Publications
For citation information, please visit my Google Scholar page.
2023
- APSDirac solitons and topological edge states in the β-Fermi-Pasta-Ulam-Tsingou dimer latticeR. Chaunsali, P. G. Kevrekidis, D. Frantzeskakis, and 1 more authorPhysical Review E Nov 2023
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 band gap 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 solitonlike wave setting into motion due to the instability.
- NatureStrain topological metamaterials and revealing hidden topology in higher-order coordinatesF. Allein, A. Anastasiadis, R. Chaunsali, and 4 more authorsNature Communications Nov 2023
Topological physics has revolutionized materials science, introducing topological phases of matter in diverse settings ranging from quantum to photonic and phononic systems. Herein, we present a family of topological systems, which we term “strain topological metamaterials”, whose topological properties are hidden and unveiled only under higher-order (strain) coordinate transformations. We firstly show that the canonical mass dimer, a model that can describe various settings such as electrical circuits and optics, among others, belongs to this family where strain coordinates reveal a topological nontriviality for the edge states at free boundaries. Subsequently, we introduce a mechanical analog of the Majorana-supporting Kitaev chain, which supports topological edge states for both fixed and free boundaries within the proposed framework. Thus, our findings not only extend the way topological edge states are identified, but also promote the fabrication of novel topological metamaterials in various fields, with more complex, tailored boundaries.
- APSTopological phase transition in a disordered elastic quantum spin Hall systemX. Shi, R. Chaunsali, G. Theocharis, and 3 more authorsPhysical Review B Aug 2023
We investigate the effect of disorder on topologically nontrivial states in a two-dimensional (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.
2022
- NatureTopological state transfer in Kresling origamiY. Miyazawa, C.-W. Chen, R. Chaunsali, and 4 more authorsCommunications Materials Aug 2022
Topological mechanical metamaterials have been widely explored for their boundary states, which can be robustly isolated or transported in a controlled manner. However, such systems often require pre-configured design or complex active actuation for wave manipulation. Here, we present the possibility of in-situ transfer of topological boundary modes by leveraging the reconfigurability intrinsic in twisted origami lattices. In particular, we employ a dimer Kresling origami system consisting of unit cells with opposite chirality, which couples longitudinal and rotational degrees of freedom in elastic waves. The quasi-static twist imposed on the lattice alters the strain landscape of the lattice, thus significantly affecting the wave dispersion relations and the topology of the underlying bands. This in turn facilitates an efficient topological state transfer from one edge to the other. This simple and practical approach to energy transfer in origami-inspired lattices can thus inspire a new class of efficient energy manipulation devices.
- APSBulk-edge correspondence in the trimer Su-Schrieffer-Heeger modelA. Anastasiadis, G. Styliaris, R. Chaunsali, and 2 more authorsPhysical Review B Aug 2022
A remarkable feature of the trimer Su-Schrieffer-Heeger (SSH3) model is that it supports localized edge states. However, in contrast to the dimer version of the model, a change in the total number of edge states in SSH3 without mirror-symmetry is not necessarily associated with a phase transition, i.e., a closing of the band gap. As such, the topological invariant predicted by the 10-fold way classification does not always coincide with the total number of edge states present. Moreover, although Zak’s phase remains quantized for the case of a mirror-symmetric chain, it is known that it fails to take integer values in the absence of this symmetry and thus it cannot play the role of a well-defined bulk invariant in the general case. Attempts to establish a bulk-edge correspondence have been made via Green’s functions or through extensions to a synthetic dimension. Here we propose a simple alternative for SSH3, utilizing the previously introduced sublattice Zak’s phase, which also remains valid in the absence of mirror symmetry and for noncommensurate chains. The defined bulk quantity takes integer values, is gauge invariant, and can be interpreted as the difference of the number of edge states between a reference and a target Hamiltonian. Our derivation further predicts the exact corrections for finite open chains, is straightforwardly generalizable, and invokes a chiral-like symmetry present in this model.
- APSNonlinear topological edge states: From dynamic delocalization to thermalizationB. M. Manda, R. Chaunsali, G. Theocharis, and 1 more authorPhysical Review B Mar 2022
We consider a mechanical lattice inspired by the Su-Schrieffer-Heeger model along with cubic Klein-Gordon–type nonlinearity. We investigate the long-time dynamics of the nonlinear edge states, which are obtained by nonlinear continuation of topological edge states of the linearized model. Linearly unstable edge states delocalize and lead to chaos and thermalization of the lattice. Linearly stable edge states also reach the same fate, but after a critical strength of perturbation is added to the initial edge state. We show that the thermalized lattice in all these cases shows an effective renormalization of the dispersion relation. Intriguingly, this renormalized dispersion relation displays a unique symmetry, i.e., its square is symmetric about a finite squared frequency, akin to the chiral symmetry of the linearized model.
