Related papers: Nonlinear dynamics of surface steps
We review the studies on the scaling of the minimal step-step distance lmin in the bunch with the bunch size N, l_min~N^(-{\gamma}). We build our retrospective around the different values of the exponent {\gamma} obtained from models and…
We study the fully nonlinear, nonlocal dynamics of two-dimensional multicomponent vesicles in a shear flow with matched viscosity of the inner and outer fluids. Using a nonstiff, pseudo-spectral boundary integral method, we investigate…
We study the dynamics of a particle in a space that is non-differentiable. Non-smooth geometrical objects have an inherently probabilistic nature and, consequently, introduce stochasticity in the motion of a body that lives in their realm.…
Fluctuations of isolated and pairs of ascending steps of monoatomic height are studied in the framework of SOS models, using mainly Monte Carlo techniques. Below the roughening transistion of the surface, the profiles of long steps show the…
We report on density functional total energy calculations of the step formation and interaction energies for vicinal TaC(001) surfaces. Our calculations show that double and triple-height steps are favored over single-height steps for a…
The thermodynamics of strongly anisotropic crystalline surfaces is analogous to that of a binary mixture exhibiting phase separation. On a metastable planar surface, formation of stable orientations requires a nucleation process, in which…
Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where…
We consider the shape of crystals which are soft in the sense that their elastic modulus $\mu$ is small compared to their surface tension $\gamma$, more precisely $ \mu a < \gamma$ where $a$ is the lattice spacing. We show that their…
Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations…
A recently introduced active phase field crystal model describes the formation of ordered resting and traveling crystals in systems of self-propelled particles. Increasing the active drive, a resting crystal can be forced to perform…
We present an experimental and theoretical study of the 2D dynamics of electrically charged nanoparticles trapped under a free surface of superfluid helium in a static vertical electric field. We focus on the dynamics of particles driven by…
We analyze the morphological transition of a one-dimensional system described by a scalar field, where a flat state looses its stability. This scalar field may for example account for the position of a crystal growth front, an order…
The Wigner crystal on liquid He accompanies with periodic corrugation of the He surface; dimples. The dynamics of the crystal is coupled with the motion and the deformation of the dimples. Nonlinear phenomena found in AC Corbino…
One of the intrinsic characteristics of far-from-equilibrium systems is the nonrelaxational nature of the system dynamics, which leads to novel properties that cannot be understood and described by conventional pathways based on…
Deformable self-propelled particles provide us with one of the most important nonlinear dissipative systems, which are related, for example, to the motion of microorganisms. It is emphasized that this is a subject of localized objects in…
Exploiting the "natural" frame of space curves, we formulate an intrinsic dynamics of twisted elastic filaments in viscous fluids. A pair of coupled nonlinear equations describing the temporal evolution of the filament's complex curvature…
The evolution of surface gravity waves is driven by nonlinear interactions that trigger an energy cascade similarly to the one observed in hydrodynamic turbulence. This process, known as wave turbulence, has been found to display anomalous…
Experiments performed on a wide range of glassy materials display many interesting phenomena, such as aging behavior. In recent years, a large body of experiments probed this nonequilibrium glassy dynamics through elaborate protocols, in…
Near-critical behavior of the free surface of an ideally conducting liquid in an external electric field is considered. Based on an analysis of three-wave processes using the method of integral estimations, sufficient criteria for hard…
Bunching and meandering instability of steps at the 4H-SiC(0001) surface is studied by the kinetic Monte Carlo simulation method. Change in the character of step instability is analyzed for different rates of particle jumps towards step. In…