NASA Astrophysics Data System (ADS)
Munz, Claus-Dieter; Dumbser, Michael; Roller, Sabine
2007-05-01
When the Mach number tends to zero the compressible Navier-Stokes equations converge to the incompressible Navier-Stokes equations, under the restrictions of constant density, constant temperature and no compression from the boundary. This is a singular limit in which the pressure of the compressible equations converges at leading order to a constant thermodynamic background pressure, while a hydrodynamic pressure term appears in the incompressible equations as a Lagrangian multiplier to establish the divergence-free condition for the velocity. In this paper we consider the more general case in which variable density, variable temperature and heat transfer are present, while the Mach number is small. We discuss first the limit equations for this case, when the Mach number tends to zero. The introduction of a pressure splitting into a thermodynamic and a hydrodynamic part allows the extension of numerical methods to the zero Mach number equations in these non-standard situations. The solution of these equations is then used as the state of expansion extending the expansion about incompressible flow proposed by Hardin and Pope [J.C. Hardin, D.S. Pope, An acoustic/viscous splitting technique for computational aeroacoustics, Theor. Comput. Fluid Dyn. 6 (1995) 323-340]. The resulting linearized equations state a mathematical model for the generation and propagation of acoustic waves in this more general low Mach number regime and may be used within a hybrid aeroacoustic approach.
Perturbed nonlinear differential equations
NASA Technical Reports Server (NTRS)
Proctor, T. G.
1974-01-01
For perturbed nonlinear systems, a norm, other than the supremum norm, is introduced on some spaces of continuous functions. This makes possible the study of new types of behavior. A study is presented on a perturbed nonlinear differential equation defined on a half line, and the existence of a family of solutions with special boundedness properties is established. The ideas developed are applied to the study of integral manifolds, and examples are given.
Perturbed nonlinear differential equations
NASA Technical Reports Server (NTRS)
Proctor, T. G.
1972-01-01
The existence of a solution defined for all t and possessing a type of boundedness property is established for the perturbed nonlinear system y = f(t,y) + F(t,y). The unperturbed system x = f(t,x) has a dichotomy in which some solutions exist and are well behaved as t increases to infinity, and some solution exists and are well behaved as t decreases to minus infinity. A similar study is made for a perturbed nonlinear differential equation defined on a half line, R+, and the existence of a family of solutions with special boundedness properties is established. The ideas are applied to integral manifolds.
Perturbation analysis of electromagnetic geodesic acoustic modes
Ren, Haijun
2014-06-15
Lagrangian displacement and magnetic field perturbation response to the geodesic acoustic mode is analyzed by using the ideal magnetohydrodynamic equations in a large-aspect-ratio tokamak. δB{sub θ}, the poloidal component of magnetic field perturbation, has poloidal wave number m = 2 created by the poloidal displacement ξ{sub θ}. The parallel perturbation of magnetic field, δB{sub ∥}, has a poloidally asymmetric structure with m = 1 and is on the same order of magnitude with δB{sub θ} to the leading order. The radial displacement ξ{sub r} is of order O(βϵξ{sub θ}) but plays a significant role in determining δB{sub ∥}, where β is the plasma/magnetic pressure ratio and ϵ is the inverse aspect ratio.
Separation of acoustic waves in isentropic flow perturbations
Henke, Christian
2015-04-15
The present contribution investigates the mechanisms of sound generation and propagation in the case of highly-unsteady flows. Based on the linearisation of the isentropic Navier–Stokes equation around a new pathline-averaged base flow, it is demonstrated for the first time that flow perturbations of a non-uniform flow can be split into acoustic and vorticity modes, with the acoustic modes being independent of the vorticity modes. Therefore, we can propose this acoustic perturbation as a general definition of sound. As a consequence of the splitting result, we conclude that the present acoustic perturbation is propagated by the convective wave equation and fulfils Lighthill’s acoustic analogy. Moreover, we can define the deviations of the Navier–Stokes equation from the convective wave equation as “true” sound sources. In contrast to other authors, no assumptions on a slowly varying or irrotational flow are necessary. Using a symmetry argument for the conservation laws, an energy conservation result and a generalisation of the sound intensity are provided. - Highlights: • First splitting of non-uniform flows in acoustic and non-acoustic components. • These result leads to a generalisation of sound which is compatible with Lighthill’s acoustic analogy. • A closed equation for the generation and propagation of sound is given.
The room acoustic rendering equation.
Siltanen, Samuel; Lokki, Tapio; Kiminki, Sami; Savioja, Lauri
2007-09-01
An integral equation generalizing a variety of known geometrical room acoustics modeling algorithms is presented. The formulation of the room acoustic rendering equation is adopted from computer graphics. Based on the room acoustic rendering equation, an acoustic radiance transfer method, which can handle both diffuse and nondiffuse reflections, is derived. In a case study, the method is used to predict several acoustic parameters of a room model. The results are compared to measured data of the actual room and to the results given by other acoustics prediction software. It is concluded that the method can predict most acoustic parameters reliably and provides results as accurate as current commercial room acoustic prediction software. Although the presented acoustic radiance transfer method relies on geometrical acoustics, it can be extended to model diffraction and transmission through materials in future.
Accuracy of perturbative master equations.
Fleming, C H; Cummings, N I
2011-03-01
We consider open quantum systems with dynamics described by master equations that have perturbative expansions in the system-environment interaction. We show that, contrary to intuition, full-time solutions of order-2n accuracy require an order-(2n+2) master equation. We give two examples of such inaccuracies in the solutions to an order-2n master equation: order-2n inaccuracies in the steady state of the system and order-2n positivity violations. We show how these arise in a specific example for which exact solutions are available. This result has a wide-ranging impact on the validity of coupling (or friction) sensitive results derived from second-order convolutionless, Nakajima-Zwanzig, Redfield, and Born-Markov master equations.
Superadiabatic evolution of acoustic and vorticity perturbations in Couette flow.
Favraud, Gael; Pagneux, Vincent
2014-03-01
Nonadiabatic transitions between the acoustic and the vorticity modes perturbing a plane Couette flow are examined in the context of higher-order WKB asymptotics. In the case of the Schrödinger equation, it is known that looking at the solution expressed in the superadiabatic base, composed of higher-order asymptotic solutions, smoothes quantum state transitions. Then, increasing the order of the superadiabatic base causes these transitions to tend to the Gauss error function, and, once an optimal order is reached, the asymptotic process starts to diverge. We show that for perturbations in Couette flow, similar results can be applied on the amplitudes of the vorticity and acoustic modes. This allows us to more closely track the emergence of the acoustic modes in the presence of the vorticity mode.
Poynting-Robertson effect. II - Perturbation equations
NASA Astrophysics Data System (ADS)
Klacka, J.
1992-12-01
The paper addresses the problem of the complete set of perturbation equations of celestial mechanics as applied to the Poynting-Robertson effect. Differential equations and initial conditions for them are justified. The sudden beginning of the operation of the Poynting-Robertson effect (e.g., sudden release of dust particles from a comet) is taken into account. Two sets of differential equations and initial conditions for them are obtained. Both of them are completely equivalent to Newton's equation of motion. It is stressed that the transformation mu yields mu(1-beta) must be made in perturbation equations of celestial mechanics.
Asymptotic stability of singularly perturbed differential equations
NASA Astrophysics Data System (ADS)
Artstein, Zvi
2017-02-01
Asymptotic stability is examined for singularly perturbed ordinary differential equations that may not possess a natural split into fast and slow motions. Rather, the right hand side of the equation is comprised of a singularly perturbed component and a regular one. The limit dynamics consists then of Young measures, with values being invariant measures of the fast contribution, drifted by the slow one. Relations between the asymptotic stability of the perturbed system and the limit dynamics are examined, and a Lyapunov functions criterion, based on averaging, is established.
Doubly perturbed neutral stochastic functional equations
NASA Astrophysics Data System (ADS)
Hu, Lanying; Ren, Yong
2009-09-01
In this paper, we prove the existence and uniqueness of the solution to a class of doubly perturbed neutral stochastic functional equations (DPNSFEs in short) under some non-Lipschitz conditions. The solution is constructed by successive approximation. Furthermore, we give the continuous dependence of the solution on the initial value by means of the corollary of Bihari inequality.
Comparison of electroglottographic and acoustic analysis of pitch perturbation.
LaBlance, G R; Maves, M D; Scialfa, T M; Eitnier, C M; Steckol, K F
1992-11-01
Pitch perturbation is a measure of the cycle-to-cycle variation in vocal fold vibration. Perturbation can be assessed by means of electroglottographic or acoustic signals. The purpose of this study was to determine if these two analysis techniques are equivalent measures. The Laryngograph, an electroglottograph, and the Visi-Pitch, an acoustic analyzer, were used to measure pitch perturbation in 80 dysphonic subjects. Both instruments use Koike's formula to calculate relative average perturbation. While intra-subject variability appeared erratic, statistical analysis of intersubject data indicated that the two instruments provided an equivalent measure of pitch perturbation.
An asymptotic model in acoustics: acoustic drift equations.
Vladimirov, Vladimir A; Ilin, Konstantin
2013-11-01
A rigorous asymptotic procedure with the Mach number as a small parameter is used to derive the equations of mean flows which coexist and are affected by the background acoustic waves in the limit of very high Reynolds number.
Speaker compensation for local perturbation of fricative acoustic feedback.
Casserly, Elizabeth D
2011-04-01
Feedback perturbation studies of speech acoustics have revealed a great deal about how speakers monitor and control their productions of segmental (e.g., formant frequencies) and non-segmental (e.g., pitch) linguistic elements. The majority of previous work, however, overlooks the role of acoustic feedback in consonant production and makes use of acoustic manipulations that effect either entire utterances or the entire acoustic signal, rather than more temporally and phonetically restricted alterations. This study, therefore, seeks to expand the feedback perturbation literature by examining perturbation of consonant acoustics that is applied in a time-restricted and phonetically specific manner. The spectral center of the alveopalatal fricative [∫] produced in vowel-fricative-vowel nonwords was incrementally raised until it reached the potential for [s]-like frequencies, but the characteristics of high-frequency energy outside the target fricative remained unaltered. An "offline," more widely accessible signal processing method was developed to perform this manipulation. The local feedback perturbation resulted in changes to speakers' fricative production that were more variable, idiosyncratic, and restricted than the compensation seen in more global acoustic manipulations reported in the literature. Implications and interpretations of the results, as well as future directions for research based on the findings, are discussed.
Perturbations From Ducts on the Modes of Acoustic Thermometers
Gillis, K. A.; Lin, H.; Moldover, M. R.
2009-01-01
We examine the perturbations of the modes of an acoustic thermometer caused by circular ducts used either for gas flow or as acoustic waveguides coupled to remote transducers. We calculate the acoustic admittance of circular ducts using a model based on transmission line theory. The admittance is used to calculate the perturbations to the resonance frequencies and half-widths of the modes of spherical and cylindrical acoustic resonators as functions of the duct’s radius, length, and the locations of the transducers along the duct's length. To verify the model, we measured the complex acoustic admittances of a series of circular tubes as a function of length between 200 Hz and 10 kHz using a three-port acoustic coupler. The absolute magnitude of the specific acoustic admittance is approximately one. For a 1.4 mm inside-diameter, 1.4 m long tube, the root mean square difference between the measured and modeled specific admittances (both real and imaginary parts) over this frequency range was 0.018. We conclude by presenting design considerations for ducts connected to acoustic thermometers. PMID:27504227
On the singular perturbations for fractional differential equation.
Atangana, Abdon
2014-01-01
The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.
Singular Perturbation for Discontinuous Ordinary Differential Equations
NASA Astrophysics Data System (ADS)
Teixeira, M. A.; da Silva, P. R.
In this article some qualitative aspects of non-smooth systems on ℝn are studied through methods of Geometric Singular Perturbation Theory (GSP-Theory). We present some results that generalize some settings in low dimension, that bridge the space between such systems and singularly perturbed smooth systems. We analyze the local behavior around typical singularities and prove that the dynamics of the so called Sliding Vector Field is determined by the reduced problem on the center manifold.
Acoustic Logging Modeling by Refined Biot's Equations
NASA Astrophysics Data System (ADS)
Plyushchenkov, Boris D.; Turchaninov, Victor I.
An explicit uniform completely conservative finite difference scheme for the refined Biot's equations is proposed. This system is modified according to the modern theory of dynamic permeability and tortuosity in a fluid-saturated elastic porous media. The approximate local boundary transparency conditions are constructed. The acoustic logging device is simulated by the choice of appropriate boundary conditions on its external surface. This scheme and these conditions are satisfactory for exploring borehole acoustic problems in permeable formations in a real axial-symmetrical situation. The developed approach can be adapted for a nonsymmetric case also.
Evolution equation for non-linear cosmological perturbations
Brustein, Ram; Riotto, Antonio E-mail: Antonio.Riotto@cern.ch
2011-11-01
We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations. Starting from the perturbed Einstein equations, we integrate out the non-relativistic degrees of freedom of the cosmic fluid and obtain a single closed equation for the gravitational potential. We then verify the validity of the new equation by comparing its approximate solutions to known results in the theory of non-linear cosmological perturbations. First, we show explicitly that the perturbative solution of our equation matches the standard perturbative solutions. Next, using the mean field approximation to the equation, we show that its solution reproduces in a simple way the exponential suppression of the non-linear propagator on small scales due to the velocity dispersion. Our approach can therefore reproduce the main features of the renormalized perturbation theory and (time)-renormalization group approaches to the study of non-linear cosmological perturbations, with some possibly important differences. We conclude by a preliminary discussion of the nature of the full solutions of the equation and their significance.
Quark Matter Equation of State from Perturbative QCD
NASA Astrophysics Data System (ADS)
Vuorinen, Aleksi
2017-03-01
In this proceedings contribution, we discuss recent developments in the perturbative determination of the Equation of State of dense quark matter, relevant for the microscopic description of neutron star cores. First, we introduce the current state of the art in the problem, both at zero and small temperatures, and then present results from two recent perturbative studies that pave the way towards extending the EoS to higher orders in perturbation theory.
Equation-of-motion coupled cluster perturbation theory revisited.
Eriksen, Janus J; Jørgensen, Poul; Olsen, Jeppe; Gauss, Jürgen
2014-05-07
The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally converges towards the full configuration interaction energy limit. The series is based on a Møller-Plesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby remedying the major deficiency inherent to previous perturbation series based on the EOM-CC ansatz.
Singular perturbation equations for flexible satellites
NASA Technical Reports Server (NTRS)
Huang, T. C.; Das, A.
1980-01-01
Force equations of motion of the individual flexible elements of a satellite were obtained in a previous paper. Moment equations of motion of the composite bodies of a flexible satellite are to be developed using two sets of equations which form the basic system for any dynamic model of flexible satellites. This basic system consists of a set of N-coupled, nonlinear, ordinary, or partial differential equations, for a flexible satellite with n generalized, structural position coordinates. For single composite body satellites, N is equal to (n + 3); for dual-spin systems, N is equal to (n + 9). These equations involve time derivatives up to the second order. The study shows a method of avoiding this linearization by reducing the N equations to 3 or 9 nonlinear, coupled, first order, ordinary, differential equations involving only the angular velocities of the composite bodies. The solutions for these angular velocities lead to linear equations in the n generalized structural position coordinates, which can be solved by known methods.
Singular perturbation equations for flexible satellites
NASA Technical Reports Server (NTRS)
Huang, T. C.; Das, A.
1973-01-01
The dynamic model of a flexible satellite with n generalized structural position coordinates requires the solution of a set of N coupled nonlinear ordinary or partial differential equations. For single composite body satellites, N is equal to (n + 3). For dual-spin systems, N is equal to (n + 9). These equations usually involve time derivatives up to the second order. For large values of n, linearization of the system has so far been the only practicable way of solution. The present study shows a method of avoiding this linearization by reducing the N equations to three or nine nonlinear, coupled, first-order ordinary differential equations involving only the angular velocities of the composite bodies. The solutions for these angular velocities lead to linear equations in the n generalized structural position coordinates, which can then be solved by known methods.
Acoustofluidics 13: Analysis of acoustic streaming by perturbation methods.
Sadhal, S S
2012-07-07
In this Part 13 of the tutorial series "Acoustofluidics--exploiting ultrasonic standing waves forces and acoustic streaming in microfluidic systems for cell and particle manipulation," the streaming phenomenon is presented from an analytical standpoint, and perturbation methods are developed for analyzing such flows. Acoustic streaming is the phenomenon that takes place when a steady flow field is generated by the absorption of an oscillatory field. This can happen either by attenuation (quartz wind) or by interaction with a boundary. The latter type of streaming can also be generated by an oscillating solid in an otherwise still fluid medium or vibrating enclosure of a fluid body. While we address the first kind of streaming, our focus is largely on the second kind from a practical standpoint for application to microfluidic systems. In this Focus article, we limit the analysis to one- and two-dimensional problems in order to understand the analytical techniques with examples that most-easily illustrate the streaming phenomenon.
An algorithm for solving the perturbed gas dynamic equations
NASA Technical Reports Server (NTRS)
Davis, Sanford
1993-01-01
The present application of a compact, higher-order central-difference approximation to the linearized Euler equations illustrates the multimodal character of these equations by means of computations for acoustic, vortical, and entropy waves. Such dissipationless central-difference methods are shown to propagate waves exhibiting excellent phase and amplitude resolution on the basis of relatively large time-steps; they can be applied to wave problems governed by systems of first-order partial differential equations.
Non-premixed acoustically perturbed swirling flame dynamics
Idahosa, Uyi; Saha, Abhishek; Xu, Chengying; Basu, Saptarshi
2010-09-15
An investigation into the response of non-premixed swirling flames to acoustic perturbations at various frequencies (f{sub p}=0-315 Hz) and swirl intensities (S=0.09 and 0.34) is carried out. Perturbations are generated using a loudspeaker at the base of an atmospheric co-flow burner with resulting velocity oscillation amplitudes vertical stroke u'/U{sub avg} vertical stroke in the 0.03-0.30 range. The dependence of flame dynamics on the relative richness of the flame is investigated by studying various constant fuel flow rate flame configurations. Flame heat release rate is quantitatively measured using a photomultiplier with a 430 nm bandpass filter for observing CH* chemiluminescence which is simultaneously imaged with a phase-locked CCD camera. The flame response is observed to exhibit a low-pass filter characteristic with minimal flame response beyond pulsing frequencies of 200 Hz. Flames at lower fuel flow rates are observed to remain attached to the central fuel pipe at all acoustic pulsing frequencies. PIV imaging of the associated isothermal fields show the amplification in flame aspect ratio is caused by the narrowing of the inner recirculation zone (IRZ). Good correlation is observed between the estimated flame surface area and the heat release rate signature at higher swirl intensity flame configurations. A flame response index analogous to the Rayleigh criterion in non-forced flames is used to assess the potential for a strong flame response at specific perturbation configurations and is found to be a good predictor of highly responsive modes. Phase conditioned analysis of the flame dynamics yield additional criteria in highly responsive modes to include the effective amplitude of velocity oscillations induced by the acoustic pulsing. In addition, highly responsive modes were characterized by velocity to heat release rate phase differences in the {+-}{pi}/2 range. A final observed characteristic in highly responsive flames is a Strouhal number between
Analytical study of acoustically perturbed Brillouin active magnetized semiconductor plasma
Shukla, Arun; Jat, K. L.
2015-07-31
An analytical study of acoustically perturbed Brillouin active magnetized semiconductor plasma has been reported. In the present analytical investigation, the lattice displacement, acousto-optical polarization, susceptibility, acousto-optical gain constant arising due to the induced nonlinear current density and acousto-optical process are deduced in an acoustically perturbed Brillouin active magnetized semiconductor plasma using the hydrodynamical model of plasma and coupled mode scheme. The influence of wave number and magnetic field has been explored. The analysis has been applied to centrosymmetric crystal. Numerical estimates are made for n-type InSb crystal duly irradiated by a frequency doubled 10.6 µm CO{sub 2} laser. It is found that lattice displacement, susceptibility and acousto-optical gain increase linearly with incident wave number and applied dc magnetic field, while decrease with scattering angle. The gain also increases with electric amplitude of incident laser beam. Results are found to be well in agreement with available literature.
Elementary derivation of the perturbation equations of celestial mechanics
NASA Technical Reports Server (NTRS)
Burns, J. A.
1976-01-01
The equations of celestial mechanics that govern the temporal rates of change of orbital elements are completely derived using elementary dynamics and proceeding only from Newton's equation and its solution. Two orbital equations and the four most meaningful orbital elements - semimajor axis, eccentricity, inclination, and longitude of pericenter - are written in terms of the orbital energy (E) and angular momentum (H) per unit mass. The six resulting equations are differentiated with respect to time to see the effect on the orbital elements of small changes in E and H. The usual perturbation equations in terms of disturbing-force components are then derived by computing the manner in which perturbing forces change E and H. The results are applied in a qualitative discussion of the orbital evolution of particles in nonspherical gravitational fields, through atmospheres, and under the action of tides.
Thermodynamical analysis of acoustical perturbations in the bronchial tree
NASA Astrophysics Data System (ADS)
Puente, Margarita; Perez-Guerrero, Armando; Alvarado, Manuel
2002-11-01
In the airways, very complex flows occur because of different conditions and the existence of a lot of complications: constantly changing temperature and pressure during the respiration process, a normally turbulent flow in the trachea which, in heavy breathing, remains so in the first three or four generations of airways, changes of the direction of the flow over the breathing cycle, from inspiration to expiration, etc. We also know the air that flows in the bronchial tree is perturbed by several sources such as the heart and the circulatory system, the diaphragm and stomach movements, etc., which produce sound waves. Thus an acoustical analysis of the phenomenon can lead us to a physical model which could help us to better understand the phenomena and to demonstrate the importance to clinical applications such as the pneumocardiograms. To this purpose we use a thermodynamical model that originally was developed to analyze supersonic air jets to explain the production of shock waves in the bronchial tree.
Newtonian perturbations and the Einstein Yang Mills-dilaton equations
NASA Astrophysics Data System (ADS)
Oliynyk, Todd A.
2005-06-01
In this paper, we show that the problem of proving the existence of a countable number of solutions to the static spherically symmetric SU(2) Einstein Yang Mills-dilaton (EYMd) equations can be reduced to proving the non-existence of solutions to the linearized Yang Mills-dilaton equations (lYMd) satisfying certain asymptotic conditions. The reduction from a nonlinear to a linear problem is achieved using a Newtonian perturbation-type argument.
Integral equation for small perturbations of irrotational flows
NASA Technical Reports Server (NTRS)
Haviland, J. K.
1973-01-01
An investigation is conducted concerning the validity of analytical methods which are based on deriving an integral equation, taking into account small perturbations in the case of a nonuniform but irrotational flow. The results obtained apply to a wide Mach number range, but are restricted to small amplitude motions and to nonviscous flows. It is shown that the integral equation relating the unknown velocity potential to the known normal flow velocity can be derived from the appropriate Green's identity.
Maximal regularity for perturbed integral equations on periodic Lebesgue spaces
NASA Astrophysics Data System (ADS)
Lizama, Carlos; Poblete, Verónica
2008-12-01
We characterize the maximal regularity of periodic solutions for an additive perturbed integral equation with infinite delay in the vector-valued Lebesgue spaces. Our method is based on operator-valued Fourier multipliers. We also study resonances, characterizing the existence of solutions in terms of a compatibility condition on the forcing term.
NASA Technical Reports Server (NTRS)
Bogdan, V. M.; Bond, V. B.
1980-01-01
The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.
Moment transport equations for the primordial curvature perturbation
Mulryne, David J.; Seery, David; Wesley, Daniel E-mail: d.seery@sussex.ac.uk
2011-04-01
In a recent publication, we proposed that inflationary perturbation theory can be reformulated in terms of a probability transport equation, whose moments determine the correlation properties of the primordial curvature perturbation. In this paper we generalize this formulation to an arbitrary number of fields. We deduce ordinary differential equations for the evolution of the moments of ζ on superhorizon scales, which can be used to obtain an evolution equation for the dimensionless bispectrum, f{sub NL}. Our equations are covariant in field space and allow identification of the source terms responsible for evolution of f{sub NL}. In a model with M scalar fields, the number of numerical integrations required to obtain solutions of these equations scales like O(M{sup 3}). The performance of the moment transport algorithm means that numerical calculations with M >> 1 fields are straightforward. We illustrate this performance with a numerical calculation of f{sub NL} in Nflation models containing M ∼ 10{sup 2} fields, finding agreement with existing analytic calculations. We comment briefly on extensions of the method beyond the slow-roll approximation, or to calculate higher order parameters such as g{sub NL}.
A new method to determine the asymptotic eigenfrequency equation of low-degree acoustic modes
NASA Astrophysics Data System (ADS)
Lopes, Ilídio P.
2001-03-01
The high accuracy of the observed solar spectra obtained from the space experiments GOLF and VIRGO has motivated us to develop a more precise asymptotic analysis of low-degree acoustic modes. Therefore we present a phase method to build an asymptotic solution to the equation of motion of acoustic oscillations. The principle consists of describing the oscillatory motion by a system of two first-order non-linear differential equations for the phase and amplitude. The equations are coupled only in the amplitude equation, leaving a single phase equation to determine the eigenfrequencies. We illustrate also the deficiency in the accuracy of standard asymptotic methods to determine the eigenfrequency, and highlight the advantages of this new method. The strength of this new technique is based on an accurate description of the phase dependence on the background state rather than on the wavefunction, as is done in standard asymptotic methods. This allows us to obtain a new asymptotic eigenvalue equation for low-degree acoustic modes, which is more accurate than the usual ones. In this case, the eigenfrequency equation is obtained without making the so-called Cowling approximation, i.e., by neglecting the Eulerian perturbation of the gravitational field. This allows us to obtain a new expression for the small separation, valid for the global acoustic modes of high and low radial orders.
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.
A perturbative solution to metadynamics ordinary differential equation.
Tiwary, Pratyush; Dama, James F; Parrinello, Michele
2015-12-21
Metadynamics is a popular enhanced sampling scheme wherein by periodic application of a repulsive bias, one can surmount high free energy barriers and explore complex landscapes. Recently, metadynamics was shown to be mathematically well founded, in the sense that the biasing procedure is guaranteed to converge to the true free energy surface in the long time limit irrespective of the precise choice of biasing parameters. A differential equation governing the post-transient convergence behavior of metadynamics was also derived. In this short communication, we revisit this differential equation, expressing it in a convenient and elegant Riccati-like form. A perturbative solution scheme is then developed for solving this differential equation, which is valid for any generic biasing kernel. The solution clearly demonstrates the robustness of metadynamics to choice of biasing parameters and gives further confidence in the widely used method.
Local density approximation for a perturbative equation of state
Astrakharchik, G. E.
2005-12-15
Knowledge of a series expansion of the equation of state provides a deep insight into the physical nature of a quantum system. Starting from a generic 'perturbative' equation of state of a homogeneous ultracold gas we make predictions for the properties of the gas in the presence of harmonic confinement. The local density approximation is used to obtain the chemical potential, total and release energies, Thomas-Fermi size, and density profile of a trapped system in three-, two-, and one-dimensional geometries. The frequencies of the lowest breathing modes are calculated using scaling and sum-rule approaches and could be used in an experiment as a high-precision tool for obtaining the expansion terms of the equation of state. The derived formalism is applied to dilute Bose and Fermi gases in different dimensions and to integrable one-dimensional models. The physical meaning of the expansion terms in a number of systems is discussed.
NASA Astrophysics Data System (ADS)
Hafez, M. G.; Talukder, M. R.; Ali, M. Hossain
2017-03-01
The Burgers equation is obtained to study the characteristics of nonlinear propagation of ion-acoustic shock, singular kink, and periodic waves in weakly relativistic plasmas containing relativistic thermal ions, nonextensive distributed electrons, Boltzmann distributed positrons, and kinematic viscosity of ions using the well-known reductive perturbation technique. This equation is solved by employing the (G'/G)-expansion method taking unperturbed positron-to-electron concentration ratio, electron-to-positron temperature ratio, strength of electrons nonextensivity, ion kinematic viscosity, and weakly relativistic streaming factor. The influences of plasma parameters on nonlinear propagation of ion-acoustic shock, periodic, and singular kink waves are displayed graphically and the relevant physical explanations are described. It is found that these parameters extensively modify the shock structures excitation. The obtained results may be useful in understanding the features of small but finite amplitude localized relativistic ion-acoustic shock waves in an unmagnetized plasma system for some astrophysical compact objects and space plasmas.
A Schamel equation for ion acoustic waves in superthermal plasmas
Williams, G. Kourakis, I.; Verheest, F.; Hellberg, M. A.; Anowar, M. G. M.
2014-09-15
An investigation of the propagation of ion acoustic waves in nonthermal plasmas in the presence of trapped electrons has been undertaken. This has been motivated by space and laboratory plasma observations of plasmas containing energetic particles, resulting in long-tailed distributions, in combination with trapped particles, whereby some of the plasma particles are confined to a finite region of phase space. An unmagnetized collisionless electron-ion plasma is considered, featuring a non-Maxwellian-trapped electron distribution, which is modelled by a kappa distribution function combined with a Schamel distribution. The effect of particle trapping has been considered, resulting in an expression for the electron density. Reductive perturbation theory has been used to construct a KdV-like Schamel equation, and examine its behaviour. The relevant configurational parameters in our study include the superthermality index κ and the characteristic trapping parameter β. A pulse-shaped family of solutions is proposed, also depending on the weak soliton speed increment u{sub 0}. The main modification due to an increase in particle trapping is an increase in the amplitude of solitary waves, yet leaving their spatial width practically unaffected. With enhanced superthermality, there is a decrease in both amplitude and width of solitary waves, for any given values of the trapping parameter and of the incremental soliton speed. Only positive polarity excitations were observed in our parametric investigation.
Nonlinear Schrödinger equation with spatiotemporal perturbations.
Mertens, Franz G; Quintero, Niurka R; Bishop, A R
2010-01-01
We investigate the dynamics of solitons of the cubic nonlinear Schrödinger equation (NLSE) with the following perturbations: nonparametric spatiotemporal driving of the form f(x,t)=a exp[iK(t)x], damping, and a linear term which serves to stabilize the driven soliton. Using the time evolution of norm, momentum and energy, or, alternatively, a Lagrangian approach, we develop a collective-coordinate-theory which yields a set of ordinary differential equations (ODEs) for our four collective coordinates. These ODEs are solved analytically and numerically for the case of a constant, spatially periodic force f(x). The soliton position exhibits oscillations around a mean trajectory with constant velocity. This means that the soliton performs, on the average, a unidirectional motion although the spatial average of the force vanishes. The amplitude of the oscillations is much smaller than the period of f(x). In order to find out for which regions the above solutions are stable, we calculate the time evolution of the soliton momentum P(t) and the soliton velocity V(t): This is a parameter representation of a curve P(V) which is visited by the soliton while time evolves. Our conjecture is that the soliton becomes unstable, if this curve has a branch with negative slope. This conjecture is fully confirmed by our simulations for the perturbed NLSE. Moreover, this curve also yields a good estimate for the soliton lifetime: the soliton lives longer, the shorter the branch with negative slope is.
3-D Acoustic Scattering from 2-D Rough Surfaces Using A Parabolic Equation Model
2013-12-01
acoustic propagation signals, especially at mid- frequencies and higher (e.g., acoustic communications systems). For many years, the effects of rough...of the effect of surface scattering on 3-D propagation , which is critical in evaluating the variability in underwater acoustic propagation . Results...14. SUBJECT TERMS Acoustic Propagation , Acoustic Scattering, Sea Surface Perturbations, Split- Step Fourier Algorithm, Finite Difference Algorithm
Stringent limitations on reductive perturbation studies of nonplanar acoustic solitons in plasmas
NASA Astrophysics Data System (ADS)
Verheest, Frank; Hellberg, Manfred A.
2016-06-01
More than fifty years ago, the Korteweg-de Vries equation was shown to describe not only solitary surface waves on shallow water, but also nonlinear ion-acoustic waves. Because of the algorithmic ease of using reductive perturbation theory, intensive research followed on a wide range of wave types. Soon, the formalism was extended to nonplanar modes by introducing a stretching designed to accommodate spherically and cylindrically symmetric ion-acoustic waves. Over the last two decades many authors followed this approach, but almost all have ignored the severe restrictions in parameter space imposed by the Ansatz. In addition, for other steps in the formalism, the justification is often not spelled out, leading to effects that are physically undesirable or ambiguous. Hence, there is a need to critically assess this approach to nonplanar modes and to use it with the utmost care, respecting the restrictions on its validity. Only inward propagation may be meaningfully studied and respect for weak nonlinearities of at most 1/10 implies that one cannot get closer to the axis or centre of symmetry than about 30 Debye lengths. Thus, one is in a regime where the modes are quasi-planar and not particularly interesting. Most papers disregard these constraints and hence reach questionable conclusions.
On the number of limit cycles for perturbed pendulum equations
NASA Astrophysics Data System (ADS)
Gasull, A.; Geyer, A.; Mañosas, F.
2016-08-01
We consider perturbed pendulum-like equations on the cylinder of the form x ¨ + sin (x) = ε∑s=0mQn,s (x)x˙s where Qn,s are trigonometric polynomials of degree n, and study the number of limit cycles that bifurcate from the periodic orbits of the unperturbed case ε = 0 in terms of m and n. Our first result gives upper bounds on the number of zeros of its associated first order Melnikov function, in both the oscillatory and the rotary regions. These upper bounds are obtained expressing the corresponding Abelian integrals in terms of polynomials and the complete elliptic functions of first and second kind. Some further results give sharp bounds on the number of zeros of these integrals by identifying subfamilies which are shown to be Chebyshev systems.
Multivalued perturbations of subdifferential type evolution equations in Hilbert spaces
NASA Astrophysics Data System (ADS)
Kravvaritis, Dimitrios; Papageorgiou, Nikolaos S.
In this paper we study the multivalued evolution equation - ẋ(t) ɛ∂ϑ(x(t)) + F(t, x(t)), x(0) = x 0, where ϑ: X → R¯ is a proper, convex, lower semicontinuous (l.s.c.) function, F(·, ·) is a multivalued perturbation, and X is an infinite dimensional, separable Hilbert space. We have an existence result for F(·, ·) being nonconvex valued, and another for F(·, ·) being convex valued but not closed valued. When ϑ = δK = indicator function of a compact, convex set K, we obtain some extensions of earlier results by Moreau and Henry. Then using the Kuratowski-Mosco convergence of sets and the τ-convergence of functions, we prove a well posedness result for the evolution inclusion we are studying. Also we consider a random version of it and prove the existence of a random solution. Finally we present applications to problems in partial differential equations.
Mehl, James B.
2007-01-01
The boundary-shape formalism of Morse and Ingard is applied to the acoustic modes of a deformed spherical resonator (quasisphere) with rigid boundaries. For boundary shapes described by r = a [1 − ε ℱ(θ, ϕ)], where ε is a small scale parameter and ℱ is a function of order unity, the frequency perturbation is calculated to order ε2. The formal results apply to acoustic modes whose angular dependence is designated by the indices ℓ and m. Specific examples are worked out for the radial (ℓ = 0) and triplet (ℓ = 1) modes, for prolate and oblate spheroids, and for triaxial ellipsoids. The exact eigenvalues for the spheroids, and eigenvalue determined with finite-element calculations, are shown to agree with perturbation theory through terms of order ε2. This work is an extension of the author’s previous papers on the acoustic eigenfrequencies of deformed spherical resonators, which were limited to the second-order perturbation for radial modes [J. Acoust. Soc. Am. 71, 1109-1113 (1982)] and the first order-perturbation for arbitrary modes [J. Acoust. Soc. Am. 79, 278–285 (1986)]. PMID:27110463
Mehl, James B
2007-01-01
The boundary-shape formalism of Morse and Ingard is applied to the acoustic modes of a deformed spherical resonator (quasisphere) with rigid boundaries. For boundary shapes described by r = a [1 - ε ℱ(θ, ϕ)], where ε is a small scale parameter and ℱ is a function of order unity, the frequency perturbation is calculated to order ε (2). The formal results apply to acoustic modes whose angular dependence is designated by the indices ℓ and m. Specific examples are worked out for the radial (ℓ = 0) and triplet (ℓ = 1) modes, for prolate and oblate spheroids, and for triaxial ellipsoids. The exact eigenvalues for the spheroids, and eigenvalue determined with finite-element calculations, are shown to agree with perturbation theory through terms of order ε (2). This work is an extension of the author's previous papers on the acoustic eigenfrequencies of deformed spherical resonators, which were limited to the second-order perturbation for radial modes [J. Acoust. Soc. Am. 71, 1109-1113 (1982)] and the first order-perturbation for arbitrary modes [J. Acoust. Soc. Am. 79, 278-285 (1986)].
Perturbation of mass accretion rate, associated acoustic geometry and stability analysis
NASA Astrophysics Data System (ADS)
Bollimpalli, Deepika A.; Bhattacharya, Sourav; Das, Tapas K.
2017-02-01
We investigate the stability of stationary integral solutions of an ideal irrotational fluid in a general static and spherically symmetric background, by studying the profile of the perturbation of the mass accretion rate. We consider low angular momentum axisymmetric accretion flows for three different accretion disk models and consider time dependent and radial linear perturbation of the mass accretion rate. First we show that the propagation of such perturbation can be determined by an effective 2 × 2 matrix, which has qualitatively similar acoustic causal properties as one obtains via the perturbation of the velocity potential. Next, using this matrix we analytically address the stability issues, for both standing and travelling wave configurations generated by the perturbation. Finally, based on this general formalism we briefly discuss the explicit example of the Schwarzschild spacetime and compare our results of stability with the existing literature, which instead address this problem via the perturbation of the velocity potential.
Propagation of acoustic perturbations in a gas flow with dissipation
NASA Astrophysics Data System (ADS)
Zavershinskii, I. P.; Molevich, N. E.
1992-10-01
In an earlier study (Ingard and Singhal, 1973), it has been found that, in a nondissipating moving medium, an acoustic wave propagating from a source in the flow direction has a smaller amplitude than a wave moving against the flow. Here, it is demonstrated that consideration of dissipation phenomena, which are related to the shear and bulk viscosities and heat conductivity of a medium, leads to an additional anisotropy of the sound amplitude, whose sign is opposite to that obtained in the above mentioned study.
Kopnin, S. I.; Popel, S. I.
2008-06-15
It is shown that, during Perseid, Geminid, Orionid, and Leonid meteor showers, the excitation of low-frequency dust acoustic perturbations by modulational instability in the Earth's ionosphere can lead to the generation of infrasonic waves. The processes accompanying the propagation of these waves are considered, and the possibility of observing the waves from the Earth's surface is discussed, as well as the possible onset of acoustic gravitational vortex structures in the region of dust acoustic perturbations. The generation of such structures during Perseid, Geminid, Orionid, and Leonid meteor showers can show up as an increase in the intensity of green nightglow by an amount on the order of 10% and can be attributed to the formation of nonlinear (vortex) structures at altitudes of 110-120 km.
Acoustic equations of state for simple lattice Boltzmann velocity sets.
Viggen, Erlend Magnus
2014-07-01
The lattice Boltzmann (LB) method typically uses an isothermal equation of state. This is not sufficient to simulate a number of acoustic phenomena where the equation of state cannot be approximated as linear and constant. However, it is possible to implement variable equations of state by altering the LB equilibrium distribution. For simple velocity sets with velocity components ξ(iα)∈(-1,0,1) for all i, these equilibria necessarily cause error terms in the momentum equation. These error terms are shown to be either correctable or negligible at the cost of further weakening the compressibility. For the D1Q3 velocity set, such an equilibrium distribution is found and shown to be unique. Its sound propagation properties are found for both forced and free waves, with some generality beyond D1Q3. Finally, this equilibrium distribution is applied to a nonlinear acoustics simulation where both mechanisms of nonlinearity are simulated with good results. This represents an improvement on previous such simulations and proves that the compressibility of the method is still sufficiently strong even for nonlinear acoustics.
Efficient traveltime solutions of the acoustic TI eikonal equation
NASA Astrophysics Data System (ADS)
Waheed, Umair bin; Alkhalifah, Tariq; Wang, Hui
2015-02-01
Numerical solutions of the eikonal (Hamilton-Jacobi) equation for transversely isotropic (TI) media are essential for imaging and traveltime tomography applications. Such solutions, however, suffer from the inherent higher-order nonlinearity of the TI eikonal equation, which requires solving a quartic polynomial for every grid point. Analytical solutions of the quartic polynomial yield numerically unstable formulations. Thus, it requires a numerical root finding algorithm, adding significantly to the computational load. Using perturbation theory we approximate, in a first order discretized form, the TI eikonal equation with a series of simpler equations for the coefficients of a polynomial expansion of the eikonal solution, in terms of the anellipticity anisotropy parameter. Such perturbation, applied to the discretized form of the eikonal equation, does not impose any restrictions on the complexity of the perturbed parameter field. Therefore, it provides accurate traveltime solutions even for models with complex distribution of velocity and anisotropic anellipticity parameter, such as that for the complicated Marmousi model. The formulation allows for large cost reduction compared to using the direct TI eikonal solver. Furthermore, comparative tests with previously developed approximations illustrate remarkable gain in accuracy in the proposed algorithm, without any addition to the computational cost.
Efficient traveltime solutions of the acoustic TI eikonal equation
Waheed, Umair bin Alkhalifah, Tariq Wang, Hui
2015-02-01
Numerical solutions of the eikonal (Hamilton–Jacobi) equation for transversely isotropic (TI) media are essential for imaging and traveltime tomography applications. Such solutions, however, suffer from the inherent higher-order nonlinearity of the TI eikonal equation, which requires solving a quartic polynomial for every grid point. Analytical solutions of the quartic polynomial yield numerically unstable formulations. Thus, it requires a numerical root finding algorithm, adding significantly to the computational load. Using perturbation theory we approximate, in a first order discretized form, the TI eikonal equation with a series of simpler equations for the coefficients of a polynomial expansion of the eikonal solution, in terms of the anellipticity anisotropy parameter. Such perturbation, applied to the discretized form of the eikonal equation, does not impose any restrictions on the complexity of the perturbed parameter field. Therefore, it provides accurate traveltime solutions even for models with complex distribution of velocity and anisotropic anellipticity parameter, such as that for the complicated Marmousi model. The formulation allows for large cost reduction compared to using the direct TI eikonal solver. Furthermore, comparative tests with previously developed approximations illustrate remarkable gain in accuracy in the proposed algorithm, without any addition to the computational cost.
Consistency of Equations in the Second-Order Gauge-Invariant Cosmological Perturbation Theory
NASA Astrophysics Data System (ADS)
Nakamura, K.
2009-06-01
Along the general framework of the gauge-invariant perturbation theory developed in the papers [K.~Nakamura, Prog.~Theor.~Phys. 110 (2003), 723; Prog.~Theor.~Phys. 113 (2005), 481], we rederive the second-order Einstein equation on four-dimensional homogeneous isotropic background universe in a gauge-invariant manner without ignoring any mode of perturbations. We consider the perturbations both in the universe dominated by the single perfect fluid and in that dominated by the single scalar field. We also confirmed the consistency of all the equations of the second-order Einstein equation and the equations of motion for matter fields, which are derived in the paper [K.~Nakamura, arXiv:0804.3840]. This confirmation implies that all the derived equations of the second order are self-consistent and these equations are correct in this sense.
Amiraliyev, Gabil M; Ucar, Aysenur
2013-01-01
The periodical in time problem for singularly perturbed second order linear ordinary differential equation is considered. The boundary layer behavior of the solution and its first and second derivatives have been established. An example supporting the theoretical analysis is presented.
Perturbation theory for Maxwell's equations with a time-dependent current source
NASA Astrophysics Data System (ADS)
Roy, T.; Ghosh, S.; Bhattacharjee, J. K.
2011-12-01
Using a set of ideas discussed in the second volume of Feynman Lectures, we develop a perturbation-theoretic scheme for solving Maxwell's equations for time-dependent currents which are switched on at t = 0.
Reducibility of 1-d Schrödinger Equation with Time Quasiperiodic Unbounded Perturbations, II
NASA Astrophysics Data System (ADS)
Bambusi, D.
2017-01-01
We study the Schrödinger equation on R with a potential behaving as {x^{2l}} at infinity, {l in [1, + ∞)} and with a small time quasiperiodic perturbation. We prove that if the perturbation belongs to a class of unbounded symbols including smooth potentials and magnetic type terms with controlled growth at infinity, then the system is reducible.
Boundary regularized integral equation formulation of the Helmholtz equation in acoustics.
Sun, Qiang; Klaseboer, Evert; Khoo, Boo-Cheong; Chan, Derek Y C
2015-01-01
A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals.
Approximate direct reduction method: infinite series reductions to the perturbed mKdV equation
NASA Astrophysics Data System (ADS)
Jiao, Xiao-Yu; Lou, Sen-Yue
2009-09-01
The approximate direct reduction method is applied to the perturbed mKdV equation with weak fourth order dispersion and weak dissipation. The similarity reduction solutions of different orders conform to formal coherence, accounting for infinite series reduction solutions to the original equation and general formulas of similarity reduction equations. Painlevé II type equations, hyperbolic secant and Jacobi elliptic function solutions are obtained for zero-order similarity reduction equations. Higher order similarity reduction equations are linear variable coefficient ordinary differential equations.
NASA Technical Reports Server (NTRS)
Fenwick, J.; Dijulio, R.; Ek, M. C.; Ehrgott, R.
1982-01-01
Coefficients are derived for equations expressing the lateral force and pitching moments associated with both planar translation and angular perturbations from a nominally centered rotating shaft with respect to a stationary seal. The coefficients for the lowest order and first derivative terms emerge as being significant and are of approximately the same order of magnitude as the fundamental coefficients derived by means of Black's equations. Second derivative, shear perturbation, and entrance coefficient variation effects are adjudged to be small.
Vorticity Preserving Flux Corrected Transport Scheme for the Acoustic Equations
Lung, Tyler B.; Roe, Phil; Morgan, Nathaniel R.
2012-08-15
Long term research goals are to develop an improved cell-centered Lagrangian Hydro algorithm with the following qualities: 1. Utilizes Flux Corrected Transport (FCT) to achieve second order accuracy with multidimensional physics; 2. Does not rely on the one-dimensional Riemann problem; and 3. Implements a form of vorticity control. Short term research goals are to devise and implement a 2D vorticity preserving FCT solver for the acoustic equations on an Eulerian mesh: 1. Develop a flux limiting mechanism for systems of governing equations with symmetric wave speeds; 2. Verify the vorticity preserving properties of the scheme; and 3. Compare the performance of the scheme to traditional MUSCL-Hancock and other algorithms.
NASA Astrophysics Data System (ADS)
Martínez-Morales, José L.
The master equations in the Euclidean Schwarzschild-Tangherlini space-time of a small static perturbation are studied. For each harmonic mode on the sphere there are two solutions that behave differently at infinity. One solution goes like the power 2-l-n of the radial variable, the other solution goes like the power l. These solutions occur in power series. The second main statement of the paper is that any eigentensor of the Lichnerowicz operator in a Euclidean Schwarzschild space-time with an eigenvalue different from zero is essentially singular at infinity. Possible applications of the stability of instantons are discussed. We present the analysis of a small static perturbation of the Euclidean Schwarzschild-Tangherlini metric tensor. The higher order perturbations will appear later. We determine independently the static perturbations of the Schwarzschild quantum black hole in dimension 1+n≥4, where the system of equations is reduced to master equations — ordinary differential equations. The solutions are hypergeometric functions which in some cases can be reduced to polynomials. In the same Schwarzschild background, we analyze static perturbations of the scalar mode and show that there does not exist any static perturbation that is regular everywhere outside the event horizon and is well-behaved at the spatial infinity. This confirms the uniqueness of the spherically symmetric static empty quantum black hole, within the perturbation framework. Our strategy for treating the stability problem is also applicable to other symmetric quantum black holes with a nonzero cosmological constant.
Non-perturbative QED Analysis with Schwinger-Dyson Equations
Kizilersue, Ayse; Sizer, Tom; Williams, Anthony G.
2011-05-24
We give a brief account of unquenched QED studies in four dimensions using Schwinger-Dyson Equations. In these numerical studies of fermion and boson propagators, we employ a recent realistic unquenched fermion-boson vertex, comparing it against commonly used vertices in previous quenched studies.
Perturbation Theory For The Landau-Lifshits-Gilbert Equation
2012-09-01
presented in the IEEE Transactions in Magnetics publication entitled “Two-Frequency Excitation of a Magnetic Microwire ” and contains ancillary...expansion in powers of the external field. 15. SUBJECT TERMS Ferromagnetic resonance, nonlinear response, magnetic microwires 16. SECURITY...sort used in laboratories or medical equipment are unavailable. 2. The Landau-Lifshits and Landau-Lifshits-Gilbert Equations In order to estimate
Detection of explosive events by monitoring acoustically-induced geomagnetic perturbations
Lewis, J P; Rock, D R; Shaeffer, D L; Warshaw, S I
1999-10-07
The Black Thunder Coal Mine (BTCM) near Gillette, Wyoming was used as a test bed to determine the feasibility of detecting explosion-induced geomagnetic disturbances with ground-based induction magnetometers. Two magnetic observatories were fielded at distances of 50 km and 64 km geomagnetically north from the northernmost edge of BTCM. Each observatory consisted of three separate but mutually orthogonal magnetometers, Global Positioning System (GPS) timing, battery and solar power, a data acquisition and storage system, and a three-axis seismometer. Explosions with yields of 1 to 3 kT of TNT equivalent occur approximately every three weeks at BTCM. We hypothesize that explosion-induced acoustic waves propagate upward and interact collisionally with the ionosphere to produce ionospheric electron density (and concomitant current density) perturbations which act as sources for geomagnetic disturbances. These disturbances propagate through an ionospheric Alfven waveguide that we postulate to be leaky (due to the imperfectly conducting lower ionospheric boundary). Consequently, wave energy may be observed on the ground. We observed transient pulses, known as Q-bursts, with pulse widths about 0.5 s and with spectral energy dominated by the Schumann resonances. These resonances appear to be excited in the earth-ionosphere cavity by Alfven solitons that may have been generated by the explosion-induced acoustic waves reaching the ionospheric E and F regions and that subsequently propagate down through the ionosphere to the atmosphere. In addition, we observe late time (> 800 s) ultra low frequency (ULF) geomagnetic perturbations that appear to originate in the upper F region ({approximately}300 km) and appear to be caused by the explosion-induced acoustic wave interacting with that part of the ionosphere. We suggest that explosion-induced Q-bursts may be discriminated from naturally occurring Q-bursts by association of the former with the late time explosion-induced ULF
Reck, Kasper; Thomsen, Erik V; Hansen, Ole
2011-01-31
The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations using two dimensional Fourier series. The solution is entirely based on analytical expressions and is not mesh dependent. The analytical results are compared to a numerical (finite element method) solution.
NASA Astrophysics Data System (ADS)
M, G. Hafez; N, C. Roy; M, R. Talukder; M Hossain, Ali
2017-01-01
A comparative study is carried out for the nonlinear propagation of ion acoustic shock waves both for the weakly and highly relativistic plasmas consisting of relativistic ions and q-distributed electrons and positions. The Burgers equation is derived to reveal the physical phenomena using the well known reductive perturbation technique. The integration of the Burgers equation is performed by the (G\\prime /G)-expansion method. The effects of positron concentration, ion-electron temperature ratio, electron-positron temperature ratio, ion viscosity coefficient, relativistic streaming factor and the strength of the electron and positron nonextensivity on the nonlinear propagation of ion acoustic shock and periodic waves are presented graphically and the relevant physical explanations are provided.
NASA Astrophysics Data System (ADS)
Guo, Shimin; Mei, Liquan; Zhang, Zhengqiang
2015-05-01
Nonlinear propagation of ion-acoustic waves is investigated in a one-dimensional, unmagnetized plasma consisting of positive ions, negative ions, and nonthermal electrons featuring Tsallis distribution that is penetrated by a negative-ion-beam. The classical Gardner equation is derived to describe nonlinear behavior of ion-acoustic waves in the considered plasma system via reductive perturbation technique. We convert the classical Gardner equation into the time-fractional Gardner equation by Agrawal's method, where the time-fractional term is under the sense of Riesz fractional derivative. Employing variational iteration method, we construct solitary wave solutions of the time-fractional Gardner equation with initial condition which depends on the nonlinear and dispersion coefficients. The effect of the plasma parameters on the compressive and rarefactive ion-acoustic solitary waves is also discussed in detail.
Guo, Shimin Mei, Liquan; Zhang, Zhengqiang
2015-05-15
Nonlinear propagation of ion-acoustic waves is investigated in a one-dimensional, unmagnetized plasma consisting of positive ions, negative ions, and nonthermal electrons featuring Tsallis distribution that is penetrated by a negative-ion-beam. The classical Gardner equation is derived to describe nonlinear behavior of ion-acoustic waves in the considered plasma system via reductive perturbation technique. We convert the classical Gardner equation into the time-fractional Gardner equation by Agrawal's method, where the time-fractional term is under the sense of Riesz fractional derivative. Employing variational iteration method, we construct solitary wave solutions of the time-fractional Gardner equation with initial condition which depends on the nonlinear and dispersion coefficients. The effect of the plasma parameters on the compressive and rarefactive ion-acoustic solitary waves is also discussed in detail.
Flatté, Stanley M; Vera, Michael D
2003-08-01
Line-integral approximations to the acoustic path integral have been used to estimate the magnitude of the fluctuations in an acoustic signal traveling through an ocean filled with internal waves. These approximations for the root-mean-square (rms) fluctuation and the bias of travel time, rms fluctuation in a vertical arrival angle, and the spreading of the acoustic pulse are compared here to estimates from simulations that use the parabolic equation (PE). PE propagations at 250 Hz with a maximum range of 1000 km were performed. The model environment consisted of one of two sound-speed profiles perturbed by internal waves conforming to the Garrett-Munk (GM) spectral model with strengths of 0.5, 1, and 2 times the GM reference energy level. Integral-approximation (IA) estimates of rms travel-time fluctuations were within statistical uncertainty at 1000 km for the SLICE89 profile, and in disagreement by between 20% and 60% for the Canonical profile. Bias estimates were accurate for the first few hundred kilometers of propagation, but became a strong function of time front ID beyond, with some agreeing with the PE results and others very much larger. The IA structure functions of travel time with depth are predicted to be quadratic with the form theta(2)vc0(-2)deltaz(2), where deltaz is vertical separation, c0 is a reference sound speed, and thetav is the rms fluctuation in an arrival angle. At 1000 km, the PE results were close to quadratic at small deltaz, with values of thetav in disagreement with those of the integral approximation by factors of order 2. Pulse spreads in the PE results were much smaller than predicted by the IA estimates. Results imply that acoustic tomography of internal waves at ranges up to 1000 km can use the IA estimate of travel-time variance with reasonable reliability.
Separable wave equations for gravitoelectromagnetic perturbations of rotating charged black strings
NASA Astrophysics Data System (ADS)
Miranda, Alex S.; Morgan, Jaqueline; Kandus, Alejandra; Zanchin, Vilson T.
