Mark F Hamilton

Dynaflow, Inc., Jessup, Maryland, United States

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Publications (166)211.78 Total impact

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    ABSTRACT: This work considers nonlinear propagation in a medium consisting of a low volume fraction of metamaterial inclusions dispersed in a fluid-like material. The metamaterial inclusions of interest are assumed to possess non-monotonic stress-strain constitutive relations, which results in regimes of negative stiffness. For modeling purposes, the constitutive relation for these inclusions is approximated with an expansion to third order in volume strain with coefficients that can be tuned with the geometry of the metamaterial structure and ambient pressure. A far-reaching goal of this research is to model the hysteretic response of the heterogeneous medium resulting from metamaterial inclusion snapping events and the associated effect on acoustic disturbances that cycle through regimes of both positive and negative stiffness. As an initial step, results are presented here for small but finite-amplitude disturbances limited to local regions of the constitutive relation. For this case, the quadratic and cubic nonlinearity parameters B/A and C/A, respectively, as traditionally defined for fluids are obtained. An evolution equation with both quadratic and cubic nonlinearity is also obtained. Numerical solutions of the evolution equation illustrate nonlinear waveform distortion as a function of the volume fraction and constitutive behavior of the inclusions. [Work supported by ARL:UT McKinney Fellowship in Acoustics.].
    The Journal of the Acoustical Society of America 11/2013; 134(5):4027. · 1.65 Impact Factor
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    ABSTRACT: In a previous presentation [J. Acoust. Soc. Am. 133, 3327 (2013)], an experimental model study of a pneumatic infrasound source that utilizes the pulsation of compressed air was discussed. The present paper discusses new measurements and theoretical modeling efforts that are currently underway. Measurements of the source level, directivity patterns, propagation loss, and frequency response are presented and analyzed. Acoustic and aerodynamic models are presented and discussed with a focus on modeling and predicting nearfield system performance using multipole (monopole, dipole, and quadrupole) representations of the sound source. Measurement techniques and engineering considerations are addressed, as are physical interpretations of the process. [Work supported by ARL:UT Austin.].
    The Journal of the Acoustical Society of America 11/2013; 134(5):4192. · 1.65 Impact Factor
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    ABSTRACT: There is concern that underwater noise generated by marine construction activities and radiated by towers supporting offshore wind turbines may disturb marine mammals, or interfere with passive sensors and communication equipment. In order to understand these effects a semi-analytic frequency-domain model was developed previously for the sound radiated in the water column by a pulsating cylindrical structure embedded in horizontally stratified layers of viscoelastic sediment. This model was in turn coupled to a parabolic equation code for long-range propagation over range-dependent environments [Hay et al., J. Acoust. Soc. Am. 133, 3396 (2013)]. A time-domain version of this model is now presented which enables simulation of impulsive sound sources such as those due to underwater pile driving, and pulsed tonal sources appropriate for use in a finite-sized laboratory tank. In order to validate the model a scaled physical model, consisting of a laboratory tank and metallic cylindrical tube driven in the high kilohertz frequency range, was constructed. Simulations will be presented for a variety of sound sources, and preliminary comparisons with measurements from the scaled model experiments will be made.
    The Journal of the Acoustical Society of America 11/2013; 134(5):4023. · 1.65 Impact Factor
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    ABSTRACT: To help resolve certain practical issues with acoustical methods for humanitarian landmine detection, we have researched using a pulsed, standoff source method for acoustical excitation of the buried mine [J. Acoust. Soc. Am. 130, 2541 (2011); J. Acoust. Soc. Am. 133, 3457 (2013)]. Pulses consisting of two primary frequencies are used in order to search for induced nonlinear vibrations at interaction frequencies such as the sum frequency, which arise due to nonlinear interaction at the mine/soil interface. To model the pulsed excitation, we employ a fully nonlinear time-domain implementation of the lumped-element model of nonlinear soil/mine interaction introduced by Donskoy et al. [J. Acoust. Soc. Am. 117, 690 (2005)]. Modeling is compared with experimental results, which are obtained with bi-frequency pulses exciting a soil with a buried landmine replica, instrumented with a geophone and a nearby microphone. Cases investigated include: (1) target only, (2) buried target under disturbed soil, (3) disturbed soil only, and (4) undisturbed soil. Excitation both on and off the resonance of the buried mine is also investigated, as is burial in different soil types at various depths. [Work supported by the ARL:UT McKinney Fellowship in Acoustics.].
