On the Ginzburg—Landau expansion of the free energy of a spatially inhomogeneous anisotropic BCS-superfluid

1974 ◽  
Vol 47 (3) ◽  
pp. 224-226 ◽  
Author(s):  
P. Wölfle
Keyword(s):  
Free Energy ◽  
Ginzburg Landau ◽  
Spatially Inhomogeneous

ELECTRODEPOSITION MODELING USING COUPLED PHASE-FIELD AND LATTICE BOLTZMANN APPROACH

2013 ◽  
Vol 25 (01) ◽  
pp. 1340018 ◽  
Author(s):  
D. V. PATIL ◽  
K. N. PREMNATH ◽  
D. DESAI ◽  
SANJOY BANERJEE
Keyword(s):  
Free Energy ◽  
Phase Field ◽  
Lattice Boltzmann ◽  
Order Parameter ◽  
Chemical Deposition ◽  
Energy Functional ◽  
Time Step ◽  
Ginzburg Landau ◽  
Two Phases ◽  
Boltzmann Method

In this paper, a coupled phase-field (PF) and lattice Boltzmann method (LBM) is presented to model the multiphysics phenomenon involving electro-chemical deposition. The deposition (or dissolution) of the electrode is represented using variations of an order-parameter. The time-evolution of an order-parameter is proportional to the variation of a Ginzburg–Landau free-energy functional. Further, the free-energy densities of the two phases are defined based on a dilute or an ideal solution approximation. An efficient LBM is used to obtain the converged electro-static potential field for each physical time-step of the evolution of the PF variable. The coupled approach demonstrates the applicability of the LBM in a multiphysics scenario. The numerical validation for the coupled approach is performed by the simulation of the electrodeposition process of Cu from CuSO 4 solution.

scholarly journals Effect of intensity and size of defect on Ginzburg-Landau free energy for type II superconductors

2020 ◽  
Author(s):  
Dyah Eka Puspitasari ◽  
Nizar Rahmanda Hardiyanto ◽  
Eny Latifah ◽  
Hari Wisodo
Keyword(s):  
Free Energy ◽  
Type Ii ◽  
Ginzburg Landau ◽  
Type Ii Superconductors ◽  
Landau Free Energy

Zeros of a complex Ginzburg–Landau order parameter with applications to superconductivity

1994 ◽  
Vol 5 (4) ◽  
pp. 431-448 ◽  
Author(s):  
C. M. Elliott ◽  
H. Matano ◽  
Tang Qi
Keyword(s):  
Free Energy ◽  
Numerical Simulations ◽  
Gibbs Free Energy ◽  
Order Parameter ◽  
Magnetic Potential ◽  
Ginzburg Landau ◽  
Absolute Value ◽  
Complex Order ◽  
Isolated Points ◽  
The Absolute

We consider the minimizers of the Gibbs free energy which couples a complex Ginzburg–Landau order parameter with a magnetic potential. It is established that the set on which the complex order parameter equals zero consists only of isolated points. Some estimates concerning the set on which the absolute value of the order parameter is small are also given. Numerical simulations are presented for the problem without a magnetic potential.

A phase-field study of domain dynamics in ferroelectric BCT-BZT system

MRS Advances ◽  
2016 ◽  
Vol 1 (40) ◽  
pp. 2783-2788 ◽  
Author(s):  
Soumya Bandyopadhyay ◽  
Tushar Jogi ◽  
Kumaraswamy Miriyala ◽  
Ranjith Ramadurai ◽  
Saswata Bhattacharyya
Keyword(s):  
Free Energy ◽  
Phase Field ◽  
Three Dimensional ◽  
Phase Field Model ◽  
Ginzburg Landau ◽  
Equimolar Composition ◽  
Electrical Boundary Conditions ◽  
Experimental Findings ◽  
Domain Dynamics ◽  
Three Dimensional Simulations

ABSTRACTWe present a thermodynamically consistent phase-field model describing the free energy of perovskite-based BCT-BZT solid solution containing an intermediate morphotropic phase boundaries. The Landau coefficients are derived as functions of composition of zirconium. The electrostrictive and elastic constants are appropriately chosen from experimental findings. The resulting Landau free energy is constructed to describe the stable polarization states as a function of composition. The evolution of the polarization order parameters at a particular composition is described by a set of time-dependent Ginzburg-Landau (TDGL) equations. Additionally, we solve Poisson’s equation and mechanical equilibrium equation to account for the ferroelectric/ferroelastic interactions. We have performed two dimensional and three-dimensional simulations with appropriate electrical boundary conditions to study the effect of external electric field on domain dynamics in BCT-BZT system at the equimolar composition.

Precursor Nanoscale Textures in Ferroelastics: Interplay between Anisotropy and Disorder

2013 ◽  
Vol 738-739 ◽  
pp. 155-159 ◽  
Author(s):  
Teresa Castán ◽  
Antoni Planes ◽  
Avadh Saxena
Keyword(s):  
Experimental Data ◽  
Free Energy ◽  
Ginzburg Landau ◽  
Landau Free Energy ◽  
Frozen State ◽  
Nanoscale Textures

We study the effect of anisotropy and disorder on the morphology of precursor microstructures within a Ginzburg-Landau free energy framework. In addition, with increasing disorder at low anisotropy we find a crossover from a twinned state to a non-transforming frozen state. Results are compared with available experimental data.

GROWTH KINETICS IN THE Φ6N-COMPONENT MODEL: NONCONSERVED ORDER PARAMETER

1994 ◽  
Vol 08 (18) ◽  
pp. 1115-1124
Author(s):  
F. CORBERI ◽  
U. MARINI BETTOLO MARCONI
Keyword(s):  
Free Energy ◽  
Growth Kinetics ◽  
Order Parameter ◽  
Energy Functional ◽  
Component Model ◽  
Ginzburg Landau ◽  
Free Energy Functional ◽  
Spherical Limit ◽  
Component Order ◽  
Component Order Parameter

The dynamics of a system with a nonconserved N-component order parameter described by a Ginzburg–Landau free energy functional containing a sixth order nonlinearity is discussed in the spherical limit. The model displays a richer behavior than the well-studied Φ4 case. In particular it shows interesting properties regarding metastability, a feature which is absent in the spherical Φ4 model.

Existence of Minimizer to the Ginzburg-Landau Free Energy of Ferromagnetic System

2013 ◽  
Vol 444-445 ◽  
pp. 717-722
Author(s):  
Li Mei Li ◽  
Hong Luo
Keyword(s):  
Free Energy ◽  
Sobolev Space ◽  
Monotone Operator ◽  
Ginzburg Landau ◽  
Landau Free Energy ◽  
Lower Semi ◽  
Ferromagnetic System ◽  
Compact Imbedding

In this paper, we obtain the existence of minimizer to Ginzburg-Landau free energy of ferromagnetic system by coercivity and weakly lower semi-continuity of the free energy, where the weakly lower semi-continuity is derived from monotone operator condition and the Sobolev space compact imbedding theorem.

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