2015-12-01
Rotating charged black strings are exact solutions of four-dimensional Einstein-Maxwell equations with a negative cosmological constant and a non-trivial spacetime topology. According to the AdS/CFT correspondence, these black strings are dual to rotating thermal states of a strongly interacting quantum field theory with nonzero chemical potential that lives in a cylinder. The dynamics of linear fluctuations in the dual field theory can be studied from the perturbation equations for classical fields in a black-string spacetime. With this motivation in mind, we develop here a completely gauge and tetrad invariant perturbation approach to deal with the gravitoelectromagnetic fluctuations of rotating charged black strings in the presence of sources. As usual, for any charged black hole, a perturbation in the background electromagnetic field induces a metric perturbation and vice versa. In spite of this coupling and the non-vanishing angular momentum, we show that linearization of equations of the Newman-Penrose formalism leads to four separated second-order complex equations for suitable combinations of the spin coefficients, the Weyl and the Maxwell scalars. Then, we generalize the Chandrasekhar transformation theory by the inclusion of sources and apply it to reduce the perturbation problem to four decoupled inhomogeneous wave equations—a pair for each sector of perturbations. The radial part of such wave equations can be put into Schrödinger-like forms after Fourier transforming them with respect to time. We find that the resulting effective potentials form two pairs of supersymmetric partner potentials and, as a consequence, the fundamental variables of one perturbation sector are related to the variables of the other sector. The relevance of such a symmetry in connection to the AdS/CFT correspondence is discussed, and future applications of the pertubation theory developed here are outlined.
The Radiation Reaction Effects in the Solutions of the Perturbed Einstein Equations
NASA Astrophysics Data System (ADS)
Sasaki, M.
1981-02-01
The gravitational radiation reaction effects in the systems described by the perturbations of given solutions of the Einstein equations are considered. There are two kinds of perturbations to be considered; one is the perturbation induced by no external source and the other is the perturbation due to the presence of a source particle. For the former case, we find that there exists a conserved current constructed from a quadratic combination of the solutions to the linearly perturbed equations, provided that the unperturbed geometry admits a Killing vector. Thus, some effects of radiation reaction are found to be included in the linear approximation. For the latter case, it is shown that the usual perturbation expansion scheme fails but there is a possible approach analogous to the one in the Lorentz-Dirac theory of charged particles in order to include the reactive effects. By this approach we find that a naive argument on the energy conservation leads an additional reactive term which contributes to the energy equation. However this term is found to be negligible if the particle is under a quasi-periodic motion.
Existence of solitary waves and periodic waves for a perturbed generalized BBM equation
NASA Astrophysics Data System (ADS)
Chen, Aiyong; Guo, Lina; Deng, Xijun
2016-11-01
The existence of solitary waves and periodic waves for a perturbed generalized BBM equation is established by using geometric singular perturbation theory. Attention goes to perturbations of the Hamiltonian vector field with an elliptic Hamiltonian of degree four, exhibiting a cuspidal loop. It is proven that the wave speed c0 (h) is decreasing on h ∈ [ 0 , 1 / 12 ] by analyzing the ratio of Abelian integrals. The upper and lower bounds of the limit wave speed are given. Moreover, the relation between the wave speed and the wavelength of traveling waves is obtained.
Attenuation of sound in ducts with acoustic treatment: A generalized approximate equation
NASA Technical Reports Server (NTRS)
Rice, E. J.
1975-01-01
A generalized approximate equation for duct lining sound attenuation is presented. The specification of two parameters, the maximum possible attenuation and the optimum wall acoustic impedance is shown to completely determine the sound attenuation for any acoustic mode at any selected wall impedance. The equation is based on the nearly circular shape of the constant attenuation contours in the wall acoustic impedance plane. For impedances far from the optimum, the equation reduces to Morse's approximate expression. The equation can be used for initial acoustic liner design. Not least important is the illustrative nature of the solutions which provide an understanding of the duct propagation problem usually obscured in the exact calculations. Sample calculations using the approximate attenuation equation show that the peak and the bandwidth of the sound attenuation spectrum can be represented by quite simple functions of the ratio of actual wall acoustic resistance to optimum resistance.
Spectral methods for some singularly perturbed third order ordinary differential equations
NASA Astrophysics Data System (ADS)
Temsah, R.
2008-01-01
Spectral methods with interface point are presented to deal with some singularly perturbed third order boundary value problems of reaction-diffusion and convection-diffusion types. First, linear equations are considered and then non-linear equations. To solve non-linear equations, Newton?s method of quasi-linearization is applied. The problem is reduced to two systems of ordinary differential equations. And, then, each system is solved using spectral collocation methods. Our numerical experiments show that the proposed methods are produce highly accurate solutions in little computer time when compared with the other methods available in the literature.
Planetary orbital equations in externally-perturbed systems: position and velocity-dependent forces
NASA Astrophysics Data System (ADS)
Veras, Dimitri; Evans, N. Wyn
2013-02-01
The increasing number and variety of extrasolar planets illustrates the importance of characterizing planetary perturbations. Planetary orbits are typically described by physically intuitive orbital elements. Here, we explicitly express the equations of motion of the unaveraged perturbed two-body problem in terms of planetary orbital elements by using a generalized form of Gauss' equations. We consider a varied set of position and velocity-dependent perturbations, and also derive relevant specific cases of the equations: when they are averaged over fast variables (the "adiabatic" approximation), and in the prograde and retrograde planar cases. In each instance, we delineate the properties of the equations. As brief demonstrations of potential applications, we consider the effect of Galactic tides. We measure the effect on the widest-known exoplanet orbit, Sedna-like objects, and distant scattered disk objects, particularly with regard to where the adiabatic approximation breaks down. The Mathematica code which can help derive the equations of motion for a user-defined perturbation is freely available upon request.
NASA Astrophysics Data System (ADS)
Shenavar, Hossein
2016-03-01
We impose Neumann boundary condition to solve cosmological perturbation equations and we derive a modified Friedmann equation and a new lensing equation. To check the new lensing equation and the value of Neumann constant, a sample that contains ten strong lensing systems is surveyed. Except for one lens, masses of the other lenses are found to be within the constrains of the observational data. Furthermore, we argue that by using the concept of geometrodynamic clocks it is possible to modify the equation of motion of massive particles too. Also, a sample that includes 101 HSB and LSB galaxies is used to re-estimate the value of the Neumann constant and we found that this value is consistent with the prior evaluation from Friedmann and lensing equations. Finally, the growth of structure is studied by a Newtonian approach which resulted in a more rapid rate of the structure formation in matter dominated era.
Generation of perturbations by means of decoupled equations and their adjoints
NASA Astrophysics Data System (ADS)
Torres Del Castillo, G. F.
1990-10-01
It is shown that the procedure introduced by Wald for constructing solutions of a coupled system of linear partial differential equations from the solution of a single equation, based on the concept of the adjoint of a linear partial differential operator, can be extended to equations involving spinor fields, matrix fields and two or more fields. Some results concerning massless spinor fields are presented and the application of the method to linear perturbations of Yang-Mills fields and of Einstein-Maxwell fields is indicated.
On an Acoustic Wave Equation Arising in Non-Equilibrium Gasdynamics. Classroom Notes
ERIC Educational Resources Information Center
Chandran, Pallath
2004-01-01
The sixth-order wave equation governing the propagation of one-dimensional acoustic waves in a viscous, heat conducting gaseous medium subject to relaxation effects has been considered. It has been reduced to a system of lower order equations corresponding to the finite speeds occurring in the equation, following a method due to Whitham. The lower…
NASA Astrophysics Data System (ADS)
Johnson, Kennita A.; Vormohr, Hannah R.; Doinikov, Alexander A.; Bouakaz, Ayache; Shields, C. Wyatt; López, Gabriel P.; Dayton, Paul A.
2016-05-01
Acoustophoresis uses acoustic radiation force to remotely manipulate particles suspended in a host fluid for many scientific, technological, and medical applications, such as acoustic levitation, acoustic coagulation, contrast ultrasound imaging, ultrasound-assisted drug delivery, etc. To estimate the magnitude of acoustic radiation forces, equations derived for an inviscid host fluid are commonly used. However, there are theoretical predictions that, in the case of a traveling wave, viscous effects can dramatically change the magnitude of acoustic radiation forces, which make the equations obtained for an inviscid host fluid invalid for proper estimation of acoustic radiation forces. To date, experimental verification of these predictions has not been published. Experimental measurements of viscous effects on acoustic radiation forces in a traveling wave were conducted using a confocal optical and acoustic system and values were compared with available theories. Our results show that, even in a low-viscosity fluid such as water, the magnitude of acoustic radiation forces is increased manyfold by viscous effects in comparison with what follows from the equations derived for an inviscid fluid.
Parabolic equation modeling of high frequency acoustic transmission with an evolving sea surface.
Senne, J; Song, A; Badiey, M; Smith, K B
2012-09-01
The present paper examines the temporal evolution of acoustic fields by modeling forward propagation subject to sea surface dynamics with time scales of less than a second to tens of seconds. A time-evolving rough sea surface model is combined with a rough surface formulation of a parabolic equation model for predicting time-varying acoustic fields. Surface waves are generated from surface wave spectra, and stepped in time using a Runge-Kutta integration technique applied to linear evolution equations. This evolving, range-dependent surface information is combined with other environmental parameters and input to the acoustic model, giving an approximation of the time-varying acoustic field. The wide-angle parabolic equation model manages the rough sea surfaces by molding them into the boundary conditions for calculations of the near-surface acoustic field. This merged acoustic model is validated using concurrently-collected acoustic and environmental information, including surface wave spectra. Data to model comparisons demonstrate that the model is able to approximate the ensemble-averaged acoustic intensity at ranges of about a kilometer for acoustic signals of around 15 kHz. Furthermore, the model is shown to capture variations due to surface fluctuations occurring over time scales of less than a second to tens of seconds.
Sun Zhiyuan; Yu Xin; Liu Ying; Gao Yitian
2012-12-15
We investigate the dynamics of the bound vector solitons (BVSs) for the coupled nonlinear Schroedinger equations with the nonhomogenously stochastic perturbations added on their dispersion terms. Soliton switching (besides soliton breakup) can be observed between the two components of the BVSs. Rate of the maximum switched energy (absolute values) within the fixed propagation distance (about 10 periods of the BVSs) enhances in the sense of statistics when the amplitudes of stochastic perturbations increase. Additionally, it is revealed that the BVSs with enhanced coherence are more robust against the perturbations with nonhomogenous stochasticity. Diagram describing the approximate borders of the splitting and non-splitting areas is also given. Our results might be helpful in dynamics of the BVSs with stochastic noises in nonlinear optical fibers or with stochastic quantum fluctuations in Bose-Einstein condensates.
The Quasi-Maxwellian Equations of General Relativity: Applications to Perturbation Theory
NASA Astrophysics Data System (ADS)
Novello, M.; Bittencourt, E.; Salim, J. M.
2014-12-01
A comprehensive review of the equations of general relativity in the quasi-Maxwellian (QM) formalism introduced by Jordan, Ehlers and Kundt is presented. Our main interest concerns its applications to the analysis of the perturbation of standard cosmology in the Friedman-Lemaître-Robertson-Walker framework. The major achievement of the QM scheme is its use of completely gauge-independent quantities. We shall see that in the QM-scheme, we deal directly with observable quantities. This reveals its advantage over the old method introduced by Lifshitz that deals with perturbation in the standard framework. For completeness, we compare the QM-scheme to the gauge-independent method of Bardeen, a procedure consisting of particular choices of the perturbed variables as a combination of gauge-dependent quantities.
NASA Astrophysics Data System (ADS)
Xin, Bo; Sun, Dakun; Jing, Xiaodong; Sun, Xiaofeng
2016-07-01
Lined ducts are extensively applied to suppress noise emission from aero-engines and other turbomachines. The complex noise/flow interaction in a lined duct possibly leads to acoustic instability in certain conditions. To investigate the instability, the full linearized Navier-Stokes equations with eddy viscosity considered are solved in frequency domain using a Galerkin finite element method to compute the sound transmission in shear flow in the lined duct as well as the flow perturbation over the impedance wall. A good agreement between the numerical predictions and the published experimental results is obtained for the sound transmission, showing that a transmission peak occurs around the resonant frequency of the acoustic liner in the presence of shear flow. The eddy viscosity is an important influential factor that plays the roles of both providing destabilizing and making coupling between the acoustic and flow motions over the acoustic liner. Moreover, it is shown from the numerical investigation that the occurrence of the sound amplification and the magnitude of transmission coefficient are closely related to the realistic velocity profile, and we find it essential that the actual variation of the velocity profile in the axial direction over the liner surface be included in the computation. The simulation results of the periodic flow patterns possess the proper features of the convective instability over the liner, as observed in Marx et al.'s experiment. A quantitative comparison between numerical and experimental results of amplitude and phase of the instability is performed. The corresponding eigenvalues achieve great agreement.
A doubly averaging method for third body perturbations in planet equator coordinates
NASA Technical Reports Server (NTRS)
Hwok, Johnny H.
1992-01-01
The first order doubly averaged potential due to third-body gravity is derived in any arbitrary coordinates. The equations of motion are nonsingular at zero eccentricity. The derivation uses a recursive method which allows easy expansion to higher order terms. Instead of using analytical quadrature to obtain the doubly averaged potential, the method presented in this paper simply eliminates the mean anomaly of the perturbed and perturbing bodies by inspection of the recursive formulation. The derivatives of the orbital elements can be numerically integrated rapidly. When a planet equator coordinate system is used, they can be added directly to the derivatives due to gravity harmonics without any coordinate transformation. The method is applied to various high altitude missions. The results are compared with a high precision numerical integration method and are found to provide excellent agreement.
Tönjes, Ralf; Blasius, Bernd
2009-01-01
The Kuramoto phase-diffusion equation is a nonlinear partial differential equation which describes the spatiotemporal evolution of a phase variable in an oscillatory reaction-diffusion system. Synchronization manifests itself in a stationary phase gradient where all phases throughout a system evolve with the same velocity, the synchronization frequency. The formation of concentric waves can be explained by local impurities of higher frequency which can entrain their surroundings. Concentric waves in synchronization also occur in heterogeneous systems, where the local frequencies are distributed randomly. We present a perturbation analysis of the synchronization frequency where the perturbation is given by the heterogeneity of natural frequencies in the system. The nonlinearity in the form of dispersion leads to an overall acceleration of the oscillation for which the expected value can be calculated from the second-order perturbation terms. We apply the theory to simple topologies, like a line or sphere, and deduce the dependence of the synchronization frequency on the size and the dimension of the oscillatory medium. We show that our theory can be extended to include rotating waves in a medium with periodic boundary conditions. By changing a system parameter, the synchronized state may become quasidegenerate. We demonstrate how perturbation theory fails at such a critical point.
Non-perturbative effects for the Quark-Gluon Plasma equation of state
NASA Astrophysics Data System (ADS)
Begun, V. V.; Gorenstein, M. I.; Mogilevsky, O. A.
2012-07-01
The non-perturbative effects for the Quark-Gluon Plasma (QGP) equation of state (EoS) are considered. The modifications of the bag model EoS are constructed to satisfy the main qualitative features observed for the QGP EoS in the lattice QCD calculations. A quantitative comparison with the lattice results is done for the SU(3) gluon plasma and for the QGP with dynamical quarks. Our analysis advocates a negative value of the bag constant B.
Master equation for a chemical wave front with perturbation of local equilibrium.
Dziekan, P; Lemarchand, A; Nowakowski, B
2011-08-28
In order to develop a stochastic description of gaseous reaction-diffusion systems, which includes a reaction-induced departure from local equilibrium, we derive a modified expression of the master equation from analytical calculations based on the Boltzmann equation. We apply the method to a chemical wave front of Fisher-Kolmogorov-Petrovsky-Piskunov type, whose propagation speed is known to be sensitive to small perturbations. The results of the modified master equation are compared successfully with microscopic simulations of the particle dynamics using the direct simulation Monte Carlo method. The modified master equation constitutes an efficient tool at the mesoscopic scale, which incorporates the nonequilibrium effect without need of determining the particle velocity distribution function.
Perturbed Equations of Motion for Formation Flight Near the Sun-Earth L2 Point
NASA Technical Reports Server (NTRS)
Luquette, Richard; Segerman, A. M.; Zedd, M. F.
2005-01-01
NASA is planning missions to the vicinity of the Sun-Earth L(sub 2) point, some involving a distributed system of telescope spacecraft, configured in a plane about a hub. Several sets of differential equations are written for the formation flight of such telescopes relative to the hub, with varying levels of fidelity. Effects are cast as additive perturbations to the circular restricted three-body problem, expanded in terms of the system distanced, to an accuracy of 10-20 m. These include Earth's orbital eccentricity, lunar motion, solar radiation pressure, and small thrusting forces. Simulations validating the expanded differential equations are presented.
On the Application of Homotopy Perturbation Method for Solving Systems of Linear Equations
Edalatpanah, S. A.; Rashidi, M. M.
2014-01-01
The application of homotopy perturbation method (HPM) for solving systems of linear equations is further discussed and focused on a method for choosing an auxiliary matrix to improve the rate of convergence. Moreover, solving of convection-diffusion equations has been developed by HPM and the convergence properties of the proposed method have been analyzed in detail; the obtained results are compared with some other methods in the frame of HPM. Numerical experiment shows a good improvement on the convergence rate and the efficiency of this method. PMID:27350974
Closed-form equation of state for Lennard-Jones molecules based on perturbation theory
Bokis, C.P.; Donohue, M.D.
1995-08-17
A comparison of virial theory and perturbation theory for spherical molecules is presented. A new equation of state is derived. This new model has the exact second virial coefficient behavior, converges to the correct mean-field behavior at high densities, and successfully interpolates between these two limits. This new equation of state is applied to molecules that interact via the Lennard-Jones potential. Comparison is made with computer simulation results for the configurational energy, the compressibility factor, and the second virial coefficient of Lennard-Jones molecules. 25 refs., 7 figs.
NASA Technical Reports Server (NTRS)
Nixon, D.
1978-01-01
The linear transonic perturbation integral equation previously derived for nonlifting airfoils is formulated for lifting cases. In order to treat shock wave motions, a strained coordinate system is used in which the shock location is invariant. The tangency boundary conditions are either formulated using the thin airfoil approximation or by using the analytic continuation concept. A direct numerical solution to this equation is derived in contrast to the iterative scheme initially used, and results of both lifting and nonlifting examples indicate that the method is satisfactory.
Dziekan, P; Lemarchand, A; Nowakowski, B
2012-02-01
We present a modified master equation for a homogeneous gaseous reactive system which includes nonequilibrium corrections due to the reaction-induced perturbation of the particle velocity distribution function. For the Schlögl model, the modified stochastic approach predicts nonequilibrium-induced transitions between different dynamical regimes, including the transformation of a monostable system into a bistable one, and vice versa. These predictions are confirmed by the comparison with microscopic simulations using the direct simulation Monte Carlo method. Compared to microscopic simulations of the particle dynamics, the modified master equation approach proves to be much more efficient.
Libin, A.
2012-12-15
A linear combination of a pair of dual anisotropic decaying Beltrami flows with spatially constant amplitudes (the Trkal solutions) with the same eigenvalue of the curl operator and of a constant velocity orthogonal vector to the Beltrami pair yields a triplet solution of the force-free Navier-Stokes equation. The amplitudes slightly variable in space (large scale perturbations) yield the emergence of a time-dependent phase between the dual Beltrami flows and of the upward velocity, which are unstable at large values of the Reynolds number. They also lead to the formation of large-scale curved prisms of streamlines with edges being the strings of singular vorticity.
NASA Astrophysics Data System (ADS)
Suárez, Abril; Chavanis, Pierre-Henri
2015-07-01
Using a generalization of the Madelung transformation, we derive the hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field limit. We consider a complex self-interacting scalar field with a λ |φ |4 potential. We study the evolution of the spatially homogeneous background in the fluid representation and derive the linearized equations describing the evolution of small perturbations in a static and in an expanding Universe. We compare the results with simplified models in which the gravitational potential is introduced by hand in the Klein-Gordon equation, and assumed to satisfy a (generalized) Poisson equation. Nonrelativistic hydrodynamic equations based on the Schrödinger-Poisson equations or on the Gross-Pitaevskii-Poisson equations are recovered in the limit c →+∞. We study the evolution of the perturbations in the matter era using the nonrelativistic limit of our formalism. Perturbations whose wavelength is below the Jeans length oscillate in time while perturbations whose wavelength is above the Jeans length grow linearly with the scale factor as in the cold dark matter model. The growth of perturbations in the scalar field model is substantially faster than in the cold dark matter model. When the wavelength of the perturbations approaches the cosmological horizon (Hubble length), a relativistic treatment is mandatory. In that case, we find that relativistic effects attenuate or even prevent the growth of perturbations. This paper exposes the general formalism and provides illustrations in simple cases. Other applications of our formalism will be considered in companion papers.
Difference equation for tracking perturbations in systems of Boolean nested canalyzing functions
NASA Astrophysics Data System (ADS)
Dimitrova, Elena S.; Yordanov, Oleg I.; Matache, Mihaela T.
2015-06-01
This paper studies the spread of perturbations through networks composed of Boolean functions with special canalyzing properties. Canalyzing functions have the property that at least for one value of one of the inputs the output is fixed, irrespective of the values of the other inputs. In this paper the focus is on partially nested canalyzing functions, in which multiple, but not all inputs have this property in a cascading fashion. They naturally describe many relationships in real networks. For example, in a gene regulatory network, the statement "if gene A is expressed, then gene B is not expressed regardless of the states of other genes" implies that A is canalyzing. On the other hand, the additional statement "if gene A is not expressed, and gene C is expressed, then gene B is automatically expressed; otherwise gene B 's state is determined by some other type of rule" implies that gene B is expressed by a partially nested canalyzing function with more than two variables, but with two canalyzing variables. In this paper a difference equation model of the probability that a network node's value is affected by an initial perturbation over time is developed, analyzed, and validated numerically. It is shown that the effect of a perturbation decreases towards zero over time if the Boolean functions are canalyzing in sufficiently many variables. The maximum dynamical impact of a perturbation is shown to be comparable to the average impact for a wide range of values of the average sensitivity of the network. Percolation limits are also explored; these are parameter values which generate a transition of the expected perturbation effect to zero as other parameters are varied, so that the initial perturbation does not scale up with the parameters once the percolation limits are reached.
Baryon acoustic oscillations in 2D: Modeling redshift-space power spectrum from perturbation theory
Taruya, Atsushi; Nishimichi, Takahiro; Saito, Shun
2010-09-15
We present an improved prescription for the matter power spectrum in redshift space taking proper account of both nonlinear gravitational clustering and redshift distortion, which are of particular importance for accurately modeling baryon acoustic oscillations (BAOs). Contrary to the models of redshift distortion phenomenologically introduced but frequently used in the literature, the new model includes the corrections arising from the nonlinear coupling between the density and velocity fields associated with two competitive effects of redshift distortion, i.e., Kaiser and Finger-of-God effects. Based on the improved treatment of perturbation theory for gravitational clustering, we compare our model predictions with the monopole and quadrupole power spectra of N-body simulations, and an excellent agreement is achieved over the scales of BAOs. Potential impacts on constraining dark energy and modified gravity from the redshift-space power spectrum are also investigated based on the Fisher-matrix formalism, particularly focusing on the measurements of the Hubble parameter, angular diameter distance, and growth rate for structure formation. We find that the existing phenomenological models of redshift distortion produce a systematic error on measurements of the angular diameter distance and Hubble parameter by 1%-2%, and the growth-rate parameter by {approx}5%, which would become non-negligible for future galaxy surveys. Correctly modeling redshift distortion is thus essential, and the new prescription for the redshift-space power spectrum including the nonlinear corrections can be used as an accurate theoretical template for anisotropic BAOs.
Beckman, D A; Wold, D C; Montague, J C
1983-06-01
This study investigated improved processing of acoustic data with two adult Down's syndrome subjects. Sustained vowel samples were processed through a fast-Fourier-transform spectrum analyzer, and digital waveform data were used to obtain period-by-period measurements of the fundamental frequencies. Unusual frequency perturbation (jitter), later identified as diplophonia, was found for one of the Down's subjects. In addition, the first three formant frequencies of the vowels were determined and, utilizing an algorithm described by Ladefoged and his colleagues, computer-generated vocal-tract shapes were plotted. Differences in vocal-tract shapes, especially for the back vowels, were observed between the Down's female and the normal shape. Correlations between vocal-tract shapes of the Down's subjects and those for a normal man or woman were computed. A partial three-way factor analysis was carried out to determine those load factors or coefficients for each subject that were due to individual differences. These procedures, offering synthesized techniques portraying the interpharyngeal/oral functioning of the speech structures, may eventually have direct noninvasive diagnostic and therapeutic benefit for voice/resonance-disordered clients.
Random Rays, Geometric Acoustics, and the Parabolic Wave Equation
1984-03-01
5). Of course. Nelson’s theory is a stochastic version of the Schrodinger equation of quantum mechanics, but this equation is formally identical... equation is just the Schrodinger equation of quantum mechanics, and since we expect ray theory to be meaningful when k »1, i.e., when 1/k « 1, where (1/k...Wave Equation 5. TYPE OF REPORT & PERIOD COVERED TECHNICAL 6. PERFORMING 07G. REPORT NUMBER LAP-4 7. AUTHORfj; Thad Dankel, Jr. 8
Dual chain perturbation theory: A new equation of state for polyatomic molecules.
Marshall, Bennett D
2016-04-28
In the development of equations of state for polyatomic molecules, thermodynamic perturbation theory (TPT) is widely used to calculate the change in free energy due to chain formation. TPT is a simplification of a more general and exact multi-density cluster expansion for associating fluids. In TPT, all contributions to the cluster expansion which contain chain-chain interactions are neglected. That is, all inter-chain interactions are treated at the reference fluid level. This allows for the summation of the cluster theory in terms of reference system correlation functions only. The resulting theory has been shown to be accurate and has been widely employed as the basis of many engineering equations of state. While highly successful, TPT has many handicaps which result from the neglect of chain-chain contributions. The subject of this document is to move beyond the limitations of TPT and include chain-chain contributions to the equation of state.
On the use of the autonomous Birkhoff equations in Lie series perturbation theory
NASA Astrophysics Data System (ADS)
Boronenko, T. S.
2017-02-01
In this article, we present the Lie transformation algorithm for autonomous Birkhoff systems. Here, we are referring to Hamiltonian systems that obey a symplectic structure of the general form. The Birkhoff equations are derived from the linear first-order Pfaff-Birkhoff variational principle, which is more general than the Hamilton principle. The use of 1-form in formulating the equations of motion in dynamics makes the Birkhoff method more universal and flexible. Birkhoff's equations have a tensorial character, so their form is independent of the coordinate system used. Two examples of normalization in the restricted three-body problem are given to illustrate the application of the algorithm in perturbation theory. The efficiency of this algorithm for problems of asymptotic integration in dynamics is discussed for the case where there is a need to use non-canonical variables in phase space.
Dual chain perturbation theory: A new equation of state for polyatomic molecules
NASA Astrophysics Data System (ADS)
Marshall, Bennett D.
2016-04-01
In the development of equations of state for polyatomic molecules, thermodynamic perturbation theory (TPT) is widely used to calculate the change in free energy due to chain formation. TPT is a simplification of a more general and exact multi-density cluster expansion for associating fluids. In TPT, all contributions to the cluster expansion which contain chain-chain interactions are neglected. That is, all inter-chain interactions are treated at the reference fluid level. This allows for the summation of the cluster theory in terms of reference system correlation functions only. The resulting theory has been shown to be accurate and has been widely employed as the basis of many engineering equations of state. While highly successful, TPT has many handicaps which result from the neglect of chain-chain contributions. The subject of this document is to move beyond the limitations of TPT and include chain-chain contributions to the equation of state.
Siminos, E; Sánchez-Arriaga, G; Saxena, V; Kourakis, I
2014-12-01
We investigate the dynamics of localized solutions of the relativistic cold-fluid plasma model in the small but finite amplitude limit, for slightly overcritical plasma density. Adopting a multiple scale analysis, we derive a perturbed nonlinear Schrödinger equation that describes the evolution of the envelope of circularly polarized electromagnetic field. Retaining terms up to fifth order in the small perturbation parameter, we derive a self-consistent framework for the description of the plasma response in the presence of localized electromagnetic field. The formalism is applied to standing electromagnetic soliton interactions and the results are validated by simulations of the full cold-fluid model. To lowest order, a cubic nonlinear Schrödinger equation with a focusing nonlinearity is recovered. Classical quasiparticle theory is used to obtain analytical estimates for the collision time and minimum distance of approach between solitons. For larger soliton amplitudes the inclusion of the fifth-order terms is essential for a qualitatively correct description of soliton interactions. The defocusing quintic nonlinearity leads to inelastic soliton collisions, while bound states of solitons do not persist under perturbations in the initial phase or amplitude.
Three new branched chain equations of state based on Wertheim's perturbation theory.
Marshall, Bennett D; Chapman, Walter G
2013-05-07
In this work, we present three new branched chain equations of state (EOS) based on Wertheim's perturbation theory. The first represents a slightly approximate general branched chain solution of Wertheim's second order perturbation theory (TPT2) for athermal hard chains, and the second represents the extension of first order perturbation theory with a dimer reference fluid (TPT1-D) to branched athermal hard chain molecules. Each athermal branched chain EOS was shown to give improved results over their linear counterparts when compared to simulation data for branched chain molecules with the branched TPT1-D EOS being the most accurate. Further, it is shown that the branched TPT1-D EOS can be extended to a Lennard-Jones dimer reference system to obtain an equation of state for branched Lennard-Jones chains. The theory is shown to accurately predict the change in phase diagram and vapor pressure which results from branching as compared to experimental data for n-octane and corresponding branched isomers.
A hybrid perturbation-Galerkin method for differential equations containing a parameter
NASA Technical Reports Server (NTRS)
Geer, James F.; Andersen, Carl M.
1989-01-01
A two-step hybrid perturbation-Galerkin method to solve a variety of differential equations which involve a parameter is presented and discussed. The method consists of: (1) the use of a perturbation method to determine the asymptotic expansion of the solution about one or more values of the parameter; and (2) the use of some of the perturbation coefficient functions as trial functions in the classical Bubnov-Galerkin method. This hybrid method has the potential of overcoming some of the drawbacks of the perturbation method and the Bubnov-Galerkin method when they are applied by themselves, while combining some of the good features of both. The proposed method is illustrated first with a simple linear two-point boundary value problem and is then applied to a nonlinear two-point boundary value problem in lubrication theory. The results obtained from the hybrid method are compared with approximate solutions obtained by purely numerical methods. Some general features of the method, as well as some special tips for its implementation, are discussed. A survey of some current research application areas is presented and its degree of applicability to broader problem areas is discussed.
NASA Astrophysics Data System (ADS)
Wu, Sean F.; Zhao, Xiang
2002-07-01
A combined Helmholtz equation-least squares (CHELS) method is developed for reconstructing acoustic radiation from an arbitrary object. This method combines the advantages of both the HELS method and the Helmholtz integral theory based near-field acoustic holography (NAH). As such it allows for reconstruction of the acoustic field radiated from an arbitrary object with relatively few measurements, thus significantly enhancing the reconstruction efficiency. The first step in the CHELS method is to establish the HELS formulations based on a finite number of acoustic pressure measurements taken on or beyond a hypothetical spherical surface that encloses the object under consideration. Next enough field acoustic pressures are generated using the HELS formulations and taken as the input to the Helmholtz integral formulations implemented through the boundary element method (BEM). The acoustic pressure and normal component of the velocity at the discretized nodes on the surface are then determined by solving two matrix equations using singular value decomposition (SVD) and regularization techniques. Also presented are in-depth analyses of the advantages and limitations of the CHELS method. Examples of reconstructing acoustic radiation from separable and nonseparable surfaces are demonstrated. copyright 2002 Acoustical Society of America.
Daeva, S.G.; Setukha, A.V.
2015-03-10
A numerical method for solving a problem of diffraction of acoustic waves by system of solid and thin objects based on the reduction the problem to a boundary integral equation in which the integral is understood in the sense of finite Hadamard value is proposed. To solve this equation we applied piecewise constant approximations and collocation methods numerical scheme. The difference between the constructed scheme and earlier known is in obtaining approximate analytical expressions to appearing system of linear equations coefficients by separating the main part of the kernel integral operator. The proposed numerical scheme is tested on the solution of the model problem of diffraction of an acoustic wave by inelastic sphere.
Nonlinear acoustic wave equations with fractional loss operators.
Prieur, Fabrice; Holm, Sverre
2011-09-01
Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlinear wave equation which describes attenuation and dispersion laws that match observations. This wave equation is a generalization of the Westervelt equation, and also leads to a fractional version of the Khokhlov-Zabolotskaya-Kuznetsov and Burgers' equations.
From charge motion in general magnetic fields to the non perturbative gyrokinetic equation
Di Troia, C.
2015-04-15
The exact analytical description of non relativistic charge motion in general magnetic fields is, apparently, a simple problem, even if it has not been solved until now, apart for rare cases. The key feature of the present derivation is to adopt a non perturbative magnetic field description to find new solutions of motion. Among all solutions, two are particularly important: guiding particle and gyro-particle solutions. The guiding particle has been characterized to be minimally coupled to the magnetic field; the gyro-particle has been defined to be maximally coupled to the magnetic field and, also, to move on a closed orbit. The generic charged particle motion is shown to be expressed as the sum of such particular solutions. This non perturbative approach corresponds to the description of the particle motion in the gyro-center and/or guiding center reference frame obtained at all the orders of the modern gyro-center transformation. The Boltzmann equation is analyzed with the described exact guiding center coordinates. The obtained gyrokinetic equation is solved for the Boltzmann equation at marginal stability conditions.
NASA Astrophysics Data System (ADS)
Nourazar, S. S.; Nazari-Golshan, A.
2015-01-01
A hybrid of Fourier transform and new modified homotopy perturbation method based on the Adomian method is developed to solve linear and nonlinear partial differential equations. The Taylor series expansion is used to expand nonlinear term of partial differential equation and the Adomian polynomial incorporated into homotopy perturbation method combined with Fourier transform, is used to solve partial differential equations. Three case study problems, partial differential equations, are handled using homotopy perturbation method and Fourier transform modified homotopy perturbation method (FTMHPM). Results obtained are compared with exact solution. The comparison reveals that for same components of recursive sequences, errors associated with Fourier transform modified method are much less than the other and are valid for a large range of x-axis coordinates.
Solovchuk, Maxim; Sheu, Tony W H; Thiriet, Marc
2013-11-01
This study investigates the influence of blood flow on temperature distribution during high-intensity focused ultrasound (HIFU) ablation of liver tumors. A three-dimensional acoustic-thermal-hydrodynamic coupling model is developed to compute the temperature field in the hepatic cancerous region. The model is based on the nonlinear Westervelt equation, bioheat equations for the perfused tissue and blood flow domains. The nonlinear Navier-Stokes equations are employed to describe the flow in large blood vessels. The effect of acoustic streaming is also taken into account in the present HIFU simulation study. A simulation of the Westervelt equation requires a prohibitively large amount of computer resources. Therefore a sixth-order accurate acoustic scheme in three-point stencil was developed for effectively solving the nonlinear wave equation. Results show that focused ultrasound beam with the peak intensity 2470 W/cm(2) can induce acoustic streaming velocities up to 75 cm/s in the vessel with a diameter of 3 mm. The predicted temperature difference for the cases considered with and without acoustic streaming effect is 13.5 °C or 81% on the blood vessel wall for the vein. Tumor necrosis was studied in a region close to major vessels. The theoretical feasibility to safely necrotize the tumors close to major hepatic arteries and veins was shown.
NASA Astrophysics Data System (ADS)
Marinca, Vasile; Ene, Remus-Daniel
2017-01-01
In this paper, the Optimal Homotopy Perturbation Method (OHPM) is employed to determine an analytic approximate solution for the nonlinear MHD Jeffery-Hamel flow and heat transfer problem. The Navier-Stokes equations, taking into account Maxwell's electromagnetism and heat transfer, lead to two nonlinear ordinary differential equations. The results obtained by means of OHPM show very good agreement with numerical results and with Homotopy Perturbation Method (HPM) results.
NASA Technical Reports Server (NTRS)
Huang, T. C.; Das, A.
1976-01-01
The formulation and existence of a generalized force in the singularly perturbed formulation of flexible satellites is described. The concept of this force sharply reduces the number of degrees of freedom and the equations of motion of satellites with a large number of flexible elements. The force is analyzed to demonstrate its existence and convergence criteria. The complete solution has been obtained in three time zones - the inner boundary layer, the outer boundary layer, and the large time extending beyond these boundary layers. A stability criterion is proposed for this generalized force.
Calculation of the neutron diffusion equation by using Homotopy Perturbation Method
NASA Astrophysics Data System (ADS)
Koklu, H.; Ersoy, A.; Gulecyuz, M. C.; Ozer, O.
2016-03-01
The distribution of the neutrons in a nuclear fuel element in the nuclear reactor core can be calculated by the neutron diffusion theory. It is the basic and the simplest approximation for the neutron flux function in the reactor core. In this study, the neutron flux function is obtained by the Homotopy Perturbation Method (HPM) that is a new and convenient method in recent years. One-group time-independent neutron diffusion equation is examined for the most solved geometrical reactor core of spherical, cubic and cylindrical shapes, in the frame of the HPM. It is observed that the HPM produces excellent results consistent with the existing literature.
Well-posedness, linear perturbations, and mass conservation for the axisymmetric Einstein equations
NASA Astrophysics Data System (ADS)
Dain, Sergio; Ortiz, Omar E.
2010-02-01
For axially symmetric solutions of Einstein equations there exists a gauge which has the remarkable property that the total mass can be written as a conserved, positive definite, integral on the spacelike slices. The mass integral provides a nonlinear control of the variables along the whole evolution. In this gauge, Einstein equations reduce to a coupled hyperbolic-elliptic system which is formally singular at the axis. As a first step in analyzing this system of equations we study linear perturbations on a flat background. We prove that the linear equations reduce to a very simple system of equations which provide, though the mass formula, useful insight into the structure of the full system. However, the singular behavior of the coefficients at the axis makes the study of this linear system difficult from the analytical point of view. In order to understand the behavior of the solutions, we study the numerical evolution of them. We provide strong numerical evidence that the system is well-posed and that its solutions have the expected behavior. Finally, this linear system allows us to formulate a model problem which is physically interesting in itself, since it is connected with the linear stability of black hole solutions in axial symmetry. This model can contribute significantly to solve the nonlinear problem and at the same time it appears to be tractable.
Solution of an inverse scattering problem for the acoustic wave equation in three-dimensional media
NASA Astrophysics Data System (ADS)
Baev, A. V.
2016-12-01
A three-dimensional inverse scattering problem for the acoustic wave equation is studied. The task is to determine the density and acoustic impedance of a medium. A necessary and sufficient condition for the unique solvability of this problem is established in the form of an energy conservation law. The interpretation of the solution to the inverse problem and the construction of medium images are discussed.
NASA Astrophysics Data System (ADS)
Olsson, Peter
2016-03-01
A new directional decomposition of the acoustic 3D wave equation is derived for spherically symmetric geometries, where the wave fields do not need to possess such a symmetry. This provides an alternative basis for various applications of techniques like invariant embedding and time domain Green functions in spherically symmetric geometries. Contrary to previous results on spherical wave splittings, the new decomposition is given in a very explicit form. The wave equation considered incorporates effects from radially varying compressibility and density, but also from anisotropic density, a property of certain so called metafluids. By applying the new spherical wave splitting, we show that all spherically symmetric acoustic metafluid cloaks are diffeomorphic images of a homogeneous and isotropic spherical ball of perfect fluid.
Wu, Sean F; Zhao, Xiang
2002-07-01
A combined Helmholtz equation-least squares (CHELS) method is developed for reconstructing acoustic radiation from an arbitrary object. This method combines the advantages of both the HELS method and the Helmholtz integral theory based near-field acoustic holography (NAH). As such it allows for reconstruction of the acoustic field radiated from an arbitrary object with relatively few measurements, thus significantly enhancing the reconstruction efficiency. The first step in the CHELS method is to establish the HELS formulations based on a finite number of acoustic pressure measurements taken on or beyond a hypothetical spherical surface that encloses the object under consideration. Next enough field acoustic pressures are generated using the HELS formulations and taken as the input to the Helmholtz integral formulations implemented through the boundary element method (BEM). The acoustic pressure and normal component of the velocity at the discretized nodes on the surface are then determined by solving two matrix equations using singular value decomposition (SVD) and regularization techniques. Also presented are in-depth analyses of the advantages and limitations of the CHELS method. Examples of reconstructing acoustic radiation from separable and nonseparable surfaces are demonstrated.
Approximating a nonlinear advanced-delayed equation from acoustics
NASA Astrophysics Data System (ADS)
Teodoro, M. Filomena
2016-10-01
We approximate the solution of a particular non-linear mixed type functional differential equation from physiology, the mucosal wave model of the vocal oscillation during phonation. The mathematical equation models a superficial wave propagating through the tissues. The numerical scheme is adapted from the work presented in [1, 2, 3], using homotopy analysis method (HAM) to solve the non linear mixed type equation under study.
NASA Astrophysics Data System (ADS)
Balasuriya, Sanjeeva
2016-12-01
State-dependent time-impulsive perturbations to a two-dimensional autonomous flow with stable and unstable manifolds are analysed by posing in terms of an integral equation which is valid in both forwards- and backwards-time. The impulses destroy the smooth invariant manifolds, necessitating new definitions for stable and unstable pseudo-manifolds. Their time-evolution is characterised by solving a Volterra integral equation of the second kind with discontinuous inhomogeniety. A criteria for heteroclinic trajectory persistence in this impulsive context is developed, as is a quantification of an instantaneous flux across broken heteroclinic manifolds. Several examples, including a kicked Duffing oscillator and an underwater explosion in the vicinity of an eddy, are used to illustrate the theory.
Joining conditions for cosmological perturbations at an equation-of-state transition
Ratra, B. )
1991-06-15
Joining conditions for cosmological spatial irregularities at an equation-of-state transition spatial hypersurface are derived by requiring that the relativistic linear perturbation theory equations of motion remain singularity-free at the transition spatial hypersurface. The transition spatial hypersurface is taken to be a spatially homogeneous local energy-density spatial hypersurface, between two spacetime-dependent speed-of-sound'' fluid-dominated epochs of a spatially flat Friedmann-Lema{cflx i}tre-Robertson-Walker cosmological model. Since the spacetime-dependent speed-of-sound'' fluid model includes, as special cases, both the scalar field model and the ideal fluid model, these joining conditions may be used at the scalar-field--radiation and radiation-baryon transitions in simple inflation-modified hot big-bang models. These joining conditions differ from two earlier sets of joining conditions (which differ from each other).
A modified diffusion equation for room-acoustic predication.
Jing, Yun; Xiang, Ning
2007-06-01
This letter presents a modified diffusion model using an Eyring absorption coefficient to predict the reverberation time and sound pressure distributions in enclosures. While the original diffusion model [Ollendorff, Acustica 21, 236-245 (1969); J. Picaut et al., Acustica 83, 614-621 (1997); Valeau et al., J. Acoust. Soc. Am. 119, 1504-1513 (2006)] usually has good performance for low absorption, the modified diffusion model yields more satisfactory results for both low and high absorption. Comparisons among the modified model, the original model, a geometrical-acoustics model, and several well-established theories in terms of reverberation times and sound pressure level distributions, indicate significantly improved prediction accuracy by the modification.
NASA Astrophysics Data System (ADS)
Müller, Clemens; Stace, Thomas M.
2017-01-01
Motivated by correlated decay processes producing gain, loss, and lasing in driven semiconductor quantum dots [Phys. Rev. Lett. 113, 036801 (2014), 10.1103/PhysRevLett.113.036801; Science 347, 285 (2015), 10.1126/science.aaa2501; Phys. Rev. Lett. 114, 196802 (2015), 10.1103/PhysRevLett.114.196802], we develop a theoretical technique by using Keldysh diagrammatic perturbation theory to derive a Lindblad master equation that goes beyond the usual second-order perturbation theory. We demonstrate the method on the driven dissipative Rabi model, including terms up to fourth order in the interaction between the qubit and both the resonator and environment. This results in a large class of Lindblad dissipators and associated rates which go beyond the terms that have previously been proposed to describe similar systems. All of the additional terms contribute to the system behavior at the same order of perturbation theory. We then apply these results to analyze the phonon-assisted steady-state gain of a microwave field driving a double quantum dot in a resonator. We show that resonator gain and loss are substantially affected by dephasing-assisted dissipative processes in the quantum-dot system. These additional processes, which go beyond recently proposed polaronic theories, are in good quantitative agreement with experimental observations.
Acoustic equations for a gas stream in rigid-body rotation
NASA Astrophysics Data System (ADS)
Garcia-Ybarra, Pedro L.; Marin-Antuña, Jose M.
2017-02-01
The classical topic of wave propagation in a rotating gas is revisited by deducing scalar wave equations for propagation of acoustic and rotational waves through a plug flow of gas in rigid-body rotation with arbitrary intensities of the radial stratification. In the light of these novel equations, wave propagation is analyzed in two different base gas states: isothermal and homentropic. In both cases, previous findings are recovered that assess the validity of the equations and new results are established. In the non-homentropic but isothermal case, the set of governing equations is reduced to two coupled scalar wave equations with space dependent coefficients for the disturbances of density and pressure. Travelling wave solutions with variable amplitude have been obtained in the limit of weak stratification both for inertial waves as for acoustic waves which, in general, propagate on different frequency bands that overlap in the small wavenumber region. Furthermore, the entropy stratification in the base state is stable and compels the propagation of internal waves, leading to hybrid acoustic-inertial-vortical modes. In the homentropic case, the adiabatic relation between pressure and density disturbances allows to reduce further the governing equations to a single fourth-order scalar wave equation. In this case, the sound propagation velocity depends on the distance to the rotation axis and solutions are found by multiple-scale analyses in the form of waves with slowly varying amplitude and wavenumber. The corresponding eikonal equation shows that acoustic rays are refracted towards the rotation axis, propagating and spinning along and around it. In that way, the swirling gas behaves as an axial waveguide trapping inside any acoustic ray propagating in the vortex with large enough azimuthal and/or vertical wavenumber component.
A novel unsplit perfectly matched layer for the second-order acoustic wave equation.
Ma, Youneng; Yu, Jinhua; Wang, Yuanyuan
2014-08-01
When solving acoustic field equations by using numerical approximation technique, absorbing boundary conditions (ABCs) are widely used to truncate the simulation to a finite space. The perfectly matched layer (PML) technique has exhibited excellent absorbing efficiency as an ABC for the acoustic wave equation formulated as a first-order system. However, as the PML was originally designed for the first-order equation system, it cannot be applied to the second-order equation system directly. In this article, we aim to extend the unsplit PML to the second-order equation system. We developed an efficient unsplit implementation of PML for the second-order acoustic wave equation based on an auxiliary-differential-equation (ADE) scheme. The proposed method can benefit to the use of PML in simulations based on second-order equations. Compared with the existing PMLs, it has simpler implementation and requires less extra storage. Numerical results from finite-difference time-domain models are provided to illustrate the validity of the approach.
Perturbative solution to the Lane-Emden equation: an eigenvalue approach
NASA Astrophysics Data System (ADS)
Yip, Kenny L. S.; Chan, T. K.; Leung, P. T.
2017-03-01
Under suitable scaling, the structure of self-gravitating polytropes is described by the standard Lane-Emden equation (LEE), which is characterized by the polytropic index n. Here, we use the known exact solutions of the LEE at n = 0 and n = 1 to solve the equation perturbatively. We first introduce a scaled LEE (SLEE) where polytropes with different polytropic indices all share a common scaled radius. The SLEE is then solved perturbatively as an eigenvalue problem. Analytical approximants of the polytrope function, the radius and the mass of polytropes as a function of n are derived. The approximant of the polytrope function is well defined and uniformly accurate from the origin down to the surface of a polytrope. The percentage errors of the radius and the mass are bounded by 8.1 × 10-7 per cent and 8.5 × 10-5 per cent, respectively, for n ∈ [0, 1]. Even for n ∈ [1, 5), both percentage errors are still less than 2 per cent.
Generalization and extension of the law of acoustic energy conservation in a nonuniform flow
NASA Technical Reports Server (NTRS)
Myers, M. K.
1986-01-01
An exact conservation equation is derived which generalizes the familiar acoustic energy equations. The new relation is valid for arbitrary disturbances to a viscous, compressible flow. It is suggested by a development of the acoustic energy equation by means of a regular perturbation expansion of the general energy equation of fluid mechanics. A perturbation energy density and flux are defined and identified as the exact physical quantities whose leading order perturbation representations are the usual acoustic energy density and flux. The conservation equation governing the perturbation energy quantities is shown to yield previously known results for several special cases.
NASA Astrophysics Data System (ADS)
Shinohara, M.; Kikuchi, T.; Nozaki, K.; Yumoto, K.
2002-12-01
Ionospheric electric field perturbations associated with a sudden commencement at 1640 UT Apr. 6, 2000 were observed by the FM-CW HF radar at the dip equator station Cebu, Philippine. Ionograms were obtained from the FM-CW HF radar at intervals of 5 minutes. The zonal electric field can be estimated from the time variation of the height profile of ionograms. A sudden increase in the westward electric field of 1.6 mV/m was observed simultaneously with the sudden increases in the H component magnetic field of 250 and 110 nT at the dayside dip equatorial station Ancon, Peru and the dayside off dip equatorial station Eusebio, Brazil, respectively. The amplitude enhancement of the magnetic variation at the dip equator suggest that an eastward electric field was imposed at the dayside equatorial ionosphere. Both the dayside and nightside electric field perturbations show that the dawn to dusk electric field of DP(MI) was imposed globally on the equatorial ionosphere. The HF Doppler frequency shift was observed at the nightside low latitude station Sugadaira, Japan. From the frequency deviation, it is found that a westward electric field of 2.0 mV/m was suddenly imposed at the beginning of the sc. The amplitude of the westward electric field observed at the nightside equator is 0.8 times that at the nightside low latitude station. It can be caused by the geometrical attenuation [Kikuchi et al., 1978, Nature]. The direction of the zonal electric field observed at Cebu was reversed from westward to eastward and returned westward again. The electric field at Sugardaira shows similar temporal variations. These variations were well correlated with fluctuations of solar wind number density. The eastward electric field may be caused by the over shielding effect of the region 2 field-aligned current [Kikuchi et al., 2000, JGR]. Acknowledgement. The HF Doppler data was provided by Sugadaira Space Radio Observatory, Univ. Electro-Comm.
Frenkel, A L; Indireshkumar, K
1999-10-01
Wavy film flow of incompressible Newtonian fluid down an inclined plane is considered. The question is posed as to the parametric conditions under which the description of evolution can be approximately reduced for all time to a single evolution equation for the film thickness. An unconventional perturbation approach yields the most general evolution equation and least restrictive conditions on its validity. The advantages of this equation for analytical and numerical studies of three-dimensional waves in inclined films are pointed out.
Eu, Byung Chan; Qin, Yuan
2007-04-12
We calculate the generic van der Waals parameters A and B for a square well model by means of a perturbation theory. To calculate the pair distribution function or the cavity function necessary for the calculation of A and B, we have used the Percus-Yevick integral equation, which is put into an equivalent form by means of the Wiener-Hopf method. This latter method produces a pair of integral equations, which are solved by a perturbation method treating the Mayer function or the well width or the functions in the square well region exterior to the hard core as the perturbation. In the end, the Mayer function times the well width is identified as the perturbation parameter in the present method. In this sense, the present perturbation method is distinct from the existing thermodynamic perturbation theory, which expands the Helmholtz free energy in a perturbation series with the inverse temperature treated as an expansion parameter. The generic van der Waals parameters are explicitly calculated in analytic form as functions of reduced temperature and density. The van der Waals parameters are recovered from them in the limits of vanishing density and high temperature. The equation of state thus obtained is tested against Monte Carlo simulation results and found reliable, provided that the temperature is in the supercritical regime. By scaling the packing fraction with a temperature-dependent hard core, it is suggested to construct an equation of state for fluids with a temperature-dependent hard core that mimicks a soft core repulsive force on the basis of the equation of state derived for the square well model.
Matching Pion-Nucleon Roy-Steiner Equations to Chiral Perturbation Theory
NASA Astrophysics Data System (ADS)
Hoferichter, Martin; Ruiz de Elvira, Jacobo; Kubis, Bastian; Meißner, Ulf-G.
2015-11-01
We match the results for the subthreshold parameters of pion-nucleon scattering obtained from a solution of Roy-Steiner equations to chiral perturbation theory up to next-to-next-to-next-to-leading order, to extract the pertinent low-energy constants including a comprehensive analysis of systematic uncertainties and correlations. We study the convergence of the chiral series by investigating the chiral expansion of threshold parameters up to the same order and discuss the role of the Δ (1232 ) resonance in this context. Results for the low-energy constants are also presented in the counting scheme usually applied in chiral nuclear effective field theory, where they serve as crucial input to determine the long-range part of the nucleon-nucleon potential as well as three-nucleon forces.
Perturbative solutions of the Ginzburg-Landau equation and the superconducting parameters
Rezlescu, N.; Agop, M.; Buzea, C.; Buzea, C.G.
1996-02-01
Using the modulus-{ital s} of the elliptic function sn({theta},{ital s}) as a parameter of nonlinearity we construct the perturbative solutions of the Ginzburg-Landau equation in the presence of spatial gradients. The resulted analytical expressions describe the temperature dependence of the superconducting parameters, except the {ital s}{r_arrow}1 limit. The analytical expressions which led to the temperature dependence of the superconducting parameters as the coherence length {xi}({ital t}), the superconducting charge carriers concentration {ital n}{sub {ital s}}({ital t}), the penetration depth {lambda}({ital t}), and the thermodynamic critical field {ital H}{sub {ital c}}({ital t}) are found. {copyright} {ital 1996 The American Physical Society.}
On the equation-of-motion versus in-in approach in cosmological perturbation theory
NASA Astrophysics Data System (ADS)
Chen, Xingang; Namjoo, Mohammad Hossein; Wang, Yi
2016-01-01
In this paper, we study several issues in the linear equation-of-motion (EoM) and in-in approaches of computing the two-point correlation functions in multi-field inflation. We prove the equivalence between this EoM approach and the first-principle in-in formalism. We check this equivalence using several explicit examples, including cases with scale-invariant corrections and scale-dependent features. Motivated by the explicit proof, we show that the usual procedures in these approaches can be extended and applied to some interesting model categories beyond what has been studied in the literature so far. These include the density perturbations with strong couplings and correlated multi-field initial states.
NASA Astrophysics Data System (ADS)
Shishkin, G. I.; Shishkina, L. P.
