Eric Herbert

Energy-based adaptive focusing of waves: application to noninvasive aberration correction of ultrasonic wavefields

An aberration correction method based on the maximization of the wave intensity at the focus of an emitting array is presented. The potential of this new adaptive focusing technique is investigated for ultrasonic focusing in biological tissues. The acoustic intensity is maximized noninvasively through direct measurement or indirect estimation of the beam energy at the focus for a series of spatially coded emissions. For ultrasonic waves, the acoustic energy at the desired focus can be indirectly estimated from the local displacements induced in tissues by the ultrasonic radiation force of the beam. Based on the measurement of these displacements, this method allows determination of the precise estimation of the phase and amplitude aberrations, and consequently the correction of aberrations along the beam travel path. The proof of concept is first performed experimentally using a large therapeutic array with strong electronic phase aberrations (up to 2pi). Displacements induced by the ultrasonic radiation force at the desired focus are indirectly estimated using the time shift of backscattered echoes recorded on the array. The phase estimation is deduced accurately using a direct inversion algorithm which reduces the standard deviation of the phase distribution from sigma = 1.89 radian before correction to sigma = 0.53 radian following correction. The corrected beam focusing quality is verified using a needle hydrophone. The peak intensity obtained through the aberrator is found to be -7.69 dB below the reference intensity obtained without any aberration. Using the phase correction, a sharp focus is restored through the aberrator with a relative peak intensity of -0.89 dB. The technique is tested experimentally using a linear transmit/receive array through a real aberrating layer. The array is used to automatically correct its beam quality, as it both generates the radiation force with coded excitations and indirectly estimates the acoustic intensity at the focus with speckle tracking. This technique could have important implications in the field of high-intensity focused ultrasound even in complex configurations such as transcranial, transcostal, or deep seated organs.

The limit of metastability of water under tension: theories and experiments

Two scenarios are proposed for explaining the thermodynamic anomalies of supercooled water, but they cannot be directly tested in this region because of the onset of homogeneous crystallization. They also give two distinct temperature dependences of the limit of metastability of water stretched beyond its boiling curve: either monotonic, as in simple liquids, or exhibiting a minimum. Therefore cavitation experiments could allow one to distinguish between the competing pictures. We review previous experiments and describe our preliminary results.

Susceptibility divergence, phase transition and multistability of a highly turbulent closed flow

Using time series of stereoscopic particle image velocimetry data, we study the response of a turbulent von Karman swirling flow to a continuous breaking of its forcing symmetry. Experiments are carried over a wide Reynolds number range, from the laminar regime at Re = 102 to the highly turbulent regime near Re = 106. We show that the flow symmetry can be quantitatively characterized by two scalars, the global angular momentum I and the mixing layer altitude zs, which are shown to be statistically equivalent. Furthermore, we report that the flow response to small forcing asymmetry is linear, with a slope depending on the Reynolds number: this response coefficient increases non-monotonically from small to large Reynolds number and presents a divergence at a critical Reynolds number Rec = 40 000 ± 5000. This divergence coincides with a change in the statistical properties of the instantaneous flow symmetry I(t): its pdf changes from Gaussian to non-Gaussian with multiple maxima, revealing metastable non-symmetrical states. For symmetric forcing, a peak of fluctuations of I(t) is also observed at Rec: these fluctuations correspond to time intermittencies between metastable states of the flow which, contrary to the very-long-time-averaged mean flow, spontaneously and dynamically break the system symmetry. We show that these observations can be interpreted in terms of divergence of the susceptibility to symmetry breaking, revealing the existence of a phase transition. An analogy with the ferromagnetic–paramagnetic transition in solid-state physics is presented and discussed.

Modelling and analysis of turbulent datasets using Auto Regressive Moving Average processes

an swirling flow experiment. We found that the ARMA analysis is well correlated with spatial structures of the flow, and can discriminate between two different flows with comparable mean velocities, obtained by changing the forcing. Moreover, we show that the ϒ is highest in regions where shear layer vortices are present, thereby establishing a link between deviations from the Kolmogorov model and coherent structures. These deviations are consistent with the ones observed by computing the Hurst exponents for the same time series. We show that some salient features of the analysis are preserved when considering global instead of local observables. Finally, we analyzeflow configurations with multistability features where the ARMA technique is efficient in discriminating different stability branches of the system. C

Dual non-Kolmogorov cascades in a von Kármán flow

The experimental spatial power spectrum of the velocity fluctuations in a von Karman flow is measured, in a wide range of Reynolds numbers, 102 105.

Cavitation in heavy water and other liquids.

We report on measurements of the cavitation pressure in several liquids subjected to tension in an acoustic wave and compare the results to classical nucleation theory (CNT). This study is motivated by the sizable discrepancy between the acoustic cavitation threshold measured in water and the value predicted by CNT. We find that the same discrepancy is present for heavy water, whereas the agreement is better for ethanol and heptane and intermediate in the case of dimethyl sulfoxide. It is well-known that water is an anomalous liquid, a consequence of its hydrogen-bonded network. The other liquids studied represent very different molecular interactions. Our results indicate that the cavitation threshold approaches the prediction of CNT as the surface tension gets smaller. Conversely, this raises the question of the validity of a simple theory such as CNT to account for high surface tension liquids and suggests that an appropriate microscopic model of such liquids may be necessary to correctly predict the cavitation threshold.

