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Showing 1 to 8 of 8 for “"Allen-Cahn equation"”.
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On two-valued minimal graphs and minimal surfaces arising from the Allen-Cahn equation
… to seven, represents one of the main technical challenges of our work. In dimension four, we are able to push this further and give a proof of the aforementioned Bernstein-type theorem. The second part deals with minimal arising from a semilinear elliptic PDE called the Allen-Cahn equation. There …
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Homoclinic snaking in discrete systems
… the discrete Swift-Hohenberg, an optical cavity equation, and the discrete Allen-Cahn equation, which have infinitely multiplicity called homoclinic snaking. First, we study the discrete Swift-Hohenberg equation with cubic and quintic nonlinearity, obtained from discretizing the spatial …
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Computational Analysis of Asphalt Binder based on Phase Field Method
… evaluation of asphalt binder has always been a challenging issue for pavement engineers. Recently, the Phase Field Method (PFM) has emerged as a powerful computational tool to simulate the microstructure evolution of asphalt binder. PFM analyzes the structure from the free energy aspect and can …
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Coupled Gradient Enhanced Damage - Viscoplasticity Model Using Phase Field Method
… (CDM). The time dependent Ginzburg-Landau equation which is also termed the Allen-Cahn equation is used to describe the damage evolution process. Specific length scale which addresses the transition region in which the process of changing the undamaged solid to the fully damaged material …
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Cardiac MRI Data Segmentation Using the Partial Differential Equation of Allen–Cahn Type
… the geometrical evolution partial differen- tial equation of the Allen-Cahn type. This equation has origin in the description of motion by mean curvature and has diffusive character. The diffusion pro- cess can be controlled by the segmented signal so that the edges of the objects or areas can be …
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Phase-field Modeling of Phase Change Phenomena
… we investigate the application of the Allen-Cahn model, a member of the phase-field family, in the simulation of phase change problems. Because phase change is usually accompanied with latent heat, heat transfer also needs to be considered. Firstly, we go through different theoretical …
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Phase-field simulation of freezing water droplet
… the water-air fluid interface are handled by the Allen-Cahn and the Cahn-Hilliard equations, respectively. The governing equations, including the two phase-field equations, the Navier-Stokes equations, and the energy equation, are designed such that the non-negative entropy production is …
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Deep Learning Approaches for PDE-based Image Analysis and Beyond: From the Total Variation Flow to Medieval Paper Analysis
Partial differential equations (PDEs) play a fundamental role in the mathematical modelling of many processes and systems in physical, biological and other sciences, as well as in engineering and computer science. Image analysis is a prime example for a field where PDEs have triggered many …