2015-03-01
An initial-boundary value problem is considered for a singularly perturbed parabolic reaction-diffusion equation. For this problem, a technique is developed for constructing higher order accurate difference schemes that converge ɛ-uniformly in the maximum norm (where ɛ is the perturbation parameter multiplying the highest order derivative, ɛ ∈ (0, 1]). A solution decomposition scheme is described in which the grid subproblems for the regular and singular solution components are considered on uniform meshes. The Richardson technique is used to construct a higher order accurate solution decomposition scheme whose solution converges ɛ-uniformly in the maximum norm at a rate of [InlineMediaObject not available: see fulltext.], where N + 1 and N 0 + 1 are the numbers of nodes in uniform meshes in x and t, respectively. Also, a new numerical-analytical Richardson scheme for the solution decomposition method is developed. Relying on the approach proposed, improved difference schemes can be constructed by applying the solution decomposition method and the Richardson extrapolation method when the number of embedded grids is more than two. These schemes converge ɛ-uniformly with an order close to the sixth in x and equal to the third in t.
NASA Astrophysics Data System (ADS)
Shishkin, G. I.; Shishkina, L. P.
2010-12-01
For the one-dimensional singularly perturbed parabolic reaction-diffusion equation with a perturbation parameter ɛ, where ɛ ∈ (0, 1], the grid approximation of the Dirichlet problem on a rectangular domain in the ( x, t)-plane is examined. For small ɛ, a parabolic boundary layer emerges in a neighborhood of the lateral part of the boundary of this domain. A new approach to the construction of ɛ-uniformly converging difference schemes of higher accuracy is developed for initial boundary value problems. The asymptotic construction technique is used to design the base decomposition scheme within which the regular and singular components of the grid solution are solutions to grid subproblems defined on uniform grids. The base scheme converges ɛ-uniformly in the maximum norm at the rate of O( N -2ln2 N + N {0/-1}), where N + 1 and N 0 + 1 are the numbers of nodes in the space and time meshes, respectively. An application of the Richardson extrapolation technique to the base scheme yields a higher order scheme called the Richardson decomposition scheme. This higher order scheme convergesɛ-uniformly at the rate of O( N -4ln4 N + N {0/-2}). For fixed values of the parameter, the convergence rate is O( N -4 + N {0/-2}).
NASA Astrophysics Data System (ADS)
Liang, Yujin; Sun, Changsen; Ansari, Farhad
2005-05-01
Damage location and damage state identification of a hybrid Carbon-glass FRP rod was performed by means of a serially multiplexed fiber optic acoustic emission sensor. The detection and identification of acoustic emission signals along a single data stream reduces the data acquisition rigor and provides for rapid real time damage location detection in materials. Linear source location method and signature frequency spectra energy of acoustic emission signals were employed for locating the fiber breakage and distinguishing the damage state in the hybrid FRP rod, respectively.
NASA Astrophysics Data System (ADS)
Mohamed, Firdawati binti; Karim, Mohamad Faisal bin Abd
2015-10-01
Modelling physical problems in mathematical form yields the governing equations that may be linear or nonlinear for known and unknown boundaries. The exact solution for those equations may or may not be obtained easily. Hence we seek an analytical approximation solution in terms of asymptotic expansion. In this study, we focus on a singular perturbation in second order ordinary differential equations. Solutions to several perturbed ordinary differential equations are obtained in terms of asymptotic expansion. The aim of this work is to find an approximate analytical solution using the classical method of matched asymptotic expansion (MMAE). The Mathematica computer algebra system is used to perform the algebraic computations. The details procedures will be discussed and the underlying concepts and principles of the MMAE will be clarified. Perturbation problem for linear equation that occurs at one boundary and two boundary layers are discussed. Approximate analytical solution obtained for both cases are illustrated by graph using selected parameter by showing the outer, inner and composite solution separately. Then, the composite solution will be compare to the exact solution to show their accuracy by graph. By comparison, MMAE is found to be one of the best methods to solve singular perturbation problems in second order ordinary differential equation since the results obtained are very close to the exact solution.
Massopust, P.R.
1997-08-01
All solutions of an in its angular coordinates continuously perturbed Laplace-Beltrami equation in the open unit ball IB{sup n+2} {contained_in} IR{sup n+2}, n {ge} 1, are characterized. Moreover, it is shown that such pertubations yield distributional boundary values which are different from, but algebraically and topologically equivalent to, the hyperfunctions of Lions & Magenes. This is different from the case of radially perturbed Laplace-Beltrami operators (cf. [7]) where one has stability of distributional boundary values under such perturbations.
Garcia-Ravelo, J.; Trujillo, A. L.; Schulze-Halberg, A.
2012-10-15
We obtain explicit formulas for perturbative corrections of the infinite quantum well model. The formulas we obtain are based on a class of matrix elements that we construct by means of two-parameter ladder operators associated with the infinite quantum well system. Our approach can be used to construct solutions to Schroedinger-type equations that involve generalized harmonic perturbations of their potentials, such as cosine powers, Fourier series, and more general functions. As a particular case, we obtain characteristic values for odd periodic solutions of the Mathieu equation.
1981-01-08
as it propagates over a small interval, and then to correct for absorption. Another nonlinear wave equation of great interest is the Korteweg - DeVries ...acoustics are described by the second-order-nonlinear wave equation , which is derived in this thesis and solved by numerical means. the validity of the...no approximations are made in the second-order-nonlinear acoustic wave equation as it is solved . This represents an advance on the prior art, in which
An Acoustic Wave Equation for Tilted Transversely Isotropic Media
Zhang, Linbin; Rector III, James W.; Hoversten, G. Michael
2005-03-15
A finite-difference method for computing the first arrival traveltimes by solving the Eikonal equation in the celerity domain has been developed. This algorithm incorporates the head and diffraction wave. We also adapt a fast sweeping method, which is extremely simple to implement in any number of dimensions, to obtain accurate first arrival times in complex velocity models. The method, which is stable and computationally efficient, can handle instabilities due to caustics and provide head waves traveltimes. Numerical examples demonstrate that the celerity-domain Eikonal solver provides accurate first arrival traveltimes. This new method is three times accurate more than the 2nd-order fast marching method in a linear velocity model with the same spacing.
NASA Astrophysics Data System (ADS)
Naka, Yusuke
Many acoustical events in our everyday lives occur in enclosures, in which echoes and reverberation impact auditory perception in many ways. Numerical models play an important role in analyzing the acoustic behavior in reverberant environments, as they allow systematic control of physical parameters that affect human perception. Most numerical models used in architectural and room acoustics are based on the ray acoustics approximation, which leads to reasonable computational costs, at the expense of excluding certain important wave phenomena such as diffraction. In order to obtain more accurate results, an approach based on solving the wave equation is appropriate. However, standard numerical methods for solving the wave equation are not practical for room acoustics applications, since these problems are acoustically large and incur prohibitively large computational costs. Even in a small room, a sound wave with audible high-frequency content must propagate for about 10,000 wavelengths before it decays to an inaudible level. To address this, three new, efficient ways of simulating acoustic responses in a room are developed in this study. First, a method for calculating the resonant frequencies and normal modes in a rectangular room with arbitrary wall impedance is developed that uses the interval Newton/generalized bisection (IN/GB) method for solving the acoustic eigenvalue equation. The second approach applies the finite element method in the frequency domain, but uses a Dirichlet-to-Neumann (DtN) map to model empty, rectangular portions of the room, thereby truncating the effective computational domain. Finally, a finite difference method with minimal dispersion and dissipation errors is developed in the time domain. The parameters in the discretization in both space and time are optimized to minimize these errors. This method has been implemented on the IBM Blue Gene platform at Boston University, and allows for the calculation of the impulse response in a
Perfectly matched layer for an elastic parabolic equation model in ocean acoustics
NASA Astrophysics Data System (ADS)
Xu, Chuanxiu; Zhang, Haigang; Piao, Shengchun; Yang, Shi'e.; Sun, Sipeng; Tang, Jun
2017-02-01
The perfectly matched layer (PML) is an effective technique for truncating unbounded domains with minimal spurious reflections. A fluid parabolic equation (PE) model applying PML technique was previously used to analyze the sound propagation problem in a range-dependent waveguide (Lu and Zhu, 2007). However, Lu and Zhu only considered a standard fluid PE to demonstrate the capability of the PML and did not take improved one-way models into consideration. They applied a [1/1] Padé approximant to the parabolic equation. The higher-order PEs are more accurate than standard ones when a very large angle propagation is considered. As for range-dependent problems, the techniques to handle the vertical interface between adjacent regions are mainly energy conserving and single-scattering. In this paper, the PML technique is generalized to the higher order elastic PE, as is to the higher order fluid PE. The correction of energy conserving is used in range-dependent waveguides. Simulation is made in both acoustic cases and seismo-acoustic cases. Range-independent and range-dependent waveguides are both adopted to test the accuracy and efficiency of this method. The numerical results illustrate that a PML is much more effective than an artificial absorbing layer (ABL) both in acoustic and seismo-acoustic sound propagation modeling.
NASA Astrophysics Data System (ADS)
Eskandar, S.; Hoseini, S. M.
2017-04-01
Using soliton perturbation theory, we analytically study weak interaction for a higher-order nonlinear Schrödinger equation. An ansatz consists of two well-separate single solitons is considered and slow variation of solitons parameters are found. Twelve different scenarios for when the initial velocities are zero are observed. A good comparison is found between numerical and analytical results.
ERIC Educational Resources Information Center
Shao, Jun; MacCallum, Julia K.; Zhang, Yu; Sprecher, Alicia; Jiang, Jack J.
2010-01-01
Acoustic analysis may provide a useful means to quantitatively characterize the tremulous voice. Signals were obtained from 25 subjects with diagnoses of either Parkinson's disease or vocal polyps exhibiting vocal tremor. These were compared to signals from 24 subjects with normal voices. Signals were analyzed via correlation dimension and several…
ERIC Educational Resources Information Center
Lee, Victoria S.; Zhou, Xiao Ping; Rahn, Douglas A., III; Wang, Emily Q.; Jiang, Jack J.
2008-01-01
Nineteen PD patients who received deep brain stimulation (DBS), 10 non-surgical (control) PD patients, and 11 non-pathologic age- and gender-matched subjects performed sustained vowel phonations. The following acoustic measures were obtained on the sustained vowel phonations: correlation dimension (D[subscript 2]), percent jitter, percent shimmer,…
On reconstruction of acoustic pressure fields using the Helmholtz equation least squares method
Wu
2000-05-01
This paper presents analyses and implementation of the reconstruction of acoustic pressure fields radiated from a general, three-dimensional complex vibrating structure using the Helmholtz equation least-squares (HELS) method. The structure under consideration emulates a full-size four-cylinder engine. To simulate sound radiation from a vibrating structure, harmonic excitations are assumed to act on arbitrarily selected surfaces. The resulting vibration responses are solved by the commercial FEM (finite element method) software I-DEAS. Once the normal component of the surface velocity distribution is determined, the surface acoustic pressures are calculated using standard boundary element method (BEM) codes. The radiated acoustic pressures over several planar surfaces at certain distances from the source are calculated by the Helmholtz integral formulation. These field pressures are taken as the input to the HELS formulation to reconstruct acoustic pressures on the entire source surface, as well as in the field. The reconstructed acoustic pressures thus obtained are then compared with benchmark values. Numerical results demonstrate that good agreements can be obtained with relatively few expansion functions. The HELS method is shown to be very effective in the low-to-mid frequency regime, and can potentially become a powerful noise diagnostic tool.
Qi, Xin; Xu, Yan-xia; Duan, Wen-shan; Yang, Lei
2014-01-15
The dust acoustic solitary waves have been numerically investigated by using one dimensional electrostatic particle-in-cell method. By comparing the numerical results with those obtained from the traditional reductive perturbation method, it is found that there exist the maximum dimensionless amplitude and propagation speed of the dust acoustic solitary wave. And these limitations of the solitary wave are explained by using the Sagdeev potential technique. Furthermore, it is noticed that although ϵ ≪ 1 is required in the reductive perturbation method generally, the reductive perturbation method is also valid for ϵ < 1 in a dusty plasma, which may be extended to branches where the reductive perturbation method is used.
Geodesic acoustic mode in anisotropic plasmas using double adiabatic model and gyro-kinetic equation
Ren, Haijun; Cao, Jintao
2014-12-15
Geodesic acoustic mode in anisotropic tokamak plasmas is theoretically analyzed by using double adiabatic model and gyro-kinetic equation. The bi-Maxwellian distribution function for guiding-center ions is assumed to obtain a self-consistent form, yielding pressures satisfying the magnetohydrodynamic (MHD) anisotropic equilibrium condition. The double adiabatic model gives the dispersion relation of geodesic acoustic mode (GAM), which agrees well with the one derived from gyro-kinetic equation. The GAM frequency increases with the ratio of pressures, p{sub ⊥}/p{sub ∥}, and the Landau damping rate is dramatically decreased by p{sub ⊥}/p{sub ∥}. MHD result shows a low-frequency zonal flow existing for all p{sub ⊥}/p{sub ∥}, while according to the kinetic dispersion relation, no low-frequency branch exists for p{sub ⊥}/p{sub ∥}≳ 2.
Acoustic Field Associated with Parabolized Stability Equation Models in Turbulent Jets
2013-05-01
discusses linear models of these wavepackets for supersonic turbulent jets based on Parabolized Stability Equations ( PSE ). In the past, results of...comparisons of the PSE models with near-field pressure fields from LES, filtered by means of Proper Orthogonal Decomposition (POD), demonstrate acceptable...fidelity of the model. Finally, the acoustic far-field associated with the PSE wavepackets is computed using a Kirchhoff surface method, capturing
Ghosh, Debashree
2014-03-07
Hybrid quantum mechanics/molecular mechanics (QM/MM) methods provide an attractive way to closely retain the accuracy of the QM method with the favorable computational scaling of the MM method. Therefore, it is not surprising that QM/MM methods are being increasingly used for large chemical/biological systems. Hybrid equation of motion coupled cluster singles doubles/effective fragment potential (EOM-CCSD/EFP) methods have been developed over the last few years to understand the effect of solvents and other condensed phases on the electronic spectra of chromophores. However, the computational cost of this approach is still dominated by the steep scaling of the EOM-CCSD method. In this work, we propose and implement perturbative approximations to the EOM-CCSD method in this hybrid scheme to reduce the cost of EOM-CCSD/EFP. The timings and accuracy of this hybrid approach is tested for calculation of ionization energies, excitation energies, and electron affinities of microsolvated nucleic acid bases (thymine and cytosine), phenol, and phenolate.
Eshkuvatov, Z K; Zulkarnain, F S; Nik Long, N M A; Muminov, Z
2016-01-01
Modified homotopy perturbation method (HPM) was used to solve the hypersingular integral equations (HSIEs) of the first kind on the interval [-1,1] with the assumption that the kernel of the hypersingular integral is constant on the diagonal of the domain. Existence of inverse of hypersingular integral operator leads to the convergence of HPM in certain cases. Modified HPM and its norm convergence are obtained in Hilbert space. Comparisons between modified HPM, standard HPM, Bernstein polynomials approach Mandal and Bhattacharya (Appl Math Comput 190:1707-1716, 2007), Chebyshev expansion method Mahiub et al. (Int J Pure Appl Math 69(3):265-274, 2011) and reproducing kernel Chen and Zhou (Appl Math Lett 24:636-641, 2011) are made by solving five examples. Theoretical and practical examples revealed that the modified HPM dominates the standard HPM and others. Finally, it is found that the modified HPM is exact, if the solution of the problem is a product of weights and polynomial functions. For rational solution the absolute error decreases very fast by increasing the number of collocation points.
NASA Astrophysics Data System (ADS)
Butuzov, V. F.
2016-08-01
Asymptotic formulae for the solution of the initial-boundary value problem for a singularly perturbed partially dissipative system of reaction-diffusion type are constructed and justified. The system consists of a parabolic and an ordinary differential equation in the case when the corresponding degenerate equation has a root of multiplicity two. The behaviour of the boundary layer functions and the algorithm for constructing them are significantly distinct from the case of a simple (multiplicity-one) root of the degenerate equation. Bibliography: 8 titles.
Evolution of higher order nonlinear equation for the dust ion-acoustic waves in nonextensive plasma
Yasmin, S.; Asaduzzaman, M.; Mamun, A. A.
2012-10-15
There are three different types of nonlinear equations, namely, Korteweg-de Vries (K-dV), modified K-dV (mK-dV), and mixed modified K-dV (mixed mK-dV) equations, for the nonlinear propagation of the dust ion-acoustic (DIA) waves. The effects of electron nonextensivity on DIA solitary waves propagating in a dusty plasma (containing negatively charged stationary dust, inertial ions, and nonextensive q distributed electrons) are examined by solving these nonlinear equations. The basic features of mixed mK-dV (higher order nonlinear equation) solitons are found to exist beyond the K-dV limit. The properties of mK-dV solitons are compared with those of mixed mK-dV solitons. It is found that both positive and negative solitons are obtained depending on the q (nonextensive parameter).
NASA Astrophysics Data System (ADS)
Müller, Mathias C. T. D.; Friedrich, Christoph; Blügel, Stefan
2016-08-01
Collective spin excitations in magnetic materials arise from the correlated motion of electron-hole pairs with opposite spins. The pair propagation is described by the transverse magnetic susceptibility, which we calculate within many-body perturbation theory from first principles employing the full-potential linearized augmented-plane-wave formalism. Ferromagnetic materials exhibit a spontaneously broken global rotation symmetry in spin space leading to the appearance of acoustic magnons (zero gap) in the long-wavelength limit. However, due to approximations used in the numerical scheme, the acoustic magnon dispersion exhibits a small but finite gap at Γ . We analyze this violation of the Goldstone mode and present an approach that implements the magnetic susceptibility using a renormalized Green function instead of the Kohn-Sham one. This much more expensive approach shows substantial improvement of the Goldstone-mode condition. In addition, we discuss a possible correction scheme, which involves an adjustment of the Kohn-Sham exchange splitting, which is motivated by the spin-wave solution of the one-band Hubbard model. The new exchange splittings turn out to be closer to experiment. We present corrected magnon spectra for the elementary ferromagnets Fe, Co, and Ni.
Acoustic wave and eikonal equations in a transformed metric space for various types of anisotropy.
Noack, Marcus M; Clark, Stuart
2017-03-01
Acoustic waves propagating in anisotropic media are important for various applications. Even though these wave phenomena do not generally occur in nature, they can be used to approximate wave motion in various physical settings. We propose a method to derive wave equations for anisotropic wave propagation by adjusting the dispersion relation according to a selected type of anisotropy and transforming it into another metric space. The proposed method allows for the derivation of acoustic wave and eikonal equations for various types of anisotropy, and generalizes anisotropy by interpreting it as a change of the metric instead of a change of velocity with direction. The presented method reduces the scope of acoustic anisotropy to a selection of a velocity or slowness surface and a tensor that describes the transformation into a new metric space. Experiments are shown for spatially dependent ellipsoidal anisotropy in homogeneous and inhomogeneous media and sandstone, which shows vertical transverse isotropy. The results demonstrate the stability and simplicity of the solution process for certain types of anisotropy and the equivalency of the solutions.
Elastic parabolic equation solutions for underwater acoustic problems using seismic sources.
Frank, Scott D; Odom, Robert I; Collis, Jon M
2013-03-01
Several problems of current interest involve elastic bottom range-dependent ocean environments with buried or earthquake-type sources, specifically oceanic T-wave propagation studies and interface wave related analyses. Additionally, observed deep shadow-zone arrivals are not predicted by ray theoretic methods, and attempts to model them with fluid-bottom parabolic equation solutions suggest that it may be necessary to account for elastic bottom interactions. In order to study energy conversion between elastic and acoustic waves, current elastic parabolic equation solutions must be modified to allow for seismic starting fields for underwater acoustic propagation environments. Two types of elastic self-starter are presented. An explosive-type source is implemented using a compressional self-starter and the resulting acoustic field is consistent with benchmark solutions. A shear wave self-starter is implemented and shown to generate transmission loss levels consistent with the explosive source. Source fields can be combined to generate starting fields for source types such as explosions, earthquakes, or pile driving. Examples demonstrate the use of source fields for shallow sources or deep ocean-bottom earthquake sources, where down slope conversion, a known T-wave generation mechanism, is modeled. Self-starters are interpreted in the context of the seismic moment tensor.
NASA Astrophysics Data System (ADS)
Natarajan, Logesh Kumar
This dissertation presents a structure-borne noise analysis technology that is focused on providing a cost-effective noise reduction strategy. Structure-borne sound is generated or transmitted through structural vibration; however, only a small portion of the vibration can effectively produce sound and radiate it to the far-field. Therefore, cost-effective noise reduction is reliant on identifying and suppressing the critical vibration components that are directly responsible for an undesired sound. However, current technologies cannot successfully identify these critical vibration components from the point of view of direct contribution to sound radiation and hence cannot guarantee the best cost-effective noise reduction. The technology developed here provides a strategy towards identifying the critical vibration components and methodically suppressing them to achieve a cost-effective noise reduction. The core of this technology is Helmholtz equation least squares (HELS) based nearfield acoustic holography method. In this study, the HELS formulations derived in spherical co-ordinates using spherical wave expansion functions utilize the input data of acoustic pressures measured in the nearfield of a vibrating object to reconstruct the vibro-acoustic responses on the source surface and acoustic quantities in the far field. Using these formulations, three steps were taken to achieve the goal. First, hybrid regularization techniques were developed to improve the reconstruction accuracy of normal surface velocity of the original HELS method. Second, correlations between the surface vibro-acoustic responses and acoustic radiation were factorized using singular value decomposition to obtain orthogonal basis known here as the forced vibro-acoustic components (F-VACs). The F-VACs enables one to identify the critical vibration components for sound radiation in a similar manner that modal decomposition identifies the critical natural modes in a structural vibration. Finally
Perturbation Selection and Local Influence Analysis for Nonlinear Structural Equation Model
ERIC Educational Resources Information Center
Chen, Fei; Zhu, Hong-Tu; Lee, Sik-Yum
2009-01-01
Local influence analysis is an important statistical method for studying the sensitivity of a proposed model to model inputs. One of its important issues is related to the appropriate choice of a perturbation vector. In this paper, we develop a general method to select an appropriate perturbation vector and a second-order local influence measure…
NASA Astrophysics Data System (ADS)
Gogoi, R.; Kalita, L.; Devi, N.
2010-02-01
Much interest was shown towards the studies on nonlinear stability in the late sixties. Plasma instabilities play an important role in plasma dynamics. More attention has been given towards stability analysis after recognizing that they are one of the principal obstacles in the way of a successful resolution of the problem of controlled thermonuclear fusion. Nonlinearity and dispersion are the two important characteristics of plasma instabilities. Instabilities and nonlinearity are the two important and interrelated terms. In our present work, the continuity and momentum equations for both ions and electrons together with the Poisson equation are considered as cold plasma model. Then we have adopted the modified reductive perturbation technique (MRPT) from Demiray [1] to derive the higher order equation of the Nonlinear Schrödinger equation (NLSE). In this work, detailed mathematical expressions and calculations are done to investigate the changing character of the modulation of ion acoustic plasma wave through our derived equation. Thus we have extended the application of MRPT to derive the higher order equation. Both progressive wave solutions as well as steady state solutions are derived and they are plotted for different plasma parameters to observe dark/bright solitons. Interesting structures are found to exist for different plasma parameters.
MacCallum, Julia K.; Zhang, Yu; Jiang, Jack J.
2009-01-01
Acoustic analysis may provide a useful means to quantitatively characterize the tremulous voice. Signals were obtained from 25 subjects with diagnoses of either Parkinson's disease or vocal polyps exhibiting vocal tremor. These were compared to signals from 24 subjects with normal voices. Signals were analyzed via correlation dimension and several parameters from the Multi-Dimensional Voice Program (MDVP): percent jitter, percent shimmer, amplitude tremor intensity index (ATRI), frequency tremor intensity index (FTRI), amplitude tremor frequency (Fatr), and fundamental frequency tremor frequency (Fftr). No significant difference was found between the tremor and control groups for ATRI and Fatr. Percent jitter, percent shimmer, FTRI, Fftr, and correlation dimension values were found to be significantly higher in the tremor group than in the control group. We conclude that these parameters may have utility for the clinical quantification of tremor severity and treatment effects. PMID:19909966
NASA Astrophysics Data System (ADS)
Rafat, A.; Rahman, M. M.; Alam, M. S.; Mamun, A. A.
2015-07-01
A precise theoretical investigation has been made on electron-acoustic (EA) Gardner solitons (GSs) and double layers (DLs) in a four-component plasma system consisting of nonextensive hot electrons and positrons, inertial cold electrons, and immobile positive ions. The well-known reductive perturbation method has been used to derive the Korteweg-de Vries (K-dV), modified K-dV (mK-dV), and Gardner equations along with their solitary wave as well as double layer solutions. It has been found that depending on the plasma parameters, the K-dV solitons and GSs are either compressive or rarefactive, whereas the mK-dV solitons are only compressive, and Gardner DLs are only rarefactive. The analytical comparison among the K-dV solitons, mK-dV solitons, and GSs are also investigated. It has been identified that the basic properties of such EA solitons and EA DLs are significantly modified due to the effects of nonextensivity and other plasma parameters related to plasma particle number densities and to temperature of different plasma species. The results of our present investigation can be helpful for understanding the nonlinear electrostatic structures associated with EA waves in various interstellar space plasma environments and cosmological scenarios (viz. quark-gluon plasma, protoneutron stars, stellar polytropes, hadronic matter, dark-matter halos, etc.)
Yan, Zai You; Hung, Kin Chew; Zheng, Hui
2003-05-01
Regularization of the hypersingular integral in the normal derivative of the conventional Helmholtz integral equation through a double surface integral method or regularization relationship has been studied. By introducing the new concept of discretized operator matrix, evaluation of the double surface integrals is reduced to calculate the product of two discretized operator matrices. Such a treatment greatly improves the computational efficiency. As the number of frequencies to be computed increases, the computational cost of solving the composite Helmholtz integral equation is comparable to that of solving the conventional Helmholtz integral equation. In this paper, the detailed formulation of the proposed regularization method is presented. The computational efficiency and accuracy of the regularization method are demonstrated for a general class of acoustic radiation and scattering problems. The radiation of a pulsating sphere, an oscillating sphere, and a rigid sphere insonified by a plane acoustic wave are solved using the new method with curvilinear quadrilateral isoparametric elements. It is found that the numerical results rapidly converge to the corresponding analytical solutions as finer meshes are applied.
NASA Astrophysics Data System (ADS)
Yin, J. L.; Xing, Q. Q.; Tian, L. X.
2015-03-01
The behavior of non-smooth solitary waves switching to chaos is studied. Firstly, we present some singular homoclinic orbits of an unperturbed system. These singular homoclinic orbits correspond to non-smooth solutions. Secondly, we find that the peculiar solitary waves are more likely to be chaos by using the Melnikov theory. Finally, chaos thresholds under different amplitudes and frequencies of a periodic perturbation are given. One interesting finding is that there exists a peculiar perturbation frequency, which has significant effect on the system. The system is not well-controlled under this frequency. However, the system can be well controlled, when the frequency of the perturbation surpasses the peculiar perturbation frequency with fixed parameters of the unperturbed system.
NASA Astrophysics Data System (ADS)
Rumyantseva, O. D.; Shurup, A. S.
2017-01-01
The paper considers the derivation of the wave equation and Helmholtz equation for solving the tomographic problem of reconstruction combined scalar-vector inhomogeneities describing perturbations of the sound velocity and absorption, the vector field of flows, and perturbations of the density of the medium. Restrictive conditions under which the obtained equations are meaningful are analyzed. Results of numerical simulation of the two-dimensional functional-analytical Novikov-Agaltsov algorithm for reconstructing the flow velocity using the the obtained Helmholtz equation are presented.
Heath-Jarrow-Morton-Musiela equation with Lévy perturbation
NASA Astrophysics Data System (ADS)
Barski, Michał; Zabczyk, Jerzy
The paper studies the Heath-Jarrow-Morton-Musiela equation of the bond market. The equation is analyzed in weighted spaces of functions defined on [0,+∞). Sufficient conditions for local and global existence are obtained. For equation with the linear diffusion term the conditions for global existence are close to the necessary ones.
Prieur, Fabrice; Vilenskiy, Gregory; Holm, Sverre
2012-10-01
A corrected derivation of nonlinear wave propagation equations with fractional loss operators is presented. The fundamental approach is based on fractional formulations of the stress-strain and heat flux definitions but uses the energy equation and thermodynamic identities to link density and pressure instead of an erroneous fractional form of the entropy equation as done in Prieur and Holm ["Nonlinear acoustic wave equations with fractional loss operators," J. Acoust. Soc. Am. 130(3), 1125-1132 (2011)]. The loss operator of the obtained nonlinear wave equations differs from the previous derivations as well as the dispersion equation, but when approximating for low frequencies the expressions for the frequency dependent attenuation and velocity dispersion remain unchanged.
Tripathi, Rajnee; Mishra, Hradyesh Kumar
2016-01-01
In this communication, we describe the Homotopy Perturbation Method with Laplace Transform (LT-HPM), which is used to solve the Lane-Emden type differential equations. It's very difficult to solve numerically the Lane-Emden types of the differential equation. Here we implemented this method for two linear homogeneous, two linear nonhomogeneous, and four nonlinear homogeneous Lane-Emden type differential equations and use their appropriate comparisons with exact solutions. In the current study, some examples are better than other existing methods with their nearer results in the form of power series. The Laplace transform used to accelerate the convergence of power series and the results are shown in the tables and graphs which have good agreement with the other existing method in the literature. The results show that LT-HPM is very effective and easy to implement.
Asymptotic Behaviour of the Ground State of Singularly Perturbed Elliptic Equations
NASA Astrophysics Data System (ADS)
Piatnitski, Andrey L.
The ground state of a singularly perturbed nonselfadjoint elliptic operator
NASA Astrophysics Data System (ADS)
Shishkin, G. I.
2013-04-01
For a singularly perturbed parabolic convection-diffusion equation, the conditioning and stability of finite difference schemes on uniform meshes are analyzed. It is shown that a convergent standard monotone finite difference scheme on a uniform mesh is not ɛ-uniformly well conditioned or ɛ-uniformly stable to perturbations of the data of the grid problem (here, ɛ is a perturbation parameter, ɛ ∈ (0, 1]). An alternative finite difference scheme is proposed, namely, a scheme in which the discrete solution is decomposed into regular and singular components that solve grid subproblems considered on uniform meshes. It is shown that this solution decomposition scheme converges ɛ-uniformly in the maximum norm at an O( N -1ln N + N {0/-1}) rate, where N + 1 and N 0 + 1 are the numbers of grid nodes in x and t, respectively. This scheme is ɛ-uniformly well conditioned and ɛ-uniformly stable to perturbations of the data of the grid problem. The condition number of the solution decomposition scheme is of order O(δ-2lnδ-1 + δ{0/-1}); i.e., up to a logarithmic factor, it is the same as that of a classical scheme on uniform meshes in the case of a regular problem. Here, δ = N -1ln N and δ0 = N {0/-1} are the accuracies of the discrete solution in x and t, respectively.
NASA Astrophysics Data System (ADS)
Ledoux, Veerle; van Daele, Marnix
2011-12-01
The piecewise perturbation methods (PPM) have proven to be very efficient for the numerical solution of the linear time-independent Schrödinger equation. The underlying idea is to replace the potential function piecewisely by simpler approximations and then to solve the approximating problem. The accuracy is improved by adding some perturbation corrections. Two types of approximating potentials were considered in the literature, that is piecewise constant and piecewise linear functions, giving rise to the so-called CP methods (CPM) and LP methods (LPM). Piecewise polynomials of higher degree have not been used since the approximating problem is not easy to integrate analytically. As suggested by Ixaru (Comput Phys Commun 177:897-907, 2007), this problem can be circumvented using another perturbative approach to construct an expression for the solution of the approximating problem. In this paper, we show that there is, however, no need to consider PPM based on higher-order polynomials, since these methods are equivalent to the CPM. Also, LPM is equivalent to CPM, although it was sometimes suggested in the literature that an LP method is more suited for problems with strongly varying potentials. We advocate that CP schemes can (and should) be used in all cases, since it forms the most straightforward way of devising PPM and there is no advantage in considering other piecewise polynomial perturbation methods.
The periodic problem for curvature-like equations with asymmetric perturbations
NASA Astrophysics Data System (ADS)
Obersnel, Franco; Omari, Pierpaolo
We discuss existence and multiplicity of solutions of the periodic problem for the curvature-like equation -(u/√{a+u} )=f(t,u) by means of variational techniques in the space of bounded variation functions. As a=0 is allowed, both the prescribed curvature equation and the 1-Laplace equation are considered. We are concerned with the case where the right-hand side f of the equation interacts with the beginning of the spectrum of the 1-Laplace operator with periodic boundary conditions on [0,T], being mainly interested in the situation where ess sup f(t,s) may differ from -ess inf f(t,s).
NASA Astrophysics Data System (ADS)
Hu, Weipeng; Deng, Zichen; Yin, Tingting
2017-01-01
Exploring the dynamic behaviors of the damping nonlinear Schrödinger equation (NLSE) with periodic perturbation is a challenge in the field of nonlinear science, because the numerical approaches available for damping-driven dynamic systems may exhibit the artificial dissipation in different degree. In this paper, based on the generalized multi-symplectic idea, the local energy/momentum loss expressions as well as the approximate symmetric form of the linearly damping NLSE with periodic perturbation are deduced firstly. And then, the local energy/momentum losses are separated from the simulation results of the NLSE with small linear damping rate less than the threshold to insure structure-preserving properties of the scheme. Finally, the breakup process of the multisoliton state is simulated and the bifurcation of the discrete eigenvalues of the associated Zakharov-Shabat spectral problem is obtained to investigate the variation of the velocity as well as the amplitude of the solitons during the splitting process.
NASA Astrophysics Data System (ADS)
Matthews, Devin A.; Gong, Justin Z.; Stanton, John F.
2014-06-01
The derivation of analytic expressions for vibrational and rovibrational constants, for example the anharmonicity constants χij and the vibration-rotation interaction constants α^B_r, from second-order vibrational perturbation theory (VPT2) can be accomplished with pen and paper and some practice. However, the corresponding quantities from fourth-order perturbation theory (VPT4) are considerably more complex, with the only known derivations by hand extensively using many layers of complicated intermediates and for rotational quantities requiring specialization to orthorhombic cases or the form of Watson's reduced Hamiltonian. We present an automatic computer program for generating these expressions with full generality based on the adaptation of an existing numerical program based on the sum-over-states representation of the energy to a computer algebra context. The measures taken to produce well-simplified and factored expressions in an efficient manner are discussed, as well as the framework for automatically checking the correctness of the generated equations.
NASA Astrophysics Data System (ADS)
Pramod Chakravarthy, P.; Nageshwar Rao, R.
2012-01-01
In this paper a modified fourth order Numerov method is presented for singularly perturbed differential-difference equation of mixed type, i.e., containing both terms having a negative shift and terms having positive shift. Similar boundary value problems are associated with expected first exit time problems of the membrane potential in the models for the neuron. To handle the negative and positive shift terms, we construct a special type of mesh, so that the terms containing shift lie on nodal points after discretization. The proposed finite difference method works nicely when the shift parameters are smaller or bigger to perturbation parameter. An extensive amount of computational work has been carried out to demonstrate the proposed method and to show the effect of shift parameters on the boundary layer behavior or oscillatory behavior of the solution of the problem.
Emamuddin, M.; Yasmin, S.; Mamun, A. A.
2013-04-15
The nonlinear propagation of dust-acoustic waves in a dusty plasma whose constituents are negatively charged dust, Maxwellian ions with two distinct temperatures, and electrons following q-nonextensive distribution, is investigated by deriving a number of nonlinear equations, namely, the Korteweg-de-Vries (K-dV), the modified Korteweg-de-Vries (mK-dV), and the Gardner equations. The basic characteristics of the hump (positive potential) and dip (negative potential) shaped dust-acoustic (DA) Gardner solitons are found to exist beyond the K-dV limit. The effects of two temperature ions and electron nonextensivity on the basic features of DA K-dV, mK-dV, and Gardner solitons are also examined. It has been observed that the DA Gardner solitons exhibit negative (positive) solitons for qq{sub c}) (where q{sub c} is the critical value of the nonextensive parameter q). The implications of our results in understanding the localized nonlinear electrostatic perturbations existing in stellar polytropes, quark-gluon plasma, protoneutron stars, etc. (where ions with different temperatures and nonextensive electrons exist) are also briefly addressed.
Radiative transfer of acoustic waves in continuous complex media: Beyond the Helmholtz equation.
Baydoun, Ibrahim; Baresch, Diego; Pierrat, Romain; Derode, Arnaud
2016-11-01
Heterogeneity can be accounted for by a random potential in the wave equation. For acoustic waves in a fluid with fluctuations of both density and compressibility (as well as for electromagnetic waves in a medium with fluctuation of both permittivity and permeability) the random potential entails a scalar and an operator contribution. For simplicity, the latter is usually overlooked in multiple scattering theory: whatever the type of waves, this simplification amounts to considering the Helmholtz equation with a sound speed c depending on position r. In this work, a radiative transfer equation is derived from the wave equation, in order to study energy transport through a multiple scattering medium. In particular, the influence of the operator term on various transport parameters is studied, based on the diagrammatic approach of multiple scattering. Analytical results are obtained for fundamental quantities of transport theory such as the transport mean-free path ℓ^{*}, scattering phase function f, and anisotropy factor g. Discarding the operator term in the wave equation is shown to have a significant impact on f and g, yet limited to the low-frequency regime, i.e., when the correlation length of the disorder ℓ_{c} is smaller than or comparable to the wavelength λ. More surprisingly, discarding the operator part has a significant impact on the transport mean-free path ℓ^{*} whatever the frequency regime. When the scalar and operator terms have identical amplitudes, the discrepancy on the transport mean-free path is around 300% in the low-frequency regime, and still above 30% for ℓ_{c}/λ=10^{3} no matter how weak fluctuations of the disorder are. Analytical results are supported by numerical simulations of the wave equation and Monte Carlo simulations.
Radiative transfer of acoustic waves in continuous complex media: Beyond the Helmholtz equation
NASA Astrophysics Data System (ADS)
Baydoun, Ibrahim; Baresch, Diego; Pierrat, Romain; Derode, Arnaud
2016-11-01
Heterogeneity can be accounted for by a random potential in the wave equation. For acoustic waves in a fluid with fluctuations of both density and compressibility (as well as for electromagnetic waves in a medium with fluctuation of both permittivity and permeability) the random potential entails a scalar and an operator contribution. For simplicity, the latter is usually overlooked in multiple scattering theory: whatever the type of waves, this simplification amounts to considering the Helmholtz equation with a sound speed c depending on position r . In this work, a radiative transfer equation is derived from the wave equation, in order to study energy transport through a multiple scattering medium. In particular, the influence of the operator term on various transport parameters is studied, based on the diagrammatic approach of multiple scattering. Analytical results are obtained for fundamental quantities of transport theory such as the transport mean-free path ℓ*, scattering phase function f , and anisotropy factor g . Discarding the operator term in the wave equation is shown to have a significant impact on f and g , yet limited to the low-frequency regime, i.e., when the correlation length of the disorder ℓc is smaller than or comparable to the wavelength λ . More surprisingly, discarding the operator part has a significant impact on the transport mean-free path ℓ* whatever the frequency regime. When the scalar and operator terms have identical amplitudes, the discrepancy on the transport mean-free path is around 300 % in the low-frequency regime, and still above 30 % for ℓc/λ =103 no matter how weak fluctuations of the disorder are. Analytical results are supported by numerical simulations of the wave equation and Monte Carlo simulations.
NASA Astrophysics Data System (ADS)
Qureshi, Mumnuna A.; Zhong, Johnny; Betouras, Joseph J.; Zagoskin, Alexandre M.
2017-03-01
Theoretical description and simulation of large quantum coherent systems out of equilibrium remains a daunting task. Here we are developing an approach to it based on the Pechukas-Yukawa formalism, which is especially convenient in the case of an adiabatically slow external perturbation, though it is not restricted to adiabatic systems. In this formalism the dynamics of energy levels in an externally perturbed quantum system as a function of the perturbation parameter is mapped on that of a fictitious one-dimensional classical gas of particles with cubic repulsion. Equilibrium statistical mechanics of this Pechukas gas allows us to reproduce the random matrix theory of energy levels. In the present work, we develop the nonequilibrium statistical mechanics of the Pechukas gas, starting with the derivation of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) chain of equations for the appropriate generalized distribution functions. Sets of approximate kinetic equations can be consistently obtained by breaking this chain at a particular point (i.e., approximating all higher-order distribution functions by the products of the lower-order ones). When complemented by the equations for the level occupation numbers and interlevel transition amplitudes, they allow us to describe the nonequilibrium evolution of the quantum state of the system, which can describe better a large quantum coherent system than the currently used approaches. In particular, we find that corrections to the factorized approximation of the distribution function scale as 1 /N , where N is the number of the "Pechukas gas particles" (i.e., energy levels in the system).
NASA Astrophysics Data System (ADS)
O'Riordan, E.; Shishkin, G. I.
2007-09-01
A priori parameter explicit bounds on the solution of singularly perturbed elliptic problems of convection-diffusion type are established. Regular exponential boundary layers can appear in the solution. These bounds on the solutions and its derivatives are obtained using a suitable decomposition of the solution into regular and layer components. By introducing extensions of the coefficients to a larger domain, artificial compatibility conditions are not imposed in the derivation of these decompositions.
Perturbed Equations of Motion for Formation Flight Near the Sun-Earth L2 Point
NASA Technical Reports Server (NTRS)
Segerman, Alan M.; Zedd, Michael F.
2005-01-01
This Memorandum Report consists of a compilation of three individual reports, of increasing complexity, describing investigations of formation flight of spacecraft in the vicinity of the L2 Sun-Earth 1ibration point. The individual reports form the following parts of this compilation: - Introduction to the relative motion of spacecraft about the Sun-Earth L2 Point - Linear and quadratic modelling and solution of the relative motion - Modelling the Perturbations - Elliptical Earth Orbit, Lunar Gravity, Solar Radiation Pressure, Thrusters. The three parts are self-contained, with somewhat, varying notation and terminology. After fair1y significant literature searches: this new work (of Parts 2 and 3) is deemed to be unique because it describes the primary perturbations to the description of relative motion between nearby spacecraft. The effect of the elliptical motion of the Earth about the Sun was verified to be the dominant perturbation to the circular restricted three body problem. Contributions due to lunar gravity and solar radiation pressure are seen to have much smaller effect.
NASA Technical Reports Server (NTRS)
Hu, Fang Q.; Pizzo, Michelle E.; Nark, Douglas M.
2016-01-01
Based on the time domain boundary integral equation formulation of the linear convective wave equation, a computational tool dubbed Time Domain Fast Acoustic Scattering Toolkit (TD-FAST) has recently been under development. The time domain approach has a distinct advantage that the solutions at all frequencies are obtained in a single computation. In this paper, the formulation of the integral equation, as well as its stabilization by the Burton-Miller type reformulation, is extended to cases of a constant mean flow in an arbitrary direction. In addition, a "Source Surface" is also introduced in the formulation that can be employed to encapsulate regions of noise sources and to facilitate coupling with CFD simulations. This is particularly useful for applications where the noise sources are not easily described by analytical source terms. Numerical examples are presented to assess the accuracy of the formulation, including a computation of noise shielding by a thin barrier motivated by recent Historical Baseline F31A31 open rotor noise shielding experiments. Furthermore, spatial resolution requirements of the time domain boundary element method are also assessed using point per wavelength metrics. It is found that, using only constant basis functions and high-order quadrature for surface integration, relative errors of less than 2% may be obtained when the surface spatial resolution is 5 points-per-wavelength (PPW) or 25 points-per-wavelength squared (PPW2).
Helmholtz and parabolic equation solutions to a benchmark problem in ocean acoustics.
Larsson, Elisabeth; Abrahamsson, Leif
2003-05-01
The Helmholtz equation (HE) describes wave propagation in applications such as acoustics and electromagnetics. For realistic problems, solving the HE is often too expensive. Instead, approximations like the parabolic wave equation (PE) are used. For low-frequency shallow-water environments, one persistent problem is to assess the accuracy of the PE model. In this work, a recently developed HE solver that can handle a smoothly varying bathymetry, variable material properties, and layered materials, is used for an investigation of the errors in PE solutions. In the HE solver, a preconditioned Krylov subspace method is applied to the discretized equations. The preconditioner combines domain decomposition and fast transform techniques. A benchmark problem with upslope-downslope propagation over a penetrable lossy seamount is solved. The numerical experiments show that, for the same bathymetry, a soft and slow bottom gives very similar HE and PE solutions, whereas the PE model is far from accurate for a hard and fast bottom. A first attempt to estimate the error is made by computing the relative deviation from the energy balance for the PE solution. This measure gives an indication of the magnitude of the error, but cannot be used as a strict error bound.
Sadovskii, V. M.
2014-11-12
The paper is devoted to the construction of the simplified mathematical model of thermomechanical behavior of a liquid crystal under the influence of weak mechanical and thermal perturbations. This model is based on the nonlinear equations of a micropolar viscoelastic medium with rotating particles. To describe small strains and finite rotations of molecules, the hypothesis of the dependence of potential energy on the volume change, on the angle of relative rotation and on the entropy is used in the framework of the method of internal thermodynamic parameters. The heat conduction process is described taking into account the anisotropy of a material due to the difference in coefficients of thermal conductivity along the axis of orientation of the particles and in the transverse direction. Separate equation for the tangential stress is obtained from the simplified model, which is useful for the analysis of the recently discussed issues of orientational thermoelasticity and resonant excitation of liquid crystals.
NASA Astrophysics Data System (ADS)
Mukherjee, Abhik; Janaki, M. S.; Kundu, Anjan
2015-07-01
A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the corresponding growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.
Mukherjee, Abhik Janaki, M. S. Kundu, Anjan
2015-07-15
A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the corresponding growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.
NASA Technical Reports Server (NTRS)
Grosse, Ralf
1990-01-01
Propagation of sound through the turbulent atmosphere is a statistical problem. The randomness of the refractive index field causes sound pressure fluctuations. Although no general theory to predict sound pressure statistics from given refractive index statistics exists, there are several approximate solutions to the problem. The most common approximation is the parabolic equation method. Results obtained by this method are restricted to small refractive index fluctuations and to small wave lengths. While the first condition is generally met in the atmosphere, it is desirable to overcome the second. A generalization of the parabolic equation method with respect to the small wave length restriction is presented.
NASA Technical Reports Server (NTRS)
Bond, Victor R.; Fraietta, Michael F.
1991-01-01
In 1961, Sperling linearized and regularized the differential equations of motion of the two-body problem by changing the independent variable from time to fictitious time by Sundman's transformation (r = dt/ds) and by embedding the two-body energy integral and the Laplace vector. In 1968, Burdet developed a perturbation theory which was uniformly valid for all types of orbits using a variation of parameters approach on the elements which appeared in Sperling's equations for the two-body solution. In 1973, Bond and Hanssen improved Burdet's set of differential equations by embedding the total energy (which is a constant when the potential function is explicitly dependent upon time.) The Jacobian constant was used as an element to replace the total energy in a reformulation of the differential equations of motion. In the process, another element which is proportional to a component of the angular momentum was introduced. Recently trajectories computed during numerical studies of atmospheric entry from circular orbits and low thrust beginning in near-circular orbits exhibited numerical instability when solved by the method of Bond and Gottlieb (1989) for long time intervals. It was found that this instability was due to secular terms which appear on the righthand sides of the differential equations of some of the elements. In this paper, this instability is removed by the introduction of another vector integral called the delta integral (which replaces the Laplace Vector) and another scalar integral which removes the secular terms. The introduction of these integrals requires a new derivation of the differential equations for most of the elements. For this rederivation, the Lagrange method of variation of parameters is used, making the development more concise. Numerical examples of this improvement are presented.
NASA Astrophysics Data System (ADS)
Belolipetskii, A. A.; Ter-Krikorov, A. M.
2016-11-01
The functional equation f( x,ɛ) = 0 containing a small parameter ɛ and admitting regular and singular degeneracy as ɛ → 0 is considered. By the methods of small parameter, a function x n 0(ɛ) satisfying this equation within a residual error of O(ɛ n+1) is found. A modified Newton's sequence starting from the element x n 0(ɛ) is constructed. The existence of the limit of Newton's sequence is based on the NK theorem proven in this work (a new variant of the proof of the Kantorovich theorem substantiating the convergence of Newton's iterative sequence). The deviation of the limit of Newton's sequence from the initial approximation x n 0(ɛ) has the order of O(ɛ n+1), which proves the asymptotic character of the approximation x n 0(ɛ). The method proposed is implemented in constructing an asymptotic approximation of a system of ordinary differential equations on a finite or infinite time interval with a small parameter multiplying the derivatives, but it can be applied to a wider class of functional equations with a small parameters.
Non-Perturbative, Unitary Quantum-Particle Scattering Amplitudes from Three-Particle Equations
Lindesay, James V
2002-03-19
We here use our non-perturbative, cluster decomposable relativistic scattering formalism to calculate photon-spinor scattering, including the related particle-antiparticle annihilation amplitude. We start from a three-body system in which the unitary pair interactions contain the kinematic possibility of single quantum exchange and the symmetry properties needed to identify and substitute antiparticles for particles. We extract from it unitary two-particle amplitude for quantum-particle scattering. We verify that we have done this correctly by showing that our calculated photon-spinor amplitude reduces in the weak coupling limit to the usual lowest order, manifestly covariant (QED) result with the correct normalization. That we are able to successfully do this directly demonstrates that renormalizability need not be a fundamental requirement for all physically viable models.
Gámez, Francisco
2014-06-21
An extensive generalisation of the discrete perturbation theory for molecular multipolar non-spherical fluids is presented. An analytical expression for the Helmholtz free energy for an equivalent discrete potential is given as a function of density, temperature, and intermolecular parameters with implicit shape and multipolar dependence. By varying the intermolecular parameters through their geometrical and multipolar dependence, a set of molecular fluids are considered and their vapor-liquid phase diagrams are tested against available simulation data. Concretely, multipolar and non-polar Kihara and chainlike fluids are tested and it is found that this theoretical approach is able to reproduce qualitatively and quantitatively well the Monte Carlo data for the selected molecular potentials, except near the critical region.
Thermodynamic of fluids from a general equation of state: The molecular discrete perturbation theory
Gámez, Francisco
2014-06-21
An extensive generalisation of the discrete perturbation theory for molecular multipolar non-spherical fluids is presented. An analytical expression for the Helmholtz free energy for an equivalent discrete potential is given as a function of density, temperature, and intermolecular parameters with implicit shape and multipolar dependence. By varying the intermolecular parameters through their geometrical and multipolar dependence, a set of molecular fluids are considered and their vapor–liquid phase diagrams are tested against available simulation data. Concretely, multipolar and non-polar Kihara and chainlike fluids are tested and it is found that this theoretical approach is able to reproduce qualitatively and quantitatively well the Monte Carlo data for the selected molecular potentials, except near the critical region.
NASA Astrophysics Data System (ADS)
Na, Seong-Won; Kallivokas, Loukas F.
2008-03-01
In this article we discuss a formal framework for casting the inverse problem of detecting the location and shape of an insonified scatterer embedded within a two-dimensional homogeneous acoustic host, in terms of a partial-differential-equation-constrained optimization approach. We seek to satisfy the ensuing Karush-Kuhn-Tucker first-order optimality conditions using boundary integral equations. The treatment of evolving boundary shapes, which arise naturally during the search for the true shape, resides on the use of total derivatives, borrowing from recent work by Bonnet and Guzina [1-4] in elastodynamics. We consider incomplete information collected at stations sparsely spaced at the assumed obstacle’s backscattered region. To improve on the ability of the optimizer to arrive at the global optimum we: (a) favor an amplitude-based misfit functional; and (b) iterate over both the frequency- and wave-direction spaces through a sequence of problems. We report numerical results for sound-hard objects with shapes ranging from circles, to penny- and kite-shaped, including obstacles with arbitrarily shaped non-convex boundaries.
Perturbation expansion and Nth order Fermi golden rule of the nonlinear Schrödinger equations
NASA Astrophysics Data System (ADS)
Zhou, Gang
2007-05-01
In this paper we consider generalized nonlinear Schrödinger equations with external potentials. We find the expressions for the fourth and the sixth order Fermi golden rules (FGRs), conjectured in Gang and Sigal [Rev. Math. Phys. 17, 1143-1207 (2005); Geom. Funct. Anal. 16, No. 7, 1377-1390 (2006)]. The FGR is a key condition in a study of the asymptotic dynamics of trapped solitons.
Decoupling of the Dirac equation correct to the third order for the magnetic perturbation.
Ootani, Y; Maeda, H; Fukui, H
2007-08-28
A two-component relativistic theory accurately decoupling the positive and negative states of the Dirac Hamiltonian that includes magnetic perturbations is derived. The derived theory eliminates all of the odd terms originating from the nuclear attraction potential V and the first-order odd terms originating from the magnetic vector potential A, which connect the positive states to the negative states. The electronic energy obtained by the decoupling is correct to the third order with respect to A due to the (2n+1) rule. The decoupling is exact for the magnetic shielding calculation. However, the calculation of the diamagnetic property requires both the positive and negative states of the unperturbed (A=0) Hamiltonian. The derived theory is applied to the relativistic calculation of nuclear magnetic shielding tensors of HX (X=F,Cl,Br,I) systems at the Hartree-Fock level. The results indicate that such a substantially exact decoupling calculation well reproduces the four-component Dirac-Hartree-Fock results.
NASA Technical Reports Server (NTRS)
Yen, D. H. Y.; Maestrello, L.; Padula, S.
1975-01-01
The response of a clamped panel to supersonically convected turbulence is considered. A theoretical model in the form of an integro-differential equation is employed that takes into account the coupling between the panel motion and the surrounding acoustic medium. The kernels of the integrals, which represent induced pressures due to the panel motion, are Green's functions for sound radiations under various moving and stationary sources. An approximate analysis is made by following a finite-element Ritz-Galerkin procedure. Preliminary numerical results, in agreement with experimental findings, indicate that the acoustic damping is the controlling mechanism of the response.
NASA Astrophysics Data System (ADS)
Trogdon, Thomas; Deconinck, Bernard
2014-01-01
All solutions of the Korteweg-de Vries equation that are bounded on the real line are physically relevant, depending on the application area of interest. Usually, both analytical and numerical approaches consider solution profiles that are either spatially localized or (quasi-)periodic. In this paper, we discuss a class of solutions that is a nonlinear superposition of these two cases: their asymptotic state for large |x| is (quasi-)periodic, but they may contain solitons, with or without dispersive tails. Such scenarios might occur in the case of localized perturbations of previously present sea swell, for instance. Such solutions have been discussed from an analytical point of view only recently. We numerically demonstrate different features of these solutions.
Brodsky, Stanley J.; de Teramond, Guy F.; Deur, Alexandre P.; Dosch, Hans G.
