Lagrangian particle calculations of distributive mixing: Limitations and applications

Experimental and Modelling Investigation of Monolayer Development with Clustering

“…Alternatively, the mean-field model and the moment dynamics model lead to very different predictions for the 231 monolayer formation. The presence, or absence, of clustering in the experimental data is confirmed by separately calculating a spatial index which allows us to quantitatively assess whether the spatial distribution of individuals is uniform or clustered Phelps and Tucker 2006). We conclude by reiterating that continuum models based on the mean-field assumption should not be applied to population dynamics problems where cell clustering is present, and we also outline further extensions to our modelling and experimental work.…”

Generalized index for spatial data sets as a measure of complete spatial randomness

“…(1)-(3) reduce to those of Phelps and Tucker [5]. Therefore our formulation generalizes their index.…”

“…The spatial distribution of a set of objects arises throughout physical, biological, and social processes, for example, in fluid mixing [1][2][3][4][5], cell biology [6][7][8][9], plant ecology [10][11][12][13][14], and pedestrian and traffic flow [15,16]. They also arise naturally in agent-based models, known as cellular automata (CA) models [17][18][19][20][21].…”

“…For example, objects dispersed uniformly at random throughout the domain (e.g., as the result of a diffusive process) are at the CSR state. Binder and Landman [25] derived a CSR limiting value for an index [5], when objects exclude volume from the domain. The index was defined by partitioning the domain into equal size bins and calculating a scaled variance of the bin counts.…”

Spatial Analysis of Multi-species Exclusion Processes: Application to Neural Crest Cell Migration in the Embryonic Gut

“…Instead, the more realistic scenario occurs when each ENC agent is equally likely to lie in any bin. Such a state is termed complete spatial randomness (CSR) (Diggle 1983;Jones 1991;Phelps and Tucker 2006), and once the CSR state is achieved the distribution of ENC agents cannot be made any more even. The CSR limit for the index is…”