In this work, we study a space-time-modulated electro-mechanical system, consisting of an array of coupled cantilevers with their on-site potential provided by electromagnets driven by AC currents. Model equations are derived, and the effect of the modulation on the dispersion bands is examined. The theory of breather existence and stability is extended to include space-time modulation. We perform numerical simulations in a time-modulated system, showing three types of breather response depending on the driving frequency: (i) the modulation frequency is an integer multiple of the breather frequency or, in other words, this phenomenon corresponds to period doubling, tripling, etc.; (ii) the opposite, that is, the breather frequency is an integer multiple of the modulation frequency, corresponding to period-halving, etc.; (iii) the breather and modulation frequencies are commensurate in a different form. We use for all of them the term Floquet breathers in analogy with Floquet solitons in photonic systems. As there is no dissipation, but periodic forcing, the energy is generally conserved but only at discrete times. There exists in this system a huge variety of breathers, site-centered, symmetric and antisymmetric, bond centered, and in-phase or in-quadrature with the modulation, and we analyze the evolution of stability of some of them as a function of the modulation frequency. The construction of a similar system would be of interest to study the properties of dynamic metamaterials.

This review article discusses wave propagation and heat transport in one-dimensional nonlinear lattices, focusing particularly on the role of symmetry. The concept of continuous translational symmetry in nonlinear lattices has recently been introduced. Furthermore, a nonlinear lattice possessing this symmetry has been explicitly constructed. This paper describes this symmetric lattice and its various properties, focusing especially on the propagation of discrete breather (DB). Effects due to the lattice discreteness emerge in traveling DBs in ordinary nonlinear lattices. In contrast, the constructed lattice removes these discrete effects, showing that the lack of this symmetry is the origin of the discrete effect. The paper also outlines recent progress regarding the construction of nonlinear lattices without umklapp processes, which possess similar symmetry, and their heat transport. Numerical results indicate that this similar symmetry vanishes thermal resistance by eliminating the umklapp process. These findings suggest a unified perspective that symmetry determines both the mobility and the heat transport of nonlinear waves in lattices.

We propose a novel type of umklapp-free lattice (UFL), where umklapp processes are completely absent. The proposed UFL incorporates cubic long-range nonlinearity, a feature not addressed in previous studies. In this paper, we derive an analytical expression for the cubic nonlinear coupling constants by imposing mathematical conditions such that the nonlinear coupling strength between particle pairs decays inversely with their separation distance. The absence of umklapp processes in the proposed lattice is confirmed through numerical comparisons with the Fermi-Pasta-Ulam-Tsingou (FPUT) lattice. Furthermore, molecular dynamics simulations are performed to investigate the thermal conductivity of the proposed lattice in the non-equilibrium steady state. Compared to the original FPUT lattice, the proposed UFL is closer to ballistic transport. Our results demonstrate that the umklapp processes induced by cubic nonlinearity are suppressed in the proposed UFL. Moreover, compared to the UFL with only quartic nonlinearity, truncation of long-range interactions plays a significant role in the proposed lattice.

It has been observed in fossil tracks and experiments in the layered silicate mica muscovite the transport of charge through the cation layers sandwiched between the layers of tetrahedra-octahedra-tetrahedra. A classical model for the propagation of anharmonic vibrations along the cation chains has been proposed based on first principles and empirical functions. In that model, several propagating entities have been found as kinks or crowdions and breathers, both with or without wings, the latter for specific velocities and energies. Crowdions are equivalent to moving interstitials and transport electric charge if the moving particle is an ion, but they also imply the movement of mass, which was not observed in the experiments. Breathers, being just vibrational entities, do not transport charge. In this work, we present a semiclassical model obtained by adding a quantum particle, electron or hole to the previous model. We present the construction of the model based on the physics of the system. In particular, the strongly nonlinear vibronic interaction between the nuclei and the extra electron or hole is essential to explain the localized charge transport, which is not compatible with the adiabatic approximation. The formation of vibrational localized charge carriers breaks the lattice symmetry group in a similar fashion to the Jahn-Teller Effect, providing a new stable dynamical state. We study the properties and the coherence of the model through numerical simulations from initial conditions obtained by tail analysis and other means. We observe that although the charge spreads from an initial localization in a lattice at equilibrium, it can be confined basically to a single particle when coupled to a chaotic quasiperiodic breather. This is coherent with the observation that experiments imply that a population of charge is formed due to the decay of potassium unstable isotopes.

We study numerically a discrete, nonlinear lattice, which is formed by a chain of pendula submitted to a harmonic-driving source with constant amplitude and parametrical excitation. A supratransmission phenomenon is obtained after the derivation of the homoclinic threshold for the case when the lattice is driven at one edge. The lattice traps gap solitons when the chain is subjected to a periodic horizontal displacement of the pivot. Discrete rogue waves are generated for the case when the pendulum is simultaneously driven and shaken. This work may pave the way for experimental generation of discrete rogue waves within simple devices.

A dynamical model for nonlinear wave propagation in phononic crystals is constructed. A lattice model is introduced as a discrete model of phononic crystals that consists of scatter and background material. Nonlinearity of material is considered as nonlinear mass density. In the proposed lattice model, massed of the mass points is described as a function of the local strain of the system. Nonlinear dynamics of the proposed lattice system is confirmed by numerical simulation. Moreover, frequency shift of phonon mode that is required for the switching dynamics is confirmed.

Human faces are mechanical systems that display emotional and linguistic information with motions of the de formable facial tissues. Since each facial action forms a different stress-strain field that characterizes the differentiated facial appearance, a detailed analysis of strain distributions for each facial action will contribute to analytical and synthetical studies on human faces. This study evaluated strain distributions of 44 facial actions of a Japanese adult male based on the three-dimensional displacements of 125 tracking markers attached to the facial surface. We investigated how much the facial skin surface is stretched and compressed in each facial region based on the evaluated area strains produced by each facial action. Then, we visualized the strain distributions and surface undulation to analyze the complexity of the deformations on a face. The results show that the positive and negative surface strains intermingled on a face even in simple facial actions, potentially reflecting the complex facial structure under the facial skin layers, where several tissues with different material properties, e.g., adipose tissues and retaining ligaments, are distributed heterogeneously. These results are beneficial for artificial face designers as a design target and evidence to consider the effective skin structure and locations of actuators for artificial faces.

We construct a nonlinear lattice model to investigate the dynamics of nonlinear behavior in phononic crystals (PnCs). Two types of mass points and springs are introduced in the model to reproduce the difference in material properties between the scatterers and background in PnCs. The nonlinearity is introduced to the model by changing the mass of each mass point depending on the displacement gradient at the mass point. We numerically confirm that both the 1D and 2D models have the bandgap in the linear dispersion relation. Moreover, in both model, switching behavior of wave propagation is found.

We introduce a class of nonlinear lattices that have a particular symmetry called NP symmetry in their potential functions. This class includes nonlinear lattices such that the umklapp process vanishes and only the normal processes appear in their potential functions. For the NP-symmetric lattices with periodic boundary conditions, we prove non-relaxation theorems of the heat flux within both classical and quantum mechanics: the heat flux never vanishes but remains strictly positive, i.e., non-existence of the thermal resistance, when the initial state gives a positive heat flux and satisfies a certain condition. The present theorems give a rigorous theoretical basis for the widely-accepted Peierls's hypothesis that there is no thermal resistance in a nonlinear lattice if it has no umklapp process but only the normal processes.