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- IOP PUBLISHING LTD
- Biblioteca Digitais de Teses e Dissertações da USP
- National Academy of Sciences
- Universidade Federal de Uberlândia
- Australian Acoustical Society; C/o Professional Centre, Private Bag 1, Darlinghurst 2010
- Optical Soc Amer
- International Frequency Sensor Association
- Universidade Cornell
- American Astronomical Society
- Taylor & Francis
- American Institute of Aeronautics and Astronautics
- Mais Publicadores...

## Rotation effect on geodesic and zonal flow modes in tokamak plasmas with isothermal magnetic surfaces

Fonte: IOP PUBLISHING LTD
Publicador: IOP PUBLISHING LTD

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

46.29%

The electrostatic geodesic mode oscillations are investigated in rotating large aspect ratio tokamak plasmas with circular isothermal magnetic surfaces. The analysis is carried out within the magnetohydrodynamic model including heat flux to compensate for the non-adiabatic pressure distribution along the magnetic surfaces in plasmas with poloidal rotation. Instead of two standard geodesic modes, three geodesic continua are found. The two higher branches of the geodesic modes have a small frequency up-shift from ordinary geodesic acoustic and sonic modes due to rotation. The lower geodesic continuum is a newzonal flowmode (geodesic Doppler mode) in plasmas with mainly poloidal rotation. Limits to standard geodesic modes are found. Bifurcation of Alfven continuum by geodesic modes at the rational surfaces is also discussed. Due to that, the frequency of combined geodesic continuum extends from the poloidal rotation frequency to the ion-sound band that can have an important role in suppressing plasma turbulence.; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); CNPq (National Council of Brazil for Science and Technology Development); Financiadora de Estudos e Projetos (FINEP); FINEP (Financiadora de Estudos e Projetos)

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## Investigação cinética de modos geodésicos de baixas frequências em plasmas magnetizados; Kinetic investigation of low frequency geodesic modes in magnetized plasmas

Fonte: Biblioteca Digitais de Teses e Dissertações da USP
Publicador: Biblioteca Digitais de Teses e Dissertações da USP

Tipo: Tese de Doutorado
Formato: application/pdf

Publicado em 29/07/2014
PT

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56.34%

#amortecimento de Landau#diamagnetic effects#drift effects#efeitos de deriva#efeitos diamagnéticos#espectroscopia em GAM#fluxos zonais#GAM#GAM#GAM spectroscopy.#geodesic acoustic modes

Devido à sua importância em turbulência causada por ondas de deriva e à aplicação com propósitos em diagnósticos de plasma, a investigação de fluxos zonais (ZF) e modos acústicos geodésicos (GAM) tem atraído bastante atenção na literatura em física de plasmas. Nesta tese, primeiramente consideramos efeitos de equilíbrio com rotação poloidal e toroidal nestes modos, posteriormente investigamos efeitos diamagnéticos em GAM a partir de um modelo de dois fluido, no qual incluímos viscosidade paralela de íons e, na parte final, consideramos amortecimento de Landau e efeitos diamagnéticos simultaneamente no estudo de GAM, porém, a partir do modelo girocinético. Efeitos diamagnéticos são causados por termos que envolvem gradientes de densidade e de temperatura provenientes da função Maxwelliana de equilíbrio. O acoplamento entre os harmônicos poloidais, $m = \pm1$, e as derivadas radiais de quantidades macroscópicas do plasma é responsável pelo aumento no valor da frequência no GAM de alta frequência e pela instabilidade no GAM de baixa frequência. Este tipo de instabilidade, que é proporcional à frequência diamagnética de elétrons e à razão entre os gradientes de temperatura e de densidade...

