such non-linear effects in order to avoid their possible deleterious consequences. The PICCOLO-2D code, which self-consistently treats the wave propagation in the antenna vicinity and its interaction with the local edge plasma density, is used to simulate Tore Supra discharges. The simulation reproduces very well the occurrence of a non-linear behavior in the coupling observed in the LHCD experiments. The important differences and trends between the FAM and the PAM antennas, especially a larger increase in RC for the FAM, are also reproduced by the PICCOLO-2D simulation. The working hypothesis of the contribution of the ponderomotive effect in the non-linear observations of LHCD coupling is therefore validated through this comprehensive modeling for the first time on the FAM and PAM antennas on Tore Supra.« less

Globally aligned states and hydrodynamic traffic jams in confined suspensions of active asymmetric particles.

PubMed

Lefauve, Adrien; Saintillan, David

2014-02-01

Strongly confined active liquids are subject to unique hydrodynamic interactions due to momentum screening and lubricated friction by the confining walls. Using numerical simulations, we demonstrate that two-dimensional dilute suspensions of fore-aft asymmetric polar swimmers in a Hele-Shaw geometry can exhibit a rich variety of novel phase behaviors depending on particle shape, including coherent polarized density waves with global alignment, persistent counterrotating vortices, density shocks and rarefaction waves. We also explain these phenomena using a linear stability analysis and a nonlinear traffic flow model, both derived from a mean-field kinetic theory.

Research on the unsteady hydrodynamic characteristics of vertical axis tidal turbine

NASA Astrophysics Data System (ADS)

Zhang, Xue-wei; Zhang, Liang; Wang, Feng; Zhao, Dong-ya; Pang, Cheng-yan

2014-03-01

The unsteady hydrodynamic characteristics of vertical axis tidal turbine are investigated by numerical simulation based on viscous CFD method. The starting mechanism of the turbine is revealed through analyzing the interaction of its motion and dynamics during starting process. The operating hydrodynamic characteristics of the turbine in wave-current condition are also explored by combining with the linear wave theory. According to possible magnification of the cyclic loads in the maximum power tracking control of vertical axis turbine, a novel torque control strategy is put forward, which can improve the structural characteristics significantly without effecting energy efficiency.

Stellar pulsations in beyond Horndeski gravity theories

NASA Astrophysics Data System (ADS)

Sakstein, Jeremy; Kenna-Allison, Michael; Koyama, Kazuya

2017-03-01

Theories of gravity in the beyond Horndeski class recover the predictions of general relativity in the solar system whilst admitting novel cosmologies, including late-time de Sitter solutions in the absence of a cosmological constant. Deviations from Newton's law are predicted inside astrophysical bodies, which allow for falsifiable, smoking-gun tests of the theory. In this work we study the pulsations of stars by deriving and solving the wave equation governing linear adiabatic oscillations to find the modified period of pulsation. Using both semi-analytic and numerical models, we perform a preliminary survey of the stellar zoo in an attempt to identify the best candidate objects for testing the theory. Brown dwarfs and Cepheid stars are found to be particularly sensitive objects and we discuss the possibility of using both to test the theory.

Fast and local non-linear evolution of steep wave-groups on deep water: A comparison of approximate models to fully non-linear simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adcock, T. A. A.; Taylor, P. H.

2016-01-15

The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest whichmore » leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum.« less

Effect of Upstream ULF Waves on the Energetic Ion Diffusion at the Earth's Foreshock. I. Theory and Simulation

NASA Astrophysics Data System (ADS)

Otsuka, Fumiko; Matsukiyo, Shuichi; Kis, Arpad; Nakanishi, Kento; Hada, Tohru

2018-02-01

Field-aligned diffusion of energetic ions in the Earth’s foreshock is investigated by using the quasi-linear theory (QLT) and test particle simulation. Non-propagating MHD turbulence in the solar wind rest frame is assumed to be purely transverse with respect to the background field. We use a turbulence model based on a multi-power-law spectrum including an intense peak that corresponds to upstream ULF waves resonantly generated by the field-aligned beam (FAB). The presence of the ULF peak produces a concave shape of the diffusion coefficient when it is plotted versus the ion energy. The QLT including the effect of the ULF wave explains the simulation result well, when the energy density of the turbulent magnetic field is 1% of that of the background magnetic field and the power-law index of the wave spectrum is less than 2. The numerically obtained e-folding distances from 10 to 32 keV ions match with the observational values in the event discussed in the companion paper, which contains an intense ULF peak in the spectra generated by the FAB. Evolution of the power spectrum of the ULF waves when approaching the shock significantly affects the energy dependence of the e-folding distance.

Wave‐induced Hydraulic Forces on Submerged Aquatic Plants in Shallow Lakes

PubMed Central

SCHUTTEN, J.; DAINTY, J.; DAVY, A. J.

2004-01-01

• Background and Aims Hydraulic pulling forces arising from wave action are likely to limit the presence of freshwater macrophytes in shallow lakes, particularly those with soft sediments. The aim of this study was to develop and test experimentally simple models, based on linear wave theory for deep water, to predict such forces on individual shoots. • Methods Models were derived theoretically from the action of the vertical component of the orbital velocity of the waves on shoot size. Alternative shoot‐size descriptors (plan‐form area or dry mass) and alternative distributions of the shoot material along its length (cylinder or inverted cone) were examined. Models were tested experimentally in a flume that generated sinusoidal waves which lasted 1 s and were up to 0·2 m high. Hydraulic pulling forces were measured on plastic replicas of Elodea sp. and on six species of real plants with varying morphology (Ceratophyllum demersum, Chara intermedia, Elodea canadensis, Myriophyllum spicatum, Potamogeton natans and Potamogeton obtusifolius). • Key Results Measurements on the plastic replicas confirmed predicted relationships between force and wave phase, wave height and plant submergence depth. Predicted and measured forces were linearly related over all combinations of wave height and submergence depth. Measured forces on real plants were linearly related to theoretically derived predictors of the hydraulic forces (integrals of the products of the vertical orbital velocity raised to the power 1·5 and shoot size). • Conclusions The general applicability of the simplified wave equations used was confirmed. Overall, dry mass and plan‐form area performed similarly well as shoot‐size descriptors, as did the conical or cylindrical models of shoot distribution. The utility of the modelling approach in predicting hydraulic pulling forces from relatively simple plant and environmental measurements was validated over a wide range of forces, plant sizes and species. PMID:14988098

Validation of three-dimensional incompressible spatial direct numerical simulation code: A comparison with linear stability and parabolic stability equation theories for boundary-layer transition on a flat plate

NASA Technical Reports Server (NTRS)

Joslin, Ronald D.; Streett, Craig L.; Chang, Chau-Lyan

1992-01-01

Spatially evolving instabilities in a boundary layer on a flat plate are computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations. In a truncated physical domain, a nonstaggered mesh is used for the grid. A Chebyshev-collocation method is used normal to the wall; finite difference and compact difference methods are used in the streamwise direction; and a Fourier series is used in the spanwise direction. For time stepping, implicit Crank-Nicolson and explicit Runge-Kutta schemes are used to the time-splitting method. The influence-matrix technique is used to solve the pressure equation. At the outflow boundary, the buffer-domain technique is used to prevent convective wave reflection or upstream propagation of information from the boundary. Results of the DNS are compared with those from both linear stability theory (LST) and parabolized stability equation (PSE) theory. Computed disturbance amplitudes and phases are in very good agreement with those of LST (for small inflow disturbance amplitudes). A measure of the sensitivity of the inflow condition is demonstrated with both LST and PSE theory used to approximate inflows. Although the DNS numerics are very different than those of PSE theory, the results are in good agreement. A small discrepancy in the results that does occur is likely a result of the variation in PSE boundary condition treatment in the far field. Finally, a small-amplitude wave triad is forced at the inflow, and simulation results are compared with those of LST. Again, very good agreement is found between DNS and LST results for the 3-D simulations, the implication being that the disturbance amplitudes are sufficiently small that nonlinear interactions are negligible.

Growth of electron plasma waves above and below f(p) in the electron foreshock

NASA Technical Reports Server (NTRS)

Cairns, Iver H.; Fung, Shing F.

1988-01-01

This paper investigates the conditions required for electron beams to drive wave growth significantly above and below the electron plasma frequency, f(p), by numerically solving the linear dispersion equation. It is shown that kinetic growth well below f(p) may occur over a broad range of frequencies due to the beam instability, when the electron beam is slow, dilute, and relatively cold. Alternatively, a cold or sharp feature at low parallel velocities in the distribution function may drive kinetic growth significantly below f(p). Kinetic broadband growth significantly above f(p) is explained in terms of faster warmer beams. A unified qualitative theory for the narrow-band and broad-band waves is proposed.

Effect of a relative phase of waves constituting the initial perturbation and the wave interference on the dynamics of strong-shock-driven Richtmyer-Meshkov flows

NASA Astrophysics Data System (ADS)

Pandian, Arun; Stellingwerf, Robert F.; Abarzhi, Snezhana I.

2017-07-01

While it is a common wisdom that initial conditions influence the evolution of the Richtmyer-Meshkov instability (RMI), the research in this area is focused primarily on the effects of the wavelength and amplitude of the interface perturbation. The information has hitherto largely ignored the influences on RMI dynamics of the relative phase of waves constituting a multiwave initial perturbation and the interference of the perturbation waves. In this work we systematically study the influence of the relative phase and the interference of waves constituting a multiwave initial perturbation on a strong-shock-driven Richtmyer-Meshkov unstable interface separating ideal fluids with contrast densities. We apply group theory analysis and smoothed particle hydrodynamics numerical simulations. For verification and validation of the simulations, qualitative and quantitative comparisons are performed with rigorous zeroth-order, linear, and nonlinear theories as well as with gas dynamics experiments achieving good agreement. For a sample case of a two-wave (two-mode) initial perturbation we select the first-wave amplitude enabling the maximum initial growth rate of the RMI and we vary the second-wave amplitude from 1% to 100% of the first-wave amplitude. We also vary the relative phase of the first and second waves and consider the in-phase, the antiphase and the random-phase cases. We find that the relative phase and the interference of waves are important factors of RMI dynamics influencing qualitatively and quantitatively the symmetry, morphology, and growth rate of the Richtmyer-Meshkov unstable interface, as well as the order and disorder in strong-shock-driven RMI.

Radiative amplification of sound waves in the winds of O and B stars

NASA Technical Reports Server (NTRS)

Macgregor, K. B.; Hartmann, L.; Raymond, J. C.

1979-01-01

The velocity perturbation associated with an outwardly propagating sound wave in a radiation-driven stellar wind gives rise to a periodic Doppler shifting of absorption lines formed in the flow. A linearized theory applicable to optically thin waves is used to show that the resulting fluctuation in the absorption-line force can cause the wave amplitude to grow. Detailed calculations of the acceleration due to a large number of lines indicate that significant amplification can occur throughout the high-velocity portion of winds in which the dominant force-producing lines have appreciable optical depths. In the particular case of the wind of Zeta Pup (O4f), it is found that the e-folding distance for wave growth is considerably shorter than the scale lengths over which the physical properties of the flow vary. A qualitative estimate of the rate at which mechanical energy due to nonlinear waves can be dissipated suggests that this mechanism may be important in heating the supersonic portion of winds of early-type stars.

Nucleon-nucleon interactions from dispersion relations: Elastic partial waves

NASA Astrophysics Data System (ADS)

Albaladejo, M.; Oller, J. A.

2011-11-01

We consider nucleon-nucleon (NN) interactions from chiral effective field theory. In this work we restrict ourselves to the elastic NN scattering. We apply the N/D method to calculate the NN partial waves taking as input the one-pion exchange discontinuity along the left-hand cut. This discontinuity is amenable to a chiral power counting as discussed by Lacour, Oller, and Meißner [Ann. Phys. (NY)APNYA60003-491610.1016/j.aop.2010.06.012 326, 241 (2011)], with one-pion exchange as its leading order contribution. The resulting linear integral equation for a partial wave with orbital angular momentum ℓ≥2 is solved in the presence of ℓ-1 constraints, so as to guarantee the right behavior of the D- and higher partial waves near threshold. The calculated NN partial waves are based on dispersion relations and are independent of regulator. This method can also be applied to higher orders in the calculation of the discontinuity along the left-hand cut and extended to triplet coupled partial waves.

Angular momentum transport with twisted exciton wave packets

NASA Astrophysics Data System (ADS)

Zang, Xiaoning; Lusk, Mark T.

2017-10-01

A chain of cofacial molecules with CN or CN h symmetry supports excitonic states with a screwlike structure. These can be quantified with the combination of an axial wave number and an azimuthal winding number. Combinations of these states can be used to construct excitonic wave packets that spiral down the chain with well-determined linear and angular momenta. These twisted exciton wave packets can be created and annihilated using laser pulses, and their angular momentum can be optically modified during transit. This allows for the creation of optoexcitonic circuits in which information, encoded in the angular momentum of light, is converted into excitonic wave packets that can be manipulated, transported, and then reemitted. A tight-binding paradigm is used to demonstrate the key ideas. The approach is then extended to quantify the evolution of twisted exciton wave packets in a many-body, multilevel time-domain density functional theory setting. In both settings, numerical methods are developed that allow the site-to-site transfer of angular momentum to be quantified.

New observations of Yanai waves and equatorial inertia-gravity waves in the Pacific Ocean

NASA Astrophysics Data System (ADS)

Farrar, J. T.; Durland, T.

2011-12-01

In the 1970's and 1980's, there was a great deal of research activity on near-equatorial variability at periods of days to weeks associated with oceanic equatorial inertia-gravity waves and Yanai waves. At that time, the measurements available for studying these waves were much more limited than today: most of the available observations were from island tide gauges and a handful of short mooring records. We use more than a decade of the extensive modern data record from the TAO/TRITON mooring array in the Pacific Ocean to re-examine the internal-wave climate in the equatorial Pacific, with a focus on interpretation of the zonal-wavenumber/frequency spectrum of surface dynamic height relative to 500-m depth. Many equatorial-wave meridional modes can be identified, for both the first and second baroclinic mode. We also estimated zonal-wavenumber/frequency spectra for the zonal and meridional wind stress components. The location and extent of spectral peaks in dynamic height is readily rationalized using basic, linear theory of forced equatorial waves and the observed wind stress spectrum.

Conceptual Foundations of Soliton Versus Particle Dualities Toward a Topological Model for Matter

NASA Astrophysics Data System (ADS)

Kouneiher, Joseph

2016-06-01

The idea that fermions could be solitons was actually confirmed in theoretical models in 1975 in the case when the space-time is two-dimensional and with the sine-Gordon model. More precisely S. Coleman showed that two different classical models end up describing the same fermions particle, when the quantum theory is constructed. But in one model the fermion is a quantum excitation of the field and in the other model the particle is a soliton. Hence both points of view can be reconciliated.The principal aim in this paper is to exhibit a solutions of topological type for the fermions in the wave zone, where the equations of motion are non-linear field equations, i.e. using a model generalizing sine- Gordon model to four dimensions, and describe the solutions for linear and circular polarized waves. In other words, the paper treat fermions as topological excitations of a bosonic field.

Dissipative tunnelling by means of scaled trajectories

NASA Astrophysics Data System (ADS)

Mousavi, S. V.; Miret-Artés, S.

2018-06-01

Dissipative quantum tunnelling through an inverted parabolic barrier is considered in the presence of an electric field. A Schrödinger-Langevin or Kostin quantum-classical transition wave equation is used and applied resulting in a scaled differential equation of motion. A Gaussian wave packet solution to the resulting scaled Kostin nonlinear equation is assumed and compared to the same solution for the scaled linear Caldirola-Kanai equation. The resulting scaled trajectories are obtained at different dynamical regimes and friction cases, showing the gradual decoherence process in this open dynamics. Theoretical results show that the transmission probabilities are always higher in the Kostin approach than in the Caldirola-Kanai approach in the presence or not of an external electric field. This discrepancy should be understood due to the presence of an environment since the corresponding open dynamics should be governed by nonlinear quantum equations, whereas the second approach is issued from an effective Hamiltonian within a linear theory.

Elastic anisotropy due to aligned cracks in porous rock

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thomsen, L.

1995-08-01

All theoretical expression which relate the characteristics of saturated aligned cracks to the associated elastic anisotropy are restricted in some important way, for example to the case of stiff pore fluids, or of the absence of equate porosity, or of a moderately high frequency band. Because of these restrictions, previous theory is not suitable for application to the upper crust, where the pore fluid is brine (K{sub f}{approx}K{sub s}/20), the equant porosity is often substantial ({phi}{sub p}>0.1), and the frequency band is sonic to seismic. This work removes these particular restrictions, recognizing in the process an important mechanism of dispersion.more » A notable feature of these more general expressions is their insensitivity, at low frequency, to the aspect ratio of the cracks; only the crack density is critical. An important conclusion of this more general model is that many insights previously achieved, concerning the shear-wave splitting due to vertical aligned saturated cracks, are sustained. However, conclusions on crack orientation or crack aspect ratio, which were derived from P-wave data or from shear-wave `critical angles`, may need to be reconsidered. Further, the non-linear coupling between pores and cracks, due to pressure equalization effects, means that the (linear) Schoenberg-Muir calculus may not be applied to such systems. The theory received strong support from recent data by Rathore et al. on artificial samples with controlled crack geometry.« less

Exact near-onset analysis of the spin-density-wave instability in ferromagnetic superconductors: The linearly polarized state

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, C.

1984-09-01

Using an approach similar to Abvikosov's theory of the vortex state near H/sub c/2, we have performed an exact, near-onset analysis of a spin-density-wave instability leading to the ''linearly polarized state'' of Greenside et al. in ferromagnetic superconductors. The approach is based on a generalized Ginzburg-Landau theory for such materials, as formulated by Blount and Varma. Two models have been considered. In the (..cap alpha..,..beta..) model, where the bulk magnetic energy is taken to be (1/2)..cap alpha../sub m/M/sup 2/+(1/4)..beta../sub m/M/sup 4/, we find the transition to be second order, and obtain explicit formulas for various physical quantities to leading ordermore » in the deviation from onset. We have also rigorously analyzed the most favored spatial structure just below onset, among all possibilities allowed by the instability, and have concluded that a plane-wave-like structure is favored in a physical limit considered. In the (..cap alpha..,..gamma..) model, where the bulk magnetic energy is taken to be (1/2)..cap alpha../sub m/M/sup 2/+(1/6)..gamma../sub m/M/sup 6/ as is supported by recent experiments for ErRh/sub 4/B/sub 4/, we find the transition to be first order. This approach is then confined to an unphysical branch, which does not permit us to calculate various physical quantities on the physical branch.« less

Faraday Waves-Based Integrated Ultrasonic Micro-Droplet Generator and Applications

PubMed Central

Tsai, Chen S.; Mao, Rong W.; Tsai, Shirley C.; Shahverdi, Kaveh; Zhu, Yun; Lin, Shih K.; Hsu, Yu-Hsiang; Boss, Gerry; Brenner, Matt; Mahon, Sari; Smaldone, Gerald C.

2017-01-01

An in-depth review on a new ultrasonic micro-droplet generator which utilizes megahertz (MHz) Faraday waves excited by silicon-based multiple Fourier horn ultrasonic nozzles (MFHUNs) and its potential applications is presented. The new droplet generator has demonstrated capability for producing micro droplets of controllable size and size distribution and desirable throughput at very low electrical drive power. For comparison, the serious deficiencies of current commercial droplet generators (nebulizers) and the other ultrasonic droplet generators explored in recent years are first discussed. The architecture, working principle, simulation, and design of the multiple Fourier horns (MFH) in resonance aimed at the amplified longitudinal vibration amplitude on the end face of nozzle tip, and the fabrication and characterization of the nozzles are then described in detail. Subsequently, a linear theory on the temporal instability of Faraday waves on a liquid layer resting on the planar end face of the MFHUN and the detailed experimental verifications are presented. The linear theory serves to elucidate the dynamics of droplet ejection from the free liquid surface and predict the vibration amplitude onset threshold for droplet ejection and the droplet diameters. A battery-run pocket-size clogging-free integrated micro droplet generator realized using the MFHUN is then described. The subsequent report on the successful nebulization of a variety of commercial pulmonary medicines against common diseases and on the experimental antidote solutions to cyanide poisoning using the new droplet generator serves to support its imminent application to inhalation drug delivery. PMID:29250438

Faraday Waves-Based Integrated Ultrasonic Micro-Droplet Generator and Applications.

PubMed

Tsai, Chen S; Mao, Rong W; Tsai, Shirley C; Shahverdi, Kaveh; Zhu, Yun; Lin, Shih K; Hsu, Yu-Hsiang; Boss, Gerry; Brenner, Matt; Mahon, Sari; Smaldone, Gerald C

2017-01-01

An in-depth review on a new ultrasonic micro-droplet generator which utilizes megahertz (MHz) Faraday waves excited by silicon-based multiple Fourier horn ultrasonic nozzles (MFHUNs) and its potential applications is presented. The new droplet generator has demonstrated capability for producing micro droplets of controllable size and size distribution and desirable throughput at very low electrical drive power. For comparison, the serious deficiencies of current commercial droplet generators (nebulizers) and the other ultrasonic droplet generators explored in recent years are first discussed. The architecture, working principle, simulation, and design of the multiple Fourier horns (MFH) in resonance aimed at the amplified longitudinal vibration amplitude on the end face of nozzle tip, and the fabrication and characterization of the nozzles are then described in detail. Subsequently, a linear theory on the temporal instability of Faraday waves on a liquid layer resting on the planar end face of the MFHUN and the detailed experimental verifications are presented. The linear theory serves to elucidate the dynamics of droplet ejection from the free liquid surface and predict the vibration amplitude onset threshold for droplet ejection and the droplet diameters. A battery-run pocket-size clogging-free integrated micro droplet generator realized using the MFHUN is then described. The subsequent report on the successful nebulization of a variety of commercial pulmonary medicines against common diseases and on the experimental antidote solutions to cyanide poisoning using the new droplet generator serves to support its imminent application to inhalation drug delivery.

Accelerated ions and self-excited Alfvén waves at the Earth's bow shock

NASA Astrophysics Data System (ADS)

Berezhko, E. G.; Taneev, S. N.; Trattner, K. J.

2011-07-01

The diffuse energetic ion event and related Alfvén waves upstream of the Earth's bow shock, measured by AMPTE/IRM satellite on 29 September 1984, 06:42-07:22 UT, was studied using a self-consistent quasi-linear theory of ion diffusive shock acceleration and associated Alfvén wave generation. The wave energy density satisfies a wave kinetic equation, and the ion distribution function satisfies the diffusive transport equation. These coupled equations are solved numerically, and calculated ion and wave spectra are compared with observations. It is shown that calculated steady state ion and Alfvén wave spectra are established during the time period of about 1000 s. Alfvén waves excited by accelerated ions are confined within the frequency range (10-2 to 1) Hz, and their spectral peak with the wave amplitude δB ≈ B comparable to the interplanetary magnetic field value B corresponds to the frequency 2 × 10-2 Hz. The high-frequency part of the wave spectrum undergoes absorption by thermal protons. It is shown that the observed ion spectra and the associated Alfvén wave spectra are consistent with the theoretical prediction.

Wiggly tails: A gravitational wave signature of massive fields around black holes

NASA Astrophysics Data System (ADS)

Degollado, Juan Carlos; Herdeiro, Carlos A. R.

2014-09-01

Massive fields can exist in long-lived configurations around black holes. We examine how the gravitational wave signal of a perturbed black hole is affected by such "dirtiness" within linear theory. As a concrete example, we consider the gravitational radiation emitted by the infall of a massive scalar field into a Schwarzschild black hole. Whereas part of the scalar field is absorbed/scattered by the black hole and triggers gravitational wave emission, another part lingers in long-lived quasibound states. Solving numerically the Teukolsky master equation for gravitational perturbations coupled to the massive Klein-Gordon equation, we find a characteristic gravitational wave signal, composed by a quasinormal ringing followed by a late time tail. In contrast to "clean" black holes, however, the late time tail contains small amplitude wiggles with the frequency of the dominating quasibound state. Additionally, an observer dependent beating pattern may also be seen. These features were already observed in fully nonlinear studies; our analysis shows they are present at linear level, and, since it reduces to a 1+1 dimensional numerical problem, allows for cleaner numerical data. Moreover, we discuss the power law of the tail and that it only becomes universal sufficiently far away from the dirty black hole. The wiggly tails, by constrast, are a generic feature that may be used as a smoking gun for the presence of massive fields around black holes, either as a linear cloud or as fully nonlinear hair.

Electromagnetic ion/ion cyclotron instability - Theory and simulations

NASA Technical Reports Server (NTRS)

Winske, D.; Omidi, N.

