In this paper, solutions of the nonlinear Schrödinger equation with a parabolic and a periodic potential modelling the dynamics of Bose–Einstein condensates are considered. A Galërkin projection approach is applied to reduce the partial differential equation to a system of nonlinear ordinary...

We study the dynamics of solitons in Bose–Einstein condensates (BECs) loaded into an optical lattice (OL), which is combined with an external parabolic potential. Chiefly, the one-dimensional (1D) case is considered. First, we demonstrate analytically that, in the case of the repulsive BEC,...

We study the dynamics of atomic Bose–Einstein condensates (BECs), when the quadrupole mode is excited. Within the Thomas–Fermi approximation, we derive an exact first-order system of differential equations that describes the parameters of the BEC wave function. Using perturbation theory...

After a brief general overview of Monte Carlo computer simulations in statistical physics, special emphasis is placed on applications to phase transitions and critical phenomena. Here, standard simulations employing local update algorithms are severely hampered by the problem of critical slowing...

A new application of the percolation theory for describing the coupled heat and mass transport phenomena through porous media is given. The space and time dependence of the temperature and moisture level functions are calculated by taking into account the discrete, sudden changes of the...