P. Allen

Dynamic models of urban growth

Abstract A model is developed in which the change in the population distribution of a region is linked to the employment pattern, and this latter in turn to the population distribution through the concepts of Central Place Theory. The result is a dynamic model of interacting urban centres in which the fluctuations (the exact history) of the system play a vital role, and with which the effect of a decision (modification of the transport system, a new town, etc.) can be estimated in the long term.

A dynamic model of urban growth: II

Abstract The dynamic model of urban growth presented by the authors in an earlier paper is further developed here, in order to take into account the possibility of daily travel between the point of residence and of employment. With this modification the model leads to a more realistic description of the urbanization of a region, giving rise to successive phases of central growth, urban sprawl, central core decay and to counter urbanization.

Experimental study of the triple-gluon vertex

Abstract In four-jet events from e+e− →Z0 →multihadrons one can separate the three principal contributions from the triple-gluon vertex, double gluon-bremsstrahlung and the secondary quark-antiquark production, using the shape of the two-dimensional angular distributions in the generalized Nachtmann-Reiter angle θ NR ∗ and the opening angle of the secondary jets. Thus one can identify directly the contribution from the triple-gluon vertex without comparison with a specific non-QCD model. Applying this new method to events taken with the DELPHI-detector we get for the ratio of the colour factor Nc to the fermionic Casimir operator C F : N c C F = 2.55 ± 0.55 ( stat. ) ± 0.4 ( fragm. + models ) ± 0.2 ( error in bias ) in agreement with the value 2.25 expected in QCD from Nc=3 and C F = 4 3 .

Darwinian evolution and a predator-prey ecology

In order to represent the biological evolution of a predator-prey ecology it is necessary to add to the equations of population dynamics terms corresponding to spontaneous mutation. Using a Volterra-Lotka ecology as an example, a model is developed for this. It is based on the assumption of two levels of description; a local one containing mutation probabilities, and the other the macroscopic average equations for the whole system. Diffusion processes link the two. The “evolutionary state” of a species is interpreted as an average effectiveness in terms of a genetic parameter space and it is shown that as a result of random mutations the ecosystem drifts irreversibly through this space.

Impact of interictal epileptic activity on normal brain function in epileptic encephalopathy: An electroencephalography–functional magnetic resonance imaging study

Using electroencephalography (EEG) in combination with functional magnetic resonance imaging (fMRI), we studied a 9.5-year-old girl who developed cognitive and behavioral regression in association with intense interictal bilaterally synchronous epileptic discharges (IBSEDs) both during the awake state and during sleep. During runs of IBSEDs, EEG-fMRI demonstrated deactivations in the lateral and medial frontoparietal cortices, posterior cingulate gyrus, and cerebellum together with focal relative activations in the right frontal, parietal, and temporal cortices. The deactivations probably reflect the repercussion of the interictal epileptic activity on normal brain function which might cause the neuropsychological regression by inducing repetitive interruptions of neurophysiological function resulting in a chronic state of specific psychomotor impairment. The relative activations could possibly indicate the source of epileptic activity rapidly spreading to other brain regions.

Evolution and the stochastic description of simple ecosystems

Abstract A stochastic description of the population dynamics of a predator-prey ecosystem is developed and the behaviour of small mutant populations studied. Expressions for their probability of survival are found and the results generalized to arbitrary ecosystems. The results of their calculations reveal the importance of neutral or near neutral mutations, and indicate the limited ability of ‘selection’ to eliminate less effective members of the population. Evolution appears as a complex dialogue between mutation and selective forces where neither is necessarily dominant and both the extremes of Neo-Darwinism and of Neutral drift are refuted. A calculation of the non-linear effects of the spatial interaction between individuals of a mutant population, shows how altruism and a division of labour can evolve because of spatial inhomogeneity, and how the ‘unit’ of selection can thereby change from individuals to social groups.

A preliminary investigation of the thermal energy flux in a dense medium

The kinetic equations, developed in earlier papers for dense systems, are solved approximately using the Chapman-Enskog method The resulting thermal conductivity for argon, krypton, xenon and methane is plotted as a function of temperature for different densities. The results appear to be in considerable accord with experience and it appears that further study of the kinetic equations should prove fruitful.

Modeling evolving spatial choice patterns

Over recent years the ideas emerging from the discovery of dissipative structures have been applied to the problem of modeling the dynamic evolution of urban systems. A dynamic model of a central place system was developed and tested, as well as a preliminary intraurban model involving six urban actors. Here we present a further development of this latter model, where an initial investigation is made of the evolving structures which characterize the interaction of seven types of urban actor. A transportation network of both public and private modes is introduced explicity into the model, and a combined transportation-land-use model capable of exploring structural urban changes is presented, which will be used to explore the possible effects of changing circumstances and tastes on urban structure and organization.

An H theorem for moderately dense gases

Abstract The problem of demonstrating an H theorem for classically interacting moderately dense gases is discussed. In particular the H quantity recently given by Prigogine, George and Henin is studied in this case in detail. The H quantity is such that it takes into account those interactions which cause an irreversible increase in entropy. The remaining interactions serve only to redefine the natural units of the description of the system. It is shown that, in terms of their theory, considering both two- and three-body interactions there is an irreversible approach to a stationary state. This stationary state implies, for macroscopic subsystems, the correct values of equilibrium thermodynamic variables, at least to second order in the density.

General transport equations in dense fluids

Abstract The shear viscosity predicted by the Allen-Cole theory of dense fluids prompts a close examination of the relationship between the Allen-Cole and the Prigogine, Nicolis and Misguich theories. As a result linear transport equations relevant to the liquid state are developed which are more general than either theory. Two possible soluble schemes arise, but the solution of these, which is very lengthy, is left to a further publication. The results presented here clarify, in a most striking way, the relationships between the various theories recently put forward for liquid transport.