1992-01-01

Linear theory and 1D and 2D hybrid simulations are employed to study electromagnetic ion/ion cyclotron (EMIIC) instability driven by the relative streaming of two field-aligned ion beams. The characteristics of the instability are studied as a function of beam density, propagation angle, electron-ion temperature ratios, and ion beta. When the propagation angle is near 90 deg the EMIIC instability has the characteristics of an electrostatic instability, while at smaller angles electromagnetic effects play a significant role as does strong beam coupling. The 2D simulations point to a narrowing of the wave spectrum and accompanying coherent effects during the linear growth stage of development. The EMIIC instability is an important effect where ion beta is low such as in the plasma-sheet boundary layer and upstream of slow shocks in the magnetotail.

On Wave Processes in the Solar Atmosphere

NASA Technical Reports Server (NTRS)

Musielak, Z. E.

1998-01-01

This grant was awarded by NASA/MSFC to The University of Alabama in Huntsville (UAH) to investigate the physical processes responsible for heating and wind acceleration in the solar atmosphere, and to construct theoretical, self-consistent and time-dependent solar wind models based on the momentum deposition by finite amplitude and nonlinear Alfven waves. In summary, there are three main goals of the proposed research: (1) Calculate the wave energy spectra and wave energy fluxes carried by magnetic non- magnetic waves. (2) Find out which mechanism dominates in supplying the wave energy to different parts of the solar atmosphere. (3) Use the results obtained in (1) and (2) to construct theoretical, self-consistent and time- dependent models of the solar wind. We have completed the first goal by calculating the amount of non-radiative energy generated in the solar convection zone as acoustic waves and as magnetic tube waves. To calculate the amount of wave energy carried by acoustic waves, we have used the Lighthill-Stein theory for sound generation modified by Musielak, Rosner, Stein & Ulmschneider (1994). The acoustic wave energy fluxes for stars located in different regions of the Hertzsprung-Russell (H-R) diagram have also been computed. The wave energy fluxes carried by longitudinal and transverse waves along magnetic flux tubes have been calculated by using both analytical and numerical methods. Our analytical approach is based a theory developed by Musielak, Rosner & Ulmschnelder and Musielak, Rosner, Gall & Ulmschneider, which allows computing the wave energy fluxes for linear tube waves. A numerical approach has been developed by Huang, Musielak & Ulmschneider and Ulmschneider & Musielak to compute the energy fluxes for nonlinear tube waves. Both methods have been used to calculate the wave energy fluxes for stars located in different regions of the HR diagram (Musielak, Rosner & Ulmschneider 1998; Ulmschneider, Musielak & Fawzy 1998). Having obtained the wave energy fluxes for acoustic and magnetic tube waves, we have investigated the behavior of these waves in the solar and stellar atmospheres. The results of our extensive studies have been published in many papers and presented at numerous scientific meetings. In these studies we have investigated different aspects of propagation of acoustic and magnetic waves, the efficiency of energy transfer along magnetic structures in the solar atmosphere, and behavior of Alfven waves in stgeady and expanding solar and stellar atmospheres. Recently, we have used some of these results to construct first purely theoretical, two component and time-dependent models of solar and stellar chromospheres. Finally, to address the third goal, we have constructed first fully theoretical, self-consistent and time dependent wind models based on the momentum deposition by non-linear Alfven waves. The full set of single-fluid MHD equations with the background flow has been solved by using a modified version of the ZEUS MHD code. The constructed wind models are radially symmetric with the magnetic field decreasing radially and the initial outflow is described by the standard Parker wind solution. In contrast to previous studies, no assumptions regarding wave linearity, wave damping, and wave-flow interaction are made; the models thus naturally account for the backreaction of the wind on the waves as well as for the nonlinear interaction between different types of MHD waves. The models have been used to explain the origin of fast speed streams in solar coronal holes. The obtained results clearly demonstrate that the momentum deposition by Alfven waves in the solar wind can be sufficient to explain the origin of fast stream components of the solar wind. The range of wave amplitudes required to obtain the desired results seems to be in good agreement with recent observations.

A linear accelerator for simulated micrometeors.

NASA Technical Reports Server (NTRS)

Slattery, J. C.; Becker, D. G.; Hamermesh, B.; Roy, N. L.

1973-01-01

Review of the theory, design parameters, and construction details of a linear accelerator designed to impart meteoric velocities to charged microparticles in the 1- to 10-micron diameter range. The described linac is of the Sloan Lawrence type and, in a significant departure from conventional accelerator practice, is adapted to single particle operation by employing a square wave driving voltage with the frequency automatically adjusted from 12.5 to 125 kHz according to the variable velocity of each injected particle. Any output velocity up to about 30 km/sec can easily be selected, with a repetition rate of approximately two particles per minute.

Electromagnetic fields with vanishing quantum corrections

NASA Astrophysics Data System (ADS)

Ortaggio, Marcello; Pravda, Vojtěch

2018-04-01

We show that a large class of null electromagnetic fields are immune to any modifications of Maxwell's equations in the form of arbitrary powers and derivatives of the field strength. These are thus exact solutions to virtually any generalized classical electrodynamics containing both non-linear terms and higher derivatives, including, e.g., non-linear electrodynamics as well as QED- and string-motivated effective theories. This result holds not only in a flat or (anti-)de Sitter background, but also in a larger subset of Kundt spacetimes, which allow for the presence of aligned gravitational waves and pure radiation.

Saturation of energetic-particle-driven geodesic acoustic modes due to wave-particle nonlinearity

NASA Astrophysics Data System (ADS)

Biancalani, A.; Chavdarovski, I.; Qiu, Z.; Bottino, A.; Del Sarto, D.; Ghizzo, A.; Gürcan, Ö.; Morel, P.; Novikau, I.

2017-12-01

The nonlinear dynamics of energetic-particle (EP) driven geodesic acoustic modes (EGAM) is investigated here. A numerical analysis with the global gyrokinetic particle-in-cell code ORB5 is performed, and the results are interpreted with the analytical theory, in close comparison with the theory of the beam-plasma instability. Only axisymmetric modes are considered, with a nonlinear dynamics determined by wave-particle interaction. Quadratic scalings of the saturated electric field with respect to the linear growth rate are found for the case of interest. As a main result, the formula for the saturation level is provided. Near the saturation, we observe a transition from adiabatic to non-adiabatic dynamics, i.e. the frequency chirping rate becomes comparable to the resonant EP bounce frequency. The numerical analysis is performed here with electrostatic simulations with circular flux surfaces, and kinetic effects of the electrons are neglected.

Shock loading predictions from application of indicial theory to shock-turbulence interactions

NASA Technical Reports Server (NTRS)

Keefe, Laurence R.; Nixon, David

1991-01-01

A sequence of steps that permits prediction of some of the characteristics of the pressure field beneath a fluctuating shock wave from knowledge of the oncoming turbulent boundary layer is presented. The theory first predicts the power spectrum and pdf of the position and velocity of the shock wave, which are then used to obtain the shock frequency distribution, and the pdf of the pressure field, as a function of position within the interaction region. To test the validity of the crucial assumption of linearity, the indicial response of a normal shock is calculated from numerical simulation. This indicial response, after being fit by a simple relaxation model, is used to predict the shock position and velocity spectra, along with the shock passage frequency distribution. The low frequency portion of the shock spectra, where most of the energy is concentrated, is satisfactorily predicted by this method.

Resonant scattering of energetic electrons in the outer radiation belt by HAARP-induced ELF/VLF waves

NASA Astrophysics Data System (ADS)

Chang, Shanshan; Zhu, Zhengping; Ni, Binbin; Cao, Xing; Luo, Weihua

2016-10-01

Several extremely low-frequency (ELF)/very low-frequency (VLF) wave generation experiments have been performed successfully at High-Frequency Active Auroral Research Program (HAARP) heating facility and the artificial ELF/VLF signals can leak into the outer radiation belt and contribute to resonant interactions with energetic electrons. Based on the artificial wave properties revealed by many of in situ observations, we implement test particle simulations to evaluate the effects of energetic electron resonant scattering driven by the HAARP-induced ELF/VLF waves. The results indicate that for both single-frequency/monotonic wave and multi-frequency/broadband waves, the behavior of each electron is stochastic while the averaged diffusion effect exhibits temporal linearity in the wave-particle interaction process. The computed local diffusion coefficients show that, the local pitch-angle scattering due to HARRP-induced single-frequency ELF/VLF whistlers with an amplitude of ∼10 pT can be intense near the loss cone with a rate of ∼10-2 rad2 s-1, suggesting the feasibility of HAARP-induced ELF/VLF waves for removal of outer radiation belt energetic electrons. In contrast, the energy diffusion of energetic electrons is relatively weak, which confirms that pitch-angle scattering by artificial ELF/VLF waves can dominantly lead to the precipitation of energetic electrons. Moreover, diffusion rates of the discrete, broadband waves, with the same amplitude of each discrete frequency as the monotonic waves, can be much larger, which suggests that it is feasible to trigger a reasonable broadband wave instead of the monotonic wave to achieve better performance of controlled precipitation of energetic electrons. Moreover, our test particle scattering simulation show good agreement with the predictions of the quasi-linear theory, confirming that both methods are applied to evaluate the effects of resonant interactions between radiation belt electrons and artificially generated discrete ELF/VLF waves.

Flight test measurements and analysis of sonic boom phenomena near the shock wave extremity

NASA Technical Reports Server (NTRS)

Haglund, G. T.; Kane, E. J.

1973-01-01

The sonic boom flight test program conducted at Jackass Flats, Nevada, during the summer and fall of 1970 consisted of 121 sonic-boom-generating flights over the 1500 ft instrumented BREN tower. This test program was designed to provide information on several aspects of sonic boom, including caustics produced by longitudinal accelerations, caustics produced by steady flight near the threshold Mach number, sonic boom characteristics near lateral cutoff, and the vertical extent of shock waves attached to near-sonic airplanes. The measured test data, except for the near-sonic flight data, were analyzed in detail to determine sonic boom characteristics for these flight conditions and to determine the accuracy and the range of validity of linear sonic boom theory. The caustic phenomena observed during the threshold Mach number flights and during the transonic acceleration flights are documented and analyzed in detail. The theory of geometric acoustics is shown to be capable of predicting shock wave-ground intersections, and current methods for calculating sonic boom pressure signature away from caustics are shown to be reasonably accurate.

Stellar pulsations in beyond Horndeski gravity theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sakstein, Jeremy; Kenna-Allison, Michael; Koyama, Kazuya, E-mail: sakstein@physics.upenn.edu, E-mail: mka1g13@soton.ac.uk, E-mail: kazuya.koyama@port.ac.uk

Theories of gravity in the beyond Horndeski class recover the predictions of general relativity in the solar system whilst admitting novel cosmologies, including late-time de Sitter solutions in the absence of a cosmological constant. Deviations from Newton's law are predicted inside astrophysical bodies, which allow for falsifiable, smoking-gun tests of the theory. In this work we study the pulsations of stars by deriving and solving the wave equation governing linear adiabatic oscillations to find the modified period of pulsation. Using both semi-analytic and numerical models, we perform a preliminary survey of the stellar zoo in an attempt to identify themore » best candidate objects for testing the theory. Brown dwarfs and Cepheid stars are found to be particularly sensitive objects and we discuss the possibility of using both to test the theory.« less

Intensity dependence of non-linear kinetic behaviour of stimulated Raman scattering in fusion relevant plasmas

NASA Astrophysics Data System (ADS)

Mašek, Martin; Rohlena, Karel

2015-05-01

Influence of kinetic effects on 3-wave interaction was examined within the frame of stimulated Raman backward scattering (SRBS) in a rarefied laser corona. The plasma is supposed to be weakly collisional with a negligible density gradient. The model is centred on the physical situation of shock ignition at a large scale direct drive compression experiments. The modelling uses a 1D geometry in a Maxwell-Vlasov model. The method used is a truncated Fourier-Hermite expansion numerically stabilized by a model collisional term with a realistic value of the collision frequency. In parallel, besides the linear theory of SRBS, a coupled mode 3-wave equation system (laser driving wave, Raman back-scattered wave and the daughter forward scattered plasma wave) is solved to demonstrate the correspondence between the full kinetic model and 3-wave interaction with no electron kinetics involved to identify the differences between both the solutions arising due to the electron kinetic effects. We concentrated mainly on the Raman reflectivity, which is one of the important parameters controlling the efficiency of the shock ignition scheme. It was found that the onset of the kinetic effects has a distinct intensity threshold, above which the Raman reflectivity may go down due to the electron kinetics. In addition, we were trying to identify the most important features of the electron phase space behaviour, such as particle trapping in potential minima of the generated plasma wave and its consequences for the 3-wave interaction. The role of the trapped electrons seems to be crucial for a deformation of the plasma wave dispersion curve, as indicated in some earlier work.

Numerical simulation of swept-wing flows

NASA Technical Reports Server (NTRS)

Reed, Helen L.

1991-01-01

Efforts of the last six months to computationally model the transition process characteristics of flow over swept wings are described. Specifically, the crossflow instability and crossflow/Tollmien-Schlichting wave interactions are analyzed through the numerical solution of the full 3D Navier-Stokes equations including unsteadiness, curvature, and sweep. This approach is chosen because of the complexity of the problem and because it appears that linear stability theory is insufficient to explain the discrepancies between different experiments and between theory and experiment. The leading edge region of a swept wing is considered in a 3D spatial simulation with random disturbances as the initial conditions.

Capillary wave theory of adsorbed liquid films and the structure of the liquid-vapor interface

NASA Astrophysics Data System (ADS)

MacDowell, Luis G.

2017-08-01

In this paper we try to work out in detail the implications of a microscopic theory for capillary waves under the assumption that the density is given along lines normal to the interface. Within this approximation, which may be justified in terms of symmetry arguments, the Fisk-Widom scaling of the density profile holds for frozen realizations of the interface profile. Upon thermal averaging of capillary wave fluctuations, the resulting density profile yields results consistent with renormalization group calculations in the one-loop approximation. The thermal average over capillary waves may be expressed in terms of a modified convolution approximation where normals to the interface are Gaussian distributed. In the absence of an external field we show that the phenomenological density profile applied to the square-gradient free energy functional recovers the capillary wave Hamiltonian exactly. We extend the theory to the case of liquid films adsorbed on a substrate. For systems with short-range forces, we recover an effective interface Hamiltonian with a film height dependent surface tension that stems from the distortion of the liquid-vapor interface by the substrate, in agreement with the Fisher-Jin theory of short-range wetting. In the presence of long-range interactions, the surface tension picks up an explicit dependence on the external field and recovers the wave vector dependent logarithmic contribution observed by Napiorkowski and Dietrich. Using an error function for the intrinsic density profile, we obtain closed expressions for the surface tension and the interface width. We show the external field contribution to the surface tension may be given in terms of the film's disjoining pressure. From literature values of the Hamaker constant, it is found that the fluid-substrate forces may be able to double the surface tension for films in the nanometer range. The film height dependence of the surface tension described here is in full agreement with results of the capillary wave spectrum obtained recently in computer simulations, and the predicted translation mode of surface fluctuations reproduces to linear order in field strength an exact solution of the density correlation function for the Landau-Ginzburg-Wilson Hamiltonian in an external field.

Ion Bernstein instability dependence on the proton-to-electron mass ratio: Linear dispersion theory

NASA Astrophysics Data System (ADS)

Min, Kyungguk; Liu, Kaijun

2016-07-01

Fast magnetosonic waves, which have as their source ion Bernstein instabilities driven by tenuous ring-like proton velocity distributions, are frequently observed in the inner magnetosphere. One major difficulty in the simulation of these waves is that they are excited in a wide frequency range with discrete harmonic nature and require time-consuming computations. To overcome this difficulty, recent simulation studies assumed a reduced proton-to-electron mass ratio, mp/me, and a reduced light-to-Alfvén speed ratio, c/vA, to reduce the number of unstable modes and, therefore, computational costs. Although these studies argued that the physics of wave-particle interactions would essentially remain the same, detailed investigation of the effect of this reduced system on the excited waves has not been done. In this study, we investigate how the complex frequency, ω = ωr+iγ, of the ion Bernstein modes varies with mp/me for a sufficiently large c/vA (such that ωpe2/Ωe2≡(me/mp)(c/vA)2≫1) using linear dispersion theory assuming two different types of energetic proton velocity distributions, namely, ring and shell. The results show that low- and high-frequency harmonic modes respond differently to the change of mp/me. For the low harmonic modes (i.e., ωr˜Ωp), both ωr/Ωp and γ/Ωp are roughly independent of mp/me, where Ωp is the proton cyclotron frequency. For the high harmonic modes (i.e., Ωp≪ωr≲ωlh, where ωlh is the lower hybrid frequency), γ/ωlh (at fixed ωr/ωlh) stays independent of mp/me when the parallel wave number, k∥, is sufficiently large and becomes inversely proportional to (mp/me)1/4 when k∥ goes to zero. On the other hand, the frequency range of the unstable modes normalized to ωlh remains independent of mp/me, regardless of k∥.

Ocean Wave Studies with Applications to Ocean Modeling and Improvement of Satellite Altimeter Measurements

NASA Technical Reports Server (NTRS)

Glazman, Roman E.

1999-01-01

Combining analysis of satellite data (altimeter, scatterometer, high-resolution visible and infrared images, etc.) with mathematical modeling of non-linear wave processes, we investigate various ocean wave fields (on scales from capillary to planetary), their role in ocean dynamics and turbulent transport (of heat and biogeochemical quantities), and their effects on satellite altimeter measuring accuracy. In 1998 my attention was focused on long internal gravity waves (10 to 1000 km), known also as baroclinic inertia-gravity (BIG) waves. We found these waves to be a major factor of altimeter measurements "noise," resulting in a greater uncertainty [up to 10 cm in terms of sea surface height (SSH) amplitude] in the measured SSH signal than that caused by the sea state bias variations (up to 5 cm or so). This effect still remains largely overlooked by the satellite altimeter community. Our studies of BIG waves address not only their influence on altimeter measurements but also their role in global ocean dynamics and in transport and turbulent diffusion of biogeochemical quantities. In particular, in collaboration with Prof Peter Weichman, Caltech, we developed a theory of turbulent diffusion caused by wave motions of most general nature. Applied to the problem of horizontal turbulent diffusion in the ocean, the theory yielded the effective diffusion coefficient as a function of BIG wave parameters obtainable from satellite altimeter data. This effort, begun in 1997, has been successfully completed in 1998. We also developed a theory that relates spatial fluctuations of scalar fields (such as sea surface temperature, chlorophyll concentration, drifting ice concentration, etc.) to statistical characteristics of BIG waves obtainable from altimeter measurements. A manuscript is in the final stages of preparation. In order to verify the theoretical predictions and apply them to observations, we are now analyzing Sea-viewing Wide Field of view Sensor (SeaWiFS) and Field of view Sensor (SeaWiFS) and Advanced Very High-Resolution Radiometer (AVHRR) data on sea surface temperature (SST) and chlorophyll concentration jointly with TOPEX/POSEIDON data on SSH variations.

Large-Amplitude Long-Wave Instability of a Supersonic Shear Layer

NASA Technical Reports Server (NTRS)

Messiter, A. F.

1995-01-01

For sufficiently high Mach numbers, small disturbances on a supersonic vortex sheet are known to grow in amplitude because of slow nonlinear wave steepening. Under the same external conditions, linear theory predicts slow growth of long-wave disturbances to a thin supersonic shear layer. An asymptotic formulation is given here which adds nonzero shear-layer thickness to the weakly nonlinear formulation for a vortex sheet. Spatial evolution is considered, for a spatially periodic disturbance having amplitude of the same order, in Reynolds number, as the shear-layer thickness. A quasi-equilibrium inviscid nonlinear critical layer is found, with effects of diffusion and slow growth appearing through nonsecularity condition. Other limiting cases are also considered, in an attempt to determine a relationship between the vortex-sheet limit and the long-wave limit for a thin shear layer; there appear to be three special limits, corresponding to disturbances of different amplitudes at different locations along the shear layer.

Christodoulou Memory of GW150914 - Prospects of Detection in LIGO and Future Detectors

NASA Astrophysics Data System (ADS)

Johnson, Aaron; Kapadia, Shasvath; Kennefick, Daniel

2017-01-01

The event GW150914 produced strains of the order 10-21 in the two instruments comprising the Laser Interferometric Gravitational Wave Observatory (LIGO). The event has been interpreted as originating in a coalescing black hole binary, with individual components of about 30 solar masses each. A striking aspect of the coalescence deduced from the signal is the emission of 3 solar masses of energy in the oscillating gravitational wave. Theory predicts a DC component of the gravitational signal associated with the emission of such large amounts of gravitational wave energy known as the Christodoulou memory. The memory, as a non-linear component of the signal, is expected to be an order of magnitude smaller than the amplitude of the primary AC component of the gravitational waves. We discuss the prospects of detecting the Christodoulou memory in similar future signals, both with LIGO and with other detectors, including future space-based instruments.

Damping of Resonantly Forced Density Waves in Dense Planetary Rings

NASA Astrophysics Data System (ADS)

Lehmann, Marius; Schmidt, Jürgen; Salo, Heikki

2016-10-01

We address the stability of resonantly forced density waves in dense planetary rings.Already by Goldreich and Tremaine (1978) it has been argued that density waves might be unstable, depending on the relationship between the ring's viscosity and the surface mass density. In the recent paper (Schmidt et al. 2016) we have pointed out that when - within a fluid description of the ring dynamics - the criterion for viscous overstability is satisfied, forced spiral density waves become unstable as well. In this case, linear theory fails to describe the damping.We apply the multiple scale formalism to derive a weakly nonlinear damping relation from a hydrodynamical model.This relation describes the resonant excitation and nonlinear viscous damping of spiral density waves in a vertically integrated fluid disk with density dependent transport coefficients. The model consistently predicts linear instability of density waves in a ring region where the conditions for viscous overstability are met. In this case, sufficiently far away from the Lindblad resonance, the surface mass density perturbation is predicted to saturate to a constant value due to nonlinear viscous damping. In general the model wave damping lengths depend on a set of input parameters, such as the distance to the threshold for viscous overstability and the ground state surface mass density.Our new model compares reasonably well with the streamline model for nonlinear density waves of Borderies et al. 1986.Deviations become substantial in the highly nonlinear regime, corresponding to strong satellite forcing.Nevertheless, we generally observe good or at least qualitative agreement between the wave amplitude profiles of both models. The streamline approach is superior at matching the total wave profile of waves observed in Saturn's rings, while our new damping relation is a comparably handy tool to gain insight in the evolution of the wave amplitude with distance from resonance, and the different regimes of wave formation and the dependence on the parameters of the model.

Experimental Observation of Bohr's Nonlinear Fluidic Surface Oscillation.

PubMed

Moon, Songky; Shin, Younghoon; Kwak, Hojeong; Yang, Juhee; Lee, Sang-Bum; Kim, Soyun; An, Kyungwon

2016-01-25

Niels Bohr in the early stage of his career developed a nonlinear theory of fluidic surface oscillation in order to study surface tension of liquids. His theory includes the nonlinear interaction between multipolar surface oscillation modes, surpassing the linear theory of Rayleigh and Lamb. It predicts a specific normalized magnitude of 0.416η(2) for an octapolar component, nonlinearly induced by a quadrupolar one with a magnitude of η much less than unity. No experimental confirmation on this prediction has been reported. Nonetheless, accurate determination of multipolar components is important as in optical fiber spinning, film blowing and recently in optofluidic microcavities for ray and wave chaos studies and photonics applications. Here, we report experimental verification of his theory. By using optical forward diffraction, we measured the cross-sectional boundary profiles at extreme positions of a surface-oscillating liquid column ejected from a deformed microscopic orifice. We obtained a coefficient of 0.42 ± 0.08 consistently under various experimental conditions. We also measured the resonance mode spectrum of a two-dimensional cavity formed by the cross-sectional segment of the liquid jet. The observed spectra agree well with wave calculations assuming a coefficient of 0.414 ± 0.011. Our measurements establish the first experimental observation of Bohr's hydrodynamic theory.

Experimental Observation of Bohr’s Nonlinear Fluidic Surface Oscillation

PubMed Central

Moon, Songky; Shin, Younghoon; Kwak, Hojeong; Yang, Juhee; Lee, Sang-Bum; Kim, Soyun; An, Kyungwon

2016-01-01

Niels Bohr in the early stage of his career developed a nonlinear theory of fluidic surface oscillation in order to study surface tension of liquids. His theory includes the nonlinear interaction between multipolar surface oscillation modes, surpassing the linear theory of Rayleigh and Lamb. It predicts a specific normalized magnitude of 0.416η2 for an octapolar component, nonlinearly induced by a quadrupolar one with a magnitude of η much less than unity. No experimental confirmation on this prediction has been reported. Nonetheless, accurate determination of multipolar components is important as in optical fiber spinning, film blowing and recently in optofluidic microcavities for ray and wave chaos studies and photonics applications. Here, we report experimental verification of his theory. By using optical forward diffraction, we measured the cross-sectional boundary profiles at extreme positions of a surface-oscillating liquid column ejected from a deformed microscopic orifice. We obtained a coefficient of 0.42 ± 0.08 consistently under various experimental conditions. We also measured the resonance mode spectrum of a two-dimensional cavity formed by the cross-sectional segment of the liquid jet. The observed spectra agree well with wave calculations assuming a coefficient of 0.414 ± 0.011. Our measurements establish the first experimental observation of Bohr’s hydrodynamic theory. PMID:26803911

The Dispersion of the Axisymmetric Longitudinal Waves in the Pre-Strained Bi-Material Hollow Cylinder with the Imperfect Interface Conditions

NASA Astrophysics Data System (ADS)

Akbarov, S. D.; Ipek, C.

