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We study a topological physics in a one-dimensional nonlinear system by taking an instance of a mechanical rotator model with alternating spring constants. This nonlinear model is smoothly connected to an acoustic model described by the…

The study of wave propagation in chains of anharmonic periodic systems is of fundamental importance to understand the response of dynamical absorbers of vibrations and acoustic metamaterials working in nonlinear regime. Here, we derive an…

We review our results for the dynamics of isolated many-body quantum systems described by one-dimensional spin-1/2 models. We explain how the evolution of these systems depends on the initial state and the strength of the perturbation that…

The dynamical behavior caused by dry friction is studied for a spring-block system pulled with constant velocity over a surface. The dynamical consequences of a general type of phenomenological friction law (stick-time dependent static…

We present the general theory of Ising transitions in isotropic elastic media with vanishing thermal expansion. By constructing a minimal model with appropriate spin-lattice couplings, we show that in two dimensions near a continuous…

The collective motion of dust particles during the mode-coupling induced melting of a two-dimensional plasma crystal is explored in molecular dynamics simulations. The crystal is compressed horizontally by an anisotropic confinement. This…

We consider a heavy, uniform, elastic beam rested on periodically distributed supports as a simplified model of a bridge. The supports are subjected to a partial destruction propagating as a failure wave along the beam. Three related models…

In many cases, beam to column connections in structural frames are semi rigid, but they are considered to be ideally rigid or pinned due to their computational complexity and shortage of designing methods. In this paper, connections are…

States of self stress, organizations of internal forces in many-body systems that are in equilibrium with an absence of external forces, can be thought of as the constitutive building blocks of the elastic response of a material. In…

We study the Hamiltonian dynamics of the spherical spin model with fully-connected two-body interactions drawn from a Gaussian probability distribution. In the statistical physics framework, the potential energy is of the so-called $p=2$…

A model of two oscillating pendula placed on a mobile support is studied. Once an overall scheme of equations, under general assumptions, is formulated via the Lagrangian equations of motion, the specific case of absence of escapement is…

The equilibrium configuration of an engineering structure, able to withstand a certain loading condition, is usually associated with a local minimum of the underlying potential energy. However, in the nonlinear context, there may be other…

We study various dynamical aspects of systems possessing a first order phase transition in their phase diagram. We isolate three qualitatively distinct types of theories depending on the structure of instabilities and the nature of the low…

The overdamped Brownian dynamics of a harmonic oscillator is a paradigmatic system in non-equilibrium statistical mechanics, which reliably models relevant stochastic systems such as colloidal particles submitted to optical confinement. In…

We study numerically stick slip motions in a model of blocks and springs being pulled slowly. The sliding friction is assumed to change dynamically with a state variable. The transition from steady sliding to stick-slip is subcritical in a…

We discuss the classical motion of a spring of arbitrary mass coupled to two arbitrary massive blocks attached at its ends. A general approach to the problem is presented and some general results are obtained. Examples for which a simple…

We study an experimental system of hard granular squares in two dimensions, energized by vibration. The interplay of order in the orientations and positions of anisotropic particles allows for a rich set of phases. We measure the structure…

Confined granular fluids, placed in a shallow box that is vibrated vertically, can achieve homogeneous stationary states thanks to energy injection mechanisms that take place throughout the system. These states can be stable even at high…

We consider finite systems of interacting Brownian particles including active friction in the framework of nonlinear dynamics and statistical/stochastic theory. First we study the statistical properties for $1-d$ systems of masses connected…

We study the role of connectivity on the linear and nonlinear elastic behavior of amorphous systems using a two-dimensional random network of harmonic springs as a model system. A natural characterization of these systems arises in terms of…