a numerical model for two-phase debris flows is developed in this paper, on the basis of understanding of the physical characteristics of debris flows from field investigations and experiments. employing a moving coordinate, the kinetic energy equation of gravel particles in unit volume in debris flow is developed by considering the potential energy of the particles, energy from the liquid phas...

in present paper, dynamic behavior and control of a fluidized bed reactor for polyethylene production has been considered. a double active sites model for ziegler-natta catalysts is used for simulation of polymerization reaction. hydrodynamic behavior of the bed is modeled using a two phase model including bubble and emulsion phases in which bubble phase has plug flow pattern with differentiall...

Determining the phase diagram of interacting quantum many-body systems is an important task for a wide range problems such as understanding and design materials. For classical equilibrium systems, Lee-Yang formalism provides rigorous foundation transitions, these ideas have also been extended to realm. Here, we develop theory transitions that can include thermal fluctuations caused by finite te...

We use finite–size scaling of Lee–Yang partition function zeroes to study the critical behaviour of the two dimensional step or sgn O(2) model. We present evidence that, like the closely related XY –model, this has a phase transition from a disordered high temperature phase to a low temperature massless phase where the model remains critical. The critical parameters (including logarithmic corre...

In 1952, Lee and Yang published two important papers [1, 2] in statistical mechanics. They gave us a new way of looking at the nature of phase transitions, and suggested that we can regard partition functions as functions of external fields (in the case of Ising model, this would be magnetic fields), whose domains can be extended to the complex plane. In particular, they proved a series of Lee-...