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.
Perturbation measurement of waveguides for acoustic thermometry
NASA Astrophysics Data System (ADS)
Lin, H.; Feng, X. J.; Zhang, J. T.
2013-09-01
Acoustic thermometers normally embed small acoustic transducers in the wall bounding a gas-filled cavity resonator. At high temperature, insulators of transducers loss electrical insulation and degrade the signal-to-noise ratio. One essential solution to this technical trouble is to couple sound by acoustic waveguides between resonator and transducers. But waveguide will break the ideal acoustic surface and bring perturbations(Δf+ig) to the ideal resonance frequency. The perturbation model for waveguides was developed based on the first-order acoustic theory in this paper. The frequency shift Δf and half-width change g caused by the position, length and radius of waveguides were analyzed using this model. Six different length of waveguides (52˜1763 mm) were settled on the cylinder resonator and the perturbation (Δf+ig) were measured at T=332 K and p=250˜500 kPa. The experiment results agreed with the theoretical prediction very well.
Superadiabatic evolution of acoustic and vorticity perturbations in Couette flow
NASA Astrophysics Data System (ADS)
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.
Dust-ion-acoustic solitons with transverse perturbation
Moslem, Waleed M.; El-Taibany, W.F.; El-Shewy, E.K.; El-Shamy, E.F.
2005-05-15
The ionization source model is considered, for the first time, to study the combined effects of trapped electrons, transverse perturbation, ion streaming velocity, and dust charge fluctuations on the propagation of dust-ion-acoustic solitons in dusty plasmas. The solitary waves are investigated through the derivation of the damped modified Kadomtsev-Petviashivili equation using the reductive perturbation method. Conditions for the formation of solitons as well as their properties are clearly explained. The relevance of our investigation to supernovae shells is also discussed.
Acoustic wave-equation-based earthquake location
NASA Astrophysics Data System (ADS)
Tong, Ping; Yang, Dinghui; Liu, Qinya; Yang, Xu; Harris, Jerry
2016-04-01
We present a novel earthquake location method using acoustic wave-equation-based traveltime inversion. The linear relationship between the location perturbation (δt0, δxs) and the resulting traveltime residual δt of a particular seismic phase, represented by the traveltime sensitivity kernel K(t0, xs) with respect to the earthquake location (t0, xs), is theoretically derived based on the adjoint method. Traveltime sensitivity kernel K(t0, xs) is formulated as a convolution between the forward and adjoint wavefields, which are calculated by numerically solving two acoustic wave equations. The advantage of this newly derived traveltime kernel is that it not only takes into account the earthquake-receiver geometry but also accurately honours the complexity of the velocity model. The earthquake location is obtained by solving a regularized least-squares problem. In 3-D realistic applications, it is computationally expensive to conduct full wave simulations. Therefore, we propose a 2.5-D approach which assumes the forward and adjoint wave simulations within a 2-D vertical plane passing through the earthquake and receiver. Various synthetic examples show the accuracy of this acoustic wave-equation-based earthquake location method. The accuracy and efficiency of the 2.5-D approach for 3-D earthquake location are further verified by its application to the 2004 Big Bear earthquake in Southern California.
Articulatory and acoustic adaptation to palatal perturbation.
Thibeault, Mélanie; Ménard, Lucie; Baum, Shari R; Richard, Gabrielle; McFarland, David H
2011-04-01
Previous work has established that speakers have difficulty making rapid compensatory adjustments in consonant production (especially in fricatives) for structural perturbations of the vocal tract induced by artificial palates with thicker-than-normal alveolar regions. The present study used electromagnetic articulography and simultaneous acoustic recordings to estimate tongue configurations during production of [s š t k] in the presence of a thin and a thick palate, before and after a practice period. Ten native speakers of English participated in the study. In keeping with previous acoustic studies, fricatives were more affected by the palate than were the stops. The thick palate lowered the center of gravity and the jaw was lower and the tongue moved further backwards and downwards. Center of gravity measures revealed complete adaptation after training, and with practice, subjects' decreased interlabial distance. The fact that adaptation effects were found for [k], which are produced with an articulatory gesture not directly impeded by the palatal perturbation, suggests a more global sensorimotor recalibration that extends beyond the specific articulatory target. PMID:21476667
Laplace homotopy perturbation method for Burgers equation with space- and time-fractional order
NASA Astrophysics Data System (ADS)
Johnston, S. J.; Jafari, H.; Moshokoa, S. P.; Ariyan, V. M.; Baleanu, D.
2016-07-01
The fractional Burgers equation describes the physical processes of unidirectional propagation of weakly nonlinear acoustic waves through a gas-filled pipe. The Laplace homotopy perturbation method is discussed to obtain the approximate analytical solution of space-fractional and time-fractional Burgers equations. The method used combines the Laplace transform and the homotopy perturbation method. Numerical results show that the approach is easy to implement and accurate when applied to partial differential equations of fractional orders.
On the thermo-acoustic Fant equation
NASA Astrophysics Data System (ADS)
Murray, P. R.; Howe, M. S.
2012-07-01
A 'reduced complexity' equation is derived to investigate combustion instabilities of a Rijke burner. The equation is nonlinear and furnishes limit cycle solutions for finite amplitude burner modes. It is a generalisation to combustion flows of the Fant equation used to investigate the production of voiced speech by unsteady throttling of flow by the vocal folds [G. Fant, Acoustic Theory of Speech Production. Mouton, The Hague, 1960]. In the thermo-acoustic problem the throttling occurs at the flame holder. The Fant equation governs the unsteady volume flow past the flame holder which, in turn, determines the acoustics of the entire system. The equation includes a fully determinate part that depends on the geometry of the flame holder and the thermo-acoustic system, and terms defined by integrals involving thermo-aerodynamic sources, such as a flame and vortex sound sources. These integrals provide a clear indication of what must be known about the flow to obtain a proper understanding of the dynamics of the thermo-acoustic system. Illustrative numerical results are presented for the linearised equation. This governs the growth rates of the natural acoustic modes, determined by system geometry, boundary conditions and mean temperature distribution, which are excited into instability by unsteady heat release from the flame and damped by large scale vorticity production and radiation losses into the environment. In addition, the equation supplies information about the 'combustion modes' excited by the local time-delay feedback dynamics of the flame.
NASA Astrophysics Data System (ADS)
Gao, Dong-Ning; Qi, Xin; Hong, Xue-Ren; Yang, Xue; Duan, Wen-Shan; Yang, Lei; Yang
2014-06-01
Numerical and theoretical investigations are carried out for the stability of the dust acoustic waves (DAWs) under the transverse perturbation in a two-ion temperature magnetized and collisionless dusty plasma. The Zakharov-Kuznetsov (ZK) equation, modified ZK equation, and Extended ZK (EZK) equation of the DAWs are given by using the reductive perturbation technique. The cut-off frequency is obtained by applying higher-order transverse perturbations to the soliton solution of the EZK equation. The propagation velocity of solitary waves, the real cut-off frequency, as well as the growth rate of the higher-order perturbation to the solitary wave are obtained.
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.
New wrinkles on black hole perturbations: Numerical treatment of acoustic and gravitational waves
NASA Astrophysics Data System (ADS)
Tenyotkin, Valery
2009-06-01
This thesis develops two main topics. A full relativistic calculation of quasinormal modes of an acoustic black hole is carried out. The acoustic black hole is formed by a perfect, inviscid, relativistic, ideal gas that is spherically accreting onto a Schwarzschild black hole. The second major part is the calculation of sourceless vector (electromagnetic) and tensor (gravitational) covariant field evolution equations for perturbations on a Schwarzschild background using the relatively recent [Special characters omitted.] decomposition method. Scattering calculations are carried out in Schwarzschild coordinates for electromagnetic and gravitational cases as validation of the method and the derived equations.
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. PMID:24683357
Acoustic perturbations on steady spherical accretion in Schwarzschild geometry
Naskar, Tapan; Chakravarty, Nabajit; Bhattacharjee, Jayanta K.; Ray, Arnab K.
2007-12-15
The stationary background flow in the spherically symmetric infall of a compressible fluid, coupled to the space-time defined by the static Schwarzschild metric, has been subjected to linearized acoustic perturbations. The perturbative procedure is based on the continuity condition and it shows that the coupling of the flow with the geometry of space-time brings about greater stability for the flow, to the extent that the amplitude of the perturbation, treated as a standing wave, decays in time, as opposed to the amplitude remaining constant in the Newtonian limit. In qualitative terms this situation simulates the effect of a dissipative mechanism in the classical Bondi accretion flow, defined in the Newtonian construct of space and time. As a result of this approach it becomes impossible to define an acoustic metric for a conserved spherically symmetric flow, described within the framework of Schwarzschild geometry. In keeping with this view, the perturbation, considered separately as a high-frequency traveling wave, also has its amplitude reduced.
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.
Staying positive: going beyond Lindblad with perturbative master equations
NASA Astrophysics Data System (ADS)
Whitney, Robert S.
2008-05-01
The perturbative master equation (Bloch-Redfield) is used extensively to study dissipative quantum mechanics—particularly for qubits—despite the 25-year-old criticism that it violates positivity (generating negative probabilities). We take an arbitrary system coupled to an environment containing many degrees-of-freedom and cast its perturbative master equation (derived from a perturbative treatment of Nakajima-Zwanzig or Schoeller-Schön equations) in the form of a Lindblad master equation. We find that the equation's parameters are time dependent. This time dependence is rarely accounted for and invalidates Lindblad's dynamical semigroup analysis. We analyse one such Bloch-Redfield master equation (for a two-level system coupled to an environment with a short but non-vanishing memory time), which apparently violates positivity. We analytically show that, once the time dependence of the parameters is accounted for, positivity is preserved.
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.
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.
Perturbative Solutions of the Extended Constraint Equations in General Relativity
NASA Astrophysics Data System (ADS)
Butscher, Adrian
2007-05-01
The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface {mathcal{Z}} in an asymptotically simple space-time satisfying the vacuum conformal Einstein equations developed by H. Friedrich. The extended constraint equations consist of a quasi-linear system of partial differential equations for the induced metric, the second fundamental form and two other tensorial quantities defined on {mathcal{Z}} , and are equivalent to the usual constraint equations that {mathcal{Z}} satisfies as a space-like hypersurface in a space-time satisfying Einstein’s vacuum equation. This article develops a method for finding perturbative, asymptotically flat solutions of the extended constraint equations in a neighbourhood of the flat solution on Euclidean space. This method is fundamentally different from the ‘classical’ method of Lichnerowicz and York that is used to solve the usual constraint equations.
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.
Perturbative Solutions of the Einstein Klein-Gordon Equations
NASA Astrophysics Data System (ADS)
Puliti, Gianluca; Jennings, Mara; Mamo, Vincent; Vuille, Chris
2005-11-01
As the Klein-Gordon equation is important in quantum theory and describes spin-0 particles, it is of interest to discover the nature of the gravity field such particles would be expected to create. In this paper, we solve the static, massive Einstein-Klein-Gordon (EKG) equations in perturbation, and compare the results with a similar calculation developed for the Einstein-Proca system. Subsequently, we study the massless static Klein-Gordon equation, and compare the result to the Reissner-Nordstrom metric.
An averaging theorem for a perturbed KdV equation
NASA Astrophysics Data System (ADS)
Guan, Huang
2013-06-01
We consider a perturbed KdV equation: \\begin{equation*} \\fl \\dot{u}+u_{xxx}-6uu_x=\\epsilon f(x,u(\\cdot)),\\quad x\\in {T},\\tqs\\int_{{T}} u \\,\\rmd x=0. \\end{equation*} For any periodic function u(x), let I(u)=(I_1(u),I_2(u),\\ldots)\\in{R}_+^{\\infty} be the vector, formed by the KdV integrals of motion, calculated for the potential u(x). Assuming that the perturbation ɛf(x, u(x)) defines a smoothing mapping u(x) ↦ f(x, u(x)) (e.g. it is a smooth function ɛ f(x), independent from u), and that solutions of the perturbed equation satisfy some mild a priori assumptions, we prove that for solutions u(t, x) with typical initial data and for 0 ⩽ t ≲ ɛ-1, the vector I(u (t)) may be well approximated by a solution of the averaged equation.
Master equation based steady-state cluster perturbation theory
NASA Astrophysics Data System (ADS)
Nuss, Martin; Dorn, Gerhard; Dorda, Antonius; von der Linden, Wolfgang; Arrigoni, Enrico
2015-09-01
A simple and efficient approximation scheme to study electronic transport characteristics of strongly correlated nanodevices, molecular junctions, or heterostructures out of equilibrium is provided by steady-state cluster perturbation theory. In this work, we improve the starting point of this perturbative, nonequilibrium Green's function based method. Specifically, we employ an improved unperturbed (so-called reference) state ρ̂S, constructed as the steady state of a quantum master equation within the Born-Markov approximation. This resulting hybrid method inherits beneficial aspects of both the quantum master equation as well as the nonequilibrium Green's function technique. We benchmark this scheme on two experimentally relevant systems in the single-electron transistor regime: an electron-electron interaction based quantum diode and a triple quantum dot ring junction, which both feature negative differential conductance. The results of this method improve significantly with respect to the plain quantum master equation treatment at modest additional computational cost.
Singular perturbation analysis of the neutron transport equation
Losey, D.C.; Lee, J.C.
1996-07-01
A singular perturbation technique is applied to the one-speed, one- dimensional neutron transport equation with isotropic scattering. Our technique extends previous singular perturbation applications to higher-order and reduces the transport problem to a series of diffusion theory problems in the interior medium and a series of analytically solvable transport problems in the boundary layers. Asymptotic matching links the two solutions, yielding boundary conditions and a composite expansion valid throughout the media. Our formulation generates an accurate correction for the material interface condition used in global diffusion theory calculations.
A hybrid perturbation-Galerkin technique for partial differential equations
NASA Technical Reports Server (NTRS)
Geer, James F.; Anderson, Carl M.
1990-01-01
A two-step hybrid perturbation-Galerkin technique for improving the usefulness of perturbation solutions to partial differential equations which contain a parameter is presented and discussed. In the first step of the method, the leading terms in the asymptotic expansion(s) of the solution about one or more values of the perturbation parameter are obtained using standard perturbation methods. In the second step, the perturbation functions obtained in the first step are used as trial functions in a Bubnov-Galerkin approximation. This semi-analytical, semi-numerical hybrid technique appears to overcome some of the drawbacks of the perturbation and Galerkin methods when they are applied by themselves, while combining some of the good features of each. The technique is illustrated first by a simple example. It is then applied to the problem of determining the flow of a slightly compressible fluid past a circular cylinder and to the problem of determining the shape of a free surface due to a sink above the surface. Solutions obtained by the hybrid method are compared with other approximate solutions, and its possible application to certain problems associated with domain decomposition is discussed.
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.
The quantum probability equation: I. Bound state perturbation theory
NASA Astrophysics Data System (ADS)
Milward, Geoffrey C.; Wilkin, Colin
2000-10-01
The partial-wave Schrödinger equation with real boundary conditions is recast as an equation for the probability density. When a small additional potential is included, the changes in the bound-state energy eigenvalues are obtained, up to third order in the perturbation, purely in terms of the perturbing potential and the unperturbed probability density. Although the approach is different, our results are equivalent to those derived by Bender (Bender C M 1978 Advanced Mathematical Methods for Scientists and Engineers (New York: McGraw-Hill) p 330). Knowledge of neither the unperturbed energy spectrum nor the wavefunctions of excited states is required. Evaluations of the second-order energy shift are given for some soluble S-wave problems.
