Function Of Wave Speed Research Articles

COMPARISON BETWEEN TWO NONINVASIVE METHODS USED TO ESTIMATE BIOMECHANICAL PROPERTIES OF THE INTERNAL CAROTID ARTERY

Background: Many cardiovascular diseases modified the arterial wall stiffness. Objectives: This work focuses on the quantification of the elastic biomechanical properties of the internal carotid (ICA) wall by applying the cepstral analysis on healthy volunteers aged from 22 to 86 years old. The purpose of this study is to compare two methods of measurement of arterial compliance ([Formula: see text], arterial distensibility ([Formula: see text], arterial elastance (Eh), and Young’s modulus ([Formula: see text]. Material and methods: First, arterial compliance and arterial distensibility were measured in function of wave speed ([Formula: see text], which is measured in our previous works by using two methods. Second, elastance Eh was estimated through the ratio between diastolic radius ([Formula: see text] and [Formula: see text]. Finally, [Formula: see text] was estimated from a statistical study from the literature on h due to the difficulty of measuring wall thickness ([Formula: see text]. Results: The Student test demonstrated that there is a very significant difference between young and old subjects in terms of elastance, compliance, and Young’s modulus ([Formula: see text]). These findings are in agreement with the reference values reported in the literature. They are very satisfying for distinguishing a pathological change in parietal elasticity. Conclusion: The in vivo application of these methods presents their potential for clinical measurement of arterial stiffness.

Superharmonic instability of nonlinear travelling wave solutions in Hamiltonian systems

The problem of linear instability of a nonlinear travelling wave in a canonical Hamiltonian system with translational symmetry subject to superharmonic perturbations is discussed. It is shown that exchange of stability occurs when energy is stationary as a function of wave speed. This generalizes a result proved by Saffman (J. Fluid Mech., vol. 159, 1985, pp. 169–174) for travelling wave solutions exhibiting a wave profile with reflectional symmetry. The present argument remains true for any non-canonical Hamiltonian system that can be cast in Darboux form, i.e. a canonical Hamiltonian form on a submanifold defined by constraints, such as a two-dimensional surface wave on a constant shearing flow, revealing a general feature of Hamiltonian dynamics.

Stability estimate for the Helmholtz equation with rapidly jumping coefficients

The goal of this paper is to investigate the stability of the Helmholtz equation in the high- frequency regime with non-smooth and rapidly oscillating coefficients on bounded domains. Existence and uniqueness of the problem can be proved using the unique continuation principle in Fredholm's alternative. However, this approach does not give directly a coefficient-explicit energy estimate. We present a new theoretical approach for the one-dimensional problem and find that for a new class of coefficients, including coefficients with an arbitrary number of discontinuities, the stability constant (i.e., the norm of the solution operator) is bounded by a term independent of the number of jumps. We emphasize that no periodicity of the coefficients is required. By selecting the wave speed function in a certain \resonant" way, we construct a class of oscillatory configurations, such that the stability constant grows exponentially in the frequency. This shows that our estimates are sharp.

A generalized spherical harmonic deconvolution to obtain texture of cubic materials from ultrasonic wave speed

In this paper, the spherical harmonic convolution approach for HCP materials (Lan et al., 2015) is extended into a generalised form for the principal purpose of bulk texture determination in cubic polycrystals from ultrasonic wave speed measurements. It is demonstrated that the wave speed function of a general single crystal convolves with the polycrystal Orientation Distribution Function (ODF) to make the resultant polycrystal wave speed function such that when the three functions are expressed in harmonic expansions, the coefficients of any one function may be determined from the coefficients of the other two. All three Euler angles are taken into account in the description of the ODF such that the theorem applies for all general crystal systems.The forward problem of predicting polycrystal wave speed with knowledge of single crystal properties and the ODF is solved for all general cases, with validation carried out on cubic textures showing strong sensitivity to texture and excellent quantitative accuracy in predicted wave speed amplitudes. Importantly, it is also revealed by the theorem that the cubic structure is one of only two crystal systems (the other being HCP) whose orientation distributions can be inversely determined from polycrystal wave velocities by virtue of their respective crystal symmetries. Proof of principle is then established by recovering the ODFs of representative cubic textures solely from the wave velocities generated from a computational model using these texture inputs, and excellent accuracies are achieved in the recovered ODF coefficients as well as the resultant pole figures. Hence the methodology is argued to provide a powerful technique for wave propagation studies and bulk texture measurement in cubic polycrystals and beyond.

