Differential Equations Seminar
Senior theses presentations
Abstract:
In this talk we recall finite element method for 1-dimensional and 2-dimensional Poisson's problem. We describe a typical implementation of the method and compare it with a vectorized approach in Matlab. We introduce an extension of the previously developed code to quadrilateral finite elements, and finally we show results of numerical experiments that compare the speed and memory usage of the typical implementation to the vectorized approach.
Abstract: Sensory input to the lamprey central pattern generator (CPG) for locomotion is known to have a significant role in modulating the neural activity produced during swimming. This sensory feedback allows the CPG to adjust its rhythm in the presence of a periodic stimulus. This phenomena is known as entrainment. Bending experiments on the lamprey spinal cord indicate that the CPG is robust to perturbations and returns to entrainment shortly after perturbations are applied. We model the bending experiments with a forced chain of coupled neural oscillators and apply triangle perturbations to both no input and sinusoidal in put to the entrained model CPG. We compare the resulting phase and frequency changes to experimental results. We also investigate patterns between cells as well as how these changes propagate up and down the chain.