Damping Of Sound Waves Research Articles

A Fast Second-order Solver for Stiff Multifluid Dust and Gas Hydrodynamics

We present MDIRK: a multifluid second-order diagonally implicit Runge–Kutta method to study momentum transfer between gas and an arbitrary number (N) of dust species. The method integrates the equations of hydrodynamics with an implicit–explicit scheme and solves the stiff source term in the momentum equation with a diagonally implicit, asymptotically stable Runge–Kutta method (DIRK). In particular, DIRK admits a simple analytical solution that can be evaluated with O(N) operations, instead of standard matrix inversion, which is O(N)3 . Therefore, the analytical solution significantly reduces the computational cost of the multifluid method, making it suitable for studying the dynamics of systems with particle-size distributions. We demonstrate that the method conserves momentum to machine precision and converges to the correct equilibrium solution with constant external acceleration. To validate our numerical method we present a series of simple hydrodynamic tests, including damping of sound waves, dusty shocks, a multifluid dusty Jeans instability, and a steady-state gas–dust drift calculation. The simplicity of MDIRK lays the groundwork to build fast high-order, asymptotically stable multifluid methods.

Altering Terahertz Sound Propagation in a Liquid upon Nanoparticle Immersion.

One of the grand challenges of new generation Condensed Matter physicists is the development of novel devices enabling the control of sound propagation at terahertz frequency. Indeed, phonon excitations in this frequency window are the leading conveyor of heat transfer in insulators. Their manipulation is thus critical to implementing heat management based on the structural design. To explore the possibility of controlling the damping of sound waves, we used high spectral contrast Inelastic X-ray Scattering (IXS) to comparatively study terahertz acoustic damping in a dilute suspension of 50 nm nanospheres in glycerol and on pure glycerol. Bayesian inference-based modeling of measured spectra indicates that, at sufficiently large distances, the spectral contribution of collective modes in the glycerol suspension becomes barely detectable due to the enhanced damping, the weakening, and the slight softening of the dominant acoustic mode.

Modification of favorable average curvature effect by changing parallel sound wave behavior in tokamak plasmas

The favorable average curvature effect, also known as the GGJ effect (Glasser et al 1975 Phys. Fluids 18 875), is intrinsically associated with parallel sound wave propagation in a tokamak plasma. This work investigates how the GGJ effect is modified by changing the parallel sound wave behavior. Two physics models beyond the standard single fluid theory, i.e. an anisotropic thermal transport model and a parallel sound wave damping model, are employed to change parallel sound waves in a toroidal plasma, and the consequence on the GGJ effect is demonstrated for two important classes of problems, i.e. the resistive plasma response to the applied resonant magnetic perturbation and the stability of the tearing mode. Toroidal modeling reveals that the GGJ effect is significantly altered by both of the aforementioned physics effects. Compared to the thermal transport physics, which completely removes the GGJ effect, the sound wave damping effect only offers partial mitigation. The differences between these two models are further illustrated in terms of the radial structure of the shielding current and the eigenfunction of the tearing instability. In particular, a fundamental reason for complete suppression of the GGJ effect by the thermal transport is identified as an extra toroidal coupling of the poloidal harmonics.

Excitation of fishbone-like mode in tokamaks due to bounce resonances of trapped thermal ions

When the drift kinetic effect of thermal ions is taken into account, a high-frequency fishbone-like mode (FLM) is found to be driven unstable by trapped thermal ions (TTIs) in tokamak plasmas, according to self-consistent magneto-hydrodynamic (MHD)-kinetic hybrid modeling utilizing the MARS-K code [Liu et al., Phys. Plasmas 15, 112503 (2008)] as well as an analytic theory. It is found that, similar to energetic particles, TTIs can also stabilize the internal kink mode, whereas the FLM is excited when the effective beta of TTIs exceeds a threshold value. The real frequency of the FLM is comparable to the bounce frequency of TTIs. The mode structure of the FLM can be significantly different from the conventional step-like function for the associated plasma radial displacement. This drift kinetic induced modification of the mode structure near the q = 1 surface is captured by non-perturbative MHD-kinetic hybrid computations with MARS-K. Furthermore, the FLM can only be triggered by TTIs at sufficiently high thermal temperatures. Both the FLM and the internal kink can be stabilized by sufficiently fast plasma toroidal rotation and parallel sound wave damping. These two conditions of high thermal temperature and (fast) flow stabilization, though making it challenging to observe the TTI-driven FLM in present day experiments, are favorable for the mode excitation in future reactor scale devices.

