icon forward
This is our 2020 curriculum. For the new structure, valid as of the 2021 intake, click here

Sem3 UAQ Agent-Based for 2020 intake

uaq large

Applications  @  UAQ  30 ECTS credits

Agent-based modelling and transport phenomena

The specialization track “Agent-based modelling and transport phenomena” will take place at the University of L’Aquila. The proposed curriculum covers newly developed mathematical modelling approaches, aiming at realizing practical solutions for smart and healthy communities. UAQ has longstanding collaborations with the Imperial College of London (UK) and with the University of Muenster (Germany) on many-agent modelling and mean-field limits in several branches of social sciences such as opinion formation, emergence of collective motion, and the social behaviour of largely crowded communities (the latter also in collaboration with the Universities of Catania and Ferrara, in Italy); the UAQ team has a longstanding expertise on "nonlocal aggregation models", an emerging subject in applied mathematical research with applications in particular to the modelling of criminal behaviour in urban areas. Important achievements have been also carried out at UAQ in the area of nonlinear conservation laws with applications to traffic modeling and population dynamics.

This track has three compulsory courses: “Advanced analysis” , providing tools to deepen the understanding of advanced nonlinear models; “Mathematical fluid dynamics”, featuring advanced analytical methods on classical and modern fluid-dynamical theories; “Mathematical model for collective behavior”, presenting a selection of topics in the modeling of collective motion in social sciences and of transport modeling in real world applications, particularly in urban and behavioural sciences.

The last two courses, "Biomathematics" and "System biology" (in collaboration with the IASI-CNR institute), specialise the student on "modelling in life sciences", which has become a classic topic in modern applied mathematics. Both of them present mathematical and modeling approach via ODEs, PDEs, and multiscale modelling, in contexts arising from modern applications such as population biology, medicine, and genetics.

 

Below you can find information about the subjects for this semester.

  • Advanced analysis [6 credits]

    Advanced analysis

    • ECTS credits 6
    • Semester 3
    • University University of L'Aquila
    • Objectives

       

      The main objectives of the course are as follows: to provide knowledge of mathematical methods that are widely used by researchers in the area of Applied Mathematics; to apply this knowledge to a variety of topics, including the basic equations of mathematical physics and some current research topics about nonlinear equations (traffic flow, gas dynamics, fluid dynamics).

    • Topics

       

      Measure and integration theory. Functions of bounded variation. Distributions theory. Fourier transform. Sobolev spaces. Application to the study of partial differential equations: elliptic equations of second order, parabolic equations of second order, hyperbolic systems of first-order equations, nonlinear conservation laws. An outline of semigroup theory.


    Open this tab in a window
  • Mathematical fluid dynamics [6 credits]

    Mathematical fluid dynamics

    • ECTS credits 6
    • Semester 3
    • University University of L'Aquila
    • Objectives

       

      This course is designed to give an overview of fluid dynamics from a mathematical viewpoint, and to introduce students to the mathematical modeling of fluid dynamic type with a particular attention to biofluid dynamics. At the end of the course the students will be able to perform a qualitative and quantitative analysis of solutions for particular fluid dynamics problems and to use concepts and mathematical techniques learned from this course for the analysis of other partial differential equations.

    • Topics

       

      Derivation of the governing equations: Euler and Navier-Stokes. Eulerian and Lagrangian description of fluid motion; examples of fluid flows. Vorticity equation in 2D and 3D. Dimensional analysis: Reynolds number, Mach Number, Frohde number. From compressible to incompressible models. Existence of solutions for viscid and inviscid fluids. Modeling for biofluids mechanics: hemodynamics, cerebrospinal fluids, animal locomotion: swimming and flying; Bioconvection for swimming microorganisms.


    Open this tab in a window
  • Mathematical models for collective behaviour [6 credits]

    Mathematical models for collective behaviour

    • ECTS credits 6
    • Semester 3
    • University University of L'Aquila
    • Objectives

       

      The course will cover some mathematical models currently used in the analysis of collective phenomena, such as vehicular and pedestrian traffic, flocking phenomena. Emphasis will be given to the mathematical treatment of specific problems coming from real world applications.

    • Topics

       

      Macroscopic traffic models: LWR model, fundamental diagrams. The Riemann problem. Point-type constraints (the "Toll gate" problem). Second order models for traffic flow: Aw-Rascle model, shocks description, instabilities near vacuum. Basics on the theory of systems of conservation laws. Junction of roads, networks. Distribution rules along the roads, optimization of the flux. Solution to the Riemann problem at a junction. Pedestrian flow: normal and panic situation. Macroscopic models, conservation of "mass", eikonal equation. The Hughes model for pedestrian flow; in one space dimension: curve of turning points, Rankine-Hugoniot conditions. Macroscopic models for pedestrian flow that include: knowledge of a preferred path, discomfort from walking along walls, tendency of avoiding high densities of pedestrian in a neighborhood (nonlocal term of convolution type), angle of vision, obstacle in the domain. Introduction to the theory of flocking. Cucker-Smale model for flocking, conservation of moment and decay of the kinetic energy. Asymptotic flocking. Singular communication rate. The kinetic limit. Introduction to synchronization: Kuramoto model, basic properties.


    Open this tab in a window

Pick 1 sub-path

a) Modelling in Life Science

 

b) Modelling in Seismology

Home Structure for 2020 intake Sem3 UAQ Agent-Based for 2020 intake

Connect with us

Our partners' addresses

University of L'Aquila, Italy (UAQ)

Department of Information Engineering, Computer Science and Mathematics, via Vetoio (Coppito), 1 – 67100 L’Aquila (Italy)

University of Hamburg , Germany (UHH)

Department of Mathematics
Bundesstr. 55
20146 Hamburg - Germany

University of Côte d'Azur, Nice - France (UCA)

Laboratoire J.A.Dieudonné
Parc Valrose, France-06108 NICE Cedex 2