arXiv subjects

Georgios Theocharis

Publications and source records attributed to Georgios Theocharis.

At least 19 recordsLinked to original sources

arXiv2026

Single-particle limit of a topological edge state in a locally resonant band gap

Topological metamaterials promise unprecedented wave control. Here, we theoretically and numerically investigate a one-dimensional Su-Schrieffer-Heeger (SSH)-inspired stiffness dimer modified with a local resonator, which imparts a frequency-dependent effective stiffness to the unit cell. The resonator introduces an attenuation singularity: at a frequency at which the effective stiffness vanishes, the spatial attenuation of waves diverges. By tuning a dimerization parameter, we migrate this singularity from one band gap to the other via an intermediate flat-band state, transferring the dominant local-resonance character between the gaps without closing either gap and while preserving the underlying band topology. Crucially, when the resulting topological edge state intersects the attenuation singularity, the edge state collapses onto a single boundary particle, forming a single-particle mode (SPM). This yields an inverse participation ratio of exactly unity, the theoretical limit for localization in a discrete system. Moreover, this extreme localization can be realized at low frequencies, below the first Bragg-type band gap. Further, we demonstrate that while random disorder detunes this mode, merely tuning the boundaries stabilizes the single-particle mode over a broad parameter range. Our findings provide a clear pathway to designing ultra-localized edge states in low-frequency regimes, where band topology guarantees the edge mode and local resonance drives its single-particle confinement.

physics.app-ph↗

arXiv2026

Anisotropic Cylindrical Waves in a Square Lattice of Acoustic Waveguides

We investigate the propagation of cylindrical waves in a square network of acoustic waveguides. We establish, both theoretically and experimentally, the anisotropic dispersion relation governing wave propagation in the network, and demonstrate excellent agreement between experimental measurements and theoretical predictions. Owing to this anisotropic band structure, each propagation direction exhibits distinct dispersive properties. Consequently, the network supports anisotropic cylindrical waves at both low- and high-amplitudes, with waveforms that vary markedly with direction: from nearly dispersionless pulses to Airy-like wave packets in the linear regime, and from sharp shock-like fronts to smooth solitary-like profiles in the nonlinear regime. The theoretical results are further corroborated by numerical simulations based on the two-dimensional Westervelt equation.

nlin.PS↗

arXiv2025

Energy transport and chaos in a one-dimensional disordered nonlinear stub lattice

We investigate energy propagation in a one-dimensional stub lattice in the presence of both disorder and nonlinearity. In the periodic case, the stub lattice hosts two dispersive bands separated by a flat band; however, we show that sufficiently strong disorder fills all intermediate band gaps. By mapping the two-dimensional parameter space of disorder and nonlinearity, we identify three distinct dynamical regimes (weak chaos, strong chaos, and self-trapping) through numerical simulations of initially localized wave packets. When disorder is strong enough to close the frequency gaps, the results closely resemble those obtained in the one-dimensional disordered discrete nonlinear Schrödinger equation and Klein-Gordon lattice model. In particular, subdiffusive spreading is observed in both the weak and strong chaos regimes, with the second moment $m_2$ of the norm distribution scaling as $m_2 \propto t^{0.33}$ and $m_2 \propto t^{0.5}$, respectively. The system's chaotic behavior follows a similar trend, with the finite-time maximum Lyapunov exponent $Λ$ decaying as $Λ\propto t^{-0.25}$ and $Λ\propto t^{-0.3}$. For moderate disorder strengths, i.e., near the point of gap closing, we find that the presence of small frequency gaps does not exert any noticeable influence on the spreading behavior. Our findings extend the characterization of nonlinear disordered lattices in both weak and strong chaos regimes to other network geometries, such as the stub lattice, which serves as a representative flat-band system.