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## Breakdown of the Debye approximation for the acoustic modes with nanometric wavelengths in glasses

Fonte: National Academy of Sciences
Publicador: National Academy of Sciences

Tipo: Artigo de Revista Científica

EN

Relevância na Pesquisa

46.24%

On the macroscopic scale, the wavelengths of sound waves in glasses are large enough that the details of the disordered microscopic structure are usually irrelevant, and the medium can be considered as a continuum. On decreasing the wavelength this approximation must of course fail at one point. We show here that this takes place unexpectedly on the mesoscopic scale characteristic of the medium range order of glasses, where it still works well for the corresponding crystalline phases. Specifically, we find that the acoustic excitations with nanometric wavelengths show the clear signature of being strongly scattered, indicating the existence of a cross-over between well-defined acoustic modes for larger wavelengths and ill-defined ones for smaller wavelengths. This cross-over region is accompanied by a softening of the sound velocity that quantitatively accounts for the excess observed in the vibrational density of states of glasses over the Debye level at energies of a few milli-electronvolts. These findings thus highlight the acoustic contribution to the well-known universal low-temperature anomalies found in the specific heat of glasses.

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## Controle ativo de ruído aplicado a dutos com propagação de modos acústicos de alta ordem via particionamento axial; Active noise control applied to ducts with propagation of high- order acoustic modes via partitioning axial

Fonte: Universidade Federal de Uberlândia
Publicador: Universidade Federal de Uberlândia

Tipo: Tese de Doutorado

POR

Relevância na Pesquisa

46.26%

#Engenharia Mecânica#Controle ativo de ruído#Dutos com modos de alta ordem#Simulação#FxLMS#Algoritmo genético hibridizado#Ruído industrial - Controle#Active noise control#Ducts with higher order modes#Simulation#Hybridized genetic algorithm

O controle ativo de ruído (CAR) aplicado a dutos onde existe a propagação de ondas planas tem sido alvo de vários estudos. Aplica-se, nesses casos, o controle ativo monocanal. Nos dutos com grandes seções transversais, a propagação acústica se dá com a presença dos modos de alta ordem. Nesses dutos é necessário o controle multicanal, o que leva o sistema CAR a utilizar muitos sensores e atuadores, resultando num projeto bastante complexo. Este trabalho procura aplicar uma metodologia de mudança de geometria dos grandes dutos, para assegurar a propagação de ondas planas no interior dos mesmos e assim possibilitar o uso de um sistema CAR monocanal. A estratégia consiste em dividir a grande seção transversal do duto em áreas menores de forma a garantir ondas planas na banda de frequência de interesse. Várias técnicas e ferramentas foram utilizadas, como simulações do sistema acústico, otimização com algoritmo genético hibridizado e o algoritmo FxLMS para o desenvolvimento do projeto do sistema de controle. Um duto de grande porte foi construído e instrumentado. Além disso, uma placa eletrônica de controle com Processador Digital de Sinais (DSP) foi usada para executar os programas do sistema CAR em tempo real. Foram obtidas atenuações significativas dos níveis de ruído...

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## Experimental study of active control of high order acoustic modes in ducts

Fonte: Australian Acoustical Society; C/o Professional Centre, Private Bag 1, Darlinghurst 2010
Publicador: Australian Acoustical Society; C/o Professional Centre, Private Bag 1, Darlinghurst 2010

Tipo: Conference paper

Publicado em //2002
EN

Relevância na Pesquisa

46.26%

Tonal noise radiated from an exhaust stack of a spray dryer system used to make powdered milk has been the source of unwanted community noise.The tone is characterised by a frequency above the first mode cut-on frequency of the exhaust duct and it is not steady in either amplitude or frequency. Passive silencing of the exhaust is a very expensive and inconvenient option and for this reason the feasibility of using active noise control was investigated. Zander and Hansen developed a theoretical model for analysing the effect of active noise control on higher order rectangular duct modes,and used it to evaluate the effects of source size,location and strength. It was shown that the total acoustic power reduction was dependent on the relative locations of the control sources. More recently this work was applied to the practical example of a cylindrical spray dryer exhaust stack to determine the most suitable location and number of control sources and error sensors. Prior to installation in the exhaust stack a half scale model was constructed to test the theory. Here, the effect of the error sensor locations on the active control on higher order acoustic modes propagating in the half scale circular duct is investigated experimentally using real time control with a multi-channel feedforward controller. A tachometer signal at the fan blade pass frequency (BPF) was fed into the controller as the reference signal for the feedforward control. Two configurations of error sensors on the duct wall were tested to evaluate how the error sensor locations affect the control performance...