2015-09-01
The valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a relativistic equation of motion with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. If one requires that the effective action which underlies the QCD Lagrangian remains conformally invariant and extends the formalism of de Alfaro, Fubini and Furlan to light front Hamiltonian theory, the potential U has a unique form of a harmonic oscillator potential, and a mass gap arises. The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories with the same slope in the radial quantum number n and orbital angular momentum L. Only one mass parameter κ appears. Light-front holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. We also show how the mass scale κ underlying confinement and hadron masses determines the scale Λ_{{ovr MS}} controlling the evolution of the perturbative QCD coupling. The relation between scales is obtained by matching the nonperturbative dynamics, as described by an effective conformal theory mapped to the light-front and its embedding in AdS space, to the perturbative QCD regime computed to four-loop order. The result is an effective coupling defined at all momenta. The predicted value Λ_{{ovr MS}}=0.328±0.034 GeV is in agreement with the world average 0.339±0.010 GeV. The analysis applies to any renormalization scheme.
NASA Astrophysics Data System (ADS)
Albeverio, Sergio; Fassari, Silvestro; Rinaldi, Fabio
2015-04-01
We discuss the probabilistic representation of the solutions of the heat equation perturbed by a repulsive point interaction in terms of a perturbation of Brownian motion, via a Feynman-Kac formula involving a local time functional. An application to option pricing is given, interpolating between the extreme cases of classical Black-Scholes options and knockouts having the barrier situated exactly at the exercise price.
Short-lived two-soliton bound states in weakly perturbed nonlinear Schrodinger equation.
Dmitriev, Sergey V.; Shigenari, Takeshi
2002-06-01
Resonant soliton collisions in the weakly discrete nonlinear Schrodinger equation are studied numerically. The fractal nature of the soliton scattering, described in our previous works, is investigated in detail. We demonstrate that the fractal scattering pattern is related to the existence of the short-lived two-soliton bound states. The bound state can be regarded as a two-soliton quasiparticle of a new type, different from the breather. We establish that the probability P of a bound state with the lifetime L follows the law P approximately L(-3). In the frame of a simple two-particle model, we derive the nonlinear map, which generates the fractal pattern similar to that observed in the numerical study of soliton collisions. (c) 2002 American Institute of Physics.
Pion-nucleon scattering: from chiral perturbation theory to Roy-Steiner equations
NASA Astrophysics Data System (ADS)
Kubis, Bastian; Hoferichter, Martin; de Elvira, Jacobo Ruiz; Meißner, Ulf-G.
2016-11-01
Ever since Weinberg's seminal predictions of the pion-nucleon scattering amplitudes at threshold, this process has been of central interest for the study of chiral dynamics involving nucleons. The scattering lengths or the pion-nucleon σ-term are fundamental quantities characterizing the explicit breaking of chiral symmetry by means of the light quark masses. On the other hand, pion-nucleon dynamics also strongly affects the long-range part of nucleon-nucleon potentials, and hence has a far-reaching impact on nuclear physics. We discuss the fruitful combination of dispersion-theoretical methods, in the form of Roy-Steiner equations, with chiral dynamics to determine pion-nucleon scattering amplitudes at low energies with high precision.
Scalar field-perfect fluid correspondence and non-linear perturbation equations
Mainini, Roberto
2008-07-15
The properties of dynamical dark energy (DE) and, in particular, the possibility that it can form or contribute to stable inhomogeneities have been widely debated in recent literature, and also in association with a possible coupling between DE and dark matter (DM). In order to clarify this issue, in this paper we present a general framework for the study of the non-linear phases of structure formation, showing the equivalence of two possible descriptions of DE: a scalar field {phi} self-interacting through a potential V ({phi}) and a perfect fluid with an assigned negative equation of state w(a). This enables us to show that, in the presence of coupling, the mass of DE quanta may increase where large DM condensations are present, with the result that also DE may be involved in the clustering process.
Perturbation of the Wigner equation in inner product C{sup *}-modules
Chmielinski, Jacek; Ilisevic, Dijana; Moslehian, Mohammad Sal; Sadeghi, Ghadir
2008-03-15
Let A be a C*-algebra and B be a von Neumann algebra that both act on a Hilbert space H. Let M and N be inner product modules over A and B, respectively. Under certain assumptions, we show that for each mapping f:M{yields}N satisfying parallel |
NASA Astrophysics Data System (ADS)
Fishman, Louis
2000-11-01
The role of mathematical modeling in the physical sciences will be briefly addressed. Examples will focus on computational acoustics, with applications to underwater sound propagation, electromagnetic modeling, optics, and seismic inversion. Direct and inverse wave propagation problems in both the time and frequency domains will be considered. Focusing on fixed-frequency (elliptic) wave propagation problems, the usual, two-way, partial differential equation formulation will be exactly reformulated, in a well-posed manner, as a one-way (marching) problem. This is advantageous for both direct and inverse considerations, as well as stochastic modeling problems. The reformulation will require the introduction of pseudodifferential operators and their accompanying phase space analysis (calculus), in addition to path integral representations for the fundamental solutions and their subsequent computational algorithms. Unlike the more traditional, purely numerical applications of, for example, finite-difference and finite-element methods, this approach, in effect, writes the exact, or, more generally, the asymptotically correct, answer as a functional integral and, subsequently, computes it directly. The overall computational philosophy is to combine analysis, asymptotics, and numerical methods to attack complicated, real-world problems. Exact and asymptotic analysis will stress the complementary nature of the direct and inverse formulations, as well as indicating the explicit structural connections between the time- and frequency-domain solutions.
NASA Astrophysics Data System (ADS)
Bean, Rachel; Doré, Olivier
2004-04-01
We review the implications of having a nontrivial matter component in the Universe and the potential for detecting such a component through the matter power spectrum and integrated Sachs-Wolfe effect. We adopt a phenomenological approach and consider the mysterious dark energy to be a cosmic fluid. It is thus fully characterized, up to linear order, by its equation of state and its speed of sound. Whereas the equation of state has been widely studied in the literature, less interest has been devoted to the speed of sound. Its observational consequences come predominantly from very large scale modes of dark matter perturbations (k<0.01h Mpc-1). Since these modes have hardly been probed so far by large scale galaxy surveys, we investigate whether joint constraints can be placed on those two quantities using the recent cosmic microwave background (CMB) fluctuations measurements by the Wilkinson Microwave Anisotropy Probe as well as the recently measured CMB large scale structure cross correlation. We find only a tentative 1 sigma detection of the speed of sound, from CMB alone, c2s<0.04 at this low significance level. Furthermore, the current uncertainties in bias in the matter power spectrum preclude any constraints being placed using the cross correlation of CMB with the NRAO VLA Sky Survey radio survey.
NASA Technical Reports Server (NTRS)
Goodman, Jerry R.; Grosveld, Ferdinand
2007-01-01
The acoustics environment in space operations is important to maintain at manageable levels so that the crewperson can remain safe, functional, effective, and reasonably comfortable. High acoustic levels can produce temporary or permanent hearing loss, or cause other physiological symptoms such as auditory pain, headaches, discomfort, strain in the vocal cords, or fatigue. Noise is defined as undesirable sound. Excessive noise may result in psychological effects such as irritability, inability to concentrate, decrease in productivity, annoyance, errors in judgment, and distraction. A noisy environment can also result in the inability to sleep, or sleep well. Elevated noise levels can affect the ability to communicate, understand what is being said, hear what is going on in the environment, degrade crew performance and operations, and create habitability concerns. Superfluous noise emissions can also create the inability to hear alarms or other important auditory cues such as an equipment malfunctioning. Recent space flight experience, evaluations of the requirements in crew habitable areas, and lessons learned (Goodman 2003; Allen and Goodman 2003; Pilkinton 2003; Grosveld et al. 2003) show the importance of maintaining an acceptable acoustics environment. This is best accomplished by having a high-quality set of limits/requirements early in the program, the "designing in" of acoustics in the development of hardware and systems, and by monitoring, testing and verifying the levels to ensure that they are acceptable.
Kierkegaard, Axel; Boij, Susann; Efraimsson, Gunilla
2010-02-01
Acoustic wave propagation in flow ducts is commonly modeled with time-domain non-linear Navier-Stokes equation methodologies. To reduce computational effort, investigations of a linearized approach in frequency domain are carried out. Calculations of sound wave propagation in a straight duct are presented with an orifice plate and a mean flow present. Results of transmission and reflections at the orifice are presented on a two-port scattering matrix form and are compared to measurements with good agreement. The wave propagation is modeled with a frequency domain linearized Navier-Stokes equation methodology. This methodology is found to be efficient for cases where the acoustic field does not alter the mean flow field, i.e., when whistling does not occur.
NASA Astrophysics Data System (ADS)
Andreev, V. B.
2015-01-01
The first boundary value problem for a one-dimensional singularly perturbed convection-diffusion equation with variable coefficients on a finite interval is considered. For the regular component of the solution, unimprovable a priori estimates in the Hölder norms are obtained. The estimates are unimprovable in the sense that they fail on any weakening of the estimating norm.
NASA Astrophysics Data System (ADS)
Churazov, E.; Arevalo, P.; Forman, W.; Jones, C.; Schekochihin, A.; Vikhlinin, A.; Zhuravleva, I.
2016-11-01
We discuss a novel technique of manipulating X-ray images of galaxy clusters to reveal the nature of small-scale density/temperature perturbations in the intracluster medium (ICM). As we show, this technique can be used to differentiate between sound waves and isobaric perturbations in Chandra images of the Perseus and M87/Virgo clusters. The comparison of the manipulated images with the radio data and with the results of detailed spectral analysis shows that this approach successfully classifies the types of perturbations and helps to reveal their nature. For the central regions (5-100 kpc) of the M87 and Perseus clusters, this analysis suggests that observed images are dominated by isobaric perturbations, followed by perturbations caused by bubbles of relativistic plasma and weak shocks. Such a hierarchy is best explained in a `slow' active galactic nuclei feedback scenario, when much of the mechanical energy output of a central black hole is captured by the bubble enthalpy that is gradually released during buoyant rise of the bubbles. The `image arithmetic' works best for prominent structure and for data sets with excellent statistics, visualizing the perturbations with a given effective equation of state. The same approach can be extended to faint perturbations via cross-spectrum analysis of surface brightness fluctuations in X-ray images in different energy bands.
Kozłowska, Marta K; Jürgens, Bas F; Schacht, Christian S; Gross, Joachim; de Loos, Theo W
2009-01-29
Vapor-liquid equilibrium data for systems of hyperbranched polymer (HBP) and carbon dioxide are reported for temperatures of 285-455 K and pressures up to 13 MPa. The bubble-point pressures of (CO2 + hyperbranched polyester) and of (CO2 + hyperbranched polyglycerol + CH3OH) samples with fixed compositions were measured using a Cailletet apparatus. The system (CO2 + polyglycerol + CH3OH) also exhibits a liquid-liquid phase split characterized by lower critical solution temperatures. For this system cloud point curves and vapor-liquid-liquid bubble-point curves were also measured. Moreover, a thermodynamic model has been developed for HBP mixtures in the framework of the perturbed-chain polar statistical association fluid theory (PCP-SAFT) equation of state accounting for branching effects. There is no additional binary interaction parameter introduced along with the branching contributions to the model. Although the miscibility gap in the system (CO2 + polyglycerol + CH3OH) is not predicted by the model, PCP-SAFT including branching effects gives a good representation of the bubble-point curves of this system at temperatures lower than the lower solution temperature (LST).
ERIC Educational Resources Information Center
Brunner, Jana; Ghosh, Satrajit; Hoole, Philip; Matthies, Melanie; Tiede, Mark; Perkell, Joseph
2011-01-01
Purpose: The aim of this study was to relate speakers' auditory acuity for the sibilant contrast, their use of motor equivalent trading relationships in producing the sibilant /[esh]/, and their produced acoustic distance between the sibilants /s/ and /[esh]/. Specifically, the study tested the hypotheses that during adaptation to a perturbation…
Kanfoud, Jamil; Ali Hamdi, Mohamed; Becot, François-Xavier; Jaouen, Luc
2009-02-01
During lift-off, space launchers are submitted to high-level of acoustic loads, which may damage sensitive equipments. A special acoustic absorber has been previously integrated inside the fairing of space launchers to protect the payload. A new research project has been launched to develop a low cost fairing acoustic protection system using optimized layers of porous materials covered by a thin layer of fabric. An analytical model is used for the analysis of acoustic wave propagation within the multilayer porous media. Results have been validated by impedance tube measurements. A parametric study has been conducted to determine optimal mechanical and acoustical properties of the acoustic protection under dimensional thickness constraints. The effect of the mounting conditions has been studied. Results reveal the importance of the lateral constraints on the absorption coefficient particularly in the low frequency range. A transmission study has been carried out, where the fairing structure has been simulated by a limp mass layer. The transmission loss and noise reduction factors have been computed using Biot's theory and the local acoustic impedance approximation to represent the porous layer effect. Comparisons between the two models show the frequency domains for which the local impedance model is valid.
NASA Astrophysics Data System (ADS)
Nazari-Golshan, A.
2016-08-01
Ion-acoustic (IA) solitary wave propagation is investigated by solving the fractional Schamel equation (FSE) in a homogenous system of unmagnetized plasma. This plasma consists of the nonextensive trapped electrons and cold fluid ions. The effects of the nonextensive q-parameter, electron trapping, and fractional parameter have been studied. The FSE is derived by using the semi-inverse and Agrawal's methods. The analytical results show that an increase in the amount of electron trapping and nonextensive q-parameter increases the soliton ion-acoustic amplitude in agreement with the previously obtained results. However, it is vice-versa for the fractional parameter. This feature leads to the fact that the fractional parameter may be used to increase the IA soliton amplitude instead of increasing electron trapping and nonextensive parameters.
NASA Astrophysics Data System (ADS)
Saeed, R.; Shah, Asif
2010-03-01
The nonlinear propagation of ion acoustic waves in electron-positron-ion plasma comprising of Boltzmannian electrons, positrons, and relativistic thermal ions has been examined. The Korteweg-de Vries-Burger equation has been derived by reductive perturbation technique, and its shock like solution is determined analytically through tangent hyperbolic method. The effect of various plasma parameters on strength and structure of shock wave is investigated. The pert graphical view of the results has been presented for illustration. It is observed that strength and steepness of the shock wave enervate with an increase in the ion temperature, relativistic streaming factor, positron concentrations, electron temperature and they accrue with an increase in coefficient of kinematic viscosity. The convective, dispersive, and dissipative properties of the plasma are also discussed. It is determined that the electron temperature has remarkable influence on the propagation and structure of nonlinear wave in such relativistic plasmas. The numerical analysis has been done based on the typical numerical data from a pulsar magnetosphere.
Saeed, R.; Shah, Asif
2010-03-15
The nonlinear propagation of ion acoustic waves in electron-positron-ion plasma comprising of Boltzmannian electrons, positrons, and relativistic thermal ions has been examined. The Korteweg-de Vries-Burger equation has been derived by reductive perturbation technique, and its shock like solution is determined analytically through tangent hyperbolic method. The effect of various plasma parameters on strength and structure of shock wave is investigated. The pert graphical view of the results has been presented for illustration. It is observed that strength and steepness of the shock wave enervate with an increase in the ion temperature, relativistic streaming factor, positron concentrations, electron temperature and they accrue with an increase in coefficient of kinematic viscosity. The convective, dispersive, and dissipative properties of the plasma are also discussed. It is determined that the electron temperature has remarkable influence on the propagation and structure of nonlinear wave in such relativistic plasmas. The numerical analysis has been done based on the typical numerical data from a pulsar magnetosphere.
NASA Technical Reports Server (NTRS)
DeChant, Lawrence J.
1997-01-01
In spite of the rapid advances in both scalar and parallel computational tools, the large number and breadth of variables involved in aerodynamic systems make the use of parabolized or even boundary layer fluid flow models impractical for both preliminary design and inverse design problems. Given this restriction, we have concluded that reduced or approximate models are an important family of tools for design purposes. This study of a combined perturbation/numerical modeling methodology with an application to ejector-mixer nozzles (shown schematically in the following figure) is nearing completion. The work is being funded by a grant from the NASA Lewis Research Center to Texas A&M University. These ejector-mixer nozzle models are designed to be of use to the High Speed Civil Transport Program and may be adopted by both NASA and industry. A computer code incorporating the ejector-mixer models is under development. This code, the Differential Reduced Ejector/Mixer Analysis (DREA), can be run fast enough to be used as a subroutine or to be called by a design optimization routine. Simplified conservation equations--x-momentum, energy, and mass conservation--are used to define the model. Unlike other preliminary design models, DREA requires minimal empirical input and includes vortical mixing and a fully compressible formulation among other features. DREA is being validated by comparing it with results obtained from open literature and proprietary industry data. Preliminary results for a subsonic ejector and a supersonic ejector are shown. In addition, dedicated experiments have been performed at Texas A&M. These experiments use a hydraulic/gas flow analog to provide information about the inviscid mixing interface structure. Final validation and documentation of this work is expected by May of 1997. However, preliminary versions of DREA can be expected in early 1997. In summary, DREA provides a sufficiently detailed and realistic ejector-mixer nozzle model at a
NASA Astrophysics Data System (ADS)
Moradi-Marani, F.; Kodjo, S. A.; Rivard, P.; Lamarche, C. P.
2012-05-01
Very few nonlinear acoustics techniques are currently applied on real structures because their large scale implementation is difficult. Recently, a new method based on nonlinear acoustics has been proposed at the Université de Sherbrooke for the characterization of the damage associated with Alkali-Silica Reaction (ASR). This method consists in quantifying the influence of an external mechanical disturbance on the propagation of a continual ultrasonic wave that probes the material. In this method, the mechanical perturbation produced by an impact causes sudden opening of microcracks and, consequently, the velocity of the probe ultrasonic wave is suddenly reduced. Then it slowly and gradually returns to its initial level as the microcracks are closing. The objective of this study is: using waves generated by traffics in infrastructures in order to monitor microdefects due to damage mechanisms like ASR. This type of mechanical disturbance (by traffic loadings) is used as a source of low frequency-high amplitude waves for opening/closing of the microdefects in the bulk of concrete. This paper presents a laboratory set-up made of three large deep concrete slabs used to study the nonlinear behavior of concrete using the disturbance caused by simulated traffic. The traffic is simulated with a controlled high accuracy jack to produce a wave similar to that produced by traffic. Results obtained from this study will be used in the future to design an in-situ protocol for assessing ASR-affected structures.
Metzler, Adam M; Collis, Jon M
2013-04-01
Shallow-water environments typically include sediments containing thin or low-shear layers. Numerical treatments of these types of layers require finer depth grid spacing than is needed elsewhere in the domain. Thin layers require finer grids to fully sample effects due to elasticity within the layer. As shear wave speeds approach zero, the governing system becomes singular and fine-grid spacing becomes necessary to obtain converged solutions. In this paper, a seismo-acoustic parabolic equation solution is derived utilizing modified difference formulas using Galerkin's method to allow for variable-grid spacing in depth. Propagation results are shown for environments containing thin layers and low-shear layers.
NASA Technical Reports Server (NTRS)
Mcaninch, G. L.; Myers, M. K.
1980-01-01
The parabolic approximation for the acoustic equations of motion is applied to the study of the sound field generated by a plane wave at or near grazing incidence to a finite impedance boundary. It is shown how this approximation accounts for effects neglected in the usual plane wave reflection analysis which, at grazing incidence, erroneously predicts complete cancellation of the incident field by the reflected field. Examples are presented which illustrate that the solution obtained by the parabolic approximation contains several of the physical phenomena known to occur in wave propagation near an absorbing boundary.
NASA Astrophysics Data System (ADS)
Thode, Aaron
2004-06-01
Semianalytic expressions are derived for the first-order derivative of a pressure field in a laterally homogeneous waveguide, with respect to an arbitrary three-dimensional refractive index perturbation in either the water column or ocean bottom. These expressions for the ``environmental derivative,'' derived using an adjoint method, require a three-dimensional spatial correlation between two Green's functions, weighted by an environmental parameter basis function, with the Green's functions expressed in terms of normal modes. When a particular set of orthogonal spatial basis functions is chosen, the three-dimensional spatial integral can be converted into a set of one-dimensional integrations over depth and azimuth. The use of the orthogonal basis permits environmental derivatives to be computed for an arbitrary sound-speed perturbation. To illustrate the formulas, a simple sensitivity study is presented that explores under what circumstances three-dimensional plane-wave and cylindrical perturbations produce non-negligible horizontal refraction effects, for a fixed source/receiver geometry. Other potential applications of these formulas include benchmarking three-dimensional propagation codes, and computing Cramer-Rao bounds for three-dimensional environmental parameter estimates, including internal wave components.
Natarajan, Logesh Kumar; Wu, Sean F
2012-06-01
This paper presents helpful guidelines and strategies for reconstructing the vibro-acoustic quantities on a highly non-spherical surface by using the Helmholtz equation least squares (HELS). This study highlights that a computationally simple code based on the spherical wave functions can produce an accurate reconstruction of the acoustic pressure and normal surface velocity on planar surfaces. The key is to select the optimal origin of the coordinate system behind the planar surface, choose a target structural wavelength to be reconstructed, set an appropriate stand-off distance and microphone spacing, use a hybrid regularization scheme to determine the optimal number of the expansion functions, etc. The reconstructed vibro-acoustic quantities are validated rigorously via experiments by comparing the reconstructed normal surface velocity spectra and distributions with the benchmark data obtained by scanning a laser vibrometer over the plate surface. Results confirm that following the proposed guidelines and strategies can ensure the accuracy in reconstructing the normal surface velocity up to the target structural wavelength, and produce much more satisfactory results than a straight application of the original HELS formulations. Experiment validations on a baffled, square plate were conducted inside a fully anechoic chamber.
Dynamics of the positron acoustic waves in electron-positron-ion magnetoplasmas
NASA Astrophysics Data System (ADS)
Ali, Rustam; Saha, Asit; Chatterjee, Prasanta
2017-01-01
Dynamics of the positron acoustic waves in electron-positron-ion (e-p-i) magnetoplasmas with κ-distributed hot electrons and positrons is investigated in the frameworks of the Kadomtsev-Petviashili (KP) and modified Kadomtsev-Petviashili (mKP) equations. Employing the reductive perturbation technique, the KP and mKP equations are derived. Using the bifurcation theory of planar dynamical systems, the positron acoustic solitary wave solutions, the kink and anti-kink wave solutions are obtained. Considering an external periodic perturbation in the electron-positron-ion magnetoplasmas, the perturbed KP and mKP equations are studied via some qualitative and quantitative approaches. To corroborate in the fact that the perturbed KP and mKP equations can indeed give rise to the quasiperiodic and chaotic motions, the phase plane plots, time series plots, and the Poincaré section are used. The quasiperiodic and developed chaos can be observed for the perturbed positron acoustic waves. The frequency (ω ) of the external periodic perturbation plays the role of the switching parameter in chaotic motions of the perturbed positron acoustic waves through quasiperiodic route to chaos. This work can be useful to understand the dynamics of nonlinear electromagnetic perturbations in space and laboratory plasmas consisting of κ-distributed hot electrons and positrons.
Brito, Ana; Lopes, Ilídio E-mail: ilidio.lopes@ist.utl.pt
2014-02-10
In the last decade, the quality and the amount of observational asteroseismic data that has been made available by space based missions had a tremendous upgrowth. The determination of asteroseismic parameters to estimate the fundamental physical processes occurring in stars' interiors can be done today in a way that has never been possible before. In this work, we propose to compute the seismic observable β, which is a proxy of the phase shift of the acoustic modes propagating in the envelope of the Sun-like stars. This seismic parameter β can be used to identify rapid variation regions usually known as glitches. We show that a small variation in the structure, smaller than 1% in the sound speed, produces a glitch in the acoustic potential that could explain the oscillatory character of β. This method allows us to determine the location and the thickness of the glitch with precision. We applied this idea to the Sun-like star α Centauri A and found a glitch located at approximately 0.94 R (1400 s) and with a thickness of 0.2% of the stars' radius. This is fully consistent with the data and also validates other seismic tests.
NASA Astrophysics Data System (ADS)
You, Jiachun; Liu, Xuewei; Wu, Ru-Shan
2017-03-01
We analyze the mathematical requirements for conventional reverse time migration (RTM) and summarize their rationale. The known information provided by current acquisition system is inadequate for the second-order acoustic wave equations. Therefore, we introduce a dual-sensor seismic acquisition system into the coupled first-order acoustic wave equations. We propose a new dual-sensor reverse time migration called dual-sensor RTM, which includes two input variables, the pressure and vertical particle velocity data. We focus on the performance of dual-sensor RTM in estimating reflection coefficients compared with conventional RTM. Synthetic examples are used for the study of estimating coefficients of reflectors with both dual-sensor RTM and conventional RTM. The results indicate that dual-sensor RTM with two inputs calculates amplitude information more accurately and images structural positions of complex substructures, such as the Marmousi model, more clearly than that of conventional RTM. This shows that the dual-sensor RTM has better accuracy in backpropagation and carries more information in the directivity because of particle velocity injection. Through a simple point-shape model, we demonstrate that dual-sensor RTM decreases the effect of multi-pathing of propagating waves, which is helpful for focusing the energy. In addition, compared to conventional RTM, dual-sensor RTM does not cause extra memory costs. Dual-sensor RTM is, therefore, promising for the computation of multi-component seismic data.
Collis, Jon M; Frank, Scott D; Metzler, Adam M; Preston, Kimberly S
2016-05-01
Sound propagation predictions for ice-covered ocean acoustic environments do not match observational data: received levels in nature are less than expected, suggesting that the effects of the ice are substantial. Effects due to elasticity in overlying ice can be significant enough that low-shear approximations, such as effective complex density treatments, may not be appropriate. Building on recent elastic seafloor modeling developments, a range-dependent parabolic equation solution that treats the ice as an elastic medium is presented. The solution is benchmarked against a derived elastic normal mode solution for range-independent underwater acoustic propagation. Results from both solutions accurately predict plate flexural modes that propagate in the ice layer, as well as Scholte interface waves that propagate at the boundary between the water and the seafloor. The parabolic equation solution is used to model a scenario with range-dependent ice thickness and a water sound speed profile similar to those observed during the 2009 Ice Exercise (ICEX) in the Beaufort Sea.
NASA Astrophysics Data System (ADS)
Negrea, Catalin; Zabotin, Nikolay; Bullett, Terry
2015-04-01
Gravity waves are known to have a major impact on the dynamics of the thermosphere-ionosphere. A number of recent studies addressed the issue of determining the characteristics of thermospheric gravity waves and associated Travelling Ionospheric Disturbances and also their impact on the background system. However, there are currently no methods that would allow for the continuous and uninterrupted study of both the spatial and temporal characteristics of gravity wave activity over a broad range of thermospheric altitudes. We present results obtained using Dynasonde measurements of electron density and ionospheric tilts. The data covers the bottom E- and F-Layers and implicitly contains information on induced perturbations in the horizontal plane at all accessible altitudes. The methodology that we developed is largely automated, allowing for the analysis of large amounts of data. A model of the thermosphere-ionosphere coupling is implemented to infer neutral atmosphere parameters from ionospheric measurements. This is done by accounting for ion-neutral interactions, changes to chemical composition due to wave propagation and the effect of the geomagnetic field. Background neutral temperature, neutral density and neutral composition are used from a numerical model. A sample dataset from October 24th at Wallops Island, Virginia is used to illustrate our approach. The frequency, wavevector components, group velocity, phase speed and amplitude of induced thermospheric and ionospheric perturbations are obtained. These include the TID amplitude as well as the underlying gravity wave amplitude in neutral density, temperature and zonal and meridional winds.
Periyaswamy, Thamizhisai; Balasubramanian, Karthikeyan; Pastore, Christopher
2015-02-01
Fibrous materials are unique hierarchical complex structures exhibiting a range of mechanical, thermal, optical and electrical properties. The inherent discontinuity at micro and macro levels, heterogeneity and multi-scale porosity differentiates fibrous materials from other engineering materials that are typically continuum in nature. These structural complexities greatly influence the techniques and modalities that can be applied to characterize fibrous materials. Typically, the material response to an applied external force is measured and used as a characteristic number of the specimen. In general, a range of equipment is in use to obtain these numbers to signify the material properties. Nevertheless, obtaining these numbers for materials like fiber ensembles is often time consuming, destructive, and requires multiple modalities. It is hypothesized that the material response to an applied acoustic frequency would provide a robust alternative characterization mode for rapid and non-destructive material analysis. This research proposes applying air-coupled ultrasonic acoustics to characterize fibrous materials. Ultrasonic frequency waves transmitted through fibrous assemblies were feature extracted to understand the correlation between the applied frequency and the material properties. Mechanical and thermal characteristics were analyzed using ultrasonic features such as time of flight, signal velocity, power and the rate of attenuation of signal amplitude. Subsequently, these temporal and spectral characteristics were mapped with the standard low-stress mechanical and thermal properties via an empirical artificial intelligence engine. A high correlation of >0.92 (S.D. 0.06) was observed between the ultrasonic features and the standard measurements. The proposed ultrasonic technique can be used toward rapid characterization of dynamic behavior of flexible fibrous assemblies.
NASA Astrophysics Data System (ADS)
Faliagas, A. C.
2016-03-01
Maxwell's theory of multicomponent diffusion and subsequent extensions are based on systems of mass and momentum conservation equations. The partial stress tensor, which is involved in these equations, is expressed in terms of the gradients of velocity fields by statistical and continuum mechanical methods. We propose a method for the solution of Maxwell's equations of diffusion coupled with Müller's expression for the partial stress tensor. The proposed method consists in a singular perturbation process, followed by a weak (finite element) analysis of the resulting PDE systems. The singularity involved in the obtained equations was treated by a special technique, by which lower-order systems were supplemented by proper combinations of higher-order equations. The method proved particularly efficient for the solution of the Maxwell-Müller system, eventually reducing the number of unknown fields to that of the classical Navier-Stokes/Fick system. It was applied to the classical Stefan tube problem and the Hagen-Poiseuille flow in a hollow-fiber membrane tube. Numerical results for these problems are presented, and compared with the Navier-Stokes/Fick approximation. It is shown that the 0-th order term of the Maxwell-Müller equations differs from a properly formulated Navier-Stokes/Fick system, by a numerically insignificant amount. Numerical results for 1st-order terms indicate a good agreement of the classical approximation (with properly formulated Navier-Stokes and Fick's equations) with the Maxwell-Müller system, in the studied cases.
Wen, Xiao-Yong; Yang, Yunqing; Yan, Zhenya
2015-07-01
In this paper, a simple and constructive method is presented to find the generalized perturbation (n,M)-fold Darboux transformations (DTs) of the modified nonlinear Schrödinger (MNLS) equation in terms of fractional forms of determinants. In particular, we apply the generalized perturbation (1,N-1)-fold DTs to find its explicit multi-rogue-wave solutions. The wave structures of these rogue-wave solutions of the MNLS equation are discussed in detail for different parameters, which display abundant interesting wave structures, including the triangle and pentagon, etc., and may be useful to study the physical mechanism of multirogue waves in optics. The dynamical behaviors of these multi-rogue-wave solutions are illustrated using numerical simulations. The same Darboux matrix can also be used to investigate the Gerjikov-Ivanov equation such that its multi-rogue-wave solutions and their wave structures are also found. The method can also be extended to find multi-rogue-wave solutions of other nonlinear integrable equations.
NASA Astrophysics Data System (ADS)
Saha, Asit; Pal, Nikhil; Saha, Tapash; Ghorui, M. K.; Chatterjee, Prasanta
2016-12-01
Bifurcations and chaotic behaviors of dust acoustic traveling waves in magnetoplasmas with nonthermal ions featuring Cairns-Tsallis distribution is investigated on the framework of the further modified Kadomtsev-Petviashili (FMKP) equation. The FMKP equation is derived employing the reductive perturbation technique (RPT). Bifurcations of dust acoustic traveling waves of the FMKP equation is presented. Using the bifurcation theory of planar dynamical systems, two new analytical traveling wave solutions for solitary and periodic waves are derived depending on the parameters α , α _1, q, l and U. Considering an external periodic perturbation, the chaotic behavior of dust acoustic traveling waves is investigated through quasiperiodic route to chaos. The parameter q significantly affects the chaotic behavior of the perturbed FMKP equation.
Kim, Ji-Wan; Kovalenko, Oleksandr; Liu, Yu; Bigot, Jean-Yves
2016-12-27
We report the anharmonic angstrom dynamics of self-assembled Au nanoparticles (Au:NPs) away from a nickel surface on top of which they are coupled by their near-field interaction. The deformation and the oscillatory excursion away from the surface are induced by picosecond acoustic pulses and probed at the surface plasmon resonance with femtosecond laser pulses. The overall dynamics are due to an efficient transfer of translational momentum from the Ni surface to the Au:NPs, therefore avoiding usual thermal effects and energy redistribution among the electronic states. Two modes are clearly revealed by the oscillatory shift of the Au:NPs surface plasmon resonance-the quadrupole deformation mode due to the transient ellipsoid shape and the excursion mode when the Au:NPs bounce away from the surface. We find that, contrary to the quadrupole mode, the excursion mode is sensitive to the distance between Au:NPs and Ni. Importantly, the excursion dynamics display a nonsinusoidal motion that cannot be explained by a standard harmonic potential model. A detailed modeling of the dynamics using a Hamaker-type Lennard-Jones potential between two media is performed, showing that each Au:NPs coherently evolves in a nearly one-dimensional anharmonic potential with a total excursion of ∼1 Å. This excursion induces a shift of the surface plasmon resonance detectable because of the strong near-field interaction. This general method of observing the spatiotemporal dynamics with angstrom and picosecond resolutions can be directly transposed to many nanostructures or biosystems to reveal the interaction and contact mechanism with their surrounding medium while remaining in their fundamental electronic states.
Comparison of an integral equation on energy and the ray-tracing technique in room acoustics.
Le Bot, A; Bocquillet, A
2000-10-01
This paper deals with a comparison of two room acoustic models. The first one is an integral formulation stemming from power balance and the second is the ray-tracing technique with a perfectly diffuse reflection law. The common assumptions to both models are the uncorrelated wave hypothesis and the perfectly diffuse reflection law. The latter allows the use of these methods for nondiffuse fields beyond the validity domain of Sabine's formula. Comparisons of numerical simulations performed with the softwares RAYON and CeReS point out that these results are close to each other and finally, a formal proof is proposed showing that both methods are actually equivalent.
Effective fractional acoustic wave equations in one-dimensional random multiscale media.
Garnier, Josselin; Solna, Knut
2010-01-01
This paper considers multiple scattering of waves propagating in a non-lossy one-dimensional random medium with short- or long-range correlations. Using stochastic homogenization theory it is possible to show that pulse propagation is described by an effective deterministic fractional wave equation, which corresponds to an effective medium with a frequency-dependent attenuation that obeys a power law with an exponent between 0 and 2. The exponent is related to the Hurst parameter of the medium, which is a characteristic parameter of the correlation properties of the fluctuations of the random medium. Moreover the frequency-dependent attenuation is associated with a special frequency-dependent phase, which ensures that causality and Kramers-Kronig relations are satisfied. In the time domain the effective wave equation has the form of a linear integro-differential equation with a fractional derivative.
Dressed ion-acoustic solitons in magnetized dusty plasmas
NASA Astrophysics Data System (ADS)
El-Labany, S. K.; El-Shamy, E. F.; El-Warraki, S. A.
2009-01-01
In the present research paper, the characteristics of ion acoustic solitary waves are investigated in hot magnetized dusty plasmas consisting of negatively charged dust grains, positively charged ion fluid, and isothermal electrons. Applying a reductive perturbation theory, a nonlinear Korteweg-de Vries (KdV) equation for the first-order perturbed potential and a linear inhomogeneous KdV-type equation for the second-order perturbed potentials are derived. Stationary solutions of these coupled equations are obtained using a renormalization method. The effects of the external oblique magnetic field, hot ion fluid, and higher-order nonlinearity on the nature of the ion acoustic solitary waves are discussed. The results complement and provide new insights into previously published results on this problem [R. S. Tiwari and M. K. Mishra, Phys. Plasmas 13, 062112 (2006)].
NASA Astrophysics Data System (ADS)
Yedlin, Matthew; Virieux, Jean
2010-05-01
As data collection in both seismic data acquisition and radar continues to improve, more emphasis is being placed on data pre-processing and inversion, in particular frequency domain waveform inversion in seismology [1], and, for example, time-domain waveform inversion in crosshole radar measurements [2]. Complementary to these methods are the sensitivity kernel techniques established initially in seismology [3, 4]. However, these methods have also been employed in crosshole radar tomography [5]. The sensitivity kernel technique has most recently been applied to the analysis of diffraction of waves in shallow water [6]. Central to the sensitivity kernel techniques is the use of an appropriate Green's function in either two or three dimensions and a background model is assumed for the calculation of the Green's function. In some situations, the constant velocity Green's function is used [5] but in other situations a smooth background model is used in a ray-type approximation. In the case of the smooth background model, computation of a ray-tracing type Green's function is problematic since at the source point the rays convergence, creating a singularity in the computation of the Jacobian used in the amplitude calculation. In fact the source is an axial caustic in two dimensions and a point caustic in three dimensions [7]. To obviate this problem, we will create a uniform asymptotic ansatz [8], explaining in detail how it is obtained in two dimensions. We will then show how to extend the results to three dimensions. In both cases, the Green's function will be obtained in the frequency domain for the acoustic equation with smoothly varying density and bulk modulus. The application of the new Green's function technique will provide more flexibility in the computation of sensitivities, both in seismological and radar applications. References [1] R. G. Pratt. 1999, Seismic waveform inversion in the frequency domain, part 1: Theory and verification in a physical scale
NASA Astrophysics Data System (ADS)
Chai, Jun; Tian, Bo; Zhen, Hui-Ling; Sun, Wen-Rong; Liu, De-Yin
2017-04-01
Effects of quantic nonlinearity on the propagation of the ultrashort optical pulses in a non-Kerr medium, like an optical fiber, can be described by a perturbed nonlinear Schrödinger equation with the power law nonlinearity, which is studied in this paper from a planar-dynamic-system view point. We obtain the equivalent two-dimensional planar dynamic system of such an equation, for which, according to the bifurcation theory and qualitative theory, phase portraits are given. Through the analysis of those phase portraits, we present the relations among the Hamiltonian, orbits of the dynamic system and types of the analytic solutions. Analytic expressions of the periodic-wave solutions, kink- and bell-shaped solitary-wave solutions are derived, and we find that the periodic-wave solutions can be reduced to the kink- and bell-shaped solitary-wave solutions.
Warner, James E.; Diaz, Manuel I.; Aquino, Wilkins; Bonnet, Marc
2014-01-01
This work focuses on the identification of heterogeneous linear elastic moduli in the context of frequency-domain, coupled acoustic-structure interaction (ASI), using either solid displacement or fluid pressure measurement data. The approach postulates the inverse problem as an optimization problem where the solution is obtained by minimizing a modified error in constitutive equation (MECE) functional. The latter measures the discrepancy in the constitutive equations that connect kinematically admissible strains and dynamically admissible stresses, while incorporating the measurement data as additional quadratic error terms. We demonstrate two strategies for selecting the MECE weighting coefficient to produce regularized solutions to the ill-posed identification problem: 1) the discrepancy principle of Morozov, and 2) an error-balance approach that selects the weight parameter as the minimizer of another functional involving the ECE and the data misfit. Numerical results demonstrate that the proposed methodology can successfully recover elastic parameters in 2D and 3D ASI systems from response measurements taken in either the solid or fluid subdomains. Furthermore, both regularization strategies are shown to produce accurate reconstructions when the measurement data is polluted with noise. The discrepancy principle is shown to produce nearly optimal solutions, while the error-balance approach, although not optimal, remains effective and does not need a priori information on the noise level. PMID:25339790
NASA Astrophysics Data System (ADS)
Wang, Enjiang; Liu, Yang; Sen, Mrinal K.
2016-09-01
The 2-D acoustic wave equation is commonly solved numerically by finite-difference (FD) methods in which the accuracy of solution is significantly affected by the FD stencils. The commonly used cross stencil can reach either only second-order accuracy for space domain dispersion-relation-based FD method or (2M)th-order accuracy along eight specific propagation directions for time-space domain dispersion-relation-based FD method, if the conventional (2M)th-order spatial FD and second-order temporal FD are used to discretize the equation. One other newly developed rhombus stencil can reach arbitrary even-order accuracy. However, this stencil adds significantly to computational cost when the operator length is large. To achieve a balance between the solution accuracy and efficiency, we develop a new FD stencil to solve the 2-D acoustic wave equation. This stencil is a combination of the cross stencil and rhombus stencil. A cross stencil with an operator length parameter M is used to approximate the spatial partial derivatives while a rhombus stencil with an operator length parameter N together with the conventional second-order temporal FD is employed in approximating the temporal partial derivatives. Using this stencil, a new FD scheme is developed; we demonstrate that this scheme can reach (2M)th-order accuracy in space and (2N)th-order accuracy in time when spatial FD coefficients and temporal FD coefficients are derived from respective dispersion relation using Taylor-series expansion (TE) method. To further increase the accuracy, we derive the FD coefficients by employing the time-space domain dispersion relation of this FD scheme using TE. We also use least-squares (LS) optimization method to reduce dispersion at high wavenumbers. Dispersion analysis, stability analysis and modelling examples demonstrate that our new scheme has greater accuracy and better stability than conventional FD schemes, and thus can adopt large time steps. To reduce the extra
Numerical computation of steady-state acoustic disturbances in flow
NASA Technical Reports Server (NTRS)
Watson, W. R.; Myers, M. K.
1992-01-01
Two time domain methods for computing two dimensional steady-state acoustic disturbances propagating through internal subsonic viscous flow fields in the presence of variable area are investigated. The first method solves the Navier-Stokes equations for the combined steady and acoustic field together and subtracts the steady flow to obtain the acoustic field. The second method solves a system of perturbation equations to obtain the acoustic disturbances, making use of a separate steady flow computation as input to the system. In each case the periodic steady-state acoustic fluctuations are obtained numerically on a supercomputer using a second order unsplit explicit MacCormack predictor-corrector method. Results show that the first method is not very effective for computing acoustic disturbances of even moderate amplitude. It appears that more accurate steady flow algorithms are required for this method to succeed. On the other hand, linear and nonlinear acoustic disturbances extracted from the perturbation approach are shown to exhibit expected behavior for the problems considered. It is also found that inflow boundary conditions for an equivalent uniform duct can be successfully applied to a nonuniform duct to obtain steady-state acoustic disturbances.
Three-dimensional acoustic wave equation modeling based on the optimal finite-difference scheme
NASA Astrophysics Data System (ADS)
Cai, Xiao-Hui; Liu, Yang; Ren, Zhi-Ming; Wang, Jian-Min; Chen, Zhi-De; Chen, Ke-Yang; Wang, Cheng
2015-09-01
Generally, FD coefficients can be obtained by using Taylor series expansion (TE) or optimization methods to minimize the dispersion error. However, the TE-based FD method only achieves high modeling precision over a limited range of wavenumbers, and produces large numerical dispersion beyond this range. The optimal FD scheme based on least squares (LS) can guarantee high precision over a larger range of wavenumbers and obtain the best optimization solution at small computational cost. We extend the LS-based optimal FD scheme from two-dimensional (2D) forward modeling to three-dimensional (3D) and develop a 3D acoustic optimal FD method with high efficiency, wide range of high accuracy and adaptability to parallel computing. Dispersion analysis and forward modeling demonstrate that the developed FD method suppresses numerical dispersion. Finally, we use the developed FD method to source wavefield extrapolation and receiver wavefield extrapolation in 3D RTM. To decrease the computation time and storage requirements, the 3D RTM is implemented by combining the efficient boundary storage with checkpointing strategies on GPU. 3D RTM imaging results suggest that the 3D optimal FD method has higher precision than conventional methods.
Nonlinear Schrödinger equations with a multiple-well potential and a Stark-type perturbation
NASA Astrophysics Data System (ADS)
Sacchetti, Andrea
2016-05-01
A Bose-Einstein condensate (BEC) confined in a one-dimensional lattice under the effect of an external homogeneous field is described by the Gross-Pitaevskii equation. Here we prove that such an equation can be reduced, in the semiclassical limit and in the case of a lattice with a finite number of wells, to a finite-dimensional discrete nonlinear Schrödinger equation. Then, by means of numerical experiments we show that the BEC's center of mass exhibits an oscillating behavior with modulated amplitude; in particular, we show that the oscillating period actually depends on the shape of the initial wavefunction of the condensate as well as on the strength of the nonlinear term. This fact opens a question concerning the validity of a method proposed for the determination of the gravitational constant by means of the measurement of the oscillating period.
NASA Astrophysics Data System (ADS)
Ivanov, I. G.; Netov, N. C.; Bogdanova, B. C.
2015-10-01
This paper addresses the problem of solving a generalized algebraic Riccati equation with an indefinite sign of its quadratic term. We extend the approach introduced by Lanzon, Feng, Anderson and Rotkowitz (2008) for solving similar Riccati equations. We numerically investigate two types of iterative methods for computing the stabilizing solution. The first type of iterative methods constructs two matrix sequences, where the sum of them converges to the stabilizing solution. The second type of methods defines one matrix sequence which converges to the stabilizing solution. Computer realizations of the presented methods are numerically tested and compared on the test of family examples. Based on the experiments some conclusions are derived.
A time-domain Kirchhoff formula for the convective acoustic wave equation
NASA Astrophysics Data System (ADS)
Ghorbaniasl, Ghader; Siozos-Rousoulis, Leonidas; Lacor, Chris
2016-03-01
Kirchhoff's integral method allows propagated sound to be predicted, based on the pressure and its derivatives in time and space obtained on a data surface located in the linear flow region. Kirchhoff's formula for noise prediction from high-speed rotors and propellers suffers from the limitation of the observer located in uniform flow, thus requiring an extension to arbitrarily moving media. This paper presents a Kirchhoff formulation for moving surfaces in a uniform moving medium of arbitrary configuration. First, the convective wave equation is derived in a moving frame, based on the generalized functions theory. The Kirchhoff formula is then obtained for moving surfaces in the time domain. The formula has a similar form to the Kirchhoff formulation for moving surfaces of Farassat and Myers, with the presence of additional terms owing to the moving medium effect. The equation explicitly accounts for the influence of mean flow and angle of attack on the radiated noise. The formula is verified by analytical cases of a monopole source located in a moving medium.
A time-domain Kirchhoff formula for the convective acoustic wave equation
Ghorbaniasl, Ghader; Siozos-Rousoulis, Leonidas; Lacor, Chris
2016-01-01
Kirchhoff’s integral method allows propagated sound to be predicted, based on the pressure and its derivatives in time and space obtained on a data surface located in the linear flow region. Kirchhoff’s formula for noise prediction from high-speed rotors and propellers suffers from the limitation of the observer located in uniform flow, thus requiring an extension to arbitrarily moving media. This paper presents a Kirchhoff formulation for moving surfaces in a uniform moving medium of arbitrary configuration. First, the convective wave equation is derived in a moving frame, based on the generalized functions theory. The Kirchhoff formula is then obtained for moving surfaces in the time domain. The formula has a similar form to the Kirchhoff formulation for moving surfaces of Farassat and Myers, with the presence of additional terms owing to the moving medium effect. The equation explicitly accounts for the influence of mean flow and angle of attack on the radiated noise. The formula is verified by analytical cases of a monopole source located in a moving medium. PMID:27118912
Ong, Eng Teo; Lee, Heow Pueh; Lim, Kian Meng
2004-09-01
This article presents a fast algorithm for the efficient solution of the Helmholtz equation. The method is based on the translation theory of the multipole expansions. Here, the speedup comes from the convolution nature of the translation operators, which can be evaluated rapidly using fast Fourier transform algorithms. Also, the computations of the translation operators are accelerated by using the recursive formulas developed recently by Gumerov and Duraiswami [SIAM J. Sci. Comput. 25, 1344-1381(2003)]. It is demonstrated that the algorithm can produce good accuracy with a relatively low order of expansion. Efficiency analyses of the algorithm reveal that it has computational complexities of O(Na), where a ranges from 1.05 to 1.24. However, this method requires substantially more memory to store the translation operators as compared to the fast multipole method. Hence, despite its simplicity in implementation, this memory requirement issue may limit the application of this algorithm to solving very large-scale problems.
Acoustic Analog to Quantum Mechanical Level-Splitting
NASA Astrophysics Data System (ADS)
Hilbert, Shawn
2010-03-01
One difficulty in teaching quantum mechanics is the lack of classroom demonstrations. To sidestep this issue, analogies can provide an enlightening alternative. Acoustics governance by the same time-independent wave equation as quantum mechanics supports it use in such analogies. This presentation examines one such analogy for an infinite potential well with a delta potential perturbation. The physical acoustic system consists of continuous sounds waves traveling in a pair of tubes which are separated by a variable diaphragm. The level-splitting nature of the quantum system can be mimicked in the acoustic system.
NASA Astrophysics Data System (ADS)
Brodsky, Stanley J.; de Téramond, Guy F.; Deur, Alexandre; Dosch, Hans Günter
2015-09-01
The valence Fock-state wavefunctions of the light-front (LF) QCD Hamiltonian satisfy a relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. If one requires that the effective action which underlies the QCD Lagrangian remains conformally invariant and extends the formalism of de Alfaro, Fubini and Furlan to LF Hamiltonian theory, the potential U has a unique form of a harmonic oscillator potential, and a mass gap arises. The result is a nonperturbative relativistic LF quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories with the same slope in the radial quantum number n and orbital angular momentum L. Only one mass parameter κ appears. The corresponding LF Dirac equation provides a dynamical and spectroscopic model of nucleons. The same LF equations arise from the holographic mapping of the soft-wall model modification of AdS5 space with a unique dilaton profile to QCD (3+1) at fixed LF time. LF holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of Anti-de Sitter (AdS) space and the boost-invariant LFWFs describing the internal structure of hadrons in physical space-time. We also show how the mass scale underlying confinement and the masses of light-quark hadrons determines the scale controlling the evolution of the perturbative QCD coupling. The relation between scales is obtained by matching the nonperturbative dynamics, as described by an effective conformal theory mapped to the LF and its embedding in AdS space, to the perturbative QCD regime computed to four-loop order. The data for the effective coupling defined from the Bjorken sum rule are remarkably consistent with the
Giacometti, Achille; Gögelein, Christoph; Lado, Fred; Sciortino, Francesco; Ferrari, Silvano
2014-03-07
Building upon past work on the phase diagram of Janus fluids [F. Sciortino, A. Giacometti, and G. Pastore, Phys. Rev. Lett. 103, 237801 (2009)], we perform a detailed study of integral equation theory of the Kern-Frenkel potential with coverage that is tuned from the isotropic square-well fluid to the Janus limit. An improved algorithm for the reference hypernetted-chain (RHNC) equation for this problem is implemented that significantly extends the range of applicability of RHNC. Results for both structure and thermodynamics are presented and compared with numerical simulations. Unlike previous attempts, this algorithm is shown to be stable down to the Janus limit, thus paving the way for analyzing the frustration mechanism characteristic of the gas-liquid transition in the Janus system. The results are also compared with Barker-Henderson thermodynamic perturbation theory on the same model. We then discuss the pros and cons of both approaches within a unified treatment. On balance, RHNC integral equation theory, even with an isotropic hard-sphere reference system, is found to be a good compromise between accuracy of the results, computational effort, and uniform quality to tackle self-assembly processes in patchy colloids of complex nature. Further improvement in RHNC however clearly requires an anisotropic reference bridge function.
Computational approaches to computational aero-acoustics
NASA Technical Reports Server (NTRS)
Hardin, Jay C.
1996-01-01
The various techniques by which the goal of computational aeroacoustics (the calculation and noise prediction of a fluctuating fluid flow) may be achieved are reviewed. The governing equations for compressible fluid flow are presented. The direct numerical simulation approach is shown to be computationally intensive for high Reynolds number viscous flows. Therefore, other approaches, such as the acoustic analogy, vortex models and various perturbation techniques that aim to break the analysis into a viscous part and an acoustic part are presented. The choice of the approach is shown to be problem dependent.
Collins, Michael D; Siegmann, William L
2015-01-01
The parabolic equation method is extended to handle problems in seismo-acoustics that have multiple fluid and solid layers, continuous depth dependence within layers, and sloping interfaces between layers. The medium is approximated in terms of a series of range-independent regions, and a single-scattering approximation is used to compute transmitted fields across the vertical interfaces between regions. The approach is implemented in terms of a set of dependent variables that is well suited to piecewise continuous depth dependence in the elastic parameters, but one of the fluid-solid interface conditions in that formulation involves a second derivative that complicates the treatment of sloping interfaces. This issue is resolved by using a non-centered, four-point difference formula for the second derivative. The approach is implemented using a matrix decomposition that is efficient when the parameters of the medium have a general dependence within the upper layers of the sediment but only depend on depth in the water column and deep within the sediment.
NASA Technical Reports Server (NTRS)
Hauschildt, P. H.
1992-01-01
A fast method for the solution of the radiative transfer equation in rapidly moving spherical media, based on an approximate Lambda-operator iteration, is described. The method uses the short characteristic method and a tridiagonal approximate Lambda-operator to achieve fast convergence. The convergence properties and the CPU time requirements of the method are discussed for the test problem of a two-level atom with background continuum absorption and Thomson scattering. Details of the actual implementation for fast vector and parallel computers are given. The method is accurate and fast enough to be incorporated in radiation-hydrodynamic calculations.
NASA Astrophysics Data System (ADS)
Shishkin, G. I.; Shishkina, L. P.
2011-06-01
In the case of the Dirichlet problem for a singularly perturbed ordinary differential reaction-diffusion equation, a new approach is used to the construction of finite difference schemes such that their solutions and their normalized first- and second-order derivatives converge in the maximum norm uniformly with respect to a perturbation parameter ɛ ∈(0, 1]; the normalized derivatives are ɛ-uniformly bounded. The key idea of this approach to the construction of ɛ-uniformly convergent finite difference schemes is the use of uniform grids for solving grid subproblems for the regular and singular components of the grid solution. Based on the asymptotic construction technique, a scheme of the solution decomposition method is constructed such that its solution and its normalized first- and second-order derivatives converge ɛ-uniformly at the rate of O( N -2ln2 N), where N + 1 is the number of points in the uniform grids. Using the Richardson technique, an improved scheme of the solution decomposition method is constructed such that its solution and its normalized first and second derivatives converge ɛ-uniformly in the maximum norm at the same rate of O( N -4ln4 N).
Acoustic Energy Estimates in Inhomogeneous Moving Media
NASA Technical Reports Server (NTRS)
Farassat, F.; Farris, Mark
1999-01-01
In ducted fan engine noise research, there is a need for defining a simple and easy to use acoustic energy conservation law to help in quantification of noise control techniques. There is a well known conservation law relating acoustic energy and acoustic energy flux in the case of an isentropic irrotational flow. Several different approaches have been taken to generalize this conservation law. For example, Morfey finds an identity by separating out the irrotational part of the perturbed flow. Myers is able to find a series of indentities by observing an algebraic relationship between the basic conservation of energy equation for a background flow and the underlying equations of motion. In an approximate sense, this algebraic relationship is preserved under perturbation. A third approach which seems to have not been pursued in the literature is a result known as Noether's theorem. There is a Lagrangian formulation for the Euler equation of fluid mechanics. Noether's theorem says that any group action that leaves the Lagrangian action invariant leads to a conserved quantity. This presentation will include a survey of current results regarding acoustic energy and preliminary results on the symmetries of the Lagrangian.