This work studies the influence of the imperfectness of the interface conditions on the dispersion of the axisymmetric longitudinal waves in the pre-strained bi-material hollow cylinder. The investigations are made within the 3D linearized theory of elastic waves in elastic bodies with initial stresses. It is assumed that the materials of the layers of the hollow cylinder are made from hyper elastic compressible materials and the elasticity relations of those are given through the harmonic potential. The shear spring type imperfectness of the interface conditions is considered and the degree of this imperfectness is estimated by the shear-spring parameter. Numerical results on the influence of this parameter on the behavior of the dispersion curves are presented and discussed.

Rossby-gravity waves in tropical total ozone data

NASA Technical Reports Server (NTRS)

Stanford, J. L.; Ziemke, J. R.

1993-01-01

Evidence for Rossby-gravity waves in tropical data fields produced by the European Center for Medium Range Weather Forecasts (ECMWF) was recently reported. Similar features are observable in fields of total column ozone from the Total Ozone Mapping Spectrometer (TOMS) satellite instrument. The observed features are episodic, have zonal (east-west) wavelengths of 6,000-10,000 km, and oscillate with periods of 5-10 days. In accord with simple linear theory, the modes exhibit westward phase progression and eastward group velocity. The significance of finding Rossby-gravity waves in total ozone fields is that (1) the report of similar features in ECMWF tropical fields is corroborated with an independent data set and (2) the TOMS data set is demonstrated to possess surprising versatility and sensitivity to relatively smaller scale tropical phenomena.

Conference on Non-linear Phenomena in Mathematical Physics: Dedicated to Cathleen Synge Morawetz on her 85th Birthday. The Fields Institute, Toronto, Canada September 18-20, 2008. Sponsors: Association for Women in Mathematics, Inc. and The Fields Institute

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lewis, Jennifer

2012-10-15

This scientific meeting focused on the legacy of Cathleen S. Morawetz and the impact that her scientific work on transonic flow and the non-linear wave equation has had in recent progress on different aspects of analysis for non-linear wave, kinetic and quantum transport problems associated to mathematical physics. These are areas where the elements of continuum, statistical and stochastic mechanics, and their interplay, have counterparts in the theory of existence, uniqueness and stability of the associated systems of equations and geometric constraints. It was a central event for the applied and computational analysis community focusing on Partial Differential Equations. Themore » goal of the proposal was to honor Cathleen Morawetz, a highly successful woman in mathematics, while encouraging beginning researchers. The conference was successful in show casing the work of successful women, enhancing the visibility of women in the profession and providing role models for those just beginning their careers. The two-day conference included seven 45-minute lectures and one day of six 45-minute lectures, and a poster session for junior participants. The conference program included 19 distinguished speakers, 10 poster presentations, about 70 junior and senior participants and, of course, the participation of Cathleen Synge Morawetz. The conference celebrated Morawetz's paramount contributions to the theory of non-linear equations in gas dynamics and their impact in the current trends of nonlinear phenomena in mathematical physics, but also served as an awareness session of current women's contribution to mathematics.« less

Waves propagating over a two-layer porous barrier on a seabed

NASA Astrophysics Data System (ADS)

Lin, Qiang; Meng, Qing-rui; Lu, Dong-qiang

2018-05-01

A research of wave propagation over a two-layer porous barrier, each layer of which is with different values of porosity and friction, is conducted with a theoretical model in the frame of linear potential flow theory. The model is more appropriate when the seabed consists of two different properties, such as rocks and breakwaters. It is assumed that the fluid is inviscid and incompressible and the motion is irrotational. The wave numbers in the porous region are complex ones, which are related to the decaying and propagating behaviors of wave modes. With the aid of the eigenfunction expansions, a new inner product of the eigenfunctions in the two-layer porous region is proposed to simplify the calculation. The eigenfunctions, under this new definition, possess the orthogonality from which the expansion coefficients can be easily deduced. Selecting the optimum truncation of the series, we derive a closed system of simultaneous linear equations for the same number of the unknown reflection and transmission coefficients. The effects of several physical parameters, including the porosity, friction, width, and depth of the porous barrier, on the dispersion relation, reflection and transmission coefficients are discussed in detail through the graphical representations of the solutions. It is concluded that these parameters have certain impacts on the reflection and transmission energy.

A fractional Fourier transform analysis of the scattering of ultrasonic waves

PubMed Central

Tant, Katherine M.M.; Mulholland, Anthony J.; Langer, Matthias; Gachagan, Anthony

2015-01-01

Many safety critical structures, such as those found in nuclear plants, oil pipelines and in the aerospace industry, rely on key components that are constructed from heterogeneous materials. Ultrasonic non-destructive testing (NDT) uses high-frequency mechanical waves to inspect these parts, ensuring they operate reliably without compromising their integrity. It is possible to employ mathematical models to develop a deeper understanding of the acquired ultrasonic data and enhance defect imaging algorithms. In this paper, a model for the scattering of ultrasonic waves by a crack is derived in the time–frequency domain. The fractional Fourier transform (FrFT) is applied to an inhomogeneous wave equation where the forcing function is prescribed as a linear chirp, modulated by a Gaussian envelope. The homogeneous solution is found via the Born approximation which encapsulates information regarding the flaw geometry. The inhomogeneous solution is obtained via the inverse Fourier transform of a Gaussian-windowed linear chirp excitation. It is observed that, although the scattering profile of the flaw does not change, it is amplified. Thus, the theory demonstrates the enhanced signal-to-noise ratio permitted by the use of coded excitation, as well as establishing a time–frequency domain framework to assist in flaw identification and classification. PMID:25792967

The use of remote sensing and linear wave theory to model local wave energy around Alphonse Atoll, Seychelles

NASA Astrophysics Data System (ADS)

Hamylton, S.

2011-12-01

This paper demonstrates a practical step-wise method for modelling wave energy at the landscape scale using GIS and remote sensing techniques at Alphonse Atoll, Seychelles. Inputs are a map of the benthic surface (seabed) cover, a detailed bathymetric model derived from remotely sensed Compact Airborne Spectrographic Imager (CASI) data and information on regional wave heights. Incident energy at the reef crest around the atoll perimeter is calculated as a function of its deepwater value with wave parameters (significant wave height and period) hindcast in the offshore zone using the WaveWatch III application developed by the National Oceanographic and Atmospheric Administration. Energy modifications are calculated at constant intervals as waves transform over the forereef platform along a series of reef profile transects running into the atoll centre. Factors for shoaling, refraction and frictional attenuation are calculated at each interval for given changes in bathymetry and benthic coverage type and a nominal reduction in absolute energy is incorporated at the reef crest to account for wave breaking. Overall energy estimates are derived for a period of 5 years and related to spatial patterning of reef flat surface cover (sand and seagrass patches).

A statistical study of EMIC waves observed by Cluster: 2. Associated plasma conditions

NASA Astrophysics Data System (ADS)

Allen, R. C.; Zhang, J.-C.; Kistler, L. M.; Spence, H. E.; Lin, R.-L.; Klecker, B.; Dunlop, M. W.; André, M.; Jordanova, V. K.

2016-07-01

This is the second in a pair of papers discussing a statistical study of electromagnetic ion cyclotron (EMIC) waves detected during 10 years (2001-2010) of Cluster observations. In the first paper, an analysis of EMIC wave properties (i.e., wave power, polarization, normal angle, and wave propagation angle) is presented in both the magnetic latitude (MLAT)-distance as well as magnetic local time (MLT)-L frames. This paper focuses on the distribution of EMIC wave-associated plasma conditions as well as two EMIC wave generation proxies (the electron plasma frequency to gyrofrequency ratio proxy and the linear theory proxy) in these same frames. Based on the distributions of hot H+ anisotropy, electron and hot H+ density measurements, hot H+ parallel plasma beta, and the calculated wave generation proxies, three source regions of EMIC waves appear to exist: (1) the well-known overlap between cold plasmaspheric or plume populations with hot anisotropic ring current populations in the postnoon to dusk MLT region; (2) regions all along the dayside magnetosphere at high L shells related to dayside magnetospheric compression and drift shell splitting; and (3) off-equator regions possibly associated with the Shabansky orbits in the dayside magnetosphere.

Discerning comb and Fourier mean frequency from an fs laser based on the principle of non-interaction of waves

NASA Astrophysics Data System (ADS)

Roychoudhuri, Chandrasekhar; Prasad, Narasimha

2012-02-01

The key objective of this article is to underscore that as engineers, we need to pay close attention in repeatedly validating and re-validating the underlying physical processes behind a working theory that models a phenomenon we are using to create tools and technologies. We use the test case, the prevailing mode-lock theory, to illustrate our views by identifying existing contradictions and showing approach towards their resolution by identifying the relevant physical processes. The current theory tells us that the Fourier summation of all the allowed cavity modes directly produces the train of pulses. It effectively assumes that electromagnetic (EM) waves are capable of re-organizing their spatial and temporal energy distribution to generate a train of temporal pulses while preserving the spatial mode energy distribution. The implication is that EM waves interact with each other by themselves. Even though the theory is working, we have three logical problems. First, in the real world, in the linear domain, waves never interact with each other. On careful analysis of all types of interference experiments, we will recognize that only in the presence of some interacting material medium can we observe the physical superposition EFFECT. In other words, detectors carryout the superposition effect we call interference phenomenon, through the summation of their multiple simultaneous linear stimulations and then absorbing energy proportional to the square modulus of the sum total stimulation. Second, a Fourier monochromatic wave, existing in all space and time, is a non-causal hypothesis. Just because our theories are working does not mean that we have understood the real physical interaction processes in nature. We need to build our theories based upon space and time finite EM wave packet containing a finite amount of energy, which is a causal approach. Third, in spite of staggering successes of Quantum Mechanics, we do not yet have a self consistent model for space and time finite model of a photon. QM only predicts that EM energy emission (spontaneous and stimulated) takes place only in a discrete amount at a time from atoms and molecules. It does not give us recipe about how to visualize a propagating photon as it expands diffractively. However, Huygens-Fresnel's classical diffraction integral gives us a rigorous model, which is the cornerstone of modeling evolution of laser cavity modes, CW or pulsed. In this paper, we highlight the contradictions that arise out of the prevailing mode-lock theory and resolve them by using causal models, already underscored above. For example, there are now a wide range of very successful technological applications of the frequency comb extracted out of fs lasers. If the Fourier summation were the correct physical process, then all the cavity modes would have been summed (converted) into a single mean frequency around the gain line center for perfectly mode-locked systems. Further, sending such fs pulses through an optical spectrometer would have always displayed a transform limited fringe, centering on the mean Fourier frequency, rather than generating the comb frequencies, albeit instrumentally broadened. Output pulse train from a phase locked laser is functionally produced due to the oscillatory time-gating behavior of the intra-cavity phase-locking devices. So, we need to pay more attention to the fast temporal behavior of the materials we use for achieving very fast time-gating, since this material imposes phase locking on the cavity modes to enhance its own high-contrast time-gating behavior.

The Parametric Decay Instability of Alfvén Waves in Turbulent Plasmas and the Applications in the Solar Wind

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shi, Mijie; Xiao, Chijie; Wang, Xiaogang

2017-06-10

We perform three-dimensional ideal magnetohydrodynamic (MHD) simulations to study the parametric decay instability (PDI) of Alfvén waves in turbulent plasmas and explore its possible applications in the solar wind. We find that, over a broad range of parameters in background turbulence amplitudes, the PDI of an Alfvén wave with various amplitudes can still occur, though its growth rate in turbulent plasmas tends to be lower than both the theoretical linear theory prediction and that in the non-turbulent situations. Spatial–temporal FFT analyses of density fluctuations produced by the PDI match well with the dispersion relation of the slow MHD waves. Thismore » result may provide an explanation of the generation mechanism of slow waves in the solar wind observed at 1 au. It further highlights the need to explore the effects of density variations in modifying the turbulence properties as well as in heating the solar wind plasmas.« less

Generation, propagation and run-up of tsunamis due to the Chicxulub impact event

NASA Astrophysics Data System (ADS)

Weisz, R.; Wuennenmann, K.; Bahlburg, H.

2003-04-01

The Chicxulub impact event can be investigated in (1) local, (2) regional and in (3) global scales. Our investigations focus on the regional scale, especially on the influence of tsunami waves on the coast around the Gulf of Mexico caused by the impact. During an impact two types of tsunamis are generated. The first wave is known as the "rim wave" and is generated in front of the ejecta curtain. The second one is linked to the late modification stage of the impact and results from the collapsing cavity of water. We designate this wave as "collapse wave". The "rim wave" and "collapse wave" are able to propagate over long distances, without a significant loss of wave amplitude. Corresponding to the amplitudes, the waves have a potentially large influence on the coastal areas. Run-up distance and run-up height can be used as parameters for describing this influence. We are utilizing a multimaterial hydrocode (SALE) to simulate the generation of tsunami waves. The propagation of the waves is based on the non-linear shallow water theory, because tsunami waves are defined to be long waves. The position of the coast line varies according to the tsunami run-up and is implemented with open boundary conditions. We show with our investigations (1) the generation of tsunami waves due to shallow water impacts, (2) wave damping during propagation, and (3) the influence of the "rim wave" and the "collapse wave" on the coastal areas. Here, we present our first results from numerical modeling of tsunami waves owing to a Chicxulub sized impactor. The characteristics of the “rim wave” depend on the size of the bolide and the water depth. However, the amplitude and velocity of the “collapse wave” is only determined by the water depth in the impact area. The numerical modeling of the tsunami propagation and run-up is calculated along a section from the impact point towards to the west and gives the moderate damping of both waves and the run-up on the coastal area. As a first approximation, the bathymetric data, used in the wave propagation and run-up, correspond to a linearized bathymetry of the Recent Gulf of Mexico. The linearized bathymetry allows to study the influence of the bathymetry on wave propagation and run-up. Additionally, we give preliminary results of the implementation of the two-dimensional propagation and run-up model for arbitrary bathymetries. The two-dimensional wave propagation model will enable us to more realistically asses the influence of the impact-related tsunamis on the coasts around the Gulf of Mexico due to the Chicxulub impact event.

Electron Interactions with Non-Linear Polyatomic Molecules and Their Radicals

DTIC Science & Technology

1993-12-01

developed which generates SCE quantities from molecular wave functions. This progress was realized in terms of some actual calculations on some molecules...section 4.A describes the basics of the Partial Differential Equation Theory; section 4.B describes the generalization to a finite element...Information Service (NTIS). At NTIS, it will be available to the general public, including foreign nations. This technical report has been reviewed and

Multi-scale and Multi-physics Numerical Methods for Modeling Transport in Mesoscopic Systems

DTIC Science & Technology

2014-10-13

function and wide band Fast multipole methods for Hankel waves. (2) a new linear scaling discontinuous Galerkin density functional theory, which provide a...inflow boundary condition for Wigner quantum transport equations. Also, a book titled "Computational Methods for Electromagnetic Phenomena...equationsin layered media with FMM for Bessel functions , Science China Mathematics, (12 2013): 2561. doi: TOTAL: 6 Number of Papers published in peer

Disorder and superfluid density in overdoped cuprate superconductors

NASA Astrophysics Data System (ADS)

Lee-Hone, N. R.; Dodge, J. S.; Broun, D. M.

2017-07-01

We calculate superfluid density for a dirty d -wave superconductor. The effects of impurity scattering are treated within the self-consistent t -matrix approximation, in weak-coupling BCS theory. Working from a realistic tight-binding parametrization of the Fermi surface, we find a superfluid density that is both correlated with Tc and linear in temperature, in good correspondence with recent experiments on overdoped La2 -xSrxCuO4 .

Measurement of attenuation coefficients of the fundamental and second harmonic waves in water

NASA Astrophysics Data System (ADS)

Zhang, Shuzeng; Jeong, Hyunjo; Cho, Sungjong; Li, Xiongbing

2016-02-01

Attenuation corrections in nonlinear acoustics play an important role in the study of nonlinear fluids, biomedical imaging, or solid material characterization. The measurement of attenuation coefficients in a nonlinear regime is not easy because they depend on the source pressure and requires accurate diffraction corrections. In this work, the attenuation coefficients of the fundamental and second harmonic waves which come from the absorption of water are measured in nonlinear ultrasonic experiments. Based on the quasilinear theory of the KZK equation, the nonlinear sound field equations are derived and the diffraction correction terms are extracted. The measured sound pressure amplitudes are adjusted first for diffraction corrections in order to reduce the impact on the measurement of attenuation coefficients from diffractions. The attenuation coefficients of the fundamental and second harmonics are calculated precisely from a nonlinear least squares curve-fitting process of the experiment data. The results show that attenuation coefficients in a nonlinear condition depend on both frequency and source pressure, which are much different from a linear regime. In a relatively lower drive pressure, the attenuation coefficients increase linearly with frequency. However, they present the characteristic of nonlinear growth in a high drive pressure. As the diffraction corrections are obtained based on the quasilinear theory, it is important to use an appropriate source pressure for accurate attenuation measurements.

Experimental measurement and theoretical modeling of microwave scattering and the structure of the sea surface influencing radar observations from space

NASA Technical Reports Server (NTRS)

Arnold, David; Kong, J. A.

1992-01-01

The electromagnetic (EM) bias 'epsilon' is an error present in radar altimetry of the ocean due to the nonuniform reflection from wave troughs and crests. The EM bias is defined as the difference between the mean reflecting surface and the mean sea surface. A knowledge of the EM bias is necessary to permit error reduction in mean sea level measurements by satellite radar altimeters. Direct measurements of the EM bias were made from a Shell Offshore oil production platform in the Gulf of Mexico for a six month period during 1989 and 1990. Measurements of the EM bias were made at 5 and 14 Ghz. During the EM bias experiments by Melville et al., a wire wave gauge was used to obtain the modulation of the high frequency waves by the low frequency waves. It became apparent that the EM bias was primarily caused by the modulation of the short waves. This was reported by Arnold et al. The EM bias is explained using physical optics scattering and an empirical model for the short wave modulation. Measurements of the short wave modulation using a wire wave gauge demonstrated a linear dependence of the normalized bias on the short wave modulation strength, M. The theory accurately predicts this dependence by the relation epsilon = -alphaMH sub 1/3. The wind speed dependence of the normalized bias is explained by the dependence of the short wave modulation strength on the wind speed. While other effects such as long wave tilt and curvature will have an effect on the bias, the primary cause of the bias is shown to be due to the short wave modulation. This report will present a theory using physical optics scattering and an empirical model of the short wave modulation to estimate the EM bias. The estimated EM bias will be compared to measurements at C and Ku bands.

Charge and pairing dynamics in the attractive Hubbard model: Mode coupling and the validity of linear-response theory

NASA Astrophysics Data System (ADS)

Bünemann, Jörg; Seibold, Götz

2017-12-01

Pump-probe experiments have turned out as a powerful tool in order to study the dynamics of competing orders in a large variety of materials. The corresponding analysis of the data often relies on standard linear-response theory generalized to nonequilibrium situations. Here we examine the validity of such an approach for the charge and pairing response of systems with charge-density wave and (or) superconducting (SC) order. Our investigations are based on the attractive Hubbard model which we study within the time-dependent Hartree-Fock approximation. In particular, we calculate the quench and pump-probe dynamics for SC and charge order parameters in order to analyze the frequency spectra and the coupling of the probe field to the specific excitations. Our calculations reveal that the "linear-response assumption" is justified for small to moderate nonequilibrium situations (i.e., pump pulses) in the case of a purely charge-ordered ground state. However, the pump-probe dynamics on top of a superconducting ground state is determined by phase and amplitude modes which get coupled far from the equilibrium state indicating the failure of the linear-response assumption.

Methods of Investigation of Equations that Describe Waves in Tubes with Elastic Walls and Application of the Theory of Reversible and Weak Dissipative Shocks

NASA Astrophysics Data System (ADS)

Bakholdin, Igor

2018-02-01

Various models of a tube with elastic walls are investigated: with controlled pressure, filled with incompressible fluid, filled with compressible gas. The non-linear theory of hyperelasticity is applied. The walls of a tube are described with complete membrane model. It is proposed to use linear model of plate in order to take the bending resistance of walls into account. The walls of the tube were treated previously as inviscid and incompressible. Compressibility of material of walls and viscosity of material, either gas or liquid are considered. Equations are solved numerically. Three-layer time and space centered reversible numerical scheme and similar two-layer space reversible numerical scheme with approximation of time derivatives by Runge-Kutta method are used. A method of correction of numerical schemes by inclusion of terms with highorder derivatives is developed. Simplified hyperbolic equations are derived.

Solution of Linearized Drift Kinetic Equations in Neoclassical Transport Theory by the Method of Matched Asymptotic Expansions

NASA Astrophysics Data System (ADS)

Wong, S. K.; Chan, V. S.; Hinton, F. L.

2001-10-01

The classic solution of the linearized drift kinetic equations in neoclassical transport theory for large-aspect-ratio tokamak flux-surfaces relies on the variational principle and the choice of ``localized" distribution functions as trialfunctions.(M.N. Rosenbluth, et al., Phys. Fluids 15) (1972) 116. Somewhat unclear in this approach are the nature and the origin of the ``localization" and whether the results obtained represent the exact leading terms in an asymptotic expansion int he inverse aspect ratio. Using the method of matched asymptotic expansions, we were able to derive the leading approximations to the distribution functions and demonstrated the asymptotic exactness of the existing results. The method is also applied to the calculation of angular momentum transport(M.N. Rosenbluth, et al., Plasma Phys. and Contr. Nucl. Fusion Research, 1970, Vol. 1 (IAEA, Vienna, 1971) p. 495.) and the current driven by electron cyclotron waves.

Migration of scattered teleseismic body waves

NASA Astrophysics Data System (ADS)

Bostock, M. G.; Rondenay, S.

1999-06-01

The retrieval of near-receiver mantle structure from scattered waves associated with teleseismic P and S and recorded on three-component, linear seismic arrays is considered in the context of inverse scattering theory. A Ray + Born formulation is proposed which admits linearization of the forward problem and economy in the computation of the elastic wave Green's function. The high-frequency approximation further simplifies the problem by enabling (1) the use of an earth-flattened, 1-D reference model, (2) a reduction in computations to 2-D through the assumption of 2.5-D experimental geometry, and (3) band-diagonalization of the Hessian matrix in the inverse formulation. The final expressions are in a form reminiscent of the classical diffraction stack of seismic migration. Implementation of this procedure demands an accurate estimate of the scattered wave contribution to the impulse response, and thus requires the removal of both the reference wavefield and the source time signature from the raw record sections. An approximate separation of direct and scattered waves is achieved through application of the inverse free-surface transfer operator to individual station records and a Karhunen-Loeve transform to the resulting record sections. This procedure takes the full displacement field to a wave vector space wherein the first principal component of the incident wave-type section is identified with the direct wave and is used as an estimate of the source time function. The scattered displacement field is reconstituted from the remaining principal components using the forward free-surface transfer operator, and may be reduced to a scattering impulse response upon deconvolution of the source estimate. An example employing pseudo-spectral synthetic seismograms demonstrates an application of the methodology.

Symmetry properties of second harmonics generated by antisymmetric Lamb waves

NASA Astrophysics Data System (ADS)

Zhu, Wujun; Xiang, Yanxun; Liu, Chang-Jun; Deng, Mingxi; Xuan, Fu-Zhen

2018-03-01

Symmetry properties of second harmonics generated by antisymmetric primary Lamb waves are systematically studied in this work. In theory, the acoustic field of second harmonic Lamb waves is obtained by using the perturbation approximation and normal modal method, and the energy flux transfer from the primary Lamb waves to second harmonics is mainly explored. Symmetry analyses indicate that either the symmetric or antisymmetric Lamb waves can merely generate the symmetric second harmonics. Finite element simulations are performed on the nonlinear Lamb wave propagation of the antisymmetric A0 mode in the low frequency region. The signals of the second harmonics and the symmetric second harmonic s0 mode are found to be exactly equivalent in the time domain. The relative acoustic nonlinearity parameter A2/A12 oscillates with the propagation distance, and the oscillation amplitude and spatial period are well consistent with the theoretical prediction of the A0-s0 mode pair, which means that only the second harmonic s0 mode is generated by the antisymmetric primary A0 mode. Experiments are further conducted to examine the cumulative generation of symmetric second harmonics for the antisymmetric-symmetric mode pair A3-s6. Results show that A2/A12 increases linearly with the propagation distance, which means that the symmetric second harmonic s6 mode is generated cumulatively by the antisymmetric primary A3 mode. The present investigation systematically corroborates the proposed theory that only symmetric second harmonics can be generated accompanying the propagation of antisymmetric primary Lamb waves in a plate.

