Phonation threshold pressure: comparison of calculations and measurements taken with physical models of the vocal fold mucosa

In an important paper on the physics of small amplitude oscillations, Titze showed that the essence of the vertical phase difference, which allows energy to be transferred from the flowing air to the motion of the vocal folds, could be captured in a surface wave model, and he derived a formula for the phonation threshold pressure with an explicit dependence on the geometrical and biomechanical properties of the vocal folds. The formula inspired a series of experiments [e.g., R. Chan and I. Titze, J. Acoust. Soc. Am 119, 2351-2362 (2006)]. Although the experiments support many aspects of Titze's formula, including a linear dependence on the glottal half-width, the behavior of the experiments at the smallest values of this parameter is not consistent with the formula. It is shown that a key element for removing this discrepancy lies in a careful examination of the properties of the entrance loss coefficient. In particular, measurements of the entrance loss coefficient at small widths done with a physical model of the glottis (M5) show that this coefficient varies inversely with the glottal width. A numerical solution of the time-dependent equations of the surface wave model shows that adding a supraglottal vocal tract lowers the phonation threshold pressure by an amount approximately consistent with Chan and Titze's experiments.     

Analytic Representation of Volume Flow as a Function of Geometry and Pressure in a Static Physical Model of the Glottis

A static physical model of the larynx (model M5) was used to obtain a large set of volume flows as a function of symmetric glottal geometry and transglottal pressure. The measurements cover ranges of these variables relevant to human phonation. A generalized equation was created to accurately estimate the glottal volume flow given specific glottal geometries and transglottal pressures. Both the data and the generalized formula give insights into the flow behavior for different glottal geometries, especially the contrast between convergent and divergent glottal angles at different glottal diameters. The generalized equation produced a fit to the entire M5 dataset (267 points) with an average accuracy of 3.4%. The accuracy was about seven times better than that of the Ishizaka-Flanagan approach to glottal flow and about four times better than that of a pressure coefficient approach. Thus, for synthesis purposes, the generalized equation presented here should provide more realistic glottal flows (based on steady flow conditions) as suitable inputs to the vocal tract, for given values of transglottal pressure and glottal geometry. Applications of the generalized formula to pulses generated by vocal fold motions typical of those produced by the Ishizaka-Flanagan coupled-oscillator model and the more recent body-cover model of Story and Titze are also included.     

Vocal fold vibration of the canine larynx: Observation from an infraglottic view

The authors studied the vibratory action of the canine vocal fold from the tracheal side utilizing high-speed cinematography. Five excised canine larynges were used, and the lower surface of the vocal fold of three of them were marked with India ink as a tracer of a specific point on the vocal fold. A mucosal prominence, called the mucosal upheaval, appeared between the anterior commissure and the vocal process. Vibration was not seen below the mucosal upheaval. The mucosal wave started to move medially from just above the mucosal upheaval. The mucosal wave then became the free edge (lower lip) and collided with that of the other side at the midline. After collision, the lower lip moved upward to become the upper lip. At the same time, a part of the lower lip reflected laterally. The mucosal wave of the next cycle started from just above the mucosal upheaval during an opening phase. The mucosal upheaval vibrated with a low amplitude and with an earlier phase than the other portion of the vocal fold. The increase in tension of the vocal fold did not change the basic vibratory pattern of the mucosal upheaval, the mucosal wave, or the free edge. However, analysis of the mark before and after the increase in tension revealed that the mucosal upheaval occurred more medially or above when the vocal fold tension increased.     

