Wave propagation in a strongly disordered 1D phononic lattice supporting rotational waves

We investigate the dynamical properties of a strongly disordered micropolar lattice made up of cubic block units. This phononic lattice model supports both transverse and rotational degrees of freedom hence its disordered variant posses an interesting problem as it can be used to model physically important systems like beam-like microstructures. Different kinds of single site excitations (momentum or displacement) on the two degrees of freedom are found to lead to different energy transport both superdiffusive and subdiffusive. We show that the energy spreading is facilitated both by the low frequency extended waves and a set of high frequency modes located at the edge of the upper branch of the periodic case for any initial condition. However, the second moment of the energy distribution strongly depends on the initial condition and it is slower than the underlying one dimensional harmonic lattice (with one degree of freedom). Finally, a limiting case of the micropolar lattice is studied where Anderson localization is found to persist and no energy spreading takes place

Chaos and Anderson Localization in Disordered Classical Chains: Hertzian vs FPUT models

International audienceWe numerically investigate the dynamics of strongly disordered 1D lattices under single particle displacements, using both the Hertzian model, describing a granular chain, and the α + β Fermi-Pasta-Ulam-Tsingou model (FPUT). The most profound difference between the two systems is the discontinuous nonlinearity of the granular chain appearing whenever neighboring particles are detached. We therefore sought to unravel the role of these discontinuities in the destruction of Anderson localization and their influence on the system's chaotic dynamics. Our results show that the dynamics of both models can be characterized by: (i) localization with no chaos; (ii) localization and chaos; (iii) spreading of energy, chaos and equipartition. The discontinuous nonlinearity of the Hertzian model is found to trigger energy spreading at lower energies. More importantly, a transition from Anderson localization to energy equipartition is found for the Hertzian chain and is associated with the"propagation" of the discontinuous nonlinearity in the chain. On the contrary, the FPUT chain exhibits an alternate behavior between localized and delocalized chaotic behavior which is strongly dependent on the initial energy excitation

The dynamical playground of a higher-order cubic Ginzburg-Landau equation: from orbital connections and limit cycles to invariant tori and the onset of chaos

The dynamical behavior of a higher-order cubic Ginzburg-Landau equation is found to include a wide range of scenarios due to the interplay of higher-order physically relevant terms. We find that the competition between the third-order dispersion and stimulated Raman scattering effects, gives rise to rich dynamics: this extends from Poincar\'{e}-Bendixson--type scenarios, in the sense that bounded solutions may converge either to distinct equilibria via orbital connections, or space-time periodic solutions, to the emergence of almost periodic and chaotic behavior. One of our main results is that the third-order dispersion has a dominant role in the development of such complex dynamics, since it can be chiefly responsible (i.e., even in the absence of the other higher-order effects) for the existence of the periodic, quasi-periodic and chaotic spatiotemporal structures. Suitable low-dimensional phase space diagnostics are devised and used to illustrate the different possibilities and identify their respective parametric intervals over multiple parameters of the model.Comment: 11 pages, 9 figures. To appear in Physical Review

Oscillons and oscillating kinks in the Abelian-Higgs model

We study the classical dynamics of the Abelian Higgs model employing an asymptotic multiscale expansion method, which uses the ratio of the Higgs to the gauge field amplitudes as a small parameter. We derive an effective nonlinear Schr\"{o}dinger equation for the gauge field, and a linear equation for the scalar field containing the gauge field as a nonlinear source. This equation is used to predict the existence of oscillons and oscillating kinks for certain regimes of the ratio of the Higgs to the gauge field masses. Results of numerical simulations are found to be in very good agreement with the analytical findings, and show that the oscillons are robust, while kinks are unstable. It is also demonstrated that oscillons emerge spontaneously as a result of the onset of the modulational instability of plane wave solutions of the model. Connections of the obtained solutions with the phenomenology of superconductors is discussed.Comment: arXiv admin note: substantial text overlap with arXiv:1306.386

Statics and dynamics of atomic dark-bright solitons in the presence of delta-like impurities

Adopting a mean-field description for a two-component atomic Bose-Einstein condensate, we study the stat- ics and dynamics of dark-bright solitons in the presence of localized impurities. We use adiabatic perturbation theory to derive an equation of motion for the dark-bright soliton center. We show that, counter-intuitively, an attractive (repulsive) delta-like impurity, acting solely on the bright soliton component, induces an effective localized barrier (well) in the effective potential felt by the soliton; this way, dark-bright solitons are reflected from (transmitted through) attractive (repulsive) impurities. Our analytical results for the small-amplitude oscil- lations of solitons are found to be in good agreement with results obtained via a Bogoliubov-de Gennes analysis and direct numerical simulations.Comment: 11 pages, 11 figures, to appear in Phys. Rev.

