Hybrid model of a stationary plasma thruster

A mathematical model is proposed for studying the processes in a stationary plasma thruster (SPT) taking into account the ionization of the working substance - Xenon, based on the hybrid equations of electromagnetic hydrodynamics (EMHD) of the plasma. The 1D2V case of plane symmetry is considered in detail, for which a numerical algorithm for investigating solutions of hybrid EMHD equations is constructed, based on the method of macroparticles. The solution of a number of fundamental issues is given: the calculation of average values, interpolation, construction of the initial distribution of macroparticles, the choice of boundary conditions for the electric field, etc. The results of calculations with and without taking into account the induction fields in the SPT are presented.

Proposal of the hybrid solution to determining the selected fracture parameters for SEN(B) specimens dominated by plane strain

In the paper, new hybrid (numerical-analytical) methods to calculate the J-integral, the CTOD, and the load line displacement are presented. The proposed solutions are based on FEM calculations which were done for SEN(B) specimens dominated by plane strain condition. The paper includes the verification of the existing limit load solution for SEN(B) specimen with proposal of the new analytical formulae, which were used for building hybrid equations for determining three selected fracture mechanics parameters.

On Fractional Order Hybrid Differential Equations

We develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order0<α<1. Using some fixed point theorems we prove the existence of mild solutions for two types of hybrid equations. Examples are given to illustrate the obtained results.

A New Method to Solve Static Voltage Collapse Point with Hybrid Power Network Equations

Electric power network components can be simulated with equivalent circuit and establish the hybrid node voltage and branch current electricity network analysis model based on it. We form the equations reflected the voltage collapse conditions, and establish the extended power flow equations with the hybrid equations, the static voltage collapse point can be calculated by solving them. The advantage of this method is that the power flow calculation can be convergence smoothly near the collapse point because of the extended power flow equations when the Jacobian matrix tends to be singular. The convergence can be achievable just because the joining of the equation reflecting the voltage collapse conditions has changed the structure of the Jacobian matrix. The simulation results show that this method is very effective.