Medium-energy electrons and heavy ions in Jupiter's magnetosphere - Effects of lower hybrid wave-particle interactions

NASA Technical Reports Server (NTRS)

Barbosa, D. D.

1986-01-01

A theory of medium-energy (about keV) electrons and heavy ions in Jupiter's magnetosphere is presented. Lower hybrid waves are generated by the combined effects of a ring instability of neutral wind pickup ions and the modified two-stream instability associated with transport of cool Iogenic plasma. The quasi-linear energy diffusion coefficient for lower hybrid wave-particle interactions is evaluated, and several solutions to the diffusion equation are given. Calculations based on measured wave properties show that the noise substantially modifies the particle distribution functions. The effects are to accelerate superthermal ions and electrons to keV energies and to thermalize the pickup ions on time scales comparable to the particle residence time. The S(2+)/S(+) ratio at medium energies is a measure of the relative contribution from Iogenic thermal plasma and neutral wind ions, and this important quantity should be determined from future measurements. The theory also predicts a preferential acceleration of heavy ions with an accleration time that scales inversely with the root of the ion mass. Electrons accelerated by the process contribute to further reionization of the neutral wind by electron impact, thus providing a possible confirmation of Alfven's critical velocity effect in the Jovian magnetosphere.

Modelling of Charles Darwin's tsunami reports

NASA Astrophysics Data System (ADS)

Galiev, Shamil

2010-05-01

Darwin landed at Valdivia and Concepcion, Chile, just before, during, and after a great 1835 earthquake. He described his impressions and results of the earthquake-induced natural catastrophe in The Voyage of the Beagle. His description of the tsunami could easily be read as a report from Indonesia or Sri Lanka, after the catastrophic tsunami of 26 December 2004. In particular, Darwin emphasised the dependence of earthquake-induced waves on a form of the coast and the coastal depth: ‘… Talcuhano and Callao are situated at the head of great shoaling bays, and they have always suffered from this phenomenon; whereas, the town of Valparaiso, which is seated close on the border of a profound ocean... has never been overwhelmed by one of these terrific deluges…' . He reports also, that ‘… the whole body of the sea retires from the coast, and then returns in great waves of overwhelming force ...' (we cite the Darwin's sentences following researchspace. auckland. ac. nz/handle/2292/4474). The coastal evolution of a tsunami was analytically studied in many publications (see, for example, Synolakis, C.E., Bernard, E.N., 2006. Philos. Trans. R. Soc., Ser. A, 364, 2231-2265; Tinti, S., Tonini, R. 205. J.Fluid Mech., 535, 11-21). However, the Darwin's reports and the influence of the coastal depth on the formation and the evolution of the steep front and the profile of tsunami did not practically discuss. Recently, a mathematical theory of these phenomena was presented in researchspace. auckland. ac. nz/handle/2292/4474. The theory describes the waves which are excited due to nonlinear effects within a shallow coastal zone. The tsunami elevation is described by two components: . Here is the linear (prime) component. It describes the wave coming from the deep ocean. is the nonlinear component. This component may become very important near the coastal line. After that the theory of the shallow waves is used. This theory yields the linear equation for and the weakly-nonlinear equation for . The last equation contains the forcing term which is generated by nonlinearity and depends on . The nonlinear shock-like solution for is constructed which is valid within the narrow coastal zone. Then the tsunami evolution near a coast is studied. It is found that the coastal evolution strongly depends on the profile of the bottom and the distance from the coastline. Far from this the wave surface is smooth and the wave is long enough. The wave profile begins to change quickly, if the coastal water is shallow. The steep (discontinuous) front of the tsunami can be generated. The water level reduces ahead of the front, or the ebb can appear there. Then this front begins to move away from the coast - into the ocean. This direction is opposite to the motion of the whole wave. The amplitude of the front is increased. The water wall is formed. This process explains the catastrophic effect of a tsunami, when a water-wall appears instantly. The wave, having two steep peaks, may be generated in the case of very shallow water. In contrast with this, the tsunami, practically, does not change, if the coastal water is deep. On the whole, the conclusions agree with the Darwin's reports.

A model for the wind of the M supergiant VX Sagittarii

NASA Astrophysics Data System (ADS)

Pijpers, F. P.

1990-11-01

The velocity distribution of the stellar wind from the M supergiant VX Sgr deduced from interferometric measurements of maser lines by Chapman and Cohen (1986) has been modeled using the linearized theory of stellar winds driven by short period sound waves proposed by Pijpers and Hearn (1989) and the theory of stellar winds driven by short period shocks proposed by Pijpers and Habing (1989). The effect of the radiative forces on the dust formed in the wind is included in a simple way. Good agreement with the observations is obtained by a range of parameters in the theory. A series of observations of the maser lines at invervals of one or a few days may provide additional constraints on the interpretation.

Research on unsteady transonic flow theory

NASA Technical Reports Server (NTRS)

Revell, J. D.

1973-01-01

A two-dimensional theory is considered for the unsteady flow disturbances caused by aeroelastic deformations of a thick wing at high subsonic freestream Mach numbers, having a single, internally embedded supercritical (locally supersonic) steady flow region adjacent to the low pressure side of the wing. The theory develops a matrix of unsteady aerodynamic influence coefficients (AICs) suitable as a strip theory for aeroelastic analysis of large aspect ratio thick wings of moderate sweep, typical of a wide class of current and future aircraft. The theory derives the linearized unsteady flow solutions separately for both the subcritical and supercritical regions. These solutions are coupled together to give the requisite (wing pressure-downwash) AICs by the intermediate step of defining flow disturbances on the sonic line, and at the shock wave; these intermediate quantities are then algebraically eliminated by expressing them in terms of the wing surface downwash.

Linear flavor-wave theory for fully antisymmetric SU(N ) irreducible representations

NASA Astrophysics Data System (ADS)

Kim, Francisco H.; Penc, Karlo; Nataf, Pierre; Mila, Frédéric

2017-11-01

The extension of the linear flavor-wave theory to fully antisymmetric irreducible representations (irreps) of SU (N ) is presented in order to investigate the color order of SU (N ) antiferromagnetic Heisenberg models in several two-dimensional geometries. The square, triangular, and honeycomb lattices are considered with m fermionic particles per site. We present two different methods: the first method is the generalization of the multiboson spin-wave approach to SU (N ) which consists of associating a Schwinger boson to each state on a site. The second method adopts the Read and Sachdev bosons which are an extension of the Schwinger bosons that introduces one boson for each color and each line of the Young tableau. The two methods yield the same dispersing modes, a good indication that they properly capture the semiclassical fluctuations, but the first one leads to spurious flat modes of finite frequency not present in the second one. Both methods lead to the same physical conclusions otherwise: long-range Néel-type order is likely for the square lattice for SU(4) with two particles per site, but quantum fluctuations probably destroy order for more than two particles per site, with N =2 m . By contrast, quantum fluctuations always lead to corrections larger than the classical order parameter for the tripartite triangular lattice (with N =3 m ) or the bipartite honeycomb lattice (with N =2 m ) for more than one particle per site, m >1 , making the presence of color very unlikely except maybe for m =2 on the honeycomb lattice, for which the correction is only marginally larger than the classical order parameter.

Quantum square-well with logarithmic central spike

NASA Astrophysics Data System (ADS)

Znojil, Miloslav; Semorádová, Iveta

2018-01-01

Singular repulsive barrier V (x) = -gln(|x|) inside a square-well is interpreted and studied as a linear analog of the state-dependent interaction ℒeff(x) = -gln[ψ∗(x)ψ(x)] in nonlinear Schrödinger equation. In the linearized case, Rayleigh-Schrödinger perturbation theory is shown to provide a closed-form spectrum at sufficiently small g or after an amendment of the unperturbed Hamiltonian. At any spike strength g, the model remains solvable numerically, by the matching of wave functions. Analytically, the singularity is shown regularized via the change of variables x = expy which interchanges the roles of the asymptotic and central boundary conditions.

Exponential stabilization of magnetoelastic waves in a Mindlin-Timoshenko plate by localized internal damping

NASA Astrophysics Data System (ADS)

Grobbelaar-Van Dalsen, Marié

2015-08-01

This article is a continuation of our earlier work in Grobbelaar-Van Dalsen (Z Angew Math Phys 63:1047-1065, 2012) on the polynomial stabilization of a linear model for the magnetoelastic interactions in a two-dimensional electrically conducting Mindlin-Timoshenko plate. We introduce nonlinear damping that is effective only in a small portion of the interior of the plate. It turns out that the model is uniformly exponentially stable when the function , that represents the locally distributed damping, behaves linearly near the origin. However, the use of Mindlin-Timoshenko plate theory in the model enforces a restriction on the region occupied by the plate.

The effect of small streamwise velocity distortion on the boundary layer flow over a thin flat plate with application to boundary layer stability theory

NASA Technical Reports Server (NTRS)

Goldstein, M. E.; Leib, S. J.; Cowley, S. J.

1990-01-01

Researchers show how an initially linear spanwise disturbance in the free stream velocity field is amplified by leading edge bluntness effects and ultimately leads to a small amplitude but linear spanwise motion far downstream from the edge. This spanwise motion is imposed on the boundary layer flow and ultimately causes an order-one change in its profile shape. The modified profiles are highly unstable and can support Tollmein-Schlichting wave growth well upstream of the theoretical lower branch of the neutral stability curve for a Blasius boundary layer.

Projection operators for the Rossby and Poincare waves in a beta-plane approximation

NASA Astrophysics Data System (ADS)

Lebedkina, Anastasia; Ivan, Karpov; Sergej, Leble

2013-04-01

Study of the wave structure variations of atmospheric parameters is a due to a solving of number practical problems associated with the weather and the state of the environment requires knowledge of the spectral characteristics of atmospheric waves. Modern methods, for identification of wave disturbances in the atmosphere, based on the harmonic analysis of observations. The success of these application is determined by the presence of sets of experimental data obtained in the long-term (over the period of the wave) of the atmosphere on a large number of independent observation stations. Currently, the system of observation in the atmosphere, both terrestrial and satellite, unevenly covers the surface of the Earth and, despite the length of observation, doesn't solve the problem of identification of waves. Thus, the problem of identification wave disturbances conflicts fundamental difficulties, and solution needs in a new methods for the analysis of observations. The work complete a procedure to construct a projection operators for large-scale waves in the atmosphere. Advantage of this method is the ability to identify type of wave and its characteristics only on the base of a time series of observations. It means that the problem of waves identification can be solved on the basis of only one station observations. In the method assumed that the observed spatial and temporal structure of the atmosphere is determined by the superposition of different type waves. For each type of waves involved in this superposition, dispersion and polarization relations (between the components of the wave vector of the field) expect as known. Based on these assumptions, we can construct projection operators on the initial superposition state on the linear basis of vectors corresponding to the known type of atmospheric waves. The action of the design on the superposition state, which, in fact, is the result of observations, determine the amplitude and phase of the waves of a known type. The idea to use the polarization relations for the classification of waves originated in radio physics in the works of A. A. Novikov. In the theory of the electromagnetic field polarization relations is traditionally included in the analysis of wave phenomena. In the theory of acoustic-gravity waves, projection operators were introduced in a works of S. B. Leble. The object of study is a four-dimentional vector (components of the velocity, pressure and temperature). Based on these assumptions, we can construct the projection operators for superposition state on the linear basis, corresponding to the well-known type of waves. In this paper we consider procedure for construction of a projection operators for planetary Rossby and Poincare waves in the Earth's atmosphere in the approximation of the "beta-plane". In a result of work we constructed projection operators in this approximation for Poincare and Rossby waves. The tests for operators shown, that separation of the contribution of corresponding waves from source of the wave field is possible. Estimation accuracy of the operators and results of applying operators to the data TEC presented.

Computation of acoustic ressure fields produced in feline brain by high-intensity focused ultrasound

NASA Astrophysics Data System (ADS)

Omidi, Nazanin

In 1975, Dunn et al. (JASA 58:512-514) showed that a simple relation describes the ultrasonic threshold for cavitation-induced changes in the mammalian brain. The thresholds for tissue damage were estimated for a variety of acoustic parameters in exposed feline brain. The goal of this study was to improve the estimates for acoustic pressures and intensities present in vivo during those experimental exposures by estimating them using nonlinear rather than linear theory. In our current project, the acoustic pressure waveforms produced in the brains of anesthetized felines were numerically simulated for a spherically focused, nominally f1-transducer (focal length = 13 cm) at increasing values of the source pressure at frequencies of 1, 3, and 9 MHz. The corresponding focal intensities were correlated with the experimental data of Dunn et al. The focal pressure waveforms were also computed at the location of the true maximum. For low source pressures, the computed waveforms were the same as those determined using linear theory, and the focal intensities matched experimentally determined values. For higher source pressures, the focal pressure waveforms became increasingly distorted, with the compressional amplitude of the wave becoming greater, and the rarefactional amplitude becoming lower than the values calculated using linear theory. The implications of these results for clinical exposures are discussed.

Realizing Broadband and Invertible Linear-to-circular Polarization Converter with Ultrathin Single-layer Metasurface

PubMed Central

Li, Zhancheng; Liu, Wenwei; Cheng, Hua; Chen, Shuqi; Tian, Jianguo

2015-01-01

The arbitrary control of the polarization states of light has attracted the interest of the scientific community because of the wide range of modern optical applications that such control can afford. However, conventional polarization control setups are bulky and very often operate only within a narrow wavelength range, thereby resisting optical system miniaturization and integration. Here, we present the basic theory, simulated demonstration, and in-depth analysis of a high-performance broadband and invertible linear-to-circular (LTC) polarization converter composed of a single-layer gold nanorod array with a total thickness of ~λ/70 for the near-infrared regime. This setup can transform a circularly polarized wave into a linearly polarized one or a linearly polarized wave with a wavelength-dependent electric field polarization angle into a circularly polarized one in the transmission mode. The broadband and invertible LTC polarization conversion can be attributed to the tailoring of the light interference at the subwavelength scale via the induction of the anisotropic optical resonance mode. This ultrathin single-layer metasurface relaxes the high-precision requirements of the structure parameters in general metasurfaces while retaining the polarization conversion performance. Our findings open up intriguing possibilities towards the realization of novel integrated metasurface-based photonics devices for polarization manipulation, modulation, and phase retardation. PMID:26667360

An Evaluation of Linear Instability Waves as Sources of Sound in a Supersonic Turbulent Jet

NASA Technical Reports Server (NTRS)

Mohseni, Kamran; Colonius, Tim; Freund, Jonathan B.

2002-01-01

Mach wave radiation from supersonic jets is revisited to better quantify the extent to which linearized equations represent the details of the actual mechanism. To this end, we solve the linearized Navier-Stokes equations (LNS) with precisely the same mean flow and inflow disturbances as a previous direct numerical simulation (DNS) of a perfectly expanded turbulent M = 1.92 jet. We restrict our attention to the first two azimuthal modes, n = 0 and n = 1, which constitute most of the acoustic field. The direction of peak radiation and the peak Strouhal number matches the DNS reasonably well, which is in accord with previous experimental justification of the linear theory. However, it is found that the sound pressure level predicted by LNS is significantly lower than that from DNS. In order to investigate the discrepancy, individual frequency components of the solution are examined. These confirm that near the peak Strouhal number, particularly for the first helical mode n = 1, the amplification of disturbances in the LNS closely matches the DNS. However, away from the peak frequency (and generally for the azimuthal mode n = 0), modes in the LNS are damped while those in the DNS grow at rates comparable to those at the peak Strouhal number.

Collisional damping of helicon waves in a high density hydrogen linear plasma device

DOE PAGES

Caneses, Juan F.; Blackwell, Boyd D.

2016-09-28

In this paper, we investigate the propagation and damping of helicon waves along the length (~50 cm) of a helicon-produced 20 kW hydrogen plasma ( ~1-2 1019 m-3, ~1-6 eV, H2 8 mTorr) operated in a magnetic mirror configuration (antenna region: 50-200 G and mirror region: 800 G). Experimental results show the presence of traveling helicon waves (~10 G and ~ 10-15 cm) propagating away from the antenna region which become collisionally absorbed within 40 to 50 cm. We describe the use of the WKB method to calculate wave damping and provide an expression to assess its validity based onmore » experimental measurements. By comparing theory and experiment, we show that for the conditions associated with this paper classical collisions are sufficient to explain the observed wave damping along the length of the plasma column. Based on these results, we provide an expression for the scaling of helicon wave damping relevant to high density discharges and discuss the location of surfaces for plasma-material interaction studies in our device (MAGPIE).« less

Size of photons and the idea of coherence

NASA Astrophysics Data System (ADS)

Pandey, Rakesh Kumar

2018-05-01

Ever since behavior of photons were explained in terms of the matter-wave duality, mystery about the size of such a photon as it behaves like a particle has never slipped out from the scientific discussions. It is normally believed that the size of the photons is of the order of the wavelength of the electromagnetic wave. This paper addresses this scientific concern and attempts at opening the issue up for discussion after making a completely theoretical but consistent proposition. The argument presented here borrows the idea from the way particles have been conceptualized in quantum mechanics. In quantum mechanics it is argued that a particle gets represented not by a single wave but a group of waves in a way that the group velocity of such a group of waves exactly gives the velocity of the particle. Based on the same argument it is explained how the coherence length instead of the wavelength of the electromagnetic wave, must estimate the linear dimension of a photon. In the end, the discussion on the size of a photon in view of the special theory of relativity is also initiated in this paper.

Measurement of Shear Elastic Moduli in Quasi-Incompressible Soft Solids

NASA Astrophysics Data System (ADS)

Rénier, Mathieu; Gennisson, Jean-Luc; Barrière, Christophe; Catheline, Stefan; Tanter, Mickaël; Royer, Daniel; Fink, Mathias

2008-06-01

Recently a nonlinear equation describing the plane shear wave propagation in isotropic quasi-incompressible media has been developed using a new expression of the strain energy density, as a function of the second, third and fourth order shear elastic constants (respectively μ, A, D) [1]. In such a case, the shear nonlinearity parameter βs depends only from these last coefficients. To date, no measurement of the parameter D have been carried out in soft solids. Using a set of two experiments, acoustoelasticity and finite amplitude shear waves, the shear elastic moduli up to the fourth order of soft solids are measured. Firstly, this theoretical background is applied to the acoustoelasticity theory, giving the variations of the shear wave speed as a function of the stress applied to the medium. From such variations, both linear (μ) and third order shear modulus (A) are deduced in agar-gelatin phantoms. Experimentally the radiation force induced by a focused ultrasound beam is used to generate quasi-plane linear shear waves within the medium. Then the shear wave propagation is imaged with an ultrafast ultrasound scanner. Secondly, in order to give rise to finite amplitude plane shear waves, the radiation force generation technique is replaced by a vibrating plate applied at the surface of the phantoms. The propagation is also imaged using the same ultrafast scanner. From the assessment of the third harmonic amplitude, the nonlinearity parameter βS is deduced. Finally, combining these results with the acoustoelasticity experiment, the fourth order modulus (D) is deduced. This set of experiments provides the characterization, up to the fourth order, of the nonlinear shear elastic moduli in quasi-incompressible soft media. Measurements of the A moduli reveal that while the behaviors of both soft solids are close from a linear point of view, the corresponding nonlinear moduli A are quite different. In a 5% agar-gelatin phantom, the fourth order elastic constant D is found to be 30±10 kPa.

The development of efficient numerical time-domain modeling methods for geophysical wave propagation

NASA Astrophysics Data System (ADS)

Zhu, Lieyuan

This Ph.D. dissertation focuses on the numerical simulation of geophysical wave propagation in the time domain including elastic waves in solid media, the acoustic waves in fluid media, and the electromagnetic waves in dielectric media. This thesis shows that a linear system model can describe accurately the physical processes of those geophysical waves' propagation and can be used as a sound basis for modeling geophysical wave propagation phenomena. The generalized stability condition for numerical modeling of wave propagation is therefore discussed in the context of linear system theory. The efficiency of a series of different numerical algorithms in the time-domain for modeling geophysical wave propagation are discussed and compared. These algorithms include the finite-difference time-domain method, pseudospectral time domain method, alternating directional implicit (ADI) finite-difference time domain method. The advantages and disadvantages of these numerical methods are discussed and the specific stability condition for each modeling scheme is carefully derived in the context of the linear system theory. Based on the review and discussion of these existing approaches, the split step, ADI pseudospectral time domain (SS-ADI-PSTD) method is developed and tested for several cases. Moreover, the state-of-the-art stretched-coordinate perfect matched layer (SCPML) has also been implemented in SS-ADI-PSTD algorithm as the absorbing boundary condition for truncating the computational domain and absorbing the artificial reflection from the domain boundaries. After algorithmic development, a few case studies serve as the real-world examples to verify the capacities of the numerical algorithms and understand the capabilities and limitations of geophysical methods for detection of subsurface contamination. The first case is a study using ground penetrating radar (GPR) amplitude variation with offset (AVO) for subsurface non-aqueous-liquid (NAPL) contamination. The numerical AVO study reveals that the normalized residual polarization (NRP) variation with offset does not respond to subsurface NAPL existence when the offset is close to or larger than its critical value (which corresponds to critical incident angle) because the air and head waves dominate the recorded wave field and severely interfere with reflected waves in the TEz wave field. Thus it can be concluded that the NRP AVO/GPR method is invalid when source-receiver angle offset is close to or greater than its critical value due to incomplete and severely distorted reflection information. In other words, AVO is not a promising technique for detection of the subsurface NAPL, as claimed by some researchers. In addition, the robustness of the newly developed numerical algorithms is also verified by the AVO study for randomly-arranged layered media. Meanwhile, this case study also demonstrates again that the full-wave numerical modeling algorithms are superior to ray tracing method. The second case study focuses on the effect of the existence of a near-surface fault on the vertically incident P- and S- plane waves. The modeling results show that both P-wave vertical incidence and S-wave vertical incidence cases are qualified fault indicators. For the plane S-wave vertical incidence case, the horizontal location of the upper tip of the fault (the footwall side) can be identified without much effort, because all the recorded parameters on the surface including the maximum velocities and the maximum accelerations, and even their ratios H/V, have shown dramatic changes when crossing the upper tip of the fault. The centers of the transition zone of the all the curves of parameters are almost directly above the fault tip (roughly the horizontal center of the model). Compared with the case of the vertically incident P-wave source, it has been found that the S-wave vertical source is a better indicator for fault location, because the horizontal location of the tip of that fault cannot be clearly identified with the ratio of the horizontal to vertical velocity for the P-wave incident case.

Ultrasonic Microtransport

NASA Astrophysics Data System (ADS)

Moroney, Richard Morgan, III

We have observed numerous kinetic effects using ultrasonic flexural plate waves (FPWs) in 4mu -thick composite plates of low-stress silicon nitride, piezoelectric zinc oxide and aluminum. The wavelength is typically 100 mum, and the area 3 x 8 mm^2. A successful new surface micromachining fabrication process is presented here for the first time. FPWs have been used to move liquids and gasses with motion typically indicated by polysilicon blocks in air and polystyrene spheres in water; the velocity in air is 4.5 mm/s (with a zero-to-peak input of 3 V), and in water it is 100 mum/s (with an input of 7.8 V). Other observations include pumping of a liquid dye, and mixing near the FPW surface. All quantitative observations demonstrate that the kinetic effects of FPWs are proportional to the square of the wave amplitude. The amplitude for a typical device is 250 A at 9 V input; the power in a typical FPW is about 2 mW. The amplitude can be accurately measured using a laser diffraction technique. Experimental error is about +/-10%, and many of the results agree well with a simple theory to predict the FPW amplitude; extensions of the theory model the fluid loading of FPW devices, but experiment and theory disagree by about 15%. Pumping by flexural plate waves is an example of the phenomenon known as acoustic streaming. A common solution approach is the method of successive approximations, where the nonlinear equations are first linearized and solved. This "first-order" solution is then used to determine the inhomogeneous source terms in the linearized, "second -order" equations of motion. Theoretical predictions of streaming theory are in excellent agreement with experiment in the case where the FPW device contacts a half-space of fluid; predictions for flow in small channels encourage the development of integrated micropumps. Applications for microflow include thermal redistribution in integrated circuits and liquid movement in analytical instruments--particularly where a small dead volume is required. Capabilities of this technology and further applications are discussed. Microflow systems that integrate transport of fluids and solids with sensing, mixing and other useful tasks may become a new market-leading application for the sensor and actuator field.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Jing-Yuan, E-mail: chjy@uchicago.edu; Stanford Institute for Theoretical Physics, Stanford University, CA 94305; Son, Dam Thanh, E-mail: dtson@uchicago.edu

We develop an extension of the Landau Fermi liquid theory to systems of interacting fermions with non-trivial Berry curvature. We propose a kinetic equation and a constitutive relation for the electromagnetic current that together encode the linear response of such systems to external electromagnetic perturbations, to leading and next-to-leading orders in the expansion over the frequency and wave number of the perturbations. We analyze the Feynman diagrams in a large class of interacting quantum field theories and show that, after summing up all orders in perturbation theory, the current–current correlator exactly matches with the result obtained from the kinetic theory.more » - Highlights: • We extend Landau’s kinetic theory of Fermi liquid to incorporate Berry phase. • Berry phase effects in Fermi liquid take exactly the same form as in Fermi gas. • There is a new “emergent electric dipole” contribution to the anomalous Hall effect. • Our kinetic theory is matched to field theory to all orders in Feynman diagrams.« less

Modulational instability in a PT-symmetric vector nonlinear Schrödinger system

NASA Astrophysics Data System (ADS)

Cole, J. T.; Makris, K. G.; Musslimani, Z. H.; Christodoulides, D. N.; Rotter, S.