nlin.CD↗

arXiv2025

Nonlinearity-induced corner states in a kagome lattice

Nonlinearity provides a powerful mechanism for controlling energy localization in structured dynamical systems. In this study, we investigate the emergence of nonlinearity-induced energy localization at the corners of a kagome lattice model featuring onsite cubic nonlinearity. Employing quench dynamics simulations and nonlinear continuation methods, we analyze the temporal and spectral characteristics of localized states under strong nonlinearity. Our results demonstrate the formation of stable, localized corner states, strikingly, even within the parameter regime corresponding to the topologically trivial phase of the underlying linear system, which normally lacks such boundary modes. Furthermore, we identify distinct families of nonlinearity-induced corner states residing within the semi-infinite spectral gap above the bulk bands in both the trivial and nontrivial phases. Stability analysis and nonlinear continuation reveal they are intrinsic nonlinear solutions, fundamentally distinct from perturbations of linear topological or bulk states. These findings elucidate a robust mechanism for generating localized states via nonlinearity, independent of linear topological protection, and provide answers to fundamental questions about the nature of nonlinear topological phenomena. The ability to create tunable, localized states in various spectral regions offers potential applications in energy harvesting, wave manipulation, and advanced signal processing.

cond-mat.mes-hall↗

arXiv2025

Gradient catastrophe and Peregrine soliton in nonlinear flexible mechanical metamaterials

We explore the generation of extreme wave events in mechanical metamaterials using the regularization of the gradient catastrophe theory developed by A. Tovbis and M. Bertola for the nonlinear Schrödinger equation. According to this theory, Peregrine solitons can locally emerge in the semiclassical limit of the nonlinear Schrödinger equation. Our objective is to determine whether the phenomenon of gradient catastrophe can occur in a class of architected structures designated as flexible mechanical metamaterials, both with and without losses. We demonstrate theoretically and numerically that this phenomenon can occur in a canonical example of such flexible mechanical metamaterial, a chain of rotating units, studied earlier for its ability to support robust nonlinear waves such as elastic vector solitons. We find that in the presence of weak losses, the gradient catastrophe persists although the amplitude of extreme generated events is smaller and their onset is delayed compared to the lossless configuration.

nlin.PS↗

arXiv2025

Observation of mechanical kink control and generation via phonons

Kinks (or domain walls) are localized transitions between distinct ground states associated with a topological invariant, and are central to many phenomena across physics, from condensed matter to cosmology. While phonon (i.e., small-amplitude vibration) wave packets have been theorized to deterministically interact with kinks and initiate their movement, this interaction has remained elusive in experiments, where only uncontrollable stochastic kink motion generated by thermal phonons or dislocation glide by low-frequency quasi-static loading have been observed. This is partly because all physical systems that support kinks are, at some level, discrete, making deterministic phonon control of kinks extremely challenging due to the existence of Peierls-Nabarro (PN) barrier. Here, we demonstrate, for the first time, experimental observation of phonon-mediated control and generation of mechanical kinks, which we enable using a topological metamaterial that constitutes an elastic realization of the Kane-Lubensky chain model. Our metamaterial overcomes the PN barrier by supporting a single, topologically protected kink that requires zero energy to form and move. Using simulations that show close agreement with our experimental observations, we also reveal unique dynamics of phonon interplay with highly discrete kinks, including long-duration motion and a continuous family of internal modes, features absent in other discrete nonlinear systems. This work introduces a new paradigm for topological kink control, with potential applications in material stiffness tuning, shape morphing, locomotion, and robust signal transmission.

nlin.PS↗

arXiv2025

Robustness of perfect transmission resonances to asymmetric perturbation

We investigate the impact of asymmetric perturbations on the perfect transmission resonances (PTRs) of one-dimensional finite periodic systems. With no perturbations, the scattering region consists of $N$ identical cells, and the transmission spectrum exhibits at least $N-1$ PTRs in each pass band of the Bloch dispersion of the unit cell. By introducing a perturbation, the periodic structure is broken, which \textit{a priori} results in the elimination of all PTRs. However, we demonstrate that PTRs can still arise under asymmetric perturbations when the unperturbed system possesses mirror symmetry, utilizing the $\mathcal{PT}$ symmetry of the unperturbed reflectionless eigenvalue problem. We also reveal an intriguing connection between two seemingly independent PTRs that lies in the symmetry of the unperturbed unit cell: If one PTR is preserved, then a dual one is necessarily also preserved. Our findings offer insights for the design of, for example, a robust antireflection setup at multiple wavelengths or all-optical diode devices.

