arXiv subjects

G. Theocharis

Publications and source records attributed to G. Theocharis.

At least 37 records · Page 2Linked to original sources

arXiv2016

Coherent Perfect Absorption induced by the nonlinearity of a Helmholtz resonator

In this work, we analytically report Coherent Perfect Absorption induced by the acoustic nonlinear response of a Helmholtz Resonator side loaded to a waveguide. In particular, we show that this two-port acoustic system can perfectly absorb two high amplitude symmetric incident waves when the additive nonlinear losses in the HR, induced by the jet flow separation, together with the weak linear viscothermal losses of the HR balance the radiation losses to the waveguide. For the case of the one-sided incidence configuration, this condition leads to an absorption equal to 0.5. This result, which is verified experimentally, is in a good agreement with an analytical nonlinear model of the impedance of the HR. The nonlinear control of perfect absorption using resonators will open new possibilities in the design of high amplitude sound attenuators for aero-engine applications.

physics.class-ph↗

arXiv2015

Energy transport in one-dimensional disordered granular solids

We investigate the energy transport in one-dimensional disordered granular solids by extensive numerical simulations. In particular, we consider the case of a polydisperse granular chain composed of spherical beads of the same material and with radii taken from a random distribution. We start by examining the linear case, in which it is known that the energy transport strongly depends on the type of initial conditions. Thus, we consider two sets of initial conditions: i) an initial displacement and ii) an initial momentum excitation of a single bead. After establishing the regime of sufficiently strong disorder, we focus our studies on the role of nonlinearity for both sets of initial conditions. By increasing the initial excitation amplitudes we are able to identify three distinct dynamical regimes with different energy transport properties: a near linear, a weakly nonlinear and a highly nonlinear regime. Although energy spreading is found to be increasing for higher nonlinearities, in the weakly nonlinear regime no clear asymptotic behavior of the spreading is found. In this regime, we additionally find that energy, initially trapped in a localized region, can be eventually detrapped and this has a direct influence on the fluctuations of the energy spreading. We also demonstrate that in the highly nonlinear regime, the differences in energy transport between the two sets of initial conditions vanish. Actually, in this regime the energy is almost ballistically transported through shock-like excitations.

nlin.CD↗

arXiv2015

Control of acoustic absorption in 1D scattering by indirect coupled resonant scatterers

We experimentally report perfect acoustic absorption through the interplay of the inherent losses and transparent modes with high $Q$ factor. These modes are generated in a two-port, one-dimensional waveguide which is side-loaded by isolated resonators of moderate $Q$ factor. In symmetric structures, we show that in the presence of small inherent losses, these modes lead to coherent perfect absorption associated with one-sided absorption slightly larger than 0.5. In asymmetric structures, near perfect one-sided absorption is possible (96 \%) with a deep sub-wavelength sample ($λ/28$). The control of strong absorption by the proper tuning of few resonators with weak losses will open new possibilities in various wave-control devices.

physics.class-ph↗

arXiv2015

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.

physics.class-ph↗

arXiv2015

Acoustic solitons in waveguides with Helmholtz resonators: transmission line approach

We report experimental results and study theoretically soliton formation and propagation in an airfilled acoustic waveguide side loaded with Helmholtz resonators. Our theoretical approach relies on a transmission-line description of this setting, which leads to a nonlinear dynamical lattice model. The latter is treated analytically, by means of dynamical systems and multiscale expansion techniques, and leads to various soliton solutions for the pressure. These include Boussinesq-like and Korteweg-de Vries pulse-shaped solitons, as well as nonlinear Schröodinger envelope solitons. The analytical predictions are in excellent agreement with direct numerical simulations and in qualitative agreement with the experimental observations.

nlin.PS↗

arXiv2015

Nonlinear Hysteretic Torsional Waves

We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities, and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other type of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short term memory as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.

physics.class-ph↗

arXiv2014

Perfect and broadband acoustic absorption by critical coupling

We experimentally and analytically report broadband and narrowband perfect absorption in two different acoustic waveguide-resonator geometries by the mechanism of critical coupling. In the first geometry the resonator (a Helmholtz resonator) is side-loaded to the waveguide and it has a moderate quality factor. In the second geometry the resonator (a viscoelastic porous plate) is in-line loaded and it contains two resonant modes with low quality factor. The interplay between the energy leakage of the resonant modes into the waveguide and the inherent losses of the system reveals a perfect and a broadband nearly perfect absorption. The results shown in this work can motivate relevant research for the design of broadband perfect absorbers in other domains of wave physics.

