Intensive Programme "If Fluid Dynamics Turns to Biology"
24 June - 5 July 2013, University of L'Aquila
Welcome to the 2013 Intensive Programme (IP) in Fluid2Bio
If Fluid Dynamics Turns to Biology
24 June - 5 July 2013, University of L'Aquila
Coordinator: Donatella Donatelli
Coordinating Institution: University of L'Aquila (Italy)
Location: University of L'Aquila (Italy)
Scientific Committee
- Donatella Donatelli (IP coordinator, Department of Information Engineering, Computer Science and Mathematics, University of L'Aquila, Italy)
- Eduard Feireisl (Institute of Mathematics of the Academy of Sciences of the Czech Republic, Czech Republic )
- Luca Formaggia (MOX, Department of Mathematics, Politecnico di Milano, Italy)
- Ansgar Jüngel (Institute for Analysis and Scientific Computation, Vienna University of Technology, Austria)
- Josef Malek (Mathematical Institute, Charles University in Prague, Czech Republic)
- Danuta Makowiec (Institute of Theoretical Physics, Gdansk University, Poland)
- Rodolfo Repetto (Department of Civil, Enviromental and Architectural Engineering, University of Genova, Italy)
- Jaroslaw Rybicki (Department of Solid State Physics, Gdansk University if Technology, Poland)
- Jennifer Siggers (Department of Bioengineering, Imperial College London, Great Britain)
- Eleuterio F. Toro (Department of Civil, Environmental and Mechanical Engineering, University of Trento, Italy)
List of Partner Institutions and Local Coordinators of the IP Fluid2Bio 2013
University of L'Aquila (Italy) - Coordinator, Prof. Donatella Donatelli
University of Genova (Italy) - Prof. Rodolfo Repetto
Politecnico di Milano (Italy) - Prof. Luca Formaggia
University of Trento (Italy) - Prof. Eleuterio F. Toro
Imperial College London (Great Britain) - Prof. Jennifer Siggers
Charles University in Prague (Czech Republic ) - Prof. Josef Malek
Vienna University of Technology (Austria ) - Prof. Ansgar Jüngel
University of Gdansk (Poland) - Prof. Danuta Makowiec
Gdansk University of Technology (Poland) - Prof. Jaroslaw Rybicki
Presentation
With a very suggestive image it has been said: “Mathematics is the lens through which to view the universe”. This IP has the aim to contribute further and to justify in a deeper sense that statement. In the common view of the sciences, physics and chemistry are thought to be heavily dependent on mathematics, while biology is often seen as a science which only in a minor way leans on quantitative methods. In contemporary biology there are many areas which depend heavily on rather advanced mathematics and in particular on fluid dynamics. The development of mathematical methodologies is now considered a major issue in the biological sciences (see the recent advances in mathematical modelling for haemodynamics, or cancer growth).
The Intensive Programme (IP) called "If Fluid dynamics turns to Biology - Fluid2Bio 2013" aims to address those issues and to provide the proper background to PhD and MSc students in order to deal with those problems and situations. Today, mathematicians with expertise as diverse as non-linear partial differential equations, dynamical systems, probability, statistics and stochastic processes, combinatorial mathematics, graphs and networks, and low dimensional topology are engaged in this broad endeavor. In this contest the present project will manly focus on the interplay between fluid dynamics and biological phenomena. Research in physiological fluid mechanics uses the techniques of mathematical modeling, and numerical and asymptotic analysis. Some of the main applications are to blood flow in the cardiovascular system, t fluid dynamics of the eye, growth and development of bacterial biofilms...
The proposed IP will consist of a set of short courses and seminars and is addressed mainly to MSc and PhD students in Applied Mathematics, Bioengineering, but also students in Biotechnology. The major target of the program is to contribute to the process of disseminating knowledge and expertise in applied mathematics methods (in particular in the fluid dynamics field) and models in biology, both at a Master and at a PhD level. Based on well- established PhD schools, we aim to provide our students with the possibility of complementary interdisciplinary training at the interface of mathematics, fluid dynamics and biology.
The participation of students and teachers from the partner universities will be supported by the LLP Erasmus Programme. The programme will be held in the period June 24 - July 5, 2013.
Reimbursement
Applicants from partner institutions are eligible for a reimbursement of living and travel expenses.
This contribution is offered by the LLP Italian National Agency. 
We assume to select:
- around 30 students (MSc or PhD) for the contribution for travel costs and the contribution for accommodation and subsistence costs: this corresponds to about 4 students for each partner institution. Applications will close on March 30, 2013.
The contact person of each institution in the Organizing Committee is responsible for the selection of students in their universities.
Details about Reimbursement
Reservation for lodging and contribution for subsistence costs.
Please notice that students and teachers from partner universities will be hosted in university premises free of charge for the whole period of the IP. Unfortunately, the Erasmus agency applies a very low daily amount for subsistence costs of students (22 euro per day, both for lodging and full board). That's why, in addition to the accommodation, we can confirm that we will only be able to offer students free access to the university canteen (open on working days). We hope we'll be able to offer some additional support to students, but we cannot guarantee anything at the moment.
Lectures
Lecture 1
TITLE
A continuum mechanics and thermodynamics primer
LECTURER
Vit Prusa, Charles University in Prague, Czech Republic
ABSTRACT
The aim of the course is to recall (or briefly introduce) the basic notions in continuum mechanics and thermodynamics with an emphasis to notions and concepts useful in modeling the fluids.
