“Dynamics of fluids in elastic tubes conveying fluid, with applications to e.g. blood flow in arteries”

May 3, 2019

James M Flaherty Visiting Professorship 2018/19 Visit Report

Name:                          Professor Vakhtang Putkaradze

Dates of visit:          February 1-April 30, 2019

Universities visited:
Host University:     TU Dublin, School of Mathematical Sciences,
Other visits:              UCD, Trinity College Dublin, UCC, NUI Galway.

Purpose of visit:
Scientific: Research with Prof. Ivanov (TU Dublin) on dynamics of fluids in elastic tubes conveying fluid, with applications to e.g. blood flow in arteries.

Administrative: To establish an exchange program between PIMS Universities (Pacific Institute for Math Sciences) and academia and industry in Ireland, for grad students, postdocs and academics.

Visit details:
• Research conducted:
Together with Prof. R. Ivanov, we have developed a theory for propagation of vorticity in elastic tubes conveying fluid. In the last two decades, the importance of swirling motion in arteries has become apparent. Our theory allows, for the first time, to describe the vorticity propagation in a flexible tube with elastic walls conveying fluid, from the variational point of view. We have derived and analyzed a new equation describing the combined motion of fluid and tube’s walls. We are currently in the process of writing up and submitting our results for publication.

Also, I have begun a collaboration with Prof. Peter Lynch and Dr. Miguel Bustamante (UCD) on the mechanics of non-holonomic systems, and with Dr. L. O’Naraigh on the mathematical models of self-aggregation.

• Lectures, seminars, talks:
1. February 8, 2019, TU Dublin, School of Mathematical Sciences
2. February 14, 2019, Department of Mathematics, UCC: Geometric theory of flexible and expandable tubes conveying fluid
3. February 20, 2019, Department of Mechanical Engineering, Trinity College:
Dynamics and control of flexible solar towers
4. March 4th, 2019: Seminar, UCD School of Mathematics and Statistics, Integrability and Chaos in Figure Skating
5. March 6th, 2019: Visit to Mechanical Engineering, TU Tallaght, discussion on sensors and applications.
6. March 11th, 2019: Seminar, UCD School of Mathematics and Statistics: Geometric theory of flexible and expandable tubes conveying fluid
7. March 14, 2019: ESHI, TU Dublin: Dynamics and control of flexible solar towers
8. 27 March – WIT (Waterford): Theoretical Figure Skating
9. April 3, 2019, Mathematics, DCU: Theoretical figure skating
10. James M Flaherty Lecture: Thursday, April 11, 2019

Professor Vakhtang with colleague in a cleanroom in TU Tallaght

• Contacts made:
1. Dr. Lennon O’Naraigh, Math & Stats (Scientific collaboration)
2. Dr. Chris Hills, Head of School, Mathematical Sciences, TU Dublin (TU Dublin lead on the new initiative on PIMS-Ireland collaboration)
3. TU Dublin Hothouse, Paul Maguire and Kieran O’Connell (Industry/PIMS collaboration)
4. TU Dublin, ESHI, Prof. Jesus Frias, Academic Leader of the Sustainability and Health Institute (Academic and industrial collaboration)
5. TU Dublin, Prof. Brian Norton, Principal of TU Dublin (Scientific collaboration)
6. UC Cork, Discussions with School of Mathematical Sciences on PIMS-Ireland collaboration program
7. NUI Galway, Discussions with School of Mathematics, Statistics and Applied Math on support on PIMS-Ireland collaboration program
8. TU Tallaght, Department of Mechanical Engineering, discussion on sensors and applications.
9. Waterford Institute of Technology (WIT), discussions with math faculty.
10. Discussions with potential industrial partners (e.g. Intel, food industry etc.) to support the application of PIMS-Ireland research center.

Future continuing collaboration:
Research: The research ties developed during the stay will provide a basis for long-term interactions for several years. For example, the work with Prof. Ivanov that we have completed opened up a possibility to develop models of tubes carrying fluid, embedded in an elastic or viscoelastic media, which is a better approximation of an artery. We are planning to continue working on this interesting and challenging project.

Administrative: We are currently working on enlarging the PIMS-Europe collaboration to include Ireland, which will fund the trips of Canadian academics, postdocs and grad students to Ireland. We are also planning a submission of a proposal of a Center to European Funding agencies on the topic of ‘Sustainable societies’, incorporating math challenges in renewable energy resources, food, agriculture and others. This Center will be opened to all interested academics in Ireland and will deal with problems that are also of interest to industry. The Center will fund the travel of Irish academics, postdocs and grad students to Canada, and hosting Canadian researchers in Ireland.

I am very grateful to ICUF for this unique opportunity to spend 3 months in Ireland and experience the science in Ireland, as well as Irish culture and history.  I am also grateful to TU Dublin, and especially the School of Mathematical Sciences (my host, Prof. Ivanov and the Head of School, Dr. Chris Hills), for providing a comfortable and creative atmosphere during my visit.

The collaboration between Ireland and Canada has a lot of potential because of the overlapping interests in the new economy, and complementary interests in agriculture, food and energy. I am glad to say that the response of Irish academics to the possibilities of collaboration was very positive, and I hope that the initiatives that have been developed during this visit will provide possibilities for collaborations and visitor exchanges for many years, and for many universities in Ireland and Canada.

Cliffs of Moher