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## Enhancement of stimulated Brillouin scattering of higher-order acoustic modes in single-mode optical fiber

Fonte: Optical Soc Amer
Publicador: Optical Soc Amer

Tipo: Artigo de Revista Científica

Publicado em //2005
EN

Relevância na Pesquisa

46.31%

Solving the elastic wave equation exactly for a GeO2-doped silica fiber with a steplike distribution of the longitudinal and shear velocities and density, we have obtained the dispersion, attenuation, and fields of the leaky acoustic modes supported by the fiber. We have developed a model for stimulated Brillouin scattering of these modes in a pump-probe configuration and provided their Brillouin gains and frequencies for an extended range of core sizes and GeO2 doping. Parameter ranges close to cutoff of the acoustic modes and pump depletion enhance the ratio of higher-order peaks to the main peak in the Brillouin spectrum and are suitable for simultaneous strain-temperature sensing.; Shahraam Afshar V., V. P. Kalosha, Xiaoyi Bao, Liang Chen; This paper was published in Optics Letters and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/abstract.cfm?URI=ol-30-20-2685. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

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## Acoustic wave parameter extraction with application to delay line modelling using finite element analysis

Fonte: International Frequency Sensor Association
Publicador: International Frequency Sensor Association

Tipo: Artigo de Revista Científica

Publicado em //2008
EN

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#Finite element analysis (FEA)#Surface acoustic wave (SAW) devices#Bulk acoustic wave (BAW)#Leaky surface acoustic wave (LSAW)#Interdigital transducer (IDT)#Coupling of modes analysis (COM)#P-matrix model#Periodic boundary conditions (PBC)

In this paper we propose a practical approach to develop a SAW parameter extraction technique and simulation method, contrary to the frequently used FEM/BEM numerical simulation technique. The new approach allows for accurate SAW device modelling through a versatile finite element method to automatically include the second order effects in the device by considering the complete set of partial differential equations. The eigenmodes and the harmonic admittance of a periodic structure obtained from the FEM simulations are used to extract the COM/P-matrix parameters based on a fitting technique that is already published in the literature. Comparison between the extracted parameters, using this technique, with currently published parameters for the same device specification was carried out and showed good agreement. As an example, a two dimensional delay line with 10 finger pairs per IDT was modelled using this approach, to outline the mechanical and electrical response of the device for variable acoustic modes and substrate thicknesses.; Ajay Tikka, Said Al-Sarawi and Derek Abbott

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## Angular Momentum Transport and Variability in Boundary Layers of Accretion Disks Driven by Global Acoustic Modes

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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Disk accretion onto a weakly magnetized central object, e.g. a star, is
inevitably accompanied by the formation of a boundary layer near the surface,
in which matter slows down from the highly supersonic orbital velocity of the
disk to the rotational velocity of the star. We perform high resolution 2D
hydrodynamical simulations in the equatorial plane of an astrophysical boundary
layer with the goal of exploring the dynamics of non-axisymmetric structures
that form there. We generically find that the supersonic shear in the boundary
layer excites non-axisymmetric quasi-stationary acoustic modes that are trapped
between the surface of the star and a Lindblad resonance in the disk. These
modes rotate in a prograde fashion, are stable for hundreds of orbital periods,
and have a pattern speed that is less than and of order the rotational velocity
at the inner edge of the disk. The origin of these intrinsically global modes
is intimately related to the operation of a corotation amplifier in the system.
Dissipation of acoustic modes in weak shocks provides a universal mechanism for
angular momentum and mass transport even in purely hydrodynamic (i.e.
non-magnetized) boundary layers. We discuss the possible implications of these
trapped modes for explaining the variability seen in accreting compact objects.; Comment: 41 pages...