Study on the effects of denier and shapes of polyester fibres on acoustic performance of needle-punched nonwovens with air-gap: comparison of artificial neural network and regression modelling approaches to predict the sound absorption coefficient of nonwovens

In this article, a comparative analysis of artificial neural network (ANN) and regression modelling approaches has been carried out to predict the sound absorption coefficient (SAC) of nonwovens plus air-gap at wide range of frequencies (50–6300 Hz). Needle-punched nonwoven fabrics were produced with different denier and cross-sectional shapes of polyester fibres to study their combined effect on acoustic performance of nonwovens. The surface area of fibres, specific airflow resistance and mean flow pore size of nonwovens were analysed to explain their sound absorption behaviour. Finer fibre nonwovens perform better than the coarser fibre nonwoven as sound absorber. The effective surface areas of fibres in the nonwoven structure greatly affects the SAC. Finer fibres will get aligned easily in z-direction compared to coarser fibres, facilitating formation of more tortuous channels in the fabric structure contributing damping of sound waves. It has been observed that ANN model predicts the SAC with high degree of accuracy than the regression model. The ranking of input parameters in predicting SAC of nonwovens was analysed. Both the models ranked frequency of sound is the major determinant for predicting SAC followed by specific airflow resistance of nonwoven fabric.

Theory of sound absorption in heterogeneous dielectric with an admixture of magnetic nanoparticles

A general theory of sound wave absorption in heterogeneous crystalline structures is proposed using the quasi-classical kinetic equation (QKE), and the microscopic dependence of sound wave damping is calculated: γ(ω, ξ*), where ω is the frequency of external sound as a fumction of concentration ξ* of ferromagnetic particles over a wide range of their average diameters (from centimeter to nanoscale).

Effects of parallel sound wave damping and drift kinetic damping on the resistive wall mode stability with various plasma rotation profiles

The effect of a parallel viscous force induced damping and the magnetic precessional drift resonance induced damping on the stability of the resistive wall mode (RWM) is numerically investigated for one of the advanced steady-state scenarios in international thermonuclear experimental reactor (ITER). The key element of the investigation is to study how different plasma rotation profiles affect the stability prediction. The single-fluid, toroidal magnetohydrodynamic (MHD) code MARS-F (Liu et al., Phys. Plasmas, vol. 7, 2000, p. 3681) and the MHD–kinetic hybrid code MARS-K (Liu et al., Phys. Plasmas, vol. 15, 2008, 112503) are used for this purpose. Three extreme rotation profiles are considered: (a) a uniform profile with no shear, (b) a profile with negative flow shear at the $q=2$ rational surface ($q$ is the equilibrium safety factor), and (c) a profile with positive shear at $q=2$. The parallel viscous force is found to be effective for the mode stabilization at high plasma flow speed (about a few percent of the Alfven speed) for the no shear flow profile and the negative shear flow profile, but the stable domain does not appear with the positive shear flow profile. The predicted eigenmode structure is different with different rotation profiles. With a self-consistent inclusion of the magnetic precession drift resonance of thermal particles in MARS-K computations, a lower critical flow speed, i.e. the minimum speed needed for full suppression of the mode, is obtained. Likewise the eigenmode structure is also modified by different rotation profiles in the kinetic results.

Damping of Sound Waves in Strong Centrifugal Field

A method for numerical calculation of the sound wave damping and dispersion law in a strong centrifugal field of the order of 106 g is considered. The damping is defined from the width of the resonance peak for different wave vectors. In the strong centrifugal field damping of the sound waves essentially exceeds the damping in the quiescent gas.

