We will present some recent work on phase-field models for twophase fluids with variable densities. The Quasi-Incompressible Navier-Stokes-Cahn-Hilliard model with the gravitational force being incorporated in the thermodynamically consistent framework will be investigated. Under a minor reformulation of the system we show that there is a continuous energy law underlying the system. For the ref...

We consider a discrete-time s S inventory model in which the stored items have a random common lifetime with a discrete phase-type distribution. Demands arrive in batches following a discrete phase-type renewal process. With zero lead time and allowing backlogs, we construct a multidimensional Markov chain to model the inventorylevel process. We obtain a closed-form expected cost function. Nume...

Random graph models and associated inference problems such as the stochastic block model play an eminent role in computer science, discrete mathematics and statistics. Based on nonrigorous arguments physicists predicted the existence of a generic phase transition that separates a “replica symmetric phase” where statistical inference is impossible from a phase where the detection of the “ground ...

This paper presents a simple model predictive control (MPC) approach to control the power injection system (PIS) for renewable energy applications. A DC voltage source and a single-phase inverter that is connected to the grid by an LCL filter form the PIS. Grid voltage is considered a disturbance for the system. For eliminating this disturbance, a modified model is proposed. It is usual to ...

This paper presents a simple model predictive control (MPC) approach to control the power injection system (PIS) for renewable energy applications. A DC voltage source and a single-phase inverter that is connected to the grid by an LCL filter form the PIS. Grid voltage is considered a disturbance for the system. For eliminating this disturbance, a modified model is proposed. It is usual to ...

A suitable model for predicting the product quality of vacuum gas oil (VGO) catalytic hydrocracking is developed. Data were obtained using an experimental catalytic hydrocracking reactor loaded with the Ni-Mo/Al2O3-SiO2 catalyst. A set of experimental runs was conducted under various operating temperatures from 380 to 450 ℃. Three distribution models were used t...