We investigate the dynamics of a plastic ball on a vibrated platform in air by introducing air damping effect into the completely inelastic bouncing ball model. The air damping gives rise to larger saddle-node bifurcation points and a chaos confirmed by the largest Lyapunov exponent of a...

The possible symmetry preserving and symmetry breaking ground states of a two-dimensional, two-component Bose-Einstein condensate are classified in terms of the intercomponent and intracomponent interaction strengths and in terms of the parameters of the trapping potential, which is taken to be...

A feedback vertex set (FVS) of an undirected graph is a set of vertices that contains at least one vertex of each cycle of the graph. The feedback vertex set problem consists of constructing a FVS of size less than a certain given value. This combinatorial optimization problem has many practical...

In this paper, we analyze the relationships between biodiesel, ethanol and related fuels and agricultural commodities with a use of minimal spanning trees and hierarchical trees. To distinguish between short term and long term effects, we construct the trees for different frequencies (weekly,...

Transport of Brownian particles in a finite channel is investigated in the presence of a symmetric potential and an unbiased external force. It is found that the phase difference between the potential (energetic barriers) and the entropic barrier can break the symmetry of the system and control...

The method of the reduction of the size of the state space based on its symmetry is presented. An important property of the method is that in its static version, it preserves probabilities of states of the system. In the reduced state space, the probability of a new state (termed below as class)...

We study the magnetic field fluctuations generated by an array of circular currents with axial symmetry. The fluctuations are induced via the random orientation of the current in each ring. By increasing the number of rings per unit length, we observe a transition from a continuous to a...

We introduce a new migration rule, the directional migration, into evolutionary prisoner’s dilemma games defined in a square domain with periodic boundary conditions. We find that cooperation can be enhanced to a much higher level than the case in the absence of migration. Additionally, the...

We consider a Gross-Pitaevskii (GP) equation with cubic-quintic nonlinearities, which governs the dynamics of Bose-Einstein condensates (BECs) matter waves with time-dependent complex potential in Jacobian elliptic functions. The complex term of the potential accounts for either the atomic...

The pattern formation produced by the aggregation of the particles in magnetorheological dispersions when they are in the presence of a static magnetic field, and the process of reconstruction of these structures induced by the application of magnetic perturbations, are investigated...