Nonlinear Analysis on Traffic Flow Based on Catastrophe and Chaos Theory

We applied catastrophe and chaos theory to analyze the traffic nonlinear characteristics of expressway condition. Catastrophe theory was generally used to explore the mathematical relationships among the traffic data collected from highway conditions, which could not be appropriate for the urban expressway conditions. Traffic flow data collected from the 3rd ring road expressway in Beijing was used to build flow-density model and speed-density Greenshields model. Then the density was discussed based on the traffic wave speed function with cusp catastrophe theory; in particular, density conditions on median lanes and shoulder lanes were deeply discussed. Meanwhile the chaotic characteristics were analyzed based on the traffic temporal sequence data collected from 29 detectors located at the 3rd ring road expressway, and C-C method was used to reconstruct the phase space and the largest Lyapunov exponents were estimated by Wolf method and the small data sets method. The results indicated that the traffic operation catastrophe density on the median lanes was a bit higher than that on the shoulder lanes; additionally chaotic characteristics obviously existed in the local corridor composed of 29 detectors in the 3rd ring road expressway traffic flow system.

Analysis of a fast method for solving the high frequency Helmholtz equation in one dimension

We propose and analyze a fast method for computing the solution of the high frequency Helmholtz equation in a bounded one-dimensional domain with a variable wave speed function. The method is based on wave splitting. The Helmholtz equation is split into one-way wave equations with source functions which are solved iteratively for a given tolerance. The source functions depend on the wave speed function and on the solutions of the one-way wave equations from the previous iteration. The solution of the Helmholtz equation is then approximated by the sum of the one-way solutions at every iteration. To improve the computational cost, the source functions are thresholded and in the domain where they are equal to zero, the one-way wave equations are solved with geometrical optics with a computational cost independent of the frequency. Elsewhere, the equations are fully resolved with a Runge–Kutta method. We have been able to show rigorously in one dimension that the algorithm is convergent and that for fixed accuracy, the computational cost is asymptotically just $\mathcal {O}(\omega^{1/ p})$ for a pth order Runge–Kutta method, where ω is the frequency. Numerical experiments indicate that the growth rate of the computational cost is much slower than a direct method and can be close to the asymptotic rate.

Nonlocally related systems, linearization and nonlocal symmetries for the nonlinear wave equation

The nonlinear wave equation u t t = ( c 2 ( u ) u x ) x arises in various physical applications. Ames et al. [W.F. Ames, R.J. Lohner, E. Adams, Group properties of u t t = [ f ( u ) u x ] x , Int. J. Nonlin. Mech. 16 (1981) 439–447] did the complete group classification for its admitted point symmetries with respect to the wave speed function c ( u ) and as a consequence constructed explicit invariant solutions for some specific cases. By considering conservation laws for arbitrary c ( u ) , we find a tree of nonlocally related systems and subsystems which include related linear systems through hodograph transformations. We use existing work on such related linear systems to extend the known symmetry classification in [W.F. Ames, R.J. Lohner, E. Adams, Group properties of u t t = [ f ( u ) u x ] x , Int. J. Nonlin. Mech. 16 (1981) 439–447] to include nonlocal symmetries. Moreover, we find sets of c ( u ) for which such nonlinear wave equations admit further nonlocal symmetries and hence significantly further extend the group classification of the nonlinear wave equation.

