Reformulation of the Fourier–Bessel steady state mode solver

2016 ◽  
Vol 375 ◽  
pp. 63-71 ◽  
Author(s):  
Robert C. Gauthier
Keyword(s):  
Steady State ◽  
Steady State Mode ◽  
Mode Solver

scholarly journals Method of Switching on and Off a Power Transformer with a Capacitor Bank in an Electrothermal Installation

2021 ◽  
Vol 2096 (1) ◽  
pp. 012196
Author(s):  
V S Klimash ◽  
B D Tabarov
Keyword(s):  
Energy Efficiency ◽  
Steady State ◽  
Reactive Power ◽  
Power Transformer ◽  
Capacitor Bank ◽  
Steady State Mode ◽  
Operating Modes ◽  
Switching Losses ◽  
Full Compensation ◽  
Special Control

Abstract The article is devoted to issues related to increasing the energy efficiency of industrial electrothermal installations, both in starting and stationary operating modes due to the use of capacitors and thyristor starters with special control. The results of a significant reduction in the duration of the transient process, elimination of surges and asymmetry of starting currents and voltage drawdowns are presented. The results of full compensation of the reactive power of the network in the steady-state mode are also presented. It is shown that the starting currents do not exceed their steady-state values and that the shutdown of the electrothermal installation is performed without the occurrence of an arc and switching losses at the contacts of the switches. Researches of an electrothermal installation with a capacity of 750 kV⋅A and a voltage of 380 / 80 V are made on the model in the Matlab environment.

Stability and Bifurcation in a Predator–Prey System with Prey-Taxis

2020 ◽  
Vol 30 (02) ◽  
pp. 2050022 ◽  
Author(s):  
Huanhuan Qiu ◽  
Shangjiang Guo ◽  
Shangzhi Li
Keyword(s):  
Steady State ◽  
Periodic Solutions ◽  
Neumann Boundary ◽  
Initial Boundary ◽  
Steady States ◽  
Mode Interaction ◽  
Small Range ◽  
Steady State Mode ◽  
Predator Prey ◽  
Prey System

In this paper, we consider a generalized predator–prey system with prey-taxis under Neumann boundary condition, that is, the predators can survive even in the absence of the prey species. It is proved that for an arbitrary spatial dimension, the corresponding initial boundary value problem possesses a unique global bounded classical solution when the prey-taxis is restricted to a small range. Moreover, the local stabilities of constant steady states (including trivial, semi-trivial and positive constant steady states) are investigated. A further study on the coexistence steady state implies that the prey-taxis term suppresses the global asymptotical stability and influences the steady-state/Hopf bifurcations (if they exist). Analyses of steady-state bifurcation, Hopf bifurcation, and even Hopf/steady-state mode interaction are carried out in detail by means of the Lyapunov–Schmidt procedure. In particular, we obtain stable or unstable steady states, time-periodic solutions, quasi-periodic solutions, and sphere-like surfaces of solutions. These results provide theoretical evidences to the complex spatiotemporal dynamics found in numerical simulations.

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