Mucosal Wave: A Normophonic Study Across Visualization Techniques

Visualization of vocal fold vibration is essential for accurate diagnoses and optimal treatment of persons with voice disorders. Recently, scientific and anecdotal reports have evidenced an increased amount of variation in the diagnostically relevant features of extent and symmetry of mucosal wave magnitude in normophonic speakers. The objectives of this study were to preliminarily ascertain the variation in mucosal wave magnitude and symmetry for normophonic speakers as assessed via standard and novel techniques, and compare findings across modal and pressed phonations. A correlational design with a multiple baseline across visualization methods approach was used. Mucosal wave presence, magnitude, and symmetry from 52 normophonic speakers were judged via stroboscopy, high-speed videoendoscopy (HSV) playback, mucosal wave playback, and mucosal wave kymography playback. Results demonstrate a prevalence of atypical magnitude and symmetry of mucosal wave during modal and pressed phonations by normophonic persons, differences across techniques, and a relationship between judgments and habitual fundamental frequency. Given the prevalence of mucosal wave magnitude and symmetry variations in the normophonic population, overdiagnosis may be possible without caution. The various visualization techniques provided unique information suggesting that it may be beneficial to use both full view and kymographic visualization techniques in combination. A major restriction of the current commercial HSV systems is the frame rate, typically limited to 2000 frames per second, which appears insufficient for most female habitual phonations.     

Resonant excitation and nonlinear evolution of waves in the equatorial waveguide in the presence of the mean current

We study interactions of planetary waves propagating across the equator with trapped Rossby or Yanai modes, and the mean flow. The equatorial waveguide with a mean current acts as a resonator and responds to planetary waves with certain wave numbers by making the trapped modes grow. Thus excited waves reach amplitudes greatly exceeding the amplitude of the incoming wave. Nonlinear saturation of the excited waves is described by an amplitude equation with one or two attracting equilibrium solutions. In the latter case spatial modulation leads to formation of characteristic defects in the wave field. The evolution of the envelopes of long trapped Rossby waves is governed by the driven complex Ginzburg-Landau equation, and by the damped-driven nonlinear Schr?dinger equation for short waves. The envelopes of the Yanai waves obey a simple wave equation with cubic nonlinearity.     

Wave propagation in a random medium: The solution of the m-nth moment equation with different wavenumbers

The moment equation with different wavenumbers and different transverse coordinates for wave propagation in a random medium is a linear differential equation. It often appears in the study of problems related to wave propagation in a random medium. The differential equation can be converted into an integral equation by using Green's functions and the integral equation can be solved by iteration. The moment equation is solved by the method of successive scatters, too. The solution of the moment equation is a Dyson expansion. The physical implication of the successive solution of the moment equation with different wavenumbers is explained.     

Lateral Phase Mucosal Wave Asymmetries in the Clinical Voice Laboratory

Anecdotally, in some persons it has been observed by the Senior Author (K.K.) that asymmetries of the mucosal wave exist when examined videostroboscopically. In the vast majority of these people, no pathology is ever discovered. Mucosal wave asymmetries could cause concern for the otolaryngologist, who may consider them to be a forewarning of subclinical pathology and subject the patient to unnecessary, expensive, and anxiety-provoking investigations or interventions. The purpose of this study was to establish the prevalence of mucosal wave asymmetries in an asymptomatic population lacking laryngeal pathology. Acoustic spectral analysis is also utilized to determine if the presence of subharmonics might be associated. A hospital-based, cross-sectional study design was used. The subjects had no known vocal or medical pathologies, and were nonsmoking. The study group was composed of 30 males aged 35-50 years and 30 women between 22-55 years. Each of the males underwent acoustic spectral analysis; and all subjects completed a medical questionnaire, subjective talkativeness rating, and videostroboscopic laryngeal examination. 10.5% of the subjects (exact 95% CI = 4.0-21.5%) exhibited mucosal wave variations at stroboscopy, characterized as periodic lateral phase asymmetries found consistently in both the modal and upper registers. There was no association with the chosen acoustic spectral parameters, talkativeness scales, or questionnaire-based variables. Mucosal wave asymmetries may be a variance of normal, and are likely to be far more common in the general population than previously believed. The prevalence detected here is expected to be important in the clinical laryngology practice, where these asymmetries may be frequently encountered and influencing management decisions. There has been little normative data published for variations of the mucosal wave specifically for epidemiological purposes. Clinically, in the absence of such data, otolaryngologists may over interpret videostroboscopic findings, leading to unnecessary investigations or interventions.     