    The Journal of the Acoustical Society of America 11/2013; 134(5):4129. · 1.65 Impact Factor
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    ABSTRACT: A parabolic equation describing the propagation of collimated shear wave beams in isotropic elastic solids was derived by Zabolotskaya [Sov. Phys. Acoust. 32, 296-299 (1986)], and was seen to contain both cubic and quadratic nonlinear terms at leading order. While second-order nonlinear effects vanish for the quasi-planar case of linearly-polarized shear wave beams, the importance of quadratic nonlinearity for more complicated polarizations is not yet well understood. The current work investigates the significance of quadratic nonlinearity by considering second-harmonic generation in shear wave beams generated by a certain class of source polarizations that includes such cases as radial and torsional polarization, among others. Corresponding to such beams with Gaussian amplitude shading, analytic solutions are derived for the propagated beam at the source frequency and the second harmonic. Diffraction characteristics are discussed, and special attention is paid to the relationship between the source polarization of the beam and the polarization of the subsequently generated second harmonic. Finally, suggestions are made for possible experiments that could be performed in tissue phantoms, exploiting the theoretical results of this work. [Work supported by the ARL:UT McKinney Fellowship in Acoustics.].
    The Journal of the Acoustical Society of America 11/2013; 134(5):3997. · 1.65 Impact Factor
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    ABSTRACT: Underwater noise due to both marine pile driving and offshore wind farm operation is not only radiated directly from the pile into the water, but also from the seabed surrounding the pile. While there is much interest in mitigating the noise from these activities, a better understanding of the source mechanisms and propagation is needed to determine optimal strategies for noise abatement. A recent analytical model of the acoustic field radiated by submerged piles includes radiation from the pile directly into the water and into a stratified viscoelastic sediment as well as propagation into a shallow water waveguide from both the direct and sediment radiation paths [Hay et al., Proceedings of Meetings on Acoustics 19, 070038 (2013)]. As a step towards validating this model, scale-model experiments were conducted in the high kilohertz frequency range with a model pile consisting of a mechanically excited metallic tube inserted into a laboratory tank filled with two stratified layers to simulate the water/sediment interface. Measurements of the acoustic field in the experiment are compared with the model predictions, and the relevance of these results to implementing noise abatement strategies will be discussed. [Work supported by ARL:UT IR&D.].
    The Journal of the Acoustical Society of America 11/2013; 134(5):4060. · 1.65 Impact Factor
  • Mark F Hamilton
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    ABSTRACT: Interest in characterizing nonlinearity in jet noise has motivated consideration of an effective Gol'dberg number for diverging waves [Baars and Tinney, Bull. Am. Phys. Soc. 57, 17 (2012)]. Fenlon [J. Acoust. Soc. Am. 50, 1299 (1971)] developed expressions for the minimum value of Γ, the Gol'dberg number as defined for plane waves, for which shock formation occurs in diverging spherical and cylindrical waves. The conditions were deduced from a generalized Khokhlov solution and depend on the ratio xsh/r0, where r0 is source radius, and xsh the plane-wave shock formation distance for Γ=∞. Alternatively, by taking the ratio of the nonlinear and thermoviscous terms in Fenlon's Eq. (2), it is proposed here that effective Gol'dberg numbers may be identified for spherical and cylindrical waves: Λ=Γexp(-πxsh/2r0) and Λ=Γ/(1 + πxsh/4r0), respectively. For a given value of Λ, the diverging waves achieve approximately the same degree of nonlinear distortion as a plane wave for which the value of Γ is the same. Conversely, to achieve the same degree of nonlinear distortion as a plane wave with a given value of Γ, the value of Γ for, e.g., a spherical wave must be larger by a factor of exp(πxsh/2r0). Extensions to other spreading laws are presented.
