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Dynamics of curved fronts
TLDR
In this paper, the Saffman-Taylor Finger is used to trace the shape of a curved flame growing from a supercooled liquid in a channel, and the shapes of a Needle Crystal Growing from a Supercooled Liquid.Abstract:
Introduction. The Saffman-Taylor Finger. Stationary Shapes of a Needle Crystal Growing from a Supercooled Liquid. Stationary Shapes of a Curved Flame Propagating in a Channel. Stability of Curved Fronts. Conclusion. References. Collected Papers. Planar Front Propagation. Dragging of a Liquid by a Moving Plate. Saffman-Taylor Finger. Dendrites. Directional Solidification. Raising Bubbles. Premixed Flames.read more
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Front propagation into unstable states
TL;DR: In this paper, the authors present an introductory review of the problem of front propagation into unstable states, which is centered around the concept of the asymptotic linear spreading velocity v ∗, the rate with which initially localized perturbations spread into an unstable state according to the linear dynamical equations obtained by linearizing the fully nonlinear equations about the unstable state.
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On the Growth of Highly Ordered Pores in Anodized Aluminum Oxide
TL;DR: In this paper, it was shown that hexagonally ordered domain structures can be formed in anodic alumina films by repeated anodization and stripping of the porous oxide, and the domain size is a linear function of time and increases with temperature.
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A history of the study of solid tumour growth: the contribution of mathematical modelling.
Robyn P. Araujo,Donald McElwain +1 more
TL;DR: This short treatise presents a concise history of the study of solid tumour growth, illustrating the development of mathematical approaches from the early decades of the twentieth century to the present time, showing the crucial relationship between experimental and theoretical approaches.
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Regular Article: Modeling Melt Convection in Phase-Field Simulations of Solidification
TL;DR: In this article, a diffuse interface model is presented for direct numerical simulation of microstructure evolution in solidification processes involving convection in the liquid phase, where the solidification front is treated as a moving interface in the diffuse approximation.
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A Simple Level Set Method for Solving Stefan Problems
TL;DR: In this paper, a simple level set method for solving the Stefan problem is presented, which can handle topology changes and complicated interfacial shapes and can numerically simulate many of the physical features of dendritic solidification.