Christopher Chong
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View article: A regularized continuum model for travelling waves and dispersive shocks of the granular chain
A regularized continuum model for travelling waves and dispersive shocks of the granular chain Open
In this paper, we focus on a discrete physical model describing granular crystals, whose equations of motion can be described by a system of differential difference equations. After revisiting earlier continuum approximations, we propose a…
View article: A regularized continuum model for traveling waves and dispersive shocks of the granular chain
A regularized continuum model for traveling waves and dispersive shocks of the granular chain Open
In this paper we focus on a discrete physical model describing granular crystals, whose equations of motion can be described by a system of differential difference equations (DDEs). After revisiting earlier continuum approximations, we pro…
View article: Dynamics of Nonlinear Lattices
Dynamics of Nonlinear Lattices Open
In this topical review we explore the dynamics of nonlinear lattices with a particular focus to Fermi-Pasta-Ulam-Tsingou type models that arise in the study of elastic media and, more specifically, granular crystals. We first revisit the w…
View article: On the Existence of Generalized Breathers and Transition Fronts in Time-Periodic Nonlinear Lattices
On the Existence of Generalized Breathers and Transition Fronts in Time-Periodic Nonlinear Lattices Open
We prove the existence of a class of time-localized and space-periodic breathers (called q-gap breathers) in nonlinear lattices with time-periodic coefficients. These q-gap breathers are the counterparts to the classical space-localized an…
View article: Hydrodynamics of a Discrete Conservation Law
Hydrodynamics of a Discrete Conservation Law Open
The Riemann problem for the discrete conservation law $2 \dot{u}_n + u^2_{n+1} - u^2_{n-1} = 0$ is classified using Whitham modulation theory, a quasi-continuum approximation, and numerical simulations. A surprisingly elaborate set of solu…
View article: Modulation instability and wavenumber bandgap breathers in a time layered phononic lattice
Modulation instability and wavenumber bandgap breathers in a time layered phononic lattice Open
We provide the first experimental realization of wavenumber bandgap (q−gap) breathers. Experiments are obtained in the setting of a time-periodic phononic lattice where the model and experiment exhibit good qualitative agreement. q−gap bre…
View article: Integrable Approximations of Dispersive Shock Waves of the Granular Chain
Integrable Approximations of Dispersive Shock Waves of the Granular Chain Open
In the present work we revisit the shock wave dynamics in a granular chain with precompression. By approximating the model by an $α$-Fermi-Pasta-Ulam-Tsingou chain, we leverage the connection of the latter in the strain variable formulatio…
View article: Integrable Approximations of Dispersive Shock Waves of the Granular Chain
Integrable Approximations of Dispersive Shock Waves of the Granular Chain Open
View article: On the Whitham modulation equations for the Toda lattice and the quantitative characterization of its dispersive shocks
On the Whitham modulation equations for the Toda lattice and the quantitative characterization of its dispersive shocks Open
The aim of this work is multifold. Firstly, it intends to present a complete, quantitative and self-contained description of the periodic traveling wave solutions and Whitham modulation equations for the Toda lattice, combining results fro…
View article: Modulation Instability and Wavenumber Bandgap Breathers in a Time Layered Phononic Lattice
Modulation Instability and Wavenumber Bandgap Breathers in a Time Layered Phononic Lattice Open
We demonstrate the existence of wavenumber bandgap (q-gap) breathers in a time-periodic phononic lattice. These breathers are localized in time and periodic in space, and are the counterparts to the classical breathers found in spatially-p…
View article: Dynamics of time-modulated, nonlinear phononic lattices
Dynamics of time-modulated, nonlinear phononic lattices Open
The propagation of acoustic and elastic waves in time-varying, spatially homogeneous media can exhibit different phenomena when compared to traditional spatially varying, temporally homogeneous media. In the present work, the response of a…
View article: Breathers in lattices with alternating strain-hardening and strain-softening interactions
Breathers in lattices with alternating strain-hardening and strain-softening interactions Open
This work focuses on the study of time-periodic solutions, including breathers, in a nonlinear lattice consisting of elements whose contacts alternate between strain-hardening and strain-softening. The existence, stability, and bifurcation…
View article: Dispersive Shock Waves in Lattices: A Dimension Reduction Approach
Dispersive Shock Waves in Lattices: A Dimension Reduction Approach Open
Dispersive shock waves (DSWs), which connect states of different amplitude via a modulated wave train, form generically in nonlinear dispersive media subjected to abrupt changes in state. The primary tool for the analytical study of DSWs i…
View article: Nonlinear localized modes in two-dimensional hexagonally-packed magnetic lattices
Nonlinear localized modes in two-dimensional hexagonally-packed magnetic lattices Open
We conduct an extensive study of nonlinear localized modes (NLMs), which are temporally periodic and spatially localized structures, in a two-dimensional array of repelling magnets. In our experiments, we arrange a lattice in a hexagonal c…
View article: Origami-based impact mitigation via rarefaction solitary wave creation
Origami-based impact mitigation via rarefaction solitary wave creation Open
We demonstrate a counterintuitive mechanism of converting compressive impact to tensile waves in origami-based metamaterials.
