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We explore the scattering of waves in designed asymmetric one-dimensional waveguide networks. We show that the reflection between two ports of an asymmetric network can be identical over a broad frequency range, as if the network was mirror-symmetric, under the condition of so-called latent symmetry between the ports. This broadband equireflectionality is validated numerically for acoustic waveguides and experimentally through measurements on microwave transmission-line networks. In addition, introducing a generalization of latent symmetry, we study the properties of an $N$-port scattering matrix $S$. When the powers of $S$ fulfill certain relations, which we coin scaled cospectrality, the setup is guaranteed to possess at least one zero eigenvalue of $S$, so that the setup features coherent perfect absorption. More importantly, scaled cospectrality introduces a scaling factor which controls the asymmetry of the incoming wave to be absorbed. Our findings introduce a novel approach for designing tunable wave manipulation devices in asymmetric setups. As evidenced by our acoustic simulations and microwave experiments, the generality of our approach extends its potential applications to a wide range of physical systems.

One of the hallmark of topological insulators is having conductivity properties that are unaffected by the possible presence of defects. In this work, we go beyond backscattering immunity and obtain topological invisibility across defects or disorder. Using a combination of chiral and mirror symmetry, the transmission coefficient is guaranteed to be unity. Importantly, but no phase shift is induced making the defect completely invisible. Many lattices possess the chiral-mirror symmetry, and we choose to demonstrate the principle on an hexagonal lattice model with Kekule distortion displaying topological edge waves, and we show analytically and numerically that the transmission across symmetry preserving defects is unity. We then realize this lattice in an acoustic system, and confirm the invisibility with numerical experiments. We foresee that the versatility of our model will trigger new experiments to observe topological invisibility in various wave systems, such as photonics, cold atoms or elastic waves., Comment: 9+6 pages, 6+5 figures. Few minor corrections and clarifications. Match published version

We numerically investigate the characteristics of the long-time dynamics of a single-site wave-packet excitation in a disordered and nonlinear Su-Schrieffer-Heeger model. In the linear regime, as the parameters controlling the topology of the system are varied, we show that the transition between two different topological phases is preceded by an anomalous diffusion, in contrast to Anderson localization within these topological phases. In the presence of on-site nonlinearity this feature is lost due to mode-mode interactions. Direct numerical simulations reveal that the characteristics of the asymptotic nonlinear wave-packet spreading are the same across the whole studied parameter space. Our findings underline the importance of mode-mode interactions in nonlinear topological systems, which must be studied in order to define reliable nonlinear topological markers., Comment: 14 pages, 11 figures

We study the propagation of high-amplitude sound waves, in the form of pulse-like solitary waves, in an air-filled acoustic waveguide of periodically varying cross section. Our numerical simulations, solving the compressible Navier-Stokes equations in two dimensions, as well as our experimental results, strongly suggest that nonlinear losses, originated from vortex shedding (at the segment changes) are crucial in the dynamics of high amplitude pulses. We find that, even in the presence of strong dissipation, the solitary wave roughly retains its characteristics (as described by the amplitude-velocity-width relations), obtained by the derivation and analysis of an effective Boussinesq equation. In addition, we propose a transmission-line based numerical scheme, able to capture well the experimental results. The proposed design offers a new playground for the study of the combined effects of dispersion, nonlinearity and dissipation in air-borne acoustics, while, due to its simplicity, it can be extended to higher dimensions.

We study the dynamical and chaotic behavior of a disordered one-dimensional elastic mechanical lattice which supports translational and rotational waves. The model used in this work is motivated by the recent experimental results of B. Deng et al., Nat. Commun. 9, 3410 (2018). This lattice is characterized by strong geometrical nonlinearities and the coupling of two degrees-of-freedom (DoFs) per site. Although the linear limit of the structure consists of a linear Fermi-Pasta-Ulam-Tsingou lattice and a linear Klein-Gordon (KG) lattice whose DoFs are uncoupled, by using single site initial excitations on the rotational DoF, we evoke the nonlinear coupling between the system's translational and rotational DoFs. Our results reveal that such coupling induces rich wave-packet spreading behavior in the presence of strong disorder. In the weakly nonlinear regime, we observe energy spreading only due to the coupling of the two DoFs (per site) which is in contrast to what is known for KG lattices with a single DoF per lattice site, where the spreading occurs due to chaoticity. Additionally, for strong nonlinearities, we show that initially localized wave-packets attain near ballistic behavior in contrast to other known models. We also reveal persistent chaos during energy spreading, although its strength decreases in time as quantified by the evolution of the system's finite-time maximum Lyapunov exponent. Our results show that flexible, disordered and strongly nonlinear lattices are a viable platform to study energy transport in combination with multiple DoFs (per site), also present an alternative way to control energy spreading in heterogeneous media., Comment: Submitted