Distribution of energy of solutions of the wave equation on singular spaces of constant curvature and on a homogeneous tree

In the paper, the Cauchy problem for the wave equation on singular spaces of constant curvature and on an infinite homogeneous tree is studied. Two singular spaces are considered: the first one consists of a three-dimensional Euclidean space to which a ray is glued, and the other is formed by two three-dimensional Euclidean spaces joined by a segment. The solution of the Cauchy problem for the wave equation on these objects is described and the behavior of the energy of a wave as time tends to infinity is studied.The Cauchy problem for the wave equation on an infinite homogeneous tree is also considered, where the matching conditions for the Laplace operator at the vertices are chosen in the form generalizing the Kirchhoff conditions. The spectrum of such an operator is found, and the solution of the Cauchy problem for the wave equation is described. The behavior of wave energy as time tends to infinity is also studied.     

非线性演化方程孤立波的同伦分析法求解

利用同伦分析法求解了Burgers方程，得到了其扭结形孤立波的近似解析解，该解非常接近于相应的精确解.结果表明，同伦分析法可用来求解非线性演化方程的孤立波解.同时，也对所用方法进行了一定扩展，得到了Kadomtsev-Petviashvili(KP)方程的钟形孤立子解.经过扩展后的方法能够更方便地用于求解更多非线性演化方程的高精度近似解析解. 关键词： Burgers方程 同伦分析法 KP方程 孤立波解     

Diffraction of sound by an elastic cylinder near the surface of an elastic halfspace

Diffraction of an acoustic wave by an elastic cylinder near the surface of an elastic halfspace is considered. The solution relies on a Helmholtz-type integral equation and uses the Green function of an elastic halfspace. The latter function is represented in the form of an integral over the Sommerfeld contour on the plane of a complex variable that has the meaning of the angle of the wave incidence on the halfspace boundary. An integral equation for the sound pressure distribution over the cylinder surface is derived. This equation is reduced to an infinite system of equations for the Fourier-series expansion coefficients of this distribution. The results obtained are valid for the diffraction of a cylindrical wave and a plane wave. They also describe the diffraction of a spherical wave when the transmitter and receiver are far from the cylinder and lie in one plane that is orthogonal to the cylinder axis.     

Nonlinear dispersion in the process of quasistationary excitation of plasma waves

A quasistationary problem of Lengmuir wave excitation by external sources in uniform plasma is considered. It is established that energy is transferred from external sources to the wave if during its excitation the wave phase velocity changes in addition to an increase in the wave amplitude. A nonlinear dispersion equation for the plasma wave of finite amplitude excited by the external sources is derived. The nonlinear contribution of this dispersion equation is caused not only by an increase in the wave amplitude but also by the wave frequency shift.     

Exact classical and quantum solutions for a covariant oscillator near the black hole horizon in Stueckelberg-Horwitz-Piron theory

We found exact solutions for canonical classical and quantum dynamics for general relativity in Horwitz general covariance theory. These solutions can be obtained by solving the generalized geodesic equation and Schrödinger-Stueckelberg-Horwitz-Piron (SHP) wave equation for a simple harmonic oscillator in the background of a two dimensional dilaton black hole spacetime metric. We proved the existence of an orthonormal basis of eigenfunctions for generalized wave equation. This basis functions form an orthogonal and normalized (orthonormal) basis for an appropriate Hilbert space. The energy spectrum has a mixed spectrum with one conserved momentum p according to a quantum number n. To find the ground state energy we used a variational method with appropriate boundary conditions. A set of mode decomposed wave functions and calculated for the Stueckelberg-Schrodinger equation on a general five dimensional blackhole spacetime in Hamilton gauge.     

Symmetries and conserved quantities of discrete wave equation associated with the Ablowitz-Ladik-Lattice system

In this paper, we present a new method to obtain the Lie symmetries and conserved quantities of the discrete wave equation with the Ablowitz-Ladik-Lattice equations. Firstly, the wave equation is transformed into a simple difference equation with the Ablowitz-Ladik-Lattice method. Secondly, according to the invariance of the discrete wave equation and the Ablowitz-Ladik-Lattice equations under infinitesimal transformation of dependent and independent variables, we derive the discrete determining equation and the discrete restricted equations. Thirdly, a series of the discrete analogs of conserved quantities, the discrete analogs of Lie groups, and the characteristic equations are obtained for the wave equation. Finally, we study a model of a biological macromolecule chain of mechanical behaviors, the Lie symmetry theory of discrete wave equation with the Ablowitz-Ladik-Lattice method is verified.     