Ion acoustic shocks in magneto rotating Lorentzian plasmas
Hussain, S.; Akhtar, N.; Hasnain, H.
2014-12-15
Ion acoustic shock structures in magnetized homogeneous dissipative Lorentzian plasma under the effects of Coriolis force are investigated. The dissipation in the plasma system is introduced via dynamic viscosity of inertial ions. The electrons are following the kappa distribution function. Korteweg-de Vries Burger (KdVB) equation is derived by using reductive perturbation technique. It is shown that spectral index, magnetic field, kinematic viscosity of ions, rotational frequency, and effective frequency have significant impact on the propagation characteristic of ion acoustic shocks in such plasma system. The numerical solution of KdVB equation is also discussed and transition from oscillatory profile to monotonic shock for different plasma parameters is investigated.
NASA Technical Reports Server (NTRS)
DeChant, Lawrence Justin
1998-01-01
In spite of rapid advances in both scalar and parallel computational tools, the large number of variables involved in both design and inverse problems make the use of sophisticated fluid flow models impractical, With this restriction, it is concluded that an important family of methods for mathematical/computational development are reduced or approximate fluid flow models. In this study a combined perturbation/numerical modeling methodology is developed which provides a rigorously derived family of solutions. The mathematical model is computationally more efficient than classical boundary layer but provides important two-dimensional information not available using quasi-1-d approaches. An additional strength of the current methodology is its ability to locally predict static pressure fields in a manner analogous to more sophisticated parabolized Navier Stokes (PNS) formulations. To resolve singular behavior, the model utilizes classical analytical solution techniques. Hence, analytical methods have been combined with efficient numerical methods to yield an efficient hybrid fluid flow model. In particular, the main objective of this research has been to develop a system of analytical and numerical ejector/mixer nozzle models, which require minimal empirical input. A computer code, DREA Differential Reduced Ejector/mixer Analysis has been developed with the ability to run sufficiently fast so that it may be used either as a subroutine or called by an design optimization routine. Models are of direct use to the High Speed Civil Transport Program (a joint government/industry project seeking to develop an economically.viable U.S. commercial supersonic transport vehicle) and are currently being adopted by both NASA and industry. Experimental validation of these models is provided by comparison to results obtained from open literature and Limited Exclusive Right Distribution (LERD) sources, as well as dedicated experiments performed at Texas A&M. These experiments have
Palenik, Mark C.; Dunlap, Brett I.
2015-07-28
Despite the fundamental importance of electron density in density functional theory, perturbations are still usually dealt with using Hartree-Fock-like orbital equations known as coupled-perturbed Kohn-Sham (CPKS). As an alternative, we develop a perturbation theory that solves for the perturbed density directly, removing the need for CPKS. This replaces CPKS with a true Hohenberg-Kohn density perturbation theory. In CPKS, the perturbed density is found in the basis of products of occupied and virtual orbitals, which becomes ever more over-complete as the size of the orbital basis set increases. In our method, the perturbation to the density is expanded in terms of a series of density basis functions and found directly. It is possible to solve for the density in such a way that it makes the total energy stationary even if the density basis is incomplete.
NASA Astrophysics Data System (ADS)
Bobodzhanov, A. A.; Safonov, V. F.
2016-04-01
We consider an algorithm for constructing asymptotic solutions regularized in the sense of Lomov (see [1], [2]). We show that such problems can be reduced to integro-differential equations with inverse time. But in contrast to known papers devoted to this topic (see, for example, [3]), in this paper we study a fundamentally new case, which is characterized by the absence, in the differential part, of a linear operator that isolates, in the asymptotics of the solution, constituents described by boundary functions and by the fact that the integral operator has kernel with diagonal degeneration of high order. Furthermore, the spectrum of the regularization operator A(t) (see below) may contain purely imaginary eigenvalues, which causes difficulties in the application of the methods of construction of asymptotic solutions proposed in the monograph [3]. Based on an analysis of the principal term of the asymptotics, we isolate a class of inhomogeneities and initial data for which the exact solution of the original problem tends to the limit solution (as \\varepsilon\\to+0) on the entire time interval under consideration, also including a boundary-layer zone (that is, we solve the so-called initialization problem). The paper is of a theoretical nature and is designed to lead to a greater understanding of the problems in the theory of singular perturbations. There may be applications in various applied areas where models described by integro-differential equations are used (for example, in elasticity theory, the theory of electrical circuits, and so on).
Acoustic resonances in cylinder bundles oscillating in a compressibile fluid
Lin, W.H.; Raptis, A.C.
1984-12-01
This paper deals with an analytical study on acoustic resonances of elastic oscillations of a group of parallel, circular, thin cylinders in an unbounded volume of barotropic, compressible, inviscid fluid. The perturbed motion of the fluid is assumed due entirely to the flexural oscillations of the cylinders. The motion of the fluid disturbances is first formulated in a three-dimensional wave form and then casted into a two-dimensional Helmholtz equation for the harmonic motion in time and in axial space. The acoustic motion in the fluid and the elastic motion in the cylinders are solved simultaneously. Acoustic resonances were approximately determined from the secular (eigenvalue) equation by the method of successive iteration with the use of digital computers for a given set of the fluid properties and the cylinders' geometry and properties. Effects of the flexural wavenumber and the configuration of and the spacing between the cylinders on the acoustic resonances were thoroughly investigated.
Canonical Acoustics and Its Application to Surface Acoustic Wave on Acoustic Metamaterials
NASA Astrophysics Data System (ADS)
Shen, Jian Qi
2016-08-01
In a conventional formalism of acoustics, acoustic pressure p and velocity field u are used for characterizing acoustic waves propagating inside elastic/acoustic materials. We shall treat some fundamental problems relevant to acoustic wave propagation alternatively by using canonical acoustics (a more concise and compact formalism of acoustic dynamics), in which an acoustic scalar potential and an acoustic vector potential (Φ ,V), instead of the conventional acoustic field quantities such as acoustic pressure and velocity field (p,u) for characterizing acoustic waves, have been defined as the fundamental variables. The canonical formalism of the acoustic energy-momentum tensor is derived in terms of the acoustic potentials. Both the acoustic Hamiltonian density and the acoustic Lagrangian density have been defined, and based on this formulation, the acoustic wave quantization in a fluid is also developed. Such a formalism of acoustic potentials is employed to the problem of negative-mass-density assisted surface acoustic wave that is a highly localized surface bound state (an eigenstate of the acoustic wave equations). Since such a surface acoustic wave can be strongly confined to an interface between an acoustic metamaterial (e.g., fluid-solid composite structures with a negative dynamical mass density) and an ordinary material (with a positive mass density), it will give rise to an effect of acoustic field enhancement on the acoustic interface, and would have potential applications in acoustic device design for acoustic wave control.
NASA Astrophysics Data System (ADS)
Cornuelle, Bruce D.; Worcester, Peter F.; Dzieciuch, Matthew A.
2008-10-01
Ocean acoustic tomography (OAT) was proposed in 1979 by Walter Munk and Carl Wunsch as an analogue to x-ray computed axial tomography for the oceans. The oceans are opaque to most electromagnetic radiation, but there is a strong acoustic waveguide, and sound can propagate for 10 Mm and more with distinct multiply-refracted ray paths. Transmitting broadband pulses in the ocean leads to a set of impulsive arrivals at the receiver which characterize the impulse response of the sound channel. The peaks observed at the receiver are assumed to represent the arrival of energy traveling along geometric ray paths. These paths can be distinguished by arrival time, and by arrival angle when a vertical array of receivers is available. Changes in ray arrival time can be used to infer changes in ocean structure. Ray travel time measurements have been a mainstay of long-range acoustic measurements, but the strong sensitivity of ray paths to range-dependent sound speed perturbations makes the ray sampling functions uncertain in real cases. In the ray approximation travel times are sensitive to medium changes only along the corresponding eigenrays. Ray theory is an infinite-frequency approximation, and its eikonal equation has nonlinearities not found in the acoustic wave equation. We build on recent seismology results (kernels for body wave arrivals in the earth) to characterize the kernel for converting sound speed change in the ocean to travel time changes using more complete propagation physics. Wave-theoretic finite frequency kernels may show less sensitivity to small-scale sound speed structure.
Cosmological perturbation theory in 1+1 dimensions
McQuinn, Matthew; White, Martin E-mail: mwhite@berkeley.edu
2016-01-01
Many recent studies have highlighted certain failures of the standard Eulerian-space cosmological perturbation theory (SPT). Its problems include (1) not capturing large-scale bulk flows [leading to an O( 1) error in the 1-loop SPT prediction for the baryon acoustic peak in the correlation function], (2) assuming that the Universe behaves as a pressureless, inviscid fluid, and (3) treating fluctuations on scales that are non-perturbative as if they were. Recent studies have highlighted the successes of perturbation theory in Lagrangian space or theories that solve equations for the effective dynamics of smoothed fields. Both approaches mitigate some or all of the aforementioned issues with SPT. We discuss these physical developments by specializing to the simplified 1D case of gravitationally interacting sheets, which allows us to substantially reduces the analytic overhead and still (as we show) maintain many of the same behaviors as in 3D. In 1D, linear-order Lagrangian perturbation theory ('the Zeldovich approximation') is exact up to shell crossing, and we prove that n{sup th}-order Eulerian perturbation theory converges to the Zeldovich approximation as narrow ∞. In no 1D cosmology that we consider (including a CDM-like case and power-law models) do these theories describe accurately the matter power spectrum on any mildly nonlinear scale. We find that theories based on effective equations are much more successful at describing the dynamics. Finally, we discuss many topics that have recently appeared in the perturbation theory literature such as beat coupling, the shift and smearing of the baryon acoustic oscillation feature, and the advantages of Fourier versus configuration space. Our simplified 1D case serves as an intuitive review of these perturbation theory results.
Alavi, Farzad; Feyzi, Farzaneh
2013-01-14
Radial and triplet correlation functions of the reference hard sphere system are determined at several solid densities by canonical Monte Carlo (MC) simulations. These customized data are used to extend the second order thermodynamic perturbation theory (TPT) to the solid phase of flexible hard chain systems. In order to test the accuracy of the TPT equation of state (EOS) for hard chains, MC simulations are carried out for systems of chain length 4 to 15. Several simulations are performed in the isobaric-isothermal ensemble to obtain the high-density EOS of hard chains in the fluid and solid phases. To determine solid-fluid equilibrium (SFE), Helmholtz free energies of solid crystals at a reference density are determined in a series of canonical MC simulations. As the chain length increases, asymptotic behaviors are observed in the coexistence pressure and densities of fluid and solid phases. It is found that the accuracy of TPT for EOS and SFE in systems of hard chains greatly improves by extending it to second order.
Coherent entropy induced and acoustic noise separation in compact nozzles
NASA Astrophysics Data System (ADS)
Tao, Wenjie; Schuller, Thierry; Huet, Maxime; Richecoeur, Franck
2017-04-01
A method to separate entropy induced noise from an acoustic pressure wave in an harmonically perturbed flow through a nozzle is presented. It is tested on an original experimental setup generating simultaneously acoustic and temperature fluctuations in an air flow that is accelerated by a convergent nozzle. The setup mimics the direct and indirect noise contributions to the acoustic pressure field in a confined combustion chamber by producing synchronized acoustic and temperature fluctuations, without dealing with the complexity of the combustion process. It allows generating temperature fluctuations with amplitude up to 10 K in the frequency range from 10 to 100 Hz. The noise separation technique uses experiments with and without temperature fluctuations to determine the relative level of acoustic and entropy fluctuations in the system and to identify the nozzle response to these forcing waves. It requires multi-point measurements of acoustic pressure and temperature. The separation method is first validated with direct numerical simulations of the nonlinear Euler equations. These simulations are used to investigate the conditions for which the separation technique is valid and yield similar trends as the experiments for the investigated flow operating conditions. The separation method then gives successfully the acoustic reflection coefficient but does not recover the same entropy reflection coefficient as predicted by the compact nozzle theory due to the sensitivity of the method to signal noises in the explored experimental conditions. This methodology provides a framework for experimental investigation of direct and indirect combustion noises originating from synchronized perturbations.
Nonlinear ion acoustic waves scattered by vortexes
NASA Astrophysics Data System (ADS)
Ohno, Yuji; Yoshida, Zensho
2016-09-01
The Kadomtsev-Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold (leaf) embedded in a larger phase space of more general ion acoustic waves (low-frequency electrostatic perturbations). The KP hierarchy is characterized not only by small amplitudes but also by irrotational (zero-vorticity) velocity fields. In fact, the KP equation is derived by eliminating vorticity at every order of the reductive perturbation. Here, we modify the scaling of the velocity field so as to introduce a vortex term. The newly derived system of equations consists of a generalized three-dimensional KP equation and a two-dimensional vortex equation. The former describes 'scattering' of vortex-free waves by ambient vortexes that are determined by the latter. We say that the vortexes are 'ambient' because they do not receive reciprocal reactions from the waves (i.e., the vortex equation is independent of the wave fields). This model describes a minimal departure from the integrable KP system. By the Painlevé test, we delineate how the vorticity term violates integrability, bringing about an essential three-dimensionality to the solutions. By numerical simulation, we show how the solitons are scattered by vortexes and become chaotic.
Zhang Jiefang; Wang Yueyue; Wu Lei
2009-06-15
The propagation of ion acoustic waves in plasmas composed of ions, positrons, and nonthermally distributed electrons is investigated. By means of the reduction perturbation technique, a nonlinear Schroedinger equation is derived and the modulation instability of ion acoustic wave is analyzed, where the nonthermal parameter is found to be of significant importance. Furthermore, analytical expressions for the bright and dark solitons are obtained, and the interaction of multiple solitons is discussed.
NASA Astrophysics Data System (ADS)
Gerlach, Ulrich H.; Sengupta, Uday K.
1980-09-01
The coupled Einstein-Maxwell system linearized away from an arbitrarily given spherically symmetric background space-time is reduced from its four-dimensional to a two-dimensional form expressed solely in terms of gauge-invariant geometrical perturbation objects. These objects, which besides the gravitational and electromagnetic, also include mass-energy degrees of freedom, are defined on the two-manifold spanned by the radial and time coordinates. For charged or uncharged arbitrary matter background the odd-parity perturbation equations for example, reduce to three second-order linear scalar equations driven by matter and charge inhomogeneities. These three equations describe the intercoupled gravitational, electromagnetic, and acoustic perturbational degrees of freedom. For a charged black hole in an asymptotically de Sitter space-time the gravitational and electromagnetic equations decouple into two inhomogeneous scalar wave equations.
NASA Astrophysics Data System (ADS)
Javidan, Kurosh; Pakzad, Hamid Reza
2012-02-01
Propagation of cylindrical and spherical electron-acoustic solitary waves in unmagnetized plasmas consisting of cold electron fluid, hot electrons obeying a superthermal distribution and stationary ions are investigated. The standard reductive perturbation method is employed to derive the cylindrical/spherical Korteweg-de-Vries equation which governs the dynamics of electron-acoustic solitons. The effects of nonplanar geometry and superthermal hot electrons on the behavior of cylindrical and spherical electron acoustic soliton and its structure are also studied using numerical simulations.
2015-07-17
under-ice scattering , bathymetric diffraction and the application of the ocean acoustic Parabolic Equation to infrasound. 2. Tasks a. Task 1...QSR-14C0172-Ocean Acoustics -063015 Figure 10. Estimated reflection coefficient as a function of frequency by taking the difference of downgoing and...OASIS, INC. 1 Report No. QSR-14C0172-Ocean Acoustics -063015 Quarterly Progress Report Technical and Financial Deep Water Ocean Acoustics
Ion-acoustic cnoidal waves in a quantum plasma
Mahmood, S.; Haas, F.
2014-10-15
Nonlinear ion-acoustic cnoidal wave structures are studied in an unmagnetized quantum plasma. Using the reductive perturbation method, a Korteweg-de Vries equation is derived for appropriate boundary conditions and nonlinear periodic wave solutions are obtained. The corresponding analytical solution and numerical plots of the ion-acoustic cnoidal waves and solitons in the phase plane are presented using the Sagdeev pseudo-potential approach. The variations in the nonlinear potential of the ion-acoustic cnoidal waves are studied at different values of quantum parameter H{sub e} which is the ratio of electron plasmon energy to electron Fermi energy defined for degenerate electrons. It is found that both compressive and rarefactive ion-acoustic cnoidal wave structures are formed depending on the value of the quantum parameter. The dependence of the wavelength and frequency on nonlinear wave amplitude is also presented.
Dust acoustic shock waves in two temperatures charged dusty grains
El-Shewy, E. K.; Abdelwahed, H. G.; Elmessary, M. A.
2011-11-15
The reductive perturbation method has been used to derive the Korteweg-de Vries-Burger equation and modified Korteweg-de Vries-Burger for dust acoustic shock waves in a homogeneous unmagnetized plasma having electrons, singly charged ions, hot and cold dust species with Boltzmann distributions for electrons and ions in the presence of the cold (hot) dust viscosity coefficients. The behavior of the shock waves in the dusty plasma has been investigated.
Bifurcations of dust ion acoustic travelling waves in a magnetized quantum dusty plasma
NASA Astrophysics Data System (ADS)
Samanta, Utpal Kumar; Saha, Asit; Chatterjee, Prasanta
2013-10-01
Bifurcation behavior of nonlinear dust ion acoustic travelling waves in a magnetized quantum dusty plasma has been studied. Applying the reductive perturbation technique (RPT), we have derived a Kadomtsev-Petviashili (KP) equation for dust ion acoustic waves (DIAWs) in a magnetized quantum dusty plasma. By using the bifurcation theory of planar dynamical systems to the KP equation, we have proved that our model has solitary wave solutions and periodic travelling wave solutions. We have derived two exact explicit solutions of the above travelling waves depending on different parameters.
Propagation of dust acoustic solitary waves in inhomogeneous plasma with dust charge fluctuations
NASA Astrophysics Data System (ADS)
Gogoi, L. B.; Deka, P. N.
2017-03-01
Propagations of dust acoustic solitary waves are theoretically investigated in a collisionless, unmagnetized weakly inhomogeneous plasma. The plasma that is considered here consists of negatively charged dust grains and Boltzmann distributed electrons and ions in the presence of dust charge fluctuations. The fluid equations that we use for description of such plasmas are reduced to a modified Korteweg-de-Vries equation by employing a reductive perturbation method. In this investigation, we have used space-time stretched coordinates appropriate for the inhomogeneous plasmas. From the numerical results, we have observed a significant influence of inhomogeneity parameters on the propagation of dust acoustic solitary waves.
Lee, Yong Woo; Lee, Duck Joo
2014-12-01
Kirchhoff's formula for the convective wave equation is derived using the generalized function theory. The generalized convective wave equation for a stationary surface is obtained, and the integral formulation, the convective Kirchhoff's formula, is derived. The formula has a similar form to the classical Kirchhoff's formula, but an additional term appears due to a moving medium effect. For convenience, the additional term is manipulated to a final form as the classical Kirchhoff's formula. The frequency domain boundary integral can be obtained from the current time domain boundary integral form. The derived formula is verified by comparison with the analytic solution of source in the uniform flow. The formula is also utilized as a boundary integral equation. Time domain boundary element method (BEM) analysis using the boundary integral equation is conducted, and the results show good agreement with the analytical solution. The formula derived here can be useful for sound radiation and scattering by arbitrary bodies in a moving medium in the time domain.
NASA Technical Reports Server (NTRS)
Haviland, J. K.
1974-01-01
The results are reported of two unrelated studies. The first was an investigation of the formulation of the equations for non-uniform unsteady flows, by perturbation of an irrotational flow to obtain the linear Green's equation. The resulting integral equation was found to contain a kernel which could be expressed as the solution of the adjoint flow equation, a linear equation for small perturbations, but with non-constant coefficients determined by the steady flow conditions. It is believed that the non-uniform flow effects may prove important in transonic flutter, and that in such cases, the use of doublet type solutions of the wave equation would then prove to be erroneous. The second task covered an initial investigation into the use of the Monte Carlo method for solution of acoustical field problems. Computed results are given for a rectangular room problem, and for a problem involving a circular duct with a source located at the closed end.
NASA Astrophysics Data System (ADS)
Paul, S. N.; Chatterjee, A.; Paul, Indrani
2017-01-01
Nonlinear propagation of ion-acoustic waves in self-gravitating multicomponent dusty plasma consisting of positive ions, non-isothermal two-temperature electrons and negatively charged dust particles with fluctuating charges and drifting ions has been studied using the reductive perturbation method. It has been shown that nonlinear propagation of ion-acoustic waves in gravitating dusty plasma is described by an uncoupled third order partial differential equation which is a modified form of Korteweg-deVries equation, in contraries to the coupled nonlinear equations obtained by earlier authors. Quasi-soliton solution for the ion-acoustic solitary wave has been obtained from this uncoupled nonlinear equation. Effects of non-isothermal two-temperature electrons, gravity, dust charge fluctuation and drift motion of ions on the ion-acoustic solitary waves have been discussed.
Berbri, Abderrezak; Tribeche, Mouloud
2009-05-15
A weakly nonlinear analysis is carried out to derive a Korteweg-de Vries Burgers-like equation for small but finite amplitude dust ion-acoustic (DIA) waves in a charge varying dusty plasma with non thermally distributed electrons. The correct expression for the nonthermal electron charging current is used. Interestingly, it may be noted that due to electron nonthermality and finite equilibrium ion streaming velocity, the present dusty plasma model can admit compressive as well as rarefactive DIA solitary waves. Furthermore, there may exist DIA shocks which have either monotonic or oscillatory behavior and the properties of which depend sensitively on the number of fast nonthermal electrons. Our results should be useful to understand the properties of localized DIA waves that may occur in space dusty plasmas.
Ma, Chunli; Wu, Xiaoxin; Huang, Fengxian; Zhou, Qiang; Li, Fangfei; Cui, Qiliang
2012-09-14
High-pressure and high-temperature Brillouin scattering studies have been performed on liquid of composition corresponding to the ammonia dihydrate stoichiometry (NH(3)·2H(2)O) in a diamond anvil cell. Using the measured Brillouin frequency shifts from 180° back- and 60° platelet-scattering geometries, the acoustic velocity, refractive index, density, and adiabatic bulk modulus have been determined under pressure up to freezing point along the 296, 338, 376, and 407 K isotherms. Along these four isotherms, the acoustic velocities increase smoothly with increasing pressure but decrease with the increased temperature. However, the pressure dependence of the refractive indexes on the four isotherms exhibits a change in slope around 1.5 GPa. The bulk modulus increases linearly with pressure and its slope, dB/dP, decreases from 6.83 at 296 K to 4.41 at 407 K. These new datasets improve our understanding of the pressure- and temperature-induced molecular structure changes in the ammonia-water binary system.
A k-space method for acoustic propagation using coupled first-order equations in three dimensions.
Tillett, Jason C; Daoud, Mohammad I; Lacefield, James C; Waag, Robert C
2009-09-01
A previously described two-dimensional k-space method for large-scale calculation of acoustic wave propagation in tissues is extended to three dimensions. The three-dimensional method contains all of the two-dimensional method features that allow accurate and stable calculation of propagation. These features are spectral calculation of spatial derivatives, temporal correction that produces exact propagation in a homogeneous medium, staggered spatial and temporal grids, and a perfectly matched boundary layer. Spectral evaluation of spatial derivatives is accomplished using a fast Fourier transform in three dimensions. This computational bottleneck requires all-to-all communication; execution time in a parallel implementation is therefore sensitive to node interconnect latency and bandwidth. Accuracy of the three-dimensional method is evaluated through comparisons with exact solutions for media having spherical inhomogeneities. Large-scale calculations in three dimensions were performed by distributing the nearly 50 variables per voxel that are used to implement the method over a cluster of computers. Two computer clusters used to evaluate method accuracy are compared. Comparisons of k-space calculations with exact methods including absorption highlight the need to model accurately the medium dispersion relationships, especially in large-scale media. Accurately modeled media allow the k-space method to calculate acoustic propagation in tissues over hundreds of wavelengths.
Mean Flow Augmented Acoustics in Rocket Systems
NASA Technical Reports Server (NTRS)
Fischbach, Sean
2014-01-01
Combustion instability in solid rocket motors and liquid engines has long been a subject of concern. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process and gas dynamics. Recent advances in energy based modeling of combustion instabilities require accurate determination of acoustic frequencies and mode shapes. Of particular interest is the acoustic mean flow interactions within the converging section of a rocket nozzle, where gradients of pressure, density, and velocity become large. The expulsion of unsteady energy through the nozzle of a rocket is identified as the predominate source of acoustic damping for most rocket systems. Recently, an approach to address nozzle damping with mean flow effects was implemented by French [1]. This new approach extends the work originated by Sigman and Zinn [2] by solving the acoustic velocity potential equation (AVPE) formulated by perturbing the Euler equations [3]. The present study aims to implement the French model within the COMSOL Multiphysiscs framework and analyzes one of the author's presented test cases.
Adaptation Strategies in Perturbed /s/
ERIC Educational Resources Information Center
Brunner, Jana; Hoole, Phil; Perrier, Pascal
2011-01-01
The purpose of this work is to investigate the role of three articulatory parameters (tongue position, jaw position and tongue grooving) in the production of /s/. Six normal speakers' speech was perturbed by a palatal prosthesis. The fricative was recorded acoustically and through electromagnetic articulography in four conditions: (1) unperturbed,…
Acoustic forcing of a liquid drop
NASA Technical Reports Server (NTRS)
Lyell, M. J.
1992-01-01
The development of systems such as acoustic levitation chambers will allow for the positioning and manipulation of material samples (drops) in a microgravity environment. This provides the capability for fundamental studies in droplet dynamics as well as containerless processing work. Such systems use acoustic radiation pressure forces to position or to further manipulate (e.g., oscillate) the sample. The primary objective was to determine the effect of a viscous acoustic field/tangential radiation pressure forcing on drop oscillations. To this end, the viscous acoustic field is determined. Modified (forced) hydrodynamic field equations which result from a consistent perturbation expansion scheme are solved. This is done in the separate cases of an unmodulated and a modulated acoustic field. The effect of the tangential radiation stress on the hydrodynamic field (drop oscillations) is found to manifest as a correction to the velocity field in a sublayer region near the drop/host interface. Moreover, the forcing due to the radiation pressure vector at the interface is modified by inclusion of tangential stresses.
Acoustic streaming of a sharp edge.
Ovchinnikov, Mikhail; Zhou, Jianbo; Yalamanchili, Satish
2014-07-01
Anomalous acoustic streaming is observed emanating from sharp edges of solid bodies that are vibrating in fluids. The streaming velocities can be orders of magnitude higher than expected from the Rayleigh streaming at similar amplitudes of vibration. Acoustic velocity of fluid relative to a solid body diverges at a sharp edge, giving rise to a localized time-independent body force acting on the fluid. This force results in a formation of a localized jet. Two-dimensional numerical simulations are performed to predict acoustic streaming for low amplitude vibration using two methods: (1) Steady-state solution utilizing perturbation theory and (2) direct transient solution of the Navier-Stokes equations. Both analyses agree with each other and correctly predict the streaming of a sharp-edged vibrating blade measured experimentally. The origin of the streaming can be attributed to the centrifugal force of the acoustic fluid flow around a sharp edge. The dependence of this acoustic streaming on frequency and velocity is examined using dimensional analysis. The dependence law is devised and confirmed by numerical simulations.
NASA Astrophysics Data System (ADS)
Bihlo, Alexander; Popovych, Roman O.
2009-10-01
Recently F. Huang [Commun. Theor. Phys. 42 (2004) 903] and X. Tang and P.K. Shukla [Commun. Theor. Phys. 49 (2008) 229] investigated symmetry properties of the barotropic potential vorticity equation without forcing and dissipation on the beta-plane. This equation is governed by two dimensionless parameters, F and β, representing the ratio of the characteristic length scale to the Rossby radius of deformation and the variation of earth' angular rotation, respectively. In the present paper it is shown that in the case F ≠ 0 there exists a well-defined point transformation to set β = 0. The classification of one- and two-dimensional Lie subalgebras of the Lie symmetry algebra of the potential vorticity equation is given for the parameter combination F ≠ 0 and β = 0. Based upon this classification, distinct classes of group-invariant solutions are obtained and extended to the case β ≠ 0.
Nonlinear Generalized Hydrodynamic Wave Equations in Strongly Coupled Dusty Plasmas
Veeresha, B. M.; Sen, A.; Kaw, P. K.
2008-09-07
A set of nonlinear equations for the study of low frequency waves in a strongly coupled dusty plasma medium is derived using the phenomenological generalized hydrodynamic (GH) model and is used to study the modulational stability of dust acoustic waves to parallel perturbations. Dust compressibility contributions arising from strong Coulomb coupling effects are found to introduce significant modifications in the threshold and range of the instability domain.
Vestibular schwannoma; Tumor - acoustic; Cerebellopontine angle tumor; Angle tumor; Hearing loss - acoustic; Tinnitus - acoustic ... Acoustic neuromas have been linked with the genetic disorder neurofibromatosis type 2 (NF2). Acoustic neuromas are uncommon.
NASA Astrophysics Data System (ADS)
Saha, Asit; Chatterjee, Prasanta
2014-02-01
For the critical values of the parameters q and V, the work (Samanta et al. in Phys. Plasma 20:022111, 2013b) is unable to describe the nonlinear wave features in magnetized dusty plasma with superthermal electrons. To describe the nonlinear wave features for critical values of the parameters q and V, we extend the work (Samanta et al. in Phys. Plasma 20:022111, 2013b). To extend the work, we derive the modified Kadomtsev-Petviashvili (MKP) equation for dust ion acoustic waves in a magnetized dusty plasma with q-nonextensive velocity distributed electrons by considering higher order coefficients of ɛ. By applying the bifurcation theory of planar dynamical systems to this MKP equation, the existence of solitary wave solutions of both types rarefactive and compressive, periodic travelling wave solutions and kink and anti-kink wave solutions is proved. Three exact solutions of these above waves are determined. The present study could be helpful for understanding the nonlinear travelling waves propagating in mercury, solar wind, Saturn and in magnetosphere of the Earth.
Ray dynamics in a long-range acoustic propagation experiment
NASA Astrophysics Data System (ADS)
Beron-Vera, Francisco J.; Brown, Michael G.; Colosi, John A.; Tomsovic, Steven; Virovlyansky, Anatoly L.; Wolfson, Michael A.; Zaslavsky, George M.
2003-09-01
A ray-based wave-field description is employed in the interpretation of broadband basin-scale acoustic propagation measurements obtained during the Acoustic Thermometry of Ocean Climate program's 1994 Acoustic Engineering Test. Acoustic observables of interest are wavefront time spread, probability density function (PDF) of intensity, vertical extension of acoustic energy in the reception finale, and the transition region between temporally resolved and unresolved wavefronts. Ray-based numerical simulation results that include both mesoscale and internal-wave-induced sound-speed perturbations are shown to be consistent with measurements of all the aforementioned observables, even though the underlying ray trajectories are predominantly chaotic, that is, exponentially sensitive to initial and environmental conditions. Much of the analysis exploits results that relate to the subject of ray chaos; these results follow from the Hamiltonian structure of the ray equations. Further, it is shown that the collection of the many eigenrays that form one of the resolved arrivals is nonlocal, both spatially and as a function of launch angle, which places severe restrictions on theories that are based on a perturbation expansion about a background ray.
Ray dynamics in a long-range acoustic propagation experiment.
Beron-Vera, Francisco J; Brown, Michael G; Colosi, John A; Tomsovic, Steven; Virovlyansky, Anatoly L; Wolfson, Michael A; Zaslavsky, George M
2003-09-01
A ray-based wave-field description is employed in the interpretation of broadband basin-scale acoustic propagation measurements obtained during the Acoustic Thermometry of Ocean Climate program's 1994 Acoustic Engineering Test. Acoustic observables of interest are wavefront time spread, probability density function (PDF) of intensity, vertical extension of acoustic energy in the reception finale, and the transition region between temporally resolved and unresolved wavefronts. Ray-based numerical simulation results that include both mesoscale and internal-wave-induced sound-speed perturbations are shown to be consistent with measurements of all the aforementioned observables, even though the underlying ray trajectories are predominantly chaotic, that is, exponentially sensitive to initial and environmental conditions. Much of the analysis exploits results that relate to the subject of ray chaos; these results follow from the Hamiltonian structure of the ray equations. Further, it is shown that the collection of the many eigenrays that form one of the resolved arrivals is nonlocal, both spatially and as a function of launch angle, which places severe restrictions on theories that are based on a perturbation expansion about a background ray.
Spa, Carlos; Reche-López, Pedro; Hernández, Erwin
2014-01-01
In the context of wave-like phenomena, Fourier pseudospectral time-domain (PSTD) algorithms are some of the most efficient time-domain numerical methods for engineering applications. One important drawback of these methods is the so-called Gibbs phenomenon. This error can be avoided by using absorbing boundary conditions (ABC) at the end of the simulations. However, there is an important lack of ABC using a PSTD methods on a wave equation. In this paper, we present an ABC model based on a PSTD damped wave equation with an absorption parameter that depends on the position. Some examples of optimum variation profiles are studied analytically and numerically. Finally, the results of this model are also compared to another ABC model based on an hybrid formulation of the scalar perfectly matched layer.
NASA Technical Reports Server (NTRS)
De Bernardis, E.; Farassat, F.
1989-01-01
Using a time domain method based on the Ffowcs Williams-Hawkings equation, a reliable explanation is provided for the origin of singularities observed in the numerical prediction of supersonic propeller noise. In the last few years Tam and, more recently, Amiet have analyzed the phenomenon from different points of view. The method proposed here offers a clear interpretation of the singularities based on a new description of sources, relating to the behavior of lines where the propeller blade surface exhibit slope discontinuity.
NASA Astrophysics Data System (ADS)
Gao, K.; van Dommelen, J. A. W.; Göransson, P.; Geers, M. G. D.
2015-09-01
In this paper, a homogenization method is proposed to obtain the parameters of Biot's poroelastic theory from a multiscale perspective. It is assumed that the behavior of a macroscopic material point can be captured through the response of a microscopic Representative Volume Element (RVE) consisting of both a solid skeleton and a gaseous fluid. The macroscopic governing equations are assumed to be Biot's poroelastic equations and the RVE is governed by the conservation of linear momentum and the adopted linear constitutive laws under the isothermal condition. With boundary conditions relying on the macroscopic solid displacement and fluid pressure, the homogenized solid stress and fluid displacement are obtained based on energy consistency. This homogenization framework offers an approach to obtain Biot's parameters directly through the response of the RVE in the regime of Darcy's flow where the pressure gradient is dominating. A numerical experiment is performed in the form of a sound absorption test on a porous material with an idealized partially open microstructure that is described by Biot's equations where the parameters are obtained through the proposed homogenization approach. The result is evaluated by comparison with Direct Numerical Simulations (DNS), showing a superior performance of this approach compared to an alternative semi-phenomenological model for estimating Biot's parameters of the studied porous material.
Scaling and dimensional analysis of acoustic streaming jets
NASA Astrophysics Data System (ADS)
Moudjed, B.; Botton, V.; Henry, D.; Ben Hadid, H.; Garandet, J.-P.
2014-09-01
This paper focuses on acoustic streaming free jets. This is to say that progressive acoustic waves are used to generate a steady flow far from any wall. The derivation of the governing equations under the form of a nonlinear hydrodynamics problem coupled with an acoustic propagation problem is made on the basis of a time scale discrimination approach. This approach is preferred to the usually invoked amplitude perturbations expansion since it is consistent with experimental observations of acoustic streaming flows featuring hydrodynamic nonlinearities and turbulence. Experimental results obtained with a plane transducer in water are also presented together with a review of the former experimental investigations using similar configurations. A comparison of the shape of the acoustic field with the shape of the velocity field shows that diffraction is a key ingredient in the problem though it is rarely accounted for in the literature. A scaling analysis is made and leads to two scaling laws for the typical velocity level in acoustic streaming free jets; these are both observed in our setup and in former studies by other teams. We also perform a dimensional analysis of this problem: a set of seven dimensionless groups is required to describe a typical acoustic experiment. We find that a full similarity is usually not possible between two acoustic streaming experiments featuring different fluids. We then choose to relax the similarity with respect to sound attenuation and to focus on the case of a scaled water experiment representing an acoustic streaming application in liquid metals, in particular, in liquid silicon and in liquid sodium. We show that small acoustic powers can yield relatively high Reynolds numbers and velocity levels; this could be a virtue for heat and mass transfer applications, but a drawback for ultrasonic velocimetry.
Scaling and dimensional analysis of acoustic streaming jets
Moudjed, B.; Botton, V.; Henry, D.; Ben Hadid, H.
2014-09-15
This paper focuses on acoustic streaming free jets. This is to say that progressive acoustic waves are used to generate a steady flow far from any wall. The derivation of the governing equations under the form of a nonlinear hydrodynamics problem coupled with an acoustic propagation problem is made on the basis of a time scale discrimination approach. This approach is preferred to the usually invoked amplitude perturbations expansion since it is consistent with experimental observations of acoustic streaming flows featuring hydrodynamic nonlinearities and turbulence. Experimental results obtained with a plane transducer in water are also presented together with a review of the former experimental investigations using similar configurations. A comparison of the shape of the acoustic field with the shape of the velocity field shows that diffraction is a key ingredient in the problem though it is rarely accounted for in the literature. A scaling analysis is made and leads to two scaling laws for the typical velocity level in acoustic streaming free jets; these are both observed in our setup and in former studies by other teams. We also perform a dimensional analysis of this problem: a set of seven dimensionless groups is required to describe a typical acoustic experiment. We find that a full similarity is usually not possible between two acoustic streaming experiments featuring different fluids. We then choose to relax the similarity with respect to sound attenuation and to focus on the case of a scaled water experiment representing an acoustic streaming application in liquid metals, in particular, in liquid silicon and in liquid sodium. We show that small acoustic powers can yield relatively high Reynolds numbers and velocity levels; this could be a virtue for heat and mass transfer applications, but a drawback for ultrasonic velocimetry.
Zhai, Yong; Chong, Parkson Lee-Gau; Taylor, Leeandrew Jacques-Asa; Erlkamp, Mirko; Grobelny, Sebastian; Czeslik, Claus; Watkins, Erik; Winter, Roland
2012-03-20
The polar lipid fraction E (PLFE) is a major tetraether lipid component in the thermoacidophilic archaeon Sulfolobus acidocaldarius. Using differential scanning and pressure perturbation calorimetry as well as ultrasound velocity and density measurements, we have determined the compressibilities and volume fluctuations of PLFE liposomes derived from different cell growth temperatures (T(g) = 68, 76, and 81 °C). The compressibility and volume fluctuation values of PLFE liposomes, which are substantially less than those detected from diester lipid membranes (e.g., DPPC), exhibit small but significant differences with T(g). Among the three T(g)s employed, 76 °C leads to the least compressible and most tightly packed PLFE membranes. This temperature is within the range for optimal cell growth (75-80 °C). It is known that a decrease in T(g) decreases the number of cyclopentane rings in archael tetraether lipids. Thus, our data enable us to present the new view that membrane packing in PLFE liposomes varies with the number of cyclopentane rings in a nonlinear manner, reaching maximal tightness when the tetraether lipids are derived from cells grown at optimal T(g)s. In addition, we have studied the effects of pressure on total layer thickness, d, and neutron scattering length density, ρ(n), of a silicon-D(2)O interface that is covered with a PLFE membrane using neutron reflectometry (NR). At 55 °C, d and ρ(n) are found to be rather insensitive to pressure up to 1800 bar, suggesting minor changes of the thickness of the membrane's hydrophobic core and headgroup orientation upon compression only.
Saha, Asit E-mail: prasantachatterjee1@rediffmail.com; Pal, Nikhil; Chatterjee, Prasanta E-mail: prasantachatterjee1@rediffmail.com
2014-10-15
The dynamic behavior of ion acoustic waves in electron-positron-ion magnetoplasmas with superthermal electrons and positrons has been investigated in the framework of perturbed and non-perturbed Kadomtsev-Petviashili (KP) equations. Applying the reductive perturbation technique, we have derived the KP equation in electron-positron-ion magnetoplasma with kappa distributed electrons and positrons. Bifurcations of ion acoustic traveling waves of the KP equation are presented. Using the bifurcation theory of planar dynamical systems, the existence of the solitary wave solutions and the periodic traveling wave solutions has been established. Two exact solutions of these waves have been derived depending on the system parameters. Then, using the Hirota's direct method, we have obtained two-soliton and three-soliton solutions of the KP equation. The effect of the spectral index κ on propagations of the two-soliton and the three-soliton has been shown. Considering an external periodic perturbation, we have presented the quasi periodic behavior of ion acoustic waves in electron-positron-ion magnetoplasmas.
Constraining dark sector perturbations II: ISW and CMB lensing tomography
NASA Astrophysics Data System (ADS)
Soergel, B.; Giannantonio, T.; Weller, J.; Battye, R. A.
2015-02-01
Any Dark Energy (DE) or Modified Gravity (MG) model that deviates from a cosmological constant requires a consistent treatment of its perturbations, which can be described in terms of an effective entropy perturbation and an anisotropic stress. We have considered a recently proposed generic parameterisation of DE/MG perturbations and compared it to data from the Planck satellite and six galaxy catalogues, including temperature-galaxy (Tg), CMB lensing-galaxy (varphi g) and galaxy-galaxy (gg) correlations. Combining these observables of structure formation with tests of the background expansion allows us to investigate the properties of DE/MG both at the background and the perturbative level. Our constraints on DE/MG are mostly in agreement with the cosmological constant paradigm, while we also find that the constraint on the equation of state w (assumed to be constant) depends on the model assumed for the perturbation evolution. We obtain w=-0.92+0.20-0.16 (95% CL; CMB+gg+Tg) in the entropy perturbation scenario; in the anisotropic stress case the result is w=-0.86+0.17-0.16. Including the lensing correlations shifts the results towards higher values of w. If we include a prior on the expansion history from recent Baryon Acoustic Oscillations (BAO) measurements, we find that the constraints tighten closely around w=-1, making it impossible to measure any DE/MG perturbation evolution parameters. If, however, upcoming observations from surveys like DES, Euclid or LSST show indications for a deviation from a cosmological constant, our formalism will be a useful tool towards model selection in the dark sector.
Banks, H T; Birch, Malcolm J; Brewin, Mark P; Greenwald, Stephen E; Hu, Shuhua; Kenz, Zackary R; Kruse, Carola; Maischak, Matthias; Shaw, Simon; Whiteman, John R
2014-04-13
We revisit a method originally introduced by Werder et al. (in Comput. Methods Appl. Mech. Engrg., 190:6685-6708, 2001) for temporally discontinuous Galerkin FEMs applied to a parabolic partial differential equation. In that approach, block systems arise because of the coupling of the spatial systems through inner products of the temporal basis functions. If the spatial finite element space is of dimension D and polynomials of degree r are used in time, the block system has dimension (r + 1)D and is usually regarded as being too large when r > 1. Werder et al. found that the space-time coupling matrices are diagonalizable over [Formula: see text] for r ⩽100, and this means that the time-coupled computations within a time step can actually be decoupled. By using either continuous Galerkin or spectral element methods in space, we apply this DG-in-time methodology, for the first time, to second-order wave equations including elastodynamics with and without Kelvin-Voigt and Maxwell-Zener viscoelasticity. An example set of numerical results is given to demonstrate the favourable effect on error and computational work of the moderately high-order (up to degree 7) temporal and spatio-temporal approximations, and we also touch on an application of this method to an ambitious problem related to the diagnosis of coronary artery disease. Copyright © 2014 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.
Banks, H T; Birch, Malcolm J; Brewin, Mark P; Greenwald, Stephen E; Hu, Shuhua; Kenz, Zackary R; Kruse, Carola; Maischak, Matthias; Shaw, Simon; Whiteman, John R
2014-01-01
We revisit a method originally introduced by Werder et al. (in Comput. Methods Appl. Mech. Engrg., 190:6685–6708, 2001) for temporally discontinuous Galerkin FEMs applied to a parabolic partial differential equation. In that approach, block systems arise because of the coupling of the spatial systems through inner products of the temporal basis functions. If the spatial finite element space is of dimension D and polynomials of degree r are used in time, the block system has dimension (r + 1)D and is usually regarded as being too large when r > 1. Werder et al. found that the space-time coupling matrices are diagonalizable over for r ⩽100, and this means that the time-coupled computations within a time step can actually be decoupled. By using either continuous Galerkin or spectral element methods in space, we apply this DG-in-time methodology, for the first time, to second-order wave equations including elastodynamics with and without Kelvin–Voigt and Maxwell–Zener viscoelasticity. An example set of numerical results is given to demonstrate the favourable effect on error and computational work of the moderately high-order (up to degree 7) temporal and spatio-temporal approximations, and we also touch on an application of this method to an ambitious problem related to the diagnosis of coronary artery disease. Copyright © 2014 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd. PMID:25834284
NASA Astrophysics Data System (ADS)
Pierce, Alan D.
This chapter deals with the physical and mathematical aspects of sound when the disturbances are, in some sense, small. Acoustics is usually concerned with small-amplitude phenomena, and consequently a linear description is usually
APL - North Pacific Acoustic Laboratory
2015-03-04
Acoustic Lab” Encl: (1) Final Technical Report for Subject Grant (2) SF298 for Enclosure Enclosure (1) is the Final Technical Report for the subject...Laboratory (hard copy with SF 298) Defense Technical Information Center (electronic files with SF298) APL - North Pacific Acoustic ...speed perturbations and the characteristics of the ambient acoustic noise field. Scattering and diffraction resulting from internal waves and other
Three-Dimensional Shallow Water Acoustics
2015-09-30
1 DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited. Three-Dimensional Shallow Water Acoustics Dr. Ying...model to predict acoustic fluctuations and derive sound pressure sensitivity kernels due to 3-D sound speed perturbation in the water column. The...numerical method to be utilized is a tangent linear solution to predict acoustic fluctuations due to 3-D sound speed perturbation in the water column. This
Stability analysis for two-dimensional ion-acoustic waves in quantum plasmas
Seadawy, A. R.
2014-05-15
The quantum hydrodynamic model is applied to two-dimensional ion-acoustic waves in quantum plasmas. The two-dimensional quantum hydrodynamic model is used to obtain a deformed Kortewegde Vries (dKdV) equation by reductive perturbation method. By using the solution of auxiliary ordinary equations, a extended direct algebraic method is described to construct the exact solutions for nonlinear quantum dKdV equation. The present results are describing the generation and evolution of such waves, their interactions, and their stability.
Liu, Gang; Jayathilake, Pahala G; Khoo, Boo Cheong; Han, Feng; Liu, Dian Kui
2012-02-01
The complex variables method with mapping function was extended to solve the linear acoustic wave scattering by an inclusion with sharp/smooth corners in an infinite ideal fluid domain. The improved solutions of Helmholtz equation, shown as Bessel function with mapping function as the argument and fractional order Bessel function, were analytically obtained. Based on the mapping function, the initial geometry as well as the original physical vector can be transformed into the corresponding expressions inside the mapping plane. As all the physical vectors are calculated in the mapping plane (η,η), this method can lead to potential vast savings of computational resources and memory. In this work, the results are validated against several published works in the literature. The different geometries of the inclusion with sharp corners based on the proposed mapping functions for irregular polygons are studied and discussed. The findings show that the variation of angles and frequencies of the incident waves have significant influence on the bistatic scattering pattern and the far-field form factor for the pressure in the fluid.
Kinetic study of ion acoustic twisted waves with kappa distributed electrons
NASA Astrophysics Data System (ADS)
Arshad, Kashif; Aman-ur-Rehman, Mahmood, Shahzad
2016-05-01
The kinetic theory of Landau damping of ion acoustic twisted modes is developed in the presence of orbital angular momentum of the helical (twisted) electric field in plasmas with kappa distributed electrons and Maxwellian ions. The perturbed distribution function and helical electric field are considered to be decomposed by Laguerre-Gaussian mode function defined in cylindrical geometry. The Vlasov-Poisson equation is obtained and solved analytically to obtain the weak damping rates of the ion acoustic twisted waves in a non-thermal plasma. The strong damping effects of ion acoustic twisted waves at low values of temperature ratio of electrons and ions are also obtained by using exact numerical method and illustrated graphically, where the weak damping wave theory fails to explain the phenomenon properly. The obtained results of Landau damping rates of the twisted ion acoustic wave are discussed at different values of azimuthal wave number and non-thermal parameter kappa for electrons.
Dust ion-acoustic shock waves in an adiabatic dusty plasma
Rahman, Armina; Sayed, Fatema; Mamun, A. A.
2007-03-15
The properties of dust ion-acoustic shock waves in an unmagnetized dusty plasma, whose constituents are adiabatic ion fluid, Boltzmann electrons, and static dust, are investigated by employing the reductive perturbation method. The Burgers equation is derived and its stationary analytical solution is numerically analyzed. It has been found that both the amplitude and the width decrease with the increase of the ion-fluid temperature. The implications of our results in space and laboratory dusty plasmas are briefly discussed.
Quaternion regularization and stabilization of perturbed central motion. II
NASA Astrophysics Data System (ADS)
Chelnokov, Yu. N.
1993-04-01
Generalized regular quaternion equations for the three-dimensional two-body problem in terms of Kustaanheimo-Stiefel variables are obtained within the framework of the quaternion theory of regularizing and stabilizing transformations of the Newtonian equations for perturbed central motion. Regular quaternion equations for perturbed central motion of a material point in a central field with a certain potential Pi are also derived in oscillatory and normal forms. In addition, systems of perturbed central motion equations are obtained which include quaternion equations of perturbed orbit orientations in oscillatory or normal form, and a generalized Binet equation is derived. A comparative analysis of the equations is carried out.
On the necessity of non-Riemannian acoustic spacetime in fluids with vorticity [rapid communication
NASA Astrophysics Data System (ADS)
Garcia de Andrade, L. C.
2005-10-01
The necessity of a newly proposed [L.C. Garcia de Andrade, Phys. Rev. D 70 (2004) 64004] non-Riemannian acoustic spacetime structure called acoustic torsion of sound wave equation in fluids with vorticity are discussed. It is shown that this structure, although not always necessary is present in fluids with vorticity even when the perturbation is rotational. This can be done by solving the Bergliaffa et al. [Physica D 191 (2004) 121] gauge invariant equations for sound, superposed to a general background flow, needs to support a non-Riemannian acoustic geometry in effective spacetime. Bergliaffa et al. have previously shown that a Riemannian structure cannot be associated to this gauge invariant general system.
NASA Astrophysics Data System (ADS)
Hafez, M. G.; Talukder, M. R.
2015-09-01
This work investigates the theoretical and numerical studies on nonlinear propagation of ion acoustic solitary waves (IASWs) in an unmagnetized plasma consisting of nonextensive electrons, Boltzmann positrons and relativistic thermal ions. The Korteweg-de Vries (KdV) equation is derived by using the well known reductive perturbation method. This equation admits the soliton like solitary wave solution. The effects of phase velocity, amplitude of soliton, width of soliton and electrostatic nonlinear propagation of weakly relativistic ion-acoustic solitary waves have been discussed with graphical representation found in the variation of the plasma parameters. The obtained results can be helpful in understanding the features of small but finite amplitude localized relativistic ion-acoustic waves for an unmagnetized three component plasma system in astrophysical compact objects.
NASA Astrophysics Data System (ADS)
Dev, A. N.; Deka, M. K.; Sarma, J.; Saikia, D.; Adhikary, N. C.
2016-10-01
The stationary solution is obtained for the K-P-Burgers equation that describes the nonlinear propagations of dust ion acoustic waves in a multi-component, collisionless, un-magnetized relativistic dusty plasma consisting of electrons, positive and negative ions in the presence of charged massive dust grains. Here, the Kadomtsev-Petviashvili (K-P) equation, three-dimensional (3D) Burgers equation, and K-P-Burgers equations are derived by using the reductive perturbation method including the effects of viscosity of plasma fluid, thermal energy, ion density, and ion temperature on the structure of a dust ion acoustic shock wave (DIASW). The K-P equation predictes the existences of stationary small amplitude solitary wave, whereas the K-P-Burgers equation in the weakly relativistic regime describes the evolution of shock-like structures in such a multi-ion dusty plasma.
NASA Astrophysics Data System (ADS)
El-Labany, S. K.; El-Taibany, W. F.; Zedan, N. A.
2015-07-01
Cylindrical and spherical amplitude modulations of dust acoustic (DA) solitary wave envelopes in a strongly coupled dusty plasma containing nonthermal distributed ions are studied. Employing a reductive perturbation technique, a modified nonlinear Schrödinger equation including the geometrical effect is derived. The influences of nonthermal ions, polarization force, and the geometries on the modulational instability conditions are analyzed and the possible rogue wave structures are discussed in detail. It is found that the spherical DA waves are more structurally stable to perturbations than the cylindrical ones. Possible applications of these theoretical findings are briefly discussed.
El-Labany, S. K. Zedan, N. A.; El-Taibany, W. F. E-mail: eltaibany@du.edu.eg
2015-07-15
Cylindrical and spherical amplitude modulations of dust acoustic (DA) solitary wave envelopes in a strongly coupled dusty plasma containing nonthermal distributed ions are studied. Employing a reductive perturbation technique, a modified nonlinear Schrödinger equation including the geometrical effect is derived. The influences of nonthermal ions, polarization force, and the geometries on the modulational instability conditions are analyzed and the possible rogue wave structures are discussed in detail. It is found that the spherical DA waves are more structurally stable to perturbations than the cylindrical ones. Possible applications of these theoretical findings are briefly discussed.
Perturbation theory in electron diffraction
NASA Astrophysics Data System (ADS)
Bakken, L. N.; Marthinsen, K.; Hoeier, R.
1992-12-01
The Bloch-wave approach is used for discussing multiple inelastic electron scattering and higher-order perturbation theory in inelastic high-energy electron diffraction. In contrast to previous work, the present work describes three-dimensional diffraction so that higher-order Laue zone (HOLZ) effects are incorporated. Absorption is included and eigenvalues and eigenvectors are calculated from a structure matrix with the inclusion of an absorptive potential. Centrosymmetric as well as non-centrosymmetric crystal structures are allowed. An iteration method with a defined generalized propagation function for solving the inelastic coupling equations is described. It is shown that a similar iteration method with the same propagation function can be used for obtaining higher-order perturbation terms for the wave-function when a perturbation is added to the crystal potential. Finally, perturbation theory by matrix calculations when a general perturbation is added to the structure matrix is considered.
Investigation of micromixing by acoustically oscillated sharp-edges.
