scholarly journals A stochastic modelling of phytoplankton aggregation

2006 ◽  
Vol Volume 5, Special Issue TAM... ◽  
Author(s):  
Nadjia El Saadi ◽  
Ovide Arino
Keyword(s):  
Differential Equation ◽  
Stochastic Partial Differential Equation ◽  
Stochastic Modelling ◽  
Point Of View ◽  
Modèle Mathématique ◽  
Initial Number ◽  
Microscopic Description ◽  
Random Dispersal ◽  
International Audience ◽  
Number Of Cells

International audience The aim of this work is to provide a stochastic mathematical model of aggregation in phytoplankton, from the point of view of modelling a system of a large but finite number of phytoplankton cells that are subject to random dispersal, mutual interactions allowing the cell motions some dependence and branching (cell division or death). We present the passage from the ''microscopic'' description to the ''macroscopic'' one, when the initial number of cells tends to infinity (large phytoplankton populations). The limit of the system is an extension of the Dawson-Watanabe superprocess: it is a superprocess with spatial interactions which can be described by a nonlinear stochastic partial differential equation. L'objectif de ce travail est de fournir un modèle mathématique stochastique qui décrit l'aggrégation du hytoplancton,à partir de la modélisation d'un système de grande taille, mais finie, de cellules de phytoplancton sujettes à une dispersion aléatoire, des interactions spatiales qui donnent aux mouvements des cellules une certaine dépendance et un branchement (division cellulaire ou mort). Nous présentons le passage de la description microscopique à une description macroscopique, lorsque le nombre de cellules devient très grand (grandes populations de phytoplancton). La limite du système est une extension du superprocessus de Dawson-Watanabe: c'est un superprocessus avec interactions qui peut être décrit par une équation aux dérivées partielles stochastique non linéaire.

scholarly journals The Size of One-Way Cellular Automata

2010 ◽  
Vol DMTCS Proceedings vol. AL,... (Proceedings) ◽  
Author(s):  
Martin Kutrib ◽  
Jonas Lefèvre ◽  
Andreas Malcher
Keyword(s):  
Cellular Automata ◽  
Real Time ◽  
Finite Automata ◽  
Fixed Number ◽  
Point Of View ◽  
Upper And Lower Bounds ◽  
Worst Case ◽  
Order Of Magnitude ◽  
International Audience ◽  
Number Of Cells

International audience We investigate the descriptional complexity of basic operations on real-time one-way cellular automata with an unbounded as well well as a fixed number of cells. The size of the automata is measured by their number of states. Most of the bounds shown are tight in the order of magnitude, that is, the sizes resulting from the effective constructions given are optimal with respect to worst case complexity. Conversely, these bounds also show the maximal savings of size that can be achieved when a given minimal real-time OCA is decomposed into smaller ones with respect to a given operation. From this point of view the natural problem of whether a decomposition can algorithmically be solved is studied. It turns out that all decomposition problems considered are algorithmically unsolvable. Therefore, a very restricted cellular model is studied in the second part of the paper, namely, real-time one-way cellular automata with a fixed number of cells. These devices are known to capture the regular languages and, thus, all the problems being undecidable for general one-way cellular automata become decidable. It is shown that these decision problems are $\textsf{NLOGSPACE}$-complete and thus share the attractive computational complexity of deterministic finite automata. Furthermore, the state complexity of basic operations for these devices is studied and upper and lower bounds are given.

Stochastic Modelling of Particle Segregation in a Horizontal Drum Mixer

1992 ◽  
Vol 57 (10) ◽  
pp. 2100-2112 ◽  
Author(s):  
Vladimír Kudrna ◽  
Pavel Hasal ◽  
Andrzej Rochowiecki
Keyword(s):  
Differential Equation ◽  
Diffusion Coefficient ◽  
Stochastic Model ◽  
Diffusion Process ◽  
Stochastic Modelling ◽  
Solid Particles ◽  
Kolmogorov Equation ◽  
Particle Segregation ◽  
Drum Mixer ◽  
Horizontal Drum

A process of segregation of two distinct fractions of solid particles in a rotating horizontal drum mixer was described by stochastic model assuming the segregation to be a diffusion process with varying diffusion coefficient. The model is based on description of motion of particles inside the mixer by means of a stochastic differential equation. Results of stochastic modelling were compared to the solution of the corresponding Kolmogorov equation and to results of earlier carried out experiments.

scholarly journals Hyperbolastic Models from a Stochastic Differential Equation Point of View

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1835
Author(s):  
Antonio Barrera ◽  
Patricia Román-Román ◽  
Francisco Torres-Ruiz
Keyword(s):  
Differential Equation ◽  
Simulated Data ◽  
Real Data ◽  
Point Of View ◽  
Likelihood Method ◽  
Numerical Resolution ◽  
The Family ◽  
The Common ◽  
Linear Differential ◽  
Mean Function

A joint and unified vision of stochastic diffusion models associated with the family of hyperbolastic curves is presented. The motivation behind this approach stems from the fact that all hyperbolastic curves verify a linear differential equation of the Malthusian type. By virtue of this, and by adding a multiplicative noise to said ordinary differential equation, a diffusion process may be associated with each curve whose mean function is said curve. The inference in the resulting processes is presented jointly, as well as the strategies developed to obtain the initial solutions necessary for the numerical resolution of the system of equations resulting from the application of the maximum likelihood method. The common perspective presented is especially useful for the implementation of the necessary procedures for fitting the models to real data. Some examples based on simulated data support the suitability of the development described in the present paper.

scholarly journals Solutions de similitude d'un jeu différentiel stochastique

2006 ◽  
Vol Volume 5, Special Issue TAM... ◽  
Author(s):  
Mario Lefebvre
Keyword(s):  
Differential Equation ◽  
Stochastic Process ◽  
Partial Differential Equation ◽  
Differential Equations ◽  
Similarity Solutions ◽  
Explicit Solutions ◽  
Two Dimensional ◽  
Controlled Processes ◽  
International Audience ◽  
First Time

International audience A two-dimensional controlled stochastic process defined by a set of stochastic differential equations is considered. Contrary to the most frequent formulation, the control variables appear only in the infinitesimal variances of the process, rather than in the infinitesimal means. The differential game ends the first time the two controlled processes are equal or their difference is equal to a given constant. Explicit solutions to particular problems are obtained by making use of the method of similarity solutions to solve the appropriate partial differential equation. On considère un processus stochastique commandé bidimensionnel défini par un ensemble d'équations différentielles stochastiques. Contrairement à la formulation la plus fréquente, les variables de commande apparaissent dans les variances infinitésimales du processus, plutôt que dans les moyennes infinitésimales. Le jeu différentiel prend fin lorsque les deux processus sont égaux ou que leur différence est égale à une constante donnée. Des solutions explicites à des problèmes particuliers sont obtenues en utilisant la méthode des similitudes pour résoudre l'équation aux dérivées partielles appropriée.

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