一种全频散波方程的反问题

基于一种全频散波方程研究了对于谐波和波包的反问题。首先根据Mindlin理论建立了描述无耗散微结构线性固体中波传播模型一一一种全频散波方程,并讨论了其频散特性。然后基于该全频散波方程,提出了利用四种不同谐波的频率和相应波数确定波方程四个未知系数的反问题,并用严格的数学理论论证了此反问题。研究证明,通过测量同一种无耗散微结构线性固体中传播的四种不同谐波的频率和相应波数,在正常频散和反常频散情况下可唯一地确定波方程的未知系数,即材料的未知参数。      

The inverse problem based on a full dispersive wave equation

The inverse problem for harmonic waves and wave packets was studied based on a full dispersive wave equation.First,a full dispersive wave equation which describes wave propagation in nondissipative microstructured linear solids is established based on the Mindlin theory,and the dispersion characteristics are discussed.Second,based on the full dispersive wave equation,an inverse problem for determining the four unknown coefficients of wave equation is posed in terms of the frequencies and corresponding wave numbers of four different harmonic waves,and the inverse problem is demonstrated with rigorous mathematical theory. Research proves that the coefficients of wave equation related to material properties can be uniquely determined in cases of normal and anomalous dispersions by measuring the frequencies and corresponding wave numbers of four different harmonic waves which propagate in a nondissipative microstructured linear solids.     

A time dependent Ginzburg-Landau equation and its application to the problem of resistivity in the mixed state

A time dependent modification of the Ginzburg-Landau equation is given which is based on the assumption that the functional derivative of the Ginzburg-Landau free energy expression with respect to the wave function is a generalized force in the sense of irreversible thermodynamics acting on the wave function. This equation implies an energy theorem, according to which the energy can be dissipated by i) production of Joule heat; ii) irreversible variation of the wave function. The theory is a limiting case of the BCS theory, and hence, it contains no adjustable parameters. The application of the modified equation to the problem of resistivity in the mixed state reveals satisfactory agreement between experiment and theory for reduced temperatures higher than 0.6.     

Application of the complex point source method to the Schrödinger equation

The paraxial wave equation is a reduced form of the Helmholtz equation. Its solutions can be directly obtained from the solutions of the Helmholtz equation by using the method of complex point source. We applied the same logic to quantum mechanics, because the Schrödinger equation is parabolic in nature as the paraxial wave equation. We defined a differential equation, which is analogous to the Helmholtz equation for quantum mechanics and derived the solutions of the Schrödinger equation by taking into account the solutions of this equation with the method of complex point source. The method is applied to the problem of diffraction of matter waves by a shutter.     

On exact solutions of the Bogoyavlenskii equation

Exact solutions for the Bogoyavlenskii equation are studied by the travelling wave method and the singular manifold method. It is found that the linear superposition of the shock wave solution and the complex solitary wave solution for the physical field is still a solution of the equation of interest, except for a phase-shift. The dromion-like structures with elastic and nonelastic interactions are found.     

Determination of the Minimum Wave Speed for the Modelling of Ventilated Cavitation

Ventilated cavitation plays an important role on the drag reduction of underwater vehicles and surface ships.For the modelling of ventilated cavitation,the minimum speed of the pressure wave is a crucial parameter for the closure of the pressure-density coupling relationship.In this study,the minimum wave speed is determined based on a theoretical model coupling the wave equation and the bubble interface motion equation.The influences of several paramount parameters(e.g.,frequency,bubble radius and void fraction) on the minimum wave speed are quantitatively demonstrated and discussed.Compared with the minimum wave speed in the traditional cavitation,values for the ventilated cavitation are much higher.The physical mechanisms for the above difference are briefly discussed with the suggestions on the usage of the present findings.