Decay Of Acoustic Waves Research Articles

Low Mach number limit of the compressible Navier–Stokes–Cattaneo equations with general initial data

In this paper, we investigate the low Mach number limit of the compressible Navier–Stokes–Cattaneo equations in the whole space R3. In particular, the large variations of density, temperature and heat flux are taken into account. By introducing an appropriate time-weighted normed space, the uniform estimates of the solutions are established for general initial data. Then, the convergence of the solutions is proved by combining the uniform estimates and the local energy decay of acoustic waves. Finally, we derive a new limit equations which reveal the effect of heat flux on the field of velocity.

Acoustic build-up in on-chip stimulated Brillouin scattering.

We investigate the role of the spatial evolution of the acoustic field in stimulated Brillouin scattering processes in short high-gain structures. When the gain is strong enough that the gain length becomes comparable to the acoustic wave decay length of order 100 microns, standard approximations treating the acoustic field as a local response no longer apply. Treating the acoustic evolution more accurately, we find that the backward SBS gain of sub-millimetre long waveguides is significantly reduced from the value obtained by the conventional treatment because the acoustic mode requires several decay lengths to build up to its nominal value. In addition, the corresponding resonance line is broadened with the development of side bands. In contrast, we argue that intra-mode forward SBS is not expected to show these effects. Our results have implications for several recent proposals and experiments on high-gain stimulated Brillouin scattering in short semiconductor waveguides.

Local Decay of Acoustic Waves in the Low Mach Number Limits on General Unbounded Domains Under Slip Boundary Conditions

We discuss several aspects of the problem of propagation and dispersion of acoustic waves arising in the low Mach number asymptotic limits of compressible fluid systems. A general approach is proposed based on analysis of the spectral measures associated to the corresponding wave propagator. In particular, the local decay estimates based on a result of Tosio Kato and on RAGE theorem are obtained as limit cases. The approach is applied to problems on domains their shape may vary with the Mach number.

Characterization of the Brillouin grating spectra in a polarization-maintaining fiber

Brillouin grating in optical fibers is of considerable interest due to its applications in optical fiber communication and distributed sensing. However, the intrinsic Brillouin grating spectrum is still unknown and several kinds of spectra were reported. In this paper, we experimentally investigate the characteristics of the Brillouin grating spectra in a polarization-maintaining fiber, and the results show that it agrees with the theory of fiber Bragg grating but not determined by the natural Brillouin gain bandwidth as thought previously, and in the case of weak grating, the bandwidth is only length-limited, i.e., inversely proportional to the length of the Brillouin grating. In addition, the apodization of the Brillouin grating induced by the acoustic wave decay, a unique feature that is different from the Bragg grating, is observed for the first time to the best of our knowledge.

Artificial compressibility method revisited: Asymptotic numerical method for incompressible Navier–Stokes equations

The artificial compressibility method for the incompressible Navier–Stokes equations is revived as a high order accurate numerical method (fourth order in space and second order in time). Similar to the lattice Boltzmann method, the mesh spacing is linked to the Mach number. An accuracy higher than that of the lattice Boltzmann method is achieved by exploiting the asymptotic behavior of the solution of the artificial compressibility equations for small Mach numbers and the simple lattice structure. An easy method for accelerating the decay of acoustic waves, which deteriorate the quality of the numerical solution, and a simple cure for the checkerboard instability are proposed. The high performance of the scheme is demonstrated not only for the periodic boundary condition but also for the Dirichlet-type boundary condition.

SBS threshold measurements and acoustic beam propagation modeling in guiding and anti-guiding single mode optical fibers

