SEMANA 1

Introduction and general concepts

This module gives an overview of the course and presents the general ideas about modeling and simulation. An emphasis is given on ways to represent space and time from a conceptual point of view. An insight of modeling of complex systems is given with the simulation of the grothw and thrombosis of giant aneurysms. Finally, a first class of modeling approaches is presented: the Monte-Carlo methods.

7 videos, 1 lectura

Reading: Course slides
Vídeo: Modeling and Simulation
Vídeo: Modeling Space and Time
Vídeo: Example of bio-medical Modeling
Vídeo: Monte Carlo methods I
Vídeo: Monte Carlo methods II
Vídeo: Monte Carlo methods III

Calificado: Introduction and general concepts

SEMANA 2

Introduction to programming with Python 3

This module intends to provide the most basic concepts of high performance computing used for modeling purposes. It also aims at teaching the basics of Python 3 which will be the programming language used for the quizzes in this course.

12 videos, 2 lecturas

Reading: Course slides
Vídeo: Concepts of code optimization
Vídeo: Concepts of parallelism
Vídeo: Palabos, a parallel lattice Boltzmann solver
Reading: Dive into python 3
Vídeo: An introduction to Python 3
Vídeo: Running a Python program
Vídeo: Variables and data types
Vídeo: Operators
Vídeo: Conditional Statements
Vídeo: Loops
Vídeo: Functions
Vídeo: NumPy

Calificado: Introduction to programming with Python 3

Calificado: Project - Piles

Calificado: Project - Class:Integration

SEMANA 3

Dynamical systems and numerical integration

Dynamical systems modeling is the principal method developed to study time-space dependent problems. It aims at translating a natural phenomenon into a mathematical set of equations. Once this basic step is performed the principal obstacle is the actual resolution of the obtained mathematical problem. Usually these equations do not possess an analytical solution and advanced numerical methods must be applied to solve them. In this module you will learn the basics of how to write mathematical equations representing natural phenomena and then how to numerically solve them.

9 videos, 3 lecturas

Reading: Course slides
Reading: References for numerical analysis
Vídeo: The random walk
Vídeo: Growth of a population
Reading: A reference for the random walk
Vídeo: Balance equations I
Vídeo: Balance equations II
Vídeo: Integration of ordinary differential equations
Vídeo: Error of the approximation
Vídeo: The implicit Euler scheme
Vídeo: Numerical integration of partial differential equations

Calificado: Dynamical systems and numerical integration

Calificado: The implicit Euler scheme

Calificado: Project - Lotka-Volterra

SEMANA 4

Cellular Automata

This module defines the concept of cellular automata by outlining the basic building blocks of this method. Then an insight of how to apply this technique to natural phenomena is given. Finally the lattice gas automata, a subclass of models used for fluid flows, is presented.

7 videos, 2 lecturas

Reading: Course slides
Vídeo: Historical background
Vídeo: A mathematical abstraction of reality
Vídeo: Cellular Automata Models for Traffic
Vídeo: Complex systems
Vídeo: Lattice-gas models
Vídeo: Microdynamics of LGA
Reading: Notes on the Parity Rule

Calificado: Cellular Automata

Calificado: Project - The Parity Rule

SEMANA 5

Lattice Boltzmann modeling of fluid flow

This module provides an introduction to the lattice Boltzmann method, a powerful tool in computational fluid dynamics. The lesson is practice oriented and show, step by step, how to write a program for the lattice Boltzmann method. The program is used to showcase an interesting problem in fluid dynamics, the simulation of a vortex street behind an obstacle.

8 videos, 1 lectura, 1 cuestionario de práctica

Reading: Course slides
Vídeo: Equations and challenges
Vídeo: From Lattice Gas to Lattice Boltzmann
Vídeo: Macroscopic Variables
Vídeo: Collision step: the BGK model
Vídeo: Streaming Step
Vídeo: Boundary Conditions
Vídeo: Flow around an obstacle
Practice Quiz: Optional - Equations and challenges

Calificado: Lattice Boltzmann modeling of fluid flow

Calificado: Project - Flow around a cylinder

Calificado: Collision Invariant

SEMANA 6

Particles and point-like objects

A short review of classical mechanics, and of numerical methods used to integrate the equations of motions for many interacting particles is presented. The student will learn that the computational expense of resolving all interaction between particles poses a major obstacle to simulating such a system. Specific algorithms are presented to allow to cut down on computational expense, both for short-range and large-range forces. The module focuses in detail on the Barnes-Hut algorithm, a tree algorithm which is popular a popular approach to solve the N-Body problem.

6 videos, 1 lectura

Reading: Course slides
Vídeo: Newton’s laws of motion, potentials and forces
Vídeo: Time-integration of equations of motion
Vídeo: The Lennard-Jones potential: Introducing a cut-off distance
Vídeo: The n-body problem: Evaluation of gravitational forces
Vídeo: Barnes-Hut algorithm: using the quadtree

Calificado: Particles and point-like objects

Calificado: Project - Barnes-Hut Galaxy Simulator

SEMANA 7

Introduction to Discrete Events Simulation

In this module, we will see an alternative approach to model systems which display a trivial behaviour most of the time, but which may change significantly under a sequence of discrete events. Initially developed to simulate queue theory systems (such as consumer waiting queue), the Discrete Event approach has been apply to a large variety of problems, such as traffic intersection modeling or volcanic hazard predictions.

6 videos, 1 lectura

Reading: Course slides
Vídeo: Definition of Discrete Events Simulations
Vídeo: Optimisation problems
Vídeo: Implementation matters
Vídeo: Traffic intersection
Vídeo: Volcano ballistics

Calificado: Introduction to Discrete Event Simulation

Calificado: Project - Simple modelling of traffic lights

SEMANA 8

Agent based models

Agent Based Models (ABM) are used to model a complex system by decomposing it in small entities (agents) and by focusing on the relations between agents and with the environment. This approach is derived from artificial intelligence research and is currently used to model various systems such as pedestrian behaviour, social insects, biological cells, etc.

6 videos, 1 lectura

Reading: Course slides
Vídeo: Agents
Vídeo: Multi-Agent systems
Vídeo: Implementation of Agent Based Models
Vídeo: Ants Corpse clustering
Vídeo: Bacteria chemotaxy

Calificado: Agent based models

Calificado: Project - Multi-agents model

Idioma	English
Cómo aprobar	Aprueba todas las tareas calificadas para completar el curso.
Calificaciones del usuario	4.3 estrellas Calificación promedio del usuario 4.3Ve los que los estudiantes dijeron

Simulation and modeling of natural processes

Simulation and modeling of natural processes