While many observers recognize the significance of the city size distribution topic, the resolution of several apparent inconsistencies in the body of literature has not yet been achieved. This may explain why geographers, sociologists, demographers, historians, economists, and planners essentially tend to describe intercity patterns, are biased toward ad hoc interpretations, and are prone to making intuitive statements in their research. The primary purpose of this thesis is to evolve a more consistent methodological viewpoint within the community size topic. Efforts are made to unite analytical statements resting upon a common premise, to qualify, in this light, the approaches prevalent in empirical research, and to relate theory and empiricism by adopting a flexible explanatory framework. The discussion necessarily involves a critique of existing arguments and certain extensions that, we can devise from those arguments. While there is considerable attention directed to presenting empirical methodologies, no original data analysis is included. Contending that the notions should be bound together within a systems framework, we naturally devote initial emphasis to the features of central place systems as outlined in the partial equilibrium theory of Christaller (1966) and Losch (1954). We place particular stress upon the Christaller model, the simpler and apparently more realistic of the two approaches. A major thrust of the paper is an integration of several city size models, all of which display a Christallarian hierarchy. The simplest models are shown to be special cases of a more general formulation given by Dacey (1966). Besides, we illustrate to what degree the characteristic property (that is, the constant proportionality factor) of the most elementary model (Beckmann, 1958) may be considered a limit of empirical generalization. Using the hierarchial concept, we also provide some rather novel views on the relation between community economic base and the distribution theme. It is felt that this subtopic may be useful in bridging the intra-and interurban scales. The widely expounded rank-size rule, essentially a consequence of empirical research, is then formally attached to the hierarchical models. At this stage our arguments become increasingly rigorous in order to qualify certain intuitive notions that seem accepted in the literature. The idea of hierarchical sets is crudely developed to complement the uni-hierarchy arguments. The basic conclusion here is that existing city size models hardly explain the rank-size phenomenon butt that the two notions cannot be considered totally incompatible. Empirical research methodologies are stressed as another fundamental subtopic. We suggest certain avenues along which empirical efforts must be strengthened before either (i) rigorous inductive generalizations or (ii) firm theory substantiation become more realizable. Particular attention is given to delimitation of the study area (and, therefore to the scale problem), the comparison of frequency curves, and the value of inferences we can make using rather crude statistical tools. At this stage we introduce other skew distributions that are genetically similar to the rank-size curve. Furthermore, the stochastic models that seemingly account for these distributions are taken to complement the deterministic theory mentioned above. Here we support the central place argument as the only existing source of models that explicate those factors inducing spatial differentiation of economic activities and, as a consequence, urban populations. Finally, we pursue the idea of growth within the interurban structure. At this time, however, discussion is certainly exploratory and so is limited to developing notions concerning the interrelations of growth variables (population, income, etc.) and hierarchal structure in the broadest sense. Within this analytic framework we can suggest only the most general factors that may be associated with low degrees of primacy (a quality of interurban structure that we view as a deviation from a characteristic skew distribution). This particular subtopic promises to be an exciting research theme in its own right as investigators move from equilibrium to dynamic modelling. / Arts, Faculty of / Geography, Department of / Graduate

Typescript. / Bibliography: leaves 115-123. / Photocopy. / xiv, 123 leaves, bound ill. 29 cm

Continuous monitoring during tissue culture is important for the success of engineered tissue development. It is also challenging due to lack of suitable established monitoring techniques. In this study, microdialysis, a sampling technique for measuring the unbound solute concentrations in the tissues and organs of the living body, was adopted to monitor functional tissue growth in a bioreactor with explanted bovine caudal intervertebral discs (IVD) as the test tissue. Apart from cell metabolic activities, cell and tissue biological functions were investigated for the development of microdialysis for monitoring purposes. Methodologies of microdialysis with large pore size membrane probes for sampling macromolecular bio-functional markers were established. The effects of pumping methods, including 'push', 'pull' or 'push-and-pull', and the effect of the resulting transmembrane pressure on the fluid balance, and the relative recovery of small molecules and of macromolecules (proteins) were experimentally studied. The validity of the internal reference in-situ calibration was examined in detail. It was concluded that a push-and-pull system was the only effective method to eliminate fluid loss or gain. The relative recovery of small solutes was hardly affected by the applied pumping methods; however the relative recovery of macromolecules was significantly influenced by them. The in situ calibration technique using Phenol Red can provide reliable results for small molecules including glucose and lactic acid. Using lOkDa and 70kDa fluorescent dextrans as the internal standard for in situ calibration of large molecules of similar size, it was found that the pull pump system did not work well but that the push-and-pull pumping method did work well. A novel bioreactor system for in vitro IVD culture with static load and microdialysis monitoring was developed. Explanted IVDs were cultured under three different loads for up to 7 days. A single microdialysis probe with 3000 kDa membrane was inserted into each of the IVDs at a defined location. The in situ calibration technique was proved valid in the experiments and membrane fouling was not significant. The tissue metabolism and extracellular matrix turnover during 7 day culture were continuously monitored to investigate the effect of different loads. Microdialysis proved to be a feasible and efficient method for multi-parameter monitoring of tissue culture. Substantial effort was directed towards the identification of functional macromolecular markers in conjunction with microdialysis sampling. Amongst several proteins sampled, chitinase-3-like protein 1 (CHI3L1), a major soluble protein secreted by cultured IVD cells in alginate beads and by cultured IVD explants was identified following its successful isolation. Then it was established as a suitable functional marker. The effect of physico-chemical and mechanical stimuli (e.g. osmolarity, pH, oxygen tension and mechanical load) on secretion of CHI3L1 by cultured IVD cells and chondrocytes in alginate beads and by cultured IVD explant were investigated. CHI3L1 release was sensitive to physico-chemical stimulation. The production of CHI3L1 was directly correlated with the cell metabolism and this could be readily monitored with microdialysis.

