Natural sonic crystal absorber constituted of seagrass (Posidonia Oceanica) fibrous spheres.

We present a 3-dimensional fully natural sonic crystal composed of spherical aggregates of fibers (called Aegagropilae) resulting from the decomposition of Posidonia Oceanica. The fiber network is first acoustically characterized, providing insights on this natural fiber entanglement due to turbulent flow. The Aegagropilae are then arranged on a principal cubic lattice. The band diagram and topology of this structure are analyzed, notably via Argand representation of its scattering elements. This fully natural sonic crystal exhibits excellent sound absorbing properties and thus represents a sustainable alternative that could outperform conventional acoustic materials.

Nonlinear dispersive waves in repulsive lattices.

The propagation of nonlinear waves in a lattice of repelling particles is studied theoretically and experimentally. A simple experimental setup is proposed, consisting of an array of coupled magnetic dipoles. By driving harmonically the lattice at one boundary, we excite propagating waves and demonstrate different regimes of mode conversion into higher harmonics, strongly influenced by dispersion and discreteness. The phenomenon of acoustic dilatation of the chain is also predicted and discussed. The results are compared with the theoretical predictions of the α-Fermi-Pasta-Ulam equation, describing a chain of masses connected by nonlinear quadratic springs and numerical simulations. The results can be extrapolated to other systems described by this equation.

Formation of high-order acoustic Bessel beams by spiral diffraction gratings.

The formation of high-order Bessel beams by a passive acoustic device consisting of an Archimedes' spiral diffraction grating is theoretically, numerically, and experimentally reported in this paper. These beams are propagation-invariant solutions of the Helmholtz equation and are characterized by an azimuthal variation of the phase along its annular spectrum producing an acoustic vortex in the near field. In our system, the scattering of plane acoustic waves by the spiral grating leads to the formation of the acoustic vortex with zero pressure on axis and the angular phase dislocations characterized by the spiral geometry. The order of the generated Bessel beam and, as a consequence, the size of the generated vortex can be fixed by the number of arms in the spiral diffraction grating. The obtained results allow for obtaining Bessel beams with controllable vorticity by a passive device, which has potential applications in low-cost acoustic tweezers and acoustic radiation force devices.

Energy localization and shape transformations in semiflexible polymer rings.

Shape transformations in driven and damped molecular chains are considered. Closed chains of weakly coupled molecular subunits under the action of spatially homogeneous time-periodic external field are studied. The coupling between the internal excitations and the bending degrees of freedom of the chain modifies the local bending rigidity of the chain. In the absence of driving the array takes a circular shape. When the energy pumped into the system exceeds some critical value the chain undergoes a nonequilibrium phase transition: The circular shape of the aggregate becomes unstable and the chain takes the shape of an ellipse or, in general, of a polygon. The excitation energy distribution becomes spatially nonuniform: It localizes in such places where the chain is more flat. The weak interaction of the chain with a flat surface restricts the dynamics to a flat manifold.

Ultradiscrete kinks with supersonic speed in a layered crystal with realistic potentials.

In this paper we develop a dynamical model of the propagating nonlinear localized excitations, supersonic kinks, in the cation layer in a silicate mica crystal. We start from purely electrostatic Coulomb interaction and add the Ziegler-Biersack-Littmark short-range repulsive potential and the periodic potential produced by other atoms of the lattice. The proposed approach allows the construction of supersonic kinks which can propagate in the lattice within a large range of energies and velocities. Due to the presence of the short-range repulsive component in the potential, the interparticle distances in the lattice kinks with high energy are limited by physically reasonable values. The introduction of the periodic lattice potential results in the important feature that the kinks propagate with the single velocity and single energy, which are independent on the excitation conditions. The unique average velocity of the supersonic kinks on the periodic substrate potential we relate with the kink amplitude of the relative particle displacements, which is determined by the interatomic distance corresponding to the minimum of the total, interparticle plus substrate, lattice potential. The found kinks are ultradiscrete and can be described with the "magic wave number" q=2π/3a, which was previously revealed in the nonlinear sinusoidal waves and supersonic kinks in the Fermi-Pasta-Ulam lattice. The extreme discreteness of the observed supersonic kinks, with basically two particles moving at the same time, allows the detailed interpretation of their double-kink structure, which is not possible for the multikinks without an account for the lattice discreteness. Analytical calculations of the displacement patterns and energies of the supersonic kinks are confirmed by numerical simulations. The computed energy of the found supersonic kinks in the considered realistic lattice potential is in a good agreement with the experimental evidence for the transport of localized energetic excitations in silicate mica crystals between the points of ^{40}K recoil and subsequent sputtering.

Extraordinary absorption of sound in porous lamella-crystals.

We present the design of a structured material supporting complete absorption of sound with a broadband response and functional for any direction of incident radiation. The structure which is fabricated out of porous lamellas is arranged into a low-density crystal and backed by a reflecting support. Experimental measurements show that strong all-angle sound absorption with almost zero reflectance takes place for a frequency range exceeding two octaves. We demonstrate that lowering the crystal filling fraction increases the wave interaction time and is responsible for the enhancement of intrinsic material dissipation, making the system more absorptive with less material.

Second-harmonic generation for dispersive elastic waves in a discrete granular chain.