Nama, Nitesh; Huang, Po-Hsun; Huang, Tony Jun; Costanzo, Francesco
2016-03-01
Recently, acoustically oscillated sharp-edges have been utilized to achieve rapid and homogeneous mixing in microchannels. Here, we present a numerical model to investigate acoustic mixing inside a sharp-edge-based micromixer in the presence of a background flow. We extend our previously reported numerical model to include the mixing phenomena by using perturbation analysis and the Generalized Lagrangian Mean (GLM) theory in conjunction with the convection-diffusion equation. We divide the flow variables into zeroth-order, first-order, and second-order variables. This results in three sets of equations representing the background flow, acoustic response, and the time-averaged streaming flow, respectively. These equations are then solved successively to obtain the mean Lagrangian velocity which is combined with the convection-diffusion equation to predict the concentration profile. We validate our numerical model via a comparison of the numerical results with the experimentally obtained values of the mixing index for different flow rates. Further, we employ our model to study the effect of the applied input power and the background flow on the mixing performance of the sharp-edge-based micromixer. We also suggest potential design changes to the previously reported sharp-edge-based micromixer to improve its performance. Finally, we investigate the generation of a tunable concentration gradient by a linear arrangement of the sharp-edge structures inside the microchannel.
Investigation of micromixing by acoustically oscillated sharp-edges
Nama, Nitesh; Huang, Po-Hsun; Huang, Tony Jun; Costanzo, Francesco
2016-01-01
Recently, acoustically oscillated sharp-edges have been utilized to achieve rapid and homogeneous mixing in microchannels. Here, we present a numerical model to investigate acoustic mixing inside a sharp-edge-based micromixer in the presence of a background flow. We extend our previously reported numerical model to include the mixing phenomena by using perturbation analysis and the Generalized Lagrangian Mean (GLM) theory in conjunction with the convection-diffusion equation. We divide the flow variables into zeroth-order, first-order, and second-order variables. This results in three sets of equations representing the background flow, acoustic response, and the time-averaged streaming flow, respectively. These equations are then solved successively to obtain the mean Lagrangian velocity which is combined with the convection-diffusion equation to predict the concentration profile. We validate our numerical model via a comparison of the numerical results with the experimentally obtained values of the mixing index for different flow rates. Further, we employ our model to study the effect of the applied input power and the background flow on the mixing performance of the sharp-edge-based micromixer. We also suggest potential design changes to the previously reported sharp-edge-based micromixer to improve its performance. Finally, we investigate the generation of a tunable concentration gradient by a linear arrangement of the sharp-edge structures inside the microchannel. PMID:27158292
Implementation of nonreflecting boundary conditions for the nonlinear Euler equations
NASA Astrophysics Data System (ADS)
Atassi, Oliver V.; Galán, José M.
2008-01-01
Computationally efficient nonreflecting boundary conditions are derived for the Euler equations with acoustic, entropic and vortical inflow disturbances. The formulation linearizes the Euler equations near the inlet/outlet boundaries and expands the solution in terms of Fourier-Bessel modes. This leads to an 'exact' nonreflecting boundary condition, local in space but nonlocal in time, for each Fourier-Bessel mode of the perturbation pressure. The perturbation velocity and density are then calculated using acoustic, entropic and vortical mode splitting. Extension of the boundary conditions to nonuniform swirling flows is presented for the narrow annulus limit which is relevant to many aeroacoustic problems. The boundary conditions are implemented for the nonlinear Euler equations which are solved in space using the finite volume approximation and integrated in time using a MacCormack scheme. Two test problems are carried out: propagation of acoustic waves in an annular duct and the scattering of a vortical wave by a cascade. Comparison between the present exact conditions and commonly used approximate local boundary conditions is made. Results show that, unlike the local boundary conditions whose accuracy depends on the group velocity of the scattered waves, the present conditions give accurate solutions for a range of problems that have a wide array of group velocities. Results also show that this approach leads to a significant savings in computational time and memory by obviating the need to store the pressure field and calculate the nonlocal convolution integral at each point in the inlet and exit boundaries.
NASA Astrophysics Data System (ADS)
Pierce, Alan
This chapter deals with the physical and mathematical aspects of sound when the disturbances are, in some sense, small. Acoustics is usually concerned with small-amplitude phenomena, and consequently a linear description is usually applicable. Disturbances are governed by the properties of the medium in which they occur, and the governing equations are the equations of continuum mechanics, which apply equally to gases, liquids, and solids. These include the mass, momentum, and energy equations, as well as thermodynamic principles. The viscosity and thermal conduction enter into the versions of these equations that apply to fluids. Fluids of typical great interest are air and sea water, and consequently this chapter includes a summary of their relevant acoustic properties. The foundation is also laid for the consideration of acoustic waves in elastic solids, suspensions, bubbly liquids, and porous media.
NASA Technical Reports Server (NTRS)
Eades, J. B., Jr.
1974-01-01
The mathematical developments carried out for this investigation are reported. In addition to describing and discussing the solutions which were acquired, there are compendia of data presented herein which summarize the equations and describe them as representative trace geometries. In this analysis the relative motion problems have been referred to two particular frames of reference; one which is inertially aligned, and one which is (local) horizon oriented. In addition to obtaining the classical initial values solutions, there are results which describe cases having applied specific forces serving as forcing functions. Also, in order to provide a complete state representation the speed components, as well as the displacements, have been described. These coordinates are traced on representative planes analogous to the displacement geometries. By this procedure a complete description of a relative motion is developed; and, as a consequence range rate as well as range information is obtained.
Oblique ion acoustic shock waves in a magnetized plasma
Shahmansouri, M.; Mamun, A. A.
2013-08-15
Ion acoustic (IA) shock waves are studied in a magnetized plasma consisting of a cold viscous ion fluid and Maxwellian electrons. The Korteweg–de Vries–Burgers equation is derived by using the reductive perturbation method. It is shown that the combined effects of external magnetic field and obliqueness significantly modify the basic properties (viz., amplitude, width, speed, etc.) of the IA shock waves. It is observed that the ion-viscosity is a source of dissipation, and is responsible for the formation of IA shock structures. The implications of our results in some space and laboratory plasma situations are discussed.
Ion acoustic kinetic Alfvén rogue waves in two temperature electrons superthermal plasmas
NASA Astrophysics Data System (ADS)
Kaur, Nimardeep; Saini, N. S.
2016-10-01
The propagation properties of ion acoustic kinetic Alfvén (IAKA) solitary and rogue waves have been investigated in two temperature electrons magnetized superthermal plasma in the presence of dust impurity. A nonlinear analysis is carried out to derive the Korteweg-de Vries (KdV) equation using the reductive perturbation method (RPM) describing the evolution of solitary waves. The effect of various plasma parameters on the characteristics of the IAKA solitary waves is studied. The dynamics of ion acoustic kinetic Alfvén rogue waves (IAKARWs) are also studied by transforming the KdV equation into nonlinear Schrödinger (NLS) equation. The characteristics of rogue wave profile under the influence of various plasma parameters (κc, μc, σ , θ) are examined numerically by using the data of Saturn's magnetosphere (Schippers et al. 2008; Sakai et al. 2013).
Modulation of a quantum positron acoustic wave
NASA Astrophysics Data System (ADS)
Amin, M. R.
2015-09-01
Amplitude modulation of a positron acoustic wave is considered in a four-component electron-positron plasma in the quantum magnetohydrodynamic regime. The important ingredients of this study are the inclusion of the particle exchange-correlation potential, quantum diffraction effects via the Bohm potential, and dissipative effect due to viscosity in the momentum balance equation of the charged carriers. A modified nonlinear Schrödinger equation is derived for the evolution of the slowly varying amplitude of the quantum positron acoustic wave by employing the standard reductive perturbation technique. Detailed analysis of the linear and nonlinear dispersions of the quantum positron acoustic wave is presented. For a typical parameter range, relevant to some dense astrophysical objects, it is found that the quantum positron acoustic wave is modulationally unstable above a certain critical wavenumber. Effects of the exchange-correlation potential and the Bohm potential in the wave dynamics are also studied. It is found that the quantum effect due to the particle exchange-correlation potential is significant in comparison to the effect due to the Bohm potential for smaller values of the carrier wavenumber. However, for comparatively larger values of the carrier wavenumber, the Bohm potential effect overtakes the effect of the exchange-correlation potential. It is found that the critical wavenumber for the modulation instability depends on the ratio of the equilibrium hot electron number density and the cold positron number density and on the ratio of the equilibrium hot positron number density and the cold positron number density. A numerical result on the growth rate of the modulation instability is also presented.
Behaviour of a Premixed Flame Subjected to Acoustic Oscillations
Qureshi, Shafiq R.; Khan, Waqar A.; Prosser, Robert
2013-01-01
In this paper, a one dimensional premixed laminar methane flame is subjected to acoustic oscillations and studied. The purpose of this analysis is to investigate the effects of acoustic perturbations on the reaction rates of different species, with a view to their respective contribution to thermoacoustic instabilities. Acoustically transparent non reflecting boundary conditions are employed. The flame response has been studied with acoustic waves of different frequencies and amplitudes. The integral values of the reaction rates, the burning velocities and the heat release of the acoustically perturbed flame are compared with the unperturbed case. We found that the flame's sensitivity to acoustic perturbations is greatest when the wavelength is comparable to the flame thickness. Even in this case, the perturbations are stable with time. We conclude that acoustic fields acting on the chemistry do not contribute significantly to the emergence of large amplitude pressure oscillations. PMID:24376501
Tachibana, Hideki
2015-01-01
Studies of the pressure-dissociation of several amyloid or amyloid-like fibrils have shown that the fibril state is considerably voluminous. Quantitative characterization of the protein fibrillation reaction with respect to volumetric parameters is necessary to elucidate mechanisms of amyloid fibrillation in molecular terms such as protein cavity and hydration. Here we discuss, firstly, basic equations in statics and kinetics of protein polymerization as employed to obtain thermodynamic, volumetric, and kinetic parameters. Equilibrium treatment of the reactions with the scheme such as one-step polymerization, linear-association polymerization, or nucleation-dependent polymerization, and kinetic treatment of seeded linear-polymerization or spontaneous nucleation-elongation polymerization are described. In particular we will detail kinetics of the dissociation of fibrils which have been produced under the linear-association mechanism and therefore the length-distribution of which conforms to a geometric sequence in the degree of polymerization with a common ratio r, which is less than, and usually very close to, unity. In this case, an observed macroscopic rate of dissociation is shown to be a product of the microscopic elementary dissociation rate constant and a factor (1-r), extremely reduced compared with the intrinsic elementary rate. Secondly, we discuss protein conformational states in fibrillogenesis with molecular and volumetric observations reported, such as the unfolded state responsible for the association with seeds and the extension of amyloid fibrils, the transition state in which protein cavity formation and dehydration occur to intermediate levels, and the fibril state in which they occur to final respective levels which, in some cases, depend on the maturity of the fibril.
... search IRSA's site Unique Hits since January 2003 Acoustic Neuroma Click Here for Acoustic Neuroma Practice Guideline ... to microsurgery. One doctor's story of having an acoustic neuroma In August 1991, Dr. Thomas F. Morgan ...
Mayout, Saliha; Tribeche, Mouloud; Sahu, Biswajit
2015-12-15
A theoretical study on the nonlinear propagation of nonplanar (cylindrical and spherical) dust ion-acoustic solitary waves (DIASW) is carried out in a dusty plasma, whose constituents are inertial ions, superthermal electrons, and charge fluctuating stationary dust particles. Using the reductive perturbation theory, a modified Korteweg-de Vries equation is derived. It is shown that the propagation characteristics of the cylindrical and spherical DIA solitary waves significantly differ from those of their one-dimensional counterpart.
2005-09-30
approximation in many practical situations. The equation for the average acoustic field in the statistically homogeneous in horizontal plane stratified...using diagrammatic technique similar to the one used in the theory of wave propagation in the homogeneous medium. The mass operator was calculated...perturbations on various eigenrays due to the horizontal refraction induced by internal waves with the Garrett-Munk spectrum: rigorous internal wave model
Recovery of burner acoustic source structure from far-field sound spectra
NASA Technical Reports Server (NTRS)
Mahan, J. R.; Jones, J. D.
1984-01-01
A method is presented that permits the thermal-acoustic efficiency spectrum in a long turbulent burner to be recovered from the corresponding far-field sound spectrum. An acoustic source/propagation model is used based on the perturbation solution of the equations describing the unsteady one-dimensional flow of an inviscid ideal gas with a distributed heat source. The technique is applied to a long cylindrical hydrogen-flame burner operating over power levels of 4.5-22.3 kW. The results show that the thermal-acoustic efficiency at a given frequency, defined as the fraction of the total burner power converted to acoustic energy at that frequency, is rather insensitive to burner power, having a maximum value on the order of 10 to the -4th at 150 Hz and rolling off steeply with increasing frequency. Evidence is presented that acoustic agitation of the flame at low frequencies enhances the mixing of the unburned fuel and air with the hot products of combustion. The paper establishes the potential of the technique as a useful tool for characterizing the acoustic source structure in any burner, such as a gas turbine combustor, for which a reasonable acoustic propagation model can be postulated.
Diffusive Propagation of Energy in a Non-acoustic Chain
NASA Astrophysics Data System (ADS)
Komorowski, Tomasz; Olla, Stefano
2017-01-01
We consider a non-acoustic chain of harmonic oscillators with the dynamics perturbed by a random local exchange of momentum, such that energy and momentum are conserved. The macroscopic limits of the energy density, momentum and the curvature (or bending) of the chain satisfy a system of evolution equations. We prove that, in a diffusive space-time scaling, the curvature and momentum evolve following a linear system that corresponds to a damped E uler-B ernoulli beam equation. The macroscopic energy density evolves following a non linear diffusive equation. In particular, the energy transfer is diffusive in this dynamics. This provides a first rigorous example of a normal diffusion of energy in a one dimensional dynamics that conserves the momentum.
Covariant generalization of cosmological perturbation theory
Enqvist, Kari; Hoegdahl, Janne; Nurmi, Sami; Vernizzi, Filippo
2007-01-15
We present an approach to cosmological perturbations based on a covariant perturbative expansion between two worldlines in the real inhomogeneous universe. As an application, at an arbitrary order we define an exact scalar quantity which describes the inhomogeneities in the number of e-folds on uniform density hypersurfaces and which is conserved on all scales for a barotropic ideal fluid. We derive a compact form for its conservation equation at all orders and assign it a simple physical interpretation. To make a comparison with the standard perturbation theory, we develop a method to construct gauge-invariant quantities in a coordinate system at arbitrary order, which we apply to derive the form of the nth order perturbation in the number of e-folds on uniform density hypersurfaces and its exact evolution equation. On large scales, this provides the gauge-invariant expression for the curvature perturbation on uniform density hypersurfaces and its evolution equation at any order.
North Pacific Acoustic Laboratory and Deep Water Acoustics
2015-09-30
of basin-wide sound speed ( temperature ) fields obtained by the combination of acoustic, altimetry, and other data types with ocean general...GOALS The ultimate limitations to the performance of long-range sonar are due to ocean sound speed perturbations and the characteristics of the...receptions. 5. To improve basin-scale ocean sound -speed predictions via assimilation of acoustic travel-time and other data into numerical ocean
Perturbative and gauge invariant treatment of gravitational wave memory
NASA Astrophysics Data System (ADS)
Bieri, Lydia; Garfinkle, David
2014-04-01
We present a perturbative treatment of gravitational wave memory. The coordinate invariance of Einstein's equations leads to a type of gauge invariance in perturbation theory. As with any gauge invariant theory, results are more clear when expressed in terms of manifestly gauge invariant quantities. Therefore we derive all our results from the perturbed Weyl tensor rather than the perturbed metric. We derive gravitational wave memory for the Einstein equations coupled to a general energy-momentum tensor that reaches null infinity.
Towards multiscale simulation of moist global flows with soundproof equations
NASA Astrophysics Data System (ADS)
Grabowski, Wojciech W.; Kurowski, Marcin J.; Smolarkiewicz, Piotr K.
2013-04-01
This presentation will discuss incorporation of phase changes of the water substance that accompany moist atmospheric flows into the all-scale atmospheric model based on soundproof equations. Specific issue concerns developing a theoretical basis and practical implementation to include pressure perturbations associated with atmospheric circulations, from small-scale to global, into representations of moist thermodynamics. In small-scale modeling using soundproof equations, pressure perturbations are obtained from the elliptic pressure solver and are typically excluded from the moist thermodynamics. For some small-scale or mesoscale extreme weather events such as a tornado or a hurricane, pressure perturbations are significant and neglecting them in the moist thermodynamics is no longer justifiable. We show through the theoretical analysis that, in larger-scale flows, at least the hydrostatic component of the pressure perturbation needs to be included because pressure variation in synoptic weather systems may affect moist thermodynamics in a way comparable to the temperature variations. As an illustration, we compare numerical solutions to the problem of moist thermal rising in a stratified environment obtained with a fully-compressible acoustic-mode-resolving model and with two versions of the anelastic model, either including or excluding small-scale pressure perturbations in moist thermodynamics. A range of initial temperature perturbations is considered. Model results show that small differences between anelastic and compressible solutions exist only for the largest initial temperature perturbation of 50~K. This paves the way to include pressure perturbations from the elliptic pressure solver in the larger-scale moist problems that will be considered in the future.
Solar wind implication on dust ion acoustic rogue waves
NASA Astrophysics Data System (ADS)
Abdelghany, A. M.; Abd El-Razek, H. N.; Moslem, W. M.; El-Labany, S. K.
2016-06-01
The relevance of the solar wind with the magnetosphere of Jupiter that contains positively charged dust grains is investigated. The perturbation/excitation caused by streaming ions and electron beams from the solar wind could form different nonlinear structures such as rogue waves, depending on the dominant role of the plasma parameters. Using the reductive perturbation method, the basic set of fluid equations is reduced to modified Korteweg-de Vries (KdV) and further modified (KdV) equation. Assuming that the frequency of the carrier wave is much smaller than the ion plasma frequency, these equations are transformed into nonlinear Schrödinger equations with appropriate coefficients. Rational solution of the nonlinear Schrödinger equation shows that rogue wave envelopes are supported by the present plasma model. It is found that the existence region of rogue waves depends on the dust-acoustic speed and the streaming temperatures for both the ions and electrons. The dependence of the maximum rogue wave envelope amplitude on the system parameters has been investigated.
Ata-ur-Rahman,; Qamar, A.; Ali, S.; Mirza, Arshad M.
2013-04-15
We have studied the propagation of ion acoustic shock waves involving planar and non-planar geometries in an unmagnetized plasma, whose constituents are non-degenerate ultra-cold ions, relativistically degenerate electrons, and positrons. By using the reductive perturbation technique, Korteweg-deVries Burger and modified Korteweg-deVries Burger equations are derived. It is shown that only compressive shock waves can propagate in such a plasma system. The effects of geometry, the ion kinematic viscosity, and the positron concentration are examined on the ion acoustic shock potential and electric field profiles. It is found that the properties of ion acoustic shock waves in a non-planar geometry significantly differ from those in planar geometry. The present study has relevance to the dense plasmas, produced in laboratory (e.g., super-intense laser-dense matter experiments) and in dense astrophysical objects.
Mizuno, Yuta; Arasaki, Yasuki; Takatsuka, Kazuo
2016-01-14
A complicated yet interesting induced photon emission can take place by a nonadiabatic intramolecular electron transfer system like LiF under an intense CW laser [Y. Arasaki, S. Scheit, and K. Takatsuka, J. Chem. Phys. 138, 161103 (2013)]. Behind this phenomena, the crossing point between two potential energy curves of covalent and ionic natures in diabatic representation is forced to oscillate, since only the ionic potential curve is shifted significantly up and down repeatedly (called the Dynamical Stark effect). The wavepacket pumped initially to the excited covalent potential curve frequently encounters such a dynamically moving crossing point and thereby undergoes very complicated dynamics including wavepacket bifurcation and deformation. Intramolecular electron transfer thus driven by the coupling between nonadiabatic state-mixing and laser fields induces irregular photon emission. Here in this report we discuss the complicated spectral features of this kind of photon emission induced by infrared laser. In the low frequency domain, the photon emission is much more involved than those of ultraviolet/visible driving fields, since many field-dressed states are created on the ionic potential, which have their own classical turning points and crossing points with the covalent counterpart. To analyze the physics behind the phenomena, we develop a perturbation theoretic approach to the Riccati equation that is transformed from coupled first-order linear differential equations with periodic coefficients, which are supposed to produce the so-called Floquet states. We give mathematical expressions for the Floquet energies, frequencies, and intensities of the photon emission spectra, and the cutoff energy of their harmonic generation. Agreement between these approximate quantities and those estimated with full quantum calculations is found to be excellent. Furthermore, the present analysis provides with notions to facilitate deeper understanding for the physical and
Mizuno, Yuta; Arasaki, Yasuki; Takatsuka, Kazuo
2016-01-14
A complicated yet interesting induced photon emission can take place by a nonadiabatic intramolecular electron transfer system like LiF under an intense CW laser [Y. Arasaki, S. Scheit, and K. Takatsuka, J. Chem. Phys. 138, 161103 (2013)]. Behind this phenomena, the crossing point between two potential energy curves of covalent and ionic natures in diabatic representation is forced to oscillate, since only the ionic potential curve is shifted significantly up and down repeatedly (called the Dynamical Stark effect). The wavepacket pumped initially to the excited covalent potential curve frequently encounters such a dynamically moving crossing point and thereby undergoes very complicated dynamics including wavepacket bifurcation and deformation. Intramolecular electron transfer thus driven by the coupling between nonadiabatic state-mixing and laser fields induces irregular photon emission. Here in this report we discuss the complicated spectral features of this kind of photon emission induced by infrared laser. In the low frequency domain, the photon emission is much more involved than those of ultraviolet/visible driving fields, since many field-dressed states are created on the ionic potential, which have their own classical turning points and crossing points with the covalent counterpart. To analyze the physics behind the phenomena, we develop a perturbation theoretic approach to the Riccati equation that is transformed from coupled first-order linear differential equations with periodic coefficients, which are supposed to produce the so-called Floquet states. We give mathematical expressions for the Floquet energies, frequencies, and intensities of the photon emission spectra, and the cutoff energy of their harmonic generation. Agreement between these approximate quantities and those estimated with full quantum calculations is found to be excellent. Furthermore, the present analysis provides with notions to facilitate deeper understanding for the physical and
NASA Astrophysics Data System (ADS)
Garai, S.; Janaki, M. S.; Chakrabarti, N.
2016-09-01
The nonlinear propagation of low frequency waves, in a collisionless, strongly coupled dusty plasma (SCDP) with a density dependent viscosity, has been studied with a proper Galilean invariant generalized hydrodynamic (GH) model. The well known reductive perturbation technique (RPT) has been employed in obtaining the solutions of the longitudinal and transverse perturbations. It has been found that the nonlinear propagation of the acoustic perturbations govern with the modified Korteweg-de Vries (KdV) equation and are decoupled from the sheared fluctuations. In the regions, where transversal gradients of the flow exists, coupling between the longitudinal and transverse perturbations occurs due to convective nonlinearity which is true for the homogeneous case also. The results, obtained here, can have relative significance to astrophysical context as well as in laboratory plasmas.
Modeling and analysis of fiber-optic mode transducers - Single fiber with periodic perturbations
NASA Astrophysics Data System (ADS)
Huang, Weiping; Xu, Chenglin; Chaudhuri, Sujeet K.
1991-11-01
The fiber-optic LP01-LP11 mode transducers are analyzed by a scalar coupled-mode theory with vector correction. The authors deal with fiber-optic mode transducers made of a single fiber with periodic perturbations due to microbends, acoustic waves, or a photoinduced index grating. Both the couplings caused by the index perturbations and by the vector property of the fields (polarization effect) are taken into account in the analysis. Approximate analytical solutions to the coupled-mode equations are obtained. The power exchange among the modes along the fiber and spectral properties of the mode transducers are examined. The functions of the mode transducers used as wavelength filters and polarizers are studied.
Mean Flow Augmented Acoustics in Rocket Systems
NASA Technical Reports Server (NTRS)
Fischbach, Sean R.
2014-01-01
Oscillatory motion in solid rocket motors and liquid engines has long been a subject of concern. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process and gas dynamics. The customary approach to modeling acoustic waves inside a rocket chamber is to apply the classical inhomogeneous wave equation to the combustion gas. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while the acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The converging section of a rocket nozzle, where gradients in pressure, density, and velocity become large, is a notable region where this approach is not applicable. The expulsion of unsteady energy through the nozzle of a rocket is identified as the predominate source of acoustic damping for most rocket systems. An accurate model of the acoustic behavior within this region where acoustic modes are influenced by the presence of a steady mean flow is required for reliable stability predictions. Recently, an approach to address nozzle damping with mean flow effects was implemented by French [1]. This new approach extends the work originated by Sigman and Zinn [2] by solving the acoustic velocity potential equation (AVPE) formulated by perturbing the Euler equations [3]. The acoustic velocity potential (psi) describing the acoustic wave motion in the presence of an inhomogeneous steady high-speed flow is defined by, (del squared)(psi) - (lambda/c)(exp 2)(psi) - M(dot)[M(dot)(del)(del(psi))] - 2(lambda(M/c) + (M(dot)del(M))(dot)del(psi)-2(lambda)(psi)[M(dot)del(1/c)]=0 (1) with M as the Mach vector, c as the speed of sound, and lambda as the complex eigenvalue. French apply the finite volume method to solve the steady flow field within the combustion chamber and nozzle with inviscid walls. The complex eigenvalues and eigenvector are determined with the use of the ARPACK eigensolver. The
A Numerical Method of Calculating Propeller Noise Including Acoustic Nonlinear Effects
NASA Technical Reports Server (NTRS)
Korkan, K. D.
1985-01-01
Using the transonic flow fields(s) generated by the NASPROP-E computer code for an eight blade SR3-series propeller, a theoretical method is investigated to calculate the total noise values and frequency content in the acoustic near and far field without using the Ffowcs Williams - Hawkings equation. The flow field is numerically generated using an implicit three dimensional Euler equation solver in weak conservation law form. Numerical damping is required by the differencing method for stability in three dimensions, and the influence of the damping on the calculated acoustic values is investigated. The acoustic near field is solved by integrating with respect to time the pressure oscillations induced at a stationary observer location. The acoustic far field is calculated from the near field primitive variables as generated by NASPROP-E computer code using a method involving a perturbation velocity potential as suggested by Hawkings in the calculation of the acoustic pressure time-history at a specified far field observed location. the methodologies described are valid for calculating total noise levels and are applicable to any propeller geometry for which a flow field solution is available.
Nonlinear ion-acoustic cnoidal waves in a dense relativistic degenerate magnetoplasma.
El-Shamy, E F
2015-03-01
The complex pattern and propagation characteristics of nonlinear periodic ion-acoustic waves, namely, ion-acoustic cnoidal waves, in a dense relativistic degenerate magnetoplasma consisting of relativistic degenerate electrons and nondegenerate cold ions are investigated. By means of the reductive perturbation method and appropriate boundary conditions for nonlinear periodic waves, a nonlinear modified Korteweg-de Vries (KdV) equation is derived and its cnoidal wave is analyzed. The various solutions of nonlinear ion-acoustic cnoidal and solitary waves are presented numerically with the Sagdeev potential approach. The analytical solution and numerical simulation of nonlinear ion-acoustic cnoidal waves of the nonlinear modified KdV equation are studied. Clearly, it is found that the features (amplitude and width) of nonlinear ion-acoustic cnoidal waves are proportional to plasma number density, ion cyclotron frequency, and direction cosines. The numerical results are applied to high density astrophysical situations, such as in superdense white dwarfs. This research will be helpful in understanding the properties of compact astrophysical objects containing cold ions with relativistic degenerate electrons.
Small amplitude electron acoustic solitary waves in a magnetized superthermal plasma
NASA Astrophysics Data System (ADS)
Devanandhan, S.; Singh, S. V.; Lakhina, G. S.; Bharuthram, R.
2015-05-01
The propagation of electron acoustic solitary waves in a magnetized plasma consisting of fluid cold electrons, electron beam and superthermal hot electrons (obeying kappa velocity distribution function) and ion is investigated in a small amplitude limit using reductive perturbation theory. The Korteweg-de-Vries-Zakharov-Kuznetsov (KdV-ZK) equation governing the dynamics of electron acoustic solitary waves is derived. The solution of the KdV-ZK equation predicts the existence of negative potential solitary structures. The new results are: (1) increase of either the beam speed or temperature of beam electrons tends to reduce both the amplitude and width of the electron acoustic solitons, (2) the inclusion of beam speed and temperature pushes the allowed Mach number regime upwards and (3) the soliton width maximizes at certain angle of propagation (αm) and then decreases for α >αm . In addition, increasing the superthermality of the hot electrons also results in reduction of soliton amplitude and width. For auroral plasma parameters observed by Viking, the obliquely propagating electron-acoustic solitary waves have electric field amplitudes in the range (7.8-45) mV/m and pulse widths (0.29-0.44) ms. The Fourier transform of these electron acoustic solitons would result in a broadband frequency spectra with peaks near 2.3-3.5 kHz, thus providing a possible explanation of the broadband electrostatic noise observed during the Burst a.
Nonlinear ion-acoustic cnoidal waves in a dense relativistic degenerate magnetoplasma
NASA Astrophysics Data System (ADS)
El-Shamy, E. F.
2015-03-01
The complex pattern and propagation characteristics of nonlinear periodic ion-acoustic waves, namely, ion-acoustic cnoidal waves, in a dense relativistic degenerate magnetoplasma consisting of relativistic degenerate electrons and nondegenerate cold ions are investigated. By means of the reductive perturbation method and appropriate boundary conditions for nonlinear periodic waves, a nonlinear modified Korteweg-de Vries (KdV) equation is derived and its cnoidal wave is analyzed. The various solutions of nonlinear ion-acoustic cnoidal and solitary waves are presented numerically with the Sagdeev potential approach. The analytical solution and numerical simulation of nonlinear ion-acoustic cnoidal waves of the nonlinear modified KdV equation are studied. Clearly, it is found that the features (amplitude and width) of nonlinear ion-acoustic cnoidal waves are proportional to plasma number density, ion cyclotron frequency, and direction cosines. The numerical results are applied to high density astrophysical situations, such as in superdense white dwarfs. This research will be helpful in understanding the properties of compact astrophysical objects containing cold ions with relativistic degenerate electrons.
NASA Astrophysics Data System (ADS)
Muste, M.; Baranya, S.; Tsubaki, R.; Kim, D.; Ho, H.; Tsai, H.; Law, D.
2016-05-01
Knowledge of sediment dynamics in rivers is of great importance for various practical purposes. Despite its high relevance in riverine environment processes, the monitoring of sediment rates remains a major and challenging task for both suspended and bed load estimation. While the measurement of suspended load is currently an active area of testing with nonintrusive technologies (optical and acoustic), bed load measurement does not mark a similar progress. This paper describes an innovative combination of measurement techniques and analysis protocols that establishes the proof-of-concept for a promising technique, labeled herein Acoustic Mapping Velocimetry (AMV). The technique estimates bed load rates in rivers developing bed forms using a nonintrusive measurements approach. The raw information for AMV is collected with acoustic multibeam technology that in turn provides maps of the bathymetry over longitudinal swaths. As long as the acoustic maps can be acquired relatively quickly and the repetition rate for the mapping is commensurate with the movement of the bed forms, successive acoustic maps capture the progression of the bed form movement. Two-dimensional velocity maps associated with the bed form migration are obtained by implementing algorithms typically used in particle image velocimetry to acoustic maps converted in gray-level images. Furthermore, use of the obtained acoustic and velocity maps in conjunction with analytical formulations (e.g., Exner equation) enables estimation of multidirectional bed load rates over the whole imaged area. This paper presents a validation study of the AMV technique using a set of laboratory experiments.
Extreme Value Analysis of Tidal Stream Velocity Perturbations
Harding, Samuel; Thomson, Jim; Polagye, Brian; Richmond, Marshall C.; Durgesh, Vibhav; Bryden, Ian
2011-04-26
This paper presents a statistical extreme value analysis of maximum velocity perturbations from the mean flow speed in a tidal stream. This study was performed using tidal velocity data measured using both an Acoustic Doppler Velocimeter (ADV) and an Acoustic Doppler Current Profiler (ADCP) at the same location which allows for direct comparison of predictions. The extreme value analysis implements of a Peak-Over-Threshold method to explore the effect of perturbation length and time scale on the magnitude of a 50-year perturbation.
Dust ion-acoustic solitary waves in a dusty plasma with nonextensive electrons.
Bacha, Mustapha; Tribeche, Mouloud; Shukla, Padma Kant
2012-05-01
The dust-modified ion-acoustic waves of Shukla and Silin are revisited within the theoretical framework of the Tsallis statistical mechanics. Nonextensivity may originate from correlation or long-range plasma interactions. Interestingly, we find that owing to electron nonextensivity, dust ion-acoustic (DIA) solitary waves may exhibit either compression or rarefaction. Our analysis is then extended to include self-consistent dust charge fluctuation. In this connection, the correct nonextensive electron charging current is rederived. The Korteweg-de Vries equation, as well as the Korteweg-de Vries-Burgers equation, is obtained, making use of the reductive perturbation method. The DIA waves are then analyzed for parameters corresponding to space dusty plasma situations.
Dust ion-acoustic solitary waves in a dusty plasma with nonextensive electrons
NASA Astrophysics Data System (ADS)
Bacha, Mustapha; Tribeche, Mouloud; Shukla, Padma Kant
2012-05-01
The dust-modified ion-acoustic waves of Shukla and Silin are revisited within the theoretical framework of the Tsallis statistical mechanics. Nonextensivity may originate from correlation or long-range plasma interactions. Interestingly, we find that owing to electron nonextensivity, dust ion-acoustic (DIA) solitary waves may exhibit either compression or rarefaction. Our analysis is then extended to include self-consistent dust charge fluctuation. In this connection, the correct nonextensive electron charging current is rederived. The Korteweg-de Vries equation, as well as the Korteweg-de Vries-Burgers equation, is obtained, making use of the reductive perturbation method. The DIA waves are then analyzed for parameters corresponding to space dusty plasma situations.
Singularity perturbed zero dynamics of nonlinear systems
NASA Technical Reports Server (NTRS)
Isidori, A.; Sastry, S. S.; Kokotovic, P. V.; Byrnes, C. I.
1992-01-01
Stability properties of zero dynamics are among the crucial input-output properties of both linear and nonlinear systems. Unstable, or 'nonminimum phase', zero dynamics are a major obstacle to input-output linearization and high-gain designs. An analysis of the effects of regular perturbations in system equations on zero dynamics shows that whenever a perturbation decreases the system's relative degree, it manifests itself as a singular perturbation of zero dynamics. Conditions are given under which the zero dynamics evolve in two timescales characteristic of a standard singular perturbation form that allows a separate analysis of slow and fast parts of the zero dynamics.
Simple Theory of Geosynchronous-Orbit Perturbations
NASA Astrophysics Data System (ADS)
Kawase, Sei-Ichiro
A simple perturbation theory is introduced for modeling geosynchronous orbits. The theory uses diagrammatic representations of orbits, and derives the perturbations in a direct manner without using differential equations. Perturbations of major importance are derived, including satellite-longitude changes due to the earth’s asymmetric shape, orbital eccentricity increase due to the sun-radiation pressure, and orbital plane inclination due to the sun/moon attraction. The theory clarifies the physical/geometrical meaning of the perturbations while using minimal mathematical analysis.
Numerical Analysis of the Acoustic Field of Tip-Clearance Flow
NASA Astrophysics Data System (ADS)
Alavi Moghadam, S. M.; M. Meinke Team; W. Schröder Team
2015-11-01
Numerical simulations of the acoustic field generated by a shrouded axial fan are studied by a hybrid fluid-dynamics-acoustics method. In a first step, large-eddy simulations are performed to investigate the dynamics of tip clearance flow for various tip gap sizes and to determine the acoustic sources. The simulations are performed for a single blade out of five blades with periodic boundary conditions in the circumferential direction on a multi-block structured mesh with 1.4 ×108 grid points. The turbulent flow is simulated at a Reynolds number of 9.36 ×105 at undisturbed inflow condition and the results are compared with experimental data. The diameter and strength of the tip vortex increase with the tip gap size, while simultaneously the efficiency of the fan decreases. In a second step, the acoustic field on the near field is determined by solving the acoustic perturbation equations (APE) on a mesh for a single blade consisting of approx. 9.8 ×108 grid points. The overall agreement of the pressure spectrum and its directivity with measurements confirm the correct identification of the sound sources and accurate prediction of the acoustic duct propagation. The results show that the longer the tip gap size the higher the broadband noise level. Senior Scientist, Institute of Aerodynamics, RWTH Aachen University.
Aminmansoor, F.; Abbasi, H.
2015-08-15
The present paper is devoted to simulation of nonlinear disintegration of a localized perturbation into ion-acoustic solitons train in a plasma with hot electrons and cold ions. A Gaussian initial perturbation is used to model the localized perturbation. For this purpose, first, we reduce fluid system of equations to a Korteweg de-Vries equation by the following well-known assumptions. (i) On the ion-acoustic evolution time-scale, the electron velocity distribution function (EVDF) is assumed to be stationary. (ii) The calculation is restricted to small amplitude cases. Next, in order to generalize the model to finite amplitudes cases, the evolution of EVDF is included. To this end, a hybrid code is designed to simulate the case, in which electrons dynamics is governed by Vlasov equation, while cold ions dynamics is, like before, studied by the fluid equations. A comparison between the two models shows that although the fluid model is capable of demonstrating the general features of the process, to have a better insight into the relevant physics resulting from the evolution of EVDF, the use of kinetic treatment is of great importance.
Lakhin, V. P.; Sorokina, E. A. E-mail: vilkiae@gmail.com; Ilgisonis, V. I.; Konovaltseva, L. V.
2015-12-15
A set of reduced linear equations for the description of low-frequency perturbations in toroidally rotating plasma in axisymmetric tokamak is derived in the framework of ideal magnetohydrodynamics. The model suitable for the study of global geodesic acoustic modes (GGAMs) is designed. An example of the use of the developed model for derivation of the integral conditions for GGAM existence and of the corresponding dispersion relation is presented. The paper is dedicated to the memory of academician V.D. Shafranov.
Ion acoustic shock waves in plasmas with warm ions and kappa distributed electrons and positrons
Hussain, S.; Mahmood, S.; Hafeez Ur-Rehman
2013-06-15
The monotonic and oscillatory ion acoustic shock waves are investigated in electron-positron-ion plasmas (e-p-i) with warm ions (adiabatically heated) and nonthermal kappa distributed electrons and positrons. The dissipation effects are included in the model due to kinematic viscosity of the ions. Using reductive perturbation technique, the Kadomtsev-Petviashvili-Burgers (KPB) equation is derived containing dispersion, dissipation, and diffraction effects (due to perturbation in the transverse direction) in e-p-i plasmas. The analytical solution of KPB equation is obtained by employing tangent hyperbolic (Tanh) method. The analytical condition for the propagation of oscillatory and monotonic shock structures are also discussed in detail. The numerical results of two dimensional monotonic shock structures are obtained for graphical representation. The dependence of shock structures on positron equilibrium density, ion temperature, nonthermal spectral index kappa, and the kinematic viscosity of ions are also discussed.
Instability of charged Lovelock black holes: Vector perturbations and scalar perturbations
NASA Astrophysics Data System (ADS)
Takahashi, Tomohiro
2013-01-01
We examine the stability of charged Lovelock black hole solutions under vector-type and scalar-type perturbations. We find suitable master variables for the stability analysis; the equations for these variables are Schrödinger-type equations with two components, and these Schrödinger operators are symmetric. By these master equations, we show that charged Lovelock black holes are stable under vector-type perturbations. For scalar-type perturbations, we show the criteria for instability and check these numerically. In our previous paper [T. Takahashi, Prog. Theor. Phys. 125, 1289 (2011)], we have shown that nearly extreme black holes show instability under tensor-type perturbations. In this paper, we find that black holes with a small charge show instability under scalar-type perturbations even if they have a relatively large mass.
An acoustic neuroma is a benign tumor that develops on the nerve that connects the ear to the brain. ... can press against the brain, becoming life-threatening. Acoustic neuroma can be difficult to diagnose, because the ...
Studies of acoustical properties of bulk porous flexible materials
NASA Technical Reports Server (NTRS)
Lambert, R. F.
1984-01-01
Acoustic prediction and measurement of bulk porous materials with flexible frames is investigated. The acoustic properties of Kevlar 29 are examined. Various acoustic tests are employed to determine impedance, sound wave propagation, and wave pressure equations for the highly porous fiber composites. The derivation of design equations and future research goals are included.
Higher-order corrections to dust ion-acoustic soliton in a quantum dusty plasma
Chatterjee, Prasanta; Das, Brindaban; Mondal, Ganesh; Muniandy, S. V.; Wong, C. S.
2010-10-15
Dust ion-acoustic soliton is studied in an electron-dust-ion plasma by employing a two-fluid quantum hydrodynamic model. Ions and electrons are assumed to follow quantum mechanical behaviors in dust background. The Korteweg-de Vries (KdV) equation and higher order contribution to KdV equations are derived using reductive perturbation technique. The higher order contribution is obtained as a higher order inhomogeneous differential equation. The nonsecular solution of the higher order contribution is obtained by using the renormalization method and the particular solution of the inhomogeneous equation is determined using a truncated series solution method. The effects of dust concentration, quantum parameter for ions and electrons, and soliton velocity on the amplitude and width of the dressed soliton are discussed.
Two-dimensional cylindrical ion-acoustic solitary and rogue waves in ultrarelativistic plasmas
Ata-ur-Rahman; Ali, S.; Moslem, W. M.; Mushtaq, A.
2013-07-15
The propagation of ion-acoustic (IA) solitary and rogue waves is investigated in a two-dimensional ultrarelativistic degenerate warm dense plasma. By using the reductive perturbation technique, the cylindrical Kadomtsev–Petviashvili (KP) equation is derived, which can be further transformed into a Korteweg–de Vries (KdV) equation. The latter admits a solitary wave solution. However, when the frequency of the carrier wave is much smaller than the ion plasma frequency, the KdV equation can be transferred to a nonlinear Schrödinger equation to study the nonlinear evolution of modulationally unstable modified IA wavepackets. The propagation characteristics of the IA solitary and rogue waves are strongly influenced by the variation of different plasma parameters in an ultrarelativistic degenerate dense plasma. The present results might be helpful to understand the nonlinear electrostatic excitations in astrophysical degenerate dense plasmas.
2008-03-07
a national naval responsibility. Acoustic sensors on mobile, autonomous platforms will enable basic research topics on temporal and spatial...problem and acoustic navigation and communications within the context of distributed autonomous persistent undersea surveillance sensor networks...Acoustic sensors on mobile, autonomous platforms will enable basic research topics on temporal and spatial coherence and the description of ambient
NASA Technical Reports Server (NTRS)
Steinetz, Bruce M. (Inventor)
2006-01-01
The invention relates to a sealing device having an acoustic resonator. The acoustic resonator is adapted to create acoustic waveforms to generate a sealing pressure barrier blocking fluid flow from a high pressure area to a lower pressure area. The sealing device permits noncontacting sealing operation. The sealing device may include a resonant-macrosonic-synthesis (RMS) resonator.
NASA Technical Reports Server (NTRS)
Steinetz, Bruce M. (Inventor)
2006-01-01
The invention relates to a sealing device having an acoustic resonator. The acoustic resonator is adapted to create acoustic waveforms to generate a sealing pressure barrier blocking fluid flow from a high pressure area to a lower pressure area. The sealing device permits noncontacting sealing operation. The sealing device may include a resonant-macrosonic-synthesis (RMS) resonator.
The spectrum of density perturbations in an expanding universe
NASA Technical Reports Server (NTRS)
Silk, J.
1974-01-01
The basic dynamic equations that govern the evolution of perturbations in a Friedmann-Lemaitre universe are derived. General solutions describing the evolution of adiabatic perturbations in the density of matter are obtained, and the choice of the appropriate initial conditions is examined. The various perturbation modes are compared, and the effects of decoupling on the perturbation spectrum are studied. The scheme used to follow the evolution of density perturbations through decoupling is based on an extension of the Eddington approximation to the radiative transfer equation, and is strictly valid in both optically thick and thin limits.
A Generalized Acoustic Analogy
NASA Technical Reports Server (NTRS)
Goldstein, M. E.
2003-01-01
The purpose of this article is to show that the Navier-Stokes equations can be rewritten as a set of linearized inhomogeneous Euler equations (in convective form) with source terms that are exactly the same as those that would result from externally imposed shear stress and energy flux perturbations. These results are used to develop a mathematical basis for some existing and potential new jet noise models by appropriately choosing the base flow about which the linearization is carried out.
Acoustic asymmetric transmission based on time-dependent dynamical scattering
NASA Astrophysics Data System (ADS)
Wang, Qing; Yang, Yang; Ni, Xu; Xu, Ye-Long; Sun, Xiao-Chen; Chen, Ze-Guo; Feng, Liang; Liu, Xiao-Ping; Lu, Ming-Hui; Chen, Yan-Feng
2015-06-01
An acoustic asymmetric transmission device exhibiting unidirectional transmission property for acoustic waves is extremely desirable in many practical scenarios. Such a unique property may be realized in various configurations utilizing acoustic Zeeman effects in moving media as well as frequency-conversion in passive nonlinear acoustic systems and in active acoustic systems. Here we demonstrate a new acoustic frequency conversion process in a time-varying system, consisting of a rotating blade and the surrounding air. The scattered acoustic waves from this time-varying system experience frequency shifts, which are linearly dependent on the blade’s rotating frequency. Such scattering mechanism can be well described theoretically by an acoustic linear time-varying perturbation theory. Combining such time-varying scattering effects with highly efficient acoustic filtering, we successfully develop a tunable acoustic unidirectional device with 20 dB power transmission contrast ratio between two counter propagation directions at audible frequencies.
Acoustic asymmetric transmission based on time-dependent dynamical scattering
Wang, Qing; Yang, Yang; Ni, Xu; Xu, Ye-Long; Sun, Xiao-Chen; Chen, Ze-Guo; Feng, Liang; Liu, Xiao-ping; Lu, Ming-Hui; Chen, Yan-Feng
2015-01-01
An acoustic asymmetric transmission device exhibiting unidirectional transmission property for acoustic waves is extremely desirable in many practical scenarios. Such a unique property may be realized in various configurations utilizing acoustic Zeeman effects in moving media as well as frequency-conversion in passive nonlinear acoustic systems and in active acoustic systems. Here we demonstrate a new acoustic frequency conversion process in a time-varying system, consisting of a rotating blade and the surrounding air. The scattered acoustic waves from this time-varying system experience frequency shifts, which are linearly dependent on the blade’s rotating frequency. Such scattering mechanism can be well described theoretically by an acoustic linear time-varying perturbation theory. Combining such time-varying scattering effects with highly efficient acoustic filtering, we successfully develop a tunable acoustic unidirectional device with 20 dB power transmission contrast ratio between two counter propagation directions at audible frequencies. PMID:26038886
NASA Astrophysics Data System (ADS)
Moses, Harry E.
1984-06-01
The object of the time-dependent inverse source problem of electromagnetic theory and acoustics is to find time-dependent sources and currents, which are turned on at a given time and then off to give rise to prescribed radiation fields. In an early paper for the three-dimensional electromagnetic case, the present writer showed that the sources and currents are not unique and gave conditions which make them so. The ideas of that paper are reformulated for the three-dimensional electromagnetic case and extended to the acoustical three-dimensional case and the one-dimensional electromagnetic and acoustic cases. The one-dimensional cases show very explicitly the nature of the ambiguity of the choice of sources and currents. This ambiguity is closely related to one which occurs in inverse scattering theory. The ambiguity in inverse scattering theory arises when one wishes to obtain the off-shell elements of the T matrix from some of the on-shell elements (i.e., from the corresponding elements of the scattering operator). In inverse scattering theory prescribing of the representation in which the potential is to be diagonal removes the ambiguity. For the inverse source problem a partial prescription of the time dependence of the sources and currents removes the ambiguity. The inverse source problem is then solved explicitly for this prescribed time dependence. The direct source problems for the one- and three-dimensional acoustic and electromagnetic cases are also given to provide a contrast with the inverse source problem and for use in later papers. Moreover, the present author's earlier work on the eigenfunctions of the curl operator is reviewed and used to simplify drastically the three-dimensional direct and inverse source problems for electromagnetic theory by splitting off the radiation field and its currents from the longitudinal field and its sources and currents. Finally, for a prescribed time dependence, the inverse source problem is solved explicitly in
Time-angle sensitivity kernels for sound-speed perturbations in a shallow ocean.
Aulanier, Florian; Nicolas, Barbara; Roux, Philippe; Mars, Jérôme I
2013-07-01
Acoustic waves traveling in a shallow-water waveguide produce a set of multiple paths that can be characterized as a geometric approximation by their travel time (TT), direction of arrival (DOA), and direction of departure (DOD). This study introduces the use of the DOA and DOD as additional observables that can be combined to the classical TT to track sound-speed perturbations in an oceanic waveguide. To model the TT, DOA, and DOD variations induced by sound-speed perturbations, the three following steps are used: (1) In the first-order Born approximation, the Fréchet kernel provides a linear link between the signal fluctuations and the sound-speed perturbations; (2) a double-beamforming algorithm is used to transform the signal fluctuations received on two source-receiver arrays in the time, receiver-depth, and source-depth domain into the eigenray equivalent measured in the time, reception-angle and launch angle domain; and finally (3) the TT, DOA, and DOD variations are extracted from the double-beamformed signal variations through a first-order Taylor development. As a result, time-angle sensitivity kernels are defined and used to build a linear relationship between the observable variations and the sound-speed perturbations. This approach is validated with parabolic-equation simulations in a shallow-water ocean context.
Dust-ion acoustic cnoidal waves and associated nonlinear ion flux in a nonthermal dusty plasma
NASA Astrophysics Data System (ADS)
Ur-Rehman, Hafeez; Mahmood, S.
2016-09-01
The dust-ion acoustic nonlinear periodic (cnoidal) waves and solitons are investigated in a dusty plasma containing dynamic cold ions, superthermal kappa distributed electrons and static charged dust particles. The massive dust particles can have positive or negative charge depending on the plasma environment. Using reductive perturbation method (RPM) with appropriate periodic boundary conditions, the evolution equations for the first and second order nonlinear potentials are derived. The first order potential is determined through Korteweg-de Vries (KdV) equation which gives dust-ion acoustic cnoidal waves and solitons structures. The solution of second order nonlinear potential is obtained through an inhomogeneous differential equation derived from collecting higher order terms of dynamic equations, which is linear for second order electrostatic potential. The nonlinear ion flux associated with the cnoidal waves is also found out numerically. The numerical plots of the dust-ion acoustic cnoidal wave and soliton structures for both positively and negatively charged dust particles cases and nonthermal electrons are also presented for illustration. It is found that only compressive nonlinear electrostatic structures are formed in case of positively dust charged particles while both compressive and rarefactive nonlinear structures are obtained in case of negatively charged particles depending on the negatively charged dust density in a nonthermal dusty plasma. The numerical results are obtained using data of the ionospheric region containing dusty plasma exist in the literature.
Perturbation growth in accreting filaments
NASA Astrophysics Data System (ADS)
Clarke, S. D.; Whitworth, A. P.; Hubber, D. A.
2016-05-01
We use smoothed particle hydrodynamic simulations to investigate the growth of perturbations in infinitely long filaments as they form and grow by accretion. The growth of these perturbations leads to filament fragmentation and the formation of cores. Most previous work on this subject has been confined to the growth and fragmentation of equilibrium filaments and has found that there exists a preferential fragmentation length-scale which is roughly four times the filament's diameter. Our results show a more complicated dispersion relation with a series of peaks linking perturbation wavelength and growth rate. These are due to gravo-acoustic oscillations along the longitudinal axis during the sub-critical phase of growth. The positions of the peaks in growth rate have a strong dependence on both the mass accretion rate onto the filament and the temperature of the gas. When seeded with a multiwavelength density power spectrum, there exists a clear preferred core separation equal to the largest peak in the dispersion relation. Our results allow one to estimate a minimum age for a filament which is breaking up into regularly spaced fragments, as well as an average accretion rate. We apply the model to observations of filaments in Taurus by Tafalla & Hacar and find accretion rates consistent with those estimated by Palmeirim et al.
Conformal invariant cosmological perturbations via the covariant approach
Li, Mingzhe; Mou, Yicen E-mail: moinch@mail.ustc.edu.cn
2015-10-01
It is known that some cosmological perturbations are conformal invariant. This facilitates the studies of perturbations within some gravitational theories alternative to general relativity, for example the scalar-tensor theory, because it is possible to do equivalent analysis in a certain frame in which the perturbation equations are simpler. In this paper we revisit the problem of conformal invariances of cosmological perturbations in terms of the covariant approach in which the perturbation variables have clear geometric and physical meanings. We show that with this approach the conformal invariant perturbations are easily identified.
The Analysis and Construction of Perfectly Matched Layers for the Linearized Euler Equations
NASA Technical Reports Server (NTRS)
Hesthaven, J. S.
1997-01-01
We present a detailed analysis of a recently proposed perfectly matched layer (PML) method for the absorption of acoustic waves. The split set of equations is shown to be only weakly well-posed, and ill-posed under small low order perturbations. This analysis provides the explanation for the stability problems associated with the split field formulation and illustrates why applying a filter has a stabilizing effect. Utilizing recent results obtained within the context of electromagnetics, we develop strongly well-posed absorbing layers for the linearized Euler equations. The schemes are shown to be perfectly absorbing independent of frequency and angle of incidence of the wave in the case of a non-convecting mean flow. In the general case of a convecting mean flow, a number of techniques is combined to obtain a absorbing layers exhibiting PML-like behavior. The efficacy of the proposed absorbing layers is illustrated though computation of benchmark problems in aero-acoustics.
Acoustic Power Suppression of a Panel Structure Using H∞OUTPUT Feedback Control
NASA Astrophysics Data System (ADS)
SIVRIOGLU, S.; TANAKA, N.; YUKSEK, I.
2002-01-01
This paper presents a robust control system design for suppressing the radiated acoustic power emitted from a vibrating planar structure, and spillover effect caused by neglected high-frequency modes. A state-space model of a simply supported panel structure is derived and an output equation is formed based on the one-dimensional PVDF film sensors. An output feedback H∞control is designed by introducing a multiplicative perturbation which represents unmodelled high-frequency dynamics in the control system. The simulation and experimental results demonstrated significant decrease in sound radiation for the considered structural power modes in control.
Passive broadband acoustic thermometry
NASA Astrophysics Data System (ADS)
Anosov, A. A.; Belyaev, R. V.; Klin'shov, V. V.; Mansfel'd, A. D.; Subochev, P. V.
2016-04-01
The 1D internal (core) temperature profiles for the model object (plasticine) and the human hand are reconstructed using the passive acoustothermometric broadband probing data. Thermal acoustic radiation is detected by a broadband (0.8-3.5 MHz) acoustic radiometer. The temperature distribution is reconstructed using a priori information corresponding to the experimental conditions. The temperature distribution for the heated model object is assumed to be monotonic. For the hand, we assume that the temperature distribution satisfies the heat-conduction equation taking into account the blood flow. The average error of reconstruction determined for plasticine from the results of independent temperature measurements is 0.6 K for a measuring time of 25 s. The reconstructed value of the core temperature of the hand (36°C) generally corresponds to physiological data. The obtained results make it possible to use passive broadband acoustic probing for measuring the core temperatures in medical procedures associated with heating of human organism tissues.
