Related papers: Nonlinear dynamics of surface steps

Step patterns on vicinal $(2\times1)$ reconstructed surfaces of noble metals Au(110) and Pt(110), miscut towards the (100) orientation, are investigated. The free energy of the reconstructed surface with a network of crossing opposite steps…

We show that the oscillatory driving of crystal surfaces can induce pattern formation or smoothening. The driving force can be of quite different origin such as a pulsed laser beam, an electric field, or elasticity. Depending on driving…

The motion of topological defects is an important feature of the dynamics of all liquid crystals, and is especially conspicuous in active liquid crystals. Understanding defect motion is a challenging theoretical problem, because the…

Because of consuming energy to drive their motion, systems of active colloids are intrinsically out of equilibrium. In the past decade, a variety of intriguing dynamic patterns have been observed in systems of active colloids, and they…

In the present work, we attempt a brief summary of various areas where nonlinear waves have been emerging in the phenomenology of lattice dynamical systems. These areas include nonlinear optics, atomic physics, mechanical systems,…

A miscut (vicinal) crystal surface can be regarded as an array of meandering but non-crossing steps. Interactions between the steps are shown to induce a faceting transition of the surface between a homogeneous Luttinger liquid state and a…

A discrete version of deposition-diffusion equations appropriate for description of step flow on a vicinal surface is analyzed for a two-dimensional grid of adsorption sites representing the stepped surface and explicitly incorporating…

A part of the theory of dislocations in crystals is revised with the aim to fit it into the framework of the nonlinear theory of plasticity initially designed for amorphous glassy materials.

We study the evolution of step bunches on vicinal surfaces using a thermodynamically consistent step-flow model that (i) circumvents the quasistatic approximation that prevails in the literature by accounting for the dynamics of adatom…

Using a Monte Carlo method on a lattice model of a vicinal surface with short-range step-step attraction, we show that, at low temperature and near equilibrium, there is an inhibition of the motion of macro-steps. This inhibition leads to a…

Drops of active liquid crystal have recently shown the ability to self-propel, which was associated with topological defects in the orientation of active filaments [Sanchez {\em et al.}, Nature {\bf 491}, 431 (2013)]. Here, we study the…

The meander instability of a vicinal surface growing under step flow conditions is studied within a solid-on-solid model. In the absence of edge diffusion the selected meander wavelength agrees quantitatively with the continuum linear…

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…

In this paper, we propose a variational formulation to study the singular evolution equations that govern the dynamics of surface modulations on crystals below the roughening temperature. The basic idea of the formulation is to expand the…

Motivated by the motion of biopolymers and membranes in solution, this article presents a formulation of the equations of motion for curves and surfaces in a viscous fluid. We focus on geometrical aspects and simple variational methods for…

We propose a mechanical model for the behaviour of rocks based on progressive damage at the elementary scale and elastic interaction. It allows us to simulate several experimental observations: mechanical behaviour ranging from brittle to…

The paper deals with systems of ordinary differential equations containing in the right-hand side controls which are discontinuous in phase variables. These controls cause the occurrence of sliding modes. If one uses one of the well-known…

We study, numerically, the collective dynamics of self-rotating nonaligning particles by considering a monolayer of spheres driven by constant clockwise or counterclockwise torques. We show that hydrodynamic interactions alter the emergence…

The nonlinear dynamics of magnetic tearing islands imbedded in a pressure gradient driven turbulence is investigated numerically in a reduced magnetohydrodynamic model. The study reveals regimes where the linear and nonlinear phases of the…

We study the driving of colloidal molecular crystals over periodic substrates such as those created with optical traps. The n-merization that occurs in the colloidal molecular crystal states produces a remarkably rich variety of distinct…