Regularized 13 moment equations for hard sphere molecules: Linear bulk equations

The regularized 13 moment equations of rarefied gas dynamics are derived for a monatomic hard sphere gas in the linear regime. The equations are based on an extended Grad-type moment system, which is systematically reduced by means of the Order of Magnitude Method [H. Struchtrup, “Stable transport equations for rarefied gases at high orders in the Knudsen number,” Phys. Fluids 16(11), 3921–3934 (2004)]10.1063/1.1782751. Chapman-Enskog expansion of the final equations yields the linear Burnett and super-Burnett equations. While the Burnett coefficients agree with literature values, this seems to be the first time that super-Burnett coefficients are computed for a hard sphere gas. As a first test of the equations the dispersion and damping of sound waves is considered.

Damping of sound waves in superfluid nucleon-hyperon matter of neutron stars

We consider sound waves in superfluid nucleon-hyperon matter of massive neutron-star cores. We calculate and analyze the speeds of sound modes and their damping times due to the shear viscosity and nonequilibrium weak processes of particle transformations. For that, we employ the dissipative relativistic hydrodynamics of a superfluid nucleon-hyperon mixture, formulated recently [1]. We demonstrate that the damping times of sound modes calculated using this hydrodynamics and the ordinary (nonsuperfluid) one, can differ from each other by several orders of magnitude.

Damping of sound waves in the terahertz range and strength of the boson peak

By applying a new two-step line-shape analysis to inelastic neutron and x-ray scattering spectra of glassy systems, we were able to resolve the acoustic excitations from the low-frequency excess modes and to accurately estimate the damping of sound waves in the terahertz frequency range. Using this approach, we estimated the damping parameter for terahertz acoustic waves in a wide class of chemically different glasses and did a quantitative comparison of the results with prediction of theoretical models. By comparing the estimates of the mean-free path of the acoustic modes in different glasses and the corresponding boson peak strengths, we show the existence of a simple correlation between these two quantities. The relationship between attenuation of the terahertz acoustic modes, strength of the boson peak, and fragility is discussed.

Effect of fluid compressibility on the flow caused by a sudden impulse applied to a sphere immersed in a viscous fluid

The flow of a viscous compressible fluid about a sphere suddenly set in motion by an applied impulse is studied on the basis of linearized hydrodynamic equations. Mixed slip-stick boundary conditions are assumed to hold at the surface of the sphere. An analytic expression for the flow pattern is presented for an idealized fluid in which the damping of sound waves is neglected. The time dependence of the pressure part and the viscous part of the fluid momentum is investigated. It is shown that at long times, one-third of the imparted momentum resides in the pressure part.

Wave kinetic description of Bogoliubov oscillations in the Bose–Einstein condensate

Abstract A wave kinetic equation, exactly equivalent to the Gross–Pitaevskii equation, describing the dynamics of bosons is presented. The resulting wave kinetic description is used to study the Bogoliubov oscillations of the Bose–Einstein condensate (BEC). An exact quantum dispersion relation and an expression for Landau damping of sound waves in the BEC are derived. Conditions for wave instability are also established. The range of validity of previous quasi-classical results is clarified.

NMR measurements and hydrodynamic simulations of phase-resolved velocity distributions within a three-dimensional vibrofluidized granular bed

We report the results of nuclear magnetic resonance imaging experiments on vertically vibrated granular beds of mustard grains. A novel spin-echo velocity profiling technique was developed that allows granular temperature, mean velocity and packing fraction distributions within the three-dimensional cell to be measured as a function of both vertical position and vibration phase. Bimodal velocity distributions were observed at certain portions of the vibration cycle, and in general the ability to acquire time-resolved data demonstrated the significant distortions to the velocity distributions and the systematic errors in calculated temperature distributions that may arise with time-averaged measurements. The experimental behaviour was compared with predictions from a time-varying one-dimensional hydrodynamic model using the experimental parameters as input to the code. In both cases, damping of longitudinal sound waves was linked to significant volume heating effects, which contrasts with the usual heat transport mechanism (i.e. diffusion from the boundaries) currently assumed in most steady-state models. This leads to a new explanation for the counterintuitive upturn in granular temperature in vibrofluidized granular beds, based on amplification and damping of sound waves in the high-altitude region.

