Multivariate stochastic mechanisms and information measures in population growth processes

A study is made of a series of stochastic growth processes related to multi-type branching models with interaction phenomena among the types with aim to ascertain criteria for extinction or non-extinction of the population. It is established that trends depicting changes of expected sizes of types generally overwhelm any effects of statistical fluctuations such that the conditions for extinction reduce to natural conditions on expected values. Three models are developed. The first two involve special mating systems for certain two sex populations. The last model is a neutralization phenomenon for two types of particles.

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Criteria for extinction of certain population growth processes with interacting types

Advances in Applied Probability ◽

10.1017/s0001867800039136 ◽

1973 ◽

Vol 5 (02) ◽

pp. 183-199 ◽

Cited By ~ 5

Author(s):

Samuel Karlin ◽

Norman Kaplan

Keyword(s):

Population Growth ◽

Mating Systems ◽

Natural Conditions ◽

Growth Processes ◽

Stochastic Growth ◽

Statistical Fluctuations ◽

Expected Values ◽

Interaction Phenomena

A study is made of a series of stochastic growth processes related to multi-type branching models with interaction phenomena among the types with aim to ascertain criteria for extinction or non-extinction of the population. It is established that trends depicting changes of expected sizes of types generally overwhelm any effects of statistical fluctuations such that the conditions for extinction reduce to natural conditions on expected values. Three models are developed. The first two involve special mating systems for certain two sex populations. The last model is a neutralization phenomenon for two types of particles.

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Simulation of 3-Dimensional Cell Population Growth Processes in Polyhedral Cellular Systems

Materials Science Forum ◽

10.4028/www.scientific.net/msf.537-538.579 ◽

2007 ◽

Vol 537-538 ◽

pp. 579-590

Author(s):

Tamás Réti ◽

Ibolya Zsoldos

Keyword(s):

Population Growth ◽

Cell Population ◽

Cell Decomposition ◽

Cellular Systems ◽

Space Filling ◽

Growth Processes ◽

Cell Nucleation ◽

Cell Population Growth ◽

Polyhedral Cells ◽

New Perspective

In order to simulate the polyhedral grain nucleation in alloys, 3-D cell population growth processes are studied in space-filling periodic cellular systems. We discussed two different methods by which space-filling polyhedral cellular systems can be constructed by topological transformations performed on “stable” 3-D cellular systems. It has been demonstrated that an infinite sequence of stable periodic space-filling polyhedral systems can be generated by means of a simple recursion procedure based on a vertex based tetrahedron insertion. On the basis of computed results it is conjectured that in a 3-D periodic, topologically stable cellular system the minimum value of the average face number 〈f〉 of polyhedral cells is larger than eight (i.e. 〈f〉 > 8). The outlined algorithms (which are based on cell decomposition and/or cell nucleation) provide a new perspective to simulate grain population growth processes in materials with polyhedral microstructure.

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