Topological systems furnish a powerful way of localizing wave energy at edges of a structured material. Usually this relies on Bragg scattering to obtain bandgaps with nontrivial topological structures. However, this limits their applicability to low frequencies since that would require very large structures. A standard approach to address the problem is to add resonating elements inside the material to open gaps in the subwavelength regime. Unfortunately, one usually has no precise control on the properties of the obtained topological modes, such as their frequency or localization length. In this work, we propose a new construction to couple acoustic resonators such that acoustic modes are mapped exactly to the eigenmodes of the Su-Schrieffer-Heeger model. The relation between energy in the lattice model and the acoustic frequency is controlled by the characteristics of the resonators. This allows us to obtain Su-Schrieffer-Heeger topological modes at any given frequency, for instance in the subwavelength regime. We also generalize the construction to obtain well-controlled topological edge modes in alternative tunable configurations., Comment: 11 pages, 6 figures

We numerically study a one dimensional, nonlinear lattice model which in the linear limit is relevant to the study of bending (flexural) waves. In contrast with the classic one dimensional mass-spring system, the linear dispersion relation of the considered model has different characteristics in the low frequency limit. By introducing disorder in the masses of the lattice particles, we investigate how different nonlinearities (cubic, quartic and their combination) lead to energy delocalization, equipartition and chaotic dynamics. We excite the lattice using single site initial momentum excitations corresponding to a strongly localized linear mode and increase the initial energy of excitation. Beyond a certain energy threshold, when the cubic nonlinearity is present, the system is found to reach energy equipartition and total delocalization. On the other hand, when only the quartic nonlinearity is activated, the system remains localized and away from equipartition at least for the energies and evolution times considered here. However, for large enough energies for all types of nonlinearities we observe chaos. This chaotic behavior is combined with energy delocalization when cubic nonlinearities are present, while the appearance of only quartic nonlinearity leads to energy localization. Our results reveal a rich dynamical behavior and show differences with the relevant Fermi-Pasta-Ulam-Tsingou model. Our findings pave the way for the study of models relevant to bending (flexural) waves in the presence of nonlinearity and disorder, anticipating different energy transport behaviors., Comment: 21 pages 10 figures, submitted for review

Topological physics strongly relies on prototypical lattice model with particular symmetries. We report here on a theoretical and experimental work on acoustic waveguides that is directly mapped to the one-dimensional Su-Schrieffer-Heeger chiral model. Starting from the continuous two dimensional wave equation we use a combination of monomadal approximation and the condition of equal length tube segments to arrive at the wanted discrete equations. It is shown that open or closed boundary conditions topological leads automatically to the existence of edge modes. We illustrate by graphical construction how the edge modes appear naturally owing to a quarter-wavelength condition and the conservation of flux. Furthermore, the transparent chirality of our system, which is ensured by the geometrical constraints allows us to study chiral disorder numerically and experimentally. Our experimental results in the audible regime demonstrate the predicted robustness of the topological edge modes., Comment: 10 pages, 11 figures. Slight modification of title, minor additions to the text

In this work, we investigate some aspects of an acoustic analogue of the two-dimensional Su-Schrieffer-Heeger model. The system is composed of alternating cross-section tubes connected in a square network, which in the limit of narrow tubes is described by a discrete model coinciding with the two-dimensional Su-Schrieffer-Heeger model. This model is known to host topological edge waves, and we develop a scattering theory to analyze how these waves scatter on edge structure changes. We show that these edge waves undergo a perfect reflection when scattering on a corner, incidentally leading to a new way of constructing corner modes. It is shown that reflection is high for a broad class of edge changes such as steps or defects. We then study consequences of this high reflectivity on finite networks. Globally, it appears that each straight part of edges, separated by corners or defects, hosts localized edge modes isolated from their neighbourhood., Comment: 19+5 pages, 15 figures. V2: small extra remarks added