Receptivity and Forced Response to Acoustic Disturbances in High-Speed Boundary Layers
NASA Technical Reports Server (NTRS)
Balakumar, P.; King, Rudolph A.; Chou, Amanda; Owens, Lewis R.; Kegerise, Michael A.
2016-01-01
Supersonic boundary-layer receptivity to freestream acoustic disturbances is investigated by solving the Navier-Stokes equations for Mach 3.5 flow over a sharp flat plate and a 7-deg half-angle cone. The freestream disturbances are generated from a wavy wall placed at the nozzle wall. The freestream acoustic disturbances radiated by the wavy wall are obtained by solving the linearized Euler equations. The results for the flat plate show that instability modes are generated at all the incident angles ranging from zero to highly oblique. However, the receptivity coefficient decreases by about 20 times when the incident angle increases from zero to a highly oblique angle of 68 degrees. The results for the cone show that no instability modes are generated when the acoustic disturbances impinge the cone obliquely. The results show that the perturbations generated inside the boundary layer by the acoustic disturbances are the response of the boundary layer to the external forcing. The amplitude of the forced disturbances inside the boundary layer are about 2.5 times larger than the incoming field for zero azimuthal wavenumber and they are about 1.5 times for large azimuthal wavenumbers.
Dust-acoustic rogue waves in a nonextensive plasma
Moslem, W. M.; Shukla, P. K.; Sabry, R.; El-Labany, S. K.
2011-12-15
We present an investigation for the generation of a dust-acoustic rogue wave in a dusty plasma composed of negatively charged dust grains, as well as nonextensive electrons and ions. For this purpose, the reductive perturbation technique is used to obtain a nonlinear Schroedinger equation. The critical wave-number threshold k{sub c}, which indicates where the modulational instability sets in, has been determined precisely for various regimes. Two different behaviors of k{sub c} against the nonextensive parameter q are found. For small k{sub c}, it is found that increasing q would lead to an increase of k{sub c} until q approaches a certain value q{sub c}, then further increase of q beyond q{sub c} decreases the value of k{sub c}. For large k{sub c}, the critical wave-number threshold k{sub c} is always increasing with q. Within the modulational instability region, a random perturbation of the amplitude grows and thus creates dust-acoustic rogue waves. In order to show that the characteristics of the rogue waves are influenced by the plasma parameters, the relevant numerical analysis of the appropriate nonlinear solution is presented. The nonlinear structure, as reported here, could be useful for controlling and maximizing highly energetic pulses in dusty plasmas.
Dust-acoustic rogue waves in a nonextensive plasma.
Moslem, W M; Sabry, R; El-Labany, S K; Shukla, P K
2011-12-01
We present an investigation for the generation of a dust-acoustic rogue wave in a dusty plasma composed of negatively charged dust grains, as well as nonextensive electrons and ions. For this purpose, the reductive perturbation technique is used to obtain a nonlinear Schrödinger equation. The critical wave-number threshold k(c), which indicates where the modulational instability sets in, has been determined precisely for various regimes. Two different behaviors of k(c) against the nonextensive parameter q are found. For small k(c), it is found that increasing q would lead to an increase of k(c) until q approaches a certain value q(c), then further increase of q beyond q(c) decreases the value of k(c). For large k(c), the critical wave-number threshold k(c) is always increasing with q. Within the modulational instability region, a random perturbation of the amplitude grows and thus creates dust-acoustic rogue waves. In order to show that the characteristics of the rogue waves are influenced by the plasma parameters, the relevant numerical analysis of the appropriate nonlinear solution is presented. The nonlinear structure, as reported here, could be useful for controlling and maximizing highly energetic pulses in dusty plasmas.
Small Amplitude Electron Acoustic Solitons in a Magnetoplasma with Non-Thermal Electrons
NASA Astrophysics Data System (ADS)
Devanandhan, Selvaraj; Lakhina, Gurbax S.; Singh, Satyavir
An important characteristic of space plasmas is their ability to sustain a great variety of wave phenomena. Such plasma waves are detected in space with the frequency ranging from few millihertz to several tens of kilohertz. The nonlinear evolutions of these waveforms are interpreted as electron-acoustic and ion-acoustic solitary waves. There have been several studies on solitary waves that are based on models using the Boltzmann distribution function for electrons/ions. However, in space plasmas, a population of superthermal electrons, where the particle distributions may deviate from the Maxwellian can exist. We have studied the small amplitude electron acoustic solitary waves in four component plasma consisting of nonthermal hot electrons, fluid cold electrons, beam electrons and ions is studied. Using reductive perturbation technique, the Korteweg-de-Vries-Zakharov-Kuznetsov (KdV-ZK) equation describing nonlinear evolution of electron acoustic solitons is derived. The effects of non-thermality, beam electron velocity and temperature, obliquity on electron acoustic solitary structures are investigated in detail. These theoretical results on solitary potential structures will be used to model satellite observations in the various regions of the Earth’s magnetosphere.
Dynamic Weakening by Acoustic Fluidization during Stick-Slip Motion.
Giacco, F; Saggese, L; de Arcangelis, L; Lippiello, E; Pica Ciamarra, M
2015-09-18
The unexpected weakness of some faults has been attributed to the emergence of acoustic waves that promote failure by reducing the confining pressure through a mechanism known as acoustic fluidization, also proposed to explain earthquake remote triggering. Here we validate this mechanism via the numerical investigation of a granular fault model system. We find that the stick-slip dynamics is affected only by perturbations applied at a characteristic frequency corresponding to oscillations normal to the fault, leading to gradual dynamical weakening as failure is approaching. Acoustic waves at the same frequency spontaneously emerge at the onset of failure in the absence of perturbations, supporting the relevance of acoustic fluidization in earthquake triggering.
Disformal invariance of curvature perturbation
Motohashi, Hayato; White, Jonathan E-mail: jwhite@post.kek.jp
2016-02-01
We show that under a general disformal transformation the linear comoving curvature perturbation is not identically invariant, but is invariant on superhorizon scales for any theory that is disformally related to Horndeski's theory. The difference between disformally related curvature perturbations is found to be given in terms of the comoving density perturbation associated with a single canonical scalar field. In General Relativity it is well-known that this quantity vanishes on superhorizon scales through the Poisson equation that is obtained on combining the Hamiltonian and momentum constraints, and we confirm that a similar result holds for any theory that is disformally related to Horndeski's scalar-tensor theory so long as the invertibility condition for the disformal transformation is satisfied. We also consider the curvature perturbation at full nonlinear order in the unitary gauge, and find that it is invariant under a general disformal transformation if we assume that an attractor regime has been reached. Finally, we also discuss the counting of degrees of freedom in theories disformally related to Horndeski's.
Non-perturbative String Theory from Water Waves
Iyer, Ramakrishnan; Johnson, Clifford V.; Pennington, Jeffrey S.; /SLAC
2012-06-14
We use a combination of a 't Hooft limit and numerical methods to find non-perturbative solutions of exactly solvable string theories, showing that perturbative solutions in different asymptotic regimes are connected by smooth interpolating functions. Our earlier perturbative work showed that a large class of minimal string theories arise as special limits of a Painleve IV hierarchy of string equations that can be derived by a similarity reduction of the dispersive water wave hierarchy of differential equations. The hierarchy of string equations contains new perturbative solutions, some of which were conjectured to be the type IIA and IIB string theories coupled to (4, 4k ? 2) superconformal minimal models of type (A, D). Our present paper shows that these new theories have smooth non-perturbative extensions. We also find evidence for putative new string theories that were not apparent in the perturbative analysis.
Newtonian limit of fully nonlinear cosmological perturbations in Einstein's gravity
Hwang, Jai-chan; Noh, Hyerim E-mail: hr@kasi.re.kr
2013-04-01
We prove that in the infinite speed-of-light limit (i.e., non-relativistic and subhorizon limits), the relativistic fully nonlinear cosmological perturbation equations in two gauge conditions, the zero-shear gauge and the uniform-expansion gauge, exactly reproduce the Newtonian hydrodynamic perturbation equations in the cosmological background; as a consequence, in the same two gauge conditions, the Newtonian hydrodynamic equations are exactly recovered in the Minkowsky background.
NASA Astrophysics Data System (ADS)
Shah, M. G.; Rahman, M. M.; Hossen, M. R.; Mamun, A. A.
2016-02-01
A theoretical investigation on heavy ion-acoustic (HIA) solitary and shock structures has been accomplished in an unmagnetized multispecies plasma consisting of inertialess kappa-distributed superthermal electrons, Boltzmann light ions, and adiabatic positively charged inertial heavy ions. Using the reductive perturbation technique, the nonplanar (cylindrical and spherical) Kortewg-de Vries (KdV) and Burgers equations have been derived. The solitary and shock wave solutions of the KdV and Burgers equations, respectively, have been numerically analyzed. The effects of superthermality of electrons, adiabaticity of heavy ions, and nonplanar geometry, which noticeably modify the basic features (viz. polarity, amplitude, phase speed, etc.) of small but finite amplitude HIA solitary and shock structures, have been carefully investigated. The HIA solitary and shock structures in nonplanar geometry have been found to distinctly differ from those in planar geometry. Novel features of our present attempt may contribute to the physics of nonlinear electrostatic perturbation in astrophysical and laboratory plasmas.
Non-perturbative QCD and hadron physics
NASA Astrophysics Data System (ADS)
Cobos-Martínez, J. J.
2016-10-01
A brief exposition of contemporary non-perturbative methods based on the Schwinger-Dyson (SDE) and Bethe-Salpeter equations (BSE) of Quantum Chromodynamics (QCD) and their application to hadron physics is given. These equations provide a non-perturbative continuum formulation of QCD and are a powerful and promising tool for the study of hadron physics. Results on some properties of hadrons based on this approach, with particular attention to the pion distribution amplitude, elastic, and transition electromagnetic form factors, and their comparison to experimental data are presented.
Cosmological perturbations in unimodular gravity
Gao, Caixia; Brandenberger, Robert H.; Cai, Yifu; Chen, Pisin E-mail: rhb@hep.physics.mcgill.ca E-mail: chen@slac.stanford.edu
2014-09-01
We study cosmological perturbation theory within the framework of unimodular gravity. We show that the Lagrangian constraint on the determinant of the metric required by unimodular gravity leads to an extra constraint on the gauge freedom of the metric perturbations. Although the main equation of motion for the gravitational potential remains the same, the shift variable, which is gauge artifact in General Relativity, cannot be set to zero in unimodular gravity. This non-vanishing shift variable affects the propagation of photons throughout the cosmological evolution and therefore modifies the Sachs-Wolfe relation between the relativistic gravitational potential and the microwave temperature anisotropies. However, for adiabatic fluctuations the difference between the result in General Relativity and unimodular gravity is suppressed on large angular scales. Thus, no strong constraints on the theory can be derived.
NASA Astrophysics Data System (ADS)
Gough, Colin
This chapter provides an introduction to the physical and psycho-acoustic principles underlying the production and perception of the sounds of musical instruments. The first section introduces generic aspects of musical acoustics and the perception of musical sounds, followed by separate sections on string, wind and percussion instruments.
Quantum positron acoustic waves
Metref, Hassina; Tribeche, Mouloud
2014-12-15
Nonlinear quantum positron-acoustic (QPA) waves are investigated for the first time, within the theoretical framework of the quantum hydrodynamic model. In the small but finite amplitude limit, both deformed Korteweg-de Vries and generalized Korteweg-de Vries equations governing, respectively, the dynamics of QPA solitary waves and double-layers are derived. Moreover, a full finite amplitude analysis is undertaken, and a numerical integration of the obtained highly nonlinear equations is carried out. The results complement our previously published results on this problem.
Coupling between plate vibration and acoustic radiation
NASA Technical Reports Server (NTRS)
Frendi, Abdelkader; Maestrello, Lucio; Bayliss, Alvin
1992-01-01
A detailed numerical investigation of the coupling between the vibration of a flexible plate and the acoustic radiation is performed. The nonlinear Euler equations are used to describe the acoustic fluid while the nonlinear plate equation is used to describe the plate vibration. Linear, nonlinear, and quasi-periodic or chaotic vibrations and the resultant acoustic radiation are analyzed. We find that for the linear plate response, acoustic coupling is negligible. However, for the nonlinear and chaotic responses, acoustic coupling has a significant effect on the vibration level as the loading increases. The radiated pressure from a plate undergoing nonlinear or chaotic vibrations is found to propagate nonlinearly into the far-field. However, the nonlinearity due to wave propagation is much weaker than that due to the plate vibrations. As the acoustic wave propagates into the far-field, the relative difference in level between the fundamental and its harmonics and subharmonics decreases with distance.
Coupling between plate vibration and acoustic radiation
NASA Technical Reports Server (NTRS)
Frendi, Abdelkader; Maestrello, Lucio; Bayliss, Alvin
1993-01-01
A detailed numerical investigation of the coupling between the vibration of a flexible plate and the acoustic radiation is performed. The nonlinear Euler equations are used to describe the acoustic fluid while the nonlinear plate equation is used to describe the plate vibration. Linear, nonlinear, and quasi-periodic or chaotic vibrations and the resultant acoustic radiation are analyzed. We find that for the linear plate response, acoustic coupling is negligible. However, for the nonlinear and chaotic responses, acoustic coupling has a significant effect on the vibration level as the loading increases. The radiated pressure from a plate undergoing nonlinear or chaotic vibrations is found to propagate nonlinearly into the far field. However, the nonlinearity due to wave propagation is much weaker than that due to the plate vibrations. As the acoustic wave propagates into the far field, the relative difference in level between the fundamental and its harmonics and subharmonics decreases with distance.
Shah, Asif; Mahmood, S.; Haque, Q.
2010-11-15
The ion acoustic solitons are studied in an inhomogeneous multi-ion component plasma in the presence of heavy and light adiabatic ions and two temperature electrons with vortex distribution. The modified Korteweg-de Vries equation with an additional term due to density gradients is derived by employing reductive perturbation technique. It is found that the amplitude of the soliton enhances as the concentration ratio of cold to hot electrons, density gradient parameter and ion temperature are increased in the system. The effects of mass, charge ratios of heavy to light ions and electron temperature are also investigated on the structural as well as propagation characteristics of solitary wave. The equilibrium density profile is taken to be exponential. The phase velocity of ion acoustic wave is also studied as a function of various plasma parameters. The numerical results are presented for illustration.
McCullagh, Nuala; Szalay, Alexander S.
2015-01-10
Baryon acoustic oscillations (BAO) are a powerful probe of the expansion history of the universe, which can tell us about the nature of dark energy. In order to accurately characterize the dark energy equation of state using BAO, we must understand the effects of both nonlinearities and redshift space distortions on the location and shape of the acoustic peak. In a previous paper, we introduced a novel approach to second order perturbation theory in configuration space using the Zel'dovich approximation, and presented a simple result for the first nonlinear term of the correlation function. In this paper, we extend this approach to redshift space. We show how to perform the computation and present the analytic result for the first nonlinear term in the correlation function. Finally, we validate our result through comparison with numerical simulations.
Linear acoustic sensitivity kernels and their applications in shallow water environments
NASA Astrophysics Data System (ADS)
Sarkar, Bikramjit
Time of arrival information from acoustic transmissions is the primary means through which ocean sound-speed structure is estimated. While initially limited to large scale coarse observations using ray theory to model the propagation of sound through the environment, ocean acoustic tomography evolved to incorporate a normal-mode representation of observed peak-arrivals. This wave-theoretic approach was enhanced, using the first Born approximation to perturbations in the wave equation, producing the travel-time sensitivity kernel (TSK): a linear relationship between sound-speed variations and observed changes in arrival times. This dissertation extends sensitivity kernel analysis to both the amplitude and phase of complex-demodulated broadband acoustic transmissions, producing both a qualitative and quantitative picture of how ocean sound-speed variability affects acoustic observations, and complementing prior work on travel-time sensitivity. The linearity and information content of these kernels is explored in simulation for a 3--4 kHz broadband pulse transmission through a 1 km shallow-water Pekeris waveguide, and in simulated inversions with a more realistic summer-type sound-speed profile, the results from which demonstrate the additional information amplitude contains over phase data alone. Differences in phase measurements were assumed to be directly relatable to travel-time changes, and thus the phase sensitivity kernel was expected to represent the same details as the travel-time sensitivity kernel. However, even a cursory visual inspection of the two kernel types shows that they have different spatial structures and hence different sensitivities to changes in the environment. A numerical survey was conducted comparing the performance of these sensitivity kernels (along with amplitude) to observations from perturbed simulations---including a synthetic time-evolving ocean---and the results suggest that phase and peak travel-time do indeed diverge in the
Multifield cosmological perturbations at third order and the ekpyrotic trispectrum
Lehners, Jean-Luc; Renaux-Petel, Sebastien
2009-09-15
Using the covariant formalism, we derive the equations of motion for adiabatic and entropy perturbations at third order in perturbation theory for cosmological models involving two scalar fields. We use these equations to calculate the trispectrum of ekpyrotic and cyclic models in which the density perturbations are generated via the entropic mechanism. In these models, the conversion of entropy into curvature perturbations occurs just before the big bang, either during the ekpyrotic phase or during the subsequent kinetic energy dominated phase. In both cases, we find that the nonlinearity parameters f{sub NL} and g{sub NL} combine to leave a very distinct observational imprint.
NASA Astrophysics Data System (ADS)
Xu, Si-Liu; Liang, Jian-Chu; Yi, Lin
2010-01-01
The (1+1)-dimensional F-expansion technique and the homogeneous nonlinear balance principle have been generalized and applied for solving exact solutions to a general (3+1)-dimensional nonlinear Schrödinger equation (NLSE) with varying coefficients and a harmonica potential. We found that there exist two kinds of soliton solutions. The evolution features of exact solutions have been numerically studied. The (3+1)D soliton solutions may help us to understand the nonlinear wave propagation in the nonlinear media such as classical optical waves and the matter waves of the Bose-Einstein condensates.
A high-fidelity method to analyze perturbation evolution in turbulent flows
Unnikrishnan, S. Gaitonde, Datta V.
2016-04-01
Small perturbation propagation in fluid flows is usually examined by linearizing the governing equations about a steady basic state. It is often useful, however, to study perturbation evolution in the unsteady evolving turbulent environment. Such analyses can elucidate the role of perturbations in the generation of coherent structures or the production of noise from jet turbulence. The appropriate equations are still the linearized Navier–Stokes equations, except that the linearization must be performed about the instantaneous evolving turbulent state, which forms the coefficients of the linearized equations. This is a far more difficult problem since in addition to the turbulent state, its rate of change and the perturbation field are all required at each instant. In this paper, we develop and use a novel technique for this problem by using a pair (denoted “baseline” and “twin”) of simultaneous synchronized Large-Eddy Simulations (LES). At each time-step, small disturbances whose propagation characteristics are to be studied, are introduced into the twin through a forcing term. At subsequent time steps, the difference between the two simulations is shown to be equivalent to solving the forced Navier–Stokes equations, linearized about the instantaneous turbulent state. The technique does not put constraints on the forcing, which could be arbitrary, e.g., white noise or other stochastic variants. We consider, however, “native” forcing having properties of disturbances that exist naturally in the turbulent environment. The method then isolates the effect of turbulence in a particular region on the rest of the field, which is useful in the study of noise source localization. The synchronized technique is relatively simple to implement into existing codes. In addition to minimizing the storage and retrieval of large time-varying datasets, it avoids the need to explicitly linearize the governing equations, which can be a very complicated task for viscous
Influence of vibrational relaxation on perturbations in a shock layer on a plate
NASA Astrophysics Data System (ADS)
Kirilovskiy, S. V.; Maslov, A. A.; Poplavskaya, T. V.; Tsyryul'nikov, I. S.
2015-05-01
The influence of excitation of molecular vibrational degrees of freedom on the mean flow and perturbation development in a hypersonic (M = 6-14) viscous shock layer is studied. The layer originates on a plate placed in a flow of air, carbon dioxide, or their mixture at high stagnation temperatures (2000-3000 K). The mean flow and pressure pulsation on the surface of the plate are measured in an IT-302M pulsed wind tunnel (Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences). Numerical simulation is carried out in terms of a model of a thermally perfect gas using the ANSYS Fluent program package based on solving nonstationary two-dimensional Navier-Stokes equations. External flow perturbations are introduced into the computational domain in the form of plane monochromatic acoustic waves using UDF modules built in the computational code. It is shown that the excitation of vibrational degrees of freedom in carbon dioxide molecules considerably influences the position of the head wave and intensifies perturbations in contrast to air in which the fraction of vibrationally excited molecules is low at the same parameters of the oncoming low. The influence of the excitation of vibrational degrees of freedom is studied both for equilibrium gas and for a vibrationally nonequilibrium gas. Nonequilibrium vibrational degrees of freedom are simulated using a two-temperature model of relaxation flows in which the time variation of the vibrational energy is described by the Landau-Teller equation with regard to a finite time of energy exchange between vibrational and translational-rotational degrees of freedom of molecules. It is found that the vibrational nonequilibrium has a damping effect on perturbations.
Automated Lattice Perturbation Theory
Monahan, Christopher
2014-11-01
I review recent developments in automated lattice perturbation theory. Starting with an overview of lattice perturbation theory, I focus on the three automation packages currently "on the market": HiPPy/HPsrc, Pastor and PhySyCAl. I highlight some recent applications of these methods, particularly in B physics. In the final section I briefly discuss the related, but distinct, approach of numerical stochastic perturbation theory.
Acoustic solitons in inhomogeneous pair-ion plasmas
Shah, Asif; Mahmood, S.; Haque, Q.
2010-12-15
The acoustic solitons are investigated in inhomogeneous unmagnetized pair ion plasmas. The Korteweg-de Vries (KdV) like equation with an additional term due to density gradients is deduced by employing reductive perturbation technique. It is noticed that pair-ion plasma system is conducive for the propagation of compressive as well as rarefactive solitons. The increase in the temperature ratio causes the amplitude of the rarefactive soliton to decrease. However, the amplitude of the compressive solitons is found to be increased as the temperature ratio of ions is enhanced. The amplitude of both compressive and rarefactive solitons is found to be increased as the density gradient parameter is increased. The equlibrium density profile is assumed to be exponential. The numerical results are shown for illustration.
Weakly dissipative dust-ion acoustic wave modulation
NASA Astrophysics Data System (ADS)
Alinejad, H.; Mahdavi, M.; Shahmansouri, M.
2016-02-01
The modulational instability of dust-ion acoustic (DIA) waves in an unmagnetized dusty plasma is investigated in the presence of weak dissipations arising due to the low rates (compared to the ion oscillation frequency) of ionization recombination and ion loss. Based on the multiple space and time scales perturbation, a new modified nonlinear Schrödinger equation governing the evolution of modulated DIA waves is derived with a linear damping term. It is shown that the combined action of all dissipative mechanisms due to collisions between particles reveals the permitted maximum time for the occurrence of the modulational instability. The influence on the modulational instability regions of relevant physical parameters such as ion temperature, dust concentration, ionization, recombination and ion loss is numerically examined. It is also found that the recombination frequency controls the instability growth rate, whereas recombination and ion loss make the instability regions wider.
Density matrix perturbation theory.
Niklasson, Anders M N; Challacombe, Matt
2004-05-14
An orbital-free quantum perturbation theory is proposed. It gives the response of the density matrix upon variation of the Hamiltonian by quadratically convergent recursions based on perturbed projections. The technique allows treatment of embedded quantum subsystems with a computational cost scaling linearly with the size of the perturbed region, O(N(pert.)), and as O(1) with the total system size. The method allows efficient high order perturbation expansions, as demonstrated with an example involving a 10th order expansion. Density matrix analogs of Wigner's 2n+1 rule are also presented.
NASA Astrophysics Data System (ADS)
El-Tantawy, S. A.
2016-05-01
We examine the likelihood of the ion-acoustic rogue waves propagation in a non-Maxwellian electronegative plasma in the framework of the family of the Korteweg-de Vries (KdV) equations (KdV/modified KdV/Extended KdV equation). For this purpose, we use the reductive perturbation technique to carry out this study. It is known that the family of the KdV equations have solutions of distinct structures such as solitons, shocks, kinks, cnoidal waves, etc. However, the dynamics of the nonlinear rogue waves is governed by the nonlinear Schrödinger equation (NLSE). Thus, the family of the KdV equations is transformed to their corresponding NLSE developing a weakly nonlinear wave packets. We show the possible region for the existence of the rogue waves and define it precisely for typical parameters of space plasmas. We investigate numerically the effects of relevant physical parameters, namely, the negative ion relative concentration, the nonthermal parameter, and the mass ratio on the propagation of the rogue waves profile. The present study should be helpful in understanding the salient features of the nonlinear structures such as, ion-acoustic solitary waves, shock waves, and rogue waves in space and in laboratory plasma where two distinct groups of ions, i.e. positive and negative ions, and non-Maxwellian (nonthermal) electrons are present.
Perturbations of the Robertson-Walker space
NASA Astrophysics Data System (ADS)
Hwang, Jai Chan
This dissertation contains three parts consisting of thirteen chapters. Each chapter is self-contained, and can be read independently. In chapter 1, we have presented a complete set of cosmological perturbation equations using the covariant equations. We also present an explicit solution for the evolution of large scale cosmological density perturbations assuming a perfect fluid. In chapter 2, two independent gauge-invariant variables are derived which are continuous at any transition where there is a discontinuous change in pressure. In chapter 3, we present a Newtonian counterpart to the general relativistic covariant approach to cosmological perturbations. In chapter 4, we present a simple way of deriving cosmological perturbation equations in generalized gravity theories which accounts for metric perturbations in gauge-invariant way. We apply this approach to the f(phi,R)-omega(phi)phi, cphi;c Lagrangian. In chapter 5, we have derived second order differential equations for cosmological perturbations in a Robertson-Walker space, for each of the following gravity theories: f(R) gravity, generalized scalar-tensor gravity, gravity with non-minimally coupled scalar field, and induced gravity. Asymptotic solutions are derived for the large and small scale limits. In chapter 6, classical evolution of density perturbations in the large scale limit is clarified in the generalized gravity theories. In chapter 7, we apply our method to a theory with the Lagrangian L approximately f(R) + gamma RR;c;c. In chapter 8, T(M)ab;b equals 0 is shown in a general ground. In chapter 9, the origin of the Friedmann-like behavior of the perturbed model in the large scale limit is clarified in a comoving gauge. Thus, when the imperfect fluid contributions are negligible, the large scale perturbations in a nearly flat background evolve like separate Friedmann models. In chapter 10, we generalize the perturbation equations applicable to a class of generalized gravity theories with multi
Perturbations of black p-branes
Abdalla, Elcio; Fernandez Piedra, Owen Pavel; Oliveira, Jeferson de; Molina, C.
2010-03-15
We consider black p-brane solutions of the low-energy string action, computing scalar perturbations. Using standard methods, we derive the wave equations obeyed by the perturbations and treat them analytically and numerically. We have found that tensorial perturbations obtained via a gauge-invariant formalism leads to the same results as scalar perturbations. No instability has been found. Asymptotically, these solutions typically reduce to a AdS{sub (p+2)}xS{sup (8-p)} space which, in the framework of Maldacena's conjecture, can be regarded as a gravitational dual to a conformal field theory defined in a (p+1)-dimensional flat space-time. The results presented open the possibility of a better understanding the AdS/CFT correspondence, as originally formulated in terms of the relation among brane structures and gauge theories.
NASA Astrophysics Data System (ADS)
Kuttruff, Heinrich; Mommertz, Eckard
The traditional task of room acoustics is to create or formulate conditions which ensure the best possible propagation of sound in a room from a sound source to a listener. Thus, objects of room acoustics are in particular assembly halls of all kinds, such as auditoria and lecture halls, conference rooms, theaters, concert halls or churches. Already at this point, it has to be pointed out that these conditions essentially depend on the question if speech or music should be transmitted; in the first case, the criterion for transmission quality is good speech intelligibility, in the other case, however, the success of room-acoustical efforts depends on other factors that cannot be quantified that easily, not least it also depends on the hearing habits of the listeners. In any case, absolutely "good acoustics" of a room do not exist.
Adiabatic and isocurvature perturbation projections in multi-field inflation
Gordon, Chris; Saffin, Paul M. E-mail: Paul.Saffin@nottingham.ac.uk
2013-08-01
Current data are in good agreement with the predictions of single field inflation. However, the hemispherical asymmetry, seen in the cosmic microwave background data, may hint at a potential problem. Generalizing to multi-field models may provide one possible explanation. A useful way of modeling perturbations in multi-field inflation is to investigate the projection of the perturbation along and perpendicular to the background fields' trajectory. These correspond to the adiabatic and isocurvature perturbations. However, it is important to note that in general there are no corresponding adiabatic and isocurvature fields. The purpose of this article is to highlight the distinction between a field redefinition and a perturbation projection. We provide a detailed derivation of the evolution of the isocurvature perturbation to show that no assumption of an adiabatic or isocurvature field is needed. We also show how this evolution equation is consistent with the field covariant evolution equations for the adiabatic perturbation in the flat field space limit.
A new model for realistic random perturbations of stochastic oscillators
NASA Astrophysics Data System (ADS)
Dieci, Luca; Li, Wuchen; Zhou, Haomin
2016-08-01
Classical theories predict that solutions of differential equations will leave any neighborhood of a stable limit cycle, if white noise is added to the system. In reality, many engineering systems modeled by second order differential equations, like the van der Pol oscillator, show incredible robustness against noise perturbations, and the perturbed trajectories remain in the neighborhood of a stable limit cycle for all times of practical interest. In this paper, we propose a new model of noise to bridge this apparent discrepancy between theory and practice. Restricting to perturbations from within this new class of noise, we consider stochastic perturbations of second order differential systems that -in the unperturbed case- admit asymptotically stable limit cycles. We show that the perturbed solutions are globally bounded and remain in a tubular neighborhood of the underlying deterministic periodic orbit. We also define stochastic Poincaré map(s), and further derive partial differential equations for the transition density function.
Mixing in Shear Coaxial Jets with and without Acoustics
2012-03-29
Force Research Laboratory (AFMC) AFRL/RZSA 10 E. Saturn Blvd. Edwards AFB CA 93524-7680 9. SPONSORING / MONITORING AGENCY NAME(S) AND...Acoustic Field Set-Up: Pressure Antinode • Pressure antinode ( PAN ) – condition of maximum pressure perturbation in the acoustic field • Piezo-sirens...forced in-phase • Superposition of quasi-1D acoustic waves traveling in opposite directions ⇒ PAN at the jet location (geometric center of test
NASA Astrophysics Data System (ADS)
Uddin, M. J.; Alam, M. S.; Mamun, A. A.
2015-02-01
Nonplanar (cylindrical and spherical) positron-acoustic (PA) Gardner solitary waves (SWs) in an unmagnetized plasma system consisting of immobile positive ions, mobile cold positrons, and superthermal (kappa distributed) hot positrons and electrons are investigated. The modified Gardner equation is derived by using the reductive perturbation technique. The effects of cylindrical and spherical geometries, superthermal parameter of hot positrons and electrons, relative temperature ratios, and relative number density ratios on the PA Gardner SWs are studied by using the numerical simulations. The implications of our results in various space and laboratory plasma environments are briefly discussed.
2006-09-30
situations. The equation for the average acoustic field in the statistically homogeneous in horizontal plane stratified waveguide satisfies an...is the vertical coordinate, and integration is along an perturbed eigenray between a source at (xS, 0, zS) and the mid-point (xR, 0, zR RR ) between...angle on the eigenray , ( ) ( )( ) ( ) ( )( ) ( ) 00 0 , ; ,, tan ; , , ; , , , cos S x R R R R R R R R R R Rx c x z x x z dxp x b z x x z x q x
El-Labany, S. K.; Selim, M. M. E-mail: mselim2000@yahoo.com; Al-Abbasy, O. M.; El-Bedwehy, N. A.
2015-02-15
The effects of adiabatic dust grain charge fluctuation and inhomogeneity on the nonlinear properties of dust acoustic (DA) solitary waves are studied. The plasma under consideration is a hot magnetized dusty plasma consisting of negatively charged dust particles, Boltzmann ions, and nonextensive electrons. A modified Zakharov-Kusnetsov equation, which admits a solitary wave solution, is derived using the reductive perturbation theory. It is found that the charge fluctuation of the dust grain modifies the nature of DA solitary structures. The numerical results may be useful to understand phenomena in laboratory and astrophysical plasmas.
Uddin, M. J. Alam, M. S.; Mamun, A. A.
2015-02-15
Nonplanar (cylindrical and spherical) positron-acoustic (PA) Gardner solitary waves (SWs) in an unmagnetized plasma system consisting of immobile positive ions, mobile cold positrons, and superthermal (kappa distributed) hot positrons and electrons are investigated. The modified Gardner equation is derived by using the reductive perturbation technique. The effects of cylindrical and spherical geometries, superthermal parameter of hot positrons and electrons, relative temperature ratios, and relative number density ratios on the PA Gardner SWs are studied by using the numerical simulations. The implications of our results in various space and laboratory plasma environments are briefly discussed.
NASA Astrophysics Data System (ADS)
Denra, Raicharan; Paul, Samit; Sarkar, Susmita
2016-12-01
In this paper, characteristics of small amplitude nonlinear dust acoustic wave have been investigated in a unmagnetized, collisionless, Lorentzian dusty plasma where electrons and ions are inertialess and modeled by generalized Lorentzian Kappa distribution. Dust grains are inertial and equilibrium dust charge is negative. Both adiabatic and nonadiabatic fluctuation of charges on dust grains have been taken under consideration. For adiabatic dust charge variation reductive perturbation analysis gives rise to a KdV equation that governs the nonlinear propagation of dust acoustic waves having soliton solutions. For nonadiabatic dust charge variation nonlinear propagation of dust acoustic wave obeys KdV-Burger equation and gives rise to dust acoustic shock waves. Numerical estimation for adiabatic grain charge variation shows the existence of rarefied soliton whose amplitude and width varies with grain charges. Amplitude and width of the soliton have been plotted for different electron Kappa indices keeping ion velocity distribution Maxwellian. For non adiabatic dust charge variation, ratio of the coefficients of Burger term and dispersion term have been plotted against charge fluctuation for different kappa indices. All these results approach to the results of Maxwellian plasma if both electron and ion kappa tends to infinity.
Frequency noise induced by fiber perturbations in a fiber-linked stabilized laser
NASA Technical Reports Server (NTRS)
Pang, YI; Hamilton, Jeffrey J.; Richard, Jean-Paul
1992-01-01
The effects of acoustic perturbations on an optical fiber that links a stabilized laser to its reference cavity are studied. An extrapolation indicates that 69 dB of acoustic noise impinging on a 1-m segment of the 10-m fiber contribute frequency noise at the level of 1 Hz/(Hz)1/2 in the 1100-2100-Hz band.
NASA Astrophysics Data System (ADS)
Mishra, M. K.; Jain, S. K.; Jain
2013-10-01
Ion-acoustic solitons in magnetized low-β plasma consisting of warm adiabatic positive and negative ions and non-thermal electrons have been studied. The reductive perturbation method is used to derive the Korteweg-de Vries (KdV) equation for the system, which admits an obliquely propagating soliton solution. It is found that due to the presence of finite ion temperature there exist two modes of propagation, namely fast and slow ion-acoustic modes. In the case of slow-mode if the ratio of temperature to mass of positive ion species is lower (higher) than the negative ion species, then there exist compressive (rarefactive) ion-acoustic solitons. It is also found that in the case of slow mode, on increasing the non-thermal parameter (γ) the amplitude of the compressive (rarefactive) soliton decreases (increases). In fast ion-acoustic mode the nature and characteristics of solitons depend on negative ion concentration. Numerical investigation in case of fast mode reveals that on increasing γ, the amplitude of compressive (rarefactive) soliton increases (decreases). The width of solitons increases with an increase in non-thermal parameters in both the modes for compressive as well as rarefactive solitons. There exists a value of critical negative ion concentration (α c ), at which both compressive and rarefactive ion-acoustic solitons appear as described by modified KdV soliton. The value of α c decreases with increase in γ.
Guo, Shimin; Mei, Liquan; Sun, Anbang
2013-05-15
The nonlinear propagation of planar and nonplanar (cylindrical and spherical) ion-acoustic waves in an unmagnetized electron–positron–ion–dust plasma with two-electron temperature distributions is investigated in the context of the nonextensive statistics. Using the reductive perturbation method, a modified nonlinear Schrödinger equation is derived for the potential wave amplitude. The effects of plasma parameters on the modulational instability of ion-acoustic waves are discussed in detail for planar as well as for cylindrical and spherical geometries. In addition, for the planar case, we analyze how the plasma parameters influence the nonlinear structures of the first- and second-order ion-acoustic rogue waves within the modulational instability region. The present results may be helpful in providing a good fit between the theoretical analysis and real applications in future spatial observations and laboratory plasma experiments. -- Highlights: ► Modulational instability of ion-acoustic waves in a new plasma model is discussed. ► Tsallis’s statistics is considered in the model. ► The second-order ion-acoustic rogue wave is studied for the first time.
Evolution of ion-acoustic plasma turbulence
NASA Astrophysics Data System (ADS)
Bychenkov, V. Iu.; Gradov, O. M.
1986-03-01
The evolution of ion-acoustic turbulence is studied on the basis of a numerical solution of the nonstationary equation for in-acoustic waves. Consideration is given to conditions under which the excitation threshold of long-wave ion-acoustic oscillations is exceeded as the result of instability saturation due to quasi-linear relaxation of electrons on turbulent pulsations and the induced scattering of ions by the ion sound. Distributed spectra of ion-acoustic turbulence are established in the plasma under these conditions.
Acoustic radiation damping of flat rectangular plates subjected to subsonic flows
NASA Technical Reports Server (NTRS)
Lyle, Karen Heitman
1993-01-01
The acoustic radiation damping for various isotropic and laminated composite plates and semi-infinite strips subjected to a uniform, subsonic and steady flow has been predicted. The predictions are based on the linear vibration of a flat plate. The fluid loading is characterized as the perturbation pressure derived from the linearized Bernoulli and continuity equations. Parameters varied in the analysis include Mach number, mode number and plate size, aspect ratio and mass. The predictions are compared with existing theoretical results and experimental data. The analytical results show that the fluid loading can significantly affect realistic plate responses. Generally, graphite/epoxy and carbon/carbon plates have higher acoustic radiation damping values than similar aluminum plates, except near plate divergence conditions resulting from aeroelastic instability. Universal curves are presented where the acoustic radiation damping normalized by the mass ratio is a linear function of the reduced frequency. A separate curve is required for each Mach number and plate aspect ratio. In addition, acoustic radiation damping values can be greater than or equal to the structural component of the modal critical damping ratio (assumed as 0.01) for the higher subsonic Mach numbers. New experimental data were acquired for comparison with the analytical results.
Shahmansouri, M.; Mamun, A. A.
2014-03-15
Linear and nonlinear propagation of dust-acoustic waves in a magnetized strongly coupled dusty plasma is theoretically investigated. The normal mode analysis (reductive perturbation method) is employed to investigate the role of ambient/external magnetic field, obliqueness, and effective electrostatic dust-temperature in modifying the properties of linear (nonlinear) dust-acoustic waves propagating in such a strongly coupled dusty plasma. The effective electrostatic dust-temperature, which arises from strong electrostatic interactions among highly charged dust, is considered as a dynamical variable. The linear dispersion relation (describing the linear propagation characteristics) for the obliquely propagating dust-acoustic waves is derived and analyzed. On the other hand, the Korteweg-de Vries equation describing the nonlinear propagation of the dust-acoustic waves (particularly, propagation of dust-acoustic solitary waves) is derived and solved. It is shown that the combined effects of obliqueness, magnitude of the ambient/external magnetic field, and effective electrostatic dust-temperature significantly modify the basic properties of linear and nonlinear dust-acoustic waves. The results of this work are compared with those observed by some laboratory experiments.
Variational Perturbation Treatment of the Confined Hydrogen Atom
ERIC Educational Resources Information Center
Montgomery, H. E., Jr.
2011-01-01
The Schrodinger equation for the ground state of a hydrogen atom confined at the centre of an impenetrable cavity is treated using variational perturbation theory. Energies calculated from variational perturbation theory are comparable in accuracy to the results from a direct numerical solution. The goal of this exercise is to introduce the…
Density perturbations in a finite scale factor singularity universe
NASA Astrophysics Data System (ADS)
Balcerzak, Adam; Denkiewicz, Tomasz
2012-07-01
We discuss evolution of density perturbations in cosmological models which admit finite scale factor singularities. After solving the matter perturbations equations we find that there exists a set of parameters which admits a finite scale factor singularity in future and instantaneously recover matter density evolution history which is indistinguishable from the standard ΛCDM scenario.
Relativistic Guiding Center Equations
White, R. B.; Gobbin, M.
2014-10-01
In toroidal fusion devices it is relatively easy that electrons achieve relativistic velocities, so to simulate runaway electrons and other high energy phenomena a nonrelativistic guiding center formalism is not sufficient. Relativistic guiding center equations including flute mode time dependent field perturbations are derived. The same variables as used in a previous nonrelativistic guiding center code are adopted, so that a straightforward modifications of those equations can produce a relativistic version.
Formulas for precession. [motion of mean equator
NASA Technical Reports Server (NTRS)
Kinoshita, H.
1975-01-01
Literal expressions for the precessional motion of the mean equator referred to an arbitrary epoch are constructed. Their numerical representations, based on numerical values recommended at the working meeting of the International Astronomical Union Commission held in Washington in September 1974, are obtained. In constructing the equations of motion, the second-order secular perturbation and the secular perturbation due to the long-periodic terms in the motions of the moon and the sun are taken into account. These perturbations contribute more to the motion of the mean equator than does the term due to the secular perturbation of the orbital eccentricity of the sun.
Cosmological implications of the dark matter equation of state
NASA Astrophysics Data System (ADS)
Yang, Weiqiang; Li, Hang; Wu, Yabo; Lu, Jianbo
In this paper, we study a model which is composed of the cosmological constant and dark matter with nonzero equation of state parameter, which could be called as ΛwDM. In the synchronous gauge, we obtain the perturbation equations of dark matter, and deduce the evolution equations of growth factor about the dark matter and baryons. Based on the Markov Chain Monte Carlo (MCMC) method, we constrain this model by the recently available cosmic observations which include cosmic microwave background (CMB) radiation, baryon acoustic oscillation (BAO), type Ia supernovae (SNIa) and fσ8(z) data points from redshift-space distortion (RSD). The results present a tighter constraint on the model than the case without fσ8(z) data. In 3σ regions, we find the dark matter equation of state parameter wdm = 0.00011‑0.00070‑0.00135‑0.00178+0.00069+0.00134+0.00179. The currently available cosmic observations do not favor the nonzero dark matter equation of state parameter, no deviation from the lambda cold dark matter (ΛCDM) model is found in 1σ region.
Oba, Roger; Finette, Steven
2002-02-01
Results of a computer simulation study are presented for acoustic propagation in a shallow water, anisotropic ocean environment. The water column is characterized by random volume fluctuations in the sound speed field that are induced by internal gravity waves, and this variability is superimposed on a dominant summer thermocline. Both the internal wave field and resulting sound speed perturbations are represented in three-dimensional (3D) space and evolve in time. The isopycnal displacements consist of two components: a spatially diffuse, horizontally isotropic component and a spatially localized contribution from an undular bore (i.e., a solitary wave packet or solibore) that exhibits horizontal (azimuthal) anisotropy. An acoustic field is propagated through this waveguide using a 3D parabolic equation code based on differential operators representing wide-angle coverage in elevation and narrow-angle coverage in azimuth. Transmission loss is evaluated both for fixed time snapshots of the environment and as a function of time over an ordered set of snapshots which represent the time-evolving sound speed distribution. Horizontal acoustic coherence, also known as transverse or cross-range coherence, is estimated for horizontally separated points in the direction normal to the source-receiver orientation. Both transmission loss and spatial coherence are computed at acoustic frequencies 200 and 400 Hz for ranges extending to 10 km, a cross-range of 1 km, and a water depth of 68 m. Azimuthal filtering of the propagated field occurs for this environment, with the strongest variations appearing when propagation is parallel to the solitary wave depressions of the thermocline. A large anisotropic degradation in horizontal coherence occurs under the same conditions. Horizontal refraction of the acoustic wave front is responsible for the degradation, as demonstrated by an energy gradient analysis of in-plane and out-of-plane energy transfer. The solitary wave packet is
A hybrid-perturbation-Galerkin technique which combines multiple expansions
NASA Technical Reports Server (NTRS)
Geer, James F.; Andersen, Carl M.
1989-01-01
A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be sued to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.
Fogel, Ronen; Seshia, Ashwin A.
2016-01-01
Resonant and acoustic wave devices have been researched for several decades for application in the gravimetric sensing of a variety of biological and chemical analytes. These devices operate by coupling the measurand (e.g. analyte adsorption) as a modulation in the physical properties of the acoustic wave (e.g. resonant frequency, acoustic velocity, dissipation) that can then be correlated with the amount of adsorbed analyte. These devices can also be miniaturized with advantages in terms of cost, size and scalability, as well as potential additional features including integration with microfluidics and electronics, scaled sensitivities associated with smaller dimensions and higher operational frequencies, the ability to multiplex detection across arrays of hundreds of devices embedded in a single chip, increased throughput and the ability to interrogate a wider range of modes including within the same device. Additionally, device fabrication is often compatible with semiconductor volume batch manufacturing techniques enabling cost scalability and a high degree of precision and reproducibility in the manufacturing process. Integration with microfluidics handling also enables suitable sample pre-processing/separation/purification/amplification steps that could improve selectivity and the overall signal-to-noise ratio. Three device types are reviewed here: (i) bulk acoustic wave sensors, (ii) surface acoustic wave sensors, and (iii) micro/nano-electromechanical system (MEMS/NEMS) sensors. PMID:27365040
Fogel, Ronen; Limson, Janice; Seshia, Ashwin A
2016-06-30
Resonant and acoustic wave devices have been researched for several decades for application in the gravimetric sensing of a variety of biological and chemical analytes. These devices operate by coupling the measurand (e.g. analyte adsorption) as a modulation in the physical properties of the acoustic wave (e.g. resonant frequency, acoustic velocity, dissipation) that can then be correlated with the amount of adsorbed analyte. These devices can also be miniaturized with advantages in terms of cost, size and scalability, as well as potential additional features including integration with microfluidics and electronics, scaled sensitivities associated with smaller dimensions and higher operational frequencies, the ability to multiplex detection across arrays of hundreds of devices embedded in a single chip, increased throughput and the ability to interrogate a wider range of modes including within the same device. Additionally, device fabrication is often compatible with semiconductor volume batch manufacturing techniques enabling cost scalability and a high degree of precision and reproducibility in the manufacturing process. Integration with microfluidics handling also enables suitable sample pre-processing/separation/purification/amplification steps that could improve selectivity and the overall signal-to-noise ratio. Three device types are reviewed here: (i) bulk acoustic wave sensors, (ii) surface acoustic wave sensors, and (iii) micro/nano-electromechanical system (MEMS/NEMS) sensors.
NASA Astrophysics Data System (ADS)
Rong, Shu-Jun; Liu, Qiu-Yu
2012-04-01
The puma model on the basis of the Lorentz and CPT violation may bring an economical interpretation to the conventional neutrinos oscillation and part of the anomalous oscillations. We study the effect of the perturbation to the puma model. In the case of the first-order perturbation which keeps the (23) interchange symmetry, the mixing matrix element Ue3 is always zero. The nonzero mixing matrix element Ue3 is obtained in the second-order perturbation that breaks the (23) interchange symmetry.
Wave Phenomena in an Acoustic Resonant Chamber
ERIC Educational Resources Information Center
Smith, Mary E.; And Others
1974-01-01
Discusses the design and operation of a high Q acoustical resonant chamber which can be used to demonstrate wave phenomena such as three-dimensional normal modes, Q values, densities of states, changes in the speed of sound, Fourier decomposition, damped harmonic oscillations, sound-absorbing properties, and perturbation and scattering problems.…
Propagation of ion acoustic shock waves in negative ion plasmas with nonextensive electrons
Hussain, S.; Akhtar, N.; Mahmood, S.
2013-09-15
Nonlinear ion acoustic shocks (monotonic as well as oscillatory) waves in negative ion plasmas are investigated. The inertialess electron species are assumed to be nonthermal and follow Tsallis distribution. The dissipation in the plasma is considered via kinematic viscosities of both positive and negative ion species. The Korteweg-de Vries Burgers (KdVB) equation is derived using small amplitude reductive perturbation technique and its analytical solution is presented. The effects of variation of density and temperature of negative ions and nonthermal parameter q of electrons on the strength of the shock structures are plotted for illustration. The numerical solutions of KdVB equation using Runge Kutta method are obtained, and transition from oscillatory to monotonic shock structures is also discussed in detail for negative ions nonthermal plasmas.
Nonlinear ion-acoustic waves in a degenerate plasma with nuclei of heavy elements
Hossen, M. A. Mamun, A. A.
2015-10-15
The ion-acoustic (IA) solitary waves propagating in a fully relativistic degenerate dense plasma (containing relativistic degenerate electron and ion fluids, and immobile nuclei of heavy elements) have been theoretically investigated. The relativistic hydrodynamic model is used to derive the Korteweg-de Vries (K-dV) equation by the reductive perturbation method. The stationary solitary wave solution of this K-dV equation is obtained to characterize the basic features of the IA solitary structures that are found to exist in such a degenerate plasma. It is found that the effects of electron dynamics, relativistic degeneracy of the plasma fluids, stationary nuclei of heavy elements, etc., significantly modify the basic properties of the IA solitary structures. The implications of this results in astrophysical compact objects like white dwarfs are briefly discussed.
Head-on-collision of modulated dust acoustic waves in strongly coupled dusty plasma
El-Labany, S. K.; El-Depsy, A.; Zedan, N. A.; El-Taibany, W. F.; El-Shamy, E. F.
2012-10-15
The derivative expansion perturbation method is applied to a strongly coupled dusty plasma system consisting of negatively charged dust grains, electrons, and ions. The basic equations are reduced to a nonlinear Schroedinger type equation appropriate for describing the modulated dust acoustic (DA) waves. We have examined the modulation (in) stability and the dependence of the system physical parameters (angular frequency and group velocity) on the polarization force variation. Finally, the extended Poincare-Lighthill-Kuo technique is employed to investigate the head-on collision (HoC) between two DA dark solitons. The analytical phase shifts and the trajectories of these dark solitons after the collision are derived. The numerical illustrations show that the polarization effect has strong influence on the nature of the phase shifts and the trajectories of the two DA dark solitons after collision.
Wave theory of turbulence in compressible media (acoustic theory of turbulence)
NASA Technical Reports Server (NTRS)
Kentzer, C. P.
1975-01-01
The generation and the transmission of sound in turbulent flows are treated as one of the several aspects of wave propagation in turbulence. Fluid fluctuations are decomposed into orthogonal Fourier components, with five interacting modes of wave propagation: two vorticity modes, one entropy mode, and two acoustic modes. Wave interactions, governed by the inhomogeneous and nonlinear terms of the perturbed Navier-Stokes equations, are modeled by random functions which give the rates of change of wave amplitudes equal to the averaged interaction terms. The statistical framework adopted is a quantum-like formulation in terms of complex distribution functions. The spatial probability distributions are given by the squares of the absolute values of the complex characteristic functions. This formulation results in nonlinear diffusion-type transport equations for the probability densities of the five modes of wave propagation.
Nonlinear features of ion acoustic shock waves in dissipative magnetized dusty plasma
NASA Astrophysics Data System (ADS)
Sahu, Biswajit; Sinha, Anjana; Roychoudhury, Rajkumar
2014-10-01
The nonlinear propagation of small as well as arbitrary amplitude shocks is investigated in a magnetized dusty plasma consisting of inertia-less Boltzmann distributed electrons, inertial viscous cold ions, and stationary dust grains without dust-charge fluctuations. The effects of dissipation due to viscosity of ions and external magnetic field, on the properties of ion acoustic shock structure, are investigated. It is found that for small amplitude waves, the Korteweg-de Vries-Burgers (KdVB) equation, derived using Reductive Perturbation Method, gives a qualitative behaviour of the transition from oscillatory wave to shock structure. The exact numerical solution for arbitrary amplitude wave differs somehow in the details from the results obtained from KdVB equation. However, the qualitative nature of the two solutions is similar in the sense that a gradual transition from KdV oscillation to shock structure is observed with the increase of the dissipative parameter.
NASA Astrophysics Data System (ADS)
Singh, S. V.; Devanandhan, S.; Lakhina, G. S.; Bharuthram, R.
2016-08-01
A theoretical investigation is carried out to study the obliquely propagating electron acoustic solitary waves having nonthermal hot electrons, cold and beam electrons, and ions in a magnetized plasma. We have employed reductive perturbation theory to derive the Korteweg-de-Vries-Zakharov-Kuznetsov (KdV-ZK) equation describing the nonlinear evolution of these waves. The two-dimensional plane wave solution of KdV-ZK equation is analyzed to study the effects of nonthermal and beam electrons on the characteristics of the solitons. Theoretical results predict negative potential solitary structures. We emphasize that the inclusion of finite temperature effects reduces the soliton amplitudes and the width of the solitons increases by an increase in the obliquity of the wave propagation. The numerical analysis is presented for the parameters corresponding to the observations of "burst a" event by Viking satellite on the auroral field lines.
NASA Technical Reports Server (NTRS)
Balakumar, Ponnampalam; King, Rudolph A.
2011-01-01
The receptivity and interaction of stationary and traveling crossflow instability of three-dimensional supersonic boundary layers over a swept biconvex wing with a blunt leading edge are numerically investigated for a freestream Mach number of 3. The steady and unsteady flow fields are obtained by solving the full Navier-Stokes equations. The receptivity of the boundary layer to surface roughness, freestream acoustic waves, and freestream vorticity waves are numerically investigated. The initial amplitudes of the stationary vortices generated by 1 micron roughness elements is about 2000 times larger than the initial amplitudes of the traveling disturbances generated by vortical disturbances. The interaction of stationary and traveling disturbances was investigated by solving the equations with both surface roughness and vortical disturbances. When the initial amplitudes of the stationary disturbances are large compared to the traveling disturbances, the stationary vortex dominates the perturbation field. When the amplitudes are comparable, the traveling vortex prevails and the stationary vortex is suppressed.
Far-field image magnification for acoustic waves using anisotropic acoustic metamaterials.
Ao, Xianyu; Chan, C T
2008-02-01
A kind of two-dimensional acoustic metamaterial is designed so that it exhibits strong anisotropy along two orthogonal directions. Based on the rectangular equal frequency contour of this metamaterial, magnifying lenses for acoustic waves, analogous to electromagnetic hyperlenses demonstrated recently in the optical regime, can be realized. Such metamaterial may offer applications in imaging for systems that obey scalar wave equations.