On the superharmonic instability of surface gravity waves on fluid of finite depth

The linear stability of two-dimensional surface gravity waves on fluid of finite depth is investigated for superharmonic disturbances. For this problem, Zufiria & Saffman suggested that an exchange of stability occurs when the total wave energy becomes stationary as a function of wave speed for fixed 'Bernoulli constant'. In defining the potential energy of the above total wave energy, the surface displacement was measured from the quiescent surface with the same 'Bernoulli constant'. We have re-examined this problem both analytically and numerically

Estimation of the density, the wave speed and the acoustic impedance function in ultrasound imaging

In this paper, we derive integral equations for estimating the density function ρ and the wave speed function c or the acoustic impedance function from boundary measurement data. A nonlinear integral equation for the special case ρ = const and c ≠ const is discussed in detail. We show that the inverse problem of estimating the acoustic impedance function from boundary data measured via a zero-offset transducer configuration can be decomposed into two successively solvable inverse problems. The first inverse problem corresponds to the estimation of the spherical mean function of the acoustic impedance function from a set of one-dimensional integral equations. The second inverse problem corresponds to the estimation of the acoustic impedance function which is closely related to the estimation of the electromagnetic absorption function in transparent media. We conclude the paper with some numerical experiments.

RAREFACTIVE SOLUTIONS TO A NONLINEAR VARIATIONAL WAVE EQUATION OF LIQUID CRYSTALS

We study a nonlinear wave equation derived from a simplified liquid crystal model, in which the wave speed is a given function of the wave amplitude. We formulate a viscous approximation of the equation and establish the global existence of smooth solutions for the viscously perturbed equation. For a monotone wave speed function in the equation, we find an invariant region in the phase space in which we discover: (a) smooth data evolve smoothly forever; (b) both the viscous regularization and the smooth solutions obtained through data smoothing for rough initial data yield weak solutions to the Cauchy problem of the nonlinear variational wave equation. The main tool is the Young measure theory and related techniques.

Reconstruction of Source and Medium Parameters via Wave-Splitting and Green Function Equations

This paper applies the time-domain wave-splitting and the Green function concepts to study two inverse problems involving an internal transient source embedded in a nondispersive inhomogeneous medium. These two inverse problems are (1) given the physical one-way travel time Green operator kernel $\bar G^ - ( {0,t} )$ and the source-space distribution function, reconstruct the wave-speed profile $c( z )$ of the medium; (2) given the same kernel $\bar G^ - ( {0,t} )$ and the medium wave-speed function, recover the source-space distribution profile $p( z )$. Both numerical inversion algorithms and approximate-reconstruction formulas are presented. Several computational examples are given.

Weakly nonlinear reactive shocks with lateral divergence

Asymptotic equations are obtained in a weakly nonlinear limit of the Wood-Kirkwood equations for slightly divergent reactive flow. Specifically, in cylindrical symmetry the equations of reactive flow are restricted to the central stream tube, and the radial component of the velocity is assumed to be a function of wavespeed of a signal propagating through the medium. Asymptotic equations are obtained in the limit where the Mach number is close to unity and the components of the velocity are small in comparison; the heat release is assumed to be small, and two cases with different chemical kinetics are examined. In one case an Arrhenius-type reaction rate with large activation energy is considered, and in another case a depletion-type rate with no Arrhenius factor is considered. The asymptotic equations are compared to the Fickett (1985) analogue of detonation. Finally, the existence of ZND type waves within the context of the model asymptotic equations is examined in special cases.

Eigenvalues, and instabilities of solitary waves

We study a type of ‘eigenvalue’ problem for systems of linear ordinary differential equations with asymptotically constant coefficients by using the analytic functionD(λ) introduced by J. W. Evans (1975) in his study of the stability of nerve impulses. We develop a general theory ofD(λ) that clarifies the role of the essential spectrum in applications. New formulae for derivatives ofD(λ) are used to study linear exponential instabilities of solitary waves for generalizations of: (1) the Korteweg-de Vries equation (KdV); (2) the Benjamin-Bona-Mahoney equation (BBM); and (3) the regularized Boussinesq equation. A pair of real eigenvalues exists, indicating a non-oscillatory instability, when the ‘momentum’ of the wave (a time-invariant functional associated with the hamiltonian structure of the equation) is a decreasing function of wave speed. Also we explain the mechanism of the transition to instability. Unexpectedly, these transitions are unlike typical transitions to instability in finite-dimensional hamiltonian systems. Instead they can be understood in terms of the motion of poles of the resolvent formula extended to a multi-sheeted Riemann surface. Finally, for a generalization of the KdV-Burgers equation (a model for bores), we show that a conjectured transition to instability doesnotinvolve real eigenvalues emerging from the origin, suggesting an oscillatory type of instability.

