We describe the dynamical and bifurcational behavior of two mutually inhibitory, leaky, neural units subject to external stimulus, random noise, and "priming biases". The model describes a simple forced choi...
We describe the dynamical and bifurcational behavior of two mutually inhibitory, leaky, neural units subject to external stimulus, random noise, and "priming biases". The model describes a simple forced choice experiment and accounts for varying levels of expectation and control. By projecting the model's dynamics onto slow manifolds, using judicious linear approximations, and solving for one-dimensional (reduced) probability densities, analytical estimates are developed for reaction time distributions and shown to compare satisfactorily with "full" numerical data. A sensitivity analysis is performed and the effects of parameters assessed. The predictions are also compared with behavioral data. These results may help correlate low-dimensional models of stochastic neural networks with cognitive test data, and hence assist in parameter choices and model building.
A central problem in the mathematical analysis of fluid dynamics is the asymptotic limit of the fluid flow as viscosity goes to *** is particularly important when boundaries are present since vorticitv is typically ge...
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A central problem in the mathematical analysis of fluid dynamics is the asymptotic limit of the fluid flow as viscosity goes to *** is particularly important when boundaries are present since vorticitv is typically generated at the boundary as a result of boundary layer *** boundary laver theory,developed by Prandtl about a hundred years ago,has become a standard tool in addressing these *** at the mathematical level,there is still a lack of fundamental understanding of these questions and the validity of the boundary layer *** this article,we review recent progresses on the analysis of Prandtl’s equation and the related issue of the zero-viscosity limit for the solutions of the Navier-Stokes *** also discuss some directions where progress is expected in the near future.
We explore time-based solvers for linear standing-wave problems, especially the oscillatory Helmholtz equation. Here, we show how to accelerate the convergence properties of timestepping. We introduce a new time-based...
We explore time-based solvers for linear standing-wave problems, especially the oscillatory Helmholtz equation. Here, we show how to accelerate the convergence properties of timestepping. We introduce a new time-based solver that we call phase-adjusted time-averaging (PATA), which we couple to timestepping to form the PATA-TS solver. Numerical experiments indicate that the PATA-TS solver is faster than the PATA solver and timestepping by a factor of 1.2 and 1.5 or more, respectively. We also explain why the PATA-TS solver is robust, efficient, and easy to program for a variety of practical applications.
B. D. Coller, P. Holmes, John Lumley; Erratum: ‘‘Interaction of adjacent bursts in the wall region’’ [Phys. Fluids 6, 954 (1994)], Physics of Fluids, Volume 9,
B. D. Coller, P. Holmes, John Lumley; Erratum: ‘‘Interaction of adjacent bursts in the wall region’’ [Phys. Fluids 6, 954 (1994)], Physics of Fluids, Volume 9,
We show that the statistical properties of the large scales of the Kuramoto-Sivashinsky equation in the extended system limit can be understood in terms of the dynamical behavior of the same equation in a small finite...
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