2016-12-01

A class of exact multi-component constant intensity solutions to a vector nonlinear Schrödinger (NLS) system in the presence of an external PT-symmetric complex potential is constructed. This type of uniform wave pattern displays a non-trivial phase whose spatial dependence is induced by the lattice structure. In this regard, light can propagate without scattering while retaining its original form despite the presence of inhomogeneous gain and loss. These constant-intensity continuous waves are then used to perform a modulational instability analysis in the presence of both non-hermitian media and cubic nonlinearity. A linear stability eigenvalue problem is formulated that governs the dynamical evolution of the periodic perturbation and its spectrum is numerically determined using Fourier-Floquet-Bloch theory. In the self-focusing case, we identify an intensity threshold above which the constant-intensity modes are modulationally unstable for any Floquet-Bloch momentum belonging to the first Brillouin zone. The picture in the self-defocusing case is different. Contrary to the bulk vector case, where instability develops only when the waves are strongly coupled, here an instability occurs in the strong and weak coupling regimes. The linear stability results are supplemented with direct (nonlinear) numerical simulations.

Acoustic investigation of the aperture dynamics of an elastic membrane closing an overpressurized cylindrical cavity

NASA Astrophysics Data System (ADS)

Sánchez, Claudia; Vidal, Valérie; Melo, Francisco

2015-08-01

We report an experimental study of the acoustic signal produced by the rupture of an elastic membrane that initially closes a cylindrical overpressurized cavity. This configuration has been recently used as an experimental model system for the investigation of the acoustic emission from the bursting of elongated gas bubbles rising in a conduit. Here, we investigate the effect of the membrane rupture dynamics on the acoustic signal produced by the pressure release by changing the initial tension of the membrane. The initial overpressure in the cavity is fixed at a value such that the system remains in the linear acoustic regime. For large initial membrane deformation, the rupture time τ rup is small compared to the wave propagation time in the cavity and the pressure wave inside the conduit can be fully captured by the linear theory. For low membrane tension, a hole is pierced in the membrane but its rupture does not occur. For intermediate deformation, finally, the rupture progresses in two steps: first the membrane opens slowly; then, after reaching a critical size, the rupture accelerates. A transversal wave is excited along the membrane surface. The characteristic signature of each opening dynamics on the acoustic emission is described.

Asymptotic theory of neutral stability of the Couette flow of a vibrationally excited gas

NASA Astrophysics Data System (ADS)

Grigor'ev, Yu. N.; Ershov, I. V.

2017-01-01

An asymptotic theory of the neutral stability curve for a supersonic plane Couette flow of a vibrationally excited gas is developed. The initial mathematical model consists of equations of two-temperature viscous gas dynamics, which are used to derive a spectral problem for a linear system of eighth-order ordinary differential equations within the framework of the classical linear stability theory. Unified transformations of the system for all shear flows are performed in accordance with the classical Lin scheme. The problem is reduced to an algebraic secular equation with separation into the "inviscid" and "viscous" parts, which is solved numerically. It is shown that the thus-calculated neutral stability curves agree well with the previously obtained results of the direct numerical solution of the original spectral problem. In particular, the critical Reynolds number increases with excitation enhancement, and the neutral stability curve is shifted toward the domain of higher wave numbers. This is also confirmed by means of solving an asymptotic equation for the critical Reynolds number at the Mach number M ≤ 4.

Simulation of electron energy loss spectra of nanomaterials with linear-scaling density functional theory

DOE PAGES

Tait, E. W.; Ratcliff, L. E.; Payne, M. C.; ...

2016-04-20

Experimental techniques for electron energy loss spectroscopy (EELS) combine high energy resolution with high spatial resolution. They are therefore powerful tools for investigating the local electronic structure of complex systems such as nanostructures, interfaces and even individual defects. Interpretation of experimental electron energy loss spectra is often challenging and can require theoretical modelling of candidate structures, which themselves may be large and complex, beyond the capabilities of traditional cubic-scaling density functional theory. In this work, we present functionality to compute electron energy loss spectra within the onetep linear-scaling density functional theory code. We first demonstrate that simulated spectra agree withmore » those computed using conventional plane wave pseudopotential methods to a high degree of precision. The ability of onetep to tackle large problems is then exploited to investigate convergence of spectra with respect to supercell size. As a result, we apply the novel functionality to a study of the electron energy loss spectra of defects on the (1 0 1) surface of an anatase slab and determine concentrations of defects which might be experimentally detectable.« less

Surfing gravitational waves: can bigravity survive growing tensor modes?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Amendola, Luca; Könnig, Frank; Martinelli, Matteo

The theory of bigravity offers one of the simplest possibilities to describe a massive graviton while having self-accelerating cosmological solutions without a cosmological constant. However, it has been shown recently that bigravity is affected by early-time fast growing modes on the tensor sector. Here we argue that we can only trust the linear analysis up to when perturbations are in the linear regime and use a cut-off to stop the growing of the metric perturbations. This analysis, although more consistent, still leads to growing tensor modes that are unacceptably large for the theory to be compatible with measurements of themore » cosmic microwave background (CMB), both in temperature and polarization spectra. In order to suppress the growing modes and make the model compatible with CMB spectra, we find it necessary to either fine-tune the initial conditions, modify the theory or set the cut-off for the tensor perturbations of the second metric much lower than unity. Initial conditions such that the growing mode is sufficiently suppresed can be achieved in scenarios in which inflation ends at the GeV scale.« less

RELATIVISTIC CYCLOTRON INSTABILITY IN ANISOTROPIC PLASMAS

DOE Office of Scientific and Technical Information (OSTI.GOV)

López, Rodrigo A.; Moya, Pablo S.; Muñoz, Víctor

2016-11-20

A sufficiently large temperature anisotropy can sometimes drive various types of electromagnetic plasma micro-instabilities, which can play an important role in the dynamics of relativistic pair plasmas in space, astrophysics, and laboratory environments. Here, we provide a detailed description of the cyclotron instability of parallel propagating electromagnetic waves in relativistic pair plasmas on the basis of a relativistic anisotropic distribution function. Using plasma kinetic theory and particle-in-cell simulations, we study the influence of the relativistic temperature and the temperature anisotropy on the collective and noncollective modes of these plasmas. Growth rates and dispersion curves from the linear theory show amore » good agreement with simulations results.« less

Electronic Structure Methods Based on Density Functional Theory

DTIC Science & Technology

2010-01-01

0188 The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing...chapter in the ASM Handbook , Volume 22A: Fundamentals of Modeling for Metals Processing, 2010. PAO Case Number: 88ABW-2009-3258; Clearance Date: 16 Jul...are represented using a linear combination, or basis, of plane waves. Over time several methods were developed to avoid the large number of planewaves

Delay-induced Turing-like waves for one-species reaction-diffusion model on a network

NASA Astrophysics Data System (ADS)

Petit, Julien; Carletti, Timoteo; Asllani, Malbor; Fanelli, Duccio

2015-09-01

A one-species time-delay reaction-diffusion system defined on a complex network is studied. Traveling waves are predicted to occur following a symmetry-breaking instability of a homogeneous stationary stable solution, subject to an external nonhomogeneous perturbation. These are generalized Turing-like waves that materialize in a single-species populations dynamics model, as the unexpected byproduct of the imposed delay in the diffusion part. Sufficient conditions for the onset of the instability are mathematically provided by performing a linear stability analysis adapted to time-delayed differential equations. The method here developed exploits the properties of the Lambert W-function. The prediction of the theory are confirmed by direct numerical simulation carried out for a modified version of the classical Fisher model, defined on a Watts-Strogatz network and with the inclusion of the delay.

Time-dependent Tonks-Langmuir model is unstable

NASA Astrophysics Data System (ADS)

Sheridan, T. E.; Baalrud, S. D.

2017-11-01

We investigate a time-dependent extension of the Tonks-Langmuir model for a one-dimensional plasma discharge with collisionless kinetic ions and Boltzmann electrons. Ions are created uniformly throughout the volume and flow from the center of the discharge to the boundary wall due to a self-consistent, zero-order electric field. Solving this model using a particle-in-cell simulation, we observe coherent low-frequency, long-wavelength unstable ion waves which move toward the boundary with a speed below both the ion acoustic speed and the average ion velocity. The maximum amplitude of the wave potential fluctuations peaks at ≈0.09 Te near the wall, where Te is the electron temperature in electron volts. Using linear kinetic theory, we identify this instability as slow ion-acoustic wave modes which are destabilized by the zero-order electric field.

Generation Process of Large-Amplitude Upper-Band Chorus Emissions Observed by Van Allen Probes

DOE PAGES

Kubota, Yuko; Omura, Yoshiharu; Kletzing, Craig; ...

2018-04-19

In this paper, we analyze large-amplitude upper-band chorus emissions measured near the magnetic equator by the Electric and Magnetic Field Instrument Suite and Integrated Science instrument package on board the Van Allen Probes. In setting up the parameters of source electrons exciting the emissions based on theoretical analyses and observational results measured by the Helium Oxygen Proton Electron instrument, we calculate threshold and optimum amplitudes with the nonlinear wave growth theory. We find that the optimum amplitude is larger than the threshold amplitude obtained in the frequency range of the chorus emissions and that the wave amplitudes grow between themore » threshold and optimum amplitudes. Finally, in the frame of the wave growth process, the nonlinear growth rates are much greater than the linear growth rates.« less

Generation Process of Large-Amplitude Upper-Band Chorus Emissions Observed by Van Allen Probes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kubota, Yuko; Omura, Yoshiharu; Kletzing, Craig

In this paper, we analyze large-amplitude upper-band chorus emissions measured near the magnetic equator by the Electric and Magnetic Field Instrument Suite and Integrated Science instrument package on board the Van Allen Probes. In setting up the parameters of source electrons exciting the emissions based on theoretical analyses and observational results measured by the Helium Oxygen Proton Electron instrument, we calculate threshold and optimum amplitudes with the nonlinear wave growth theory. We find that the optimum amplitude is larger than the threshold amplitude obtained in the frequency range of the chorus emissions and that the wave amplitudes grow between themore » threshold and optimum amplitudes. Finally, in the frame of the wave growth process, the nonlinear growth rates are much greater than the linear growth rates.« less

Assessing the performance of formulations for nonlinear feedback of surface gravity waves on ocean currents over coastal waters

NASA Astrophysics Data System (ADS)

Wang, Pengcheng; Sheng, Jinyu; Hannah, Charles

2017-08-01

This study presents applications of a two-way coupled wave-circulation modelling system over coastal waters, with a special emphasis of performance assessments of two different methods for nonlinear feedback of ocean surface gravity waves on three-dimensional (3D) ocean currents. These two methods are the vortex force (VF) formulation suggested by Bennis et al. (2011) and the latest version of radiation stress (RS) formulation suggested by Mellor (2015). The coupled modelling system is first applied to two idealized test cases of surf-zone scales to validate implementations of these two methods in the coupled wave-circulation system. Model results show that the latest version of RS has difficulties in producing the undertow over the surf zone. The coupled system is then applied to Lunenburg Bay (LB) of Nova Scotia during Hurricane Juan in 2003. The coupled system using both the VF and RS formulations generates much stronger and more realistic 3D circulation in the Bay during Hurricane Juan than the circulation-only model, demonstrating the importance of surface wave forces to the 3D ocean circulation over coastal waters. However, the RS formulation generates some weak unphysical currents outside the wave breaking zone due to a less reasonable representation for the vertical distribution of the RS gradients over a slopping bottom. These weak unphysical currents are significantly magnified in a two-way coupled system when interacting with large surface waves, degrading the model performance in simulating currents at one observation site. Our results demonstrate that the VF formulation with an appropriate parameterization of wave breaking effects is able to produce reasonable results for applications over coastal waters during extreme weather events. The RS formulation requires a complex wave theory rather than the linear wave theory for the approximation of a vertical RS term to improve its performance under both breaking and non-breaking wave conditions.

Simulating energy cascade of shock wave formation process in a resonator by gas kinetic scheme

NASA Astrophysics Data System (ADS)

Qu, Chengwu; Zhang, Xiaoqing; Feng, Heying

2017-12-01

The temporal-spatial evolution of gas oscillation was simulated by gas kinetic scheme (GKS) in a cylindrical resonator, driven by a piston at one end and rigidly closed at the other end. Periodic shock waves propagating back and forth were observed in the resonator under finite amplitude of gas oscillation. The studied results demonstrated that the acoustic pressure is a saw-tooth waveform and the oscillatory velocity is a square waveform at the central position of the resonant tube. Moreover, it was found by harmonic analysis that there was no presence of obvious feature for pressure node in such a typical standing wave resonator, and the distribution of acoustic fields displayed a one-dimensional feature for the acoustic pressure while a quasi-one-dimensional form for oscillatory velocity, which demonstrated the nonlinear effects. The simulation results for axial distribution of acoustic intensity showed a good consistency with the published experimental data in the open literature domain, which provides a verification for the effectiveness of the GKS model proposed. The influence of displacement amplitude of the driving piston on the formation of shock wave was numerically investigated, and the simulated results revealed the cascade process of harmonic wave energy from the fundamental wave to higher harmonics. In addition, this study found that the acoustic intensity at the driving end of the resonant tube would increase linearly with the displacement amplitude of the piston due to nonlinear effects, rather than the exponential variation by linear theory. This research demonstrates that the GKS model is strongly capable of simulating nonlinear acoustic problems.

Shapes of star-gas waves in spiral galaxies

NASA Technical Reports Server (NTRS)

Lubow, Stephen H.

1988-01-01

Density-wave profile shapes are influenced by several effects. By solving viscous fluid equations, the nonlinear effects of the gas and its gravitational interaction with the stars can be analyzed. The stars are treated through a linear theory developed by Lin and coworkers. Short wavelength gravitational forces are important in determining the gas density profile shape. With the inclusion of disk finite thickness effects, the gas gravitational field remains important, but is significantly reduced at short wavelengths. Softening of the gas equation of state results in an enhanced response and a smoothing of the gas density profile. A Newtonian stress relation is marginally acceptable for HI gas clouds, but not acceptable for giant molecular clouds.

Subcritical Transition in Channel Flows

NASA Astrophysics Data System (ADS)

Maestri, Joseph; Hall, Philip

2014-11-01

Exact-coherent structures, or colloquially non-linear solutions to the Navier-Stokes equations, have been the subject of great interest over the past decade due to their relevance in understanding the process of transition to turbulence in shear flows. Over the past few years the relationship between high Reynolds number vortex-wave interaction theory and such states has been elucidated in a number of papers and has provided a solid asymptotic framework to understand the so-called self-sustaining process that maintains such structures. In this talk, we will discuss this relationship before talking about recent work on solving the vortex-wave interaction equations using numerical techniques in order to propose laminar-flow control techniques.

On the global "two-sided" characteristic Cauchy problem for linear wave equations on manifolds

NASA Astrophysics Data System (ADS)

Lupo, Umberto

2018-04-01

The global characteristic Cauchy problem for linear wave equations on globally hyperbolic Lorentzian manifolds is examined, for a class of smooth initial value hypersurfaces satisfying favourable global properties. First it is shown that, if geometrically well-motivated restrictions are placed on the supports of the (smooth) initial datum and of the (smooth) inhomogeneous term, then there exists a continuous global solution which is smooth "on each side" of the initial value hypersurface. A uniqueness result in Sobolev regularity H^{1/2+ɛ }_{loc} is proved among solutions supported in the union of the causal past and future of the initial value hypersurface, and whose product with the indicator function of the causal future (resp. past) of the hypersurface is past compact (resp. future compact). An explicit representation formula for solutions is obtained, which prominently features an invariantly defined, densitised version of the null expansion of the hypersurface. Finally, applications to quantum field theory on curved spacetimes are briefly discussed.

Quantization of wave equations and hermitian structures in partial differential varieties

PubMed Central

Paneitz, S. M.; Segal, I. E.

1980-01-01

Sufficiently close to 0, the solution variety of a nonlinear relativistic wave equation—e.g., of the form □ϕ + m2ϕ + gϕp = 0—admits a canonical Lorentz-invariant hermitian structure, uniquely determined by the consideration that the action of the differential scattering transformation in each tangent space be unitary. Similar results apply to linear time-dependent equations or to equations in a curved asymptotically flat space-time. A close relation of the Riemannian structure to the determination of vacuum expectation values is developed and illustrated by an explicit determination of a perturbative 2-point function for the case of interaction arising from curvature. The theory underlying these developments is in part a generalization of that of M. G. Krein and collaborators concerning stability of differential equations in Hilbert space and in part a precise relation between the unitarization of given symplectic linear actions and their full probabilistic quantization. The unique causal structure in the infinite symplectic group is instrumental in these developments. PMID:16592923

Analysis of Instabilities in Non-Axisymmetric Hypersonic Boundary Layers Over Cones

NASA Technical Reports Server (NTRS)

Li, Fei; Choudhari, Meelan M.; Chang, Chau-Lyan; White, Jeffery A.

2010-01-01

Hypersonic flows over circular cones constitute one of the most important generic configurations for fundamental aerodynamic and aerothermodynamic studies. In this paper, numerical computations are carried out for Mach 6 flows over a 7-degree half-angle cone with two different flow incidence angles and a compression cone with a large concave curvature. Instability wave and transition-related flow physics are investigated using a series of advanced stability methods ranging from conventional linear stability theory (LST) and a higher-fidelity linear and nonlinear parabolized stability equations (PSE), to the 2D eigenvalue analysis based on partial differential equations. Computed N factor distribution pertinent to various instability mechanisms over the cone surface provides initial assessments of possible transition fronts and a guide to corresponding disturbance characteristics such as frequency and azimuthal wave numbers. It is also shown that strong secondary instability that eventually leads to transition to turbulence can be simulated very efficiently using a combination of advanced stability methods described above.

LASER APPLICATIONS AND OTHER TOPICS IN QUANTUM ELECTRONICS: Reflection of an electromagnetic pulse from a subcritical waveguide taper and from a supercritical-density plasma in a waveguide

NASA Astrophysics Data System (ADS)

Rukhadze, Anri A.; Tarakanov, V. P.

2006-09-01

Two related problems are studied by numerical simulations using the KARAT code: the reflection of the TM01 mode of an electromagnetic pulse from the subcritical taper of the section of a circular waveguide and the reflection of the same pulse from a 'cold' collisionless plasma with a density increasing up to a supercritical value along the waveguide axis. It is shown that in the former case the pulse is totally reflected with an insignificant distortion of its shape, in accordance with the linear theory. In the latter case, the character of reflection depends substantially on the plasma density increase length, the pulse duration, and the wave field amplitude, a significant field deceleration and amplitude growth occurring near the critical point; the pulse absorption in the plasma far exceeds the absorption due to the linear transformation of the incident transverse wave to the longitudinal plasma oscillations.

Pseudospectral modeling and dispersion analysis of Rayleigh waves in viscoelastic media

USGS Publications Warehouse

Zhang, K.; Luo, Y.; Xia, J.; Chen, C.

2011-01-01

Multichannel Analysis of Surface Waves (MASW) is one of the most widely used techniques in environmental and engineering geophysics to determine shear-wave velocities and dynamic properties, which is based on the elastic layered system theory. Wave propagation in the Earth, however, has been recognized as viscoelastic and the propagation of Rayleigh waves presents substantial differences in viscoelastic media as compared with elastic media. Therefore, it is necessary to carry out numerical simulation and dispersion analysis of Rayleigh waves in viscoelastic media to better understand Rayleigh-wave behaviors in the real world. We apply a pseudospectral method to the calculation of the spatial derivatives using a Chebyshev difference operator in the vertical direction and a Fourier difference operator in the horizontal direction based on the velocity-stress elastodynamic equations and relations of linear viscoelastic solids. This approach stretches the spatial discrete grid to have a minimum grid size near the free surface so that high accuracy and resolution are achieved at the free surface, which allows an effective incorporation of the free surface boundary conditions since the Chebyshev method is nonperiodic. We first use an elastic homogeneous half-space model to demonstrate the accuracy of the pseudospectral method comparing with the analytical solution, and verify the correctness of the numerical modeling results for a viscoelastic half-space comparing the phase velocities of Rayleigh wave between the theoretical values and the dispersive image generated by high-resolution linear Radon transform. We then simulate three types of two-layer models to analyze dispersive-energy characteristics for near-surface applications. Results demonstrate that the phase velocity of Rayleigh waves in viscoelastic media is relatively higher than in elastic media and the fundamental mode increases by 10-16% when the frequency is above 10. Hz due to the velocity dispersion of P and S waves. ?? 2011 Elsevier Ltd.

Nonlinear dead water resistance at subcritical speed

NASA Astrophysics Data System (ADS)

Grue, John

2015-08-01

The dead water resistance F 1 = /1 2 C d w ρ S U 2 (ρ fluid density, U ship speed, S wetted body surface, Cdw resistance coefficient) on a ship moving at subcritical speed along the upper layer of a two-layer fluid is calculated by a strongly nonlinear method assuming potential flow in each layer. The ship dimensions correspond to those of the Polar ship Fram. The ship draught, b0, is varied in the range 0.25h0-0.9h0 (h0 the upper layer depth). The calculations show that Cdw/(b0/h0)2 depends on the Froude number only, in the range close to critical speed, Fr = U/c0 ˜ 0.875-1.125 (c0 the linear internal long wave speed), irrespective of the ship draught. The function Cdw/(b0/h0)2 attains a maximum at subcritical Froude number depending on the draught. Maximum Cdw/(b0/h0)2 becomes 0.15 for Fr = 0.76, b0/h0 = 0.9, and 0.16 for Fr = 0.74, b0/h0 = 1, where the latter extrapolated value of the dead water resistance coefficient is about 60 times higher than the frictional drag coefficient and relevant for the historical dead water observations. The nonlinear Cdw significantly exceeds linear theory (Fr < 0.85). The ship generated waves have a wave height comparable to the upper layer depth. Calculations of three-dimensional wave patterns at critical speed compare well to available laboratory experiments. Upstream solitary waves are generated in a wave tank of finite width, when the layer depths differ, causing an oscillation of the force. In a wide ocean, a very wide wave system develops at critical speed. The force approaches a constant value for increasing time.

VTOL controls for shipboard landing. M.S.Thesis

NASA Technical Reports Server (NTRS)

Mcmuldroch, C. G.

1979-01-01

The problem of landing a VTOL aircraft on a small ship in rough seas using an automatic controller is examined. The controller design uses the linear quadratic Gaussian results of modern control theory. Linear time invariant dynamic models are developed for the aircraft, ship, and wave motions. A hover controller commands the aircraft to track position and orientation of the ship deck using only low levels of control power. Commands for this task are generated by the solution of the steady state linear quadratic gaussian regulator problem. Analytical performance and control requirement tradeoffs are obtained. A landing controller commands the aircraft from stationary hover along a smooth, low control effort trajectory, to a touchdown on a predicted crest of ship motion. The design problem is formulated and solved as an approximate finite-time linear quadratic stochastic regulator. Performance and control results are found by Monte Carlo simulations.