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}.
Feng, Xue; Ben Tahar, Mabrouk; Baccouche, Ryan
2016-01-01
This paper presents a solution for aero-acoustic problems using the Galbrun equation in the time domain with a non-uniform steady mean flow in a two-dimensional coordinate system and the perfectly matched layer technique as the boundary conditions corresponding to an unbounded domain. This approach is based on an Eulerian-Lagrangian description corresponding to a wave equation written only in terms of the Lagrangian perturbation of the displacement. It is an alternative to the Linearized Euler Equations for solving aero-acoustic problems. The Galbrun equation is solved using a mixed pressure-displacement Finite Element Method. A complex Laplace transform scheme is used to study the time dependent variables. Several numerical examples are presented to validate and illustrate the efficiency of the proposed approach. PMID:26827028
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. PMID:24070825
A perturbative solution to metadynamics ordinary differential equation
NASA Astrophysics Data System (ADS)
Tiwary, Pratyush; Dama, James F.; Parrinello, Michele
2015-12-01
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.
Parallel coupled perturbed CASSCF equations and analytic CASSCF second derivatives.
Dudley, Timothy J; Olson, Ryan M; Schmidt, Michael W; Gordon, Mark S
2006-02-01
A parallel algorithm for solving the coupled-perturbed MCSCF (CPMCSCF) equations and analytic nuclear second derivatives of CASSCF wave functions is presented. A parallel scheme for evaluating derivative integrals and their subsequent use in constructing other derivative quantities is described. The task of solving the CPMCSCF equations is approached using a parallelization scheme that partitions the electronic hessian matrix over all processors as opposed to simple partitioning of the 3 N solution vectors among the processors. The scalability of the current algorithm, up to 128 processors, is demonstrated. Using three test cases, results indicate that the parallelization of derivative integral evaluation through a simple scheme is highly effective regardless of the size of the basis set employed in the CASSCF energy calculation. Parallelization of the construction of the MCSCF electronic hessian during solution of the CPMCSCF equations varies quantitatively depending on the nature of the hessian itself, but is highly scalable in all cases. PMID:16365869
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. PMID:26696051
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.
A Schamel equation for ion acoustic waves in superthermal plasmas
NASA Astrophysics Data System (ADS)
Williams, G.; Verheest, F.; Hellberg, M. A.; Anowar, M. G. M.; Kourakis, I.
2014-09-01
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 u0. 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.
NASA Technical Reports Server (NTRS)
Cooke, K. L.; Meyer, K. R.
1966-01-01
Extension of problem of singular perturbation for linear scalar constant coefficient differential- difference equation with single retardation to several retardations, noting degenerate equation solution
The fracture flow equation and its perturbation solution
NASA Astrophysics Data System (ADS)
Basha, H. A.; El-Asmar, W.
2003-12-01
This work derives the fracture flow equation from the two-dimensional steady form of the Navier-Stokes equation. Asymptotic solutions are obtained whereby the perturbation parameter is the ratio of the mean width over the length of the fracture segment. The perturbation expansion can handle arbitrary variation of the fracture walls as long as the dominant velocity is in the longitudinal direction. The effect of the matrix-fracture interaction is also taken into account by allowing leakage through the fracture walls. The perturbation solution is used to obtain an estimate of the flow rate and the fracture transmissivity as well as the velocity and the pressure distribution in fractures of various geometries. The analysis covers eight different configurations of fracture geometry including linear and curvilinear variation as well as sinusoidal variation in the top and bottom walls with varying horizontal alignment and roughness wavelengths. The zero-order solution yields the Reynolds lubrication approximation, and the higher-order equations provide a correction term to the flow rate in terms of the roughness frequency and the Reynolds number. For sinusoidal and linear walls, the mathematical analysis shows that the zero-order flow rate could be expressed in terms of the maximum to minimum width ratio. For equal widths at both ends of the fracture, the first-order correction is zero. For sinusoidal fractures, the flow rate decreases with increasing Reynolds number and with increasing roughness amplitude and frequency. The effect of leakage is to create a nonuniform flow distribution in the fracture that deviates significantly from the flow rate estimate for impermeable walls. The derived flow expressions can provide a more reliable tool for flow and transport predictions in fractured domain.
Global solutions to two nonlinear perturbed equations by renormalization group method
NASA Astrophysics Data System (ADS)
Kai, Yue
2016-02-01
In this paper, according to the theory of envelope, the renormalization group (RG) method is applied to obtain the global approximate solutions to perturbed Burger's equation and perturbed KdV equation. The results show that the RG method is simple and powerful for finding global approximate solutions to nonlinear perturbed partial differential equations arising in mathematical physics.
Solutions of perturbed p-Laplacian equations with critical nonlinearity
NASA Astrophysics Data System (ADS)
Wang, Chunhua; Wang, Jiangtao
2013-01-01
In this paper, we study a perturbed p-Laplacian equation. Under some given conditions on V(x), we prove that the equation has at least one positive solution provided that ɛ le E; for any n^{*}in {N}, it has at least n* pairs solutions if ɛ le E_{n^{*}}; and suppose there exists an orthogonal involution T:{R}NrArr {R}N such that V(x), P(x), and K(x) are T-invariant, then it has at least one pair of solutions, which change sign exactly once provided that ɛ le E, where E and E_{n^{*}} are sufficiently small positive numbers. Moreover, these solutions uɛ → 0 in W^{1,p}({R}N) as ɛ → 0.
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.
Transition of ion-acoustic perturbations in multicomponent plasma with negative ions
Sharma, Sumita Kumari; Devi, Kavita; Adhikary, Nirab Chandra; Bailung, Heremba
2008-08-15
Evolution of ion-acoustic compressive (positive) and rarefactive (negative) perturbations in a multicomponent plasma with negative ions has been investigated in a double plasma device. Transition of compressive solitons in electron-positive ion plasma, into a dispersing train of oscillations in a multicomponent plasma, when the negative ion concentration r exceeds a critical value r{sub c}, has been observed. On the other hand, an initial rarefactive perturbation initially evolves into a dispersing train of oscillations in electron-positive ion plasma and transforms into rarefactive solitons in a multicomponent plasma when the negative ion concentration is higher than the critical value. The Mach velocity and width of the compressive and rarefactive solitons are measured. The compressive solitons in the range 0
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.
Stauber, Douglas A.
1985-01-01
A Born approximation is used to linearize the relationship, in the horizontal-wavenumber and frequency domains, between lateral perturbations of modulus and density in a layered half-space and the acoustic wave field observed at the surface when a plane wave is incident from below. The resulting equations can be used to perform a linear inversion of observed acoustic wave fields to obtain lateral perturbations in modulus and density. Since modulus and density effects are separated, gravity observations can be included in the inversion procedure without any assumptions about the relationship between density and acoustic velocity. Tests with synthetic data sets reveal that the inversion method gives useful results when the spatial scales of the inhomogeneities are smaller than several acoustic wavelengths. Refs.
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
The KdV equation under periodic boundary conditions and its perturbations
NASA Astrophysics Data System (ADS)
Guan, Huang; Kuksin, Sergei
2014-09-01
In this paper we discuss properties of the Korteweg-de Vries (KdV) equation under periodic boundary conditions, especially those which are important for studying perturbations of the equation. We then review what is known about the long-time behaviour of solutions for perturbed KdV equations.
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.
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.
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.
Response of turbine flow meters to acoustic perturbations
NASA Astrophysics Data System (ADS)
Stoltenkamp, P. W.; Bergervoet, J. T. M.; Willems, J. F. H.; van Uittert, F. M. R.; Hirschberg, A.
2008-08-01
Acoustic pulsations can have a significant effect on gas turbine flow meters during volume flow measurements. These systematic errors are investigated experimentally for high-frequency pulsations and are compared to the results of a quasi-steady theory. Although significant deviations were found from the quasi-steady theory, the quadratic dependence of the velocity amplitude appears to remain valid for all measurements. The exact quadratic dependence is a function of Strouhal number of the pulsations. In the range of Strouhal numbers below 2.5, based on the chord length at the tip of the rotor blade and the flow velocity at the rotor inlet plane, we find a slow decrease in the error with increasing Strouhal number, Sr. The shape of the leading edge of the rotor blades does not affect this behaviour.
Căruntu, Bogdan
2014-01-01
The paper presents the optimal homotopy perturbation method, which is a new method to find approximate analytical solutions for nonlinear partial differential equations. Based on the well-known homotopy perturbation method, the optimal homotopy perturbation method presents an accelerated convergence compared to the regular homotopy perturbation method. The applications presented emphasize the high accuracy of the method by means of a comparison with previous results. PMID:25003150
Deriving average soliton equations with a perturbative method
Ballantyne, G.J.; Gough, P.T.; Taylor, D.P. )
1995-01-01
The method of multiple scales is applied to periodically amplified, lossy media described by either the nonlinear Schroedinger (NLS) equation or the Korteweg--de Vries (KdV) equation. An existing result for the NLS equation, derived in the context of nonlinear optical communications, is confirmed. The method is then applied to the KdV equation and the result is confirmed numerically.
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. PMID:26064591
NASA Astrophysics Data System (ADS)
Kutzelnigg, W.
1989-03-01
After a discussion of the problems associated with the non-relativistic limit of the Dirac equation and of the expansion of the exact eigenvalues and eigenfunctions of the H atom in powers of c -2 the traditional approaches for a perturbation theory of relativistic effects are critically reviewed. Then a direct perturbation theory is presented, that is characterized by a change of the metric in 4-component spinor space such that the Lévy-Leblond equation appears as the straightforward non-relativistic limit of the Dirac equation. The various orders in perturbation theory of the energy and the wave function are derived first in a direct way, then in a resolvent formalism. The formulas are very compact and easily generalizeable to arbitrary order. All integrals that arise to any order exist, and no controlled cancellation of divergent terms (as in other approaches) is necessary. In the same philosophy an iterative approach towards the solution of the Dirac equation is derived, in which the solution of the Schrödinger equation is the first iteration step.
Locus equations are an acoustic expression of articulator synergy
Iskarous, Khalil; Fowler, Carol A.; Whalen, D. H.
2010-01-01
The study investigated the articulatory basis of locus equations, regression lines relating F2 at the start of a Consonant-Vowel (CV) transition to F2 at the middle of the vowel, with C fixed and V varying. Several studies have shown that consonants of different places of articulation have locus equation slopes that descend from labial to velar to alveolar, and intercept magnitudes that increase in the opposite order. Using formulas from the theory of bivariate regression that express regression slopes and intercepts in terms of standard deviations and averages of the variables, it is shown that the slope directly encodes a well-established measure of coarticulation resistance. It is also shown that intercepts are directly related to the degree to which the tongue body assists the formation of the constriction for the consonant. Moreover, it is shown that the linearity of locus equations and the linear relation between locus equation slopes and intercepts originates in linearity in articulation between the horizontal position of the tongue dorsum in the consonant and to that in the vowel. It is concluded that slopes and intercepts of acoustic locus equations are measures of articulator synergy. PMID:20968373
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.
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.
NASA Astrophysics Data System (ADS)
Emad, K. El-Shewy; Abeer, A. Mahmoud; Ashraf, M. Tawfik; Essam, M. Abulwafa; Ahmed, Elgarayhi
2014-07-01
The KdV—Burgers equation for dust acoustic waves in unmagnetized plasma having electrons, singly charged nonthermal ions, and hot and cold dust species is derived using the reductive perturbation method. The Boltzmann distribution is used for electrons in the presence of the cold (hot) dust viscosity coefficients. The semi-inverse method and Agrawal variational technique are applied to formulate the space—time fractional KdV—Burgers equation which is solved using the fractional sub-equation method. The effect of the fractional parameter on the behavior of the dust acoustic shock waves in the dusty plasma is investigated.
Analytical method for space-fractional telegraph equation by homotopy perturbation transform method
NASA Astrophysics Data System (ADS)
Prakash, Amit
2016-06-01
The object of the present article is to study spacefractional telegraph equation by fractional Homotopy perturbation transform method (FHPTM). The homotopy perturbation transform method is an innovative adjustment in Laplace transform algorithm. Three test examples are presented to show the efficiency of the proposed technique.
Theory of Perturbed Equilibria for Solving the Grad-Shafranov Equation
A. Pletzer; L.E. Zakharov
1999-07-01
The theory of perturbed magnetohydrodynamic equilibria is presented for different formulations of the tokamak equilibrium problem. For numerical codes, it gives an explicit Newton scheme for solving the Grad-Shafranov equation subject to different constraints. The problem of stability of axisymmetric modes is shown to be a particular case of the equilibrium perturbation theory.
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.
NASA Astrophysics Data System (ADS)
Nakamura, K.
2007-01-01
Following the general framework of the gauge invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. 110 (2003), 723; ibid. 113 (2005), 481], we formulate second-order gauge invariant cosmological perturbation theory in a four-dimensional homogeneous isotropic universe. We consider perturbations both in the universe dominated by a single perfect fluid and in that dominated by a single scalar field. We derive all the components of the Einstein equations in the case that the first-order vector and tensor modes are negligible. All equations are derived in terms of gauge invariant variables without any gauge fixing. These equations imply that second-order vector and tensor modes may be generated due to the mode-mode coupling of the linear-order scalar perturbations. We also briefly discuss the main progress of this work through comparison with previous works.
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.
On the equations governing the gravitational perturbations of the Kerr black hole
NASA Technical Reports Server (NTRS)
Chandrasekhar, S.; Detweiler, S.
1976-01-01
Teukolsky's radial equation governing the general, non-axisymmetric, gravitational perturbations of the Kerr black hole is reduced to the form of a one-dimensional wave equation by making use of the transformation which enables the treatment of the non-axisymmetric modes in exactly the same way as the axisymmetric modes.
Response of partially premixed flames to acoustic velocity and equivalence ratio perturbations
Kim, K.T.; Lee, J.G.; Quay, B.D.; Santavicca, D.A.
2010-09-15
This article describes an experimental investigation of the forced response of a swirl-stabilized partially premixed flame when it is subjected to acoustic velocity and equivalence ratio fluctuations. The flame's response is analyzed using phase-resolved CH{sup *} chemiluminescence images and flame transfer function (FTF) measurements, and compared with the response of a perfectly premixed flame under acoustic perturbations. The nonlinear response of the partially premixed flame is manifested by a partial extinction of the reaction zone, leading to rapid reduction of flame surface area. This nonlinearity, however, is observed only when the phase difference between the acoustic velocity and the equivalence ratio at the combustor inlet is close to zero. The condition, {delta}{phi}{sub {phi}}'-V'{approx}0 , indicates that reactant mixtures with high equivalence ratio impinge on the flame front with high velocity, inducing large fluctuations of the rate of heat release. It is found that the phase difference between the acoustic velocity and equivalence ratio nonuniformities is a key parameter governing the linear/nonlinear response of a partially premixed flame, and it is a function of modulation frequency, inlet velocity, fuel injection location, and fuel injector impedance. The results presented in this article will provide insight into the response of a partially premixed flame, which has not been well explored to date. (author)
Time-sliced perturbation theory II: baryon acoustic oscillations and infrared resummation
NASA Astrophysics Data System (ADS)
Blas, Diego; Garny, Mathias; Ivanov, Mikhail M.; Sibiryakov, Sergey
2016-07-01
We use time-sliced perturbation theory (TSPT) to give an accurate description of the infrared non-linear effects affecting the baryonic acoustic oscillations (BAO) present in the distribution of matter at very large scales. In TSPT this can be done via a systematic resummation that has a simple diagrammatic representation and does not involve uncontrollable approximations. We discuss the power counting rules and derive explicit expressions for the resummed matter power spectrum up to next-to leading order and the bispectrum at the leading order. The two-point correlation function agrees well with N-body data at BAO scales. The systematic approach also allows to reliably assess the shift of the baryon acoustic peak due to non-linear effects.