Design of acoustic metamaterials made of Helmholtz resonators for perfect absorption by using the complex frequency plane

[Otros] Dans cette revue, nous présentons des résultats sur l'absorption acoustique parfaite sub-longueur d'onde faisant appel à des métamatériaux acoustiques avec des résonateurs Helmholtz pour différentes configurations. L'absorption parfaite à basse fréquence nécessite une augmentation du nombre d'états aux basses fréquences ainsi que de trouver les bonnes conditions pour une adaptation d'impédance avec le milieu environnant. Si en outre, on souhaite réduire les dimensions géométriques des structures proposées pour des questions pratiques, on peut utiliser des résonateurs locaux judicieusement conçus afin d'attendre une absorption parfaite sub-longueur d'onde. Les résonateurs de Helmholtz se sont révélés de bons candidats en raison de leur accordabilité aisée de la géométrie, donc de la fréquence de résonance, de la fuite d'énergie et des pertes intrinsèques. Lorsqu'ils sont branchés à un guide d'ondes ou à un milieu environnant, ils se comportent comme des systèmes ouverts, avec pertes et résonances caractérisés par leur fuite d'énergie et leurs pertes intrinsèques. L'équilibre entre ces deux aspects représente la condition de couplage critique et donne lieu à un maximum d'absorption d'énergie. Le mécanisme de couplage critique est ici représenté dans le plan de fréquence complexe afin d'interpréter la condition d'adaptation d'impédance. Dans cette revue, nous discutons en détail la possibilité d'obtenir une absorption parfaite par ces conditions de couplage critiques dans différents systèmes tels que la réflexion (à un port), la transmission (à deux ports) ou les systèmes à trois ports.[EN] In this review, we present the results on sub-wavelength perfect acoustic absorption using acoustic metamaterials made of Helmholtz resonators with different setups. Low frequency perfect absorption requires to increase the number of states at low frequencies and finding the good conditions for impedance matching with the background medium. If, in addition, one wishes to reduce the geometric dimensions of the proposed structures for practical issues, one can use properly designed local resonators and achieve subwavelength perfect absorption. Helmholtz resonators have been shown good candidates due to their easy tunability of the geometry, so of the resonance frequency, the energy leakage and the intrinsic losses. When plugged to a waveguide or a surrounding medium they behave as open, lossy and resonant systems characterized by their energy leakage and intrinsic losses. The balance between these two represents the critical coupling condition and gives rise to maximum energy absorption. The critical coupling mechanism is represented here in the complex frequency plane in order to interpret the impedance matching condition. In this review we discuss in detail the possibility to obtain perfect absorption by these critical coupling conditions in different systems such as reflection (one-port), transmission (two-ports) or three-ports systems.The authors gratefully acknowledge the ANR-RGC METARoom (ANR-18-CE08-0021) project and the project HYPERMETA funded under the program Étoiles Montantes of the Région Pays de la Loire. NJ acknowledges financial support from the Spanish Ministry of Science, Innovation and Universities (MICINN) through grant ¿Juan de la Cierva-Incorporación¿ (IJC2018-037897- I). This article is based upon work from COST Action DENORMS CA15125, supported by COST (European Cooperation in Science and Technology).Romero-García, V.; Jimenez, N.; Theocharis, G.; Achilleos, V.; Merkel, A.; Richoux, O.; Tournat, V.... (2020). Design of acoustic metamaterials made of Helmholtz resonators for perfect absorption by using the complex frequency plane. 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Emergent non-Hermitian models

The Hatano-Nelson and the non-Hermitian Su-Schrieffer-Heeger models are paradigmatic examples of non-Hermitian systems that host nontrivial boundary phenomena. In this work, we use recently developed graph-theoretical tools to design systems whose isospectral reduction, akin to an effective Hamiltonian, has the form of either of these two models. In the reduced version, the couplings and onsite potentials become energy dependent. We show that this leads to interesting phenomena such as an energy-dependent non-Hermitian skin effect, where eigenstates can simultaneously localize on either ends of the systems, with different localization lengths. Moreover, we predict the existence of various topological edge states, pinned at nonzero energies, with different exponential envelopes, depending on their energy. Overall, our work sheds light on the nature of topological phases and the non-Hermitian skin effect in one-dimensional systems