View article: Breathers and other time-periodic solutions in an array of cantilevers decorated with magnets
Breathers and other time-periodic solutions in an array of cantilevers decorated with magnets Open
In this article, the existence, stability and bifurcation structure of time-periodic solutions (including ones that also have the property of spatial localization, i.e., breathers) are studied in an array of cantilevers that have magnetic …
View article: Phononic rogue waves
Phononic rogue waves Open
We present a theoretical study of extreme events occurring in phononic lattices. In particular, we focus on the formation of rogue or freak waves, which are characterized by their localization in both spatial and temporal domains. We consi…
View article: Origami-based impact mitigation via rarefaction solitary wave creation
Origami-based impact mitigation via rarefaction solitary wave creation Open
The principles underlying the art of origami paper folding can be applied to design sophisticated metamaterials with unique mechanical properties. By exploiting the flat crease patterns that determine the dynamic folding and unfolding moti…
View article: Demonstration of Dispersive Rarefaction Shocks in Hollow Elliptical Cylinder Chains
Demonstration of Dispersive Rarefaction Shocks in Hollow Elliptical Cylinder Chains Open
We report an experimental and numerical demonstration of dispersive rarefaction shocks (DRS) in a 3D-printed soft chain of hollow elliptical cylinders. We find that, in contrast to conventional nonlinear waves, these DRS have their lower a…
View article: Introduction and Motivation of Models
Introduction and Motivation of Models Open
In the present short volume our aim will be to explore a variety of nonlinear wave structures that are found in a particular physical system, i.e., granular crystals. Many of the readers have almost certainly encountered a variant of the g…
View article: Emergence of dispersive shocks and rarefaction waves in power-law contact models
Emergence of dispersive shocks and rarefaction waves in power-law contact models Open
In the present work, motivated by generalized forms of the Hertzian dynamics associated with granular crystals, we consider the possibility of such models to give rise to both dispersive shock and rarefaction waves. Depending on the value …
View article: Discrete breathers in a mass-in-mass chain with Hertzian local resonators
Discrete breathers in a mass-in-mass chain with Hertzian local resonators Open
We report on the existence of discrete breathers in a one-dimensional, mass-in-mass chain with linear intersite coupling and nonlinear, precompressed Hertzian local resonators, which is motivated by recent studies of the dynamics of micros…
View article: Mechanical Autonomous Stochastic Heat Engine
Mechanical Autonomous Stochastic Heat Engine Open
Stochastic heat engines are devices that generate work from random thermal motion using a small number of highly fluctuating degrees of freedom. Proposals for such devices have existed for more than a century and include the Maxwell demon …
View article: Wave mixing in coupled phononic crystals via a variable stiffness mechanism
Wave mixing in coupled phononic crystals via a variable stiffness mechanism Open
View article: Unidirectional Transition Waves in Bistable Lattices
Unidirectional Transition Waves in Bistable Lattices Open
We present a model system for strongly nonlinear transition waves generated in a periodic lattice of bistable members connected by magnetic links. The asymmetry of the on-site energy wells created by the bistable members produces a mechani…
View article: Nonlinear vibrational-state excitation and piezoelectric energy conversion in harmonically driven granular chains
Nonlinear vibrational-state excitation and piezoelectric energy conversion in harmonically driven granular chains Open
This article explores the excitation of different vibrational states in a spatially extended dynamical system through theory and experiment. As a prototypical example, we consider a one-dimensional packing of spherical particles (a so-call…
View article: Formation of rarefaction waves in origami-based metamaterials
Formation of rarefaction waves in origami-based metamaterials Open
We investigate the nonlinear wave dynamics of origami-based metamaterials composed of Tachi-Miura polyhedron (TMP) unit cells. These cells exhibit strain softening behavior under compression, which can be tuned by modifying their geometric…
View article: Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices
Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices Open
Linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices are explored in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in…
View article: Exciting and Harvesting Vibrational States in Harmonically Driven Granular Chains
Exciting and Harvesting Vibrational States in Harmonically Driven Granular Chains Open
This article explores the excitation of different vibrational states in a spatially extended dynamical system through theory and experiment. As a prototypical example, we consider a one-dimensional packing of spherical particles (a so-call…
View article: Exciting and Harvesting Vibrational States in Harmonically Driven Granular Chains
Exciting and Harvesting Vibrational States in Harmonically Driven Granular Chains Open
This article explores the excitation of different vibrational states in a spatially extended dynamical system through theory and experiment. As a prototypical example, we consider a one-dimensional packing of spherical particles (a so-call…