Simon model

Abstract: The SIMon (Simulated Injury Monitor) software package is being developed to advance the interpretation of injury mechanisms based on kinematic and kinetic data measured in the advanced anthropomorphic test dummy (AATD) and applying the measured dummy response to the human mathematical models imbedded in SIMon. The human finite element head model (FEHM) within the SIMon environment is presented in this paper. Three-dimensional head kinematic data in the form of either a nine accelerometer array or three linear CG head accelerations combined with three angular velocities serves as an input to the model. Three injury metrics are calculated: Cumulative strain damage measure (CSDM) - a correlate for diffuse axonal injury (DAI); Dilatational damage measure (DDM) - to estimate the potential for contusions; and Relative motion damage measure (RMDM) - a correlate for acute subdural hematoma (ASDH). During the development, the SIMon FEHM was tuned using cadaveric neutral density targets (NDT) data and further validated against the other available cadaveric NDT data and animal brain injury experiments. The hourglass control methods, integration schemes, mesh density, and contact stiffness penalty coefficient were parametrically altered to investigate their effect on the model's response. A set of numerical and physical parameters was established that allowed a satisfactory prediction of the motion of the brain with respect to the skull, when compared with the NDT data, and a proper separation of injury/no injury cases, when compared with the brain injury data. Critical limits for each brain injury metric were also established. Finally, the SIMon FEHM performance was compared against HIC15 through the use of NHTSA frontal and side impact crash test data. It was found that the injury metrics in the current SIMon model predicted injury in all cases where HIC15 was greater than 700 and several cases from the side impact test data where HIC15 was relatively small. Side impact was found to be potentially more injurious to the human brain than frontal impact due to the more severe rotational kinematics.

Abstract: This note is a discussion of H. A. Simon's model (1955) concerning the class of frequency distributions generally associated with the name of G. K. Zipf. The main purpose is to show that Simon's model is analytically circular in the case of the linguistic laws of Estoup-Zipf and Willis-Yule. Insofar as the economic law of Pareto is concerned, Simon has himself noted that his model is a particular case of that of Champernowne; this is correct, with some reservation. A simplified version of Simon's model is included.

Abstract: While the implications of the Simon model of urban growth, e.g., the rank-size rule, have been explored in numerous papers, the assumptions of that model have not, to my knowledge, been subjected to empirical verification. This paper represents an initial attempt to do so, emphasizing those sources of variation in the growth of cities typically singled out in Simon's verbal statements of the model: births, deaths, rural-urban, urban-rural, and urban-urban migration. It is found that over the recent past the assumptions concerning these components are all violated and violated in the direction of upward curvature away from the log-linear relationship between city size and rank predicted by the model, an upward curvature which we in fact observe.