Call number: LD2668 .P7 1975 N48

Thesis. 1976. M.S.--Massachusetts Institute of Technology. Dept. of Civil Engineering. / Microfiche copy available in Archives and Engineering. / Bibliography: leaves 63-64. / M.S.

A new developmental model for growth of the echinoid test is based on a review of the growth patterns in regular echinoids. Echinoids are structurally composed of a tessellation of hundreds to thousands of individual plates. The two major aspects of echinoid growth are treated separately. (1) New plates are added in accordance with the Ocular Plate Rule and plate addition is hypothesized to be constitutively active but inhibited by a morphogen originating in coronal plates. Morphogen production is modeled as an inverse function of plate size and the concentration of inhibiting morphogen at a plate nucleation point is inversely proportional to the distance from surrounding plate centers. Plate addition is triggered whenever the inhibiting morphogen concentration falls below a threshold value. (2) The growth of individual plates is described using the Bertalanffy growth equation to model change in plate perimeter. The geometric model is based on a spherical frame of reference, and all calculations of position and growth are modeled over the surface of the sphere (i.e., along geodesics). The data structure defined to maintain the geometric parameters is based on a spherical Delaunay triangulation of plate centers, and the edge geometry approximated by the dual Voronoi polygonalization. Echinoid plates are thus modeled as Voronoi polygons covering the sphere. Growth is modeled by the increasing radius of the sphere and the changing topology of the plates as new plates are added and existing plates grow. Final form of the complete test is generated by an affine deformation of the sphere. The growth model is implemented as the program EFORECHINOID, coded in the object-oriented programming language C++ with significant usage of the Standard Template Library (STL) for efficient coding and memory management. Most parameters are available to a user via a Graphical User Interface (GUI), and output of 3-dimensional simulations is via standard 3-D AutoCAD[trademark] Drawing Exchange Format (DXF) files. Program efficiency is O(nlogn) and reasonably parameterized growth simulations with several hundred time steps can be performed in a matter of minutes per run. / text

No description available.

