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- W1594697986 abstract "Theories of dendritic growth use capillarity as a boundary condition on the normal (Ivantsov) field transporting latent heat and/or solute during solidification. We demonstrate that the Gibbs–Thomson temperature distribution acts as a weak interfacial thermal field along the solid–liquid interface. Provided that the interfacial conductivity is not exactly zero, energy conservation along any nonequilibrium interface shape shows varying rates of deposition and removal of small amounts of capillary-mediated thermal energy. Local energy conservation, via the Stefan energy balance, requires that where capillary energy is released (a source term) the freezing rate is retarded slightly. Where capillary energy is withdrawn (a sink term), the rate of freezing is enhanced. These contravening kinetic responses balance at special points along an advancing interface where the surface Laplacian of the interface potential vanishes. The small bias in the freezing rates surrounding certain “balance” points induces rotation (tilting) of the interface. Interfacial rotations with favorable chirality couple with the normal transport field in the melt by changing the local curvature and, eventually, produce a side branch. A precision, noise-free, Greens function solver confirms for closed interface shapes, such as an ellipse, that interface rotations and branches arise dynamically at the locations predicted analytically. Subsequent rotations develop episodically as the tip shape and rotation points co-evolve. A synchronous limit cycle may develop under conditions not yet fully understood. Noise, per se, and stochastic stability, play no direct roles in this proposed mechanism of branching morphogenesis." @default.
- W1594697986 created "2016-06-24" @default.
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- W1594697986 date "2013-07-31" @default.
- W1594697986 modified "2023-09-27" @default.
- W1594697986 title "Capillary-Mediated Interface Energy Fields: Deterministic Dendritic Branching" @default.
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- W1594697986 doi "https://doi.org/10.1002/9783527652815.ch13" @default.
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