quant-ph↗

arXiv2024

Topologically invisible defects in chiral mirror lattices

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.

cond-mat.mes-hall↗

arXiv2024

Transient amplification in stable Floquet media

The Mathieu equation occurs naturally in the description of vibrations or in the propagation of waves in media with time-periodic refractive index. It is known to lead to exponential parametric instability in some regions of the parameter space. However, even in the stable region the matrix that propagates the initial conditions forward in time is non-normal and therefore it can result in transient amplification. By optimizing over initial conditions as well as initial time we show that significant transient amplifications can be obtained, going beyond the one simply stemming from adiabatic invariance. Moreover, we explore the monodromy matrix in more depth, by studying its $ε$-pseudospectra and Petermann factors, demonstrating that is the degree of non-normality of this matrix that determines the global amplifying features. In the context of wave propagation in time-varying media, this transient behavior allows us to display arbitrary amplification of the wave amplitude that is not due to exponential parametric instability.

cond-mat.other↗

arXiv2024

Edge States with Hidden Topology in Spinner Lattices

Symmetries -- whether explicit, latent, or hidden -- are fundamental to understanding topological materials. This work introduces a prototypical spring-mass model that extends beyond established canonical models, revealing topological edge states with distinct profiles at opposite edges. These edge states originate from hidden symmetries that become apparent only in deformation coordinates, as opposed to the conventional displacement coordinates used for bulk-boundary correspondence. Our model, realized through the intricate connectivity of a spinner chain, demonstrates experimentally distinct edge states at opposite ends. By extending this framework to two dimensions, we explore the conditions required for such edge waves and their hidden symmetry in deformation coordinates. We also show that these edge states are robust against disorders that respect the hidden symmetry. This research paves the way for advanced material designs with tailored boundary conditions and edge state profiles, offering potential applications in fields such as photonics, acoustics, and mechanical metamaterials.

cond-mat.mes-hall↗

arXiv2024

Envelope vector solitons in nonlinear flexible mechanical metamaterials

In this paper, we employ a combination of analytical and numerical techniques to investigate the dynamics of lattice envelope vector soliton solutions propagating within a one-dimensional chain of flexible mechanical metamaterial. To model the system, we formulate discrete equations that describe the longitudinal and rotational displacements of each individual rigid unit mass using a lump element approach. By applying the multiple-scales method in the context of a semi-discrete approximation, we derive an effective nonlinear Schrödinger equation that characterizes the evolution of rotational and slowly varying envelope waves from the aforementioned discrete motion equations. We thus show that this flexible mechanical metamaterial chain supports envelope vector solitons where the rotational component has the form of either a bright or a dark soliton. In addition, due to nonlinear coupling, the longitudinal displacement displays kink-like profiles thus forming the 2-components vector soliton. These findings, which include specific vector envelope solutions, enrich our knowledge on the nonlinear wave solutions supported by flexible mechanical metamaterials and open new possibilities for the control of nonlinear waves and vibrations.

