A significant density of pelagic fish and fish schools in underwater environments can lead to higher acoustic reverberation, thus affecting applications, such as environmental remote sensing or fish abundance estimation. Fish aggregations can also increase absorptivity in the water column and increase transmission loss. This phenomenon is described by bio-alpha, i.e., the attenuation coefficient within the scattering layer. Theoretical models and historical databases exist which describe volume scattering strength in underwater environments of interest. Additionally, effects of bio-alpha on transmission loss have been studied [for example, see Diachok, J. Acoust. Soc. Am. 105, 2107–2128 (1999)]. However, less consideration has been given to quantifying the effect of bio-alpha on volume reverberation. Presented here is a simple volume reverberation model which directly accounts for biological absorptivity due to bio-alpha in the scattering layer. Representative cases for different frequencies and environments are presented. Based on the known diurnal behavior of many species of pelagic fish, it is shown in nighttime conditions that reverberation is high but decays quickly whereas during daytime reverberation is relatively lower with a relatively smaller rate of decay. [Work supported by the ARL:UT Internal Research and Development Program.]

A general theory for obtaining spherical wave function expansion coefficients for a sound beam transmitted by a planar velocity source is presented. By neglecting evanescent wave components and thus making the proposed method only approximate in the near field, it is shown that these coefficients can be obtained for any expansion point using just the normal velocity condition in the source plane. Additionally, simplifications are presented for axisymmetric sources. Results are compared with direct numerical evaluation of the Rayleigh integral for source conditions corresponding to a circular and rectangular piston. The present theory can be used in calculations of acoustic scattering and radiation force for spherical objects, or in spherical acoustical holography applications.

An analytical solution is developed for the acoustic radiation force and torque caused by an arbitrary sound field that is incident on a compressible spheroid of any size near a planar boundary that is either rigid or pressure release. The analysis is an extension of a recent solution for a compressible sphere near a planar boundary [Simon and Hamilton, J. Acoust. Soc. Am. 153, 627-642 (2023)]. Approximations that account for a boundary formed by a two-fluid interface may be incorporated as in the previous analysis for a sphere. The present solution is based on expansions of the total acoustic pressure field in spheroidal wave functions and the use of addition theorems. Verification of the solution is accomplished by comparison with a finite element model. Examples are presented for incident fields that are either plane or spherical waves. Effects resulting from the presence of the boundary are studied by comparing the full theory with a simplified model in which multiple scattering is neglected. Numerical implementation of the proposed solution is also discussed.

Acoustic radiation force on a sphere in an inviscid fluid near a planar boundary, which may be rigid or pressure release, is calculated using spherical wave functions to expand the total pressure field. The condition at the boundary is satisfied with the addition of a reflected wave and an image sphere. The total pressure field, which is exact in the linear approximation, is composed of the incident field, the reflected field, and the scattered fields due to the physical sphere and the image sphere. The expansion coefficients for the pressure field are used to evaluate the acoustic radiation force on the sphere using a known analytical expression obtained from integration of the radiation stress tensor. Calculations illustrate the influence of multiple scattering effects on the radiation force acting on the sphere. The model applies to compressible and elastic spheres and for any incident field structure. An approximation is introduced that extends the analytical model to other types of interfaces, including a fluid-fluid interface. The analytical model is validated by comparisons with an independent finite element model.

An analytical approach for calculating radiation force and torque on a sphere or spheroid near a rigid or pressure release boundary due to an arbitrary incident acoustic field was developed recently by the authors [Proc. Meet. Acoust. 48, 045004 (2022)]. In that approach, the linear scattering problem is solved using the method of images along with expansions of the acoustic fields in spherical or spheroidal wave functions. The expansion coefficients can then be substituted into an existing expression to obtain the radiation force and torque on the object. In the present work, the aforementioned theory is extended to include penetrable interfaces and impedance boundaries using an approximation of the interfacial boundary conditions. For fluid-fluid interfaces, the object can be placed on either side of the interface with respect to the incident field. This approximate analytical approach is computationally efficient and compares well with the results from an independent finite element model. In addition, an experiment was conducted with a plastic sphere submerged in water and positioned near a boundary. Results from the experiment are discussed in relation to the analytical model. [BES is supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics.]