2021
- APSDisorder-induced topological phase transition in a one-dimensional mechanical systemX. Shi, I. Kiorpelidis, R. Chaunsali, and 3 more authorsPhysical Review Research Jul 2021
We numerically investigate the topological phase transition induced purely by disorder in a spring-mass chain. We employ two types of disorders—chiral and random types—to explore the interplay between topology and disorder. By tracking the evolution of real-space topological invariants, we obtain the topological phase diagrams and demonstrate the bilateral capacity of disorder to drive topological transitions, from topologically nontrivial to trivial and vice versa. The corresponding transition is accompanied by the realization of a mechanical topological Anderson insulator. The findings from this study hint that the combination of disorder and topology can serve as an efficient control knob to manipulate the transfer of mechanical energy.
- NatureCorner states in a second-order mechanical topological insulatorC.-W. Chen, R. Chaunsali, J. Christensen, and 2 more authorsCommunications Materials Apr 2021
Demonstration of topological boundary modes in elastic systems has attracted a great deal of attention over the past few years due to its unique protection characteristic. Recently, second-order topological insulators have been proposed in manipulating the topologically protected localized states emerging only at corners. Here, we numerically and experimentally study corner states in a two-dimensional phononic crystal, namely a continuous elastic plate with embedded bolts in a hexagonal pattern. We create interfacial corners by adjoining trivial and non-trivial topological configurations. Due to the rich interaction between the bolts and the continuous elastic plate, we find a variety of corner states of and devoid of topological origin. Strikingly, some of the corner states are not only highly-localized but also tunable. Taking advantage of this property, we experimentally demonstrate asymmetric corner localization in a Z-shaped domain wall. This finding could create interest in exploration of tunable corner states for the use of advanced control of wave localization.
- APSStability of topological edge states under strong nonlinear effectsR. Chaunsali, H. Xu, J. Yang, and 2 more authorsPhysical Review B Jan 2021
We examine the role of strong nonlinearity on the topologically robust edge state in a one-dimensional system. We consider a chain inspired from the Su-Schrieffer-Heeger model but with a finite-frequency edge state and the dynamics governed by second-order differential equations. We introduce a cubic onsite nonlinearity and study this nonlinear effect on the edge state’s frequency and linear stability. Nonlinear continuation reveals that the edge state loses its typical shape enforced by the chiral symmetry and becomes generally unstable due to various types of instabilities that we analyze using a combination of spectral stability and Krein signature analysis. This results in an initially excited nonlinear-edge state shedding its energy into the bulk over a long time. However, the stability trends differ both qualitatively and quantitatively when softening and stiffening types of nonlinearity are considered. In the latter, we find a frequency regime where nonlinear edge states can be linearly stable. This enables high-amplitude edge states to remain spatially localized without shedding their energy, a feature that we have confirmed via long-time dynamical simulations. Finally, we examine the robustness of frequency and stability of nonlinear edge states against disorder, and find that those are more robust under a chiral disorder compared to a nonchiral disorder. Moreover, the frequency-regime where high-amplitude edge states were found to be linearly stable remains intact in the presence of a small amount of disorder of both types.
2019
- APSSelf-induced topological transition in phononic crystals by nonlinearity managementR. Chaunsali, and G. TheocharisPhysical Review B Jul 2019
A design paradigm of topology has recently emerged to manipulate the flow of phonons. At its heart lies a topological transition to a nontrivial state with exotic properties. This framework has been limited to linear lattice dynamics so far. Here we show a topological transition in a nonlinear regime and its implication in emerging nonlinear solutions. We employ nonlinearity management such that the system consists of masses connected with two types of nonlinear springs, “stiffening” and “softening” types, alternating along the length. We show, analytically and numerically, that the lattice makes a topological transition simply by changing the excitation amplitude and invoking nonlinear dynamics. Consequently, we witness the emergence of a family of finite-frequency edge modes, not observed in linear phononic systems. We also report the existence of kink solitons at the topological transition point. These correspond to heteroclinic orbits that form a closed curve in the phase portrait separating the two topologically distinct regimes. These findings suggest that nonlinearity can be used as a strategic tuning knob to alter topological characteristics of phononic crystals. These also provide fresh perspectives towards understanding a different family of nonlinear solutions in light of topology.
