# Fluid2Bio IP 2013

### 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