Linear and fully decoupled scheme for a hydrodynamics coupled phase-field surfactant system based on a multiple auxiliary variables approach

2022 ◽  
pp. 110909
Author(s):  
Junxiang Yang ◽  
Zhijun Tan ◽  
Junseok Kim
Keyword(s):  
Phase Field ◽  
Auxiliary Variables ◽  
Surfactant System

Energy quadratization Runge-Kutta method for the modified phase field crystal equation

2021 ◽  
Author(s):  
Jaemin Shin ◽  
Hyun Geun Lee ◽  
June-Yub Lee
Keyword(s):  
Energy Dissipation ◽  
Phase Field ◽  
Mass Conservation ◽  
Energy Functional ◽  
Original Model ◽  
Auxiliary Variables ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Phase Field Crystal

Abstract In this paper, we propose high order and unconditionally energy stable methods for a modified phase field crystal equation by applying the strategy of the energy quadratization Runge–Kutta methods. We transform the original model into an equivalent system with auxiliary variables and quadratic free energy. The modified system preserves the laws of mass conservation and energy dissipation with the associated energy functional. We present rigorous proofs of the mass conservation and energy dissipation properties of the proposed numerical methods and present numerical experiments conducted to demonstrate their accuracy and energy stability. Finally, we compare long-term simulations using an indicator function to characterize the pattern formation.

A new phase-field model for a water–oil-surfactant system

2014 ◽  
Vol 229 ◽  
pp. 422-432 ◽  
Author(s):  
Ana Yun ◽  
Yibao Li ◽  
Junseok Kim
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Surfactant System ◽  
New Phase

A TEM study of the influence of microstructure on the superplastic behavior of a U-5.8 wt.% Nb alloy

1986 ◽  
Vol 44 ◽  
pp. 568-569
Author(s):  
G. Mackiewicz Ludtka
Keyword(s):  
Grain Size ◽  
Heating Rate ◽  
Phase Field ◽  
Single Phase ◽  
Superplastic Behavior ◽  
Two Phase ◽  
Single Phase Field

Historically, metals exhibit superplasticity only while forming in a two-phase field because a two-phase microstructure helps ensure a fine, stable grain size. In the U-5.8 Nb alloy, superplastici ty exists for up to 2 h in the single phase field (γ1) at 670°C. This is above the equilibrium monotectoid temperature of 647°C. Utilizing dilatometry, the superplastic (SP) U-5.8 Nb alloy requires superheating to 658°C to initiate the α+γ2 → γ1 transformation at a heating rate of 1.5°C/s. Hence, the U-5.8 Nb alloy exhibits an anomolous superplastic behavior.

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