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Scheuer KG, Romero FB, Hornig GJ, DeCorby RG. Ultrasonic spectroscopy of sessile droplets coupled to optomechanical sensors. LAB ON A CHIP 2023; 23:5131-5138. [PMID: 37937401 DOI: 10.1039/d3lc00609c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/09/2023]
Abstract
We describe a system for interrogating the acoustic properties of sub-nanoliter liquid samples within an open microfluidics platform. Sessile droplets were deposited onto integrated optomechanical sensors, which possess ambient-medium-noise-limited sensitivity and can thus passively sense the thermally driven acoustic spectrum of the droplets. The droplet acoustic breathing modes manifest as resonant features in the thermomechanical noise spectrum of the sensor, in some cases hybridized with the sensor's own vibrational modes. Excellent agreement is found between experimental observations and theoretical predictions, over the entire ∼0-40 MHz operating range of our sensors. As an application example, we used the technique to monitor the temporal evolution of evaporating droplets. With suitable control over droplet size and morphology, this technique has the potential for precision acoustic sensing of small-volume biological and chemical samples.
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Affiliation(s)
- K G Scheuer
- Ultracoustics Technologies Ltd., Sherwood Park, AB, T8A 3H5, Canada
| | - F B Romero
- ECE Department, University of Alberta, 9211-116 St. NW, Edmonton, AB, T6G 1H9, Canada.
| | - G J Hornig
- ECE Department, University of Alberta, 9211-116 St. NW, Edmonton, AB, T6G 1H9, Canada.
| | - R G DeCorby
- ECE Department, University of Alberta, 9211-116 St. NW, Edmonton, AB, T6G 1H9, Canada.
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Davy M, Besnier P, Del Hougne P, de Rosny J, Richalot E, Sarrazin F, Savin DV, Mortessagne F, Kuhl U, Legrand O. Diffuse field cross-correlations: Scattering theory and electromagnetic experiments. Phys Rev E 2021; 104:044204. [PMID: 34781571 DOI: 10.1103/physreve.104.044204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2021] [Accepted: 09/23/2021] [Indexed: 11/07/2022]
Abstract
The passive estimation of impulse responses from ambient noise correlations arouses increasing interest in seismology, acoustics, optics, and electromagnetism. Assuming the equipartition of the noise field, the cross-correlation function measured with noninvasive receiving probes converges towards the difference of the causal and anticausal Green's functions. Here, we consider the case when the receiving field probes are antennas which are well coupled to a complex medium-a scenario of practical relevance in electromagnetism. We propose a general approach based on the scattering matrix formalism to explore the convergence of the cross-correlation function. The analytically derived theoretical results for chaotic systems are confirmed in microwave measurements within a mode-stirred reverberation chamber. This study provides fundamental insight into the Green's function retrieval technique and paves the way for a new technique to characterize electromagnetic antennas.
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Affiliation(s)
- Matthieu Davy
- Univ Rennes, INSA Rennes, CNRS, IETR - UMR 6164, F-35000 Rennes, France
| | - Philippe Besnier
- Univ Rennes, INSA Rennes, CNRS, IETR - UMR 6164, F-35000 Rennes, France
| | - Philipp Del Hougne
- Univ Rennes, INSA Rennes, CNRS, IETR - UMR 6164, F-35000 Rennes, France.,Université Côte d'Azur, CNRS, Institut de Physique de Nice, UMR 7010, 06108 Nice, France
| | - Julien de Rosny
- ESPCI Paris, PSL Research University, Institut Langevin, F-75005 Paris, France
| | - Elodie Richalot
- ESYCOM lab, Univ Gustave Eiffel, CNRS, F-77454 Marne-la-Vallée, France
| | - François Sarrazin
- ESYCOM lab, Univ Gustave Eiffel, CNRS, F-77454 Marne-la-Vallée, France
| | - Dmitry V Savin
- Department of Mathematics, Brunel University London, Uxbridge UB8 3PH, United Kingdom
| | - Fabrice Mortessagne
- Université Côte d'Azur, CNRS, Institut de Physique de Nice, UMR 7010, 06108 Nice, France
| | - Ulrich Kuhl
- Université Côte d'Azur, CNRS, Institut de Physique de Nice, UMR 7010, 06108 Nice, France
| | - Olivier Legrand
- Université Côte d'Azur, CNRS, Institut de Physique de Nice, UMR 7010, 06108 Nice, France
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Stochastic Model for Energy Propagation in Disordered Granular Chains. MATERIALS 2021; 14:ma14071815. [PMID: 33917618 PMCID: PMC8038819 DOI: 10.3390/ma14071815] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/18/2021] [Revised: 03/18/2021] [Accepted: 03/31/2021] [Indexed: 11/17/2022]
Abstract
Energy transfer is one of the essentials of mechanical wave propagation (along with momentum transport). Here, it is studied in disordered one-dimensional model systems mimicking force-chains in real systems. The pre-stressed random masses (other types of disorder lead to qualitatively similar behavior) interact through (linearized) Hertzian repulsive forces, which allows solving the deterministic problem analytically. The main goal, a simpler, faster stochastic model for energy propagation, is presented in the second part, after the basic equations are re-visited and the phenomenology of pulse propagation in disordered granular chains is reviewed. First, the propagation of energy in space is studied. With increasing disorder (quantified by the standard deviation of the random mass distribution), the attenuation of pulsed signals increases, transiting from ballistic