- APSElastic Weyl Points and Surface Arc States in Three-Dimensional StructuresX. Shi, R. Chaunsali, F. Li, and 1 more authorPhysical Review Applied Aug 2019
The study of Weyl points in electronic systems has inspired much recent research in classical systems such as photonic and acoustic lattices. Here we show how Weyl physics can also inspire the design of novel elastic structures. We construct a single-phase three-dimensional structure, an analog of the AA-stacked honeycomb lattice, and predict the existence of Weyl points with opposite topological charges (±1), elastic Fermi arcs, and the associated gapless topologically protected surface states. We apply full-scale numerical simulations on the elastic three-dimensional structure and present a clear visualization of topological surface states that are directional and robust. Such designed lattices can pave the way for novel vibration control and energy harvesting on structures that are ubiquitous in many engineering applications.
- WileyMechanical Analogue of a Majorana Bound StateC.-W. Chen, N. Lera, R. Chaunsali, and 5 more authorsAdvanced Materials Aug 2019
The discovery of topologically nontrivial electronic systems has opened a new age in condensed matter research. From topological insulators to topological superconductors and Weyl semimetals, it is now understood that some of the most remarkable and robust phases in electronic systems (e.g., quantum Hall or anomalous quantum Hall) are the result of topological protection. These powerful ideas have recently begun to be explored also in bosonic systems. Topologically protected acoustic, mechanical, and optical edge states have been demonstrated in a number of systems that recreate the requisite topological conditions. Such states that propagate without backscattering could find important applications in communications and energy technologies. Here, a topologically bound mechanical state, a different class of nonpropagating protected state that cannot be destroyed by local perturbations, is demonstrated. It is in particular a mechanical analogue of the well-known Majorana bound states (MBSs) of electronic topological superconductor systems. The topological binding is implemented by creating a Kekulé distortion vortex on a 2D mechanical honeycomb superlattice that can be mapped to a magnetic flux vortex in a topological superconductor.
- APSGradient-Index Granular Crystals: From Boomerang Motion to Asymmetric Transmission of WavesE. Kim, R. Chaunsali, and J. YangPhysical Review Letters Nov 2019
We present a gradient-index crystal that offers extreme tunability in terms of manipulating the propagation of elastic waves. For small-amplitude excitations, we achieve control over wave transmission depth into the crystal. We numerically and experimentally demonstrate a boomeranglike motion of a wave packet injected into the crystal. For large-amplitude excitations on the same crystal, we invoke nonlinear effects. We numerically and experimentally demonstrate asymmetric wave transmission from two opposite ends of the crystal. Such tunable systems can thus inspire a novel class of designed materials to control linear and nonlinear elastic wave propagation in multiscales.
2018
- IOPExperimental demonstration of topological waveguiding in elastic plates with local resonatorsR. Chaunsali, C.-W. Chen, and J. YangNew Journal of Physics Nov 2018
The recent emergence of topological insulators in condensed matter physics has inspired analogous wave phenomena in mechanical systems. However, to date, the design of these mechanical systems has been limited mostly to discrete lattices or perforated structures. Here, we take a ubiquitous design of a bolted elastic plate and demonstrate that it can guide flexural waves crisply around sharp bends. We show that this continuum system eliminates unwanted in-plane plate modes and allows the manipulation of low-frequency flexural modes by exploiting the local resonance of the bolts. We report the existence of a pair of double Dirac cones near the resonant frequency of the bolts, one of which leads to the creation of a topological complete bandgap that forbids all the plate modes. These findings open new possibilities of managing multiple wave modes in elastic solids for applications in energy harvesting, impact mitigation, and structural health monitoring.
- R SocDemonstration of accelerating and decelerating nonlinear impulse waves in functionally graded granular chainsR. Chaunsali, E. Kim, and J. YangPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Nov 2018
We propose a tunable cylinder-based granular system that is functionally graded in its stiffness distribution in space. With no initial compression given to the system, it supports highly nonlinear waves propagating under an impulse excitation. We investigate analytically, numerically and experimentally the ability to accelerate and decelerate the impulse wave without a significant scattering in the space domain. Moreover, the gradient in stiffness results in the scaling of contact forces along the chain. We envision that such tunable systems can be used for manipulating highly nonlinear impulse waves for novel sensing and impact mitigation purposes. This article is part of the theme issue ‘Nonlinear energy transfer in dynamical and acoustical systems’.
