A dynamic phase transition model for spatial agglomeration processes

A nonlinear model of population migration is presented in order to provide a dynamic explanation for the formation of metropolitan areas. "In Section 2 the model is introduced in terms of the rate equations for the mean values of the regional population numbers with specifically chosen individual transition rates. Section 3 gives a survey of concepts and results for the convenience of the reader not interested in the details of the mathematical derivations. Section 4 derives the stationary solutions of the rate equations, that is, the equilibria of the system. Section 5 treats the time dependent solutions of the model equations focussing on the exact analytic solutions along so-called symmetry paths. Section 6 analyzes the dynamic stability of the symmetry path solutions and decides which stationary states are unstable and which are stable equilibrium states."     

Dynamic Models of Agricultural Location in a Spatial Interaction Framework

Recent research demonstrates that spatial interaction models may also be made to function as location models by the addition of appropriate hypotheses about structural adjustment. An appealing feature of the approach is that dynamics are explicitly incorporated. In this paper, the attempt is made to recast a problem from classical economic-geographic theory—that of agricultural location—within a spatial interaction framework. It is shown that a wide variety of models is potentially available, and the properties of a range of these models are selectively explored.     

Circum-mortem damage to some ancient African hominid crania: a taphonomic and evolutionary essay

Close examination of three early hominid crania from Africa yields taphonomic information long after they were excavated, and can contribute information relevant to their dating and taxonomic status. The condition of the bone and breaks and markings are reviewed in the Florisbad, Saldanha and Broken Hill (Kabwe) crania, indicating animal biting while the bone was still fresh in the first and last of these specimens. However, the damage to the base of the Kabwe cranium indicates that there may also have been breakage by hominids, including scorings near the margin of the squamous suture. No tooth marks are observed on the Saldanha cranium, but a depressed fracture and other lesions indicate hominid damage to fresh bone. Postmortem weathering indicates cranial thickness even greater than the original measurements, which implies a more primitive evolutionary status for Saldanha than for Kabwe. This view is supported by other morphological evidence, and suggests a considerably earlier date for Saldanha and a classification asHomo erectus.

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Résumé L'examen à fond de trois crânes d'hominidés anciens de l'Afrique fournit des données taphonomiques longtemps après la fouille, et peut livrer informations quant à leur date et à leur statut taxonomique. L'état de l'os et les cassures et d'autres traces sont étudiés dans les crânes de Florisbad, Saldanha et Broken Hill (Kabwe); dans ceux de Florisbad et de Broken Hill on constate que l'os a été mordu par des animaux lorsqu'il était encore frais. Cependant les dégâts à la base du crâne de Kabwe—y compris des stries près du bord de la suture squameuse—indiquent qu'il peut aussi avoir été cassé par des hominidés.Il n'y a pas de traces de morsures sur le crâne de Saldanha, mais on y observe une fracture aplatie et d'autres lésions qui indiquent que l'os frais a été endommagé par des hominidés. A cause des altérations survenues après la mort, on constate que le crâne original était même plus épais que les premières mésures l'indiquaient, ce qui implique un statut évolutionnaire plus primitif pour Saldanha que pour Kabwe. Cette idée, renforcée par d'autres indices morphologiques, suggère que Saldanha est beaucoup plus ancien que l'on ne croyait, et doit être classifié commeHomo erectus.