    The Journal of the Acoustical Society of America 11/2013; 134(5):4099. · 1.65 Impact Factor
  • Derek C Thomas, Yurii A Ilinskii, Mark F Hamilton
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    ABSTRACT: Most common methods to include the effects of liquid compressibility in models for single-bubble dynamics rely on series expansions to some order in the inverse of the sound speed in the liquid. It has been shown that the Keller-Miksis model for single-bubble dynamics can be obtained from a series expansion of a delay differential equation related to the Rayleigh-Plesset equation for a single bubble. The iterative approach used to obtain the series expansion of the delay-based model becomes unworkable for more complicated models of bubble dynamics. Therefore, to provide an alternative, simpler method to model the effects of liquid compressibility, the delay differential equation model proposed by Ilinskii and Zabolotskaya [J. Acoust. Soc. Am. 92, 2837 (1992)] is analyzed directly. The results of the delay-based formulations are compared to those produced by models based on common series expansions. Alternative formulations of the delay differential equation are also considered and compared.
    The Journal of the Acoustical Society of America 11/2013; 134(5):3991. · 1.65 Impact Factor
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    ABSTRACT: Acoustic radiation force on a scatterer in tissue depends on the compressibility and shear modulus of both the tissue and the scatterer. This force is related to the monopole and dipole scattering coefficients. The finite shear modulus of the tissue decreases the radiation force in comparison with the force exerted on the same scatterer surrounded by liquid. Shear moduli for soft tissue range from several kilopascals (breast, liver) to tens of kilopascals and higher for cornea, cartilage, and cancerous tissue. As reported previously, the radiation force on a bubble in tissue having 100 kPa shear modulus is 50% less than if the bubble is in water. This difference decreases for scatterers with finite shear moduli, examples of which are reported here. Additionally, displacement of a scatterer due to radiation force is inversely proportional to the shear modulus of the tissue, which permits measurement of the latter. Experiments demonstrating this technique are reviewed. In these experiments, the radiation force is applied to a gas microbubble produced by laser-induced optical breakdown, while displacement of the microbubble is measured by high-frequency ultrasound as a function of time. Results are reported for tissue-mimicking phantoms and animal crystalline lenses in vitro.
    The Journal of the Acoustical Society of America 11/2013; 134(5):4009. · 1.65 Impact Factor
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    Derek C. Thomas, Yurii A. Ilinskii, Mark F. Hamilton
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    ABSTRACT: Various models for interacting spherical bubbles in a compressible liquid based on delay differential equations are considered. It is shown that most previously proposed models for interacting spherical bubbles in a compressible liquid based on the Keller-Miksis and Gilmore-Akulichev models are unstable for closely spaced bubbles. A new model for a single spherical bubble in a compressible liquid is proposed and used to derive a stable model for interacting bubbles. A qualitative comparison to the results of direct numerical integration of the fluid equations of motion suggests that the new model provides more accurate results than the standard Keller-Miksis or Gilmore-Akulichev models for single bubble dynamics.
    10/2013;
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    ABSTRACT: A model is developed for a pulsating and translating gas bubble immersed in liquid in a channel formed by two soft, thin elastic parallel layers having densities equal to that of the surrounding liquid and small, but finite, shear moduli. The bubble is nominally spherical but free to undergo small shape deformations. Shear strain in the elastic layers is estimated in a way which is valid for short, transient excitations of the system. Coupled nonlinear second-order differential equations are obtained for the shape and position of the bubble, and numerical integration of an expression for the liquid velocity at the layer interfaces yields an estimate of the elastic layer displacement. Numerical integration of the dynamical equations reveals behavior consistent with laboratory observations of acoustically excited bubbles in ex vivo vessels reported by Chen et al. [Phys. Rev. Lett. 106, 034301 (2011) and Ultrasound Med. Biol. 37, 2139-2148 (2011)].
    The Journal of the Acoustical Society of America 08/2013; 134(2):1454-62. · 1.65 Impact Factor
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    ABSTRACT: The analysis presented at the previous ASA meeting related to investigation of the acoustic radiation force on a sphere embedded in a soft elastic medium with shear modulus that is several orders of magnitude smaller than its bulk modulus. The acoustic field was assumed to be axisymmetric and the spherical scatterer to be located on the axis of the acoustic beam. When one of these conditions is violated, the problem loses its symmetry. In this talk, the acoustic radiation force is considered in the more general case of nonaxisymmetric fields. The calculation is performed in Lagrangian coordinates. All acoustic fields, incident as well as scattered, depend on all three spherical coordinates. The incident and scattered waves, which include both potential and solenoidal parts, are expanded with respect to spherical harmonics. An analytical expression for the acoustic radiation force derived in this investigation may contain as many spherical harmonics as needed. In limiting cases when the scatterer is in liquid and only two modes, monopole and dipole, remain in the scattered fields, the solution for the acoustic radiation force recovers the results reported by Gor'kov [Sov. Phys. Doklady 6, 773 (1962)]. [Work supported by NIH DK070618 and EB011603.].