Acoustic radiation force and torque on a sphere or spheroid near a pressure release or rigid planar boundary are calculated using expansions of the pressure field in terms of both spherical and spheroidal wavefunctions. There is no restriction on the size or aspect ratio of the object. The condition at the boundary is satisfied through the use of a virtual (image) object that is a mirror reflection of the physical object with respect to the boundary. The boundary conditions at the object surface are satisfied after expressing the expansions of each component of the total field in a common coordinate frame using addition theorems for spherical and spheroidal wavefunctions. The radiation force and torque are expressed as a summation of terms involving products of the coefficients in spherical wave expansions of the incident and scattered fields. Results from the present analytical model are compared with those from a finite element model. The importance of object-boundary interaction effects is assessed by comparing the radiation force predicted by the proposed theory with that obtained by a similar model that does not include the image.

Acoustic radiation force and torque on a spheroid of arbitrary size near a rigid or pressure release interface are calculated using expansions of the pressure field in terms of both spherical and spheroidal wave functions. The spheroidal expansion coefficients are obtained by satisfying the boundary conditions at the interface and at the surface of the spheroid. Conditions at the interface are satisfied using a virtual (image) spheroid, while satisfying conditions at the spheroid surface require the use of addition theorems for spheroidal wave functions. The radiation force and torque are expressed as a summation of terms involving products of the coefficients in spherical wave expansions of the incident and scattered fields [Ilinskii et al., J. Acoust. Soc. Am. 144, 568–576 (2018)]. Far-field asymptotes are used to relate the spheroidal and spherical harmonic expansion coefficients analytically. Results from the present analytical model are compared with those from a finite-element model. The effect of the interface on the radiation force and torque relative to that on a spheroid in a free field is discussed. [B.E.S. is supported by the Applied Research Laboratories Chester M. McKinney Graduate Fellowship in Acoustics.]

AbstractAlthough neuroimaging provides powerful tools for assessing brain structure and function, their utility for elucidating mechanisms underlying neuropsychiatric disorders is limited by their sensitivity to head motion. Several publications have shown that standard retrospective motion correction and arduous quality assessment are insufficient to fully remove the deleterious impacts of motion on functional (fMRI) and structural (sMRI) neuroimaging data. These residual errors tend to be correlated with age and clinical diagnosis, resulting in artifactual findings in studies of clinical, developmental, and aging populations. As such there is a continued need to explore and evaluate novel methods for reducing head motion, and their applicability in these populations. Recently, a custom-fitted styrofoam head mold was reported to reduce motion across a range of ages, mostly adolescents, during a resting state fMRI scan.In the present study, we tested the efficacy of these head molds in a sample exclusively of young children (N = 19; mean age = 7.9 years) including those with ADHD (N = 6). We evaluated the head mold’s impact on head motion, data quality, and analysis results derived from the data. Importantly, we also evaluated whether the head molds were tolerated by our population. We also assessed the extent to which the head mold’s efficacy was related to anxiety levels and ADHD symptoms. In addition to fMRI, we examined the head mold’s impact on sMRI by using a specialized sequence with embedded volumetric navigators (vNAV) to determine head motion during sMRI. We evaluated the head mold’s impact on head motion, data quality, and analysis results derived from the data. Additionally, we conducted acoustic measurements and analyses to determine the extent to which the head mold reduced the noise dosage from the scanner. We found that some individuals benefited while others did not improve significantly. One individual’s sMRI motion was made worse by the head mold. We were unable to identify predictors of the head mold response due to the smaller sample size. The head molds were tolerated well by young children, including those with ADHD, and they provided ample hearing protection. Although the head mold was not a universal solution for reducing head motion and improving data quality, we believe the time and cost required for using the head mold may outweigh the potential loss of data from excessive head motion for developmental studies.

