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The motion of magnetization domains front. Black state (a magnetization direction in the material) invades the white state (opposite magnetization direction). The fronts are the interfaces between black and white
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where the front is the interface between populated and unpopulated places. Fronts can be static or mobile depending on the conditions of the system, and the causes of the motion can be the variation of a
254:. This solution corresponds to extinction and saturation of population. Observe that this model is spatially-extended, because it includes a diffusion term given by the second derivative. The state
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From a mathematical point of view, fronts are solutions of spatially extended systems connecting two steady states, and from dynamical systems point of view, a front corresponds to a
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The most simple example of front solution connecting a homogeneous stable state with a homogeneous unstable state can be shown in the one-dimensional
621:
Alvarez-Socorro, A. J.; Clerc, M.G.; González-Cortés, G; Wilson, M. (2017). "Nonvariational mechanism of front propagation: Theory and experiments".
20:, a front can be understood as an interface between two different possible states (either stable or unstable) in a physical system. For example, a
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or shape induced motion due to non-variation dynamics in the system, according to
Alvarez-Socorro, Clerc, González-Cortés and Wilson.
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55:
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Pomeau, Y. (1986). "Front motion, metastability and subcritical bifurcations in hydrodynamics".
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Reaction-transport systems : mesoscopic foundations, fronts, and spatial instabilities
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372:, and such solution are propagative. Particularly, there exist one solution of the form
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Front solution connecting two steady states in a generic spatially extended system.
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676:"The behavior of solutions of the equation of Kolmogorov–Petrovsky–Piskunov"
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where the flame is the interface between burned and unburned material or in
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Proceedings of the Japan
Academy, Series A, Mathematical Sciences
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is the interface between two different density masses of air, in
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is unstable. There exist a family of front solutions connecting
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is stable as a simple linear analysis can show and the state
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Horsthemke, Vicenç Mendéz, Sergei
Fedotov, Werner (2010).
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Fronts connecting stable - unstable homogeneous states
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of population. This equation has two steady states,
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148:{\displaystyle N_{t}=DN_{xx}+rN(N_{0}-N)}
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71:Fisher–Kolmogorov equation
505:Propagative front profile
674:Uchiyama, Kohei (1977).
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339:{\displaystyle N=N_{0}}
247:{\displaystyle N=N_{0}}
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365:{\displaystyle N=0}
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