The first part of the course will be focused on kinematics and dynamicsof continuous media. The most popular fluid model --the Navier-Stokes fluid model-- will be discussed in the second part of the course, and it will be shown that the model is, in many cases, not the right one to be applied in many practical problems in technology and medicine.
In the third part of the course we will go back to the fundamental principles discussed in the first part, and we will extend the theory by introducing some basic ideas from continuum thermodynamics. Finally, we will illustrate how to use these ideas in developing thermodynamically consistent fluid-like models that go beyond the classical Navier--Stokes fluid model.
TEACHING MATERIAL
Lecture 2
TITLE
A Review of classical models of mathematical biology
LECTURER
Piotr Zwierkowski, University of Gdansk, Poland
ABSTRACT
The aim of our presentation is to acquaint the participants with the fundamental models of mathematical biology and to discuss their basic properties. We start with the problem of the growth of rabbits population living in an isolated area, which was discussed in a book by Leonardo Pisano Fibonacci, entitled Liber Abbaci in 1202. An influential model of exponential growth, proposed by Rev. T. Malthus appeared in 1798. According to the assumptions of this simple model, the fast growth of human population was supposed to lead to war, pestilence, or famine. To make the exponential growth model more realistic, P. Verhulst (1838) proposed a model which took into consideration the availability of resources. The solution of this model, unlike the Malthusian, fitted surprisingly well the census data. In 1926 V. Volterra published a model in order to explain the oscillations of the numbers of predator and prey fish in the Adriatic Sea, which were observed before and after the World War I. The above models are based on untrue assumption that populations arehomogeneous. The following models take into consideration the diversity of members of populations. The simplest way to incorporate astructure in the population is to divide the population into groups being in a similar age. This approach leads to a~discrete age-structured model, introduced by Leslie in 1945. We assume that an initial distribution of inhabitants, age-specific mortality and fertility rates are given. Using the discrete renewal equation one can calculate the number of the offspring, the total number of population, and the distribution of its members. There are models with continuous age structure of the population, which were proposed by A. McKendrick (1926) and H. von Foerster (1959).
TEACHING MATERIAL
Lecture 3
TITLE
Introduction to cellular automata, lattice gas automata and their applications
LECTURER
Jacek Dziedzic, Gdańsk University of Technology, Poland
ABSTRACT
Cellular Automata (CA) are a class of discrete models which constitute an idealization of a physical system, with discrete space and time, and where physical quantities are confined to a discrete set of values. Despite their microscopic simplicity, they exhibit surprisingly complex macroscopic behaviour and are successfully applied to a wide variety of problems.
Among these are: fluid mechanics, urban geography, immune responses in biological systems, cryptography, modelling traffic flow, formation of lava tubes, crack propagation, the study of diffusion, wetting, percolation and many, many others.
This short course starts with an explanation of what exactly CA are and how they function, briefly touches on their fascinating history, and for the most part deals concentrates on their, sometimes startling, applications. The second part of the course focuses on models with underlying physical significance, such as Lattice Gas Automata (LGA) and the Lattice Boltzmann Model (LBM) that are directly applicable in fluid dynamics.
Interesting reading on the subject:
TEACHING MATERIAL
Lecture 4
TITLE
Numerical solution of the fluid-structure interaction problem in haemodynamics
LECTURER
Christian Vergara, Politecnico di Milano, Italy
ABSTRACT
We consider the fluid-structure interaction problem arising when considering the coupling between the blood and the vessel wall. The numerical solution of such a problem is complex since it is highly non-linear and could be obtained either with monolithic approaches or with partitiones strategies, which rely on the solution of pre-existing fluid and structure codes. We study here the main features of such a system, focusing in particular on partitioned strategies and highlighting the problems arising in haemodynamics, where the densities of fluid and structure are similar, making the numerical solution with partitioned strategies very challenging.
TEACHING MATERIAL
Lecture 5
TITLE
Elements of Computational Haemodynamics
LECTURERS
Eleuterio F. Toro, University of Trento, Italy
ABSTRACT
In this set of lectures I shall give an elementary introduction to computational haemodynamics, covering all main aspects that enter in the construction of a mathematical model for the human circulation. I start by giving a succinct overview of the physiology of the cardiovascular system. Then I review some biomechanical concepts and formulate mathematical models for blood flow. There follows an analysis of the differential equations and the construction of exact solutions. Selected numerical methods to solve the equations are then studied and standard models for junctions are reviewed. Finally, I illustrate the application of the global human circulation model constructed in Trento to the study of the physical aspects of extracranial vein anomalies and discuss their potential medical consequences.
TEACHING MATERIAL
Lecture 6
TITLE
Micro-hydrodynamics
LECTURER
Alessandro Bottaro, University of Genova, Italy
ABSTRACT
The course aims to illustrate certain aspects related to the motions at low Reynolds number (very viscous fluids, or motions of micro-organisms) starting from the Stokes equations, and continuing to the approximation called "lubrication", flows with free surface (bubbles and drops), ending with motions within porous media and/or pore-elastic.
TEACHING MATERIAL
Lecture 7
TITLE
Introduction to percolation theory and applications
LECTURER
Jaroslaw Rybicki, Gdańsk University of Technology, Poland
ABSTRACT
Percolation theory deals with clustering, criticality, diffusion, fractals, phase transitions, disordered and porous media. It provides a quantitative and conceptual model for understanding statistical background to many physical and natural science disciplines dealing with randomness. Most of the course deals with systems lying close to the critical point. The topics to be discussed are: cluster statistics and structures, finite-size scaling and the renormalization group, conductivity of composite materials, diffusion fronts and fluid percolation
TEACHING MATERIAL