physics.class-ph↗

arXiv2014

Highly Nonlinear Wave Propagation in Elastic Woodpile Periodic Structures

In the present work, we experimentally implement, numerically compute with and theoretically analyze a configuration in the form of a single column woodpile periodic structure. Our main finding is that a Hertzian, locally-resonant, woodpile lattice offers a test bed for the formation of genuinely traveling waves composed of a strongly-localized solitary wave on top of a small amplitude oscillatory tail. This type of wave, called a nanopteron, is not only motivated theoretically and numerically, but are also visualized experimentally by means of a laser Doppler vibrometer. This system can also be useful for manipulating stress waves at will, for example, to achieve strong attenuation and modulation of high-amplitude impacts without relying on damping in the system.

cond-mat.other↗

arXiv2013

Slow sound propagation in lossy locally resonant periodic structures

We investigate the sound propagation in an air-filled tube periodically loaded with Helmholtz resonators. By tuning the Helmholtz with the Bragg resonance, we study the efficiency of slow sound propagation in the presence of the intrinsic viscothermal losses of the system. While in the lossless case the overlapping of the resonances results in slow sound induced transparency of a narrow frequency band surrounded by a strong and broadband gap, the inclusion of the unavoidable losses imposes limits to the slowdown factor and the maximum transmission. Experiments, theory and finite element simulations have been used for the characterization of acoustic wave propagation. Experiments, in good agreement with the lossy theory, reveal the possibility of slowing sound at low frequencies by 20 times. A trade-off among the relevant parameters (delay time, maximum transmission, bandwidth) as a function of the tuning between Bragg and Helmholtz resonance frequency is also presented.

cond-mat.mtrl-sci↗

arXiv2012

Hysteresis Loops and Multi-stability: From Periodic Orbits to Chaotic Dynamics (and Back) in Diatomic Granular Crystals

In the present work we consider a diatomic granular crystal, consisting of alternating aluminum and steel spheres, where the first sphere is an aluminum one. The combination of dissipation, driving of the boundary, and intrinsic nonlinearity leads to complex dynamics. Specifically, we find that the interplay of nonlinear surface modes with modes created by the driver create the possibility, as the driving amplitude is increased, of limit cycle saddle-node bifurcations beyond which the dynamics of the system becomes chaotic. In this chaotic state, part of the applied energy can propagate through the chain. We also find that the chaotic branch depends weakly on the driving frequency and speculate a connection between the chaotic dynamics with the gap openings between the spheres. Finally, a reverse parametric continuation reveals hysteretic dynamics and the existence of an interval of multi-stability involving stable periodic solutions and genuinely chaotic ones. The computational identification and theoretical interpretation of the bifurcation diagram of the system is corroborated by direct experimental measurements showcasing all of the above features.

nlin.PS↗

arXiv2012

Dark Breathers in Granular Crystals

We present a study of the existence, stability and bifurcation structure of families of dark breathers in a one-dimensional uniform chain of spherical beads under static load. A defocus- ing nonlinear Schrodinger equation (NLS) is derived for frequencies that are close to the edge of the phonon band and is used to construct targeted initial conditions for numerical computations. Salient features of the system include the existence of large amplitude solutions that bifurcate with the small amplitude solutions described by the NLS equation, and the presence of a nonlinear instability that, to the best of the authors knowledge, has not been observed in classical Fermi- Pasta-Ulam lattices. Finally, it is also demonstrated that these dark breathers can be detected in a physically realistic way by merely actuating the ends of an initially at rest chain of beads and inducing destructive interference between their signals.

nlin.PS↗

arXiv2011

Stationary states of a nonlinear Schrödinger lattice with a harmonic trap

We study a discrete nonlinear Schrödinger lattice with a parabolic trapping potential. The model, describing, e.g., an array of repulsive Bose-Einstein condensate droplets confined in the wells of an optical lattice, is analytically and numerically investigated. Starting from the linear limit of the problem, we use global bifurcation theory to rigorously prove that - in the discrete regime - all linear states lead to nonlinear generalizations thereof, which assume the form of a chain of discrete dark solitons (as the density increases). The stability of the ensuing nonlinear states is studied and it is found that the ground state is stable, while the excited states feature a chain of stability/instability bands. We illustrate the mechanisms under which discreteness destabilizes the dark-soliton configurations, which become stable only inside the continuum regime. Continuation from the anti-continuum limit is also considered, and a rich bifurcation structure is revealed.

