16-31 July 2019

Prof. Gareth Alexander, Dr. Jack Binysh
Home Institutions
Department of Physics and Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, United Kingdom.
Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, United Kingdom.
Host Contact
Prof. Miha Ravnik
Host Institution
Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia and  Jozef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia.

Aim of the mission
The objective of the STSM was to initiate the study of active knotted fields and to create stable, localised active knotted structures in confined geometries. Specifically, we sought to study the dynamics of knotted disclination lines and of Hopf textures in thin cells, where the bulk instability is suppressed. The STSM aligned particularly with the activities and objectives of EUTOPIA WG5. It facilitated the exchange of expertise between ECIs — Jack Binysh (UK) and Ziga Kos (Slovenia) — as well as their general career development, and also the start of a longer collaboration between the Alexander and Ravnik groups.

Summary of the results
The STSM itself invovled a short 15 day visit to Ljubljana (16th — 31st July  2019), although due to prior commitments Alexander (UK) was only able to join from 21st July. The initial days were devoted to integration of numerical code and was undertaken by Binysh and Kos, supervised by Ravnik. This permitted initial simulations of Hopf textures in active cholesterics to begin already before Alexander arrived the following week. The typical pattern for the remainder of the time was for Alexander and Ravnik to discuss in the morning, while Binysh and Kos continued with simulations and analysis, and then the entire team would meet to discuss together in the afternoon. The evenings were devoted to performing calculations for the next morning. Binysh gave his seminar on Knotted Fields on Monday 29th July.
During the visit Alexander took the opportunity to also discuss with Prof. Slobodan Zumer (WG5 co-leader) about the organisation and activities of WG5, and also to continue interaction with Dr. Gregor Posnjak, Dr. Simon Copar and Prof. Igor Musevic on their joint work on defects in cholesteric droplets. The universities of Warwick and Ljubljana are part of a new EU alliance (also called Eutopia) and Alexander and Ravnik availed of the opportunity to draft a joint  proposal to this alliance.
The STSM was an unabridged success. The initial plans rapidly expanded to four separate problems: the dynamics of defect lines and loops in three dimensional active nematics; growth and decay of Hopf solitons in cholesterics and Derrick’s theorem; energy injection and dissipation in three-dimensional active nematics; and topological flows and solitons in three-dimensional chiral active liquid crystals. Outlines for all four were produced and manuscripts for each begun by the end of the STSM. It is anticipated that the first paper will be submitted by the end of August 2019 and all four by the end of the year.
The STSM has led directly to a strong collaboration with four joint projects currently ongoing. The first joint publication was submitted in mid September  and is currently under review. Binysh presented a poster on this work at a one day workshop in Warwick on 20th September. Binysh visited Ljubljana again for the last week of September to first week of October to boost progress on our joint projects on stability of Hopf textures, and dissipation in active nematics. We are aiming for submission on at least one of these by the end of the year. Plans were made during the STSM for Alexander to visit Ljubljana again in December 2019 and March 2020 in order to continue the collaboration started. Plans are in progress for Alexander and Ravnik to seek joint support from the EU alliance Eutopia, that both Warwick and Ljubljana are members of.