Breathers in periodic granular chains with multiple band gaps.

We consider the localized nonlinear breathing modes that emerge in heterogeneous granular configurations of two materials with a periodicity of three and four beads. We examine as characteristic examples chains with one steel and two aluminum beads, as well as ones with one steel and three aluminum beads, although we briefly touch upon other configurations as well, illustrating their similar characteristics. We analyze the higher order gaps that emerge in such settings and explore the intrinsic localized modes that bifurcate from the edge of the upper bands. A generic surprising feature of such states is that they appear to be more robust than their counterparts bifurcating from the edges of the lower bands. Direct numerical simulations, using driving of the system at suitable frequencies through an actuator or taking advantage of the modulational instabilities of extended band edge states in the system, illustrate the spontaneous formation of localized modes within the corresponding nearest gaps. In these numerical experiments, we also account for the presence of dissipation and analyze its potential role.

Discrete breathers in a nonlinear polarizability model of ferroelectrics.

We present a family of discrete breathers, which exists in a nonlinear polarizability model of ferroelectric materials. The core-shell model is set up in its nondimensionalized Hamiltonian form and its linear spectrum is examined in a range of temperatures. Subsequently, seeking localized solutions in the gap of the linear spectrum, we establish that numerically exact and potentially stable discrete breathers exist for a wide range of frequencies therein. In addition, we present nonlinear normal mode, extended spatial profile solutions from which the breathers bifurcate, as well as other associated phenomena such as the formation of phantom breathers within the model. The full bifurcation picture of the emergence and disappearance of the breathers is complemented by direct numerical simulations of their dynamical instability, when the latter arises. The effect of breathers on properties such as nonlinear dielectric response is discussed.

Discrete breathers at the interface between a diatomic and a 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.