Neutron scattering evidence on the nature of the boson peak

Literature and unpublished neutron spectra of seven classical glass formers in the bosonpeak region are evaluated in terms of eigenvalue densities. The boson peak translates into atrue maximum of the eigenvalue density, lying about a factor of two higher than theboson peak eigenvalue and followed by a slow decrease towards higher eigenvalues.We interpret the data in terms of a crossover from sound waves at low eigenvaluesto a more or less constant eigenvalue density at high eigenvalues. TheIoffe–Regel limit of strong sound wave damping lies at the crossover eigenvalueλc, slightly higher than the boson peak. A four-parameter fit form based on the soft-potentialmodel provides reasonable fits up to and including the beginning of the slowdecrease. The parameters from the neutron data agree within their error bars withthose determined from the low-temperature anomalies in the heat capacity andin the thermal conductivity. The results indicate that the strong scattering ofsound waves in glasses is due to the interaction with the excess vibrational modes.

Measurement of resistive wall mode stability in rotating high-β DIII-D plasmas

Toroidal plasma rotation of the order of a few per cent of the Alfvén velocity can stabilize the resistive wall mode (RWM) and extend the operating regime of tokamaks from the conventional, ideal magnetohydrodynamic (MHD) no-wall limit up to the ideal MHD ideal-wall limit. The stabilizing effect has been measured in DIII-D passively by measuring the critical plasma rotation required for stability and actively by probing the plasma with externally applied resonant magnetic fields. The comparison of these measurements to predictions of rotational stabilization of the sound wave damping and of the kinetic damping model using the MARS-F code results in qualitative agreement, but also indicates the need for further refinement of the measurements and models.

Damping of sound waves propagating in optically thin plasmas

The effects of the second viscosity on sound waves propagating in plasmas at thermochemical equilibrium are analyzed. It is found that this viscosity can be more important than the dynamical viscosity as well as than the thermometric conductivity, in particular, in photoionized plasmas with arbitrary metallicity Z. The strongest damping per unit wavelength always occurs for sound waves with a period of the order of the ionization relaxation time. Additionally, such a damping is more efficient for plasmas with solar abundances (Z=1) than for primordial plasmas (Z=0). In collisionally heated pure hydrogen plasmas the second viscosity becomes zero.

Radiation of sound from a charged dust particle moving at high velocity

Radiation of sound waves from a rapidly moving charged dust particle in dusty plasmas is considered. For the limiting case, where the dusty plasma can be described by a Vlasov-type equation, analytical expressions are derived for the fully three-dimensional radiation pattern, including the effects of the Landau damping of sound waves. The results are illustrated by simple cases, which can be expressed by known functions. The radiation pattern obtained can be used to determine the sound speed, but also the temperature ratio of dust and singly charged particles, electrons, and ions. The analysis applies equally well for a fast charged dust particle propagating through a thermal plasma. The analytical results are supported by numerical simulations, including also a study of magnetized plasmas which are not as easily tractable for analytical investigations.

Sound damping in ferrofluids: magnetically enhanced compressional viscosity.

The damping of sound waves in magnetized ferrofluids is investigated and shown to be considerably higher than in the nonmagnetized case. This fact may be interpreted as a field-enhanced, effective compressional viscosity-in analogy to the ubiquitous field-enhanced shear viscosity that is known to be the reason for many unusual behaviors of ferrofluids under shear.

Minimal model of the phonon-phason dynamics in icosahedral quasicrystals and its application to the problem of internal friction in thei-AlPdMn alloy

Different existing elastodynamical models of icosahedral quasicrystals are analyzed. The simplest minimal model of the phonon-phason dynamics is formulated. Physical restrictions and possible applications of the proposed model are considered. Several generalizations of the minimal model are discussed. It is shown that the phonon-phason coupling induces a resonant absorption peak of low-frequency sound waves in the temperature region corresponding to a thermal activation of phason excitations. The maximum value of the logarithmic decrement of the sound wave damping depends on the propagation direction and the wave polarization. The anisotropy is proportional to the square of the phonon-phason coupling constant ${K}_{3}.$ Our estimation shows that the effect can be resolved experimentally if the relative value of ${K}_{3}$ is not negligible with respect to four other elastic constants of the icosahedral quasicrystal. Namely, the difference should not exceed two orders of magnitude.