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
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.
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.
NASA Technical Reports Server (NTRS)
Ardema, M. D.; Yang, L.
1985-01-01
A method of solving the boundary-layer equations that arise in singular-perturbation analysis of flightpath optimization problems is presented. The method is based on Picard iterations of the integrated form of the equations and does not require iteration to find unknown boundary conditions. As an example, the method is used to develop a solution algorithm for the zero-order boundary-layer equations of the aircraft minimum-time-to-climb problem.
Guo Shimin; Wang Hongli; Mei Liquan
2012-06-15
By combining the effects of bounded cylindrical geometry, azimuthal and axial perturbations, the nonlinear dust acoustic waves (DAWs) in an unmagnetized plasma consisting of negatively charged dust grains, nonextensive ions, and nonextensive electrons are studied in this paper. Using the reductive perturbation method, a (3 + 1)-dimensional variable-coefficient cylindrical Korteweg-de Vries (KdV) equation describing the nonlinear propagation of DAWs is derived. Via the homogeneous balance principle, improved F-expansion technique and symbolic computation, the exact traveling and solitary wave solutions of the KdV equation are presented in terms of Jacobi elliptic functions. Moreover, the effects of the plasma parameters on the solitary wave structures are discussed in detail. The obtained results could help in providing a good fit between theoretical analysis and real applications in space physics and future laboratory plasma experiments where long-range interactions are present.
Computer difference scheme for a singularly perturbed convection-diffusion equation
NASA Astrophysics Data System (ADS)
Shishkin, G. I.
2014-08-01
The Dirichlet problem for a singularly perturbed ordinary differential convection-diffusion equation with a perturbation parameter ɛ (that takes arbitrary values from the half-open interval (0, 1]) is considered. For this problem, an approach to the construction of a numerical method based on a standard difference scheme on uniform meshes is developed in the case when the data of the grid problem include perturbations and additional perturbations are introduced in the course of the computations on a computer. In the absence of perturbations, the standard difference scheme converges at an (δ st ) rate, where δ st = (ɛ + N -1)-1 N -1 and N + 1 is the number of grid nodes; the scheme is not ɛ-uniformly well conditioned or stable to perturbations of the data. Even if the convergence of the standard scheme is theoretically proved, the actual accuracy of the computed solution in the presence of perturbations degrades with decreasing ɛ down to its complete loss for small ɛ (namely, for ɛ = (δ-2max i, j |δ a {/i j }| + δ-1 max i, j |δ b {/i j }|), where δ = δ st and δ a {/i j }, δ b {/i j } are the perturbations in the coefficients multiplying the second and first derivatives). For the boundary value problem, we construct a computer difference scheme, i.e., a computing system that consists of a standard scheme on a uniform mesh in the presence of controlled perturbations in the grid problem data and a hypothetical computer with controlled computer perturbations. The conditions on admissible perturbations in the grid problem data and on admissible computer perturbations are obtained under which the computer difference scheme converges in the maximum norm for ɛ ∈ (0, 1] at the same rate as the standard scheme in the absence of perturbations.
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. PMID:21368995
Perturbed Hankel determinant, correlation functions and Painlevé equations
NASA Astrophysics Data System (ADS)
Chen, Min; Chen, Yang; Fan, Engui
2016-02-01
In this paper, we continue with the study of the Hankel determinant, generated by a Pollaczek-Jacobi type weight, w(x; t, α, β) ≔ xα(1 - x)βe-t/x, x ∈ [0, 1], α > 0, β > 0, t ≥ 0. This reduces to the "pure" Jacobi weight at t = 0. It was shown in the work of Chen and Dai [J. Approximation Theory 162(2), 2149-2167 (2010)] that the logarithmic derivative of this Hankel determinant satisfies a Jimbo-Miwa-Okamoto σ-form of Painlevé V (PV). We show that, under a double scaling, where n the dimension of the Hankel matrix tends to ∞ and t tends to 0, such that s ≔ 2n2t is finite, the double scaled Hankel determinant (effectively an operator determinant) has an integral representation in terms of a particular PIII'. Expansions of the scaled Hankel determinant for small and large s are found. We also consider another double scaling with α = - 2n + λ, where n → ∞, and t tends to 0, such that s ≔ nt is finite. In this situation, the scaled Hankel determinant has an integral representation in terms of a particular PV, and its small and large s asymptotic expansions are also found. The reproducing kernel in terms of monic polynomials orthogonal with respect to the Pollaczek-Jacobi type weight under the origin (or hard edge) scaling may be expressed in terms of the solutions of a second order linear ordinary differential equation (ODE). With special choices of the parameters, the limiting (double scaled) kernel and the second order ODE degenerate to Bessel kernel and the Bessel differential equation, respectively.
NASA Astrophysics Data System (ADS)
Sadlej, A. J.; Snijders, J. G.; van Lenthe, E.; Baerends, E. J.
1995-01-01
By combining the ideas of the direct perturbation theory approach to the solution of the Dirac equation with those underlying the regular expansion as used to obtain the two-component Chang-Pélissier-Durand Hamiltonian, a four-component form of the regular expansion is proposed. This formulation lends itself naturally to systematic improvement by a nonsingular form of perturbation theory. Alternatively it can be viewed as a double perturbation version of direct perturbation theory, where relativistic effects on the Hamiltonian and the metric are considered separately and the Hamiltonian perturbation is summed to infinite order. The scaling procedure that was earlier shown to be exact in the case of a hydrogenic potential and that greatly improved the core orbital energies, is found to follow naturally from the current formulation. The accuracy of the various approximations to the wave functions is assessed with respect to several radial expectation values weighing different regions in the uranium atom as a test case.
Perturbations of linear delay differential equations at the verge of instability
NASA Astrophysics Data System (ADS)
Lingala, N.; Namachchivaya, N. Sri
2016-06-01
The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e., a pair of roots of the characteristic equation lies on the imaginary axis of the complex plane and all other roots have negative real parts. It is shown that when small noise perturbations are present, the probability distribution of the dynamics can be approximated by the probability distribution of a certain one-dimensional stochastic differential equation (SDE) without delay. This is advantageous because equations without delay are easier to simulate and one-dimensional SDEs are analytically tractable. When the perturbations are also linear, it is shown that the stability depends on a specific complex number. The theory is applied to study oscillators with delayed feedback. Some errors in other articles that use multiscale approach are pointed out.
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.
Zakharov-Kuznestov-Burger Equation for Ion-Acoustic Waves in Cylindrical Geometry
NASA Astrophysics Data System (ADS)
Mandal, Pankaj Kumar; Ghosh, Uday Narayan; Chaterjee, Prasanta
2015-07-01
The nonlinear wave structures of ion acoustic waves in magnetized plasma comprising ions, non-extensive distributed electrons and kinematic viscosity are investigated through dynamical study. In a bounded cylindrical geometry Zakharov-Kuznestov-Burger (ZKB) equation is derived, for the first time, using reductive perturbation technic. System of coupled nonlinear ordinary differential equations is derived from ZKB equation and is solved numerically using fourth order Runge-kutta method. Equilibrium points are obtained and the features are studied dynamically in the neighbourhood of these points. With the variation of the non-extensive parameter and the kinematic viscosity parameter some important features in the nonlinear waves like oscillatory shocks to steady state propagation and vis-a-vis steady state propagation to oscillatory shocks emerge. When the values of the non-extensive parameter decrease, the phase portrait of the system shows that the change from stable spiral to stable closed and stable to unstable equilibrium happens . When the effect of dissipative term i.e. kinematic viscosity is considered some other significant features also evolve .The reduction of the value of kinematic viscosity results the change in nature of the waves from oscillatory shocks to periodic one.
Nonlocal Symmetry and its Applications in Perturbed mKdV Equation
NASA Astrophysics Data System (ADS)
Ren, Bo; Lin, Ji
2016-06-01
Based on the modified direct method, the variable-coefficient perturbed mKdV equation is changed to the constant-coefficient perturbed mKdV equation. The truncated Painlevé method is applied to obtain the nonlocal symmetry of the constant-coefficient perturbed mKdV equation. By introducing one new dependent variable, the nonlocal symmetry can be localized to the Lie point symmetry. Thanks to the localization procedure, the finite symmetry transformation is presented by solving the initial value problem of the prolonged systems. Furthermore, many explicit interaction solutions among different types of solutions such as solitary waves, rational solutions, and Painlevé II solutions are obtained using the symmetry reduction method to the enlarged systems. Two special concrete soliton-cnoidal interaction solutions are studied in both analytical and graphical ways.
NASA Astrophysics Data System (ADS)
Thoma, Carsten Hilmar
1997-12-01
The coupling of stress and strain fields to electric fields present in anisotropic piezoelectric crystals makes them ideal for use as electromechanical transducers in a wide variety of applications. In recent years such crystals have been utilized to produce surface acoustic wave devices for signal processing applications, in which an applied metallic grating both transmits and receives, through the piezoelectric effect, electromechanical surface waves. The design of such interdigital transducers requires an accurate knowledge of wave propagation and reflection. The presence of the metal grating in addition to its ideal transduction function, by means of electrical and mechanical loading, also introduces a velocity shift as well as reflection into substrate surface waves. We seek to obtain a consistent formulation of the wave behavior due to the electrical and mechanical loading of the substrate crystal by the metallic grating. A perturbative solution up to second order in h//lambda is developed, where h is the maximum grating height and λ the acoustic wavelength. For the operating frequencies and physical parameters of modern surface acoustic wave devices such an analysis will provide an adequate description of device behavior in many cases, thereby circumventing the need for more computationally laborious methods. Numerical calculations are presented and compared with available experimental data.
Homotopic Approximate Solutions for the Perturbed CKdV Equation with Variable Coefficients
Lu, Dianchen; Chen, Tingting
2014-01-01
This work concerns how to find the double periodic form of approximate solutions of the perturbed combined KdV (CKdV) equation with variable coefficients by using the homotopic mapping method. The obtained solutions may degenerate into the approximate solutions of hyperbolic function form and the approximate solutions of trigonometric function form in the limit cases. Moreover, the first order approximate solutions and the second order approximate solutions of the variable coefficients CKdV equation in perturbation εun are also induced. PMID:24737983
Homotopic approximate solutions for the perturbed CKdV equation with variable coefficients.
Lu, Dianchen; Chen, Tingting; Hong, Baojian
2014-01-01
This work concerns how to find the double periodic form of approximate solutions of the perturbed combined KdV (CKdV) equation with variable coefficients by using the homotopic mapping method. The obtained solutions may degenerate into the approximate solutions of hyperbolic function form and the approximate solutions of trigonometric function form in the limit cases. Moreover, the first order approximate solutions and the second order approximate solutions of the variable coefficients CKdV equation in perturbation εu (n) are also induced. PMID:24737983
NASA Astrophysics Data System (ADS)
Sharma, Dinkar; Singh, Prince; Chauhan, Shubha
2016-01-01
In this paper, a combined form of the Laplace transform method with the homotopy perturbation method (HPTM) is applied to solve nonlinear systems of partial differential equations viz. the system of third order KdV Equations and the systems of coupled Burgers' equations in one- and two- dimensions. The nonlinear terms can be easily handled by the use of He's polynomials. The results shows that the HPTM is very efficient, simple and avoids the round-off errors. Four test examples are considered to illustrate the present scheme. Further the results are compared with Homotopy perturbation method (HPM) which shows that this method is a suitable method for solving systems of partial differential equations.
NASA Astrophysics Data System (ADS)
A. N., Dev; Sarma, J.; M. K., Deka; A. P., Misra; N. C., Adhikary
2014-12-01
We study the nonlinear propagation of dust-ion acoustic (DIA) shock waves in an un-magnetized dusty plasma which consists of electrons, both positive and negative ions and negatively charged immobile dust grains. Starting from a set of hydrodynamic equations with the ion thermal pressures and ion kinematic viscosities included, and using a standard reductive perturbation method, the Kadomtsev—Petviashivili—Burgers (K-P-Burgers) equation is derived, which governs the evolution of DIA shocks. A stationary solution of the K-P-Burgers equation is obtained and its properties are analysed with different plasma number densities, ion temperatures and masses. It is shown that a transition from shocks with negative potential to positive one occurs depending on the negative ion concentration in the plasma and the obliqueness of propagation of DIA waves.
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. PMID:24369452
Chaos in the perturbed Korteweg-de Vries equation with nonlinear terms of higher order
NASA Astrophysics Data System (ADS)
Pan, Wei-Zhen; Song, Xiang-Jiong; Yu, Jun
2010-03-01
The dynamical behaviour of the generalized Korteweg-de Vries (KdV) equation under a periodic perturbation is investigated numerically. The bifurcation and chaos in the system are observed by applying bifurcation diagrams, phase portraits and Poincaré maps. To characterise the chaotic behaviour of this system, the spectra of the Lyapunov exponent and Lyapunov dimension of the attractor are also employed.
Many-body-QED perturbation theory: Connection to the two-electron Bethe-Salpeter equation
NASA Astrophysics Data System (ADS)
Lindgren, I.; Salomonson, S.; Hedendahl, D.
2005-03-01
The connection between many-body perturbation theory (MBPT) and quantum electrodynamics (QED) is reviewed for systems of two fermions in an external field. The treatment is mainly based on the recently developed covariant-evolution-operator method for QED calculations (I. Lindgren, S. Salomonson, and B. Asen. Phys. Rep. 389, 161 (2004)), which is quite similar in structure to MBPT. At the same time, this procedure is closely related to the S-matrix and Green's-function formalisms and can therefore serve as a bridge connecting various approaches. It is demonstrated that the MBPT-QED scheme, when carried to all orders, leads to a Schrodinger-like equation, equivalent to the Bethe-Salpeter (BS) equation. A Bloch equation in commutator form that can be used for an "extended" or quasi-degenerate model space is derived. This is a multi-state equation that has the same relation to the single-state BS equation as the standard Bloch equation has to the ordinary Schrodinger equation. It can be used to generate a perturbation expansion compatible with the BS equation even in the case of a quasi-degenerate model space.
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.
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)
Shaldanbayev, Amir; Shomanbayeva, Manat; Kopzhassarova, Asylzat
2016-08-01
This paper proposes a fundamentally new method of investigation of a singularly perturbed Cauchy problem for a linear system of ordinary differential equations based on the spectral theory of equations with deviating argument.
Coherent acoustic perturbation of second-harmonic generation in NiO
NASA Astrophysics Data System (ADS)
Huber, L.; Ferrer, A.; Kubacka, T.; Huber, T.; Dornes, C.; Sato, T.; Ogawa, K.; Tono, K.; Katayama, T.; Inubushi, Y.; Yabashi, M.; Tanaka, Yoshikazu; Beaud, P.; Fiebig, M.; Scagnoli, V.; Staub, U.; Johnson, S. L.
2015-09-01
We investigate the structural and magnetic origins of the unusual ultrafast second-harmonic-generation (SHG) response of femtosecond-laser-excited nickel oxide (NiO) previously attributed to oscillatory reorientation dynamics of the magnetic structure induced by d -d excitations. Using time resolved x-ray diffraction from the (3/2 3/2 3/2 ) magnetic planes, we show that changes in the magnitude of the magnetic structure factor following ultrafast optical excitation are limited to Δ
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.
