Local minimisers of a three-phase partition problem with triple junctions

1994 ◽  
Vol 124 (6) ◽  
pp. 1059-1073 ◽  
Author(s):  
Peter Sternberg ◽  
William P. Zeimer
Keyword(s):  
Triple Junction ◽  
Special Property ◽  
Interfacial Area ◽  
Dynamical Problem ◽  
Two Dimensional ◽  
Triple Junctions ◽  
Ginzburg Landau ◽  
Three Phase ◽  
Motion By Curvature ◽  
Junction Structure

We establish the existence of isolated local minimisers to the problem of partitioning certain two-dimensional domains into three subdomains having least interfacial area. The solution we exhibit has the special property that the three boundaries of the minimising partition meet at a common point or “triple junction”. The configuration represents a likely candidate for a stable equilibrium in the dynamical problem of two-dimensional motion by curvature and also leads to the existence of local minimisers possessing triple junction structure to the energy associated with the vector Ginzburg–Landau and Cahn–Hilliard evolutions.

Spiral Solutions of the Two-Dimensional Complex Ginzburg–Landau Equation

2001 ◽  
Vol 35 (2) ◽  
pp. 159-161
Author(s):  
Liu Shi-Da ◽  
Liu Shi-Kuo ◽  
Fu Zun-Tao ◽  
Zhao Qiang
Keyword(s):  
Landau Equation ◽  
Two Dimensional ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation

scholarly journals Study of electric field stress on the surface contour and at the triple junction in three phase GIS with FGM spacer under the depression defect

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Janaki Pakalapati ◽  
Venkata N. Kumar Gundavarapu ◽  
Deepak Chowdary Duvvada ◽  
Sravana Kumar Bali
Keyword(s):  
Electric Field ◽  
Triple Junction ◽  
Dielectric Strength ◽  
Functionally Graded ◽  
Uniform Electric Field ◽  
Filler Materials ◽  
Field Stress ◽  
As Doping ◽  
Three Phase ◽  
Graded Material

AbstractNow days, the establishment of spacers is in wide usage in three-phase Gas Insulated Busduct (GIB) for providing mechanical support and better insulation to the conductors. The region of the intersection of SF6 gas, enclosure end and the spacer is one of the weakest links in GIB, so the major concentration is done on minimization of electric field stress at this junction by using Functionally Graded Material (FGM) technique. The other incidents of insulation failures are due to several defects like depression, delamination etc. reduces the dielectric strength of the spacers. In this paper, an FGM post type spacer has been designed for a three-phase GIB under depression and further electric field stress at Triple Junction (TJ) is reduced by introducing a metal insert (MI) nearer to the TJ. Several filler materials are used as doping materials for obtaining different permittivity values using FGM technique to achieve uniform electric field stress. Simulation is carried out for the designed spacer at various operating voltages with different types of FGM gradings. The effect of depression with different dimensions and positions is analyzed before and after inserting MI to the FGM post type spacer in three-phase GIB.

Maze energetics revealed by a large-scale two-dimensional Ginzburg-Landau type simulation

2014 ◽  
Vol 115 (17) ◽  
pp. 17D134 ◽  
Author(s):  
Kaoru Iwano ◽  
Chiharu Mitsumata ◽  
Kanta Ono
Keyword(s):  
Large Scale ◽  
Two Dimensional ◽  
Ginzburg Landau

Generation of Tunable Necklace-Pattern Solitons in Two-Dimensional Dissipative System

2013 ◽  
Vol 339 ◽  
pp. 645-650
Author(s):  
Bin Liu ◽  
Shu Jing Li ◽  
Lin Ting Ma
Keyword(s):  
Landau Equation ◽  
Dissipative System ◽  
Gaussian Pulse ◽  
Two Dimensional ◽  
Balance Equations ◽  
Ginzburg Landau ◽  
Quintic Nonlinearity ◽  
Elliptical Ring ◽  
Energy And Momentum ◽  
Triangular Ring

We obtain necklace-pattern solitons (NPSs) from the same-pattern initial Gaussian pulse modulated by alternating azimuthal phase sections (AAPSs) of out-phase based on the two-dimensional (2D) complex Ginzburg-Landau equation with the cubic-quintic nonlinearity. The initial radially symmetrical Gaussian pulse can evolves into general necklace-rings solitons (NRSs). The number and distribution of pearls is tunable by adjusting sections-number and sections-distribution of AAPSs. In addition, we study the linear increased relationship between size of initial pulses and ring-radii of NRSs. Moreover, we predict the number-threshold of pearls in theoretical analysis by using of balance equations for energy and momentum. Final, we extend the research results to obtain arbitrary NPSs, such as elliptical ring, triangular-ring, and pentagonal ring.

Reactive Power Compensation for Unbalanced Fluctuating Loads by Using Two-Dimensional Space Vector and a Static Var Compensator

2014 ◽  
Vol 533 ◽  
pp. 397-400 ◽  
Author(s):  
Chi Jui Wu ◽  
Yu Wei Liu ◽  
Shou Chien Huang
Keyword(s):  
Power Factor ◽  
Reactive Power ◽  
Dimensional Space ◽  
Measurement Data ◽  
Power Source ◽  
Active Power ◽  
Two Dimensional ◽  
Static Var Compensator ◽  
Space Vector ◽  
Three Phase

To modify the power factor and balance the three-phase currents simultaneously, this paper proposes the instantaneous compensator to calculate the compensation current. The instantaneous compensator utilizes two-dimensional instantaneous space vector and setting the active power as a constant for each cycle which can improve power quality effectively. Moreover, the instantaneous compensator requires an independent power source, whose capacity can be reduce by using a static var compensator (SVC). An SVC does not interfere with the capability of the instantaneous compensator. Field measurement data were analyzed. Simulation results confirmed the feasibility of correcting the power factor and balancing load currents simultaneously using the proposed method.

Use of Ultrasonic Technique for Measuring Interfacial Area in a Two-Dimensional Bubble Column

2006 ◽  
Vol 39 (7) ◽  
pp. 687-692 ◽  
Author(s):  
Muhammad Dani Supardan ◽  
Yoshifumi Masuda ◽  
Akinori Maezawa ◽  
Shigeo Uchida
Keyword(s):  
Bubble Column ◽  
Interfacial Area ◽  
Ultrasonic Technique ◽  
Two Dimensional
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