Vibration responses of h-BN sheet to charge doping and external strain

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Wei; Yang, Yu; Zheng, Fawei

2013-12-07

Based on density functional theory and density functional perturbation theory calculations, we systematically investigate the vibration responses of h-BN sheet to charge doping and external strains. It is found that under hole doping, the phonon frequencies of the ZO and TO branches at different wave vector q shift linearly with different slopes. Under electron doping, although the phonon frequencies shift irregularly, the shifting values are different at different phonon wave vectors. Interestingly, we find that external strain can restrain the irregular vibration responses of h-BN sheet to electron doping. The critical factor is revealed to be the relative position ofmore » the nearly free electron and boron p{sub z} states of h-BN sheet. Under external strains, the vibration responses of h-BN sheet are also found to be highly dependent on the phonon branches. Different vibration modes at different q points are revealed to be responsible for the vibration responses of h-BN sheet to charge doping and external strain. Our results point out a new way to detect the doping or strain status of h-BN sheet by measuring the vibration frequencies at different wave vector.« less

On the stimulated Raman sidescattering in inhomogeneous plasmas: revisit of linear theory and three-dimensional particle-in-cell simulations

NASA Astrophysics Data System (ADS)

Xiao, C. Z.; Zhuo, H. B.; Yin, Y.; Liu, Z. J.; Zheng, C. Y.; Zhao, Y.; He, X. T.

2018-02-01

Stimulated Raman sidescattering (SRSS) in inhomogeneous plasma is comprehensively revisited on both theoretical and numerical aspects due to the increasing concern of its detriments to inertial confinement fusion. Firstly, two linear mechanisms of finite beam width and collisional effects that could suppress SRSS are investigated theoretically. Thresholds for the eigenmode and wave packet in a finite-width beam are derived as a supplement to the theory proposed by Mostrom and Kaufman (1979 Phys. Rev. Lett. 42 644). Collisional absorption of SRSS is efficient at high-density plasma and high-Z material, otherwise, it allows emission of sidescattering. Secondly, we have performed the first three-dimensional particle-in-cell simulations in the context of SRSS to investigate its linear and nonlinear effects. Simulation results are qualitatively agreed with the linear theory. SRSS with the maximum growth gain is excited at various densities, grows to an amplitude that is comparable with the pump laser, and evolutes to lower densities with a large angle of emergence. Competitions between SRSS and other parametric instabilities such as stimulated Raman backscattering, two-plasmon decay, and stimulated Brillouin scattering are discussed. These interaction processes are determined by gains, occurrence sites, scattering geometries of each instability, and will affect subsequent evolutions. Nonlinear effects of self-focusing and azimuthal magnetic field generation are observed to be accompanied with SRSS. In addition, it is found that SRSS is insensitive to ion motion, collision (low-Z material), and electron temperature.

Radiating Instabilities of Internal Inertio-gravity Waves

NASA Astrophysics Data System (ADS)

Kwasniok, F.; Schmitz, G.

The vertical radiation of local convective and shear instabilities of internal inertio- gravity waves is examined within linear stability theory. A steady, plane-parallel Boussinesq flow with vertical profiles of horizontal velocity and static stability re- sembling an internal inertio-gravity wave packet without mean vertical shear is used as dynamical framework. The influence of primary-wave frequency and amplitude as well as orientation and horizontal wavenumber of the instability on vertical radi- ation is discussed. Considerable radiation occurs at small to intermediate instability wavenumbers for basic state gravity waves with high to intermediate frequencies and moderately convectively supercritical amplitudes. Radiation is then strongest when the horizontal wavevector of the instability is aligned parallel to the horizontal wavevector of the basic state gravity wave. These radiating modes are essentially formed by shear instability. Modes of convective instability, that occur at large instability wavenum- bers or strongly convectively supercritical amplitudes, as well as modes at convec- tively subcritical amplitudes are nonradiating, trapped in the region of instability. The radiation of an instability is found to be related to the existence of critical levels, a radiating mode being characterized by the absence of critical levels outside the region of instability of the primary wave.

Hybrid simulations of positively and negatively charged pickup ions and cyclotron wave generation at Europa

DOE Office of Scientific and Technical Information (OSTI.GOV)

Desai, Ravindra T.; Cowee, Misa; Wei, Hanying

In the vicinity of Europa, Galileo observed bursty Alfvén-cyclotron wave power at the gyrofrequencies of a number of species including K +, math formula, Na +, and Cl +, indicating the localised pickup of these species. Additional evidence for the presence of Chlorine was the occurrence of both left-hand (LH) and right-hand (RH) polarised transverse wave power near the Cl + gyrofrequency, thought to be due to the pickup of both Cl + and the easily formed Chlorine anion, Cl –. To test this hypothesis we use one-dimensional hybrid (kinetic ion, massless fluid electron) simulations for both positive and negativemore » pickup ions and self-consistently reproduce the growth of both LH and RH Alfvén-cyclotron waves in agreement with linear theory. We show how the simultaneous generation of LH and RH waves can result in non-gyrotropic ion distributions and increased wave amplitudes, and how even trace quantities of negative pickup ions are able to generate an observable RH signal. Here, through comparing simulated and observed wave amplitudes, we are able to place the first constraints on the densities of Chlorine pickup ions in localised regions at Europa.« less

Surface waves generated by shallow underwater explosions

NASA Technical Reports Server (NTRS)

Falade, A.; Holt, M.

1978-01-01

Surface water waves generated by surface and near surface point explosions are calculated. Taking the impulse distribution imparted at the water surface by the explosion as the overriding mechanism for transferring energy of the explosive to surface wave motion, the linearized theory of Kranzer and Keller is used to obtain the wave displacement in the far field. The impulse distribution is obtained by integrating the pressure wave over an appropriate time interval on a horizontal surface just beneath the undisturbed water surface. For surface explosions, a modified form of the similarity method first used by Collins and Holt is used to obtain the flow field. In the case of submerged explosions, the flow field is estimated by making necessary modifications to Sedov's similarity solution to account for the venting that accompanies the interaction of the leading (blast) wave with the ocean surface. Surface waves generated by a charge at six depths of placement (0.15 m, 0.30 m, 0.61 m, 0.91 m, 1.37 m, 3.05 m) are considered in addition to surface explosions. The results seem to support the existence of an upper critical depth phenomenon (of the type already established for chemical explosions) for point (nuclear) explosions.

Hybrid simulations of positively and negatively charged pickup ions and cyclotron wave generation at Europa

DOE PAGES

Desai, Ravindra T.; Cowee, Misa; Wei, Hanying; ...

2017-09-19

In the vicinity of Europa, Galileo observed bursty Alfvén-cyclotron wave power at the gyrofrequencies of a number of species including K +, math formula, Na +, and Cl +, indicating the localised pickup of these species. Additional evidence for the presence of Chlorine was the occurrence of both left-hand (LH) and right-hand (RH) polarised transverse wave power near the Cl + gyrofrequency, thought to be due to the pickup of both Cl + and the easily formed Chlorine anion, Cl –. To test this hypothesis we use one-dimensional hybrid (kinetic ion, massless fluid electron) simulations for both positive and negativemore » pickup ions and self-consistently reproduce the growth of both LH and RH Alfvén-cyclotron waves in agreement with linear theory. We show how the simultaneous generation of LH and RH waves can result in non-gyrotropic ion distributions and increased wave amplitudes, and how even trace quantities of negative pickup ions are able to generate an observable RH signal. Here, through comparing simulated and observed wave amplitudes, we are able to place the first constraints on the densities of Chlorine pickup ions in localised regions at Europa.« less

Wave-induced fluid flow in random porous media: Attenuation and dispersion of elastic waves

NASA Astrophysics Data System (ADS)

Müller, Tobias M.; Gurevich, Boris

2005-05-01

A detailed analysis of the relationship between elastic waves in inhomogeneous, porous media and the effect of wave-induced fluid flow is presented. Based on the results of the poroelastic first-order statistical smoothing approximation applied to Biot's equations of poroelasticity, a model for elastic wave attenuation and dispersion due to wave-induced fluid flow in 3-D randomly inhomogeneous poroelastic media is developed. Attenuation and dispersion depend on linear combinations of the spatial correlations of the fluctuating poroelastic parameters. The observed frequency dependence is typical for a relaxation phenomenon. Further, the analytic properties of attenuation and dispersion are analyzed. It is shown that the low-frequency asymptote of the attenuation coefficient of a plane compressional wave is proportional to the square of frequency. At high frequencies the attenuation coefficient becomes proportional to the square root of frequency. A comparison with the 1-D theory shows that attenuation is of the same order but slightly larger in 3-D random media. Several modeling choices of the approach including the effect of cross correlations between fluid and solid phase properties are demonstrated. The potential application of the results to real porous materials is discussed. .

Hybrid Simulations of Positively and Negatively Charged Pickup Ions and Cyclotron Wave Generation at Europa.

PubMed

Desai, R T; Cowee, M M; Wei, H; Fu, X; Gary, S P; Volwerk, M; Coates, A J

2017-10-01

In the vicinity of Europa, Galileo observed bursty Alfvén-cyclotron wave power at the gyrofrequencies of a number of species including K + , O 2+, Na + , and Cl + , indicating the localized pickup of these species. Additional evidence for the presence of chlorine was the occurrence of both left-hand (LH) and right-hand (RH) polarized transverse wave power near the Cl + gyrofrequency, thought to be due to the pickup of both Cl + and the easily formed chlorine anion, Cl - . To test this hypothesis, we use one-dimensional hybrid (kinetic ion, massless fluid electron) simulations for both positive and negative pickup ions and self-consistently reproduce the growth of both LH and RH Alfvén-cyclotron waves in agreement with linear theory. We show how the simultaneous generation of LH and RH waves can result in nongyrotropic ion distributions and increased wave amplitudes, and how even trace quantities of negative pickup ions are able to generate an observable RH signal. Through comparing simulated and observed wave amplitudes, we are able to place the first constraints on the densities of Chlorine pickup ions in localized regions at Europa.

Experimental Basis for IED Particle Model

NASA Astrophysics Data System (ADS)

Zheng-Johansson, J.

2009-03-01

The internally electrodynamic (IED) particle model is built on three experimental facts: a) electric charges present in all matter particles, b) an accelerated charge generates electromagnetic (EM) waves by Maxwell's equations and Planck energy equation, and c) source motion gives Doppler effect. A set of well-kwon basic particle equations have been predicted based on first-principles solutions for IED particle (e.g. J Phys CS128, 012019, 2008); the equations are long experimentally validated. A critical review of the key experiments suggests that the IED process underlies these equations not just sufficiently but also necessarily. E.g.: 1) A free IED electron solution is a plane wave ψ= Ce^i(kdX-φT) requisite for producing the diffraction fringe in a Davisson-Germer experiment, and of also all basic point-like attributes facilitated by a linear momentum kd and the model structure. It needs not further be a wave packet which produces not a diffraction fringe. 2)The radial partial EM waves, hence the total ψ, of an IED electron will, on both EM theory and experiment basis -not by assumption, enter two slits at the same time, as is requisite for an electron to interfere with itself as shown in double slit experiments. 3) On annihilation, an electron converts (from mass m) to a radiation energy φ without an acceleration which is externally observable and yet requisite by EM theory. So a charge oscillation of frequency φ and its EM waves must regularly present internal of a normal electron, whence the IED model.

A statistical study of EMIC waves observed by Cluster: 2. Associated plasma conditions

DOE PAGES

Allen, R. C.; Zhang, J. -C.; Kistler, L. M.; ...

2016-07-01

This is the second in a pair of papers discussing a statistical study of electromagnetic ion cyclotron (EMIC) waves detected during 10 years (2001–2010) of Cluster observations. In the first paper, an analysis of EMIC wave properties (i.e., wave power, polarization, normal angle, and wave propagation angle) is presented in both the magnetic latitude (MLAT)-distance as well as magnetic local time (MLT)-L frames. In addition, this paper focuses on the distribution of EMIC wave-associated plasma conditions as well as two EMIC wave generation proxies (the electron plasma frequency to gyrofrequency ratio proxy and the linear theory proxy) in these samemore » frames. Based on the distributions of hot H + anisotropy, electron and hot H+ density measurements, hot H + parallel plasma beta, and the calculated wave generation proxies, three source regions of EMIC waves appear to exist: (1) the well-known overlap between cold plasmaspheric or plume populations with hot anisotropic ring current populations in the postnoon to dusk MLT region; (2) regions all along the dayside magnetosphere at high L shells related to dayside magnetospheric compression and drift shell splitting; and (3) off-equator regions possibly associated with the Shabansky orbits in the dayside magnetosphere.« less

A statistical study of EMIC waves observed by Cluster: 2. Associated plasma conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Allen, R. C.; Zhang, J. -C.; Kistler, L. M.

This is the second in a pair of papers discussing a statistical study of electromagnetic ion cyclotron (EMIC) waves detected during 10 years (2001–2010) of Cluster observations. In the first paper, an analysis of EMIC wave properties (i.e., wave power, polarization, normal angle, and wave propagation angle) is presented in both the magnetic latitude (MLAT)-distance as well as magnetic local time (MLT)-L frames. In addition, this paper focuses on the distribution of EMIC wave-associated plasma conditions as well as two EMIC wave generation proxies (the electron plasma frequency to gyrofrequency ratio proxy and the linear theory proxy) in these samemore » frames. Based on the distributions of hot H + anisotropy, electron and hot H+ density measurements, hot H + parallel plasma beta, and the calculated wave generation proxies, three source regions of EMIC waves appear to exist: (1) the well-known overlap between cold plasmaspheric or plume populations with hot anisotropic ring current populations in the postnoon to dusk MLT region; (2) regions all along the dayside magnetosphere at high L shells related to dayside magnetospheric compression and drift shell splitting; and (3) off-equator regions possibly associated with the Shabansky orbits in the dayside magnetosphere.« less

Ulysses Observations of Magnetic Waves due to Newborn Interstellar Pickup Ions. I. New Observations and Linear Analysis

NASA Astrophysics Data System (ADS)

Cannon, Bradford E.; Smith, Charles W.; Isenberg, Philip A.; Vasquez, Bernard J.; Murphy, Neil; Nuno, Raquel G.

2014-04-01

We have examined Ulysses magnetic field data using dynamic spectrogram techniques that compute wave amplitude, polarization, and direction of propagation over a broad range of frequencies and time. Events were identified that showed a strong polarization signature and an enhancement of power above the local proton gyrofrequency. We perform a statistical study of 502 wave events in an effort to determine when, where, and why they are observed. Most notably, we find that waves arising from newborn interstellar pickup ions are relatively rare and difficult to find. The quantities normally employed in theories of wave growth are neutral atom density and quantities related to their ionization and the subsequent dynamics such as wind speed, solar wind flux, and magnetic field orientation. We find the observations of waves to be largely uncorrelated to these quantities except for mean field direction where quasi-radial magnetic fields are favored and solar wind proton flux where wave observations appear to be favored by low flux conditions which runs contrary to theoretical expectations of wave generation. It would appear that an explanation based on source physics and instability growth rates alone is not adequate to account for the times when these waves are seen.

Interference between wave modes may contribute to the apparent negative dispersion observed in cancellous bone

PubMed Central

Anderson, Christian C.; Marutyan, Karen R.; Holland, Mark R.; Wear, Keith A.; Miller, James G.

2008-01-01

Previous work has shown that ultrasonic waves propagating through cancellous bone often exhibit a linear-with-frequency attenuation coefficient, but a decrease in phase velocity with frequency (negative dispersion) that is inconsistent with the causality-imposed Kramers–Kronig relations. In the current study, interfering wave modes similar to those observed in bone are shown to potentially contribute to the observed negative dispersion. Biot theory, the modified Biot–Attenborogh model, and experimental results are used to aid in simulating multiple-mode wave propagation through cancellous bone. Simulations entail constructing individual wave modes exhibiting a positive dispersion using plausible velocities and amplitudes, and then summing the individual modes to create mixed-mode output wave forms. Results of the simulations indicate that mixed-mode wave forms can exhibit negative dispersion when analyzed conventionally under the assumption that only one wave is present, even when the individual interfering waves exhibit positive dispersions in accordance with the Kramers–Kronig relations. Furthermore, negative dispersion is observed when little or no visual evidence of interference exists in the time-domain data. Understanding the mechanisms responsible for the observed negative dispersion could aid in determining the true material properties of cancellous bone, as opposed to the apparent properties measured using conventional data analysis techniques. PMID:19045668

New formulations for tsunami runup estimation

NASA Astrophysics Data System (ADS)

Kanoglu, U.; Aydin, B.; Ceylan, N.

2017-12-01

We evaluate shoreline motion and maximum runup in two folds: One, we use linear shallow water-wave equations over a sloping beach and solve as initial-boundary value problem similar to the nonlinear solution of Aydın and Kanoglu (2017, Pure Appl. Geophys., https://doi.org/10.1007/s00024-017-1508-z). Methodology we present here is simple; it involves eigenfunction expansion and, hence, avoids integral transform techniques. We then use several different types of initial wave profiles with and without initial velocity, estimate shoreline properties and confirm classical runup invariance between linear and nonlinear theories. Two, we use the nonlinear shallow water-wave solution of Kanoglu (2004, J. Fluid Mech. 513, 363-372) to estimate maximum runup. Kanoglu (2004) presented a simple integral solution for the nonlinear shallow water-wave equations using the classical Carrier and Greenspan transformation, and further extended shoreline position and velocity to a simpler integral formulation. In addition, Tinti and Tonini (2005, J. Fluid Mech. 535, 33-64) defined initial condition in a very convenient form for near-shore events. We use Tinti and Tonini (2005) type initial condition in Kanoglu's (2004) shoreline integral solution, which leads further simplified estimates for shoreline position and velocity, i.e. algebraic relation. We then use this algebraic runup estimate to investigate effect of earthquake source parameters on maximum runup and present results similar to Sepulveda and Liu (2016, Coast. Eng. 112, 57-68).

Earth Sciences Push Radiative Transfer Theory

NASA Astrophysics Data System (ADS)

Davis, Anthony; Mishchenko, Michael

2009-12-01

2009 International Conference on Advances in Mathematics, Computational Methods, and Reactor Physics; Saratoga Springs, New York, 4-7 May 2009; The theories of radiative transfer and particle—particularly neutron—transport are grounded in distinctive microscale physics that deals with either optics or particle dynamics. However, it is not practical to track every wave or particle in macroscopic systems, nor do all of these details matter. That is why Newton's laws, which describe individual particles, are replaced by those of Euler, Navier-Stokes, Maxwell, Boltzmann, Gibbs, and others, which describe the collective behavior of vast numbers of particles. And that is why the radiative transfer (RT) equation is used to describe the flow of radiation through geophysical-scale systems, leaving to Maxwell's wave equations only the task of providing the optical properties of the medium, be it air, water, snow, ice, or biomass. Interestingly, particle transport is determined by the linear transport equation, which is mathematically identical to the RT equation, so geophysicists and nuclear scientists are interested in the same mathematics and computational techniques.

Bulk solitary waves in elastic solids

NASA Astrophysics Data System (ADS)

Samsonov, A. M.; Dreiden, G. V.; Semenova, I. V.; Shvartz, A. G.

2015-10-01

A short and object oriented conspectus of bulk solitary wave theory, numerical simulations and real experiments in condensed matter is given. Upon a brief description of the soliton history and development we focus on bulk solitary waves of strain, also known as waves of density and, sometimes, as elastic and/or acoustic solitons. We consider the problem of nonlinear bulk wave generation and detection in basic structural elements, rods, plates and shells, that are exhaustively studied and widely used in physics and engineering. However, it is mostly valid for linear elasticity, whereas dynamic nonlinear theory of these elements is still far from being completed. In order to show how the nonlinear waves can be used in various applications, we studied the solitary elastic wave propagation along lengthy wave guides, and remarkably small attenuation of elastic solitons was proven in physical experiments. Both theory and generation for strain soliton in a shell, however, remained unsolved problems until recently, and we consider in more details the nonlinear bulk wave propagation in a shell. We studied an axially symmetric deformation of an infinite nonlinearly elastic cylindrical shell without torsion. The problem for bulk longitudinal waves is shown to be reducible to the one equation, if a relation between transversal displacement and the longitudinal strain is found. It is found that both the 1+1D and even the 1+2D problems for long travelling waves in nonlinear solids can be reduced to the Weierstrass equation for elliptic functions, which provide the solitary wave solutions as appropriate limits. We show that the accuracy in the boundary conditions on free lateral surfaces is of crucial importance for solution, derive the only equation for longitudinal nonlinear strain wave and show, that the equation has, amongst others, a bidirectional solitary wave solution, which lead us to successful physical experiments. We observed first the compression solitary wave in the duct-like polymer shell and proved, that there is no tensile area behind the wave, the bulk soliton propagates on a distance many times longer than its wave length, while both its shape and amplitude remain unchanged. We demonstrated recently how the strain solitons can be used for non-destructive testing (NDT) of laminated composites, used nowadays for various applications, e.g., in microelectronics, aerospace and automotive industries, and bulk strain solitons are among prospective instruments for NDT. Being aimed to propose the bulk strain solitons as an instrument for NDT in solids, we studied numerically the evolution of them in various wave guides with local defects, and shown that the strain soliton undergoes changes in amplitude, phase shift and the shape, that are distinctive and can be estimated. To sum up, now we are able to propose a new NDT technique, based on bulk strain soliton propagation in structural elements.

How to test gravitation theories by means of gravitational-wave measurements

NASA Technical Reports Server (NTRS)

Thorne, K. S.

1974-01-01

Gravitational-wave experiments are a potentially powerful tool for testing gravitation theories. Most theories in the literature predict rather different polarization properties for gravitational waves than are predicted by general relativity; and many theories predict anomalies in the propagation speeds of gravitational waves.

Numerical studies of identification in nonlinear distributed parameter systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Lo, C. K.; Reich, Simeon; Rosen, I. G.

1989-01-01

An abstract approximation framework and convergence theory for the identification of first and second order nonlinear distributed parameter systems developed previously by the authors and reported on in detail elsewhere are summarized and discussed. The theory is based upon results for systems whose dynamics can be described by monotone operators in Hilbert space and an abstract approximation theorem for the resulting nonlinear evolution system. The application of the theory together with numerical evidence demonstrating the feasibility of the general approach are discussed in the context of the identification of a first order quasi-linear parabolic model for one dimensional heat conduction/mass transport and the identification of a nonlinear dissipation mechanism (i.e., damping) in a second order one dimensional wave equation. Computational and implementational considerations, in particular, with regard to supercomputing, are addressed.

Asymptotic analysis of the shear strain effect on the wave characteristics of a multilayered cylindrical shell filled with fluid

NASA Astrophysics Data System (ADS)

Amenzade, R. Yu.; Kiiko, I. A.

2007-06-01

It is commonly assumed that the theory based on the Kirchhoff hypotheses describes the properties inherent in the wave processes occurring in shells filled with fluids. But there are several new effects that cannot be described by this theory (in particular, the appearance of new types of waves). In this paper, we present a linearized description of axisymmetric wave motion of a perfect incompressible fluid in a multilayered cylindrical shell with allowance for shear strain; the shell is assumed to be infinite and simply supported. This description is aimed at finding new mechanical effects and hence at estimating the influence of the multiple layers and the shear strain on the wave characteristics. In a sense, it generalizes and develops well-known studies of this type. Practice necessitates deriving equations constructed under the assumption that the physical and mechanical properties of the shell material are inhomogeneous along the thickness direction or the shell is multilayered; the development of refined theories (compared with the classical theory based on the Kirchhoff—Love straight normal hypothesis) is also inspired by practice. This is primarily related to the fact that multilayered thin-walled shells made of composite materials are used in various fields of technology. It is of interest to note that, as a result of long evolution, the phenomenon of being multilayered also predominates in living organisms. For example, this is typical of big blood vessels [1] (arteries and veins). In [2], on the basis of a three-dimensional variational principle of mixed type, the equations of motion and physical relations for elastic anisotropic shells rigidly inhomogeneous in the thickness direction are derived under the assumptions of the theory of thin shells and with shear strains taken into account. It is also noted that the case of multilayered shells can be modeled by introducing functions with integrable singularities. When studying wave propagation in deformable shells containing fluid, hydroelasticity problems arise; the solution of such problems is of both theoretical and practical importance. Of topical problems in this field, problems related to pulsating blood flow in big blood vessels [3] (the theory of pulse waves) are worth mentioning. The incentive for such studies is that they can help to understand the normal operation of the blood circulatory system, predict its reaction to variations, and propose methods for artificial intervention. Thus, diagnostics, surgery, and prosthesis are closely related to biomechanics. But the applied value of such problems is not bounded by their applications in hemodynamics. They are also very important in technology because of the wide use of systems of fluid and gas transportation through pipelines with corrosion-resistant coating.