- AIPElastic Wannier-Stark ladders and Bloch oscillations in 1D granular crystalsX. Shi, R. Chaunsali, Y. Wu, and 1 more authorJournal of Applied Physics Nov 2018
We report the numerical and experimental study of elastic Wannier-Stark ladders and Bloch oscillations in a tunable one-dimensional granular chain consisting of cylindrical particles. The Wannier-Stark ladders are obtained by tuning the contact angles to introduce a gradient in the contact stiffness along the granular chain. These ladders manifest as resonant modes localized in the space. When excited at the corresponding resonant frequencies, we demonstrate the existence of time-resolved Bloch oscillations. The direct velocity measurements using laser Doppler vibrometry agree well with the numerical simulation results. We also show the possibility of further tailoring these Bloch oscillations by numerical simulations. Such tunable systems could be useful for applications involving the spatial localization of elastic energy.
- APSSubwavelength and directional control of flexural waves in zone-folding induced topological platesR. Chaunsali, C.-W. Chen, and J. YangPhysical Review B Feb 2018
Inspired by the quantum spin Hall effect shown by topological insulators, we propose a plate structure that can be used to demonstrate the pseudospin Hall effect for flexural waves. The system consists of a thin plate with periodically arranged resonators mounted on its top surface. We extend a technique based on the plane-wave expansion method to identify a double Dirac cone emerging due to the zone-folding in frequency band structures. This particular design allows us to move the double Dirac cone to a lower frequency than the resonating frequency of local resonators. We then manipulate the pattern of local resonators to open subwavelength Bragg band gaps that are topologically distinct. Building on this method, we verify numerically that a waveguide at an interface between two topologically distinct resonating plate structures can be used for guiding low-frequency, spin-dependent one-way flexural waves along a desired path with bends.
- NatureDial-in Topological Metamaterials Based on Bistable Stewart PlatformY. Wu, R. Chaunsali, H. Yasuda, and 2 more authorsScientific Reports Feb 2018
Recently, there have been significant efforts to guide mechanical energy in structures by relying on a novel topological framework popularized by the discovery of topological insulators. Here, we propose a topological metamaterial system based on the design of the Stewart Platform, which can not only guide mechanical waves robustly in a desired path, but also can be tuned in situ to change this wave path at will. Without resorting to any active materials, the current system harnesses bistablilty in its unit cells, such that tuning can be performed simply by a dial-in action. Consequently, a topological transition mechanism inspired by the quantum valley Hall effect can be achieved. We show the possibility of tuning in a variety of topological and traditional waveguides in the same system, and numerically investigate key qualitative and quantitative differences between them. We observe that even though both types of waveguides can lead to significant wave transmission for a certain frequency range, topological waveguides are distinctive as they support robust, back scattering immune, one-way wave propagation.
2017
- ElsevierExtreme control of impulse transmission by cylinder-based nonlinear phononic crystalsR. Chaunsali, M. Toles, J. Yang, and 1 more authorJournal of the Mechanics and Physics of Solids Feb 2017
We present a novel device that can offer two extremes of elastic wave propagation — nearly complete transmission and strong attenuation under impulse excitation. The mechanism of this highly tunable device relies on intermixing effects of dispersion and nonlinearity. The device consists of identical cylinders arranged in a chain, which interact with each other as per nonlinear Hertz contact law. For a ‘dimer’ configuration, i.e., two different contact angles alternating in the chain, we analytically, numerically, and experimentally show that impulse excitation can either propagate as a localized wave, or it can travel as a highly dispersive wave. Remarkably, these extremes can be achieved in this periodic arrangement simply by in-situ control of contact angles between cylinders. We close the discussion by highlighting the key characteristics of the mechanisms that facilitate strong attenuation of incident impulse. These include low-to-high frequency scattering, and turbulence-like cascading in a periodic system. We thus envision that these adaptive, cylinder-based nonlinear phononic crystals, in conjunction with conventional impact mitigation mechanisms, could be used to design highly tunable and efficient impact manipulation devices.
- APSDemonstrating an In Situ Topological Band Transition in Cylindrical Granular ChainsR. Chaunsali, E. Kim, A. Thakkar, and 2 more authorsPhysical Review Letters Jul 2017
We numerically investigate and experimentally demonstrate an in situ topological band transition in a highly tunable mechanical system made of cylindrical granular particles. This system allows us to tune its interparticle stiffness in a controllable way, simply by changing the contact angles between the cylinders. The spatial variation of particles’ stiffness results in an in situ transition of the system’s topology. This manifests as the emergence of a boundary mode in the finite system, which we observe experimentally via laser Doppler vibrometry. When two topologically different systems are placed adjacently, we analytically predict and computationally and experimentally demonstrate the existence of a finite-frequency topologically protected mode at their interface.