Deep-Water Ambient Noise Profiling; Marine Sediment Acoustics; and Doppler Geo-Acoustic Spectroscopy
2012-09-30
explosive volcanic eruptions ,” J. Comp. Acoust., 9 (3), 1215-1225 (2001) [keynote address, published, refereed]. 24. N. G. Lehtinen, S. Adam, G...B02209, doi:10, 1-12 (2009) [published, refereed] 9. M. J. Buckingham, “On the transient solutions of three acoustic wave equations: van Wijngaarden’s
Deep-Water Ambient Noise Profiling; Marine Sediment Acoustics; and Doppler Geo-Acoustic Spectroscopy
2013-09-30
explosive volcanic eruptions ,” J. Comp. Acoust., 9 (3), 1215-1225 (2001) [keynote address, published, refereed]. 25. N. G. Lehtinen, S. Adam, G. Gratta...doi:10, 1-12 (2009) [published, refereed] 10. M. J. Buckingham, “On the transient solutions of three acoustic wave equations: van Wijngaarden’s
Galilean invariant resummation schemes of cosmological perturbations
NASA Astrophysics Data System (ADS)
Peloso, Marco; Pietroni, Massimo
2017-01-01
Many of the methods proposed so far to go beyond Standard Perturbation Theory break invariance under time-dependent boosts (denoted here as extended Galilean Invariance, or GI). This gives rise to spurious large scale effects which spoil the small scale predictions of these approximation schemes. By using consistency relations we derive fully non-perturbative constraints that GI imposes on correlation functions. We then introduce a method to quantify the amount of GI breaking of a given scheme, and to correct it by properly tailored counterterms. Finally, we formulate resummation schemes which are manifestly GI, discuss their general features, and implement them in the so called Time-Flow, or TRG, equations.
Perturbative approach to Markovian open quantum systems
Li, Andy C. Y.; Petruccione, F.; Koch, Jens
2014-01-01
The exact treatment of Markovian open quantum systems, when based on numerical diagonalization of the Liouville super-operator or averaging over quantum trajectories, is severely limited by Hilbert space size. Perturbation theory, standard in the investigation of closed quantum systems, has remained much less developed for open quantum systems where a direct application to the Lindblad master equation is desirable. We present such a perturbative treatment which will be useful for an analytical understanding of open quantum systems and for numerical calculation of system observables which would otherwise be impractical. PMID:24811607
Ahmad, Zulfiqar; Mushtaq, A.; Mamun, A. A.
2013-03-15
Dust acoustic solitary waves in a dusty plasma containing dust of opposite polarity (adiabatic positive and negative dust), non-isothermal electrons and ions (following vortex like distribution) are theoretically investigated by employing pseudo-potential approach, which is valid for arbitrary amplitude structures. The propagation of small but finite amplitude solitary structures is also examined by using the reductive perturbation method. The basic properties of large (small) amplitude solitary structures are investigated by analyzing the energy integral (modified Korteweg-de Vries equation). It is shown that the effects of dust polarity, trapping of plasma particles (electrons and ions), and temperatures of dust fluids significantly modify the basic features of the dust-acoustic solitary structures that are found to exist in such an opposite polarity dust-plasma medium. The relevance of the work in opposite polarity dust-plasma, which may occur in cometary tails, upper mesosphere, Jupiter's magnetosphere, is briefly discussed.
NASA Astrophysics Data System (ADS)
Kostov, Ivan; Serban, Didina; Volin, Dmytro
2008-08-01
We give a realization of the Beisert, Eden and Staudacher equation for the planar Script N = 4 supersymetric gauge theory which seems to be particularly useful to study the strong coupling limit. We are using a linearized version of the BES equation as two coupled equations involving an auxiliary density function. We write these equations in terms of the resolvents and we transform them into a system of functional, instead of integral, equations. We solve the functional equations perturbatively in the strong coupling limit and reproduce the recursive solution obtained by Basso, Korchemsky and Kotański. The coefficients of the strong coupling expansion are fixed by the analyticity properties obeyed by the resolvents.
NASA Astrophysics Data System (ADS)
Gan, W. S.
2008-12-01
This paper is to be dedicated to Prof C N Yang's 85th birthday celebration because the idea here was inspired by Prof Yang's public lecture in Singapore in 2006. There are many similarities between electromagnetic waves and acoustic waves. Maxwell's equations for em waves is the oldest gauge theory. We discover symmetries in the pair of wave equations in the acoustic stress field and the velocity field. We also derive a new equation in terms of the stress field for sound propagation in solids. This is different from the Christoffel's equation which is in term of the velocity field. We feel that stress field can better characterize the elastic properties of the sound waves. We also derive the acoustic gauge field condition and gauge invariance and symmetries for the acoustic fields. We also apply symmetries to study negative refraction. Note from Publisher: This article contains the abstract only.
Talking while chewing: speaker response to natural perturbation of speech.
Mayer, Connor; Gick, Bryan
2012-01-01
This study looks at how the conflicting goals of chewing and speech production are reconciled by examining the acoustic and articulatory output of talking while chewing. We consider chewing to be a type of perturbation with regard to speech production, but with some important differences. Ultrasound and acoustic measurements were made while participants chewed gum and produced various utterances containing the sounds /s/, /ʃ/, and /r/. Results show a great deal of individual variation in articulation and acoustics between speakers, but consistent productions and maintenance of relative acoustic distances within speakers. Although chewing interfered with speech production, and this interference manifested itself in a variety of ways across speakers, the objectives of speech production were indirectly achieved within the constraints and variability introduced by individual chewing strategies.
Nonlinear Interaction of a Shock Wave with an Anisotropic Entropy Perturbation Field
NASA Astrophysics Data System (ADS)
Gorodnichev, K. E.; Kuratov, S. E.; Gorodnichev, E. E.
2017-01-01
The problem of the interaction of a shock wave with an anisotropic entropy perturbation field has been solved including second-order corrections to hydrodynamic quantities. It has been shown that nonlinear interactions between acoustic waves result in the localization of acoustic perturbations behind the shock front. This effect is observed when sound attenuation is absent in the linear approximation. The problem of the propagation of the shock wave in an incident sample, where the spatially anisotropic density perturbation field initially exists, has been numerically solved in application to the collision of two plates. Numerical calculations confirm the results of the theoretical analysis.
Haider, M. M.; Mamun, A. A.
2012-10-15
A rigorous theoretical investigation has been made on Zakharov-Kuznetsov (ZK) equation of ion-acoustic (IA) solitary waves (SWs) and their multi-dimensional instability in a magnetized degenerate plasma which consists of inertialess electrons, inertial ions, negatively, and positively charged stationary heavy ions. The ZK equation is derived by the reductive perturbation method, and multi-dimensional instability of these solitary structures is also studied by the small-k (long wave-length plane wave) perturbation expansion technique. The effects of the external magnetic field are found to significantly modify the basic properties of small but finite-amplitude IA SWs. The external magnetic field and the propagation directions of both the nonlinear waves and their perturbation modes are found to play a very important role in changing the instability criterion and the growth rate of the unstable IA SWs. The basic features (viz., amplitude, width, instability, etc.) and the underlying physics of the IA SWs, which are relevant to space and laboratory plasma situations, are briefly discussed.
Gauge invariant perturbations of Petrov type D space-times
NASA Astrophysics Data System (ADS)
Whiting, Bernard; Shah, Abhay
2016-03-01
The Regge-Wheeler and Zerilli equations are satisfied by gauge invariant perturbations of the Schwarzschild black hole geometry. Both the perturbation of the imaginary part of Ψ2 (a component of the Weyl curvature), and its time derivative, are gauge invariant and solve the Regge-Wheeler equation with different sources. The Ψ0 and Ψ4 perturbations of the Weyl curvature are not only gauge, but also tetrad, invariant. We explore the framework in which these results hold, and consider what generalizations may extend to the Kerr geometry, and presumably to Petrov type D space-times in general. NSF Grants PHY 1205906 and 1314529, ERC (EU) FP7 Grant 304978.
Cosmological perturbations of a perfect fluid and noncommutative variables
De Felice, Antonio; Gerard, Jean-Marc; Suyama, Teruaki
2010-03-15
We describe the linear cosmological perturbations of a perfect fluid at the level of an action, providing thus an alternative to the standard approach based only on the equations of motion. This action is suited not only to perfect fluids with a barotropic equation of state, but also to those for which the pressure depends on two thermodynamical variables. By quantizing the system we find that (1) some perturbation fields exhibit a noncommutativity quite analogous to the one observed for a charged particle moving in a strong magnetic field, (2) local curvature and pressure perturbations cannot be measured simultaneously, (3) ghosts appear if the null energy condition is violated.
Nondimensional forms for singular perturbation analyses of aircraft energy climbs
NASA Technical Reports Server (NTRS)
Calise, A. J.; Markopoulos, N.; Corban, J. E.
1991-01-01
This paper proposes a systematic approach for identifying the perturbation parameter in singular perturbation analysis of aircraft optimal guidance, and in particular considers a family of problems related to aircraft energy climbs. The approach, which is based on a nondimensionalization of the equations of motion, is used to evaluatae the appropriateness of forced singular perturbation formulations used in the past for transport and fighter aircraft, and to assess the applicability of energy state approximations and singular perturbation analysis for airbreathing transatmospheric vehicles with hypersonic cruise and orbital capabilities.
Radiative Amplification of Acoustic Waves in Hot Stars
NASA Technical Reports Server (NTRS)
Wolf, B. E.
1985-01-01
The discovery of broad P Cygni profiles in early type stars and the detection of X-rays emitted from the envelopes of these stars made it clear, that a considerable amount of mechanical energy has to be present in massive stars. An attack on the problem, which has proven successful when applied to late type stars is proposed. It is possible that acoustic waves form out of random fluctuations, amplify by absorbing momentum from stellar radiation field, steepen into shock waves and dissipate. A stellar atmosphere was constructed, and sinusoidal small amplitude perturbations of specified Mach number and period at the inner boundary was introduced. The partial differential equations of hydrodynamics and the equations of radiation transfer for grey matter were solved numerically. The equation of motion was augmented by a term which describes the absorption of momentum from the radiation field in the continuum and in lines, including the Doppler effect and allows for the treatment of a large number of lines in the radiative acceleration term.
Evolution of dark energy perturbations in scalar-tensor cosmologies
Bueno Sanchez, J. C.; Perivolaropoulos, L.
2010-05-15
We solve analytically and numerically the generalized Einstein equations in scalar-tensor cosmologies to obtain the evolution of dark energy and matter linear perturbations. We compare our results with the corresponding results for minimally coupled quintessence perturbations. We find that scalar-tensor dark energy density perturbations are amplified by a factor of about 10{sup 4} compared to minimally coupled quintessence perturbations on scales less than about 1000 h{sup -1} Mpc (sub-Hubble scales). On these scales dark energy perturbations constitute a fraction of about 10% compared to matter density perturbations. Scalar-tensor dark energy density perturbations are anticorrelated with matter linear perturbations on sub-Hubble scales. This anticorrelation of matter with negative pressure perturbations induces a mild amplification of matter perturbations by about 10% on sub-Hubble scales. The evolution of scalar field perturbations on sub-Hubble scales is scale independent and therefore corresponds to a vanishing effective speed of sound (c{sub s{Phi}=}0). We briefly discuss the observational implications of our results, which may include predictions for galaxy and cluster halo profiles that are modified compared to {Lambda}CDM. The observed properties of these profiles are known to be in some tension with the predictions of {Lambda}CDM.
1974-02-14
Wester- velt. [60] Streaming. In 1831, Michael Faraday [61] noted that currents of air were set up in the neighborhood of vibrating plates-the first... ducei in the case of a paramettc amy (from Berktay an Leahy 141). C’ "". k•, SEC 10.1 NONLINEAR ACOUSTICS 345 The principal results of their analysis
NASA Astrophysics Data System (ADS)
Shalaby, M.; EL-Labany, S. K.; EL-Shamy, E. F.; El-Taibany, W. F.; Khaled, M. A.
2009-12-01
Obliquely propagating dust ion acoustic solitary waves (DIASWs) are investigated in hot adiabatic magnetized dusty plasmas consisting of hot adiabatic inertial ions, hot adiabatic inertialess electrons, and negatively/positively charged static dust grains. Using a reductive perturbation method, a nonlinear Zakharov-Kuznetsov equation is derived. The effects of the concentration of negatively/positively charged dust particles and ion-neutral collision on the basic characteristics of DIASWs are studied. The three-dimensional stability of these waves is examined by the use of small-k (long wavelength plane wave) perturbation expansion technique. It is shown that the instability criterion and their growth rate depend on external magnetic field, obliqueness, the concentration of charged dust grains, ion-neutral, and ion-dust collisions.
EL-Shamy, E. F.
2014-08-15
The solitary structures of multi–dimensional ion-acoustic solitary waves (IASWs) have been considered in magnetoplasmas consisting of electron-positron-ion with high-energy (superthermal) electrons and positrons are investigated. Using a reductive perturbation method, a nonlinear Zakharov-Kuznetsov equation is derived. The multi-dimensional instability of obliquely propagating (with respect to the external magnetic field) IASWs has been studied by the small-k (long wavelength plane wave) expansion perturbation method. The instability condition and the growth rate of the instability have been derived. It is shown that the instability criterion and their growth rate depend on the parameter measuring the superthermality, the ion gyrofrequency, the unperturbed positrons-to-ions density ratio, the direction cosine, and the ion-to-electron temperature ratio. Clearly, the study of our model under consideration is helpful for explaining the propagation and the instability of IASWs in space observations of magnetoplasmas with superthermal electrons and positrons.
NASA Astrophysics Data System (ADS)
Haider, M. M.; Rahman, O.
2016-12-01
An attempt has been made to study the multi-dimensional instability of dust-ion-acoustic (DIA) solitary waves (SWs) in magnetized multi-ion plasmas containing opposite polarity ions, opposite polarity dusts and non-thermal electrons. First of all, we have derived Zakharov-Kuznetsov (ZK) equation to study the DIA SWs in this case using reductive perturbation method as well as its solution. Small- k perturbation technique was employed to find out the instability criterion and growth rate of such a wave which can give a guideline in understanding the space and laboratory plasmas, situated in the D-region of the Earth's ionosphere, mesosphere, and solar photosphere, as well as the microelectronics plasma processing reactors.
Underwater Acoustic Propagation in the Philippine Sea: Intensity Fluctuations
NASA Astrophysics Data System (ADS)
White, Andrew W.
In the spring of 2009, broadband transmissions from a ship-suspended source with a 284 Hz center frequency were received on a moored and navigated vertical array of hydrophones over a range of 107 km in the Philippine Sea. During a 60-hour period over 19 000 transmissions were carried out. The observed wavefront arrival structure reveals four distinct purely refracted acoustic paths: one with a single upper turning point near 80 m depth, two with a pair of upper turning points at a depth of roughly 300 m, and one with three upper turning points at 420 m. Individual path intensity, defined as the absolute square of the center frequency Fourier component for that arrival, was estimated over the 60-hour duration and used to compute scintillation index and log-intensity variance. Monte Carlo parabolic equation simulations using internal-wave induced sound speed perturbations obeying the Garrett-Munk internal-wave en- ergy spectrum were in agreement with measured data for the three deeper-turning paths but differed by as much as a factor of four for the near surface-interacting path. Estimates of the power spectral density and temporal autocorrelation function of intensity were attempted, but were complicated by gaps in the measured time-series. Deep fades in intensity were observed in the near surface-interacting path. Hypothesized causes for the deep fades were examined through further acoustic propagation modeling and analysis of various available oceanographic measurements.
El-Tantawy, S. A.; Moslem, W. M.
2014-05-15
Solitons (small-amplitude long-lived waves) collision and rogue waves (large-amplitude short-lived waves) in non-Maxwellian electron-positron-ion plasma have been investigated. For the solitons collision, the extended Poincaré-Lighthill-Kuo perturbation method is used to derive the coupled Korteweg-de Vries (KdV) equations with the quadratic nonlinearities and their corresponding phase shifts. The calculations reveal that both positive and negative polarity solitons can propagate in the present model. At critical value of plasma parameters, the coefficients of the quadratic nonlinearities disappear. Therefore, the coupled modified KdV (mKdV) equations with cubic nonlinearities and their corresponding phase shifts have been derived. The effects of the electron-to-positron temperature ratio, the ion-to-electron temperature ratio, the positron-to-ion concentration, and the nonextensive parameter on the colliding solitons profiles and their corresponding phase shifts are examined. Moreover, generation of ion-acoustic rogue waves from small-amplitude initial perturbations in plasmas is studied in the framework of the mKdV equation. The properties of the ion-acoustic rogue waves are examined within a nonlinear Schrödinger equation (NLSE) that has been derived from the mKdV equation. The dependence of the rogue wave profile on the relevant physical parameters has been investigated. Furthermore, it is found that the NLSE that has been derived from the KdV equation cannot support the propagation of rogue waves.
Nonlinear gyrokinetic equations
Dubin, D.H.E.; Krommes, J.A.; Oberman, C.; Lee, W.W.
1983-03-01
Nonlinear gyrokinetic equations are derived from a systematic Hamiltonian theory. The derivation employs Lie transforms and a noncanonical perturbation theory first used by Littlejohn for the simpler problem of asymptotically small gyroradius. For definiteness, we emphasize the limit of electrostatic fluctuations in slab geometry; however, there is a straight-forward generalization to arbitrary field geometry and electromagnetic perturbations. An energy invariant for the nonlinear system is derived, and various of its limits are considered. The weak turbulence theory of the equations is examined. In particular, the wave kinetic equation of Galeev and Sagdeev is derived from an asystematic truncation of the equations, implying that this equation fails to consider all gyrokinetic effects. The equations are simplified for the case of small but finite gyroradius and put in a form suitable for efficient computer simulation. Although it is possible to derive the Terry-Horton and Hasegawa-Mima equations as limiting cases of our theory, several new nonlinear terms absent from conventional theories appear and are discussed.
Acoustic transducer for acoustic microscopy
Khuri-Yakub, Butrus T.; Chou, Ching H.
1990-01-01
A shear acoustic transducer-lens system in which a shear polarized piezoelectric material excites shear polarized waves at one end of a buffer rod having a lens at the other end which excites longitudinal waves in a coupling medium by mode conversion at selected locations on the lens.
Acoustic transducer for acoustic microscopy
Khuri-Yakub, B.T.; Chou, C.H.
1990-03-20
A shear acoustic transducer-lens system is described in which a shear polarized piezoelectric material excites shear polarized waves at one end of a buffer rod having a lens at the other end which excites longitudinal waves in a coupling medium by mode conversion at selected locations on the lens. 9 figs.
Delta-Measure Perturbations of a Contact Discontinuity
NASA Astrophysics Data System (ADS)
Baty, Roy
2012-11-01
In this presentation, nonstandard analysis is applied to study generalized function perturbations of contact discontinuities in compressible, inviscid fluids. Nonstandard analysis is an area of modern mathematics that studies extensions of the real number system to nonstandard number systems that contain infinitely large and infinitely small numbers. Perturbations of a contact discontinuity are considered that represent one-dimensional analogs of the two-dimensional perturbations observed in the initial evolution of a Richtmyer-Meshkov instability on a density interface. Nonstandard predistributions of the Dirac delta measure and its derivatives are applied as the perturbations of a contact discontinuity. The one-dimensional Euler equations are used to model the flow field of a fluid containing a perturbed density interface and generalized solutions are constructed for the perturbed flow field.
NASA Technical Reports Server (NTRS)
Criminale, W. O.; Lasseigne, D. G.; Jackson, T. L.
1995-01-01
An initial value approach is used to examine the dynamics of perturbations introduced into a vortex under strain. Both the basic vortex considered and the perturbations are taken as fully three-dimensional. An explicit solution for the time evolution of the vorticity perturbations is given for arbitrary initial vorticity. Analytical solutions for the resulting velocity components are found when the initial vorticity is assumed to be localized. For more general initial vorticity distributions, the velocity components are determined numerically. It is found that the variation in the radial direction of the initial vorticity disturbance is the most important factor influencing the qualitative behavior of the solutions. Transient growth in the magnitude of the velocity components is found to be directly attributable to the compactness of the initial vorticity.
Perturbations for transient acceleration
Vargas, Cristofher Zuñiga; Zimdahl, Winfried; Hipólito-Ricaldi, Wiliam S. E-mail: hipolito@ceunes.ufes.br
2012-04-01
According to the standard ΛCDM model, the accelerated expansion of the Universe will go on forever. Motivated by recent observational results, we explore the possibility of a finite phase of acceleration which asymptotically approaches another period of decelerated expansion. Extending an earlier study on a corresponding homogeneous and isotropic dynamics, in which interactions between dark matter and dark energy are crucial, the present paper also investigates the dynamics of the matter perturbations both on the Newtonian and General Relativistic (GR) levels and quantifies the potential relevance of perturbations of the dark-energy component. In the background, the model is tested against the Supernova type Ia (SNIa) data of the Constitution set and on the perturbative level against growth rate data, among them those of the WiggleZ survey, and the data of the 2dFGRS project. Our results indicate that a transient phase of accelerated expansion is not excluded by current observations.
On Dirac equations for linear magnetoacoustic waves propagating in an isothermal atmosphere
NASA Technical Reports Server (NTRS)
Alicki, R.; Musielak, E. Z.; Sikorski, J.; Makowiec, D.
1994-01-01
A new analytical approach to study linear magnetoacoustic waves propagating in an isothermal, stratified, and uniformly magnetized atmosphere is presented. The approach is based on Dirac equations, and the theory of Sturm-Liouville operators is used to investigate spectral properties of the obtained Dirac Hamiltonians. Two cases are considered: (1) the background magnetic field is vertical, and the waves are separated into purely magnetic (transverse) and purely acoustic (longitudinal) modes; and (2) the field is tilted with respect to the vertical direction and the magnetic and acoustic modes become coupled giving magnetoacoustic waves. For the first case, the Dirac Hamiltonian possesses either a discrete spectrum, which corresponds to standing magnetic waves, or a continuous spectrum, which can be clearly identified with freely propagating acoustic waves. For the second case, the quantum mechanical perturbation calculus is used to study coupling and energy exchange between the magnetic and acoustic components of magnetoacoustic waves. It is shown that this coupling may efficiently prevent trapping of magnetoacoustic waves instellar atmospheres.
Gauge invariant perturbations of scalar-tensor cosmologies: The vacuum case
Carloni, Sante; Dunsby, Peter K. S.; Rubano, Claudio
2006-12-15
The covariant gauge-invariant perturbation theory of scalar cosmological perturbations is developed for a general scalar-tensor Friedmann-Lemaitre-Robertson-Walker cosmology in a vacuum. The perturbation equations are then solved exactly in the long wavelength limit for a specific coupling, potential, and background. Differences with the minimally coupled case are briefly discussed.
NASA Astrophysics Data System (ADS)
Elwakil, S. A.; Abulwafa, E. M.; El-Shewy, E. K.; Abd-El-Hamid, H. M.
2011-11-01
A theoretical investigation has been made for electron acoustic waves propagating in a system of unmagnetized collisionless plasma consists of a cold electron fluid and ions with two different temperatures in which the hot ions obey the non-thermal distribution. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude electrostatic waves. It is found that the presence of the energetic population of non-thermal hot ions δ, initial normalized equilibrium density of low temperature ions μ and the ratio of temperatures of low temperature ions to high temperature ions β do not only significantly modify the basic properties of solitary structure, but also change the polarity of the solitary profiles. At the critical hot ions density, the KdV equation is not appropriate for describing the system. Hence, a new set of stretched coordinates is considered to derive the modified KdV equation. In the vicinity of the critical hot ions density, neither KdV nor modified KdV equation is appropriate for describing the electron acoustic waves. Therefore, a further modified KdV equation is derived. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the various KdV-type equations, is used here. Numerical studies have been reveals different solutions e.g., bell-shaped solitary pulses, singular solitary "blowup" solutions, Jacobi elliptic doubly periodic wave, Weierstrass elliptic doubly periodic type solutions, in addition to explosive pulses. The results of the present investigation may be applicable to some plasma environments, such as Earth's magnetotail region.
Lauterborn, W.; Parlitz, U.; Holzfuss, J.; Billo, A.; Akhatov, I.
1996-06-01
Acoustic cavitation, a complex, spatio-temporal dynamical system, is investigated with respect to its chaotic properties. The sound output, the {open_quote}{open_quote}noise{close_quote}{close_quote}, is subjected to time series analysis. The spatial dynamics of the bubble filaments is captured by high speed holographic cinematography and subsequent digital picture processing from the holograms. Theoretical models are put forward for describing the pattern formation. {copyright} {ital 1996 American Institute of Physics.}
NASA Astrophysics Data System (ADS)
Beach, Kirk W.; Dunmire, Barbrina
Medical acoustics can be subdivided into diagnostics and therapy. Diagnostics are further separated into auditory and ultrasonic methods, and both employ low amplitudes. Therapy (excluding medical advice) uses ultrasound for heating, cooking, permeablizing, activating and fracturing tissues and structures within the body, usually at much higher amplitudes than in diagnostics. Because ultrasound is a wave, linear wave physics are generally applicable, but recently nonlinear effects have become more important, even in low-intensity diagnostic applications.
Consistent perturbations in an imperfect fluid
Sawicki, Ignacy; Amendola, Luca; Saltas, Ippocratis D.; Kunz, Martin E-mail: i.saltas@sussex.ac.uk E-mail: martin.kunz@unige.ch
2013-01-01
We present a new prescription for analysing cosmological perturbations in a more-general class of scalar-field dark-energy models where the energy-momentum tensor has an imperfect-fluid form. This class includes Brans-Dicke models, f(R) gravity, theories with kinetic gravity braiding and generalised galileons. We employ the intuitive language of fluids, allowing us to explicitly maintain a dependence on physical and potentially measurable properties. We demonstrate that hydrodynamics is not always a valid description for describing cosmological perturbations in general scalar-field theories and present a consistent alternative that nonetheless utilises the fluid language. We apply this approach explicitly to a worked example: k-essence non-minimally coupled to gravity. This is the simplest case which captures the essential new features of these imperfect-fluid models. We demonstrate the generic existence of a new scale separating regimes where the fluid is perfect and imperfect. We obtain the equations for the evolution of dark-energy density perturbations in both these regimes. The model also features two other known scales: the Compton scale related to the breaking of shift symmetry and the Jeans scale which we show is determined by the speed of propagation of small scalar-field perturbations, i.e. causality, as opposed to the frequently used definition of the ratio of the pressure and energy-density perturbations.
Second order density perturbations for dust cosmologies
NASA Astrophysics Data System (ADS)
Uggla, Claes; Wainwright, John
2014-08-01
We present simple expressions for the relativistic first and second order fractional density perturbations for Friedmann-Lemaître cosmologies with dust, in four different gauges: the Poisson, uniform curvature, total matter and synchronous-comoving gauges. We include a cosmological constant and arbitrary spatial curvature in the background. A distinctive feature of our approach is our description of the spatial dependence of the perturbations using a canonical set of quadratic differential expressions involving an arbitrary spatial function that arises as a conserved quantity. This enables us to unify, simplify and extend previous seemingly disparate results. We use the primordial matter and metric perturbations that emerge at the end of the inflationary epoch to determine the additional arbitrary spatial function that arises when integrating the second order perturbation equations. This introduces a non-Gaussianity parameter into the expressions for the second order density perturbation. In the special case of zero spatial curvature we show that the time evolution simplifies significantly, and requires the use of only two nonelementary functions, the so-called growth suppression factor at the linear level, and one new function at the second order level. We expect that the results will be useful in applications, for example, studying the effects of primordial non-Gaussianity on the large scale structure of the Universe.
Mode coupling of Schwarzschild perturbations: Ringdown frequencies
NASA Astrophysics Data System (ADS)
Pazos, Enrique; Brizuela, David; Martín-García, José M.; Tiglio, Manuel
2010-11-01
Within linearized perturbation theory, black holes decay to their final stationary state through the well-known spectrum of quasinormal modes. Here we numerically study whether nonlinearities change this picture. For that purpose we study the ringdown frequencies of gauge-invariant second-order gravitational perturbations induced by self-coupling of linearized perturbations of Schwarzschild black holes. We do so through high-accuracy simulations in the time domain of first and second-order Regge-Wheeler-Zerilli type equations, for a variety of initial data sets. We consider first-order even-parity (ℓ=2, m=±2) perturbations and odd-parity (ℓ=2, m=0) ones, and all the multipoles that they generate through self-coupling. For all of them and all the initial data sets considered we find that—in contrast to previous predictions in the literature—the numerical decay frequencies of second-order perturbations are the same ones of linearized theory, and we explain the observed behavior. This would indicate, in particular, that when modeling or searching for ringdown gravitational waves, appropriately including the standard quasinormal modes already takes into account nonlinear effects.
Noninflationary model with scale invariant cosmological perturbations
Peter, Patrick; Pinho, Emanuel J. C.; Pinto-Neto, Nelson
2007-01-15
We show that a contracting universe which bounces due to quantum cosmological effects and connects to the hot big-bang expansion phase, can produce an almost scale invariant spectrum of perturbations provided the perturbations are produced during an almost matter dominated era in the contraction phase. This is achieved using Bohmian solutions of the canonical Wheeler-DeWitt equation, thus treating both the background and the perturbations in a fully quantum manner. We find a very slightly blue spectrum (n{sub S}-1>0). Taking into account the spectral index constraint as well as the cosmic microwave background normalization measure yields an equation of state that should be less than {omega} < or approx. 8x10{sup -4}, implying n{sub S}-1{approx}O(10{sup -4}), and that the characteristic curvature scale of the Universe at the bounce is L{sub 0}{approx}10{sup 3}l{sub Pl}, a region where one expects that the Wheeler-DeWitt equation should be valid without being spoiled by string or loop quantum gravity effects. We have also obtained a consistency relation between the tensor-to-scalar ratio T/S and the scalar spectral index as T/S{approx}4.6x10{sup -2}{radical}(n{sub S}-1), leading to potentially measurable differences with inflationary predictions.
A Theoretical Investigation of Acoustic Cavitation.
1985-07-15
dynamics known as the Rayleigh - Plesset equation. This equation was shown to work quite well under some conditions. , Recent experiments have shown...that when the acoustic driving frequency is near one of A-Oe bubble’s harmonic resonances, the theoretical values predicted by the Rayleigh - Plesset ...equation are inconsistent with observed values. This inconsistency lead Prosperetti to consider the internal pressure term in the Rayleigh - Plesset
Acoustic dose and acoustic dose-rate.
Duck, Francis
2009-10-01
Acoustic dose is defined as the energy deposited by absorption of an acoustic wave per unit mass of the medium supporting the wave. Expressions for acoustic dose and acoustic dose-rate are given for plane-wave conditions, including temporal and frequency dependencies of energy deposition. The relationship between the acoustic dose-rate and the resulting temperature increase is explored, as is the relationship between acoustic dose-rate and radiation force. Energy transfer from the wave to the medium by means of acoustic cavitation is considered, and an approach is proposed in principle that could allow cavitation to be included within the proposed definitions of acoustic dose and acoustic dose-rate.
Perturbing turbulence beyond collapse
NASA Astrophysics Data System (ADS)
Kühnen, Jakob; Scarselli, Davide; Hof, Björn; Nonlinear Dynamics; Turbulence Group Team
2016-11-01
Wall-bounded turbulent flows are considered to be in principle stable against perturbations and persist as long as the Reynolds number is sufficiently high. We show for the example of pipe flow that a specific perturbation of the turbulent flow field disrupts the genesis of new turbulence at the wall. This leads to an immediate collapse of the turbulent flow and causes complete relaminarisation further downstream. The annihilation of turbulence is effected by a steady manipulation of the streamwise velocity component only, greatly simplifying control efforts which usually require knowledge of the highly complex three dimensional and time dependent velocity fields. We present several different control schemes from laboratory experiments which achieve the required perturbation of the flow for total relaminarisation. Transient growth, a linear amplification mechanism measuring the efficiency of eddies in redistributing shear that quantifies the maximum perturbation energy amplification achievable over a finite time in a linearized framework, is shown to set a clear-cut threshold below which turbulence is impeded in its formation and thus permanently annihilated.
Cosmological perturbations in antigravity
NASA Astrophysics Data System (ADS)
Oltean, Marius; Brandenberger, Robert
2014-10-01
We compute the evolution of cosmological perturbations in a recently proposed Weyl-symmetric theory of two scalar fields with oppositely signed conformal couplings to Einstein gravity. It is motivated from the minimal conformal extension of the standard model, such that one of these scalar fields is the Higgs while the other is a new particle, the dilaton, introduced to make the Higgs mass conformally symmetric. At the background level, the theory admits novel geodesically complete cyclic cosmological solutions characterized by a brief period of repulsive gravity, or "antigravity," during each successive transition from a big crunch to a big bang. For simplicity, we consider scalar perturbations in the absence of anisotropies, with potential set to zero and without any radiation. We show that despite the necessarily wrong-signed kinetic term of the dilaton in the full action, these perturbations are neither ghostlike nor tachyonic in the limit of strongly repulsive gravity. On this basis, we argue—pending a future analysis of vector and tensor perturbations—that, with respect to perturbative stability, the cosmological solutions of this theory are viable.
Perturbations of matter fields in the second-order gauge-invariant cosmological perturbation theory
NASA Astrophysics Data System (ADS)
Nakamura, Kouji
2009-12-01
To show that the general framework of the second-order gauge-invariant perturbation theory developed by K. Nakamura [Prog. Theor. Phys. 110, 723 (2003)PTPKAV0033-068X10.1143/PTP.110.723; Prog. Theor. Phys. 113, 481 (2005)PTPKAV0033-068X10.1143/PTP.113.481] is applicable to a wide class of cosmological situations, some formulas for the perturbations of the matter fields are summarized within the framework of the second-order gauge-invariant cosmological perturbation theory in a four-dimensional homogeneous isotropic universe, which is developed in Prog. Theor. Phys. 117, 17 (2007)PTPKAV0033-068X10.1143/PTP.117.17. We derive the formulas for the perturbations of the energy-momentum tensors and equations of motion for a perfect fluid, an imperfect fluid, and a single scalar field, and show that all equations are derived in terms of gauge-invariant variables without any gauge fixing. Through these formulas, we may say that the decomposition formulas for the perturbations of any tensor field into gauge-invariant and gauge-variant parts, which are proposed in the above papers, are universal.
Baryonic matter perturbations in decaying vacuum cosmology
Marttens, R.F. vom; Zimdahl, W.; Hipólito-Ricaldi, W.S. E-mail: wiliam.ricaldi@ufes.br
2014-08-01
We consider the perturbation dynamics for the cosmic baryon fluid and determine the corresponding power spectrum for a Λ(t)CDM model in which a cosmological term decays into dark matter linearly with the Hubble rate. The model is tested by a joint analysis of data from supernovae of type Ia (SNIa) (Constitution and Union 2.1), baryonic acoustic oscillations (BAO), the position of the first peak of the anisotropy spectrum of the cosmic microwave background (CMB) and large-scale-structure (LSS) data (SDSS DR7). While the homogeneous and isotropic background dynamics is only marginally influenced by the baryons, there are modifications on the perturbative level if a separately conserved baryon fluid is included. Considering the present baryon fraction as a free parameter, we reproduce the observed abundance of the order of 5% independently of the dark-matter abundance which is of the order of 32% for this model. Generally, the concordance between background and perturbation dynamics is improved if baryons are explicitly taken into account.
Classical Chaos in Mesoscale Ocean Dynamics: Lateral Stirring and Geometric Acoustics.
NASA Astrophysics Data System (ADS)
Smith, Kevin Barkley
construction of Poincare' sections consistently predict the appearance of chaos in simple, periodically range-dependent models of the sound speed profile. When a realistic model of oceanic mesoscale sound speed perturbations is introduced, consisting of a randomly phased superposition of baroclinic Rossby wave modes, numerical integration of the ray equations yields Lyapunov exponent estimates for near-axial rays of ~(400 km)^{ -1} when perturbation strengths are consistent with ocean observations. This implies that prediction of near-axial underwater acoustic rays is not feasible at ranges beyond one or two thousand km.
NASA Technical Reports Server (NTRS)
Heyman, J. S.
1984-01-01
Acoustically-energized water jet aids in plaque breakdown. Acoustic Wand includes acoustic transducer 1/4 wave plate, and tapered cone. Together elements energize solution of water containing mild abrasive injected into mouth to help prevent calculous buildup.
Green’s functions and energy eigenvalues for delta-perturbed space-fractional quantum systems
Nayga, M. M. Esguerra, J. P.
2016-02-15
Starting from the propagator, we introduced a time-ordered perturbation expansion and employed Wick rotation to obtain a general energy-dependent Green’s function expressions for space-fractional quantum systems with Dirac delta-function perturbation. We then obtained the Green’s functions and equations for the bound state energies for the space-fractional Schrödinger equation with single and double Dirac delta well potentials and the delta-perturbed infinite well.
Acoustic modes in fluid networks
NASA Technical Reports Server (NTRS)
Michalopoulos, C. D.; Clark, Robert W., Jr.; Doiron, Harold H.
1992-01-01
Pressure and flow rate eigenvalue problems for one-dimensional flow of a fluid in a network of pipes are derived from the familiar transmission line equations. These equations are linearized by assuming small velocity and pressure oscillations about mean flow conditions. It is shown that the flow rate eigenvalues are the same as the pressure eigenvalues and the relationship between line pressure modes and flow rate modes is established. A volume at the end of each branch is employed which allows any combination of boundary conditions, from open to closed, to be used. The Jacobi iterative method is used to compute undamped natural frequencies and associated pressure/flow modes. Several numerical examples are presented which include acoustic modes for the Helium Supply System of the Space Shuttle Orbiter Main Propulsion System. It should be noted that the method presented herein can be applied to any one-dimensional acoustic system involving an arbitrary number of branches.
NASA Technical Reports Server (NTRS)
Cantrell, John H.
2006-01-01
A comprehensive, analytical treatment is presented of the microelastic-plastic nonlinearities resulting from the interaction of a stress perturbation with dislocation substructures (veins and persistent slip bands) and cracks that evolve during high-cycle fatigue of wavy slip metals. The nonlinear interaction is quantified by a material (acoustic) nonlinearity parameter beta extracted from acoustic harmonic generation measurements. The contribution to beta from the substructures is obtained from the analysis of Cantrell [Cantrell, J. H., 2004, Proc. R. Soc. London A, 460, 757]. The contribution to beta from cracks is obtained by applying the Paris law for crack propagation to the Nazarov-Sutin crack nonlinearity equation [Nazarov, V. E., and Sutin, A. M., 1997, J. Acoust. Soc. Am. 102, 3349]. The nonlinearity parameter resulting from the two contributions is predicted to increase monotonically by hundreds of percent during fatigue from the virgin state to fracture. The increase in beta during the first 80-90 percent of fatigue life is dominated by the evolution of dislocation substructures, while the last 10-20 percent is dominated by crack growth. The model is applied to the fatigue of aluminium alloy 2024-T4 in stress-controlled loading at 276MPa for which experimental data are reported. The agreement between theory and experiment is excellent.
Das, K.P.; Majumdar, S.R.; Paul, S.N. ||
1995-05-01
An integrated form of the governing equations in terms of pseudopotential higher-order nonlinear and dispersive effects is obtained by applying the reductive perturbation method for ion-acoustic solitary waves in a collisionless unmagnetized multicomponent plasma having warm ions and two-component nonisothermal electrons. The present method is advantageous because instead of solving an inhomogeneous second-order differential equation at each order, as in the standard procedure, we solve a first-order inhomogeneous equation at each order except at the lowest. The expressions of both Mach number and width of the solitary wave are obtained as a function of the amplitude of the wave for third-order nonlinear and dispersive effects. The variations of potential, width, and Mach number against soliton amplitude are shown graphically, taking into consideration the nonisothermality of two-component electrons in the plasma.
Aerodynamics Via Acoustics: Application of Acoustic Formulas for Aerodynamic Calculations
NASA Technical Reports Server (NTRS)
Farassat, F.; Myers, M. K.
1986-01-01
Prediction of aerodynamic loads on bodies in arbitrary motion is considered from an acoustic point of view, i.e., in a frame of reference fixed in the undisturbed medium. An inhomogeneous wave equation which governs the disturbance pressure is constructed and solved formally using generalized function theory. When the observer is located on the moving body surface there results a singular linear integral equation for surface pressure. Two different methods for obtaining such equations are discussed. Both steady and unsteady aerodynamic calculations are considered. Two examples are presented, the more important being an application to propeller aerodynamics. Of particular interest for numerical applications is the analytical behavior of the kernel functions in the various integral equations.
NASA Astrophysics Data System (ADS)
El-Depsy, A.; Selim, M. M.
2016-12-01
The propagation of ion acoustic waves (IAWs) in a cylindrical collisionless unmagnetized plasma, containing ions and electrons is investigated. The electrons are considered to be nonextensive and follow nonthermal distribution. The reductive perturbation technique (RPT) is used to obtain a nonlinear cylindrical Kadomtsev-Petviashvili (CKP) evolution equation. This equation is solved analytically. The effects of plasma parameters on the IAWs characteristics are discussed in details. Both compressive and rarefactive solitons are found to be created in the proposed plasma system. The profile of IAWs is found to depend on the nonextensive and nonthermal parameters. The present study is useful for understanding IAWs in the regions where mixed electron distribution in space, or laboratory plasmas, exist.
NASA Astrophysics Data System (ADS)
El-Hanbaly, A. M.; El-Shewy, E. K.; Elgarayhi, A.; Kassem, A. I.
2015-11-01
The nonlinear properties of small amplitude electron-acoustic (EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma with nonextensive distribution for hot electrons have been investigated. A reductive perturbation method used to obtain the Kadomstev-Petviashvili-Burgers equation. Bifurcation analysis has been discussed for non-dissipative system in the absence of Burgers term and reveals different classes of the traveling wave solutions. The obtained solutions are related to periodic and soliton waves and their behavior are shown graphically. In the presence of the Burgers term, the EXP-function method is used to solve the Kadomstev-Petviashvili-Burgers equation and the obtained solution is related to shock wave. The obtained results may be helpful in better conception of waves propagation in various space plasma environments as well as in inertial confinement fusion laboratory plasmas.
Perturbations of nested branes with induced gravity
Sbisà, Fulvio; Koyama, Kazuya E-mail: kazuya.koyama@port.ac.uk
2014-06-01
We study the behaviour of weak gravitational fields in models where a 4D brane is embedded inside a 5D brane equipped with induced gravity, which in turn is embedded in a 6D spacetime. We consider a specific regularization of the branes internal structures where the 5D brane can be considered thin with respect to the 4D one. We find exact solutions corresponding to pure tension source configurations on the thick 4D brane, and study perturbations at first order around these background solutions. To perform the perturbative analysis, we adopt a bulk-based approach and we express the equations in terms of gauge invariant and master variables using a 4D scalar-vector-tensor decomposition. We then propose an ansatz on the behaviour of the perturbation fields when the thickness of the 4D brane goes to zero, which corresponds to configurations where gravity remains finite everywhere in the thin limit of the 4D brane. We study the equations of motion using this ansatz, and show that they give rise to a consistent set of differential equations in the thin limit, from which the details of the internal structure of the 4D brane disappear. We conclude that the thin limit of the ''ribbon'' 4D brane inside the (already thin) 5D brane is well defined (at least when considering first order perturbations around pure tension configurations), and that the gravitational field on the 4D brane remains finite in the thin limit. We comment on the crucial role of the induced gravity term on the 5D brane.
Renormalized Lie perturbation theory
Rosengaus, E.; Dewar, R.L.
1981-07-01
A Lie operator method for constructing action-angle transformations continuously connected to the identity is developed for area preserving mappings. By a simple change of variable from action to angular frequency a perturbation expansion is obtained in which the small denominators have been renormalized. The method is shown to lead to the same series as the Lagrangian perturbation method of Greene and Percival, which converges on KAM surfaces. The method is not superconvergent, but yields simple recursion relations which allow automatic algebraic manipulation techniques to be used to develop the series to high order. It is argued that the operator method can be justified by analytically continuing from the complex angular frequency plane onto the real line. The resulting picture is one where preserved primary KAM surfaces are continuously connected to one another.
Nonlinear Electron Acoustic Waves in Dissipative Plasma with Superthermal Electrons
NASA Astrophysics Data System (ADS)
El-Hanbaly, A. M.; El-Shewy, E. K.; Kassem, A. I.; Darweesh, H. F.
2016-01-01
The nonlinear properties of small amplitude electron-acoustic ( EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma consisted of a cold electron fluid and superthermal hot electrons obeying superthermal distribution, and stationary ions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili-Burgers (KP-Brugers) equation. Some solutions of physical interest are obtained. These solutions are related to soliton, monotonic and oscillatory shock waves and their behaviour are shown graphically. The formation of these solutions depends crucially on the value of the Burgers term and the plasma parameters as well. By using the tangent hyperbolic (tanh) method, another interesting type of solution which is a combination between shock and soliton waves is obtained. The topology of phase portrait and potential diagram of the KP-Brugers equation is investigated.The advantage of using this method is that one can predict different classes of the travelling wave solutions according to different phase orbits. The obtained results may be helpful in better understanding of waves propagation in various space plasma environments as well as in inertial confinement fusion laboratory plasmas.
Modeling Steady Acoustic Fields Bounded in Cavities with Geometrical Imperfections
NASA Astrophysics Data System (ADS)
Albo, P. A. Giuliano; Gavioso, R. M.; Benedetto, G.
2010-07-01
A mathematical method is derived within the framework of classical Lagrangian field theory, which is suitable for the determination of the eigenstates of acoustic resonators of nearly spherical shape. The method is based on the expansion of the Helmholtz differential operator and the boundary condition in a power series of a small geometrical perturbation parameter {ɛ} . The method extends to orders higher than {ɛ^2} the calculation of the perturbed acoustic eigenvalues, which was previously limited by the use of variational formalism and the methods of Morse and Ingard. A specific example is worked out for radial modes of a prolate spheroid, with the frequency perturbation calculated to order {ɛ^3} . A possible strategy to tackle the problem of calculating the acoustic eigenvalues for cavities presenting non-smooth geometrical imperfections is also described.
Perturbative Methods in Path Integration
NASA Astrophysics Data System (ADS)
Johnson-Freyd, Theodore Paul
This dissertation addresses a number of related questions concerning perturbative "path" integrals. Perturbative methods are one of the few successful ways physicists have worked with (or even defined) these infinite-dimensional integrals, and it is important as mathematicians to check that they are correct. Chapter 0 provides a detailed introduction. We take a classical approach to path integrals in Chapter 1. Following standard arguments, we posit a Feynman-diagrammatic description of the asymptotics of the time-evolution operator for the quantum mechanics of a charged particle moving nonrelativistically through a curved manifold under the influence of an external electromagnetic field. We check that our sum of Feynman diagrams has all desired properties: it is coordinate-independent and well-defined without ultraviolet divergences, it satisfies the correct composition law, and it satisfies Schrodinger's equation thought of as a boundary-value problem in PDE. Path integrals in quantum mechanics and elsewhere in quantum field theory are almost always of the shape ∫ f es for some functions f (the "observable") and s (the "action"). In Chapter 2 we step back to analyze integrals of this type more generally. Integration by parts provides algebraic relations between the values of ∫ (-) es for different inputs, which can be packaged into a Batalin--Vilkovisky-type chain complex. Using some simple homological perturbation theory, we study the version of this complex that arises when f and s are taken to be polynomial functions, and power series are banished. We find that in such cases, the entire scheme-theoretic critical locus (complex points included) of s plays an important role, and that one can uniformly (but noncanonically) integrate out in a purely algebraic way the contributions to the integral from all "higher modes," reducing ∫ f es to an integral over the critical locus. This may help explain the presence of analytic continuation in questions like the
Revised Perturbation Statistics for the Global Scale Atmospheric Model
NASA Technical Reports Server (NTRS)
Justus, C. G.; Woodrum, A.
1975-01-01
Magnitudes and scales of atmospheric perturbations about the monthly mean for the thermodynamic variables and wind components are presented by month at various latitudes. These perturbation statistics are a revision of the random perturbation data required for the global scale atmospheric model program and are from meteorological rocket network statistical summaries in the 22 to 65 km height range and NASA grenade and pitot tube data summaries in the region up to 90 km. The observed perturbations in the thermodynamic variables were adjusted to make them consistent with constraints required by the perfect gas law and the hydrostatic equation. Vertical scales were evaluated by Buell's depth of pressure system equation and from vertical structure function analysis. Tables of magnitudes and vertical scales are presented for each month at latitude 10, 30, 50, 70, and 90 degrees.
Covariant Bardeen perturbation formalism
NASA Astrophysics Data System (ADS)
Vitenti, S. D. P.; Falciano, F. T.; Pinto-Neto, N.
2014-05-01
In a previous work we obtained a set of necessary conditions for the linear approximation in cosmology. Here we discuss the relations of this approach with the so-called covariant perturbations. It is often argued in the literature that one of the main advantages of the covariant approach to describe cosmological perturbations is that the Bardeen formalism is coordinate dependent. In this paper we will reformulate the Bardeen approach in a completely covariant manner. For that, we introduce the notion of pure and mixed tensors, which yields an adequate language to treat both perturbative approaches in a common framework. We then stress that in the referred covariant approach, one necessarily introduces an additional hypersurface choice to the problem. Using our mixed and pure tensors approach, we are able to construct a one-to-one map relating the usual gauge dependence of the Bardeen formalism with the hypersurface dependence inherent to the covariant approach. Finally, through the use of this map, we define full nonlinear tensors that at first order correspond to the three known gauge invariant variables Φ, Ψ and Ξ, which are simultaneously foliation and gauge invariant. We then stress that the use of the proposed mixed tensors allows one to construct simultaneously gauge and hypersurface invariant variables at any order.
Amplitudes of Spiral Perturbations
NASA Astrophysics Data System (ADS)
Grosbol, P.; Patsis, P. A.
2014-03-01
It has proven very difficult to estimate the amplitudes of spiral perturbations in disk galaxies from observations due to the variation of mass-to-light ratio and extinction across spiral arms. Deep, near-infrared images of grand-design spiral galaxies obtained with HAWK-I/VLT were used to analyze the azimuthal amplitude and shape of arms, which, even in the K-band may, be significantly biased by the presence of young stellar populations. Several techniques were applied to evaluate the relative importance of young stars across the arms, such as surface brightness of the disk with light from clusters subtracted, number density of clusters detected, and texture of the disk. The modulation of the texture measurement, which correlates with the number density of faint clusters, yields amplitudes of the spiral perturbation in the range 0.1-0.2. This estimate gives a better estimate of the mass perturbation in the spiral arms, since it is dominated by old clusters.
Near-field acoustic streaming jet
NASA Astrophysics Data System (ADS)
Moudjed, B.; Botton, V.; Henry, D.; Millet, S.; Garandet, J. P.; Ben Hadid, H.
2015-03-01
A numerical and experimental investigation of the acoustic streaming flow in the near field of a circular plane ultrasonic transducer in water is performed. The experimental domain is a parallelepipedic cavity delimited by absorbing walls to avoid acoustic reflection, with a top free surface. The flow velocities are measured by particle image velocimetry, leading to well-resolved velocity profiles. The theoretical model is based on a linear acoustic propagation model, which correctly reproduces the acoustic field mapped experimentally using a hydrophone, and an acoustic force term introduced in the Navier-Stokes equations under the plane-wave assumption. Despite the complexity of the acoustic field in the near field, in particular in the vicinity of the acoustic source, a good agreement between the experimental measurements and the numerical results for the velocity field is obtained, validating our numerical approach and justifying the planar wave assumption in conditions where it is a priori far from obvious. The flow structure is found to be correlated with the acoustic field shape. Indeed, the longitudinal profiles of the velocity present a wavering linked to the variations in acoustic intensity along the beam axis and transverse profiles exhibit a complex shape strongly influenced by the transverse variations of the acoustic intensity in the beam. Finally, the velocity in the jet is found to increase as the square root of the acoustic force times the distance from the origin of the jet over a major part of the cavity, after a strong short initial increase, where the velocity scales with the square of the distance from the upstream wall.
Cox, Trevor J
2011-03-01
An investigation has been undertaken into acoustic iridescence, exploring how a device can be constructed which alter sound waves, in a similar way to structures in nature that act on light to produce optical iridescence. The main construction had many thin perforated sheets spaced half a wavelength apart for a specified design frequency. The sheets create the necessary impedance discontinuities to create backscattered waves, which then interfere to create strongly reflected sound at certain frequencies. Predictions and measurements show a set of harmonics, evenly spaced in frequency, for which sound is reflected strongly. And the frequency of these harmonics increases as the angle of observation gets larger, mimicking the iridescence seen in natural optical systems. Similar to optical systems, the reflections become weaker for oblique angles of reflection. A second construction was briefly examined which exploited a metamaterial made from elements and inclusions which were much smaller than the wavelength. Boundary element method predictions confirmed the potential for creating acoustic iridescence from layers of such a material.
Drumheller, D.S.
1997-12-30
An acoustic transducer is described comprising a one-piece hollow mandrel into the outer surface of which is formed a recess with sides perpendicular to the central axis of the mandrel and separated by a first distance and with a bottom parallel to the central axis and within which recess are a plurality of washer-shaped discs of a piezoelectric material and at least one disc of a temperature-compensating material with the discs being captured between the sides of the recess in a pre-stressed interference fit, typically at 2,000 psi of compressive stress. The transducer also includes a power supply and means to connect to a measurement device. The transducer is intended to be used for telemetry between a measurement device located downhole in an oil or gas well and the surface. The transducer is of an construction that is stronger with fewer joints that could leak fluids into the recess holding the piezoelectric elements than is found in previous acoustic transducers. 4 figs.
Drumheller, Douglas S.
1997-01-01
An acoustic transducer comprising a one-piece hollow mandrel into the outer surface of which is formed a recess with sides perpendicular to the central axis of the mandrel and separated by a first distance and with a bottom parallel to the central axis and within which recess are a plurality of washer-shaped discs of a piezoelectric material and at least one disc of a temperature-compensating material with the discs being captured between the sides of the recess in a pre-stressed interference fit, typically at 2000 psi of compressive stress. The transducer also includes a power supply and means to connect to a measurement device. The transducer is intended to be used for telemetry between a measurement device located downhole in an oil or gas well and the surface. The transducer is of an construction that is stronger with fewer joints that could leak fluids into the recess holding the piezoelectric elements than is found in previous acoustic transducers.
Linear perturbations of a Schwarzschild blackhole by thin disc - convergence
NASA Astrophysics Data System (ADS)
Čížek, P.; Semerák, O.
2012-07-01
In order to find the perturbation of a Schwarzschild space-time due to a rotating thin disc, we try to adjust the method used by [4] in the case of perturbation by a one-dimensional ring. This involves solution of stationary axisymmetric Einstein's equations in terms of spherical-harmonic expansions whose convergence however turned out questionable in numerical examples. Here we show, analytically, that the series are almost everywhere convergent, but in some regions the convergence is not absolute.
Matter-wave localization in a weakly perturbed optical lattice
Cheng, Yongshan; Adhikari, S. K.
2011-11-15
By numerical solution and variational approximation of the Gross-Pitaevskii equation, we studied the localization of a noninteracting and weakly interacting Bose-Einstein condensate in a weakly perturbed optical lattice in one and three dimensions. The perturbation achieved through a weak delocalizing expulsive or a linear potential as well as a weak localizing harmonic potential removes the periodicity of the optical lattice and leads to localization. We also studied some dynamics of the localized state confirming its stability.