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. PMID:27300980
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.
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.
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. PMID:19257112
Non-perturbative effects for the Quark-Gluon Plasma equation of state
Begun, V. V. Gorenstein, M. I. Mogilevsky, O. A.
2012-07-15
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.
NASA Astrophysics Data System (ADS)
Awadallah, Ra'id S.; Brown, Gary S.
1998-07-01
This paper consists of two parts. In the first part, the solution of the Helmholtz equation under forward-scattering or propagation conditions is sought as a uniform asymptotic perturbation expansion using the method of multiple scales. It is then shown that the parabolic wave equation (PWE) solution is the zeroth-order term in this expansion. In the second part, the electric-field integral equation and the magnetic-field integral equation, derived under the PWE approximation, are solved for surface currents induced on a sinusoidal surface. The scattered fields produced by these currents are then calculated using the appropriate radiation integrals. Results are compared to those obtained using the method of ordered multiple interactions developed by Kapp and Brown.
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 equations governing the axisymmetric perturbations of the Kerr black hole
NASA Technical Reports Server (NTRS)
Chandrasekhar, S.; Detweiler, S.
1975-01-01
It is shown how Teukolsky's equation, governing the perturbations of the Kerr black hole, can be reduced, in the axisymmetric case, to a one-dimensional wave equation with four possible potentials. The potentials are implicitly dependent on the frequency; and besides, depending on circumstances, they can be complex. In all cases (i.e. whether or not the potentials are real or complex), the problem of the reflexion and the transmission of gravitational waves by the potential barriers can be formulated, consistently, with the known conservation laws. It is further shown that all four potentials lead to the same reflexion and transmission coefficients.
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.
Multimodal far-field acoustic radiation pattern: An approximate equation
NASA Technical Reports Server (NTRS)
Rice, E. J.
1977-01-01
The far-field sound radiation theory for a circular duct was studied for both single mode and multimodal inputs. The investigation was intended to develop a method to determine the acoustic power produced by turbofans as a function of mode cut-off ratio. With reasonable simplifying assumptions the single mode radiation pattern was shown to be reducible to a function of mode cut-off ratio only. With modal cut-off ratio as the dominant variable, multimodal radiation patterns can be reduced to a simple explicit expression. This approximate expression provides excellent agreement with an exact calculation of the sound radiation pattern using equal acoustic power per mode.
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.
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.
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.
Dynamics of perturbed wavetrain solutions to the Ginzburg-Landau equation
Keefe, L.R.
1984-01-01
The bifurcation structure of even, spatially periodic solutions to the time-dependent Ginzburg-Landau equation is investigated analytically and numerically. A rich variety of behavior, including limit cycles, two-tori, period-doubling sequences, and strange attractors are found to exist in the phase space of the solutions constructed from spatial Fourier modes. Beginning with unstable perturbations to the spatially homogeneous Stokes solution, changes in solution behavior are examined as the perturbing wavenumber q is varied in the range 0.6 to 1.3. Solution bifurcations as q changes are often found to be associated with symmetry making or breaking changes in the structure of attractors in phase space. Two distinct mirror image attractors are found to coexist for many values of q. Chaotic motion is found for two ranges of q Lyapunov exponents of the solutions and the Lyapunov dimension of the corresponding attractors are calculated for the larger of these regions. Poincare sections of the attractors within this chaotic range are consistent with the dimension calculation and also reveal a bifurcation structure within the chaos which broadly resembles that found in one-dimensional quadratic maps. The integrability of the Ginzburg-Landau equation is also examined. It is demonstrated that the equation does not possess the Painleve property, except for a special case of the coefficients which corresponds to the integrable non-linear Schroedinger (NLS) equation.
NASA Astrophysics Data System (ADS)
Jiang, Daqing; Shi, Ningzhong; Li, Xiaoyue
2008-04-01
This paper discusses a randomized non-autonomous logistic equation , where B(t) is a 1-dimensional standard Brownian motion. In [D.Q. Jiang, N.Z. Shi, A note on non-autonomous logistic equation with random perturbation, J. Math. Anal. Appl. 303 (2005) 164-172], the authors show that E[1/N(t)] has a unique positive T-periodic solution E[1/Np(t)] provided a(t), b(t) and [alpha](t) are continuous T-periodic functions, a(t)>0, b(t)>0 and . We show that this equation is stochastically permanent and the solution Np(t) is globally attractive provided a(t), b(t) and [alpha](t) are continuous T-periodic functions, a(t)>0, b(t)>0 and mint[set membership, variant][0,T]a(t)>maxt[set membership, variant][0,T][alpha]2(t). By the way, the similar results of a generalized non-autonomous logistic equation with random perturbation are yielded.
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. PMID:24180802
Exponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their Perturbation
Caraballo, Tomas Kloeden, Peter E. Schmalfuss, Bjoern
2004-10-15
We consider the exponential stability of stochastic evolution equations with Lipschitz continuous non-linearities when zero is not a solution for these equations. We prove the existence of anon-trivial stationary solution which is exponentially stable, where the stationary solution is generated by the composition of a random variable and the Wiener shift. We also construct stationary solutions with the stronger property of attracting bounded sets uniformly. The existence of these stationary solutions follows from the theory of random dynamical systems and their attractors. In addition, we prove some perturbation results and formulate conditions for the existence of stationary solutions for semilinear stochastic partial differential equations with Lipschitz continuous non-linearities.
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. PMID:25615203
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.
Kumar Samanta, Utpal; Saha, Asit; Chatterjee, Prasanta
2013-05-15
Bifurcations of nonlinear propagation of ion acoustic waves (IAWs) in a magnetized plasma whose constituents are cold ions and kappa distributed electron are investigated using a two component plasma model. The standard reductive perturbation technique is used to derive the Zakharov-Kuznetsov (ZK) equation for IAWs. By using the bifurcation theory of planar dynamical systems to this ZK equation, the existence of solitary wave solutions and periodic travelling wave solutions is established. All exact explicit solutions of these travelling waves are determined. The results may have relevance in dense space plasmas.
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.
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. PMID:17552680
Collis, Jon M; Siegmann, William L; Jensen, Finn B; Zampolli, Mario; Küsel, Elizabeth T; Collins, Michael D
2008-01-01
Recent improvements in the parabolic equation method are combined to extend this approach to a larger class of seismo-acoustics problems. The variable rotated parabolic equation [J. Acoust. Soc. Am. 120, 3534-3538 (2006)] handles a sloping fluid-solid interface at the ocean bottom. The single-scattering solution [J. Acoust. Soc. Am. 121, 808-813 (2007)] handles range dependence within elastic sediment layers. When these methods are implemented together, the parabolic equation method can be applied to problems involving variations in bathymetry and the thickness of sediment layers. The accuracy of the approach is demonstrated by comparing with finite-element solutions. The approach is applied to a complex scenario in a realistic environment. PMID:18177137
From charge motion in general magnetic fields to the non perturbative gyrokinetic equation
NASA Astrophysics Data System (ADS)
Di Troia, C.
2015-04-01
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.
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.
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. PMID:24794509
Chaotic motion for the generalized KdV-Burgers equation with external perturbation
NASA Astrophysics Data System (ADS)
Yu, Jun; Li, Jieru; Ng, Tick Wan
2009-12-01
The bifurcation and chaos in the generalized KdV-Burgers equation under periodic perturbation are investigated numerically in some detail. It is shown that dynamical chaos can occur when we choose appropriately systematic parameters and initial conditions. Abundant bifurcation structures and different routes to chaos such as period-doubling and inverse period-doubling cascades, intermittent bifurcation and crisis are found by using bifurcation diagrams, Poincaré maps and phase portraits. To characterize the chaotic behavior of this system, the spectrum of the Lyapunov exponent and the Lyapunov dimension of the attractor are also employed.
Bifurcation and chaos in a perturbed soliton equation with higher-order nonlinearity
NASA Astrophysics Data System (ADS)
Yu, Jun; Zhang, Rongbo; Jin, Guojuan
2011-12-01
The influence of a soliton system under external perturbation is considered. We take the compound Korteweg-de Vries-Burgers-type equation with nonlinear terms of any order as an example, and investigate numerically the chaotic behavior of the system with periodic forcing. It is shown that dynamical chaos can occur when we appropriately choose system parameters. Abundant bifurcation structures and different routes to chaos, such as period doubling, intermittent bifurcation and crisis, are found by applying bifurcation diagrams, Poincaré maps and phase portraits. To characterize the chaotic behavior of this system, a spectrum of Lyapunov exponents and Lyapunov dimensions of attractors are also employed.
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.
On the limit cycles of a class of planar singular perturbed differential equations.
Wu, Yuhai; Zhou, Jingjing
2014-01-01
Relaxation oscillations of two-dimensional planar singular perturbed systems with a layer equation exhibiting canard cycles are studied. The canard cycles under consideration contain two turning points and two jump points. We suppose that there exist three parameters permitting generic breaking at both the turning points and the connecting fast orbit. The conditions of one (resp., two, three) relaxation oscillation near the canard cycles are given by studying a map from the space of phase parameters to the space of breaking parameters. PMID:25143973
On the Limit Cycles of a Class of Planar Singular Perturbed Differential Equations
Zhou, Jingjing
2014-01-01
Relaxation oscillations of two-dimensional planar singular perturbed systems with a layer equation exhibiting canard cycles are studied. The canard cycles under consideration contain two turning points and two jump points. We suppose that there exist three parameters permitting generic breaking at both the turning points and the connecting fast orbit. The conditions of one (resp., two, three) relaxation oscillation near the canard cycles are given by studying a map from the space of phase parameters to the space of breaking parameters. PMID:25143973
NASA Astrophysics Data System (ADS)
Aoki, Ken-Ichi; Kumamoto, Shin-Ichiro; Sato, Daisuke
2014-04-01
We analyze dynamical chiral symmetry breaking (Dχ SB) in the Nambu-Jona-Lasinio model by using the non-perturbative renormalization group equation. The equation takes the form of a two-dimensional partial differential equation for the multi-fermion effective interactions V(x,t) where x is the bar {ψ }ψ operator and t is the logarithm of the renormalization scale. The Dχ SB occurs due to the quantum corrections, which means it emerges at some finite tc while integrating the equation with respect to t. At t_c some singularities suddenly appear in V which is compulsory in the spontaneous symmetry breakdown. Therefore there is no solution of the equation beyond tc. We newly introduce the notion of a weak solution to get the global solution including the infrared limit t rArr ∞ and investigate its properties. The obtained weak solution is global and unique, and it perfectly describes the physically correct vacuum even in the case of the first order phase transition appearing in a finite-density medium. The key logic of deduction is that the weak solution we defined automatically convexifies the effective potential when treating the singularities.
The construction of high-accuracy schemes for acoustic equations
NASA Technical Reports Server (NTRS)
Tang, Lei; Baeder, James D.
1995-01-01
An accuracy analysis of various high order schemes is performed from an interpolation point of view. The analysis indicates that classical high order finite difference schemes, which use polynomial interpolation, hold high accuracy only at nodes and are therefore not suitable for time-dependent problems. Thus, some schemes improve their numerical accuracy within grid cells by the near-minimax approximation method, but their practical significance is degraded by maintaining the same stencil as classical schemes. One-step methods in space discretization, which use piecewise polynomial interpolation and involve data at only two points, can generate a uniform accuracy over the whole grid cell and avoid spurious roots. As a result, they are more accurate and efficient than multistep methods. In particular, the Cubic-Interpolated Psuedoparticle (CIP) scheme is recommended for computational acoustics.
Investigating perturbed pathway modules from gene expression data via structural equation models
2014-01-01
Background It is currently accepted that the perturbation of complex intracellular networks, rather than the dysregulation of a single gene, is the basis for phenotypical diversity. High-throughput gene expression data allow to investigate changes in gene expression profiles among different conditions. Recently, many efforts have been made to individuate which biological pathways are perturbed, given a list of differentially expressed genes (DEGs). In order to understand these mechanisms, it is necessary to unveil the variation of genes in relation to each other, considering the different phenotypes. In this paper, we illustrate a pipeline, based on Structural Equation Modeling (SEM) that allowed to investigate pathway modules, considering not only deregulated genes but also the connections between the perturbed ones. Results The procedure was tested on microarray experiments relative to two neurological diseases: frontotemporal lobar degeneration with ubiquitinated inclusions (FTLD-U) and multiple sclerosis (MS). Starting from DEGs and dysregulated biological pathways, a model for each pathway was generated using databases information biological databases, in order to design how DEGs were connected in a causal structure. Successively, SEM analysis proved if pathways differ globally, between groups, and for specific path relationships. The results confirmed the importance of certain genes in the analyzed diseases, and unveiled which connections are modified among them. Conclusions We propose a framework to perform differential gene expression analysis on microarray data based on SEM, which is able to: 1) find relevant genes and perturbed biological pathways, investigating putative sub-pathway models based on the concept of disease module; 2) test and improve the generated models; 3) detect a differential expression level of one gene, and differential connection between two genes. This could shed light, not only on the mechanisms affecting variations in gene
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.
Jing, Yun; Xiang, Ning
2008-01-01
This paper proposes a modified boundary condition to improve the room-acoustic prediction accuracy of a diffusion equation model. Previous boundary conditions for the diffusion equation model have certain limitations which restrict its application to a certain number of room types. The boundary condition employing the Sabine absorption coefficient [V. Valeau et al., J. Acoust. Soc. Am. 119, 1504-1513 (2006)] cannot predict the sound field well when the absorption coefficient is high, while the boundary condition employing the Eyring absorption coefficient [Y. Jing and N. Xiang, J. Acoust. Soc. Am. 121, 3284-3287 (2007); A. Billon et al., Appl. Acoust. 69, (2008)] has a singularity whenever any surface material has an absorption coefficient of 1.0. The modified boundary condition is derived based on an analogy between sound propagation and light propagation. Simulated and experimental data are compared to verify the modified boundary condition in terms of room-acoustic parameter prediction. The results of this comparison suggest that the modified boundary condition is valid for a range of absorption coefficient values and successfully eliminates the singularity problem. PMID:18177146
Field transformations and the classical equation of motion in chiral perturbation theory
Scherer, S.; Fearing, H.W.
1995-12-01
The construction of effective Lagrangians commonly involves the application of the ``classical equation of motion`` to eliminate redundant structures and thus generate the minimal number of independent terms. We investigate this procedure in the framework of chiral perturbation theory with particular emphasis on the new features which appear at {ital O}({ital p}{sup 6}). The use of the ``classical equation of motion`` is interpreted in terms of field transformations. Such an interpretation is crucial if one wants to bring a given Lagrangian into a canonical form with a minimal number of terms. We emphasize that the application of field transformations leads to a modification of the coefficients of higher-order terms as well as eliminating structures, or what is equivalent, expressing certain structures in terms of already known different structures. This will become relevant once one considers the problem of expressing in canonical form a model effective interaction containing terms beyond next-to-leading order, i.e., beyond {ital O}({ital p}{sup 4}). In such circumstances the naive application of the clasical equation of motion to simply drop terms, as is commonly done at lowest order, leads to subtle errors, which we discuss.
NASA Astrophysics Data System (ADS)
Petrov, P. S.; Zakharenko, A. D.; Trofimov, M. Yu.