- IOPLinear and nonlinear dynamics of isospectral granular chainsR. Chaunsali, H. Xu, J. Yang, and 1 more authorJournal of Physics A: Mathematical and Theoretical Mar 2017
We study the dynamics of isospectral granular chains that are highly tunable due to the nonlinear Hertz contact law interaction between the granular particles. The system dynamics can thus be tuned easily from being linear to strongly nonlinear by adjusting the initial compression applied to the chain. In particular, we introduce both discrete and continuous spectral transformation schemes to generate a family of granular chains that are isospectral in their linear limit. Inspired by the principle of supersymmetry in quantum systems, we also introduce a methodology to add or remove certain eigenfrequencies, and we demonstrate numerically that the corresponding physical system can be constructed in the setting of one-dimensional granular crystals. In the linear regime, we highlight the similarities in the elastic wave transmission characteristics of such isospectral systems, and emphasize that the presented mathematical framework allows one to suitably tailor the wave transmission through a general class of granular chains, both ordered and disordered. Moreover, we show how the dynamic response of these structures deviates from its linear limit as we introduce Hertzian nonlinearity in the chain and how nonlinearity breaks the notion of linear isospectrality.
2016
- NatureStress Wave Isolation by Purely Mechanical Topological Phononic CrystalsR. Chaunsali, F. Li, and J. YangScientific Reports Mar 2016
We present an active, purely mechanical stress wave isolator that consists of short cylindrical particles arranged in a helical architecture. This phononic structure allows us to change inter-particle stiffness dynamically by controlling the contact angles of the cylinders. We use torsional travelling waves to control the contact angles, thereby imposing a desired spatio-temporal stiffness variation to the phononic crystal along the longitudinal direction. Such torsional excitation is a form of parametric pumping in the system, which results in the breakage of the time-reversal symmetry. We report that, in quasi-static sense, the system shows topologically non-trivial band-gaps. However, in a dynamic regime where the pumping effect is significant, these band-gaps become asymmetric with respect to the frequency and wavenumber domains in the dispersion relationship. By using numerical simulations, we show that such asymmetry has a direct correspondence to the topological invariant, i.e., Chern number, of the system. We propose that this asymmetry, accompanied by selective inter-band transition, can be utilized for directional isolation of the stress wave propagating along the phononic crystal.
2015
- APSNonlinear low-to-high-frequency energy cascades in diatomic granular crystalsE. Kim, R. Chaunsali, H. Xu, and 4 more authorsPhysical Review E Dec 2015
We study wave propagation in strongly nonlinear one-dimensional diatomic granular crystals under an impact load. Depending on the mass ratio of the “light” to “heavy” beads, this system exhibits rich wave dynamics from highly localized traveling waves to highly dispersive waves featuring strong attenuation. We demonstrate experimentally the nonlinear resonant and antiresonant interactions of particles, and we verify that the nonlinear resonance results in strong wave attenuation, leading to highly efficient nonlinear energy cascading without relying on material damping. In this process, mechanical energy is transferred from low to high frequencies, while propagating waves emerge in both ordered and chaotic waveforms via a distinctive spatial cascading. This energy transfer mechanism from lower to higher frequencies and wave numbers is of particular significance toward the design of novel nonlinear acoustic metamaterials with inherently passive energy redistribution properties.
2011
- ASAEstimating material viscoelastic properties based on surface wave measurements: A comparison of techniques and modeling assumptionsT. J. Royston, Z. Dai, R. Chaunsali, and 3 more authorsThe Journal of the Acoustical Society of America Dec 2011
Previous studies of the first author and others have focused on low audible frequency (<1 kHz) shear and surface wave motion in and on a viscoelastic material comprised of or representative of soft biological tissue. A specific case considered has been surface (Rayleigh) wave motion caused by a circular disk located on the surface and oscillating normal to it. Different approaches to identifying the type and coefficients of a viscoelastic model of the material based on these measurements have been proposed. One approach has been to optimize coefficients in an assumed viscoelastic model type to match measurements of the frequency-dependent Rayleigh wave speed. Another approach has been to optimize coefficients in an assumed viscoelastic model type to match the complex-valued frequency response function (FRF) between the excitation location and points at known radial distances from it. In the present article, the relative merits of these approaches are explored theoretically, computationally, and experimentally. It is concluded that matching the complex-valued FRF may provide a better estimate of the viscoelastic model type and parameter values; though, as the studies herein show, there are inherent limitations to identifying viscoelastic properties based on surface wave measurements.