Phase field
Phase-field models for the approximation of the willmore functional and flow*,**
... the phase-field model (1) at fixed parameter ε has been studied in [9] with a volume constraint fixing the average of u, and in [10] with both volume and area ...the phase field system (1) as ...
10
A new approach to multi-phase field for the solidification of alloys
... of phase-field simulation as a tool to understanding microstructure formation during solidification has grown ...(differentiable) phase variable, φ, the value of which represents the phase of ...
9
Phase Field Crystal Approach to the Solidification of Ferromagnetic Materials
... The phase field method is used to study non-equilibrium interface phenomena ...in phase field model of solidification is to employ a phase-field variable which is a function of ...
129
Phase Field Modeling of Microstructure Evolution in Nuclear Materials
... This paper reports two examples of applying phase-field method in predicting microstructure evolution in nuclear materials. These modelling efforts help us for better understanding of controlling parameters ...
5
An energy stable time integrator for phase field models
... problems, phase-field methods represent the sharp interfaces between the different phases through thin transition regions that distribute the interfacial ...the phase-field or order- parameter ...
63
Soluble phase field model
... solid phase in multicomponent solutions, where one of the components is to be diffused away from the interface in order to form a stable crystal ...the Phase field ...the field of ordering ...
22
Large-scale multiscale modeling of phase transformation in nanocrystalline materials: Atomistic and Phase-Field methods
... ferent phase-transformation temperatures quantitatively for atomistic (MD) and mesoscopic (phase-field) ap- proaches, the grain diameter versus square root of phase- transformation time is ...
8
Phase field analysis of eutectic breakdown.
... Phase field modelling has been used to study both single phase ([1],[2],[3],[4]) systems (single phase models have only one solid phase with the liquid and hence require only a scalar ...
19
Some remarks on stability for a phase-field model with memory
... the phase field equations with memory in which memory is included in the energy balance equation only, see for example Aizicovici & Barbu [1], Colli & Lauren¸cot [6, 7], Aizicovici & Feireisl ...
29
Phase field material point method for brittle fracture
... 2 phase field modelling for brittle fracture is briefly described to facilitate presentation of subsequent ...coupled field system of equation is described in Section ...standard phase ...
47
A Combined Entropy/Phase-Field Approach to Gravity
... scalar field of an “order parameter”, which is alternatively named “feature indicator” or most common “phase–field ...a phase-field model just drawing on the definition of the ...The ...
13
Phase field theory of edges in an anisotropic crystal
... The dynamic evolution of an interface with anisotropic surface energy is problem that has been extensively studied. A particularly interesting situation is the evolu- tion of a planar interface in a direction for which ...
25
Review on Phase field Simulation on PVD
... Phase-field models contain a large number of phenomenological parameters, which have to be determined in order to obtain quantitative results for real material. The parameters are related to the ...
10
Concepts of modeling surface energy anisotropy in phase-field approaches
... As mentioned, the crystalline anisotropy in Eq. (11) allows to, respectively, construct arbitrary convex crystals with corners, lines, and planar facets in two and three dimen- sions. The incorporation of the faceted ...
21
Computational phase field modeling
... elevated phase-field modeling to a point in which it can be used as a predictive model for a number of problems in computational mechanics which were very difficult to treat with conventional ...
43
Phase field modelling of surfactants in multi phase flow
... In this section we aim to support the results of the asymptotic analysis and showcase the capability of the new phase field model by some numerical computations. The results are on a qualitative level. We ...
59
A phase-field model for cohesive fracture
... The development of a phase-field model for cohesive fracture is a non-trivial extension of the model available for brittle fracture. In fact, considering well-established numerical methods for discrete ...
21
Phase field models on evolving surfaces
... [2012], phase field equations have been coupled to fluid flows for the modelling of multi-component ...one phase is preferable, Allen-Cahn type phase field equations have been used Alt ...
135
Optimal Control of Moving Interface and Phase-Field Separations.
... In the classical temperature formulation of the two-phase Stefan problem, the location of the moving interface has to be determines as part of the solution and cannot be identified in advanced. Therefore, ...
120
Phase Field Simulations
... Context Principles : Landau model Kim-Kim-Suzuki approach Superalloys Martensitic transition Conclusion. Martensitic transition and shape memory alloys[r] ...
43