A model of the intensity probability distribution for wave propagation in random media

Ewart and Percival [J. Acoust. Soc. Am. 80, 1745 (1986)] have shown that the generalized gamma distribution effectively models intensity probability distributions of temporal fluctuations observed in a field experiment and transverse spatial fluctuations simulated in numerical experiments. In both cases the fluctuations are due to wave propagation through a medium with a random index of refraction. Here, the transverse spatial intensity fluctuations of a wave propagating through a medium with a power-law autocorrelation function of wave speed are modeled over a regime that spans 108 in scattering strength and 106 in scaled range (range divided by the Fresnel length). This scattering parameter regime transforms to ranges between 100 m and 100 km and to frequencies between 100 Hz and 100 kHz when normalizations typical of observed ocean internal wave fluctuations are used. Contour plots of the variance, skewness, and kurtosis of the intensity distribution are presented for the range/frequency plane. It is shown that the region of saturation, i.e., exponential intensity distribution, cannot be attained except for very large source strengths. Also, the lognormal intensity distribution, which is assumed for scintillation indices near zero, can be applied only in the region of vanishingly small intensity fluctuations. This work, while based on plane-wave propagation and a fourth-order power-law transverse spectrum of the medium, retains the essential character of the intensity fluctuations and provides a prescription for modeling the intensity distribution for any medium where the random index of refraction process can be assumed stationary.

Shock Thickness in Viscoplastic Solids

In this paper a system of constitutive relations for plane-strain finite deformation in strain-rate sensitive elastic-plastic materials is developed. A method is presented for computing the main features of steady-state one-dimensional plastic-strain waves by elementary numerical techniques in materials of this type. This method is applicable to a wide variety of material constitutive relations and provides an alternative to computing complete wave profiles for investigators interested primarily in the effects of certain numerical parameters on the principal features of waves. The method is illustrated by use of particular constitutive relations but is applicable to a much wider class of relations. Maximum normal stress, pressure, and shear stress are computed, using this method, as a function of wave speed. For two different plastic strain-rate relations the maximum plastic strain rate and total strain are computed as a function of wave speed. Making use of these results, estimates are provided for the wave-front thickness in terms of wave speed and the parameters of the particular viscoplastic constitutive equations used. These results suggest ways in which plastic wave experiments can be used to motivate the construction of constitutive equations for finite deformation in strain-rate sensitive plastic solids.

On the generation of surface waves by shear flows

A mechanism for the generation of surface waves by a parallel shear flow U(y) is developed on the basis of the inviscid Orr-Sommerfeld equation. It is found that the rate at which energy is transferred to a wave of speed c is proportional to the profile curvature -U(y) at that elevation where U = c. The result is applied to the generation of deep-water gravity waves by wind. An approximate solution to the boundary value problem is developed for a logarithmic profile and the corresponding spectral distribution of the energy transfer coefficient calculated as a function of wave speed. The minimum wind speed for the initiation of gravity waves against laminar dissipation in water having negligible mean motion is found to be roughly 100cm/sec. A spectral mean value of the sheltering coefficient, as defined by Munk, is found to be in order-of-magnitude agreement with total wave drag measurements of Van Dorn. It is concluded that the model yields results in qualitative agreement with observation, but truly quantitative comparisons would require a more accurate solution of the boundary value problem and more precise data on wind profiles than are presently available. The results also may have application to the flutter of membranes and panels.