A coupled model of fish-phytoplankton: motion and evolution. Yaya - - PowerPoint PPT Presentation

A coupled model of fish-phytoplankton: motion and evolution. Yaya Youssouf

Department of Mathematics, Gaston-Berger University Department of Mathematics, Uppsala University

First Network Meeting for Sida- and ISP-funded PhD Students in Mathematics Stockholm 7–8 March 2017

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My Advisors

• Pr. Mamadou Sy
• Pr. David J. T. Sumpter
• Dr. Maksym Romenskyy

Main advisor Assistant advisor Assistant advisor Gaston-Berger University Uppsala University Uppsala University

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Research Topic.

Interest

• Dynamic of populations.

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Research Topic.

Interest

• Dynamic of populations.
• Transport-diffusion models.

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Research Topic.

Interest

• Dynamic of populations.
• Transport-diffusion models.

Problematic

• How to construct a like Lotka-Voltera model to describe the dynamic
• f fish-phytoplankton using a self-proppled particles (SPP) and agent

beased model (ABM)?

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Research Topic.

Interest

• Dynamic of populations.
• Transport-diffusion models.

Problematic

• How to construct a like Lotka-Voltera model to describe the dynamic
• f fish-phytoplankton using a self-proppled particles (SPP) and agent

beased model (ABM)?

• Which transport-diffusion model should be associated to take in

account the motion of population ?

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Research Topic.

Interest

• Dynamic of populations.
• Transport-diffusion models.

Problematic

• How to construct a like Lotka-Voltera model to describe the dynamic
• f fish-phytoplankton using a self-proppled particles (SPP) and agent

beased model (ABM)?

• Which transport-diffusion model should be associated to take in

account the motion of population ?

Goals

• Constuction of the model, full anlysis and simulations;

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Research Topic.

Interest

• Dynamic of populations.
• Transport-diffusion models.

Problematic

• How to construct a like Lotka-Voltera model to describe the dynamic
• f fish-phytoplankton using a self-proppled particles (SPP) and agent

beased model (ABM)?

• Which transport-diffusion model should be associated to take in

account the motion of population ?

Goals

• Constuction of the model, full anlysis and simulations;
• Make a comparaison between Lotka-Voltera model.

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General view.

SPP

Self-propelled particles (SPP), is a concept used by physicists to describe autonomous agents, which convert energy from the environment into directed or persistent motiona. Here are somme examples for autonomous agents: Walking, swimming or flying animals;

aWikipedia 4 / 10

General view.

SPP

Self-propelled particles (SPP), is a concept used by physicists to describe autonomous agents, which convert energy from the environment into directed or persistent motiona. Here are somme examples for autonomous agents: Walking, swimming or flying animals; Bacteria, phytoplankton, cells, algae and other micro-organisms;

aWikipedia 4 / 10

General view.

SPP

Self-propelled particles (SPP), is a concept used by physicists to describe autonomous agents, which convert energy from the environment into directed or persistent motiona. Here are somme examples for autonomous agents: Walking, swimming or flying animals; Bacteria, phytoplankton, cells, algae and other micro-organisms; Any system of physical particles with coherent collective behavior for exemple a robot system .

aWikipedia 4 / 10

General view.

SPP

Self-propelled particles (SPP), is a concept used by physicists to describe autonomous agents, which convert energy from the environment into directed or persistent motiona. Here are somme examples for autonomous agents: Walking, swimming or flying animals; Bacteria, phytoplankton, cells, algae and other micro-organisms; Any system of physical particles with coherent collective behavior for exemple a robot system .

aWikipedia

The following pictures illustrates some autonomous agents.

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General view.

Figure: Spectacular folk of starlings.

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General view.

Figure: School of Fishs.

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General view.

Figure: traffic jam in Madagascar.

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General view.

Figure: A herd of zebra..

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A general SPP model

Figure: The two zona in the Vicsek-model.

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A general SPP model

Figure: The two zona in the Vicsek-model.

ri(t + τ) = ri(t) + τvi(t) (1) vi(t + τ) = R(ξi(t))V d

i (t)

(2)

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Impact and Applications of My Research

Impact

Find the basic laws describing the essential aspects of collective motion;

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Impact and Applications of My Research

Impact

Find the basic laws describing the essential aspects of collective motion;

Application

The applications are a lot and for many discipline:

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Impact and Applications of My Research

Impact

Find the basic laws describing the essential aspects of collective motion;

Application

The applications are a lot and for many discipline: In mathematics, SPP and ABM gives an alternative for the usual PDEs and ODEs models;

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Impact and Applications of My Research

Impact

Find the basic laws describing the essential aspects of collective motion;

Application

The applications are a lot and for many discipline: In mathematics, SPP and ABM gives an alternative for the usual PDEs and ODEs models; In physic, SPP and ABM can be used to describe and understand patterns of physicals systems as gases, crystals, liquids ...

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Impact and Applications of My Research

Impact

Find the basic laws describing the essential aspects of collective motion;

Application

The applications are a lot and for many discipline: In mathematics, SPP and ABM gives an alternative for the usual PDEs and ODEs models; In physic, SPP and ABM can be used to describe and understand patterns of physicals systems as gases, crystals, liquids ... For society, one can solve the problems of crowd panic, trafic jam etc.

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Some patterns of fish, phytoplankton and coupled model

500 1000 1500 2000 Time 100 200 300 400 500 600 700 800 Number of particles Fish 200 250 300 350 400 450 500 550 600 650 Fish 100 200 300 400 500 600 700 800 900 Phase Map

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Animation of fish-phytoplankton interaction

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Thank you!

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