nlin.PS↗

arXiv2024

Nonlinear Corner States in Topologically Nontrivial Kagome Lattice

We investigate a higher-order topological insulator (HOTI) under strong nonlinearity, focusing on the existence and stability of high-amplitude corner states, which can find applications in optics, acoustics, elastodynamics, and other wave-based systems. Our study centers on a breathing Kagome lattice composed of point masses and springs known to exhibit edge and corner states in its linear regime. By introducing onsite cubic nonlinearity, we analyze its impact on both edge and corner states. The nonlinear continuation of the corner state unveils stable high-amplitude corner states within the lattice, featuring non-zero displacements at even sites from the corner -- a characteristic absent in the linear limit. Interestingly, the nonlinear continuation of the edge state reveals its transformation into distinct families of high-amplitude corner states via two pitchfork bifurcations. While some states maintain stability, others become unstable through real instability and Neimark-Sacker bifurcation. These unstable corner states dissipate their energy into the edges and the bulk over an extended period, as corroborated by long-time dynamical simulations. Consequently, our study provides insights into achieving significant energy localization at the corners of HOTIs through various classes of nonlinear states.

cond-mat.mes-hall↗

arXiv2023

Dirac Solitons and Topological Edge States in the $β$-Fermi-Pasta-Ulam-Tsingou dimer lattice

We consider a dimer lattice of the Fermi-Pasta-Ulam-Tsingou (FPUT) type, where alternating linear couplings have a controllably small difference, and the cubic nonlinearity ($β$-FPUT) is the same for all interaction pairs. We use a weakly nonlinear formal reduction within the lattice bandgap to obtain a continuum, nonlinear Dirac-type system. We derive the Dirac soliton profiles and the model's conservation laws analytically. We then examine the cases of the semi-infinite and the finite domains and illustrate how the soliton solutions of the bulk problem can be ``glued'' to the boundaries for different types of boundary conditions. We thus explain the existence of various kinds of nonlinear edge states in the system, of which only one leads to the standard topological edge states observed in the linear limit. We finally examine the stability of bulk and edge states and verify them through direct numerical simulations, in which we observe a solitary wave setting into motion due to the instability.

nlin.PS↗

arXiv2023

Equireflectionality and customized unbalanced coherent perfect absorption in asymmetric waveguide networks

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.

physics.class-ph↗

arXiv2023

Wave-packet spreading in the disordered and nonlinear Su-Schrieffer-Heeger chain

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.

physics.optics↗

arXiv2022

Topological phase transition in disordered elastic quantum spin Hall system

We investigate the effect of disorder on topologically nontrivial states in a two dimension (2D) mechanical system. We first propose a quantum spin Hall (QSH) insulator based on an out-of-plane spring-mass model and analytically study the interplay between the disorder and topology in both topologically trivial and nontrivial systems. We adopt the spin Bott index to characterize the topological property in disordered mechanical systems. By tracking the evolution of the spin Bott index with the increase of disorders, we quantitatively demonstrate the disorder induced transition from a topologically nontrivial QSH insulator to a trivial insulator. We then validate the topological phase transition through transient analysis in discrete lattices. Finally, we design a phononic crystal based on the discrete spring-mass model and numerically verify the topologically protected states along the boundary between the trivial insulator and disordered topological QSH insulator in a continuous system. This work puts a step forward in understanding the role of disorder in a 2D topological classical system.

physics.app-ph↗

arXiv2022

Modulation instability in nonlinear flexible mechanical metamaterials

In this paper, we study modulation instabilities (MI) in a one-dimensional chain configuration of a flexible mechanical metamaterial (flexMM). Using the lumped element approach, flexMMs can be modeled by a coupled system of discrete equations for the longitudinal displacements and rotations of the rigid mass units. In the long wavelength regime, and applying the multiple-scales method we derive an effective nonlinear Schrödinger equation for slowly varying envelope rotational waves. We are then able to establish a map of the occurrence of MI to the parameters of the metamaterials and the wavenumbers. We also highlight the key role of the rotation-displacement coupling between the two degrees of freedom in the manifestation of MI. All analytical findings are confirmed by numerical simulations of the full discrete and nonlinear lump problem. These results provide interesting design guidelines for nonlinear metamaterials offering either stability to high amplitude waves, or conversely being good candidates to observe instabilities.

physics.app-ph↗

arXiv2022

Acoustic solitons in a periodic waveguide: theory and experiments

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.

nlin.PS↗