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## Angular Momentum Transport by Acoustic Modes Generated in the Boundary Layer I: Hydrodynamical Theory and Simulations

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/12/2012

Relevância na Pesquisa

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The nature of angular momentum transport in the boundary layers of accretion
disks has been one of the central and long-standing issues of accretion disk
theory. In this work we demonstrate that acoustic waves excited by supersonic
shear in the boundary layer serve as an efficient mechanism of mass, momentum
and energy transport at the interface between the disk and the accreting
object. We develop the theory of angular momentum transport by acoustic modes
in the boundary layer, and support our findings with 3D hydrodynamical
simulations, using an isothermal equation of state. Our first major result is
the identification of three types of global modes in the boundary layer. We
derive dispersion relations for each of these modes that accurately capture the
pattern speeds observed in simulations to within a few percent. Second, we show
that angular momentum transport in the boundary layer is intrinsically
nonlocal, and is driven by radiation of angular momentum away from the boundary
layer into both the star and the disk. The picture of angular momentum
transport in the boundary layer by waves that can travel large distances before
dissipating and redistributing angular momentum and energy to the disk and star
is incompatible with the conventional notion of local transport by turbulent
stresses. Our results have important implications for semianalytical models
that describe the spectral emission from boundary layers.; Comment: 53 pages...

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## Double adiabatic theory of collisionless geodesic acoustic modes in tokamaks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 31/08/2011

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46.25%

Collisionless geodesic acoustic modes in tokamaks being supersonic for large
"safety factor" q, the CGL (G. Chew, M. Goldberger, F. Low, 1956)1
double-adiabatic fluid closure is applied to formulate a theory for these
modes. The basic linear normal mode is obtained. External means to drive these
modes at resonance, as has been proposed earlier, are explored. The external
drivers considered include external magnetic forces to effect flux surface
displacements, as well as non-axisymmetric ion heating. Finally, the damping of
these modes from collisional magnetic pumping is investigated using a model set
of CGL collision-corrected equations.

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## Asymptotic analysis of high-frequency acoustic modes in rapidly rotating stars

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/03/2009

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#Astrophysics - Solar and Stellar Astrophysics#Astrophysics - Earth and Planetary Astrophysics#Nonlinear Sciences - Chaotic Dynamics

The asteroseismology of rapidly rotating pulsating stars is hindered by our
poor knowledge of the effect of the rotation on the oscillation properties.
Here we present an asymptotic analysis of high-frequency acoustic modes in
rapidly rotating stars. We study the Hamiltonian dynamics of acoustic rays in
uniformly rotating polytropic stars and show that the phase space structure has
a mixed character, regions of chaotic trajectories coexisting with stable
structures like island chains or invariant tori. In order to interpret the ray
dynamics in terms of acoustic mode properties, we then use tools and concepts
developed in the context of quantum physics. Accordingly, the high-frequency
acoustic spectrum is a superposition of frequency subsets associated with
dynamically independent phase space regions. The sub-spectra associated with
stable structures are regular and can be modelled through EBK quantization
methods while those associated with chaotic regions are irregular but with
generic statistical properties. The results of this asymptotic analysis are
successfully confronted with the properties of numerically computed
high-frequency acoustic modes. The implications for the asteroseismology of
rapidly rotating stars are discussed.; Comment: 21 pages...

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## A magnetic model for acoustic modes in roAp stars

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/09/1998

Relevância na Pesquisa

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The mechanism for excitation of p-modes in rapidly oscillating, peculiar A
(roAp, or cool chemically peculiar, CP) stars is unknown. Observations strongly
suggest that acoustic modes in roAp stars are causally linked to the stars'
magnetic field. We propose that small fluctuations in the shape of the mean
magnetic field drive magnetosonic waves, which are observed as p-modes in these
stars.
The dynamic edge region of roAp stars is a force-free spherical shell. When
strongly coupled to the magnetic field, a force-free plasma can oscillate about
a minimum in its mean magnetic energy. We describe the stable eigenmodes for
this energy minimum in a spherical shell with an open boundary. The
wavenumbers, frequencies, and energies of resulting oscillations are consistent
with observations of p-modes in roAp stars. Our magnetic model for p-mode
oscillations in stars does not invoke convection or opacity mechanisms. We also
suggest the possibility of a nonlinear dynamo for such magnetic stars, which
lack the convection needed for the usual (-( dynamo.

