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Full-Text Articles in Mathematics
Dynamics Of Spatial Pattern Formation: Cases Of Spikes And Droplets, Yuya Sasaki
Dynamics Of Spatial Pattern Formation: Cases Of Spikes And Droplets, Yuya Sasaki
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
This thesis studies the gradient system that forms spatial patterns such that the minimum distances of pairs among various points are maximized in the end. As this problem innately involves singularity issues, an extended system of the gradient system is proposed. Motivated by the spatial pattern suggested by a numerical example, this extended system is applied to a three-point problem and then to a two-point problem in a quotient space of ℝ2 modulo a lattice.
Quickest Flows Over Time, Lisa Fleischer, Martin Skutella
Quickest Flows Over Time, Lisa Fleischer, Martin Skutella
Dartmouth Scholarship
Flows over time (also called dynamic flows) generalize standard network flows by introducing an element of time. They naturally model problems where travel and transmission are not instantaneous. Traditionally, flows over time are solved in time‐expanded networks that contain one copy of the original network for each discrete time step. While this method makes available the whole algorithmic toolbox developed for static flows, its main and often fatal drawback is the enormous size of the time‐expanded network. We present several approaches for coping with this difficulty. First, inspired by the work of Ford and Fulkerson on maximal s‐t …
Trench's Perturbation Theorem For Dynamic Equations, Stevo Stevic, Martin Bohner
Trench's Perturbation Theorem For Dynamic Equations, Stevo Stevic, Martin Bohner
Mathematics and Statistics Faculty Research & Creative Works
We consider a nonoscillatory second-order linear dynamic equation on a time scale together with a linear perturbation of this equation and give conditions on the perturbation that guarantee that the perturbed equation is also nonoscillatory and has solutions that behave asymptotically like a recessive and dominant solutions of the unperturbed equation. As the theory of time scales unifies continuous and discrete analysis, our results contain as special cases results for corresponding differential and difference equations by William F. Trench.