In this paper, Forchheimer equation is used as the constitutive equation for flow through rockfill, and the non-linear two-dimensional governing equation with free surface is solved by a new finite element method in a fixed grid. The model is verified by applying it to different flow conditions. The first scenario, which is assumed to be one-dimensional with analytical solution available for it...

The one-dimensional chain of coupled oscillators with long-range power-law interaction is considered. The equation of motion in the infrared limit are mapped onto the continuum equation with the Riesz fractional derivative of order α, when 0 < α < 2. The evolution of soliton-like and breather-like structures are obtained numerically and compared for both types of simulations: using the chain of...

Time evolution of the probability density is investigated for initially quiescent dynamical systems exposed suddenly to random excitations. A variety of dynamical systems is considered, including the usual linear oscillator, and nonlinear oscillators of hardening spring, of softening spring, and of the van del Pol type. The random excitations are assumed to be stationary stochastic processes, s...

In undergraduate classrooms, while teaching chaos and fractals, it is taught as if there no relation between these two. By using some non linear oscillators we demonstrate that a connection fractals. plotting the phase space diagrams of four nonlinear box counting method finding fractal dimension established chaotic nature oscillators. The awareness all systems are good fractals will add more i...