A two-parameter continuation method for computing numerical solutions of spin-1 Bose–Einstein condensates

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

International Journal of Chemical Reactor Engineering ◽

10.1515/ijcre-2020-0135 ◽

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.

Download Full-text

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

Communications in Computational Physics ◽

10.4208/cicp.110711.170212a ◽

2013 ◽

Vol 13 (2) ◽

pp. 442-460 ◽

Cited By ~ 14

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.

Download Full-text

ROBUST DECENTRALIZED H∞ CONTROLLER DESIGN FOR POWER SYSTEMS: A MATRIX INEQUALITY APPROACH USING PARAMETER CONTINUATION METHOD

IFAC Proceedings Volumes ◽

10.3182/20060625-4-ca-2906.00010 ◽

2006 ◽

Vol 39 (7) ◽

pp. 23-28

Author(s):

Getachew K. Befekadu ◽

I. Erlich

Keyword(s):

Power Systems ◽

Controller Design ◽

Continuation Method ◽

Matrix Inequality ◽

Parameter Continuation Method ◽

Parameter Continuation

Download Full-text

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

SCIENTIFIC JOURNAL OF TAN TRAO UNIVERSITY ◽

10.51453/2354-1431/2021/521 ◽

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.

Download Full-text