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## Electrostatic acoustic modes in a self-gravitating complex plasma with variable charge impurities

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 08/01/2005

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46.24%

A linear theory of dust acoustic (DA) and dust ion-acoustic (DIA) waves in a
self-gravitating collisional dusty plasma contaminated by variable-charge
impurities is presented for a self-consistent closed system. The ion-drag force
arising from the ion orbital motion as well as momentum transfer from all the
ions and self-gravitation are taken into consideration. The physical processes,
viz., dust-charge relaxation, ionization, recombination and collisional
dissipations are also taken into account self-consistently. The generalized
dispersion relation describing the coupling of the acoustic modes with the
dust-charge relaxation mode (CRM) and damping of the waves is derived and
analyzed numerically.; Comment: 13 pages, 5 figures. Physics Letters A (2005,To be published)

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## Acoustic modes in spheroidal cavities

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/10/2001

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46.22%

Oscillation modes of rapidly rotating stars have not yet been calculated with
precision, rotational effects being generally approximated by perturbation
methods. We are developing a numerical method able to account for the
deformation of the star by the centrifugal force and, as a first step, we
determined the acoustic modes of a uniform density spheroid and studied how the
spheroid flatness affects these modes.; Comment: 4 pages, Proceedings of "Semaine de l'Astrophysique Francaise", Edts,
SF2A, EdP-Sciences Conf. Series

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## Optomechanical characterization of acoustic modes in a mirror

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/05/2003

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46.31%

We present an experimental study of the internal mechanical vibration modes
of a mirror. We determine the frequency repartition of acoustic resonances via
a spectral analysis of the Brownian motion of the mirror, and the spatial
profile of the acoustic modes by monitoring their mechanical response to a
resonant radiation pressure force swept across the mirror surface. We have
applied this technique to mirrors with cylindrical and plano-convex geometries,
and compared the experimental results to theoretical predictions. We have in
particular observed the gaussian modes predicted for plano-convex mirrors.; Comment: 8 pages, 8 figures, RevTeX

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## Are Solar Acoustic Modes Correlated ?

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/09/1997

Relevância na Pesquisa

46.25%

We have studied the statistical properties of the energy of individual
acoustic modes, extracted from 310 days of GOLF data near the solar minimum.
The exponential distribution of the energy of each mode is clearly seen. The
modes are found to be uncorrelated with a +-0.6 % accuracy, thus supporting the
hypothesis of stochastic excitation by the solar convection. Nevertheless, the
same analysis performed on the same modes just before the solar maximum, using
IPHIR data, rejects the hypothesis of no correlation at a 99.3 % confidence
level. A simple model suggests that 31.3 +-9.4 % of the energy of each mode is
coherent among the modes studied in IPHIR data, correponding to a mean
correlation of 10.7 +-5.9 %.; Comment: 10 pages A&A Latex, 13 EPSF figures, to appear in A&A

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## Corotational Instability of Inertial-Acoustic Modes in Black Hole Accretion Discs and Quasi-Periodic Oscillations

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

46.25%

We study the global stability of non-axisymmetric p-modes (also called
inertial-acoustic modes) trapped in the inner-most regions of accretion discs
around black holes. We show that the lowest-order (highest-frequency) p-modes,
with frequencies $\omega=(0.5-0.7) m\Omega_{\rm ISCO}$, can be overstable due
to general relativistic effects, according to which the radial epicyclic
frequency is a non-monotonic function of radius near the black hole. The mode
is trapped inside the corotation resonance radius and carries a negative
energy. The mode growth arises primarily from wave absorption at the corotation
resonance, and the sign of the wave absorption depends on the gradient of the
disc vortensity. When the mode frequency is sufficiently high, such that the
slope of the vortensity is positive at corotation positive wave energy is
absorbed at the resonance, leading to the growth of mode amplitude. We also
study how the rapid radial inflow at the inner edge of the disc affects the
mode trapping and growth. Our analysis of the behavior of the fluid
perturbations in the transonic flow near the ISCO indicates that, while the
inflow tends to damp the mode, the damping effect is sufficiently small under
some conditions so that net mode growth can still be achieved. We further
clarify the role of the Rossby wave instability and show that it does not
operate for black hole accretion discs with smooth-varying vortensity profiles.
Overstable non-axisymmetric p-modes driven by the corotational instability
provide a plausible explanation for the high-frequency (> 100 Hz)
quasi-periodic oscillations (HFQPOs) observed from a number of black-hole X-ray
binaries in the very high state. The absence of HFQPOs in the soft (thermal)
state may result from mode damping due to the radial infall at the ISCO.; Comment: 19 pages...