2012-11-01
A suitable tool for the simulation of low frequency acoustic pulse signals propagating in a shallow sea is the numerical integration of the nonstationary wave equation. The main feature of such simulation problems is that in this case the sound waves propagate in the geoacoustic waveguide formed by the upper layers of the bottom and the water column. By this reason, the correct dependence of the attenuation of sound waves in the bottom on their frequency must be taken into account. In this paper we obtain an integro-differential equation for the sound waves in the viscoelastic fluid, which allows to simulate the arbitrary dependence of acoustic wave attenuation on frequency in the time domain computations. The procedure of numerical solution of this equation based on its approximation by a system of differential equations is then considered and the methods of artificial limitation of computational domain are described. We also construct a simple finite-difference scheme for the proposed equation suitable for the numerical solution of nonstationary problems arising in the shallow-sea acoustics.
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.
Entanglement entropy of excited states in conformal perturbation theory and the Einstein equation
NASA Astrophysics Data System (ADS)
Speranza, Antony J.
2016-04-01
For a conformal field theory (CFT) deformed by a relevant operator, the entanglement entropy of a ball-shaped region may be computed as a perturbative expansion in the coupling. A similar perturbative expansion exists for excited states near the vacuum. Using these expansions, this work investigates the behavior of excited state entanglement entropies of small, ball-shaped regions. The motivation for these calculations is Jacobson's recent work on the equivalence of the Einstein equation and the hypothesis of maximal vacuum entropy [arXiv:1505.04753], which relies on a conjecture stating that the behavior of these entropies is sufficiently similar to a CFT. In addition to the expected type of terms which scale with the ball radius as R d , the entanglement entropy calculation gives rise to terms scaling as R 2Δ, where Δ is the dimension of the deforming operator. When \\varDelta ≤ d/2 , the latter terms dominate the former, and suggest that a modification to the conjecture is needed.
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)
Li, Min; Xu, Tao; Wang, Lei
2016-04-01
In this paper, the modified nonlinear Schrödinger equation is investigated via the direct perturbation method, which can describe the femtosecond optical pulse propagation in a monomodal optical fiber. Considering the quintic nonlinear perturbation, we obtain the approximate solution with the first-order correction, which can be expressed by the solution and symmetry of the derivative nonlinear Schrödinger equation. Under the nonvanishing boundary conditions, the approximate dark and anti-dark soliton solutions are derived and the existence conditions are also given. The effects of the perturbation on the propagations and interactions of the solitons on the nonzero background are discussed by comparing the physical quantities of solitons with the unperturbed case. It is found that the quintic nonlinear perturbation can lead to the change of the velocity as well as the pulse compression, but has no influence on the dynamics of the elastic interactions. Finally, numerical simulations are performed to support the theoretical results.
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.
Gauge invariant cosmological perturbation equations with corrections from loop quantum gravity
Bojowald, Martin; Hossain, Golam Mortuza; Kagan, Mikhail; Shankaranarayanan, S.
2009-02-15
A consistent implementation of quantum gravity is expected to change the familiar notions of space, time, and the propagation of matter in drastic ways. This will have consequences on very small scales, but also gives rise to correction terms in evolution equations of modes relevant for observations. In particular, the evolution of inhomogeneities in the very early Universe should be affected. In this paper consistent evolution equations for gauge-invariant perturbations in the presence of inverse triad corrections of loop quantum gravity are derived. Some immediate effects are pointed out, for instance, concerning conservation of power on large scales and nonadiabaticity. It is also emphasized that several critical corrections can only be seen to arise in a fully consistent treatment where the gauge freedom of canonical gravity is not fixed before implementing quantum corrections. In particular, metric modes must be allowed to be inhomogeneous: it is not consistent to assume only matter inhomogeneities on a quantum-corrected homogeneous background geometry. In this way, stringent consistency conditions arise for possible quantization ambiguities, which will eventually be further constrained observationally.
NASA Astrophysics Data System (ADS)
Guo, Shimin; Mei, Liquan; He, Yaling; Li, Yibao
2016-03-01
Nonlinear propagation of dust-ion-acoustic (DIA) waves is investigated in a one-dimensional, unmagnetized plasma containing positive ions, negative ions, trapped electrons featuring vortex-like distribution, and immobile dust grains having both positive and negative charges. Via reductive perturbation method, Agrawal's method, and Euler-Lagrange equation, the time-fractional Schamel-KdV equation under the sense of Riesz fractional derivative is derived to describe nonlinear behavior of DIA waves. The approximate solution of the time-fractional Schamel-KdV equation is constructed in terms of Jacobi elliptic functions by variational iteration method. The effect of the plasma parameters on the DIA solitary waves is also discussed in detail.
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.
Kang, H.S.; Ree, F.H.
1997-12-01
Recently, we developed the perturbative hypernetted-chain (PHNC) integral equation which can predict reliable thermodynamic and structural data for a system of particles interacting with either short range or long range (Coulomb) potential. The present work extends this earlier work to mixtures. This is done by employing a reference potential which is designed to satisfy a thermodynamic consistency on the isothermal compressibility as described in the next section. We test the present theory in Sec. III by applying it to plasma mixtures interacing with either an unscreened or a screened Coulomb potential. We made comparisons of results from the present theory with those from the best available theory, i.e., Rosenfeld`s density functional theory (DFT). The DFT was shown to give internal energy with three to five fignre accuracy compared to a wide range of Monte Carlo data. Meanwhile, small deviations of excess internal energy from the so-called ``liner mixing rule`` (LMR) are better predicted by a less sophiscated theory like the hypernetted- chain (HNC) equation. This rule relates thermodynamics of an unscreened mixture to those for individual components in a strongly coupled regime where the potential energy of a constituent particle is much larger than its kinetic energy. We also apply the present theory to a H{sub 2} + H mixture interacting with Morse potentials. For this sytem, comparison of thermodynamic properties and radial distribution functions from the present theory will be made with those from another successful theory of dense fluid, i.e., the HMSA equation of Zerah and Hansen.
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.
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).
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,…
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…
Analytic solution to leading order coupled DGLAP evolution equations: A new perturbative QCD tool
NASA Astrophysics Data System (ADS)
Block, Martin M.; Durand, Loyal; Ha, Phuoc; McKay, Douglas W.
2011-03-01
We have analytically solved the LO perturbative QCD singlet DGLAP equations [V. N. Gribov and L. N. Lipatov, Sov. J. Nucl. Phys. 15, 438 (1972)SJNCAS0038-5506][G. Altarelli and G. Parisi, Nucl. Phys. B126, 298 (1977)][Y. L. Dokshitzer, Sov. Phys. JETP 46, 641 (1977)SPHJAR0038-5646] using Laplace transform techniques. Newly developed, highly accurate, numerical inverse Laplace transform algorithms [M. M. Block, Eur. Phys. J. C 65, 1 (2010)EPCFFB1434-604410.1140/epjc/s10052-009-1195-8][M. M. Block, Eur. Phys. J. C 68, 683 (2010)EPCFFB1434-604410.1140/epjc/s10052-010-1374-7] allow us to write fully decoupled solutions for the singlet structure function Fs(x,Q2) and G(x,Q2) as Fs(x,Q2)=Fs(Fs0(x0),G0(x0)) and G(x,Q2)=G(Fs0(x0),G0(x0)), where the x0 are the Bjorken x values at Q02. Here Fs and G are known functions—found using LO DGLAP splitting functions—of the initial boundary conditions Fs0(x)≡Fs(x,Q02) and G0(x)≡G(x,Q02), i.e., the chosen starting functions at the virtuality Q02. For both G(x) and Fs(x), we are able to either devolve or evolve each separately and rapidly, with very high numerical accuracy—a computational fractional precision of O(10-9). Armed with this powerful new tool in the perturbative QCD arsenal, we compare our numerical results from the above equations with the published MSTW2008 and CTEQ6L LO gluon and singlet Fs distributions [A. D. Martin, W. J. Stirling, R. S. Thorne, and G. Watt, Eur. Phys. J. C 63, 189 (2009)EPCFFB1434-604410.1140/epjc/s10052-009-1072-5], starting from their initial values at Q02=1GeV2 and 1.69GeV2, respectively, using their choice of αs(Q2). This allows an important independent check on the accuracies of their evolution codes and, therefore, the computational accuracies of their published parton distributions. Our method completely decouples the two LO distributions, at the same time guaranteeing that both G and Fs satisfy the singlet coupled DGLAP equations. It also allows one to easily obtain the effects of
Qi, Xin; Xu, Yan-xia; Duan, Wen-shan; Yang, Lei; Department of Physics, Lanzhou University, Lanzhou 730000
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.
Ménard, Lucie; Perrier, Pascal; Aubin, Jero Me; Savariaux, Christophe; Thibeault, Mélanie
2008-08-01
The relations between production and perception in 4-year-old children were examined in a study of compensation strategies for a lip-tube perturbation. Acoustic and perceptual analyses of the rounded vowel [u] produced by twelve 4-year-old French speakers were conducted under two conditions: normal and with a 15-mm-diam tube inserted between the lips. Recordings of isolated vowels were made in the normal condition before any perturbation (N1), immediately upon insertion of the tube and for the next 19 trials in this perturbed condition, with (P2) or without articulatory instructions (P1), and in the normal condition after the perturbed trials (N2). The results of the acoustic analyses reveal speaker-dependent alterations of F1, F2, and/or F0 in the perturbed conditions and after the removal of the tube. For some subjects, the presence of the tube resulted in very little change; for others, an increase in F2 was observed in P1, which was generally reduced in some of the 20 repetitions, but not systematically and not continuously. The use of articulatory instructions provided in the P2 condition was detrimental to the achievement of a good acoustic target. Perceptual data are used to determine optimal combinations of F0, F1, and F2 (in bark) related to these patterns. The data are compared to a previous study conducted with adults [Savariaux et al., J. Acoust. Soc. Am. 106, 381-393 (1999)]. PMID:18681607
NASA Astrophysics Data System (ADS)
Coraggio, L.; Holt, J. W.; Itaco, N.; Machleidt, R.; Marcucci, L. E.; Sammarruca, F.
2014-04-01
We compute the energy per particle of infinite symmetric nuclear matter from chiral NLO3 (next-to-next-to-next-to-leading order) two-body potentials plus NLO2 three-body forces. The low-energy constants of the chiral three-nucleon force that cannot be constrained by two-body observables are fitted to reproduce the triton binding energy and the H3-He3 Gamow-Teller transition matrix element. In this way, the saturation properties of nuclear matter are reproduced in a parameter-free approach. The equation of state is computed up to third order in many-body perturbation theory, with special emphasis on the role of the third-order particle-hole diagram. The dependence of these results on the cutoff scale and regulator function is studied. We find that the inclusion of three-nucleon forces consistent with the applied two-nucleon interaction leads to a reduced dependence on the choice of the regulator only for lower values of the cutoff.
Equation of state of imbalanced cold matter from chiral perturbation theory
NASA Astrophysics Data System (ADS)
Carignano, Stefano; Mammarella, Andrea; Mannarelli, Massimo
2016-03-01
We study the thermodynamic properties of matter at vanishing temperature for nonextreme values of the isospin chemical potential and of the strange quark chemical potential. From the leading-order pressure obtained by maximizing the static chiral Lagrangian density, we derive a simple expression for the equation of state in the pion condensed phase and in the kaon condensed phase. We find an analytical expression for the maximum of the ratio between the energy density and the Stefan-Boltzmann energy density and for the isospin chemical potential at the peak, both in good agreement with lattice simulations of quantum chromodynamics. We speculate on the location of the crossover from the Bose-Einstein condensate state to the Bardeen-Cooper-Schrieffer state by a simple analysis of the thermodynamic properties of the system. For μI≳2 mπ, the leading-order chiral perturbation theory breaks down; for example, it underestimates the energy density of the system and leads to a wrong asymptotic behavior.
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.
Ghosh, Debashree
2014-03-01
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. PMID:24606347
Ménard, Lucie; Perrier, Pascal; Aubin, Jérôme
2016-05-01
The nature of the speech goal in children was investigated in a study of compensation strategies for a lip-tube perturbation. Acoustic, articulatory, and perceptual analyses of the vowels /y/ and /u/ produced by ten 4-year-old French speakers and ten adult French speakers were conducted under two conditions: normal and with a large tube inserted between the lips. Ultrasound and acoustic recordings of isolated vowels were made in the normal condition before any perturbation, for each of the trials in the perturbed condition, and in the normal condition after the perturbed trials. Data revealed that adult participants moved their tongues in the perturbed condition more than children did. The perturbation was generally at least partly compensated for during the perturbed trials in adults, but children did not show a typical learning effect. In particular, unsystematic improvements were observed during the sequence of perturbed trials, and after-effects were not clear in the articulatory domain. This suggests that children may establish associative links between multisensory phonemic representations and articulatory maneuvers, but those links may mainly rely on trial-to-trial, error-based feedback correction mechanisms rather than on the internal model of the speech production apparatus, as they are in adults. PMID:27250147
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. {copyright} {ital 1999} {ital The American Physical Society}
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. PMID:23464007
Density-velocity equations with bulk modulus for computational hydro-acoustics
NASA Astrophysics Data System (ADS)
Lin, Po-Hsien; Chen, Yung-Yu; John Yu, S.-T.
2014-02-01
This paper reports a new set of model equations for Computational Hydro Acoustics (CHA). The governing equations include the continuity and the momentum equations. The definition of bulk modulus is used to relate density with pressure. For 3D flow fields, there are four equations with density and velocity components as the unknowns. The inviscid equations are proved to be hyperbolic because an arbitrary linear combination of the three Jacobian matrices is diagonalizable and has a real spectrum. The left and right eigenvector matrices are explicitly derived. Moreover, an analytical form of the Riemann invariants are derived. The model equations are indeed suitable for modeling wave propagation in low-speed, nearly incompressible air and water flows. To demonstrate the capability of the new formulation, we use the CESE method to solve the 2D equations for aeolian tones generated by air flows passing a circular cylinder at Re = 89,000, 46,000, and 22,000. Numerical results compare well with previously published data. By simply changing the value of the bulk modulus, the same code is then used to calculate three cases of water flows passing a cylinder at Re = 89,000, 67,000, and 44,000.
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
A new aerodynamic integral equation based on an acoustic formula in the time domain
NASA Technical Reports Server (NTRS)
Farassat, F.
1984-01-01
An aerodynamic integral equation for bodies moving at transonic and supersonic speeds is presented. Based on a time-dependent acoustic formula for calculating the noise emanating from the outer portion of a propeller blade travelling at high speed (the Ffowcs Williams-Hawking formulation), the loading terms and a conventional thickness source terms are retained. Two surface and three line integrals are employed to solve an equation for the loading noise. The near-field term is regularized using the collapsing sphere approach to obtain semiconvergence on the blade surface. A singular integral equation is thereby derived for the unknown surface pressure, and is amenable to numerical solutions using Galerkin or collocation methods. The technique is useful for studying the nonuniform inflow to the propeller.
A single-scattering correction for the seismo-acoustic parabolic equation.
Collins, Michael D
2012-04-01
An efficient single-scattering correction that does not require iterations is derived and tested for the seismo-acoustic parabolic equation. The approach is applicable to problems involving gradual range dependence in a waveguide with fluid and solid layers, including the key case of a sloping fluid-solid interface. The single-scattering correction is asymptotically equivalent to a special case of a single-scattering correction for problems that only have solid layers [Küsel et al., J. Acoust. Soc. Am. 121, 808-813 (2007)]. The single-scattering correction has a simple interpretation (conservation of interface conditions in an average sense) that facilitated its generalization to problems involving fluid layers. Promising results are obtained for problems in which the ocean bottom interface has a small slope. PMID:22501044
Lenhart, S. |; Protopopescu, V.; Yong, J.
