We present an experimental study of the mechanical impulse propagation through a horizontal alignment of elastic spheres of progressively decreasing diameter phi(n): namely, a tapered chain. Experimentally, the diameters of spheres which interact via the Hertz potential are selected to keep as close as possible to an exponential decrease, phi(n+1) = (1-q)phi(n), where the experimental tapering factor is either q(1) approximately equal to 5.60% or q(2) approximately equal to 8.27%. In agreement with recent numerical results, an impulse initiated in a monodisperse chain (a chain of identical beads) propagates without shape changes and progressively transfers its energy and momentum to a propagating tail when it further travels in a tapered chain. As a result, the front pulse of this wave decreases in amplitude and accelerates. Both effects are satisfactorily described by the hard-sphere approximation, and basically, the shock mitigation is due to partial transmissions, from one bead to the next, of momentum and energy of the front pulse. In addition when small dissipation is included, better agreement with experiments is found. A close analysis of the loading part of the experimental pulses demonstrates that the front wave adopts a self-similar solution as it propagates in the tapered chain. Finally, our results corroborate the capability of these chains to thermalize propagating impulses and thereby act as shock absorbing devices.

We investigate the dynamical response of a mass defect in a one-dimensional non-loaded horizontal chain of identical spheres which interact via the nonlinear Hertz potential. Our experiments show that the interaction of a solitary wave with a light intruder excites localized mode. In agreement with dimensional analysis, we find that the frequency of localized oscillations exceeds the incident wave frequency spectrum and nonlinearly depends on the size of the intruder and on the incident wave strength. The absence of tensile stress between grains allows some gaps to open, which in turn induce a significant enhancement of the oscillations amplitude. We performed numerical simulations that precisely describe our observations without any adjusting parameters. [3]. For example, the presence of an isotope in a perfect linear crystal is known to enhance optical waves absorption at given frequencies [4]. One-dimensional chains of beads interacting via the Hertz potential are systems suitable to observe nonlinear localization effects. A loaded chain of identical beads is dispersive, allowing small perturbations to propagate as linear or weakly nonlinear acoustic waves [5]. In contrast, when grains in a chain barely touch one another, the energy of an impulse only propagates as fully nonlinear solitary waves [5,6,7] resulting from the balance between dispersion and nonlinearity of the medium. Nesterenko early described this regime as a sonic vacuum limit [8]. Dissipative effects such as viscoelasticity or friction only attenuate and spread these solitary waves [7,9]. In contrast, any heterogeneity of the medium capable of unbalancing dispersion and nonlinearity results in breaking the solitary wave symmetry. For example, a narrow pulse propagating in a chain of beads with decreasing sizes develops a long tail which spreads in time the momentum transfer [10,11,12]. Designing powerfull impact protection systems takes advantage of these features [10,11,13]. Granular chains made of successions of heavy and light beads also proved valuable efficiency in energy absorption [14]. More recently, fully nonlinear waves with finite-width were observed in chains containing periodic mass defects or soft inclusions [15]. Such nonlinear dimer chains are expected to support additionnal optical modes and forbidden band gap when subjected to a static load [15].The elementary interaction of either lighter or heavier intruders with solitary waves in non-loaded monodisperse chains of beads has been investigated numerically [16]. When a solitary wave reaches a mass defect, energy is partially reflected into a backward traveling solitary wave and is partially transmitted to the intruder. A heavy impurity slowly translates, leading to a large transmitted solitary waves train in the forward direction [16], similarly to what was observed in stepped chains [5,8,12]. A light intruder oscillates and scatters forward and backward weak delayed solitary waves trains [16].In this letter, we investigate experimentally the interaction of a solitary wave wi...

We study experimentally the interaction between two solitary waves that approach one another in a linear chain of spheres interacting via the Hertz potential. When these counterpropagating waves collide, they cross each other and a phase shift in respect to the noninteracting waves is introduced as a result of the nonlinear interaction potential. This observation is well reproduced by our numerical simulations and is shown to be independent of viscoelastic dissipation at the bead contact. In addition, when the collision of equal amplitude and synchronized counterpropagating waves takes place, we observe that two secondary solitary waves emerge from the interacting region. The amplitude of the secondary solitary waves is proportional to the amplitude of incident waves. However, secondary solitary waves are stronger when the collision occurs at the middle contact in chains with an even number of beads. Although numerical simulations correctly predict the existence of these waves, experiments show that their respective amplitudes are significantly larger than predicted. We attribute this discrepancy to the rolling friction at the bead contact during solitary wave propagation.

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Rationale: Structure and function of the microvasculature provides critical information about disease state, can be used to identify local regions of pathology, and has been shown to be an indicator of response to therapy. Improved methods of assessing the microvasculature with non-invasive imaging modalities such as ultrasound will have an impact in biomedical theranostics. Ultrasound localization microscopy (ULM) is a new technology which allows processing of ultrasound data for visualization of microvasculature at a resolution better than allowed by acoustic diffraction with traditional ultrasound systems. Previous application of this modality in brain imaging has required the use of invasive procedures, such as a craniotomy, skull-thinning, or scalp removal, all of which are not feasible for the purpose of longitudinal studies. Methods: The impact of ultrasound localization microscopy is expanded using a 1024 channel matrix array ultrasonic transducer, four synchronized programmable ultrasound systems with customized high-performance hardware and software, and high-performance GPUs for processing. The potential of the imaging hardware and processing approaches are demonstrated in-vivo. Results: Our unique implementation allows asynchronous acquisition and data transfer for uninterrupted data collection at an ultra-high fixed frame rate. Using these methods, the vasculature was imaged using 100,000 volumes continuously at a volume acquisition rate of 500 volumes per second. With ULM, we achieved a resolution of 31 µm, which is a resolution improvement on conventional ultrasound imaging by nearly a factor of ten, in 3-D. This was accomplished while imaging through the intact skull with no scalp removal, which demonstrates the utility of this method for longitudinal studies. Conclusions:The results demonstrate new capabilities to rapidly image and analyze complex vascular networks in 3-D volume space for structural and functional imaging in disease assessment, targeted therapeutic delivery, monitoring response to therapy, and other theranostic applications.