Computational process to study the wave propagation In a non-linear medium by quasi- linearization

NASA Astrophysics Data System (ADS)

Sharath Babu, K.; Venkata Brammam, J.; Baby Rani, CH

2018-03-01

Two objects having distinct velocities come into contact an impact can occur. The impact study i.e., in the displacement of the objects after the impact, the impact force is function of time‘t’ which is behaves similar to compression force. The impact tenure is very short so impulses must be generated subsequently high stresses are generated. In this work we are examined the wave propagation inside the object after collision and measured the object non-linear behavior in the one-dimensional case. Wave transmission is studied by means of material acoustic parameter value. The objective of this paper is to present a computational study of propagating pulsation and harmonic waves in nonlinear media using quasi-linearization and subsequently utilized the central difference scheme. This study gives focus on longitudinal, one- dimensional wave propagation. In the finite difference scheme Non-linear system is reduced to a linear system by applying quasi-linearization method. The computed results exhibit good agreement on par with the selected non-liner wave propagation.

Z mode radiation in Jupiter's magnetosphere - The source of Jovian continuum radiation

NASA Technical Reports Server (NTRS)

Barbosa, D. D.; Kurth, W. S.; Moses, S. L.; Scarf, F. L.

1990-01-01

Observations of Z-mode waves in Jupiter's magnetosphere are analyzed. The assumption that the frequency of the intensity minimum, which isolates the signal, corresponds to the electron plasma frequency provides a consistent interpretation of all spectral features in terms of plasma resonances and cutoffs. It is shown that the continuum radiation is composed of both left-hand and right-hand polarized waves with distinct cutoffs observed at the plasma frequency and right-hand cutoff frequency, respectively. It is found that the Z-mode peak frequency lies close to the left-hand cutoff frequency, suggesting that the observed characteristics of the emission are the result of wave reflection at the cutoff layer. Another distinct emission occurring near the upper hybrid resonance frequency is detected simultaneously with the Z mode. The entire set of observations gives strong support to the linear mode theory of the conversion of upper hybrid waves to continuum radiation mediated by the Z mode via the Budden radio window mechanism.

Numerical modeling of guided ultrasonic waves generated and received by piezoelectric wafer in a Delaminated composite beam

NASA Astrophysics Data System (ADS)

Xu, G. D.; Xu, B. Q.; Xu, C. G.; Luo, Y.

2017-05-01

A spectral finite element method (SFEM) is developed to analyze guided ultrasonic waves in a delaminated composite beam excited and received by a pair of surface-bonded piezoelectric wafers. The displacements of the composite beam and the piezoelectric wafer are represented by Timoshenko beam and Euler Bernoulli theory respectively. The linear piezoelectricity is used to model the electrical-mechanical coupling between the piezoelectric wafer and the beam. The coupled governing equations and the boundary conditions in time domain are obtained by using the Hamilton's principle, and then the SFEM are formulated by transforming the coupled governing equations into frequency domain via the discrete Fourier transform. The guided waves are analyzed while the interaction of waves with delamination is also discussed. The elements needed in SFEM is far fewer than those for finite element method (FEM), which result in a much faster solution speed in this study. The high accuracy of the present SFEM is verified by comparing with the finite element results.

Time-periodic solutions of the Benjamin-Ono equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ambrose , D.M.; Wilkening, Jon

2008-04-01

We present a spectrally accurate numerical method for finding non-trivial time-periodic solutions of non-linear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is positive unless the solution is periodic, in which case it is zero. We solve an adjoint PDE to compute the gradient of this functional with respect to the initial condition. We include additional terms in the functional to specify the free parameters, which, in the case of the Benjamin-Ono equation, are the mean, a spatial phase, a temporal phase and the real part of one ofmore » the Fourier modes at t = 0. We use our method to study global paths of non-trivial time-periodic solutions connecting stationary and traveling waves of the Benjamin-Ono equation. As a starting guess for each path, we compute periodic solutions of the linearized problem by solving an infinite dimensional eigenvalue problem in closed form. We then use our numerical method to continue these solutions beyond the realm of linear theory until another traveling wave is reached (or until the solution blows up). By experimentation with data fitting, we identify the analytical form of the solutions on the path connecting the one-hump stationary solution to the two-hump traveling wave. We then derive exact formulas for these solutions by explicitly solving the system of ODE's governing the evolution of solitons using the ansatz suggested by the numerical simulations.« less

Self-propulsion of a planar electric or magnetic microbot immersed in a polar viscous fluid

NASA Astrophysics Data System (ADS)

Felderhof, B. U.

2011-05-01

A planar sheet immersed in an electrically polar liquid like water can propel itself by means of a plane wave charge density propagating in the sheet. The corresponding running electric wave polarizes the fluid and causes an electrical torque density to act on the fluid. The sheet is convected by the fluid motion resulting from the conversion of rotational particle motion, generated by the torque density, into translational fluid motion by the mechanism of friction and spin diffusion. Similarly, a planar sheet immersed in a magnetic ferrofluid can propel itself by means of a plane wave current density in the sheet and the torque density acting on the fluid corresponding to the running wave magnetic field and magnetization. The effect is studied on the basis of the micropolar fluid equations of motion and Maxwell’s equations of electrostatics or magnetostatics, respectively. An analytic expression is derived for the velocity of the sheet by perturbation theory to second order in powers of the amplitude of the driving charge or current density. Under the assumption that the equilibrium magnetic equation of state may be used in linearized form and that higher harmonics than the first may be neglected, a set of self-consistent integral equations is derived which can be solved numerically by iteration. In typical situations the second-order perturbation theory turns out to be quite accurate.

Application of relativistic coupled-cluster theory to electron impact excitation of Mg+ in the plasma environment

NASA Astrophysics Data System (ADS)

Sharma, Lalita; Sahoo, Bijaya Kumar; Malkar, Pooja; Srivastava, Rajesh

2018-01-01

A relativistic coupled-cluster theory is implemented to study electron impact excitations of atomic species. As a test case, the electron impact excitations of the 3 s 2 S 1/2-3 p 2 P 1/2;3/2 resonance transitions are investigated in the singly charged magnesium (Mg+) ion using this theory. Accuracies of wave functions of Mg+ are justified by evaluating its attachment energies of the relevant states and compared with the experimental values. The continuum wave function of the projectile electron are obtained by solving Dirac equations assuming distortion potential as static potential of the ground state of Mg+. Comparison of the calculated electron impact excitation differential and total cross-sections with the available measurements are found to be in very good agreements at various incident electron energies. Further, calculations are carried out in the plasma environment in the Debye-Hückel model framework, which could be useful in the astrophysics. Influence of plasma strength on the cross-sections as well as linear polarization of the photon emission in the 3 p 2 P 3/2-3 s 2 S 1/2 transition is investigated for different incident electron energies.

Theory of ITG turbulent saturation in stellarators: identifying mechanisms to reduce turbulent transport

DOE PAGES

Hegna, Chris C.; Terry, Paul W.; Faber, Ben J.

2018-02-01

A three-field fluid model that allows for general three-dimensional equilibrium geometry is developed to describe ion temperature gradient turbulent saturation processes in stellarators. The theory relies on the paradigm of nonlinear transfer of energy from unstable to damped modes at comparable wavelength as the dominant saturation mechanism. The unstable-to-damped mode interaction is enabled by a third mode that for dominant energy transfer channels primarily serves as a regulator of the nonlinear energy transfer rate. The identity of the third wave in the interaction defines different scenarios for turbulent saturation with the dominant scenario depending upon the properties of the 3Dmore » geometry. The nonlinear energy transfer physics is quantified by the product of a turbulent correlation lifetime and a geometric coupling coefficient. The turbulent correlation time is determined by a three-wave frequency mismatch, which at long wavelength can be calculated from the sum of the linear eigenfrequencies of the three modes. Larger turbulent correlation times denote larger levels of nonlinear energy transfer and hence smaller turbulent transport. The theory provides an analytic prediction for how 3D shaping can be tuned to lower turbulent transport through saturation processes.« less

Theory of ITG turbulent saturation in stellarators: identifying mechanisms to reduce turbulent transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hegna, Chris C.; Terry, Paul W.; Faber, Ben J.

A three-field fluid model that allows for general three-dimensional equilibrium geometry is developed to describe ion temperature gradient turbulent saturation processes in stellarators. The theory relies on the paradigm of nonlinear transfer of energy from unstable to damped modes at comparable wavelength as the dominant saturation mechanism. The unstable-to-damped mode interaction is enabled by a third mode that for dominant energy transfer channels primarily serves as a regulator of the nonlinear energy transfer rate. The identity of the third wave in the interaction defines different scenarios for turbulent saturation with the dominant scenario depending upon the properties of the 3Dmore » geometry. The nonlinear energy transfer physics is quantified by the product of a turbulent correlation lifetime and a geometric coupling coefficient. The turbulent correlation time is determined by a three-wave frequency mismatch, which at long wavelength can be calculated from the sum of the linear eigenfrequencies of the three modes. Larger turbulent correlation times denote larger levels of nonlinear energy transfer and hence smaller turbulent transport. The theory provides an analytic prediction for how 3D shaping can be tuned to lower turbulent transport through saturation processes.« less

Ab Initio Theory of Nuclear Magnetic Resonance Shifts in Metals

NASA Astrophysics Data System (ADS)

D'Avezac, Mayeul; Marzari, Nicola; Mauri, Francesco

2005-03-01

A comprehensive approach for the first-principles determination of all-electron NMR shifts in metallic systems is presented. Our formulation is based on a combination of density-functional perturbation theory and all-electron wavefunction reconstruction, starting from periodic-boundary calculations in the pseudopotential approximation. The orbital contribution to the NMR shift (the chemical shift) is obtained by combining the gauge-including projector augmented-wave approach (GIPAW), originally developed for the case of insulatorsootnotetextC. J. Pickard, Francesco Mauri, Phys. Rev. B, 63, 245101(2001), with the extension of linear-response theory to the case of metallic systemsootnotetextS. de Gironcoli, Phys. Rev. B, 51, 6773(1995). The spin contribution (the Knight shift) is obtained as a response to a finite uniform magnetic field, and through reconstructing the hyperfine interaction between the electron-spin density and the nuclear spins with the projector augmented-wave method (PAWootnotetextC. G. Van de Walle, P. E. Blöchl, Phys. Rev. B, 47, 4244(1993)). Our method is validated with applications to the case of the homogeneous electron gas and of simple metals. (Work supported by MURI grant DAAD 19-03-1-0169 and MIT-France)

Variability of Kelvin wave momentum flux from high-resolution radiosonde and radio occultation data

NASA Astrophysics Data System (ADS)

Sjoberg, J. P.; Zeng, Z.; Ho, S. P.; Birner, T.; Anthes, R. A.; Johnson, R. H.

2017-12-01

Direct measurement of momentum flux from Kelvin waves in the stratosphere remains challenging. Constraining this flux from observations is an important step towards constraining the flux from models. Here we present results from analyses using linear theory to estimate the Kelvin wave amplitudes and momentum fluxes from both high-resolution radiosondes and from radio occultation (RO) data. These radiosonde data are from a contiguous 11-year span of soundings performed at two Department of Energy Atmospheric Radiation Measurement sites, while the RO data span 14 years from multiple satellite missions. Daily time series of the flux from both sources are found to be in quantitative agreement with previous studies. Climatological analyses of these data reveal the expected seasonal cycle and variability associated with the quasi-biennial oscillation. Though both data sets provide measurements on distinct spatial and temporal scales, the estimated flux from each provides insight into separate but complimentary aspects of how the Kelvin waves affect the stratosphere. Namely, flux derived from radiosonde sites provide details on the regional Kelvin wave variability, while the flux from RO data are zonal mean estimates.

An Optimal Image-Based Method for Identification of Acoustic Emission (AE) Sources in Plate-Like Structures Using a Lead Zirconium Titanate (PZT) Sensor Array.

PubMed

Yan, Gang; Zhou, Li

2018-02-21

This paper proposes an innovative method for identifying the locations of multiple simultaneous acoustic emission (AE) events in plate-like structures from the view of image processing. By using a linear lead zirconium titanate (PZT) sensor array to record the AE wave signals, a reverse-time frequency-wavenumber (f-k) migration is employed to produce images displaying the locations of AE sources by back-propagating the AE waves. Lamb wave theory is included in the f-k migration to consider the dispersive property of the AE waves. Since the exact occurrence time of the AE events is usually unknown when recording the AE wave signals, a heuristic artificial bee colony (ABC) algorithm combined with an optimal criterion using minimum Shannon entropy is used to find the image with the identified AE source locations and occurrence time that mostly approximate the actual ones. Experimental studies on an aluminum plate with AE events simulated by PZT actuators are performed to validate the applicability and effectiveness of the proposed optimal image-based AE source identification method.

An Optimal Image-Based Method for Identification of Acoustic Emission (AE) Sources in Plate-Like Structures Using a Lead Zirconium Titanate (PZT) Sensor Array

PubMed Central

Zhou, Li

2018-01-01

This paper proposes an innovative method for identifying the locations of multiple simultaneous acoustic emission (AE) events in plate-like structures from the view of image processing. By using a linear lead zirconium titanate (PZT) sensor array to record the AE wave signals, a reverse-time frequency-wavenumber (f-k) migration is employed to produce images displaying the locations of AE sources by back-propagating the AE waves. Lamb wave theory is included in the f-k migration to consider the dispersive property of the AE waves. Since the exact occurrence time of the AE events is usually unknown when recording the AE wave signals, a heuristic artificial bee colony (ABC) algorithm combined with an optimal criterion using minimum Shannon entropy is used to find the image with the identified AE source locations and occurrence time that mostly approximate the actual ones. Experimental studies on an aluminum plate with AE events simulated by PZT actuators are performed to validate the applicability and effectiveness of the proposed optimal image-based AE source identification method. PMID:29466310

Nonlinear guided wave propagation in prestressed plates.

PubMed

Pau, Annamaria; Lanza di Scalea, Francesco

2015-03-01

The measurement of stress in a structure presents considerable interest in many fields of engineering. In this paper, the diagnostic potential of nonlinear elastic guided waves in a prestressed plate is investigated. To do so, an analytical model is formulated accounting for different aspects involved in the phenomenon. The fact that the initial strains can be finite is considered using the Green Lagrange strain tensor, and initial and final configurations are not merged, as it would be assumed in the infinitesimal strain theory. Moreover, an appropriate third-order expression of the strain energy of the hyperelastic body is adopted to account for the material nonlinearities. The model obtained enables to investigate both the linearized case, which gives the variation of phase and group velocity as a function of the initial stress, and the nonlinear case, involving second-harmonic generation as a function of the initial state of stress. The analysis is limited to Rayleigh-Lamb waves propagating in a plate. Three cases of initial prestress are considered, including prestress in the direction of the wave propagation, prestress orthogonal to the direction of wave propagation, and plane isotropic stress.

Polarization ratio property and material classification method in passive millimeter wave polarimetric imaging

NASA Astrophysics Data System (ADS)

Cheng, Yayun; Qi, Bo; Liu, Siyuan; Hu, Fei; Gui, Liangqi; Peng, Xiaohui

2016-10-01

Polarimetric measurements can provide additional information as compared to unpolarized ones. In this paper, linear polarization ratio (LPR) is created to be a feature discriminator. The LPR properties of several materials are investigated using Fresnel theory. The theoretical results show that LPR is sensitive to the material type (metal or dielectric). Then a linear polarization ratio-based (LPR-based) method is presented to distinguish between metal and dielectric materials. In order to apply this method to practical applications, the optimal range of incident angle have been discussed. The typical outdoor experiments including various objects such as aluminum plate, grass, concrete, soil and wood, have been conducted to validate the presented classification method.

Effects of discrete-electrode arrangement on traveling-wave electroosmotic pumping

NASA Astrophysics Data System (ADS)

Liu, Weiyu; Shao, Jinyou; Ren, Yukun; Wu, Yupan; Wang, Chunhui; Ding, Haitao; Jiang, Hongyuan; Ding, Yucheng

2016-09-01

Traveling-wave electroosmotic (TWEO) pumping arises from the action of an imposed traveling-wave (TW) electric field on its own induced charge in the diffuse double layer, which is formed on top of an electrode array immersed in electrolyte solutions. Such a traveling field can be merely realized in practice by a discrete electrode array upon which the corresponding voltages of correct phase are imposed. By employing the theory of linear and weakly nonlinear double-layer charging dynamics, a physical model incorporating both the nonlinear surface capacitance of diffuse layer and Faradaic current injection is developed herein in order to quantify the changes in TWEO pumping performance from a single-mode TW to discrete electrode configuration. Benefiting from the linear analysis, we investigate the influence of using discrete electrode array to create the TW signal on the resulting fluid motion, and several approaches are suggested to improve the pumping performance. In the nonlinear regime, our full numerical analysis considering the intervening isolation spacing indicates that a practical four-phase discrete electrode configuration of equal electrode and gap width exhibits stronger nonlinearity than expected from the idealized pump applied with a single-mode TW in terms of voltage-dependence of the ideal pumping frequency and peak flow rate, though it has a much lower pumping performance. For model validation, pumping of electrolytes by TWEO is achieved over a confocal spiral four-phase electrode array covered by an insulating microchannel; measurement of flow velocity indicates the modified nonlinear theory considering moderate Faradaic conductance is indeed a more accurate physical description of TWEO. These results offer useful guidelines for designing high-performance TWEO microfluidic pumps with discrete electrode array.

Study the Precipitation of Radiation Belt Electrons during the Rapid Dropout Events

NASA Astrophysics Data System (ADS)

Tu, W.; Cunningham, G.; Li, X.; Chen, Y.

2015-12-01

During the main phase of storms, the relativistic electron flux in the radiation belt can drop by orders of magnitude on timescales of a few hours. Where do the electrons go? This is one of the most important outstanding questions in radiation belt studies. Radiation belt electrons can be lost either by transport across the magnetopause into interplanetary space or by precipitation into the atmosphere. In this work we first conduct a survey of the MeV electron dropouts using the Van Allen Probes data in conjunction with the low-altitude measurements of precipitating electrons by 6 NOAA/POES satellites. The dropout events are categorized into three types: precipitation-loss dominant, outward radial diffusion dominant, or with contributions from both mechanisms. The survey results suggest the relative importance of precipitation and outward radial diffusion to the fast dropouts of radiation belt electrons, and their extent in L-shell and electron energy. Then, for specific events identified as dominated by precipitation loss, we use the Drift-Diffusion model, which includes the effects of azimuthal drift and pitch angle diffusion, to simulate both the electron dropout observed by Van Allen Probes and the distributions of drift-loss-cone electrons observed by multiple low-earth-orbit satellites (6 POES and the Colorado Student Space Weather Experiment). The model quantifies the electron precipitation loss and pitch angle diffusion coefficient, Dxx, with high temporal and spatial resolution. Finally, by comparing the Dxx derived from the model with those estimated from the quasi-linear theory using wave data from Van Allen Probes and other event-specific wave models, we are able to test the validity of quasi-linear theory and seek direct evidence of the wave-particle interactions during the dropouts.

Results of Computing Amplitude and Phase of the VLF Wave Using Wave Hop Theory

NASA Astrophysics Data System (ADS)

Pal, Sujay; Basak, Tamal; Chakrabarti, Sandip K.

2011-07-01

We present the basics of the wave hop theory to compute the amplitude and phase of the VLF signals. We use the Indian Navy VTX transmitter at 18.2 kHz as an example of the source and compute the VLF propagation characteristics for several propagation paths using the wave-hop theory. We find the signal amplitudes as a function of distance from the transmitter using wave hop theory in different bearing angles and compare with the same obtained from the Long Wave Propagation Capability (LWPC) code which uses the mode theory. We repeat a similar exercise for the diurnal and seasonal behavior. We note that the signal variation by wave hop theory gives more detailed information in the day time. We further present the spatial variation of the signal amplitude over whole of India at a given time including the effect of sunrise and sunset terminator and also compare the same with that from the mode theory. We point out that the terminator effect is clearly understood in wave hop results than that from the mode theory.

On the correct implementation of Fermi-Dirac statistics and electron trapping in nonlinear electrostatic plane wave propagation in collisionless plasmas

NASA Astrophysics Data System (ADS)

Schamel, Hans; Eliasson, Bengt

2016-05-01

Quantum statistics and electron trapping have a decisive influence on the propagation characteristics of coherent stationary electrostatic waves. The description of these strictly nonlinear structures, which are of electron hole type and violate linear Vlasov theory due to the particle trapping at any excitation amplitude, is obtained by a correct reduction of the three-dimensional Fermi-Dirac distribution function to one dimension and by a proper incorporation of trapping. For small but finite amplitudes, the holes become of cnoidal wave type and the electron density is shown to be described by a ϕ ( x ) 1 / 2 rather than a ϕ ( x ) expansion, where ϕ ( x ) is the electrostatic potential. The general coefficients are presented for a degenerate plasma as well as the quantum statistical analogue to these steady state coherent structures, including the shape of ϕ ( x ) and the nonlinear dispersion relation, which describes their phase velocity.

Exact relativistic expressions for wave refraction in a generally moving fluid.

PubMed

Cavalleri, G; Tonni, E; Barbero, F

2013-04-01

The law for the refraction of a wave when the two fluids and the interface are moving with relativistic velocities is given in an exact form, at the same time correcting a first order error in a previous paper [Cavalleri and Tonni, Phys. Rev. E 57, 3478 (1998)]. The treatment is then extended to a generally moving fluid with variable refractive index, ready to be applied to the refraction of acoustic, electromagnetic, or magnetohydrodynamic waves in the atmosphere of rapidly rotating stars. In the particular case of a gas cloud receding because of the universe expansion, our result can be applied to predict observable micro- and mesolensings. The first order approximation of our exact result for the deviation due to refraction of the light coming from a further quasar has a relativistic dependence equal to the one obtained by Einsteins' linearized theory of gravitation.

Analytic computation of energy derivatives - Relationships among partial derivatives of a variationally determined function

NASA Technical Reports Server (NTRS)

King, H. F.; Komornicki, A.

1986-01-01

Formulas are presented relating Taylor series expansion coefficients of three functions of several variables, the energy of the trial wave function (W), the energy computed using the optimized variational wave function (E), and the response function (lambda), under certain conditions. Partial derivatives of lambda are obtained through solution of a recursive system of linear equations, and solution through order n yields derivatives of E through order 2n + 1, extending Puley's application of Wigner's 2n + 1 rule to partial derivatives in couple perturbation theory. An examination of numerical accuracy shows that the usual two-term second derivative formula is less stable than an alternative four-term formula, and that previous claims that energy derivatives are stationary properties of the wave function are fallacious. The results have application to quantum theoretical methods for the computation of derivative properties such as infrared frequencies and intensities.

Spin-wave dynamics and exchange interactions in multiferroic NdFe3(BO3)4 explored by inelastic neutron scattering

NASA Astrophysics Data System (ADS)

Golosovsky, I. V.; Ovsyanikov, A. K.; Aristov, D. N.; Matveeva, P. G.; Mukhin, A. A.; Boehm, M.; Regnault, L.-P.; Bezmaternykh, L. N.

2018-04-01

Magnetic excitations and exchange interactions in multiferroic NdFe3(BO3)4 were studied by inelastic neutron scattering in the phase with commensurate antiferromagnetic structure. The observed spectra were analyzed in the frame of the linear spin-wave theory. It was shown that only the model, which includes the exchange interactions within eight coordination spheres, describes satisfactorily all observed dispersion curves. The calculation showed that the spin-wave dynamics is governed by the strongest antiferromagnetic intra-chain interaction and three almost the same inter-chain interactions. Other interactions, including ferromagnetic exchange, appeared to be insignificant. The overall energy balance of the antiferromagnetic inter-chain exchange interactions, which couple the moments from the adjacent ferromagnetic layers as well as within a layer, stabilizes ferromagnetic arrangement in the latter. It demonstrates that the pathway geometry plays a crucial role in forming of the magnetic structure.

Wave propagation in viscoelastic horns using a fractional calculus rheology model

NASA Astrophysics Data System (ADS)

Margulies, Timothy

2003-10-01

The complex mechanical behavior of materials are characterized by fluid and solid models with fractional calculus differentials to relate stress and strain fields. Fractional derivatives have been shown to describe the viscoelastic stress from polymer chain theory for molecular solutions [Rouse and Sittel, J. Appl. Phys. 24, 690 (1953)]. Here the propagation of infinitesimal waves in one dimensional horns with a small cross-sectional area change along the longitudinal axis are examined. In particular, the linear, conical, exponential, and catenoidal shapes are studied. The wave amplitudes versus frequency are solved analytically and predicted with mathematical computation. Fractional rheology data from Bagley [J. Rheol. 27, 201 (1983); Bagley and Torvik, J. Rheol. 30, 133 (1986)] are incorporated in the simulations. Classical elastic and fluid ``Webster equations'' are recovered in the appropriate limits. Horns with real materials that employ fractional calculus representations can be modeled to examine design trade-offs for engineering or for scientific application.