It is believed that the process-based model 3-PG (Physiological Principles Predicting Growth; Landsberg and Waring, 1997) can potentially play a useful role within South African forestry, both as an operational and a strategic tool. Strategic applications may include the prediction of potential productivity on a site-by-site basis; broadscale productivity estimates based on remote sensing and the spatial application of 3-PG; identification of production constraints; and estimation of carbon fluxes to help address sustainability issues. Operationally, 3-PG could complement empiricallybased models or be used in conjunction with them as a hybridised product. The challenges of this study were therefore to see whether it is possible to adapt 3-PG to predict the growth and yield of E. grandis under South African conditions, test that model predictions are consistent with observed growth data and are biologically reasonable, and to assess the practicality of using 3-PG as either a strategic or operational tool. The main emphasis of this study was to understand the internal logic of 3-PG and how physiological processes are represented, and to develop methods to objectively parameterise and initialise the model. Thereafter a detailed model validation study was performed, ending off with selected potential applications of 3-PG within the South African context. The sensitivity of predicted stand volume (SV) and leaf area index (LAI) to the values of the species-specific parameters in 3-PG was examined. These analyses enabled the development of three distinct parameter sensitivity classes: insensitive parameters (i.e. those that can be varied widely without affecting the outputs studied), sensitive parameters (i.e. those whose value strongly affects the outputs, and non-linear parameters (i.e. those for which the outputs depend in a non-linear manner on the parameter value). Minimum data requirements for the parameterisation and initialisation of 3-PG are considered in detail. Conventional methods used for the parameterisation of models, specifically 3-PG, are reflected upon. An automated parameter estimation technique was examined and used for the estimation of selected parameters. Species-specific parameters were categorised according to data source estimation and sensitivity classes. Parameters describing allometric and age-dependent relationships were assigned values using observed data from biomass harvests. Critical parameters that could not be directly assigned using observed data were the ratio of foliage to stem allocation (i.e. P2 and p2o), allocation of net primary production (NPP) to roots (TJRX and T]Rn), optimum temperature for growth (7^,) and maximum canopy quantum efficiency (acx)- These were estimated using Parameter ESTimation, by fitting model output to corresponding observed growth data. As well as species-specific parameter values, mandatory inputs required by 3-PG include weather data, site-specific factors such as site fertility (FR) and physical properties of the soils, and stand initialisation data. Objective techniques to determine these site-specific factors and the initial values for the biomass pools were proposed. Most of these data are readily available for sites where experimental trials exist, or where monitoring networks are in place. However, this is the exception rather than the rule, so alternative data and information sources are required. These, together with the need for accurate weather inputs (especially monthly rainfall) and physical properties (especially soil texture, maximum available soil water and FR) of the sites being modelled were explored. 3-PG was validated using four simple tests by comparing predicted versus observed SV. Results showed that 3-PG predictions are relatively consistent with observed stand data. Analyses performed using time-series data showed model predictions accurately tracked observed growth in response to erratic and fluctuating weather conditions. Results from the initial model validation showed production on high and low productivity sites was under- and over-predicted, respectively. Further results presented here show a similar, but less marked trend (i.e. over- and under-predictions are not as extreme), and individual biases are less than those from predictions made using another locally developed parameter set. The application of 3-PG showed that the model is able to make estimates of tree growth that are consistent with those used within the forestry site classification. This showed the considerable potential 3-PG has for strategic planning by the forest industry (i.e. projected wood supplies etc) and in research planning (refining existing site classifications). The model could be useful in predicting growth in various areas where E. grandis is not grown, assisting in future decision making. 3-PG was able to identify growth constraints on a site-by-site basis and distinguish among them, and was able to identify environmental and site limitations to plantation growth, and how they vary in space and time. These results together with predictions of site productivity demonstrate the potential for 3-PG to be used to improve existing forest site classifications. The model comparison study between empirically-based models and 3-PG showed that although the empirical models made accurate predictions of volume under static climatic conditions, under fluctuating weather conditions empirical estimates of volume were less accurate than those made with 3-PG. 3-PG can therefore be used operationally with minimum input data to predict growth using enumeration data. This is useful in saving time and cutting costs. The use of process-based models (PBMs) in general, and 3-PG in particular, needs to be "championed'' to the South African forest industry. This is necessary for two reasons. Firstly, the model and the manner with which it describes physiological processes of growth need to be explained in layman's terms. This will demonstrate how and why a process-based model can work better in a fluctuating environment than empirically based models. Secondly the comparison between 3-PG and the local empirical models needs to be presented as an example of how 3-PG can be applied on an operational basis. It is accepted that much convincing is still required. / Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2005.

No description available.

A mathematical model has been developed to describe the growth of trees in stands of Douglas fir (Pseudotsuga menziesii (Mirb.) Franco) from age ten to age 100 years. An initial square pattern of spacing was assumed. At age ten years the trees were assumed to be open-grown, that is, growing in diameter at breast height at a maximum rate. A regression of d.b.h. on age was obtained from eighteen open-grown, Douglas fir trees measured on the Saanich Peninsula, Vancouver Island. The relationship derived from these data agreed with further data collected elsewhere in the coastal regions of British Columbia and Washington and in the interior of British Columbia. The d.b.h. growth of individual trees was predicted by five-year periods. Relationships between crown width and d.b.h. were calculated from data on 426 open-grown, Douglas fir trees. There was a close correlation between crown width and root spread for open-grown trees. A multiple regression equation was obtained for height of 869 trees on d.b.h. and basal area per acre. All regression equations calculated for use in the model, were highly significant statistically. The model is initiated with a matrix of 15 x 15 trees (or tree "locations”). The initial d.b.h. of each tree is specified and, from the crown width/d.b.h. regressions, the crown width of each tree is calculated. As long as the tree remains free of competition, this calculated crown width is reduced by 40 per cent by the reduction factor "REDFAC", to give the "competitive" crown width. This was because it was found that, in young Douglas fir plantations, there could be considerable overlapping of the crowns before d.b.h. growth was reduced. As soon as competition sets in the original 40 per cent reduction is systematically reduced. The proportion of the circumference of each tree that is occupied by the crowns of surrounding competitors is then calculated. This proportion indicates the amount of competition to which the tree is being subjected and varies between zero, if the tree is open-grown, and one or more, if the tree is completely enclosed by the surrounding competitors. If the reduction is sufficiently great, continued survival of the tree is considered unlikely, and the tree is assumed to have died. The periodic d.b.h. growth of the surviving trees is calculated at five-year intervals to age 100 years. All calculations are performed using am I.B.M. 7090 electronic computer. A summary of the structure of the stand can be printed out at the end of each five-year period if required. Height growth can be described by modifying the stand model by including an appropriate regression equation. Similarly, volume growth can be estimated by modifying the basic stand model. The mathematical model developed here satisfactorily describes the growth of Douglas fir stands on an individual tree basis, over a wide range of site conditions, stand densities, amounts and distributions of mortality and thinning regimes. Field data cannot be secured to evaluate the accuracy of all the tests made. However, there are no gross errors in absolute values and results are accurate proportionately. The model described here can aid the forester in managing Douglas fir stands in the Pacific Northwest. By simulating the growth of his stands from age ten to age 100 years in a few minutes he can study questions that would otherwise require several human generations to evaluate. / Forestry, Faculty of / Graduate