scholarly journals Universal fractality of morphological transitions in stochastic growth processes

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
J. R. Nicolás-Carlock ◽  
J. L. Carrillo-Estrada ◽  
V. Dossetti
Keyword(s):  
Growth Processes ◽  
Stochastic Growth ◽  
Morphological Transitions

scholarly journals On the Asymptotic Behaviour of Discrete Time Stochastic Growth Processes

1987 ◽  
Vol 15 (1) ◽  
pp. 305-343 ◽  
Author(s):  
G. Keller ◽  
G. Kersting ◽  
U. Rosler
Keyword(s):  
Asymptotic Behaviour ◽  
Discrete Time ◽  
Growth Processes ◽  
Stochastic Growth

Random growth in a tessellation

1973 ◽  
Vol 74 (3) ◽  
pp. 515-528 ◽  
Author(s):  
Daniel Richardson
Keyword(s):  
Euclidean Space ◽  
Growth Process ◽  
Dimensional Euclidean Space ◽  
Growth Processes ◽  
Stochastic Growth ◽  
Random Growth

Let S be n dimensional Euclidean space and let T be a division of S into cells. Assume that each cell must be either white or black at any time t. At time 0 the cell at the origin, α0, is black and all other cells are white. Let G be some stochastic growth process which tends to change white cells with black neighbours into black cells. Let C(t) be the black shape at time t. For a family, F, of such growth processes we prove the following theorem.

Criteria for extinction of certain population growth processes with interacting types

1973 ◽  
Vol 5 (2) ◽  
pp. 183-199 ◽  
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.

Criteria for extinction of certain population growth processes with interacting types

1973 ◽  
Vol 5 (02) ◽  
pp. 183-199 ◽  
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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