1997-12-31
The authors apply optimal control techniques to find approximate solutions to an inverse problem for the acoustic wave equation. The inverse problem (assumed here to have a solution) is to determine the boundary reflection coefficient from partial measurements of the acoustic signal. The sought reflection coefficient is treated as a control and the goal--quantified by an approximate functional--is to drive the model solution close to the experimental data by adjusting this coefficient. The problem is solved by finding the optimal control that minimizes the approximate functional. Then by driving the cost of the control to zero one proves that the corresponding sequence of optimal controls represents a converging sequence of estimates for the solution of the inverse problem. Compared to classical regularization methods (e.g., Tikhonov coupled with optimization schemes), their approach yields: (1) a systematic procedure to solve inverse problems of identification type and (ii) an explicit expression for the approximations of the solution.
Misra, Amar P.; Roy Chowdhury, K.; Roy Chowdhury, A.
2007-01-15
Using the standard reductive perturbation technique, a nonlinear Schroedinger equation (NLSE) with complex coefficients is derived in a dusty plasma consisting of positive ions, nonthermal electrons, and charged dust grains. The effect of ion kinematic viscosity is taken into consideration, which makes the coefficients of NLSE complex. By means of a matching approach, the appearance mechanism of static pulses through a saddle-node bifurcation in the complex nonlinear Schroedinger equation is studied analytically. The analytical results are in good agreement with the direct numerical simulation. The modulational instability analysis is carried out for the dust ion-acoustic envelope solitary waves. The important role of the real part of the complex group velocity in the propagation of the one-dimensional wave packets in homogeneous active medium is predicted.
Mushtaq, A.; Shah, H.A.
2005-07-15
The purpose of this work is to investigate the linear and nonlinear properties of the ion-acoustic waves (IAW), propagating obliquely to an external magnetic field in a weakly relativistic, rotating, and magnetized electron-positron-ion plasma. The Zakharov-Kuznetsov equation is derived by employing the reductive perturbation technique for this wave in the nonlinear regime. This equation admits the solitary wave solution. The amplitude and width of this solitary wave have been discussed with the effects of obliqueness, relativity, ion temperature, positron concentration, magnetic field, and rotation of the plasma and it is observed that for IAW these parameters affect the propagation properties of solitary waves and these plasmas behave differently from the simple electron-ion plasmas. Likewise, the current density and electric field of these waves are investigated for their dependence on the above-mentioned parameters.
NASA Astrophysics Data System (ADS)
Kumar, Manoj; Srivastava, Akanksha
2013-01-01
This paper presents a survey of innovative approaches of the most effective computational techniques for solving singular perturbed partial differential equations, which are useful because of their numerical and computer realizations. Many applied problems appearing in semiconductors theory, biochemistry, kinetics, theory of electrical chains, economics, solid mechanics, fluid dynamics, quantum mechanics, and many others can be modelled as singularly perturbed systems. Here, we summarize a wide range of research articles published by numerous researchers during the last ten years to get a better view of the present scenario in this area of research.
NASA Astrophysics Data System (ADS)
Valeau, Vincent; Sakout, Anas; Li, Feng; Picaut, Judicael
2002-11-01
Over the last years, some publications [e.g., Picaut, Simon, and Hardy, J. Acoust. Soc. Am. 106, 2638-2645 (1999)] showed that the acoustic energy density in closed or semiclosed spaces is the solution of a diffusion equation. This approach allows the nonuniform repartition of energy, and is especially relevant in room acoustics for complex spaces or long rooms. In this work, the 3-D diffusion equation is solved directly by using a finite element solver, for a set of long rooms and absorbing rooms. The stationary equation is first solved. A constant-power acoustic source is modelized by setting appropriate boundary conditions. The time-dependent problem is also solved to simulate the sound decay, with an impulse source defined in a subregion with relevant initial conditions. Results concerning sound attenuation and reverberation times match satisfactorily with other theoretical and numerical models. An application is also given for two coupled rooms.
NASA Astrophysics Data System (ADS)
Bowling, T. J.; Calais, E.; Dautermann, T.
2010-12-01
Rocket launches are known to produce infrasonic pressure waves that propagate into the ionosphere where coupling between electrons and neutral particles induces fluctuations in ionospheric electron density observable in GPS measurements. We have detected ionospheric perturbations following the launch of space shuttle Atlantis on 11 May 2009 using an array of continually operating GPS stations across the Southeastern coast of the United States and in the Caribbean. Detections are prominent to the south of the westward shuttle trajectory in the area of maximum coupling between the acoustic wave and Earth’s magnetic field, move at speeds consistent with the speed of sound, and show coherency between stations covering a large geographic range. We model the perturbation as an explosive source located at the point of closest approach between the shuttle path and each sub-ionospheric point. The neutral pressure wave is propagated using ray tracing, resultant changes in electron density are calculated at points of intersection between rays and satellite-to-reciever line-of-sight, and synthetic integrated electron content values are derived. Arrival times of the observed and synthesized waveforms match closely, with discrepancies related to errors in the apriori sound speed model used for ray tracing. Current work includes the estimation of source location and energy.
Investigation of acoustically coupled enclosures using a diffusion-equation model.
Xiang, Ning; Jing, Yun; Bockman, Alexander C
2009-09-01
Recent application of coupled-room systems in performing arts spaces has prompted active research on sound fields in these complex geometries. This paper applies a diffusion-equation model to the study of acoustics in coupled-rooms. Acoustical measurements are conducted on a scale-model of two coupled-rooms. Using the diffusion model and the experimental results the current work conducts in-depth investigations on sound pressure level distributions, providing further evidence supporting the valid application of the diffusion-equation model. Analysis of the results within the Bayesian framework allows for quantification of the double-slope characteristics of sound-energy decays obtained from the diffusion-equation numerical modeling and the experimental measurements. In particular, Bayesian decay analysis confirms sound-energy flux modeling predictions that time-dependent sound-energy flows in coupled-room systems experience feedback in the form of energy flow-direction change across the aperture connecting the two rooms in cases where the dependent room is more reverberant than the source room. PMID:19739732
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)
Ablowitz, Mark J.; Curtis, Christopher W.
2011-05-01
The Benney-Luke equation, which arises as a long wave asymptotic approximation of water waves, contains the Kadomtsev-Petviashvilli (KP) equation as a leading-order maximal balanced approximation. The question analyzed is how the Benney-Luke equation modifies the so-called web solutions of the KP equation. It is found that the Benney-Luke equation introduces dispersive radiation which breaks each of the symmetric soliton-like humps well away from the interaction region of the KP web solution into a tail of multi-peaked oscillating profiles behind the main solitary hump. Computation indicates that the wave structure is modified near the center of the interaction region. Both analytical and numerical techniques are employed for working with non-periodic, non-decaying solutions on unbounded domains.
NASA Astrophysics Data System (ADS)
Feng, Xiaojing
2016-06-01
This paper focuses on the following Schrödinger-Poisson equations involving a fractional nonlocal operator -Δ u+u+φ u=f(x,u),&in {R}^3,(-Δ)^{α/2}φ=u^2,lim_{|x|to ∞}φ(x)=0,&in {R}^3, where {α in (1,2]}. Under certain assumptions, we obtain the existence of nontrivial solution of the above problem without compactness by using the methods of perturbation and the mountain pass theorem.
Modelling baryon acoustic oscillations with perturbation theory and stochastic halo biasing
NASA Astrophysics Data System (ADS)
Kitaura, Francisco-Shu; Yepes, Gustavo; Prada, Francisco
2014-03-01
In this work we investigate the generation of mock halo catalogues based on perturbation theory and non-linear stochastic biasing with the novel PATCHY code. In particular, we use Augmented Lagrangian Perturbation Theory (ALPT) to generate a dark matter density field on a mesh starting from Gaussian fluctuations and to compute the peculiar velocity field. ALPT is based on a combination of second order LPT (2LPT) on large scales and the spherical collapse model on smaller scales. We account for the systematic deviation of perturbative approaches from N-body simulations together with halo biasing adopting an exponential bias model. We then account for stochastic biasing by defining three regimes: a low-, an intermediate- and a high-density regime, using a Poisson distribution in the intermediate regime and the negative binomial distribution - including an additional parameter - to model over-dispersion in the high-density regime. Since we focus in this study on massive haloes, we suppress the generation of haloes in the low-density regime. The various non-linear and stochastic biasing parameters, and density thresholds, are calibrated with the large BigMultiDark N-body simulation to match the power spectrum of the corresponding halo population. Our model effectively includes only five parameters, as they are additionally constrained by the halo number density. Our mock catalogues show power spectra, in both real- and redshift-space, which are compatible with N-body simulations within about 2 per cent up to k ˜ 1 h Mpc-1 at z = 0.577 for a sample of haloes with the typical Baryon Oscillation Spectroscopic Survey (BOSS) CMASS (constant stellar mass galaxy sample) galaxy number density. The corresponding correlation functions are compatible down to a few Mpc. We also find that neglecting over-dispersion in high-density regions produces power spectra with deviations of 10 per cent at k ˜ 0.4 h Mpc-1. These results indicate the need to account for an accurate
NASA Astrophysics Data System (ADS)
Sabetkar, Akbar; Dorranian, Davoud
2015-08-01
In this paper, our attention is first concentrated on obliquely propagating properties of low-frequency (ω ≪ ωcd) "fast" and "slow" dust acoustic waves, in the linear regime, in dusty electronegative plasmas with Maxwellian electrons, kappa distributed positive ions, negative ions (following the combination of kappa-Schamel distribution), and negatively charged dust particles. So, an explicit expression for dispersion relation is derived by linearizing a set of dust-fluid equations. The results show that wave frequency ω in long and short-wavelengths limit is conspicuously affected by physical parameters, namely, positive to negative temperature ion ratio (βp), trapping parameter of negative ions (μ), magnitude of the magnetic field B0 (via ωcd), superthermal index ( κn,κp ), and positive ion to dust density ratio (δp). The signature of the penultimate parameter (i.e., κn) on wave frequency reveals that the frequency gap between the modes reduces (escalates) for k
Equation-free Modeling of Ion Acoustic Wave with Particle Trapping
NASA Astrophysics Data System (ADS)
Stantchev, George
2005-10-01
Recently, Shay et al.[1] have successfully implemented equation-free projective integraion methods to simulate the propagation and steepening of a 1D ion acoustic wave. For the forward extrapolation step they have been using only a small number of lower moments of the probability density function (PDF) based on the assumption that the distribution would remain Maxwellian at all times. This however is no longer valid in many interesting situations, in particular for the case of particle trapping. To solve this problem we propose a generalization of Shay's algorithm to allow for tracking of an arbitrary PDF. We estimate the PDF at each micro-time step using statistical wavelet analysis. The resulting vectors of wavelet coefficents are used for forward extrapolation in time to obtain a multi-scale representation of the projected PDF after a coarse time step. An optimal wavelet basis is selected through adaptive refinement at the beginning of each microscopic simulation sequence. We discuss the application of this technique to the 1D acoustic wave problem with particle trapping. [1] M. Shay, J. Drake, W. Dorland, Multiscale modeling of plasmas via equation-free projective integration, in preparation
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
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.
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.
A new perturbed-chain equation of state for square-well chains in fluid and solid phases.
Alavi, Farzad; Feyzi, Farzaneh
2013-08-21
Considering the hard-chain system as reference, a perturbed-chain equation of state (EOS) is developed. The second-order thermodynamic perturbation theory EOS is applied to the reference system. Monte Carlo simulation data for average intra-molecular and inter-molecular segment-segment radial distribution function of hard-chain systems with a chain length of 3-10 in the range of packing fraction between 0.1 and 0.72, covering both fluid and solid phases, are reported. A disordered solid phase structure is considered in this work. These customized data are used to develop the perturbation term of square-well (SW) attractions. The performance of perturbed-chain EOS is tested against computer simulation data from the literature for compressibility factor and phase equilibrium in the systems of SW chains. Results within good accuracy are obtained for all the test cases. Global vapor-liquid-solid equilibrium diagrams for SW chain systems predicted by the new EOS are reported. PMID:23968069
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).
NASA Astrophysics Data System (ADS)
Davletshin, A. I.; Khalitova, T. F.
2016-01-01
A mathematical model of spatial hydrodynamic interaction of gas bubbles in liquid in an acoustic field taking into account small deformations of their surfaces is proposed. It is a system of ordinary differential equations of the second order in radii of the bubbles, the position vectors of their centers and the amplitudes of deviation of their shape from the spherical one in the form of spherical harmonics. The equations derived are of the first order of accuracy in A / R and of the fourth order in R / D, where R is the characteristic radius of the bubbles, A is the amplitude of characteristic deviation of their surface from the spherical one in the form of spherical harmonics, D is the characteristic distance between bubbles. The derivation of the equations is carried out by the method of spherical functions with the use of the Bernoulli integral, the kinematic and dynamic boundary conditions on the surface of the bubbles. The effects of viscosity and compressibility of the liquid are considered approximately, the gas in the bubbles is assumed homobaric.
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. PMID:12765364
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)
Zhang, Zai-yun; Li, Yun-xiang; Liu, Zhen-hai; Miao, Xiu-jin
2011-08-01
In this paper, the modified trigonometric function series method is employed to solve the perturbed nonlinear Schrödinger's equation (NLSE) with Kerr law nonlinearity. Exact traveling wave solutions are obtained.
NASA Astrophysics Data System (ADS)
Wan, Ling; Wang, Tao; Zou, Qingyang
2016-04-01
We investigate the large-time behavior of solutions to an outflow problem of the compressible Navier-Stokes equations for viscous and heat-conducting ideal polytropic gases in the half line. The non-degenerate stationary solution is shown to be asymptotically stable under large initial perturbation with no restriction on the adiabatic exponent, provided that the boundary strength is sufficiently small. The proofs are based on the nonlinear energy estimates and the crucial step is to obtain positive lower and upper bounds of the density and the temperature uniformly in time and space.
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.
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.
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)
Sadovskii, V. M.
2014-11-01
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.
Model-independent dark energy equation of state from unanchored baryon acoustic oscillations
NASA Astrophysics Data System (ADS)
Evslin, Jarah
2016-09-01
Ratios of line of sight baryon acoustic oscillation (BAO) peaks at two redshifts only depend upon the average dark energy equation of states between those redshifts, as the dependence on anchors such as the BAO scale or the Hubble constant is canceled in a ratio. As a result, BAO ratios provide a probe of dark energy which is independent of both the cosmic distance ladder and the early evolution of universe. In this note, we use ratios to demonstrate that the known tension between the Lyman alpha forest BAO measurement and other probes arises entirely from recent (0.57 < z < 2.34) cosmological expansion. Using ratios of the line of sight Lyman alpha forest and BOSS CMASS BAO scales, we show that there is already more than 3 σ tension with the standard ΛCDM cosmological model which implies that either (i) The BOSS Lyman alpha forest measurement of the Hubble parameter was too low as a result of a statistical fluctuation or systematic error or else (ii) the dark energy equation of state falls steeply at high redshift.
