A coupled map lattice model of tree dispersion
Miaohua Jiang Qiang Zhang
Discrete & Continuous Dynamical Systems - B 2008, 9(1): 83-101 doi: 10.3934/dcdsb.2008.9.83
We study the coupled map lattice model of tree dispersion. Under quite general conditions on the nonlinearity of the local growth function and the dispersion (coupling) function, we show that when the maximal dispersal distance is finite and the spatial redistribution pattern remains unchanged in time, the moving front will always converge in the strongest sense to an asymptotic state: a traveling wave with finite length of the wavefront. We also show that when the climate becomes more favorable to growth or germination, the front at any nonzero density level will have a positive acceleration. An estimation of the magnitude of the acceleration is given.
keywords: tree dispersion acceleration in dispersion. traveling wave solution Coupled map lattice
Inelastic Collapse in a Corner
Ming Gao Jonathan J. Wylie Qiang Zhang
Communications on Pure & Applied Analysis 2009, 8(1): 275-293 doi: 10.3934/cpaa.2009.8.275
We consider the interaction of a rigid, frictionless, inelastic particle with a rigid boundary that has a corner. Typically, two possible final outcomes can occur: the particle escapes from the corner after experiencing a certain number of collisions with the corner, or the particle experiences an inelastic collapse in which an infinite number of collisions can occur in a finite time interval. For the former case, we determine the number of collisions that the particle will experience with the boundary before escaping the corner. For the latter case, we determine the conditions for which inelastic collapse can occur. For a corner composed of two straight walls, we derive simple analytic solutions and show that for a given coefficient of restitution, there is a critical corner angle above which inelastic collapse cannot occur. We show that as the corner angle tends to the critical corner angle from below, the process of inelastic collapse takes infinitely long. We also show a surprising phenomenon that if the corner has the form of a cusp, the particle can have an infinite number of collisions with the boundary in a finite time interval without losing all of its energy, and eventually escapes from the corner.
keywords: Inelastic collapse corner

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