A 4.3 dB stimulated Brillouin scattering (SBS) threshold suppression is measured in a passive Al-doped acoustically anti-guiding single mode optical fiber relative to that of a Ge-doped acoustically guiding single mode optical fiber. Stimulated scattering is generated by the electrostrictive acoustic wave generated in the fiber core. This acoustic excitation has a decay length L(d) related to the sound absorption decay length L(abs) and the acoustic waveguide decay length L(wg) by: L(d)(-1)= L(abs)(-1)+ L(wg)(-1). The acoustic waveguide decay length L(wg) is associated with the diffraction, refraction and reflection of the acoustic wave in the elastically inhomogeneous optical fiber cores. The SBS gain is proportional to the net acoustic decay length L(d) and the relative SBS suppression is proportional to the ratio of the net decay lengths of the Al and Ge doped cores (L(Al)/ L(Ge)). An acoustic beam propagation model is used to calculate the evolution of the complex acoustic excitations in the optical cores and determine the acoustic wave decay lengths L(wg). Model predictions for the relative SBS suppression for the two fibers are in good agreement with experimental values obtained from Stokes power and optical heterodyne linewidth measurements.

Miniature, narrow band, non-collinear acoustic optical tunable filter for telecom applications

This invention includes an Acousto-optical tuning device by employing the TeO2 in share mode, non-collinear and in high RF frequency (or large Bragg's deflection region), it is able to achieve the telecomm worthy tunable filter that provides high tuning speed, no-moving parts, very narrow filter line-width (0.2 nm for instance) and with miniature size practical for a optical telecom active module. This tuning characteristic is achieved by taking the particular advantages that the angle of incidence (AOI) and angle of diffraction (AOD) are divergent in a frequency range just suitable for a shorter wavelength application required by modern telecommunication systems while the acoustic wave decay in this frequency range can be properly managed to achieve the design goals. Furthermore, by generating a diffracted beam with larger AOD, implementation of filtering for optical propagations of different wavelengths can be conveniently selected. Other than the TeO2 crystals, the AOTF can also be formed with AsS3 and GeAsSe crystals based on the same acoustic-optical interaction processes at a higher RF frequency range as discussed in the above descriptions.

Kinetics of interfacial nucleic acid hybridization studied by acoustic network analysis

A novel acoustic network analysis technique has been developed to study DNA hybridization kinetics at a sensor-solution interface. The series resonant frequency change is related to the DNA hybridization process through the DNA concentration-dependent viscosity change in the acoustic wave decay length region. The kinetics of hybridization of pPT-2 cDNA probe to ss DNA immobilized on thickness-shear-mpde (TSM) acoustic wave sensors has been examined. The process measured by this device does not conform to the generally assumed theoretical second order reaction in solution and one-step mechanism on a typical membrane filter. The pseudo-first order effective rate constants are (8·0 ± 0·5) × 10 −5 s −1 when hybridization is performed in solution without the presence of moieties employed to prevent non-specific effects (blocking reagents), and (3·8 ± 0·1) × 10 −5 s −1 with them. The calculated Mark-Houwink constant, α, is 1·8, and the intrinsic viscosity is 9·0 × 10 4 (M −1) under the hybridization conditions. Inflection points due to the formation of intermediate hybrids are observed during continuous measurement of series resonant frequency with time.

Studies of domain‐based formulations for computing exterior problems of acoustics

AbstractThe propagation and decay of acoustic waves in exterior domains in an essential ingredient in the study of fluid–structure interaction. A strategy must be devised to compute solutions over domains which are unbounded. Exact impedance conditions at an artificial external boundary are specified by the DtN method, yielding an equivalent problem that is suitable for domain‐based computation. The DtN boundary condition is non‐reflective, giving rise to exact (and thereby unique) solutions. The truncated DtN operator, which is employed in practice, fails to inhibit the reflection of higher modes, so that non‐unique solutions may occur at their harmonics. Simple expressions determine a sufficient number of terms in the truncated operator for unique solutions at any given wave number. There are three characteristic length scales in the computational problem: the radius of the artificial boundary, the geometry of the body (represented by the internal boundary) and the mesh size. Numerical studies examine the dependence of the conditioning of finite element coefficient matrices on the number of terms in the truncated DtN operator vs. the wave number non‐dimensionalized by each of the length scales. Analytic results regarding the number of terms sufficient for unique solutions are confirmed. As long as this criterion is respected, no upper limit on the allowable wave number is detected. A local approximation of the boundary conditions restores uniqueness for all wave numbers.

Note on the decay of acoustic waves

Note on the decay of acoustic waves