    The Journal of the Acoustical Society of America 05/2013; 133(5):3237. · 1.65 Impact Factor
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    ABSTRACT: Sustained tonal noise radiated by towers supporting offshore wind turbines contains energy in frequency bands that may disturb marine mammals, or interfere with passive sonar and seismic sensors and underwater communication equipment. Understanding the generation and propagation of underwater noise due to the operation of wind farms is important for determining strategies for mitigating the environmental impact of these noise sources. An analytic model based on a Green's function approach was previously developed for the sound radiated in the water column by a pulsating cylindrical structure embedded in horizontally stratified layers of viscoelastic sediment [Hay et al., J. Acoust. Soc. Am. 130, 2558 (2011)]. This model has since been adapted to include relaxation and viscous losses in seawater and empirical loss factors for the sedimentary layers. In order to validate the model simulations were compared with reported measurements collected near an operating wind turbine that include radial acceleration of the tower, taken to be the source condition, and sound pressure levels in the water column. For long-range propagation over range-dependent environments, the analytic model has been coupled to a parabolic equation code. Simulations are presented for several bathymetries, sediment types, and tower array configurations. [Work supported by Department of Energy DE-EE0005380.].
    The Journal of the Acoustical Society of America 05/2013; 133(5):3396. · 1.65 Impact Factor
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    ABSTRACT: Previous models and experiments have shown that direction of bubble translation near a viscoelastic layer depends on both the standoff distance of the bubble and the elastic properties of the layer. Here the individual forces due to the incident sound field and the field reflected from the viscoelastic layer are shown to compete with one another and ultimately determine the direction of bubble translation. In addition, many other factors pertinent to the direction of bubble translation such as the incident acoustic waveform, the phase and propagation direction of the incident field, and the radial bubble dynamics are considered. The force due to the viscoelastic layer is calculated using a Green's function, which takes into account elastic waves and viscosity in the layer and the viscous boundary layer at the solid-liquid interface. [Work supported by the ARL:UT McKinney Fellowship in Acoustics and NIH DK070618.].
    The Journal of the Acoustical Society of America 05/2013; 133(5):3409. · 1.65 Impact Factor
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    ABSTRACT: An array of 16 loudspeakers, deployed along a segment of the base of a right circular cone, was used to focus intense tone bursts at low audio frequencies on a soil, with and without a buried target, having a compliant lid. The response of the target site was examined as a function of source frequency, intensity level, and excitation signal type, including multi-tone radiations. Nonlinear interaction to produce sum and difference frequencies at the target site was examined and compared with observations of Korman and Sabatier [J. Acoust. Soc. Am. 116, 3354 (2004)]. [Work supported by the ARL:UT McKinney Fellowship in Acoustics.].
    The Journal of the Acoustical Society of America 05/2013; 133(5):3457. · 1.65 Impact Factor
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    ABSTRACT: Carefully timed tandem microbubbles have been shown to produce directional and targeted membrane poration of individual cells in microfluidic systems, which could be of use in ultrasound-mediated drug and gene delivery. This study aims at contributing to the understanding of the mechanisms at play in such an interaction. The dynamics of single and tandem microbubbles between two parallel plates is studied numerically and analytically. Comparisons are then made between the numerical results and the available experimental results. Numerically, assuming a potential flow, a three-dimensional boundary element method (BEM) is used to describe complex bubble deformations, jet formation, and bubble splitting. Analytically, compressibility and viscous boundary layer effects along the channel walls, neglected in the BEM model, are considered while shape of the bubble is not considered. Comparisons show that energy losses modify the bubble dynamics when the two approaches use identical initial conditions. The initial conditions in the boundary element method can be adjusted to recover the bubble period and maximum bubble volume when in an infinite medium. Using the same conditions enables the method to recover the full dynamics of single and tandem bubbles, including large deformations and fast re-entering jet formation. This method can be used as a design tool for future tandem-bubble sonoporation experiments.
