Dynamics in nature often proceed in the form of rare transition events: The system under study spends very long periods of time at various metastable states; only very rarely it hops from one metastable state to another. Understanding the dynamics of such systems requires us to study the ensemble of transition paths between the different metastable states. Transition path theory is a general ma...

A wind farm is a collection of wind turbines built in an area to provide electricity. Wind power is a renewable energy resource and an alternative to non-renewable fossil fuels. In this paper impact of wind farms in power system reliability is investigate and a new procedure for reliability assessment of wind farms in HL1 level is proposed. In proposed procedure, application of Fuzzy – Markov f...

The ultra-cold non-interacting Boson gases form so-called Bose-Einstein condensates (BECs). It is desirable to have a rigorous mathematical theory for such quantum phenomenon. In this talk, I will report our numerical and analytical results on the ground state patterns and their phase transitions of spin-1 BECs in a uniform magnetic field. The macroscopic model for spin-1 BECs is a generalized ...

We predict a dynamical classical superfluid-insulator transition in a Bose-Einstein condensate (BEC) trapped in a combined optical and axially-symmetric harmonic potentials initiated by a periodic modulation of the radial trapping potential. The transition is marked by a loss of phase coherence in the BEC and a subsequent destruction of the interference pattern upon free expansion. For a weak m...

We study the problem of finding a path that joins a given initial state with a final one, where the evolution is governed by classical (Hamiltonian) dynamics. A new algorithm for the computation of long time transition trajectories connecting two configurations is presented. In particular, a strategy for finding transition paths between two stable basins is established. The starting point is th...

We study the ground-state properties of weakly frustrated Heisenberg ferrimagnetic chains with nearest and next-nearest neighbor antiferromagnetic exchange interactions and two types of alternating sublattice spins S1 > S2, using 1/S spin-wave expansions, density-matrix renormalization group, and exact-diagonalization techniques. It is argued that the zero-point spin fluctuations completely des...