propagation (in ordered systems) towards diffusive-like characteristics, due to energy localization at the source. Second, the evolution of energy in time by transfer across wavenumbers is examined, using the standing wave initial conditions of all wavenumbers. Again, the decay of energy (both the rate and amount) increases with disorder, as well as with the wavenumber. The dispersive ballistic transport in ordered systems transits to low-pass filtering, due to disorder, where localization of energy occurs at the lowest masses in the chain. Instead of dealing with the too many degrees of freedom or only with the lowest of all the many eigenmodes of the system, we propose a stochastic master equation approach with reduced complexity, where all frequencies/energies are grouped into bands. The mean field stochastic model, the matrix of energy-transfer probabilities between bands, is calibrated from the deterministic analytical solutions by ensemble averaging various band-to-band transfer situations for short times, as well as considering the basis energy levels (decaying with the wavenumber increasing) that are not transferred. Finally, the propagation of energy in the wavenumber space at transient times validates the stochastic model, suggesting applications in wave analysis for non-destructive testing, underground resource exploration, etc.
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Shrivastava RK, Luding S. Wave propagation of spectral energy content in a granular chain. EPJ WEB OF CONFERENCES 2017. [DOI: 10.1051/epjconf/201714002023] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Lu L, Ding Z, Zeng RS, He Z. Retrieval of Green's function and generalized optical theorem for the scattering of complete dyadic fields. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2011; 129:1935-1944. [PMID: 21476649 DOI: 10.1121/1.3553224] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Green's function retrieval has been widely used in different research fields due to the fact that the Green's function can be extracted by cross-correlating the records at two receivers. In this paper, the retrieval of the dyadic Green's function is studied by investigating the representation theorem. The generalized optical theorem for the dyadic fields is derived based on the elastic dynamic interferometric equation. By addressing the cross-correlation recorded at two receivers, the important role of the generalized optical theorem and energy equipartition in retrieving the exact Green's function is shown. The presented derivation also shows the Newton-Marchenko equation holdsif the condition of equipartition is not satisfied.
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Affiliation(s)
- Laiyu Lu
- Institute of Geophysics, China Earthquake Administration, Beijing 100081, USA.
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Hein B, Tanner G. Wave communication across regular lattices. PHYSICAL REVIEW LETTERS 2009; 103:260501. [PMID: 20366299 DOI: 10.1103/physrevlett.103.260501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2009] [Indexed: 05/29/2023]
Abstract
We propose a novel way to communicate signals in the form of waves across a d-dimensional lattice. The mechanism is based on quantum search algorithms and makes it possible to both search for marked positions in a regular grid and to communicate between two (or more) points on the lattice. Remarkably, neither the sender nor the receiver needs to know the position of each other despite the fact that the signal is only exchanged between the contributing parties. This is an example of using wave interference as a resource by controlling localization phenomena effectively. Possible experimental realizations will be discussed.
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Affiliation(s)
- Birgit Hein
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
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Perton M, Sánchez-Sesma FJ, Rodríguez-Castellanos A, Campillo M, Weaver RL. Two perspectives on equipartition in diffuse elastic fields in three dimensions. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2009; 126:1125-1130. [PMID: 19739726 DOI: 10.1121/1.3177262] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
The elastodynamic Green function can be retrieved from the cross correlations of the motions of a diffuse field. To extract the exact Green function, perfect diffuseness of the illuminating field is required. However, the diffuseness of a field relies on the equipartition of energy, which is usually described in terms of the distribution of wave intensity in direction and polarization. In a full three dimensional (3D) elastic space, the transverse and longitudinal waves have energy densities in fixed proportions. On the other hand, there is an alternative point of view that associates equal energies with the independent modes of vibration. These two approaches are equivalent and describe at least two ways in which equipartition occurs. The authors gather theoretical results for diffuse elastic fields in a 3D full-space and extend them to the half-space problem. In that case, the energies undergo conspicuous fluctuations as a function of depth within about one Rayleigh wavelength. The authors derive diffuse energy densities from both approaches and find they are equal. The results derived here are benchmarks, where perfect diffuseness of the illuminating field was assumed. Some practical implications for the normalization of correlations for Green function retrieval arise and they have some bearing for medium imaging.