NASA Astrophysics Data System (ADS)
The acoustics research activities of the DLR fluid-mechanics department (Forschungsbereich Stroemungsmechanik) during 1988 are surveyed and illustrated with extensive diagrams, drawings, graphs, and photographs. Particular attention is given to studies of helicopter rotor noise (high-speed impulsive noise, blade/vortex interaction noise, and main/tail-rotor interaction noise), propeller noise (temperature, angle-of-attack, and nonuniform-flow effects), noise certification, and industrial acoustics (road-vehicle flow noise and airport noise-control installations).
NASA Astrophysics Data System (ADS)
McKinney, Brett; Watson, Deborah
2000-06-01
We apply low-order dimensional perturbation theory to both the Gross-Pitaevskii equation and to the full many-body Hamiltonian. The perturbation parameter is 1/D, where D is the condensate dimensionality. Unlike the Thomas-Fermi approximation, the zeroth-order DPT solution (Darrow ∞) of the GPE retains a centrifugal term of the kinetic energy. This results in an analytic approximation that is more accurate than TF except for extremely large N where the two approximations agree. The low-order DPT approximation of the full many-body Schrödinger equation for N trapped condensate atoms is an analytic semiclassical approximation that becomes more accurate as the condensate enters a denser regime; precisely the regime where the delta-function potential (pseudopotential) and the GPE should break down. We compare the low-order many-body results for the ground state using the delta-function approximation, which breaks down for high density, with a more realistic interaction potential that reproduces the correct s-wave scattering length.
NASA Astrophysics Data System (ADS)
Wellenhofer, Corbinian; Holt, Jeremy W.; Kaiser, Norbert
2016-05-01
The isospin-asymmetry dependence of the nuclear-matter equation of state obtained from microscopic chiral two- and three-body interactions in second-order many-body perturbation theory is examined in detail. The quadratic, quartic, and sextic coefficients in the Maclaurin expansion of the free energy per particle of infinite homogeneous nuclear matter with respect to the isospin asymmetry are extracted numerically using finite differences, and the resulting polynomial isospin-asymmetry parametrizations are compared to the full isospin-asymmetry dependence of the free energy. It is found that in the low-temperature and high-density regime where the radius of convergence of the expansion is generically zero, the inclusion of higher-order terms beyond the leading quadratic approximation leads overall to a significantly poorer description of the isospin-asymmetry dependence. In contrast, at high temperatures and densities well below nuclear saturation density, the interaction contributions to the higher-order coefficients are negligible and the deviations from the quadratic approximation are predominantly from the noninteracting term in the many-body perturbation series. Furthermore, we extract the leading logarithmic term in the isospin-asymmetry expansion of the equation of state at zero temperature from the analysis of linear combinations of finite differences. It is shown that the logarithmic term leads to a considerably improved description of the isospin-asymmetry dependence at zero temperature.
Generating scale-invariant perturbations from rapidly-evolving equation of state
NASA Astrophysics Data System (ADS)
Khoury, Justin; Steinhardt, Paul J.
2011-06-01
Recently, we introduced an ekpyrotic model based on a single, canonical scalar field that generates nearly scale-invariant curvature fluctuations through a purely “adiabatic mechanism” in which the background evolution is a dynamical attractor. Despite the starkly different physical mechanism for generating fluctuations, the two-point function is identical to inflation. In this paper, we further explore this concept, focusing in particular on issues of non-Gaussianity and quantum corrections. We find that the degeneracy with inflation is broken at three-point level: for the simplest case of an exponential potential, the three-point amplitude is strongly scale dependent, resulting in a breakdown of perturbation theory on small scales. However, we show that the perturbative breakdown can be circumvented—and all issues raised in Linde et al. (arXiv:0912.0944) can be addressed—by altering the potential such that power is suppressed on small scales. The resulting range of nearly scale-invariant, Gaussian modes can be as much as 12 e-folds, enough to span the scales probed by microwave background and large-scale structure observations. On smaller scales, the spectrum is not scale invariant but is observationally acceptable.
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.
Quasi-periodic solutions for d-dimensional beam equation with derivative nonlinear perturbation
Mi, Lufang; Cong, Hongzi
2015-07-15
In this paper, we consider the d-dimensional beam equation with convolution potential under periodic boundary conditions. We will apply the Kolmogorov-Arnold-Moser theorem in Eliasson and Kuksin [Ann. Math. 172, 371-435 (2010)] into this system and obtain that for sufficiently small ε, there is a large subset S′ of S such that for all s ∈ S′, the solution u of the unperturbed system persists as a time-quasi-periodic solution which has all Lyapunov exponents equal to zero and whose linearized equation is reducible to constant coefficients.
NASA Astrophysics Data System (ADS)
Sokolov, I. M.
2006-06-01
The work by Barbi, Bologna, and Grigolini [Phys. Rev. Lett. 95, 220601 (2005)] discusses a response to alternating external field of a non-Markovian two-state system, where the waiting time between the two attempted changes of state follows a power law. It introduced a new instrument for description of such situations based on a stochastic master equation with reset. In the present Brief Report we provide an alternative description of the situation within the framework of a generalized master equation. The results of our analytical approach are corroborated by direct numerical simulations of the system.
NASA Astrophysics Data System (ADS)
Sabetkar, Akbar; Dorranian, Davoud
2015-03-01
In this paper, a theoretical investigation is presented to study the existence and characteristics of the propagation of dust acoustic (DA) waves in an obliquely propagating magnetized dusty plasma with two populations of ions having two distinct temperatures, electrons that are modeled by three-dimensional nonextensive and κ -distribution functions, respectively, and negative dust particles. Normal mode analysis (reductive perturbation method) is used to derive lower- and higher-order nonlinear equations governing the evolution of small but finite amplitude DA waves, namely the Zakharov-Kuznetsov (ZK) and the modified Zakharov-Kuznetsov (mZK) equations. The basic features (e.g., amplitude, width, phase speed, polarity) of both DA ZK and mZK solitons have been thoroughly examined by the numerical analysis of their equations. It is observed that the characteristics and properties of the DA solitary waves (DASWs) are significantly modified by the superthermality of electrons, nonextensivity of ions, cold-to-hot ion temperature ratio, relative number densities of two species of ions, and the strength of the magnetic field and obliqueness of the system. Furthermore, it has been found that the DA ZK solitons exhibit only negative polarity of solitary waves when the superthermality of electrons, nonextensivity of ions, and temperature ratio of ions are smaller or greater than their critical values. The present study may add to the understanding of the nonlinear propagation features of DA wave structures in high-energy astrophysical plasma systems.
NASA Astrophysics Data System (ADS)
Wu, Haijun; Jiang, Weikang; Zhang, Haibin
2016-07-01
In the procedure of the near-field acoustic holography (NAH) based on the fundamental solutions for Helmholtz equation (FS), the number of FS and the measurement setup to obtain their coefficients are two crucial issues to the successful reconstruction. The current work is motivated to develop a framework for the NAH which supplies a guideline to the determination of the number of FS as well as an optimized measurement setup. A mapping relationship between modes on surfaces of boundary and hologram is analytically derived by adopting the modes as FS in spherical coordinates. Thus, reconstruction is converted to obtain the coefficients of participant modes on holograms. In addition, an integral identity is firstly to be derived for the modes on convex surfaces, which is useful in determining the inefficient or evanescent modes for acoustic radiation in free space. To determine the number of FS adopted in the mapping relationship based NAH (MRS-based NAH), two approaches are proposed to supply reasonable estimations with criteria of point-wise pressure and energy, respectively. A technique to approximate a specific degree of mode on patches by a set of locally orthogonal patterns is explored for three widely used holograms, such as planar, cylindrical and spherical holograms, which results in an automatic determinations of the number and position of experimental setup for a given tolerance. Numerical examples are set up to validate the theory and techniques in the MRS-based NAH. Reconstructions of a cubic model demonstrate the potential of the proposed method for regular models even with corners and shapers. Worse results for the elongated cylinder with two spherical caps reveal the deficiency of the MRS-based NAH for irregular models which is largely due to the adopted modes are FS in spherical coordinates. The NAH framework pursued in the current work provides a new insight to the reconstruction procedure based on the FS in spherical coordinates.
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.
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.
Combustion-acoustic stability analysis for premixed gas turbine combustors
NASA Technical Reports Server (NTRS)
Darling, Douglas; Radhakrishnan, Krishnan; Oyediran, Ayo; Cowan, Lizabeth
1995-01-01
Lean, prevaporized, premixed combustors are susceptible to combustion-acoustic instabilities. A model was developed to predict eigenvalues of axial modes for combustion-acoustic interactions in a premixed combustor. This work extends previous work by including variable area and detailed chemical kinetics mechanisms, using the code LSENS. Thus the acoustic equations could be integrated through the flame zone. Linear perturbations were made of the continuity, momentum, energy, chemical species, and state equations. The qualitative accuracy of our approach was checked by examining its predictions for various unsteady heat release rate models. Perturbations in fuel flow rate are currently being added to the model.
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.
Causality, Stokes' wave equation, and acoustic pulse propagation in a viscous fluid.
Buckingham, Michael J
2005-08-01
Stokes' acoustic wave equation is solved for the impulse response of an isotropic viscous fluid. Two exact integral forms of solution are derived, both of which are causal, predicting a zero response before the source is activated at time t = 0. Moreover, both integral solutions satisfy a stronger causality condition: the pressure pulse is maximally flat, with all its time derivatives identically zero at t = 0, signifying that there is no instantaneous response to the source anywhere in the fluid. A closed-form approximation for each of the two integrals is derived, with distinctly different properties in the two cases, even though the original integrals are equivalent in that they predict identical pulse shapes. One of these approximations, reminiscent of transient solutions that have appeared previously in the literature, is noncausal due to the incorrect representation of high-frequency components in the propagating pulse. In the second approximation, all frequency components are treated correctly, leading to an impulse response that satisfies the strong causality condition, also satisfied by the original integrals, whereby the predicted pressure pulse is zero when t < 0 and maximally flat everywhere in the fluid immediately after t = 0. PMID:16196738
Analysis of measured broadband acoustic propagation using a parabolic equation approach
NASA Astrophysics Data System (ADS)
Gray, Mason; Knobles, D. P.; Koch, Robert
2003-10-01
A broadband parabolic equation (PE) approach is employed to simulate data taken from two Shallow Water Acoustic Measurement Instrument (SWAMI) bottom mounted horizontal line array (HLA) experiments in shallow water environments off the east coast of the U.S. and in the Gulf of Mexico. In both experiments the HLA was deployed along an isobath. Light bulbs were imploded at known depths and ranges in both the range-independent (array end fire) and range-dependent (array broadside) directions. For the east coast experimental data, the PE model is used to infer a seabed geoacoustic description in both the range-dependent and range-independent directions. Also, comparisons of modeled time series were made for the range-independent case with a broadband normal mode model to validate the PE calculations. In the Gulf of Mexico experiment, the sediment geoacoustic profile is well known from previous inversions and geophysical measurements. This known seabed description was used to simulate the range-dependent data. A broadband energy-conserving coupled mode approach is also employed to model the range-dependent propagation. This allows the physical mechanisms associated with range-dependent propagation to be examined in a quantitative manner for this shallow water environment. [Work supported by ONR.
NASA Astrophysics Data System (ADS)
Shishkin, G. I.
2012-06-01
The Dirichlet problem for a singularly perturbed ordinary differential convection-diffusion equation with a small parameter ɛ (ɛ ∈ (0, 1]) multiplying the higher order derivative is considered. For the problem, a difference scheme on locally uniform meshes is constructed that converges in the maximum norm conditionally, i.e., depending on the relation between the parameter ɛ and the value N defining the number of nodes in the mesh used; in particular, the scheme converges almost ɛ-uniformly (i.e., its accuracy depends weakly on ɛ). The stability of the scheme with respect to perturbations in the data and its conditioning are analyzed. The scheme is constructed using classical monotone approximations of the boundary value problem on a priori adapted grids, which are uniform on subdomains where the solution is improved. The boundaries of these subdomains are determined by a majorant of the singular component of the discrete solution. On locally uniform meshes, the difference scheme converges at a rate of O(min[ɛ-1 N - K ln N, 1] + N -1ln N), where K is a prescribed number of iterations for refining the discrete solution. The scheme converges almost ɛ-uniformly at a rate of O( N -1ln N) if N -1 ≤ ɛν, where ν (the defect of ɛ-uniform convergence) determines the required number K of iterations ( K = K(ν) ˜ ν-1) and can be chosen arbitrarily small from the half-open interval (0, 1]. The condition number of the difference scheme satisfies the bound κ P = O(ɛ-1/ K ln1/ K ɛ-1δ-( K + 1)/ K ), where δ is the accuracy of the solution of the scheme in the maximum norm in the absence of perturbations. For sufficiently large K, the scheme is almost ɛ-uniformly strongly stable.
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.
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.
NASA Astrophysics Data System (ADS)
Broerse, Taco; Riva, Riccardo; Vermeersen, Bert
2014-11-01
During megathrust earthquakes, great ruptures are accompanied by large scale mass redistribution inside the solid Earth and by ocean mass redistribution due to bathymetry changes. These large scale mass displacements can be detected using the monthly gravity maps of the GRACE satellite mission. In recent years it has become increasingly common to use the long wavelength changes in the Earth's gravity field observed by GRACE to infer seismic source properties for large megathrust earthquakes. An important advantage of space gravimetry is that it is independent from the availability of land for its measurements. This is relevant for observation of megathrust earthquakes, which occur mostly offshore, such as the M_{text{w}} ˜ 9 2004 Sumatra-Andaman, 2010 Maule (Chile) and 2011 Tohoku-Oki (Japan) events. In Broerse et al., we examined the effect of the presence of an ocean above the rupture on long wavelength gravity changes and showed it to be of the first order. Here we revisit the implementation of an ocean layer through the sea level equation and compare the results with approximated methods that have been used in the literature. One of the simplifications usually lies in the assumption of a globally uniform ocean layer. We show that especially in the case of the 2010 Maule earthquake, due to the closeness of the South American continent, the uniform ocean assumption is not valid and causes errors up to 57 per cent for modelled peak geoid height changes (expressed at a spherical harmonic truncation degree of 40). In addition, we show that when a large amount of slip occurs close to the trench, horizontal motions of the ocean floor play a mayor role in the ocean contribution to gravity changes. Using a slip model of the 2011 Tohoku-Oki earthquake that places the majority of slip close to the surface, the peak value in geoid height change increases by 50 per cent due to horizontal ocean floor motion. Furthermore, we test the influence of the maximum spherical
NASA Astrophysics Data System (ADS)
Broerse, T.; Riva, R.; Vermeersen, B. L. A.
2014-12-01
During megathrust earthquakes, great ruptures are accompanied by large scale mass redistribution inside the solid Earth and by ocean mass redistribution due to bathymetry changes. These large scale mass displacements can be detected using the monthly gravity maps of the GRACE satellite mission. In recent years it has become increasingly common to use the long wavelength changes in the Earth's gravity field observed by GRACE to infer seismic source properties for large megathrust earthquakes, such as the Mw ~ 9 2004 Sumatra-Andaman, 2010 Maule (Chile) and 2011 Tohoku-Oki (Japan) events. In Broerse et al. (2011) we examined the effect of the presence of an ocean above the rupture on long wavelength gravity changes and showed it to be of the first order. Here we revisit the implementation of an ocean layer through the sea level equation and compare the results with approximated methods that have been used in the literature. One of the simplifications usually lies in the assumption of a globally uniform ocean layer. We show that especially in the case of the 2010 Maule earthquake, due to the closeness of the South American continent, the uniform ocean assumption causes errors up to 57% for modeled peak geoid height changes (expressed at a spherical harmonic truncation degree of 40). In addition, we show that when a large amount of slip occurs close to the trench, horizontal motions of the ocean floor play a mayor role in the ocean contribution to gravity changes. Using a slip model of the 2011 Tohoku-Oki earthquake that places the majority of slip close to the surface, the peak value in geoid height change increases by 50% due to horizontal ocean floor motion. When GRACE observations are used to determine earthquake parameters such as seismic moment or source depth, the uniform ocean layer method introduces large biases, depending on the location of the rupture with respect to the continent. The same holds for interpreting shallow slip when horizontal motions are not
Fox, D.J.
