Pattern formation in a mean field model of electrocortical activity

Periodic solutions to a mean-field model for electrocortical activity

We consider a continuum model of electrical signals in the human cortex, which takes the form of a system of semilinear, hyperbolic partial differential equations for the inhibitory and excitatory membrane potentials and the synaptic inputs. The coupling of these components is represented by sigmoidal and quadratic nonlinearities. We consider these equations on a square domain with periodic bou...

simulation and experimental studies for prediction mineral scale formation in oil field during mixing of injection and formation water

abstract: mineral scaling in oil and gas production equipment is one of the most important problem that occurs while water injection and it has been recognized to be a major operational problem. the incompatibility between injected and formation waters may result in inorganic scale precipitation in the equipment and reservoir and then reduction of oil production rate and water injection rate. ...

Emergence of spatially heterogeneous burst suppression in a neural field model of electrocortical activity

Burst suppression in the electroencephalogram (EEG) is a well-described phenomenon that occurs during deep anesthesia, as well as in a variety of congenital and acquired brain insults. Classically it is thought of as spatially synchronous, quasi-periodic bursts of high amplitude EEG separated by low amplitude activity. However, its characterization as a "global brain state" has been challenged ...

Dynamics of labyrinthine pattern formation in magnetic fluids : a mean-field theory

We are interested in the flow of a droplet of viscous ferrofluid in the Hele-Shaw cell under a transverse magnetic field. The (twodimensional) phase configuration is observed to evolve into a labyrinthine pattern. We show that the conventional model for this flow has the form of a gradient flux w.r.t. an energy functional, which is the sum of magnetic and surface energy. In particular, we are i...

A Simplified Perturbation Model for Prediction of Mean Ionic Activity Coefficient in Aqueous Electrolyte Solution