We study the two-dimensional extension of the Su-Schrieffer-Heeger model in its higher order topological insulator phase, which is known to host corner states. Using the separability of the model into a product of one-dimensional Su-Schrieffer-Heeger chains, we analytically describe the eigen-modes, and specifically the zero-energy level, which includes states localized in corners. We then consider networks with disordered hopping coefficients that preserve the chiral (sublattice) symmetry of the model. We show that the corner mode and its localization properties are robust against disorder if the hopping coefficients have a vanishing flux on appropriately defined super plaquettes. We then show how this model with disorder can be realised using an acoustic network of air channels, and confirm the presence and robustness of corner modes., Comment: 18 pages, 13 figures. V2: small clarifications added, subsections of section III re-ordered, color scales added on figures, new appendix B-2

We demonstrate that asymmetric 3-port devices can be used to design a multi-functional set-up operating as a symmetric combiner and splitter at the same frequency. For a concrete implementation of the proposed multi-functionality protocol, we employ a resonant acoustic 3-port device operating in a subwavelength regime, showing splitting/combining abilities with nearly perfect transmission in presence of losses, induced by the interactions of the system's resonances. Finally, as an extension of the 3-port multi-functionality concept, we propose a new type of 4-port networks, consisting in an assembly of 3-port unit cells with combining/splitting properties, capable to achieve various wave guiding features with perfect transmission depending on the phase of the inputs.

In this work, we experimentally report the acoustic realization the two-dimensional (2D) Su-Schrieffer-Heeger (SSH) model in a simple network of air channels. We analytically study the steady state dynamics of the system using a set of discrete equations for the acoustic pressure, leading to the 2D SSH Hamiltonian matrix without using tight binding approximation. By building an acoustic network operating in audible regime, we experimentally demonstrate the existence of topological band gap. More supremely, within this band gap we observe the associated edge waves even though the system is open to free space. Our results not only experimentally demonstrate topological edge waves in a zero Berry curvature system but also provide a flexible platform for the study of topological properties of sound waves.

We study analytically and numerically envelope solitons (bright and gap solitons) in a one-dimensional, nonlinear acoustic metamaterial, composed of an air-filled waveguide periodically loaded by clamped elastic plates. Based on the transmission line approach, we derive a nonlinear dynamical lattice model which, in the continuum approximation, leads to a nonlinear, dispersive and dissipative wave equation. Applying the multiple scales perturbation method, we derive an effective lossy nonlinear Schr\"odinger equation and obtain analytical expressions for bright and gap solitons. We also perform direct numerical simulations to study the dissipation-induced dynamics of the bright and gap solitons. Numerical and analytical results, relying on the analytical approximations and perturbation theory for solions, are found to be in good agreement.

This article presents the experimental characterization of nonreciprocal elastic wave transmission in a single-mode elastic waveguide. This asymmetric system is obtained by coupling a selection layer with a conversion layer: the selection component is provided by a phononic crystal, while the conversion is achieved by a nonlinear self-demodulation effect in a 3D unconsolidated granular medium. A quantitative experimental study of this acoustic rectifier indicates a high rectifying ratio, up to $10^6$, with wide band (10 kHz) and an audible effect. Moreover, this system allows for wave-packet rectification and extends the future applications of asymmetric systems.

Acoustic solitons can be obtained by considering the propagation of large amplitude sound waves across a set of Helmholtz resonators. The model proposed by Sugimoto and his coauthors has been validated experimentally in previous works. Here we examine some of its theoretical properties: low-frequency regime, balance of energy, stability. We propose also numerical experiments illustrating typical features of solitary waves.