    Journal of Fluid Mechanics 02/2013; 716. · 2.29 Impact Factor
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    ABSTRACT: Carefully timed tandem microbubbles have been shown to produce directional and targeted membrane poration of individual cells in microfluidic systems, which could be of use in ultrasound-mediated drug and gene delivery. This study aims at contributing to the understanding of the mechanisms at play in such an interaction. The dynamics of single and tandem microbubbles between two parallel plates is studied numerically and analytically. Comparisons are then made between the numerical results and the available experimental results. Numerically, assuming a potential flow, a three-dimensional boundary element method (BEM) is used to describe complex bubble deformations, jet formation, and bubble splitting. Analytically, compressibility and viscous boundary layer effects along the channel walls, neglected in the BEM model, are considered while shape of the bubble is not considered. Comparisons show that energy losses modify the bubble dynamics when the two approaches use identical initial conditions. The initial conditions in the boundary element method can be adjusted to recover the bubble period and maximum bubble volume when in an infinite medium. Using the same conditions enables the method to recover the full dynamics of single and tandem bubbles, including large deformations and fast re-entering jet formation. This method can be used as a design tool for future tandem-bubble sonoporation experiments.
    · 2.29 Impact Factor
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    ABSTRACT: Underwater noise generated by pile driving, rotating machinery, or towers supporting offshore wind turbines may disturb marine life and inhibit detection of coastal activities via passive sonar and seismic sensors. Noise abatement techniques have therefore been proposed to limit the propagation of such noise into the far field, and many of these employ a curtain of freely-rising bubbles or tethered encapsulated bubbles to surround the towers [Lee et al., J. Acoust. Soc. Am. 131, 3507(A) (2012)]. An analytic model, based on a Green's function approach, is presented for the passive noise suppression provided by a discrete number of bubbles surrounding submerged point sources or pulsating cylindrical towers above horizontally-stratified layers of sediment. The sediment layers are modeled as viscoelastic media and the Green's function is derived via angular spectrum decomposition [Hay et al., J. Acoust. Soc. Am. 129, 2477(A), (2011)]. Simulations in which the bubbles are assumed to react independently to the incident field will be compared to those in which bubble-bubble interaction is taken into account. The effects of bubble size distributions and void fractions on noise suppression will be investigated for different source configurations. [This work was supported by the Department of Energy under Grant DE-EE0005380.].
    The Journal of the Acoustical Society of America 09/2012; 132(3):2061. · 1.65 Impact Factor
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    ABSTRACT: Accurate models for clusters of interacting bubbles are sought for both biomedical and underwater applications. Multiple bubble models have been developed by treating the bubbles as a system of interacting oscillators. The models are obtained initially for bubbles in an incompressible, irrotational, and inviscid liquid; additional effects are included in an ad hoc fashion. The existing oscillator models for the dynamics of interacting bubbles are improved by including the effect of liquid compressibility. In particular, while existing models have been improved by including propagation delays in the bubble interactions, the effect of bubble interaction on radiation damping has not been considered. The current work develops corrections for the radiation damping of coupled bubbles in both linear and nonlinear models of bubble dynamics. These corrections eliminate certain instabilities that have been observed in delay differential equation models of coupled-bubble dynamics. Additionally, an increase in the coupling strength between bubbles undergoing high-amplitude radial motion is predicted when coupled radiation damping is included; this increase in coupling strength strongly affects the predicted motion of the system and the resultant pressure in the surrounding medium. [Work supported by the ARL:UT McKinney Fellowship in Acoustics and NIH DK070618.].
    The Journal of the Acoustical Society of America 09/2012; 132(3):1919. · 1.65 Impact Factor

Publication Stats

637 Citations
211.78 Total Impact Points

Institutions

  • 2013
    • Dynaflow, Inc.
      Jessup, Maryland, United States
  • 2012–2013
    • Brigham Young University - Provo Main Campus
      • Department of Physics and Astronomy
      Provo, Utah, United States
  • 1989–2013
    • University of Texas at Austin
      • Department of Mechanical Engineering
      Port Aransas, TX, United States
  • 2009
    • Universiteit Twente
      Enschede, Overijssel, Netherlands
  • 2007
    • Stanford University
      • E. L. Ginzton Laboratory
      Palo Alto, CA, United States
  • 2003
    • National Institute of Standards and Technology
      Maryland, United States