A nonlinear, fractional, surface wave equation with a spatial derivative of second order was developed by Kappler, Shrivastava, Schneider, and Netz [Phys. Rev. Fluids 2, 114804 (2017)] for propagation along an elastic interface coupled to a viscous incompressible liquid. Linear theory for the attenuation and dispersion was developed originally by Lucassen [Trans. Faraday Soc. 64, 2221 (1968)]. Kappler et al. introduced a fractional time derivative to account for the Lucassen wave attenuation and dispersion, and they included quadratic and cubic nonlinearity associated with compression of the elastic interface. Presented here is an integrated form of their time domain equation for progressive waves that is first order in the spatial derivative. Solutions of this evolution equation capture the main features of waveforms predicted by the full model equation of Kappler et al., especially the formation and propagation of shocks, while the evolution equation can be solved numerically with substantially less computational cost. Approximate analytical expressions obtained from the evolution equation for the nonlinear propagation speed and attenuation of a compression pulse reveal that a threshold phenomenon discussed by Kappler et al. is due to competition between quadratic and cubic nonlinearity associated with a lipid monolayer interface.

Acoustic radiation force exerted on an object of arbitrary shape and composition by an arbitrary incident sound beam can be calculated using spherical harmonic expansions of the pressure field. The coefficients in the expansions of the incident and scattered fields, when substituted into existing models, determine the radiation force on the object. Analytical expressions for the coefficients of both the incident and scattered fields are available for very few cases, such as a plane wave incident on a rigid sphere. In the present work, finite element modeling is used to calculate the coefficients, and resulting radiation force, for a variety of incident fields and object geometries. Different compositions of the objects are also considered. Validation of the approach is demonstrated by comparison with semi-analytical results available for the radiation force exerted by progressive and standing plane waves scattered by compressible spheroids in different orientations with respect to the incident field. Motivation for this approach is development of a model that can be used to compare with direct measurements of radiation force on irregularly shaped objects of different compositions. [BES is supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics.]

Fractional calculus models used for biomedical ultrasound are associated with attenuation proportional to ωy, where y is typically in the range 1 < y < 2. To determine whether the attenuation and accompanying dispersion are sufficient to stabilize shock formation, the models are formulated as a Burgers equation with the traditional loss term replaced by a fractional derivative of order y. For y < 1 the resulting equation predicts unphysical solutions beyond the shock-formation distance. The second example pertains to nonlinear Lucassen interface waves, a model equation for which has been proposed to describe mechanical perturbations that accompany the transmission of nerve impulses. Linear Lucassen waves are defined by a second-order space derivative and a fractional time derivative of order 3/2, which falls between order 2 in the wave equation and order 1 in the diffusion equation. The resulting attenuation is proportional to ω3/4, and the corresponding nonlinear “fractional diffusive waves,” while strongly attenuated on the scale of a wavelength, may be lacking essential physics beyond the predicted shock-formation distance. Calculations are presented that determine wave amplitudes and propagation distances for which these two fractional calculus models may be of questionable physical significance due to nonlinearity. [B.E.S. is supported by the ARL:UT McKinney Fellowship in Acoustics.]

Linear theory for quasi-longitudinal surface wave propagation along an elastic interface coupled to a viscous, incompressible liquid was first developed by Lucassen [Trans. Faraday Soc. 1968]. Lucassen waves are modeled with a fractional diffusion-wave equation in which the order of the fractional time derivative is 3/2. Nonlinearity in the elastic interface was taken into account recently by Kappler et al. [Phys. Rev. Fluids 2017]. Nonlinear Lucassen interface waves exhibit certain features associated with the mechanical disturbance that accompanies the electric action potential in the biological membranes of nerve axons, such as the “all-or-none” principle in which wave speed and pulse shape change dramatically above some amplitude threshold. While Lucassen waves are highly damped, for nonlinear propagation the attenuation described by the fractional time derivative provides insufficient energy loss near regions where shocks form in the waveform, resulting in the failure of conventional numerical algorithms such as Runge-Kutta schemes. Presented here is a modified model equation for nonlinear Lucassen waves that includes viscoelastic effects in the interface. The inclusion of viscosity in the interface results in greater losses at shock fronts and increased stability for numerical calculations. [B.E.S. is supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics.]

