Determination of catastrophic sets of a tubular chemical reactor by two-parameter continuation method

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Marek Berezowski
Keyword(s):  
Continuation Method ◽  
Extreme Points ◽  
Chemical Reactor ◽  
Stationary States ◽  
Parameter Continuation Method ◽  
It Systems ◽  
Parametric Continuation ◽  
Parameter Continuation ◽  
Two Parameter

AbstractThe work relates to development and presentation a two-parameter continuation method for determining catastrophic sets of stationary states of a tubular chemical reactor with mass recycle. The catastrophic set is a set of extreme points occurring in the bifurcation diagrams of the reactor. There are many large IT systems that use the parametric continuation method. The most popular is AUTO’97. However, its use is sometimes not convenient. The method developed in this work allows to eliminate the necessity to use huge IT systems from the calculations. Unlike these systems, it can be inserted into the program as a short subroutine. In addition, this method eliminates time-consuming iterations from the calculations.

scholarly journals Homotopic Parametric Continuation Method for Determining Stationary States of Chemical Reactors with Dispersion

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2324
Author(s):  
Marek Berezowski ◽  
Marcin Lawnik
Keyword(s):  
Mathematical Model ◽  
Nonlinear Differential Equations ◽  
Continuation Method ◽  
Chemical Reactor ◽  
Systems Of Nonlinear Equations ◽  
Stationary States ◽  
Physical Processes ◽  
Chemical Reactors ◽  
Parametric Continuation

Physical processes occurring in devices with distributed variables and a turbulent tide with a dispersion of mass and heat are often modeled using systems of nonlinear equations. Solving such a system is sometimes impossible in an analytical manner. The iterative methods, such as Newton’s method, are not always sufficiently effective in such cases. In this article, a combination of the homotopy method and the parametric continuation method was proposed to solve the system of nonlinear differential equations. These methods are symmetrical, i.e., the calculations can be made by increasing or decreasing the value of the parameters. Thanks to this approach, the determination of all roots of the system does not require any iterative method. Moreover, when the solutions of the system are close to each other, the proposed method easily determines all of them. As an example of the method use a mathematical model of a non-adiabatic catalytic pseudohomogeneous tubular chemical reactor with longitudinal dispersion was chosen.

scholarly journals A NEW EXTENSION OF PARAMETER CONTINUATION METHOD FOR SOLVING OPERATOR EQUATIONS OF THE SECOND KIND

2021 ◽  
Vol 7 (21) ◽  
pp. 157-165
Author(s):  
Bình Ngô Thanh
Keyword(s):  
Continuation Method ◽  
Operator Equations ◽  
Lipschitz Continuous ◽  
Parameter Continuation Method ◽  
Parameter Continuation

In this paper, we propose an extension of the parameter continuation method for solving operator equations of the second kind. By splitting of the operator into a sum of two operators: one monotone, Lipschitz-continuous and one contractive, the applicability of the method is broader. The suitability of the proposed approach is presented through an example.

scholarly journals Application of parameter continuation method for analysis of vibroimpact 2-dof systems

2014 ◽  
Vol 5 (3(19)) ◽  
pp. 11
Author(s):  
Ольга Семеновна Погорелова ◽  
Татьяна Георгиевна Постникова ◽  
Валентина Владимировна Отрашевская
Keyword(s):  
Continuation Method ◽  
Parameter Continuation Method ◽  
Parameter Continuation

A Two-Parameter Continuation Method for Rotating Two-Component Bose-Einstein Condensates in Optical Lattices

2013 ◽  
Vol 13 (2) ◽  
pp. 442-460 ◽  
Author(s):  
Y.-S. Wang ◽  
B.-W. Jeng ◽  
C.-S. Chien
Keyword(s):  
Optical Lattices ◽  
Continuation Method ◽  
Tangent Vector ◽  
Numerical Results ◽  
Continuation Methods ◽  
Two Component ◽  
Continuation Algorithm ◽  
Bose Einstein ◽  
Parameter Continuation ◽  
Two Parameter

AbstractWe study efficient spectral-collocation and continuation methods (SCCM) for rotating two-component Bose-Einstein condensates (BECs) and rotating two-component BECs in optical lattices, where the second kind Chebyshev polynomials are used as the basis functions for the trial function space. A novel two-parameter continuation algorithm is proposed for computing the ground state and first excited state solutions of the governing Gross-Pitaevskii equations (GPEs), where the classical tangent vector is split into two constraint conditions for the bordered linear systems. Numerical results on rotating two-component BECs and rotating two-component BECs in optical lattices are reported. The results on the former are consistent with the published numerical results.

scholarly journals Landing Trajectory Design for UAV Considering Control Restrictions and Landing Speed

2021 ◽  
pp. 179-186
Author(s):  
Ngo Van Toan ◽  
Doan The Tuan ◽  
Pham Ngoc Van ◽  
Nguyen Thanh Tung ◽  
Nguyen Ngoc Dien
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Continuation Method ◽  
Trajectory Design ◽  
Optimal Controls ◽  
Parameter Continuation Method ◽  
Parameter Continuation ◽  
Reference Trajectories ◽  
The Pontryagin Maximum Principle

The article presents a method for designing the trajectory of the UAV in space, taking into account the restriction on control. The chosen optimal controls are namely normal overload with restrictions, tangential overload with restrictions, and lateral overload. The Pontryagin maximum principle allows the transition of the optimal control problem to a boundary value problem. The parameter continuation method is applied to solve the boundary problem. The article results reveal reference trajectories in different cases of UAV landing. This result allows the design of reference trajectories for the UAV to attain the highest landing efficiency.

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