Anatomy of quantum critical wave functions in dissipative impurity problems

NASA Astrophysics Data System (ADS)

Blunden-Codd, Zach; Bera, Soumya; Bruognolo, Benedikt; Linden, Nils-Oliver; Chin, Alex W.; von Delft, Jan; Nazir, Ahsan; Florens, Serge

2017-02-01

Quantum phase transitions reflect singular changes taking place in a many-body ground state; however, computing and analyzing large-scale critical wave functions constitutes a formidable challenge. Physical insights into the sub-Ohmic spin-boson model are provided by the coherent-state expansion (CSE), which represents the wave function by a linear combination of classically displaced configurations. We find that the distribution of low-energy displacements displays an emergent symmetry in the absence of spontaneous symmetry breaking while experiencing strong fluctuations of the order parameter near the quantum critical point. Quantum criticality provides two strong fingerprints in critical low-energy modes: an algebraic decay of the average displacement and a constant universal average squeezing amplitude. These observations, confirmed by extensive variational matrix-product-state (VMPS) simulations and field theory arguments, offer precious clues into the microscopics of critical many-body states in quantum impurity models.

Nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating embedded in water

NASA Astrophysics Data System (ADS)

Jiménez, N.; Romero-García, V.; Picó, R.; Garcia-Raffi, L. M.; Staliunas, K.

2015-11-01

We report the nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating immersed in water. In the linear regime, the system presents high focal gain (32 dB), with a narrow beam-width and intense side lobes as it is common in focusing by Fresnel-like lenses. Activating the nonlinearity of the host medium by using high amplitude incident waves, the focusing properties of the lens dramatically change. Theoretical predictions show that the focal gain of the system extraordinary increases in the strongly nonlinear regime (Mach number of 6.1 × 10-4). Particularly, the harmonic generation is locally activated at the focal spot, and the second harmonic beam is characterized by strongly reduced side-lobes and an excellent beam profile as experiments show in agreement with theory. The results can motivate applications in medical therapy or second harmonic imaging.

Tunable ferromagnetic resonance in La-Co substituted barium hexaferrites at millimeter wave frequencies

NASA Astrophysics Data System (ADS)

Korolev, Konstantin A.; Wu, Chuanjian; Yu, Zhong; Sun, Ke; Afsar, Mohammed N.; Harris, Vincent G.

2018-05-01

Transmittance measurements have been performed on La-Co substituted barium hexaferrites in millimeter waves. Broadband millimeter-wave measurements have been carried out using the free space quasi-optical spectrometer, equipped with a set of high power backward wave oscillators covering the frequency range of 30 - 120 GHz. Strong absorption zones have been observed in the millimeter-wave transmittance spectra of all La-Co substituted barium hexaferrites due to the ferromagnetic resonance. Linear shift of ferromagnetic resonance frequency as functions of La-Co substitutions have been found. Real and imaginary parts of dielectric permittivity of La-Co substituted barium hexaferrites have been calculated using the analysis of recorded high precision transmittance spectra. Frequency dependences of magnetic permeability of La-Co substituted barium hexaferrites, as well as saturation magnetization and anisotropy field have been determined based on Schlömann's theory for partially magnetized ferrites. La-Co substituted barium hexaferrites have been further investigated by DC magnetization to assess magnetic behavior and compare with millimeter wave data. Consistency of saturation magnetization determined independently by both millimeter wave absorption and DC magnetization have been found for all La-Co substituted barium hexaferrites. These materials seem to be quite promising as tunable millimeter wave absorbers, filters, circulators, based on the adjusting of their substitution parameters.

A geometric theory of waves and its applications to plasma physics.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ruiz, Daniel

Waves play an essential role in many aspects of plasma dynamics. For example, they are indispensable in plasma manipulation and diagnostics. Although the physics of waves is well understood in the context of relatively simple problems, difficulties arise when studying waves that propagate in inhomogeneous or nonlinear media. This thesis presents a new systematic wave theory based on phase-space variational principles. In this dissertation, waves are treated as geometric objects of a variational theory rather than formal solutions of specific PDEs. This approach simplifies calculations, highlights the underlying wave symmetries, and leads to improved modeling of wave dynamics. Specifically, thismore » dissertation presents two important breakthroughs that were obtained in the general theory of waves. The first main contribution of the present dissertation is an extension of the theory of geometrical optics (GO) in order to include polarization effects. Even when diffraction is ignored, the GO ray equations are not entirely accurate. This occurs because GO treats wave rays as classical particles described by their position and momentum coordinates. However, vector waves have another degree of freedom, their polarization. As a result, wave rays can behave as particles with spin and show polarization dynamics, such as polarization precession and polarization-driven bending of ray trajectories. In this thesis, the theory of GO is reformulated as a first-principle Lagrangian wave theory that governs both mentioned polarization phenomena simultaneously. The theory was applied successfully to several systems of interest, such as relativistic spin-$1/2$ particles and radio-frequency waves propagating in magnetized plasmas. The second main contribution of this thesis is the development of a phase-space method to study basic properties of nonlinear wave--wave interactions. Specifically, a general theory is proposed that describes the ponderomotive refraction that a wave can experience when interacting with another wave. It is also shown that phase-space methods can be useful to study problems in the field of wave turbulence, such as the nonlinear interaction of high-frequency waves with large-scale structures. Overall, the results obtained can serve as a basis for future studies on more complex nonlinear wave--wave interactions, such as modulational instabilities in general wave ensembles or wave turbulence.« less

Internal wave scattering in continental slope canyons, part 1: Theory and development of a ray tracing algorithm

NASA Astrophysics Data System (ADS)

Nazarian, Robert H.; Legg, Sonya

2017-10-01

When internal waves interact with topography, such as continental slopes, they can transfer wave energy to local dissipation and diapycnal mixing. Submarine canyons comprise approximately ten percent of global continental slopes, and can enhance the local dissipation of internal wave energy, yet parameterizations of canyon mixing processes are currently missing from large-scale ocean models. As a first step in the development of such parameterizations, we conduct a parameter space study of M2 tidal-frequency, low-mode internal waves interacting with idealized V-shaped canyon topographies. Specifically, we examine the effects of varying the canyon mouth width, shape and slope of the thalweg (line of lowest elevation). This effort is divided into two parts. In the first part, presented here, we extend the theory of 3-dimensional internal wave reflection to a rotated coordinate system aligned with our idealized V-shaped canyons. Based on the updated linear internal wave reflection solution that we derive, we construct a ray tracing algorithm which traces a large number of rays (the discrete analog of a continuous wave) into the canyon region where they can scatter off topography. Although a ray tracing approach has been employed in other studies, we have, for the first time, used ray tracing to calculate changes in wavenumber and ray density which, in turn, can be used to calculate the Froude number (a measure of the likelihood of instability). We show that for canyons of intermediate aspect ratio, large spatial envelopes of instability can form in the presence of supercritical sidewalls. Additionally, the canyon height and length can modulate the Froude number. The second part of this study, a diagnosis of internal wave scattering in continental slope canyons using both numerical simulations and this ray tracing algorithm, as well as a test of robustness of the ray tracing, is presented in the companion article.

Calculation of periodic flows in a continuously stratified fluid

NASA Astrophysics Data System (ADS)

Vasiliev, A.

2012-04-01

Analytic theory of disturbances generated by an oscillating compact source in a viscous continuously stratified fluid was constructed. Exact solution of the internal waves generation problem was constructed taking into account diffusivity effects. This analysis is based on set of fundamental equations of incompressible flows. The linearized problem of periodic flows in a continuously stratified fluid, generated by an oscillating part of the inclined plane was solved by methods of singular perturbation theory. A rectangular or disc placed on a sloping plane and oscillating linearly in an arbitrary direction was selected as a source of disturbances. The solutions include regularly perturbed on dissipative component functions describing internal waves and a family of singularly perturbed functions. One of the functions from the singular components family has an analogue in a homogeneous fluid that is a periodic or Stokes' flow. Its thickness is defined by a universal micro scale depending on kinematics viscosity coefficient and a buoyancy frequency with a factor depending on the wave slope. Other singular perturbed functions are specific for stratified flows. Their thickness are defined the diffusion coefficient, kinematic viscosity and additional factor depending on geometry of the problem. Fields of fluid density, velocity, vorticity, pressure, energy density and flux as well as forces acting on the source are calculated for different types of the sources. It is shown that most effective source of waves is the bi-piston. Complete 3D problem is transformed in various limiting cases that are into 2D problem for source in stratified or homogeneous fluid and the Stokes problem for an oscillating infinite plane. The case of the "critical" angle that is equality of the emitting surface and the wave cone slope angles needs in separate investigations. In this case, the number of singular component is saved. Patterns of velocity and density fields were constructed and analyzed by methods of computational mathematics. Singular components of the solution affect the flow pattern of the inhomogeneous stratified fluid, not only near the source of the waves, but at a large distance. Analytical calculations of the structure of wave beams are matched with laboratory experiments. Some deviations at large distances from the source are formed due to the contribution of background wave field associated with seiches in the laboratory tank. In number of the experiments vortices with closed contours were observed on some distances from the disk. The work was supported by Ministry of Education and Science RF (Goscontract No. 16.518.11.7059), experiments were performed on set up USU "HPC IPMec RAS".

Wind tunnel wall effects in a linear oscillating cascade

NASA Technical Reports Server (NTRS)

Buffum, Daniel H.; Fleeter, Sanford

1991-01-01

Experiments in a linear oscillating cascade reveal that the wind tunnel walls enclosing the airfoils have, in some cases, a detrimental effect on the oscillating cascade aerodynamics. In a subsonic flow field, biconvex airfoils are driven simultaneously in harmonic, torsion-mode oscillations for a range of interblade phase angle values. It is found that the cascade dynamic periodicity - the airfoil to airfoil variation in unsteady surface pressure - is good for some values of interblade phase angle but poor for others. Correlation of the unsteady pressure data with oscillating flat plate cascade predictions is generally good for conditions where the periodicity is good and poor where the periodicity is poor. Calculations based upon linearized unsteady aerodynamic theory indicate that pressure waves reflected from the wind tunnel walls are responsible for the cases where there is poor periodicity and poor correlation with the predictions.

Analytic wave solution with helicon and Trivelpiece-Gould modes in an annular plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carlsson, Johan; Pavarin, Daniele; Walker, Mitchell

2009-11-26

Helicon sources in an annular configuration have applications for plasma thrusters. The theory of Klozenberg et al.[J. P. Klozenberg B. McNamara and P. C. Thonemann, J. Fluid Mech. 21(1965) 545-563] for the propagation and absorption of helicon and Trivelpiece-Gould modes in a cylindrical plasma has been generalized for annular plasmas. Analytic solutions are found also in the annular case, but in the presence of both helicon and Trivelpiece-Gould modes, a heterogeneous linear system of equations must be solved to match the plasma and inner and outer vacuum solutions. The linear system can be ill-conditioned or even exactly singular, leading tomore » a dispersion relation with a discrete set of discontinuities. The coefficients for the analytic solution are calculated by solving the linear system with singular-value decomposition.« less

The effect of the cosmological constant on a quadrupole signal in the linearized approximation

NASA Astrophysics Data System (ADS)

Somlai, László Ábel; Vasúth, Mátyás

In this study the effects of a nonzero cosmological constant Λ on a quadrupole gravitational wave (GW) signal are analyzed. The linearized approximation of general relativity was used, so the perturbed metric can be written as the sum of hGW GWs and hΛ background term, originated from Λ. The ΛhGW term was also included in this study. To derive physically relevant consequences of Λ≠0 comoving coordinates are used. In these coordinates, the equations of motion (EoMs) are not self-consistent so the result of the linearized theory has to be transformed to the FRW frame. The luminosity distance and the same order of the magnitude of frequency in accordance with the detected GWs were used to demonstrate the effects of the cosmological constant.

Shear wave velocity structure in North America from large-scale waveform inversions of surface waves

USGS Publications Warehouse

Alsina, D.; Woodward, R.L.; Snieder, R.K.

1996-01-01

A two-step nonlinear and linear inversion is carried out to map the lateral heterogeneity beneath North America using surface wave data. The lateral resolution for most areas of the model is of the order of several hundred kilometers. The most obvious feature in the tomographic images is the rapid transition between low velocities in the technically active region west of the Rocky Mountains and high velocities in the stable central and eastern shield of North America. The model also reveals smaller-scale heterogeneous velocity structures. A high-velocity anomaly is imaged beneath the state of Washington that could be explained as the subducting Juan de Fuca plate beneath the Cascades. A large low-velocity structure extends along the coast from the Mendocino to the Rivera triple junction and to the continental interior across the southwestern United States and northwestern Mexico. Its shape changes notably with depth. This anomaly largely coincides with the part of the margin where no lithosphere is consumed since the subduction has been replaced by a transform fault. Evidence for a discontinuous subduction of the Cocos plate along the Middle American Trench is found. In central Mexico a transition is visible from low velocities across the Trans-Mexican Volcanic Belt (TMVB) to high velocities beneath the Yucatan Peninsula. Two elongated low-velocity anomalies beneath the Yellowstone Plateau and the eastern Snake River Plain volcanic system and beneath central Mexico and the TMVB seem to be associated with magmatism and partial melting. Another low-velocity feature is seen at depths of approximately 200 km beneath Florida and the Atlantic Coastal Plain. The inversion technique used is based on a linear surface wave scattering theory, which gives tomographic images of the relative phase velocity perturbations in four period bands ranging from 40 to 150 s. In order to find a smooth reference model a nonlinear inversion based on ray theory is first performed. After correcting for the crustal thickness the phase velocity perturbations obtained from the subsequent linear waveform inversion for the different period bands are converted to a three-layer model of S velocity perturbations (layer 1, 25-100 km; layer 2, 100-200 km) layer 3, 200-300 km). We have applied this method on 275 high-quality Rayleigh waves recorded by a variety of instruments in North America (IRIS/USGS, IRIS/IDA, TERRAscope, RSTN). Sensitivity tests indicate that the lateral resolution is especially good in the densely sampled western continental United States, Mexico, and the Gulf of Mexico.

The cooling time scales of growing sunspots

NASA Technical Reports Server (NTRS)

Chou, Dean-Yi

1987-01-01

The evolution of brightness and magnetic fields of growing sunspots is studied. Growing sunspots are found to be brighter (or less dark) than stable sunspots with the same magnetic field strength. From comparison of brightness and magnetic fields of a growing sunspot with those of stable sunspots, a dynamical parameter, the cooling time, of the growing sunspot is obtained. Ten growing sunspots are studied, and cooling times of 0.5 to 9 hr are found. Two models, the inhibition model and the Alfven wave model, give cooling times of about 0.05 hr, based on linear theory. The discrepancy between theory and observation may be due to the fact that the observed sunspots are in the nonlinear regime.

Infrared spectroscopy of copper-resveratrol complexes: A joint experimental and theoretical study

NASA Astrophysics Data System (ADS)

Chiavarino, B.; Crestoni, M. E.; Fornarini, S.; Taioli, S.; Mancini, I.; Tosi, P.

2012-07-01

Infrared multiple-photon dissociation spectroscopy has been used to record vibrational spectra of charged copper-resveratrol complexes in the 3500-3700 cm-1 and 1100-1900 cm-1 regions. Minimum energy structures have been determined by density functional theory calculations using plane waves and pseudopotentials. In particular, the copper(I)-resveratrol complex presents a tetra-coordinated metal bound with two carbon atoms of the alkenyl moiety and two closest carbons of the adjoining resorcinol ring. For these geometries vibrational spectra have been calculated by using linear response theory. The good agreement between experimental and calculated IR spectra for the selected species confirms the overall reliability of the proposed geometries.

Wave drift damping acting on multiple circular cylinders (model tests)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kinoshita, Takeshi; Sunahara, Shunji; Bao, W.

1995-12-31

The wave drift damping for the slow drift motion of a four-column platform is experimentally investigated. The estimation of damping force of the slow drift motion of moored floating structures in ocean waves, is one of the most important topics. Bao et al. calculated an interaction of multiple circular cylinders based on the potential flow theory, and showed that the wave drift damping is significantly influenced by the interaction between cylinders. This calculation method assumes that the slow drift motion is approximately replaced by steady current, that is, structures on slow drift motion are supposed to be equivalent to onesmore » in both regular waves and slow current. To validate semi-analytical solutions of Bao et al., experiments were carried out. At first, added resistance due to waves acting on a structure composed of multiple (four) vertical circular cylinders fixed to a slowly moving carriage, was measured in regular waves. Next, the added resistance of the structure moored by linear spring to the slowly moving carriage were measured in regular waves. Furthermore, to validate the assumption that the slow drift motion is replaced by steady current, free decay tests in still water and in regular waves were compared with the simulation of the slow drift motion using the wave drift damping coefficient obtained by the added resistance tests.« less

Analysis of Oblique Wave Interaction with a Comb-Type Caisson Breakwater

NASA Astrophysics Data System (ADS)

Wang, Xinyu; Liu, Yong; Liang, Bingchen

2018-04-01

This study develops an analytical solution for oblique wave interaction with a comb-type caisson breakwater based on linear potential theory. The fluid domain is divided into inner and outer regions according to the geometrical shape of breakwater. By using periodic boundary condition and separation of variables, series solutions of velocity potentials in inner and outer regions are developed. Unknown expansion coefficients in series solutions are determined by matching velocity and pressure of continuous conditions on the interface between two regions. Then, hydrodynamic quantities involving reflection coefficients and wave forces acting on breakwater are estimated. Analytical solution is validated by a multi-domain boundary element method solution for the present problem. Diffusion reflection due to periodic variations in breakwater shape and corresponding surface elevations around the breakwater are analyzed. Numerical examples are also presented to examine effects of caisson parameters on total wave forces acting on caissons and total wave forces acting on side plates. Compared with a traditional vertical wall breakwater, the wave force acting on a suitably designed comb-type caisson breakwater can be significantly reduced. This study can give a better understanding of the hydrodynamic performance of comb-type caisson breakwaters.

Fire Hose Instability in the Multiple Magnetic Reconnection

NASA Astrophysics Data System (ADS)

Alexandrova, A.; Retino, A.; Divin, A. V.; Le Contel, O.; Matteini, L.; Breuillard, H.; Deca, J.; Catapano, F.; Cozzani, G.; Nakamura, R.; Panov, E. V.; Voros, Z.

2017-12-01

We present observations of multiple reconnection in the Earth's magnetotail. In particular, we observe an ion temperature anisotropy characterized by large temperature along the magnetic field, between the two active X-lines. The anisotropy is associated with right-hand polarized waves at frequencies lower than the ion cyclotron frequency and propagating obliquely to the background magnetic field. We show that the observed anisotropy and the wave properties are consistent with linear kinetic theory of fire hose instability. The observations are in agreement with the particle-in-cell simulations of multiple reconnection. The results suggest that the fire hose instability can develop during multiple reconnection as a consequence of the ion parallel anisotropy that is produced by counter-streaming ions trapped between the X-lines.

Electric dipole radiation at VLF in a uniform warm magneto-plasma.

NASA Technical Reports Server (NTRS)

Wang, T. N. C.; Bell, T. F.

1972-01-01

Use of a linear full electromagnetic wave theory to calculate the input impedance of an electric antenna embedded in a uniform, lossless, unbounded warm magnetoplasma, which is assumed to consist of warm electrons and cold ions. In calculating the dipole radiation resistance for the thermal modes and the thermally modified whistler mode the analysis includes the finite temperature only for the electrons. In deriving the formal solution of the warm plasma dipole input impedance a full-wave analysis is used and two antenna orientations are considered, parallel and perpendicular to the static magnetic field. A general dispersion equation governing the modes of propagation is derived and a detailed analysis is made of the propagation characteristics of these modes.

Theory of the corrugation instability of a piston-driven shock wave.

PubMed

Bates, J W

2015-01-01

We analyze the two-dimensional stability of a shock wave driven by a steadily moving corrugated piston in an inviscid fluid with an arbitrary equation of state. For h≤-1 or h>h(c), where h is the D'yakov parameter and h(c) is the Kontorovich limit, we find that small perturbations on the shock front are unstable and grow--at first quadratically and later linearly--with time. Such instabilities are associated with nonequilibrium fluid states and imply a nonunique solution to the hydrodynamic equations. The above criteria are consistent with instability limits observed in shock-tube experiments involving ionizing and dissociating gases and may have important implications for driven shocks in laser-fusion, astrophysical, and/or detonation studies.

Surface wave tomography of North America and the Caribbean using global and regional broad-band networks: Phase velocity maps and limitations of ray theory

USGS Publications Warehouse

Godey, S.; Snieder, R.; Villasenor, A.; Benz, H.M.

2003-01-01

We present phase velocity maps of fundamental mode Rayleigh waves across the North American and Caribbean plates. Our data set consists of 1846 waveforms from 172 events recorded at 91 broad-band stations operating in North America. We compute phase velocity maps in four narrow period bands between 50 and 150 s using a non-linear waveform inversion method that solves for phase velocity perturbations relative to a reference Earth model (PREM). Our results show a strong velocity contrast between high velocities beneath the stable North American craton, and lower velocities in the tectonically active western margin, in agreement with other regional and global surface wave tomography studies. We perform detailed comparisons with global model results, which display good agreement between phase velocity maps in the location and amplitude of the anomalies. However, forward modelling shows that regional maps are more accurate for predicting waveforms. In addition, at long periods, the amplitude of the velocity anomalies imaged in our regional phase velocity maps is three time larger than in global phase velocity models. This amplitude factor is necessary to explain the data accurately, showing that regional models provide a better image of velocity structures. Synthetic tests show that the raypath coverage used in this study enables one to resolve velocity features of the order of 800-1000 km. However, only larger length-scale features are observed in the phase velocity maps. The limitation in resolution of our maps can be attributed to the wave propagation theory used in the inversion. Ray theory does not account for off-great-circle ray propagation effects, such as ray bending or scattering. For wavelengths less than 1000 km, scattering effects are significant and may need to be considered.

Bi-directional vibration control of offshore wind turbines using a 3D pendulum tuned mass damper

NASA Astrophysics Data System (ADS)

Sun, C.; Jahangiri, V.

2018-05-01

Offshore wind turbines suffer from excessive bi-directional vibrations due to wind-wave misalignment and vortex induced vibrations. However, most of existing research focus on unidirectional vibration attenuation which is inadequate for real applications. The present paper proposes a three dimensional pendulum tuned mass damper (3d-PTMD) to mitigate the tower and nacelle dynamic response in the fore-aft and side-side directions. An analytical model of the wind turbine coupled with the 3d-PTMD is established wherein the interaction between the blades, the tower and the 3d-PTMD is modeled. Aerodynamic loading is computed using the Blade Element Momentum method where the Prandtls tip loss factor and the Glauert correction are considered. JONSWAP spectrum is adopted to generate wave data. Wave loading is computed using Morisons equation in collaboration with the strip theory. Via a numerical search approach, the design formula of the 3d-PTMD is obtained and examined on a National Renewable Energy Lab (NREL) monopile 5 MW baseline wind turbine model under misaligned wind, wave and seismic loading. Dual linear tuned mass dampers (TMDs) deployed in the fore-aft and side-side directions are utilized for comparison. It is found that the 3d-PTMD with a mass ratio of 2 % can improve the mitigation of the root mean square and peak response by around 10 % when compared with the dual linear TMDs in controlling the bi-directional vibration of the offshore wind turbines under misaligned wind, wave and seismic loading.

Simulations of neutral wind shear effect on the equatorial ionosphere irregularities

NASA Astrophysics Data System (ADS)

Kim, J.; Chagelishvili, G.; Horton, W.

2005-12-01

We present numerical calculations of the large-scale electron density driven by the gradient drift instability in the daytime equatorial electrojet. Under two-fluid theory the linear analysis for kilometer scale waves lead to the result that all the perturbations are transformed to small scales through linear convection by shear and then damped by diffusion. The inclusion of the nonlinearity enables inverse energy cascade to provide energy to long scale. The feedback between velocity shear and nonlinearity keeps waves growing and leads to the turbulence. In strongly turbulent regime, the nonlinear states are saturated [1]. Since the convective nonlinearities are isotropic while the interactions of velocity shear with waves are anisotropic, the feedback do not necessarily enable waves to grow. The growth of waves are highly variable on k-space configuration [2]. Our simulations show that the directional relationship between vorticity of irregularities and shear are one of key factors. Thus during the transient period, the irregularities show the anisotropy of the vorticity power spectrum. We report the evolution of the power spectrum of the vorticity and density of irregularties and its anistropic nature as observed. The work was supported in part by the Department of NSF Grant ATM-0229863 and ISTC Grant G-553. C. Ronchi, R.N. Sudan, and D.T. Farley. Numerical simulations of large-scale plasma turbulece in teh day time equatorial electrojet. J. Geophys. Res., 96:21263--21279, 1991. G.D. Chagelishvili, R.G. Chanishvili, T.S. Hristov, and J.G. Lominadze. A turbulence model in unbounded smooth shear flows : The weak turbulence approach. JETP, 94(2):434--445, 2002.