In this paper, the influence of disorder on 1D periodic lattice of resonant scatterers is inspected. These later have multiple resonance frequencies which produce bandgap in the transmission spectrum. One peculiarity of the presented system is that it is chosen with a nearly perfect overlap between the Bragg and the second hybridization bandgaps. In the case of a perfect ordered lattice, and around this overlap, this produces a narrow transparency band within a large second bandgap. As expected, the effect of the disorder is generally to increase the width of the bandgaps. Nevertheless, the transparency band appears to be robust with respect to an increase of the disorder. In this paper, we study this effect by means of experimental investigations and numerical simulations., Comment: 7 pages, 5 figures

We are interested in the experimental characterization of the Hofstadter butterfly by means of acoustical waves. The transmission of an acoustic pulse through an array of 60 variable and resonant scatterers periodically distribued along a waveguide is studied. An arbitrary scattering arrangement is realized by using the variable length of each resonator cavity. For a periodic modulation, the structures of forbidden bands of the transmission reproduce the Hofstadter butterfly. We compare experimental, analytical, and computational realizations of the Hofstadter butterfly and we show the influence of the resonances of the scatterers on the structure of the butterfly.

This paper presents an application of time-frequency methods to characterize the dispersion of acoustic waves travelling in a one-dimensional periodic or disordered lattice made up of Helmholtz resonators connected to a cylindrical tube. These methods allow (1) to evaluate the velocity of the wave energy when the input signal is an acoustic pulse ; (2) to display the evolution of the spectral content of the transient signal ; (3) to show the role of the localized nonlinearities on the propagation .i.e the emergence of higher harmonics. The main result of this paper is that the time-frequency methods point out how the nonlinearities break the localization of the waves and/or the filter effects of the lattice.

This paper presents a least mean square (LMS) algorithm for the joint estimation of acoustic and mean flow velocities from laser doppler velocimetry (LDV) measurements. The usual algorithms used for measuring with LDV purely acoustic velocity or mean flow velocity may not be used when the acoustic field is disturbed by a mean flow component. The LMS-based algorithm allows accurate estimations of both acoustic and mean flow velocities. The Cram\'er-Rao bound (CRB) of the associated problem is determined. The variance of the estimators of both acoustic and mean flow velocities is also given. Simulation results of this algorithm are compared with the CRB and the comparison leads to validate this estimator.

A new approach for for estimating the acoustic pressure in the near field of a microphone based on non-intrusive direct measurement of acoustic particle velocity is proposed. This method enables the estimation of the acoustic pressure inside a domain located in front of the microphone membrane. The acoustic pressure is calculated using the acoustic particle velocity on the frontiers of this domain and a physical model based on the Green function of the system. Results are obtained using the acoustic velocity measured with Particle Image Velocimetry (PIV) in front of a microphone excited with a plane wave inside a rectangular waveguide. They show that the diffraction of the plane wave by the microphone leads to an increase of the acoustic pressure on the microphone edge in the order of magnitude of 0.1 dB.

This paper presents an experimental, numerical and analytical study of the effect of open roof on acoustic propagation along a 3D urban canyon. The experimental study is led by means of a street scale model. The numerical results are performed with a 2D Finite Difference in Time Domain approach adapted to take into account the acoustic radiation losses due to the street open roof. An analytical model, based on the modal decomposition of the pressure field in a horizontal plane mixed with a 2D image sources model to describe the attenuation along the street, is also proposed. Results are given for several frequencies in the low frequency domain (1000-2500 Hz). The comparison of the three approaches shows a good agreement until f=100 Hz at full scale, the analytical model and the 2D numerical simulation adapted to 3D permit to modelize the acoustic propagation along a street. For higher frequency, experimental results show that the leakeage, due to the street open roof, is not anymore uniformly distributed on all modes of the street. The notion of leaky modes must be introduced to modelize the acoustic propagation in a street canyon.

This paper presents an analytical approach of the propagation of an acoustic wave through a normally distributed disordered lattice made up of Helmholtz resonators connected to a cylindrical duct. This approach allows to determine analytically the exact transmission coefficient of a weakly disordered lattice. Analytical results are compared to a well-known numerical method based on a matrix product. Furthermore, this approach gives an analytical expression of the localization length apart from the Bragg stopband which depends only on the standard deviation of the normal distribution disorder. This expression permits to study on one hand the localization length as a function of both disorder strength and frequency, and on the other hand, the propagation characteristics on the edges of two sorts of stopbands (Bragg and Helmholtz stopbands). Lastly, the value of the localization length inside the Helmholtz stopband is compared to the localization length in the Bragg stopband.