110 research outputs found
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
Acoustic characterization of Hofstadter butterfly with resonant scatterers
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
Invariant currents in lossy acoustic waveguides with complete local symmetry
We implement the concept of complete local symmetry in lossy acoustic
waveguides. Despite the presence of losses, the existence of a spatially
invariant current is shown theoretically and observed experimentally. We
demonstrate how this invariant current leads to the generalization of the Bloch
and parity theorems for lossy systems defining a mapping of the pressure field
between symmetry related spatial domains. Using experimental data we verify
this mapping with remarkable accuracy. For the performed experiment we employ a
construction technique based on local symmetries which allows the design of
setups with prescribed perfect transmission resonances in the lossless case.
Our results reveal the fundamental role of symmetries in restricted spatial
domains and clearly indicate that completely locally symmetric devices
constitute a promising class of setups, regarding the manipulation of wave
propagation.Comment: 11 pages, 5 figure
Duality of bounded and scattering wave systems with local symmetries
We investigate the spectral properties of a class of hard-wall bounded
systems, described by potentials exhibiting domain-wise different local
symmetries. Tuning the distance of the domains with locally symmetric potential
from the hard wall boundaries leads to extrema of the eigenenergies. The
underlying wavefunction becomes then an eigenstate of the local symmetry
transform in each of the domains of local symmetry. These extrema accumulate
towards eigenenergies which do not depend on the position of the potentials
inside the walls. They correspond to perfect transmission resonances of the
associated scattering setup, obtained by removing the hard walls. We argue that
this property characterizes the duality between scattering and bounded systems
in the presence of local symmetries. Our findings are illustrated at hand of a
numerical example with a potential consisting of two domains of local symmetry,
each one comprised of Dirac ? barriers.Comment: 8 pages, 6 figure
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
Perfect and broadband acoustic absorption by critically coupled sub-wavelength resonators
International audiencePerfect absorption is an interdisciplinary topic with a large number of applications, the challenge of which consists of broadening its inherently narrow frequency-band performance. We experimentally and analytically report perfect and broadband absorption for audible sound, by the mechanism of critical coupling, with a sub-wavelength multi-resonant scatterer (SMRS) made of a plate-resonator/ closed waveguide structure. In order to introduce the role of the key parameters, we first present the case of a single resonant scatterer (SRS) made of a Helmholtz resonator/closed waveguide structure. In both cases the controlled balance between the energy leakage of the several resonances and the inherent losses of the system leads to perfect absorption peaks. In the case of the SMRS we show that systems with large inherent losses can be critically coupled using resonances with large leakage. In particular, we show that in the SMRS system, with a thickness of λ/12 and diameter of λ/7, several perfect absorption peaks overlap to produce absorption bigger than 93% for frequencies that extend over a factor of 2 in audible frequencies. The reported concepts and methodology provide guidelines for the design of broadband perfect absorbers which could contribute to solve the major issue of noise reduction
Perfect absorption in mirror-symmetric acoustic metascreens
Mirror-symmetric acoustic metascreens producing perfect absorption
independently of the incidence side are theoretically and experimentally
reported in this work. The mirror-symmetric resonant building blocks of the
metascreen support symmetric and antisymmetric resonances that can be tuned to
be at the same frequency (degenerate resonances). The geometry of the building
blocks is optimized to critically couple both the symmetric and the
antisymmetric resonances at the same frequency allowing perfect absorption of
sound from both sides of the metascreen. A hybrid analytical model based on the
transfer matrix method and the modal decomposition of the exterior acoustic
field is developed to analyze the scattering properties of the metascreen. The
resulting geometry is 3D printed and experimentally tested in an impedance
tube. Experimental results agree well with the theoretical predictions proving
the efficiency of these metascreens for the perfect absorption of sound in the
ventilation problems
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