The propagation of nonlinear compressional waves in a one-dimensional granular chain driven at one end by a harmonic excitation is studied. The chain is described by a Fermi-Pasta-Ulam (FPU) lattice model with quadratic nonlinearity (α-FPU model), valid for strong initial compression of the chain by an external static force. A successive approximations method is used to obtain the analytical expressions for the amplitudes of the static displacement field and of the fundamental and second harmonics propagating through the lattice. Both propagating and evanescent second harmonics are shown to influence the nonlinear propagation characteristics of the fundamental frequency. The propagating regime is characterized by a periodic energy transfer between first and second harmonics, resulting from dispersion, which disappears when the second harmonic becomes evanescent.

Sound diffusers based on sonic crystals.

A sound diffuser is proposed based on sonic crystals, structures formed by a periodic distribution of cylindrical scatterers in a host medium, which is usually air. The diffuser is a so-called biperiodic structure, as formed by two arrays of sonic crystals with slightly different periodicities. Large diffusivity at low frequencies is achieved when the typical scale of the blocks is much larger than the periodicity of the crystals, determined by its lattice constant. An interpretation of the low frequency behavior of the diffuser is given in the homogenization limit in terms of multiple reflections and interference between the fields scattered by the different blocks. It is also shown that sonic crystal based diffusers enhance time spreading in comparison with other conventional diffusers.

Nonlinear change of on-axis pressure and intensity maxima positions and its relation with the linear focal shift effect.

A comprehensive experimental, analytical and numerical study of the true focal region drift relative to the geometrical focus (focal shift effect) in acoustic focused beams and its nonlinear evolution is presented. For this aim, the concept of Fresnel number, proportional to the linear gain, is introduced as a convenient parameter for characterizing focused sources. It is shown that the magnitude of the shift is strongly dependent on the Fresnel number of the source, being larger for weakly focused systems where a large initial shift occurs. Analytical expressions for axial pressure distributions in linear regime are presented for the general case of truncated Gaussian beams. The main new contribution of this work is the examination of the connection between the linear and nonlinear stages of the focal shift effect, and its use for the estimation of the more complicated nonlinear stage. Experiments were carried out using a continuous-wave ultrasonic beam in water, radiated by a focused source with nominal frequency f=1 MHz, aperture radius a=1.5 cm and geometrical focal distance R=11.7 cm, corresponding to a Fresnel number N(F)=1.28. The maximum measured shifts for peak pressure and intensity were 4.4 and 1.1cm, respectively. The evolution of the different maxima with the source amplitude, and the disparity in their axial positions, is interpreted in terms of the dynamics of the nonlinear distortion process. Analytical results for the particular case of a sound beam with initial Gaussian distribution are also presented, demonstrating that the motion of peak pressure and peak intensity may occur in opposite directions.

Excitability in a nonlinear magnetoacoustic resonator.

We report a nonlinear acoustic system displaying excitability. The considered system is a magnetostrictive material where acoustic waves are parametrically generated. For a set of parameters, the system presents homoclinic and heteroclinic dynamics, whose boundaries define an excitability domain. The excitable behavior is characterized by analyzing the response of the system to different external stimuli. Single-spiking and bursting regimes have been identified. All these neuronlike properties are here predicted to occur in magnetostrictive materials, which are the basis of many smart systems and applications.

Self-pulsing dynamics of ultrasound in a magnetoacoustic resonator.

A theoretical model of parametric magnetostrictive generation of ultrasound is considered, taking into account magnetic and magnetoacoustic nonlinearities. The stability and temporal dynamics of the system is analyzed with standard techniques revealing that, for a given set of parameters, the model presents a homoclinic or saddle-loop bifurcation, which predicts that the ultrasound is emitted in the form of pulses or spikes with arbitrarily low frequency.

Spontaneous pattern formation in an acoustical resonator .

A dynamical system of equations describing parametric sound generation (PSG) in a dispersive large aspect ratio resonator is derived. The model generalizes previously proposed descriptions of PSG by including diffraction effects and is analogous to the model used in theoretical studies of optical parametric oscillation. A linear stability analysis of the solution below the threshold of subharmonic generation reveals the existence of a pattern forming instability, which is confirmed by numerical integration. The conditions of emergence of periodic patterns in transverse space are discussed in the acoustical context.

Role of pump diffraction on the stability of localized structures in degenerate optical parametric oscillators.

We show that the stability range of localized structures (LS's) in the form of minimum size phase domains in degenerate optical parametric oscillators is enhanced by increasing the diffraction of the pump wave. Pump diffraction enhances spatial oscillations of decaying tails of domain boundaries, whereas spatially oscillating (weakly decaying) tails prevent the collapse of LS's, enhance their stability range, and allow the existence of more complex LS's in the form of molecules.

Vectorial Kerr-cavity solitons.

It is shown that a Kerr cavity with different losses for the two polarization components of the field can support both dark and bright cavity solitons (CS's). A parametrically driven Ginzburg-Landau equation is shown to describe the system for large-cavity anisotropy. In one transverse dimension the nonlinear dynamics of the bright CS's is numerically investigated.

Stability of localized structures in the Swift-Hohenberg equation.

We show that nonmonotonic (oscillatory) decay of the boundaries of phase domains is crucial for the stability of localized structures in systems described by Swift-Hohenberg equation. The less damped (more oscillatory) are the boundaries, the larger are the existence ranges of the localized structures. For very weakly damped spatial oscillations, higher-order localized structures are possible.