1983-10-01
Analytic derivatives of the potential energy for Self-Consistent-Field (SCF) wave functions have been developed in recent years and found to be useful tools. The first derivative for configuration interaction (CI) wave functions is also available. This work details the extension of analytic methods to energy second derivatives for CI wave functions. The principal extension required for second derivatives is evaluation of the first order change in the CI wave function with respect to a nuclear perturbation. The shape driven graphical unitary group approach (SDGUGA) direct CI program was adapted to evaluate this term via the coupled-perturbed CI equations. Several iterative schemes are compared for use in solving these equations. The pilot program makes no use of molecular symmetry but the timing results show that utilization of molecular symmetry is desirable. The principles for defining and solving a set of symmetry adapted equations are discussed. Evaluation of the second derivative also requires the solution of the second order coupled-perturbed Hartree-Fock equations to obtain the correction to the molecular orbitals due to the nuclear perturbation. This process takes a consistently higher percentage of the computation time than for the first order equations alone and a strategy for its reduction is discussed.
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. PMID:19206863
NASA Astrophysics Data System (ADS)
Kutzelnigg, Werner; Mukherjee, Debashis
2004-04-01
The k-particle irreducible Brillouin conditions IBCk and the k-particle irreducible contracted Schrödinger equations ICSEk for a closed-shell state are analyzed in terms of a Møller-Plesset-type perturbation expansion. The zeroth order is Hartree-Fock. From the IBC2(1), i.e., from the two-particle IBC to first order in the perturbation parameter μ, one gets the leading correction λ2(1) to the two-particle cumulant λ2 correctly. However, in order to construct the second-order energy E2, one also needs the second-order diagonal correction γD(2) to the one-particle density matrix γ. This can be obtained: (i) from the idempotency of the n-particle density matrix, i.e., essentially from the requirement of n-representability; (ii) from the ICSE1(2); or (iii) by means of perturbation theory via a unitary transformation in Fock space. Method (ii) is very unsatisfactory, because one must first solve the ICSE3(2) to get λ3(2), which is needed in the ICSE2(2) to get λ2(2), which, in turn, is needed in the ICSE1(2) to get γ(2). Generally the (k+1)-particle approximation is needed to obtain Ek correctly. One gains something, if one replaces the standard hierarchy, in which one solves the ICSEk, ignoring λk+1 and λk+2, by a renormalized hierarchy, in which only λk+2 is ignored, and λk+1 is expressed in terms of the λp of lower particle rank via the partial trace relation for λk+2. Then the k-particle approximation is needed to obtain Ek correctly. This is still poorer than coupled-cluster theory, where the k-particle approximation yields Ek+1. We also study the possibility to use some simple necessary n-representability conditions, based on the non-negativity of γ(2) and two related matrices, in order to get estimates for γD(2) in terms of λ2(1). In general these estimates are rather weak, but they can become close to the best possible bounds in special situations characterized by a very sparse structure of λ2 in terms of a localized representation. The
NASA Astrophysics Data System (ADS)
Churazov, E.; Arevalo, P.; Forman, W.; Jones, C.; Schekochihin, A.; Vikhlinin, A.; Zhuravleva, I.
2016-08-01
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 intra cluster 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" AGN 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 datasets 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.
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.
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…
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)
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)
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.
NASA Astrophysics Data System (ADS)
Song, Peng; Liu, Zhaolun; Zhang, Xiaobo; Tan, Jun; Xia, Dongming; Li, Jing; Zhu, Bo
2015-12-01
This paper introduces the fourth-order absorbing boundary condition (ABC) into staggered-grid finite difference forward modeling of the first-order stress-velocity acoustic equation, and develops a new method to optimize coefficients of the fourth-order ABC to further improve its overall absorbing effect. Theoretical analysis and the results of numerical tests demonstrate that the fourth-order ABC with optimized coefficients has much higher absorbing efficiency than both the conventional second-order and fourth-order ABCs without optimized coefficients, for waves with large incident angles. Compared with the perfectly matched layer (PML) with 40 layers, the fourth-order ABC not only has a much better absorbing effect, but also uses far less computer memory for calculation. We present the fourth-order ABC with optimized coefficients as an ideal artificial boundary for the simulation of the acoustic equation based on extensive and complex structure models. Supported by the Fundamental Research Funds for the Central Universities (201513005).
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. PMID:27250161
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)
Aoki, Ken-Ichi; Sato, Daisuke
The method of non-perturbative renormalization group (NPRG) is applied to the analysis of dynamical chiral symmetry breaking (DχSB) in QCD. We show that the DχSB solution of the NPRG flow equation can be obtained without the bosonization. The solution, having the singular point, can be authorized as the weak solution of partial differential equation, and can be easily evaluated using the method of the characteristic curve. Also we show that our non-ladder extended approximation improves almost perfectly the gauge dependence of the chiral condensates.
Dust acoustic dressed soliton with dust charge fluctuations
Asgari, H.; Muniandy, S. V.; Wong, C. S.
2010-06-15
Modeling of dust acoustic solitons observed in dusty plasma experiment [Bandyopadhyay et al., Phys. Rev. Lett. 101, 065006 (2008)] using the Korteweg-de Vries (KdV) equation showed significant discrepancies in the regime of large amplitudes (or high soliton speed). In this paper, higher order perturbation corrections to the standard KdV soliton are proposed and the resulting dressed soliton is shown to describe the experimental data better, in particular, at high soliton speed. The effects of dust charge fluctuations on the dust acoustic dressed soliton in a dusty plasma system are also investigated. The KdV equation and a linear inhomogeneous equation, governing the evolution of first and second order potentials, respectively, are derived for the system by using reductive perturbation technique. Renormalization procedure is used to obtain nonsecular solutions of these coupled equations. The characteristics of dust acoustic dressed solitons with and without dust charge fluctuations are discussed.
Cylindrical and spherical ion acoustic waves in a plasma with nonthermal electrons and warm ions
Sahu, Biswajit; Roychoudhury, Rajkumar
2005-05-15
Using the reductive perturbation technique, nonlinear cylindrical and spherical Korteweg-de Vries (KdV) and modified KdV equations are derived for ion acoustic waves in an unmagnetized plasma consisting of warm adiabatic ions and nonthermal electrons. The effects of nonthermally distributed electrons on cylindrical and spherical ion acoustic waves are investigated. It is found that the nonthermality has a very significant effect on the nature of ion acoustic waves.
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.
NASA Astrophysics Data System (ADS)
Langenberg, Karl J.
2003-04-01
It is well-known that solutions of electromagnetic scattering integral equations of the first or second kind (EFIE and MFIE) for perfectly electric or perfectly magnetic conducting scatterers are nonunique for those frequencies which correspond to interior Maxwell resonances of the scatterer; hence, the null spaces of the respective interior problem operators are under concern. In principle, all mathematical facts and proofs regarding this problem and cited in this paper are available from the book by [1983], yet, these authors mainly concentrate on single and double layer potentials for the scalar acoustic (Dirichlet and Neumann) as well as the magnetic dipole layer ansatz for the perfectly electric conducting (Maxwell) problem and treat the Huygens-type representation, which is more common in the electrical engineering community, not in the same detail. This might be the reason that part of the electrical engineering literature suffers from some confusion regarding the proper null spaces and their physical relevance, in particular, if the electromagnetic problem is considered in 2-D, where it reduces to scalar TM/TE-problems. The present contribution comments on these issues emphasizing that the null spaces of 2-D electromagnetics are the nonphysical null spaces originating from the Huygens-type representation of scalar acoustics.
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. PMID:26274257
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. PMID:23556690
NASA Technical Reports Server (NTRS)
Bayliss, A.; Goldstein, C. I.; Turkel, E.
1984-01-01
The Helmholtz Equation (-delta-K(2)n(2))u=0 with a variable index of refraction, n, and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems. A numerical algorithm was developed and a computer code implemented that can effectively solve this equation in the intermediate frequency range. The equation is discretized using the finite element method, thus allowing for the modeling of complicated geometrices (including interfaces) and complicated boundary conditions. A global radiation boundary condition is imposed at the far field boundary that is exact for an arbitrary number of propagating modes. The resulting large, non-selfadjoint system of linear equations with indefinite symmetric part is solved using the preconditioned conjugate gradient method applied to the normal equations. A new preconditioner is developed based on the multigrid method. This preconditioner is vectorizable and is extremely effective over a wide range of frequencies provided the number of grid levels is reduced for large frequencies. A heuristic argument is given that indicates the superior convergence properties of this preconditioner.
NASA Astrophysics Data System (ADS)
Saha, Asit; Pal, Nikhil; Saha, Tapash; Ghorui, M. K.; Chatterjee, Prasanta
2016-06-01
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.
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)
Warner, James E.; Diaz, Manuel I.; Aquino, Wilkins; Bonnet, Marc
2014-09-01
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.
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.
2016-07-01
The 2D 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 (2 M)th-order accuracy along eight specific propagation directions for time-space domain dispersion-relation-based FD method, if the conventional (2 M)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 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 2D 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 2nd-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 (2 M)th-order accuracy in space and (2 N)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 computational
Dressed ion-acoustic solitons in magnetized dusty plasmas
El-Labany, S. K.; El-Shamy, E. F.; El-Warraki, S. A.
2009-01-15
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)
Chapman, Alexander Lloyd
Recently, a sound source identification technique called CRAFT was developed as an advance in the state of the art in inverse noise problems. It addressed some limitations associated with nearfield acoustic holography and a few of the issues with inverse boundary element method. This work centers on two critical issues associated with the CRAFT algorithm. Although CRAFT employs the complete general solution associated with the Helmholtz equation, the approach taken to derive those equations results in computational inefficiency when implemented numerically. In this work, a mathematical approach to derivation of the basis equations results in a doubling in efficiency. This formulation of CRAFT is termed general Helmholtz equation, least-squares method (GEN-HELS). Additionally, the numerous singular points present in the gradient of the basis functions are shown here to resolve to finite limits. As a realistic test case, a diesel engine surface pressure and velocity are reconstructed to show the increase in efficiency from CRAFT to GEN-HELS. Keywords: Inverse Numerical Acoustics, Acoustic Holography, Helmholtz Equation, HELS Method, CRAFT Algorithm.
Bobodzhanov, A A; Safonov, V F
2013-07-31
The paper deals with extending the Lomov regularization method to classes of singularly perturbed Fredholm-type integro-differential systems, which have not so far been studied. In these the limiting operator is discretely noninvertible. Such systems are commonly known as problems with unstable spectrum. Separating out the essential singularities in the solutions to these problems presents great difficulties. The principal one is to give an adequate description of the singularities induced by 'instability points' of the spectrum. A methodology for separating singularities by using normal forms is developed. It is applied to the above type of systems and is substantiated in these systems. Bibliography: 10 titles.
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.
NASA Astrophysics Data System (ADS)
Boyd, John P.; Xu, Zhengjie
2012-02-01
Computation of solitons of the cubically-nonlinear Benjamin-Ono equation is challenging. First, the equation contains the Hilbert transform, a nonlocal integral operator. Second, its solitary waves decay only as O(1/∣ x∣ 2). To solve the integro-differential equation for waves traveling at a phase speed c, we introduced the artificial homotopy H( uXX) - c u + (1 - δ) u2 + δu3 = 0, δ ∈ [0, 1] and solved it in two ways. The first was continuation in the homotopy parameter δ, marching from the known Benjamin-Ono soliton for δ = 0 to the cubically-nonlinear soliton at δ = 1. The second strategy was to bypass continuation by numerically computing perturbation series in δ and forming Padé approximants to obtain a very accurate approximation at δ = 1. To further minimize computations, we derived an elementary theorem to reduce the two-parameter soliton family to a parameter-free function, the soliton symmetric about the origin with unit phase speed. Solitons for higher order Benjamin-Ono equations are also computed and compared to their Korteweg-deVries counterparts. All computations applied the pseudospectral method with a basis of rational orthogonal functions invented by Christov, which are eigenfunctions of the Hilbert transform.
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. PMID:25618077
Quasinormal acoustic oscillations in the Michel flow
NASA Astrophysics Data System (ADS)
Chaverra, Eliana; Morales, Manuel D.; Sarbach, Olivier
2015-05-01
We study spherical and nonspherical linear acoustic perturbations of the Michel flow, which describes the steady radial accretion of a perfect fluid into a nonrotating black hole. The dynamics of such perturbations are governed by a scalar wave equation on an effective curved background geometry determined by the acoustic metric, which is constructed from the spacetime metric and the particle density and four-velocity of the fluid. For the problem under consideration in this paper the acoustic metric has the same qualitative features as an asymptotically flat, static and spherically symmetric black hole, and thus it represents a natural astrophysical analogue black hole. As for the case of a scalar field propagating on a Schwarzschild background, we show that acoustic perturbations of the Michel flow exhibit quasinormal oscillations. Based on a new numerical method for determining the solutions of the radial mode equation, we compute the associated frequencies and analyze their dependency on the mass of the black hole, the radius of the sonic horizon and the angular momentum number. Our results for the fundamental frequencies are compared to those obtained from an independent numerical Cauchy evolution, finding good agreement between the two approaches. When the radius of the sonic horizon is large compared to the event horizon radius, we find that the quasinormal frequencies scale approximately like the surface gravity associated with the sonic horizon.
Quasi-normal acoustic oscillations in the transonic Bondi flow
NASA Astrophysics Data System (ADS)
Chaverra, Eliana; Sarbach, Olivier
2016-01-01
We analyze the dynamics of nonspherical acoustic perturbations of the transonic Bondi flow, describing the steady radial accretion of a polytropic perfect fluid into a gravity center. The propagation of such perturbations can be described by a wave equation on the curved effective background geometry determined by the acoustic metric introduced by Unruh in the context of experimental black hole evaporation. We show that for the transonic Bondi flow, Unruh's acoustic metric describes an analogue black hole and that the acoustic perturbations undergo quasi-normal oscillations. The associated quasi-normal frequencies are computed and they are proven to scale like the surface gravity of the acoustic black hole. This provides an explanation for results given in an earlier work, where it was shown that the acoustic perturbations of a relativistic fluid accreted by a nonrotating black hole possess quasi-normal modes, and where it was found empirically that the associated frequencies scaled like the surface gravity of the analogue black hole in the limit where the radius of the sonic horizon is much larger than the Schwarzschild radius.
Nonlinear acoustic wave propagation in atmosphere
NASA Technical Reports Server (NTRS)
Hariharan, S. I.
1985-01-01
A model problem that simulates an atmospheric acoustic wave propagation situation that is nonlinear is considered. The model is derived from the basic Euler equations for the atmospheric flow and from the regular perturbations for the acoustic part. The nonlinear effects are studied by obtaining two successive linear problems in which the second one involves the solution of the first problem. Well posedness of these problems is discussed and approximations of the radiation boundary conditions that can be used in numerical simulations are presented.