Large Rayleigh number thermal convection: heat flux predictions and strongly nonlinear solutions

We investigate the structure of strongly nonlinear Rayleigh–Bénard convection cells in the asymptotic limit of large Rayleigh number and fixed, moderate Prandtl number. Unlike the flows analyzed in prior theoretical studies of infinite Prandtl number convection, our cellular solutions exhibit dynamically inviscid constant-vorticity cores. By solving an integral equation for the cell-edge temperature distribution, we are able to predict, as a function of cell aspect ratio, the value of the core vorticity, details of the flow within the thin boundary layers and rising/falling plumes adjacent to the edges of the convection cell, and, in particular, the bulk heat flux through the layer. The results of our asymptotic analysis are corroborated using full pseudospectral numerical simulations and confirm that the heat flux is maximized for convection cells that are roughly square in cross section.

'Enhanced Direct and Indirect Genetic Algorithm Approaches for a Mall Layout and Tenant Selection Problem'

During our earlier research, it was recognised that in order to be successful with an indirect genetic algorithm approach using a decoder, the decoder has to strike a balance between being an optimiser in its own right and finding feasible solutions. Previously this balance was achieved manually. Here we extend this by presenting an automated approach where the genetic algorithm itself, simultaneously to solving the problem, sets weights to balance the components out. Subsequently we were able to solve a complex and non-linear scheduling problem better than with a standard direct genetic algorithm implementation.

The importance of different timings of excitatory and inhibitory pathways in neural field models

In this paper we consider a neural field model comprised of two distinct populations of neurons, excitatory and inhibitory, for which both the velocities of action potential propagation and the time courses of synaptic processing are different. Using recently-developed techniques we construct the Evans function characterising the stability of both stationary and travelling wave solutions, under the assumption that the firing rate function is the Heaviside step. We find that these differences in timing for the two populations can cause instabilities of these solutions, leading to, for example, stationary breathers. We also analyse $quot;anti-pulses,$quot; a novel type of pattern for which all but a small interval of the domain (in moving coordinates) is active. These results extend previous work on neural fields with space dependent delays, and demonstrate the importance of considering the effects of the different time-courses of excitatory and inhibitory neural activity.

Enhanced Direct and Indirect Genetic Algorithm Approaches for a Mall Layout and Tenant Selection Problem

During our earlier research, it was recognised that in order to be successful with an indirect genetic algorithm approach using a decoder, the decoder has to strike a balance between being an optimiser in its own right and finding feasible solutions. Previously this balance was achieved manually. Here we extend this by presenting an automated approach where the genetic algorithm itself, simultaneously to solving the problem, sets weights to balance the components out. Subsequently we were able to solve a complex and non-linear scheduling problem better than with a standard direct genetic algorithm implementation.

'Enhanced Direct and Indirect Genetic Algorithm Approaches for a Mall Layout and Tenant Selection Problem'

During our earlier research, it was recognised that in order to be successful with an indirect genetic algorithm approach using a decoder, the decoder has to strike a balance between being an optimiser in its own right and finding feasible solutions. Previously this balance was achieved manually. Here we extend this by presenting an automated approach where the genetic algorithm itself, simultaneously to solving the problem, sets weights to balance the components out. Subsequently we were able to solve a complex and non-linear scheduling problem better than with a standard direct genetic algorithm implementation.

Neural fields with sigmoidal firing rates: approximate solutions

Many tissue level models of neural networks are written in the language of nonlinear integro-differential equations. Analytical solutions have only been obtained for the special case that the nonlinearity is a Heaviside function. Thus the pursuit of even approximate solutions to such models is of interest to the broad mathematical neuroscience community. Here we develop one such scheme, for stationary and travelling wave solutions, that can deal with a certain class of smoothed Heaviside functions. The distribution that smoothes the Heaviside is viewed as a fundamental object, and all expressions describing the scheme are constructed in terms of integrals over this distribution. The comparison of our scheme and results from direct numerical simulations is used to highlight the very good levels of approximation that can be achieved by iterating the process only a small number of times.