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Affiliation(s)
- M Perton
- Instituto de Ingeniería, Universidad Nacional Autónoma de Mexico, Ciudad Universitaria, Coyoacán, México D. F., Mexico
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Godin OA. Retrieval of Green's functions of elastic waves from thermal fluctuations of fluid-solid systems. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2009; 125:1960-1970. [PMID: 19354372 DOI: 10.1121/1.3082101] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Fluctuation-dissipation and flow reversal theorems are used to study long-range correlation of thermal phonons in a stationary heterogeneous mechanical system comprised of arbitrary inhomogeneous fluid flow and anisotropic solid. At thermal equilibrium, with an appropriate choice of physical observables to characterize thermal fluctuations within the fluid and within the solid, the general integral expression for the two-point correlation function of the fluctuations reduces to a linear combination of deterministic Green's functions, which describe wave propagation in opposite directions between the two points. It is demonstrated that the cross-correlation of thermal noise contains as much information about the environment as can be obtained in active reciprocal transmission experiments with transceivers placed at the two points. These findings suggest a possible application of ambient noise cross-correlation to passive acoustic characterization of inhomogeneous flows in fluid-solid systems in laboratory and geophysical settings.
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Affiliation(s)
- Oleg A Godin
- CIRES, University of Colorado, Boulder, Colorado 80309-0216, USA.
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Site effects on earthquake ground motion based on microtremor measurements for metropolitan Beijing. Sci Bull (Beijing) 2008. [DOI: 10.1007/s11434-008-0422-2] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Kedar S, Longuet-Higgins M, Webb F, Graham N, Clayton R, Jones C. The origin of deep ocean microseisms in the North Atlantic Ocean. Proc Math Phys Eng Sci 2008. [DOI: 10.1098/rspa.2007.0277] [Citation(s) in RCA: 201] [Impact Index Per Article: 12.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Oceanic microseisms are small oscillations of the ground, in the frequency range of 0.05–0.3 Hz, associated with the occurrence of energetic ocean waves of half the corresponding frequency. In 1950, Longuet-Higgins suggested in a landmark theoretical paper that (i) microseisms originate from surface pressure oscillations caused by the interaction between oppositely travelling components with the same frequency in the ocean wave spectrum, (ii) these pressure oscillations generate seismic Stoneley waves on the ocean bottom, and (iii) when the ocean depth is comparable with the acoustic wavelength in water, compressibility must be considered. The efficiency of microseism generation thus depends on both the wave frequency and the depth of water. While the theory provided an estimate of the magnitude of the corresponding microseisms in a compressible ocean, its predictions of microseism amplitude heretofore have never been tested quantitatively. In this paper, we show a strong agreement between observed microseism and calculated amplitudes obtained by applying Longuet-Higgins' theory to hindcast ocean wave spectra from the North Atlantic Ocean. The calculated vertical displacements are compared with seismic data collected at stations in North America, Greenland, Iceland and Europe. This modelling identifies a particularly energetic source area stretching from the Labrador Sea to south of Iceland, where wind patterns are especially conducive to generating oppositely travelling waves of same period, and the ocean depth is favourable for efficient microseism generation through the ‘organ pipe’ resonance of the compression waves, as predicted by the theory. This correspondence between observations and the model predictions demonstrates that deep ocean nonlinear wave–wave interactions are sufficiently energetic to account for much of the observed seismic amplitudes in North America, Greenland and Iceland.
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Affiliation(s)
- Sharon Kedar
- Jet Propulsion Laboratory, California Institute of TechnologyPasadena, CA 91109, USA
| | - Michael Longuet-Higgins
- Institute for Nonlinear Science, University of California, San DiegoLa Jolla, CA 92093-0402, USA
| | - Frank Webb
- Jet Propulsion Laboratory, California Institute of TechnologyPasadena, CA 91109, USA
| | | | - Robert Clayton
- Seismological Laboratory, California Institute of TechnologyPasadena, CA 91125-2100, USA
| | - Cathleen Jones
- Jet Propulsion Laboratory, California Institute of TechnologyPasadena, CA 91109, USA
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