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## Nonlinear interactions among solar acoustic modes

Fonte: American Astronomical Society
Publicador: American Astronomical Society

Tipo: Article; PeerReviewed
Formato: application/pdf

Publicado em 01/07/1989

Relevância na Pesquisa

46.52%

We evaluate the rates at which nonlinear interactions transfer energy among the normal modes of a plane-parallel,
stratified atmosphere. The atmosphere resembles the outer part of the Sun including the convection
zone and the optically thin region above the photosphere up to the temperature minimum. The acoustic
modes are assigned energies such that their photospheric velocities match those of the Sun's p-modes. The
nonlinearity parameter is the acoustic Mach number, M, the ratio of the total acoustic velocity due to all of
the modes to the sound speed. For M^2 ≪ 1 the leading nonlinear interactions are those which couple three-modes.
We show that every p-mode in the 5 minute band is involved in many near-resonant triplets. As a
consequence, the energy transfer rates are independent of the mode line widths. Because M increases with
height, the dominant contributions to the three-mode coupling coefficients occur in the upper part of the convection
zone and in the optically thin isothermal layer. Moreover, the coupling coefficients tend to increase
with ω and k_h.
Nonlinear interactions which couple two trapped modes and one propagating mode drain energy from the
trapped modes. They are far more effective than interactions among three trapped modes which drive the
modes toward equipartition of energy. Thus...

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## On the Existence and Stability of Limit Cycles for Longitudinal Acoustic Modes in a Combustion Chamber

Fonte: Taylor & Francis
Publicador: Taylor & Francis

Tipo: Article; PeerReviewed
Formato: application/pdf

Publicado em //1986

Relevância na Pesquisa

46.43%

Unsteady motions in combustion chambers have previously been treated with an approximate analysis in which an acoustic field is represented as a collection of coupled nonlinear oscillators constructed in one-to-one correspondence to the acoustic modes. Two parameters
characterize the linear behavior of each oscillator; a single parameter arises from the nonlinear acoustics carried out to second order in small fluctuations. The formal results are used here as the basis for studying the existence and stability of limit cycles for longitudinal modes. Owing to the special structure of the equations, explicit and precise conclusions can be reached. Existence
and stability depend only on the parameters defining the linear motions. The nonlinear gasdynamics influence the amplitudes of motion in the limit cycle. At least one of the acoustic modes must be linearly unstable to produce a nontrivial limit cycle. Generally, energy flows both up and down among the modes, but there are exceptional cases when limit cycles exist only if the fundamental mode is unstable. Explicit results are given for the special cases of two and three modes; the analysis is extendible to any number of modes.

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## Nonlinear Energy Transport Between Longitudinal Acoustic Modes in Cylindrical Combustion Chambers

Fonte: American Institute of Aeronautics and Astronautics
Publicador: American Institute of Aeronautics and Astronautics

Tipo: Report or Paper; PeerReviewed
Formato: application/pdf

Publicado em //1994

Relevância na Pesquisa

46.4%

The second order nonlinear longitudinal acoustics
in a cylindrical combustion chamber are studied
for the case of an unstable second mode. A modal
analysis is undertaken and a continuation method
is used to determine the limit cycle behavior of the
time dependent amplitudes of the acoustic modes
as functions of the linear stability of the unstable
acoustic mode. It is shown that if an insufficient
number of modes are included in the truncated system,
bifurcations of the primary limit cycle occur.
The energy in the limit cycles is analyzed and the
bifurcations are shown to occur as a means of increasing
the amount of energy transfer out of the
unstable acoustic mode and into the stable acoustic
modes through the nonlinear terms.

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