Superfluid high REynolds von Kármán experiment

The Superfluid High REynolds von Kármán experiment facility exploits the capacities of a high cooling power refrigerator (400 W at 1.8 K) for a large dimension von Kármán flow (inner diameter 0.78 m), which can work with gaseous or subcooled liquid (He-I or He-II) from room temperature down to 1.6 K. The flow is produced between two counter-rotating or co-rotating disks. The large size of the experiment allows exploration of ultra high Reynolds numbers based on Taylor microscale and rms velocity [S. B. Pope, Turbulent Flows (Cambridge University Press, 2000)] (Rλ > 10000) or resolution of the dissipative scale for lower Re. This article presents the design and first performance of this apparatus. Measurements carried out in the first runs of the facility address the global flow behavior: calorimetric measurement of the dissipation, torque and velocity measurements on the two turbines. Moreover first local measurements (micro-Pitot, hot wire,…) have been installed and are presented.

Probing quantum and classical turbulence analogy in von Kármán liquid helium, nitrogen, and water experiments

SHREK Collaboration: B. Saint-Michel, E. Herbert, J. Salort, C. Baudet, M. Bon Mardion, P. Bonnay, M. Bourgoin, B. Castaing, L. Chevillard, F. Daviaud, P. Diribarne, B. Dubrulle, Y. Gagne, M. Gibert, A. Girard, B. Hébral, Th. Lehner, and B. Rousset Laboratoire SPHYNX, CEA/IRAMIS/SPEC, CNRS URA 2464, F-91191 Gif-sur-Yvette, France Laboratoire FAST, CNRS UMR 7608, Université Paris-Sud, Université Pierre-et-Marie-Curie, Bât. 502, Campus universitaire, 91405 Orsay, France Laboratoire de Physique de l’ÉNS de Lyon, CNRS/Université Lyon F-69364 Lyon cedex 7, France Laboratoire des Écoulements Géophysiques et Industriels, CNRS/UJF/INPG, F-38041 Grenoble Cedex 9, France Service des Basses Températures, INAC/SBT, UMR CEA-UJF 9004, CEA Grenoble, 17 rue des Martyrs 38054 Grenoble Cedex France Université Grenoble Alpes, Institut NÉEL, F-38042 Grenoble, France, CNRS, Institut NÉEL, F-38042 Grenoble, France LUTH, Observatoire Paris-Meudon, 5 Pl. Jules Janssen, F-92195 Meudon Cedex, FranceWe report measurements of the dissipation in the Superfluid helium high REynold number von Karman flow experiment for different forcing conditions. Statistically steady flows are reached; they display a hysteretic behavior similar to what has been observed in a 1:4 scale water experiment. Our macroscopical measurements indicate no noticeable difference between classical and superfluid flows, thereby providing evidence of the same dissipation scaling laws in the two phases. A detailed study of the evolution of the hysteresis cycle with the Reynolds number supports the idea that the stability of the steady states of classical turbulence in this closed flow is partly governed by the dissipative scales. It also supports the idea that the normal and the superfluid components at these temperatures (1.6 K) are locked down to the dissipative length scale.

Energy-based adaptive focusing of waves: Application to ultrasonic imaging and therapy

A novel aberration correction method based on the maximization of the acoustic intensity at the focus of a transducer array is presented. The potential of this new adaptive focusing technique is investigated in for ultrasonic focusing in biological tissues. The acoustic intensity is maximized non-invasively through the measurement or indirect estimation of the beam energy at focus for a series of spatial coded emissions. The acoustic energy at the desired focus location can be indirectly estimated from the local displacements induced by the ultrasonic radiation force of the beam. Based on these displacement estimates, this method allow the precise estimation of the phase and amplitude aberrations and consequently the corrections of aberrations along the beam travel path. The proof of concept is first performed experimentally using a large therapeutic array with strong simulated phase aberrations (up to 2 pi). Displacements induced by the ultrasonic radiation force at the desired focus are indirectly estimated using the time shifts of backscattered echoes recorded on the array. The phase estimation is deduced accurately using a direct inversion algorithm. The corrected beam focusing quality is controlled using the needle hydrophone. A sharp focus is restored and a strong increase of the acoustic intensity at focus is obtained. Secondly, the technique is tested experimentally using a linear imaging array through a real aberrating layer. Acoustic intensity is indirectly estimated using focal displacements measurements obtained using conventional speckle tracking of backscattered echoes. A strong improvement of both spatial resolution and sidelobes level is found.

Closed-loop approach to thermodynamics

We present the closed-loop approach to linear nonequilibrium thermodynamics considering a generic heat engine dissipatively connected to two temperature baths. The system is usually quite generally characterized by two parameters: the output power P and the conversion efficiency η, to which we add a third one, the working frequency ω. We establish that a detailed understanding of the effects of the dissipative coupling on the energy conversion process requires only knowing two quantities: the systems feedback factor β and its open-loop gain A_{0}, which product A_{0}β characterizes the interplay between the efficiency, the output power, and the operating rate of the system. By raising the abstract hermodynamic analysis to a higher level, the feedback loop approach provides a versatile and economical, hence fairly efficient, tool for the study of any conversion engine operation for which a feedback factor can be defined.