cond-mat.quant-gas↗

arXiv2011

Defect Modes in One-Dimensional Granular Crystals

We study the vibrational spectra of one-dimensional statically compressed granular crystals (arrays of elastic particles in contact) containing defects. We focus on the prototypical settings of one or two spherical defects (particles of smaller radii) interspersed in a chain of larger uniform spherical particles. We measure the near-linear frequency spectrum within the spatial vicinity of the defects, and identify the frequencies of the localized defect modes. We compare the experimentally determined frequencies with those obtained by numerical eigen-analysis and by analytical expressions based on few-site considerations. We also present a brief numerical and experimental example of the nonlinear generalization of a single-defect localized mode.

cond-mat.other↗

arXiv2010

Discrete breathers at the interface between a diatomic and monoatomic granular chain

In the present work, we develop a systematic examination of the existence, stability and dynamical properties of a discrete breather at the interface between a diatomic and a monoatomic granular chain. We remarkably find that such an "interface breather" is more robust than its bulk diatomic counterpart throughout the gap of the linear spectrum. The latter linear spectral gap needs to exist for the breather state to arise and the relevant spectral conditions are discussed. We illustrate the minimal excitation conditions under which such an interface breather can be "nucleated" and analyze its apparently weak interaction with regular highly nonlinear solitary waveforms.

nlin.PS↗

arXiv2010

Tunable Vibrational Band Gaps in One-Dimensional Diatomic Granular Crystals with Three-Particle Unit Cells

We investigate the tunable vibration filtering properties of one-dimensional diatomic granular crystals composed of arrays of stainless steel spheres and cylinders interacting via Hertzian contact. The arrays consist of periodically repeated three-particle unit cells (steel-cylinder-sphere) in which the length of the cylinder is varied systematically. We apply static compression to linearize the dynamic response of the crystals and characterize their linear frequency spectrum. We find good agreement between theoretical dispersion relation analysis (for infinite systems), state-space analysis (for finite systems), and experiments. We report the observation of up to three distinct pass bands and two finite band gaps and show their tunability for variations in cylinder length and static compression.

cond-mat.other↗

arXiv2010

Intrinsic Energy Localization through Discrete Gap Breathers in One-Dimensional Diatomic Granular Crystals

We present a systematic study of the existence and stability of discrete breathers that are spatially localized in the bulk of a one-dimensional chain of compressed elastic beads that interact via Hertzian contact. The chain is diatomic, consisting of a periodic arrangement of heavy and light spherical particles. We examine two families of discrete gap breathers: (1) an unstable discrete gap breather that is centered on a heavy particle and characterized by a symmetric spatial energy profile and (2) a potentially stable discrete gap breather that is centered on a light particle and is characterized by an asymmetric spatial energy profile. We investigate their existence, structure, and stability throughout the band gap of the linear spectrum and classify them into four regimes: a regime near the lower optical band edge of the linear spectrum, a moderately discrete regime, a strongly discrete regime that lies deep within the band gap of the linearized version of the system, and a regime near the upper acoustic band edge. We contrast discrete breathers in anharmonic FPU-type diatomic chains with those in diatomic granular crystals, which have a tensionless interaction potential between adjacent particles, and highlight in that the asymmetric nature of the latter interaction potential may lead to a form of hybrid bulk-surface localized solutions.

cond-mat.other↗

arXiv2010

Dark solitons in cigar-shaped Bose-Einstein condensates in double-well potentials

We study the statics and dynamics of dark solitons in a cigar-shaped Bose-Einstein condensate confined in a double-well potential. Using a mean-field model with a non-cubic nonlinearity, appropriate to describe the dimensionality crossover regime from one to three dimensional, we obtain branches of solutions in the form of single- and multiple-dark soliton states, and study their bifurcations and stability. It is demonstrated that there exist dark soliton states which do not have a linear counterpart and we highlight the role of anomalous modes in the excitation spectra. Particularly, we show that anomalous mode eigenfrequencies are closely connected to the characteristic soliton frequencies as found from the solitons' equations of motion, and how anomalous modes are related to the emergence of instabilities. We also analyze in detail the role of the height of the barrier in the double well setting, which may lead to instabilities or decouple multiple dark soliton states.

cond-mat.quant-gas↗

arXiv2009

Discrete Breathers in One-Dimensional Diatomic Granular Crystals

We report the experimental observation of discrete breathers in a one-dimensional diatomic granular crystal composed of compressed elastic beads that interact via Hertzian contact. We first characterize their effective linear spectrum both theoretically and experimentally. We then illustrate theoretically and numerically the modulational instability of the lower edge of the optical band. This leads to the dynamical formation of long-lived breather structures, whose families of solutions we compute throughout the linear spectral gap. Finally, we observe experimentally such localized breathing modes with quantitative characteristics that agree with our numerical results.

nlin.PS↗