Related papers: Kadanoff Sand Piles, following the snowball
The main purpose of this work is to provide a non-local approach to study aspects of structural stability of 3D Filippov systems. We introduce a notion of semi-local structural stability which detects when a piecewise smooth vector field is…
The evolution of two grains, which lie on a substrate and are in contact with each other, can be roughly described by a model in which the exterior surfaces of the grains evolve by surface diffusion and the grain boundary, namely the…
It is often assumed that a warped galaxy can be modeled by a set of rings. This paper verifies numerically the validity of this assumption by the study of periodic orbits populating a heavy self-gravitating warped disk. The phase space…
We show that deterministic systems with strong nonlinearities seem to be more appropriate to model sandpiles than stochastic systems or deterministic systems in which discontinuities are the only nonlinearity. In particular, we are able to…
The stability of periodically placed slabs occurring in neutron stars (lasagna phase) is examined by exact geometrical methods for the first time. It appears that the slabs are stable against any shape perturbation modes for the whole range…
We introduce a new type of mappings in metric spaces which are three-point analogue of the well-known Kannan type mappings and call them generalized Kannan type mappings. It is shown that in general case such mappings are discontinuous but…
We introduce a simple one-dimensional sandpile model that undergoes relaxation oscillations. A single model can account for self-organized critical behavior and relaxation oscillations, depending on the manner in which it is driven,…
We prove the existence and we study the stability of the kink-like fixed points in a simple Coupled Map Lattice for which the local dynamics has two stable fixed points. The condition for the existence allows us to define a critical value…
A popular theory of self-organized criticality relates the critical behavior of driven dissipative systems to that of systems with conservation. In particular, this theory predicts that the stationary density of the abelian sandpile model…
We analyze in detail a one-dimensional stochastically driven running sandpile. The dynamics shows three different phases, depending on the on-site relaxation rate and stochastic driving rate. Two phases are characterized by the presence of…
A droplet placed on a hydrophilic conical fiber tends to move toward the end of larger radii due to capillary action. Experimental investigations are performed to explore the dynamics of droplets with varying viscosities and volumes on…
The intermittent transition between slow growth and rapid shrinkage in polymeric assemblies is termed dynamic instability, a feature observed in a variety of biochemically distinct assemblies including microtubules, actin and their…
Many physical systems can be modeled as large sets of domains "glued" together along boundaries - biological cells meet along cell membranes, soap bubbles meet along thin films, countries meet along geopolitical boundaries, and metallic…
We investigate the fixed points of a shell model for the turbulent advection of passive scalars introduced Jensen, Paladin and Vulpiani. The passive scalar field is driven by the velocity field of the popular GOY shell model. The scaling…
We introduce the liquid bin model as a continuous-time deterministic dynamics, arising as the hydrodynamic limit of a discrete-time stochastic interacting particle system called the infinite bin model. For the liquid bin model, we prove the…
The nonlinear behaviour of low-viscosity warped discs is poorly understood. We verified a nonlinear bending-wave theory, in which fluid columns undergo affine transformations, with direct 3D hydrodynamical simulations. We employed a…
The motion of a spinning football brings forth the possible existence of a whole class of finite dynamical systems where there may be non-denumerably infinite number of fixed points. They defy the very traditional meaning of the fixed point…
A continuum description of granular flows would be of considerable help in predicting natural geophysical hazards or in designing industrial processes. However, the constitutive equations for dry granular flows, which govern how the…
We study the stability and dynamics of traveling-front solutions of a modified Kuramoto--Sivashinsky equation arising in the modeling of nanoscale ripple patterns that form when a nominally flat solid surface is bombarded with a broad ion…
We report numerical investigations of a three-dimensional model of diffusive growth of fine particles, the internal structure of which corresponds to different crystal lattices. A growing cluster (particle) is immersed in, and exchanges…