A nonlinear, fractional, surface-wave equation was developed recently by Kappler et al. [Phys. Rev. Fluids 2, 114804 (2017)] for propagation along an elastic interface coupled to a viscous incompressible medium. Linear theory for attenuation and dispersion of such a wave was developed originally by Lucassen [Trans. Faraday Soc. 64, 2221 (1968)]. Kappler et al. employ a fractional derivative to account for the Lucassen attenuation and dispersion, and they include quadratic and cubic nonlinearity of the elastic interface. Presented here is a simplified form of their model equation for plane progressive waves. The resulting nonlinear evolution equation has the form of a Burgers equation but with a fractional derivative in place of the second derivative for viscosity, and with cubic as well as quadratic nonlinearity. In addition to facilitating analytical and numerical calculations, the evolution equation enables interpretation of a threshold phenomenon, revealed in numerical simulations presented by Kappler et al., as competition between quadratic and cubic nonlinearity. It is also suitable for determining critical source amplitudes above which Lucassen attenuation and dispersion alone cannot preclude formation of unphysical multivalued waveforms [Cormack and Hamilton, Wave Motion 85, 18 (2019)]. [BES and JMC were supported by the ARL:UT McKinney Fellowship in Acoustics.]

Fractional partial differential equations (FPDEs) with a time derivative of fractional order are used to describe wave motion in complex viscoelastic media with non-traditional equations of motion. Kappler et al. [Phys. Rev. Fluids 2, 114804 (2017)] derived a fractional diffusion-wave equation for a nonlinear Lucassen wave propagating along an elastic layer coupled to a viscous substrate. The fractional time derivative of order 3/2 in the linear form of this equation lies midway between order 1 for a diffusion process described by a parabolic equation, and order 2 for the traditional hyperbolic wave equation. The inclusion of nonlinear elasticity tends to inhibit purely progressive wave motion that is associated with classical nonlinear plane waves in fluids and solids, and which is described accurately by parabolic-like, Burgers-type evolution equations. In this work, a general FPDE is analyzed in a parameter space consisting of varying nonlinearity and time fractional orders. The focus is on conditions under which the FPDE can be modeled accurately with a Burgers-type evolution equation for progressive wave motion. The method of lines in combination with a general Runge-Kutta method for forward integration is used for numerical analysis. [B.E.S. is supported by the ARL:UT McKinney Fellowship in Acoustics.]

A three-dimensional, longitudinally invariant finite element model of acoustic propagation and reverberation in an ice-covered shallow water waveguide has been developed. The ice is modeled as both an elastic medium and a pressure release surface. Transmission loss levels are calculated and compared for both assumptions of ice. Using Fourier synthesis, the time-harmonic acoustic pressure results are transformed into the time domain, and reverberation levels are then compared for both models. Finally, using a fully three-dimensional version of the finite element model, compressional-to-shear wave conversion at the elastic ice and water interface is characterized to inform propagation mechanisms of acoustic waves in Arctic ice sheets. [Work supported by ONR, Ocean Acoustics and the Robert W. Young Award for Undergraduate Student Research in Acoustics.]

Although models of acoustic propagation in an ice-covered environment have been calculated using only finite elements, ray theory models can cover longer distances and higher frequency ranges much more efficiently. In this study, a hybrid approach is taken by calculating the reflection coefficient of the ice using finite elements over a range of frequencies and angles. These values are then inserted into a ray-theory model. Using this model, a study of the sensitivity of common approximations of the ice cover on acoustic propagation is conducted. For example, the ice can be described simply as a pressure release surface or much more complexly as an elastic body with range and depth geo-acoustic property variations. The hybrid finite element-ray theory model will be verified numerically by comparing it to a full finite element propagation model for appropriate ranges and frequencies. [Work sponsored by ONR, Ocean Acoustics.]

Finite element analysis provides an accurate way of calculating acoustic scattering from underwater objects. The method provides an exact solution to the Helmholtz equation to the order of the discretization. Although commercial finite element software is capable of solving fully 3D scattering problems, it has been previously shown by Zampolli et al. [J. Acoust. Soc. Am. 122, 1472–1485 (2007)] that 3D axisymmetric targets can be solved more efficiently using 2D geometry. This method uses an axial wavenumber decomposition technique, which simulates an incident plane wave from an off-axis direction. In this study, results from this analysis are converted from the frequency domain to the time domain using Fourier synthesis. Elastic spheres and cylinders are considered because the analytical solutions for scattering by these targets are known and can be used to verify the finite element results. The success of this model to simulate time domain scattering will inform the applicability of finite element analysis for more complex targets. [Work supported by ONR, Ocean Acoustics.]