ACCA

Applied and Computational Complex Analysis (ACCA) Group

Welcome to the Applied and Computational Complex Analysis (ACCA) Group page

 

Looking for codes to evaluate the prime function? Here you go! For more information, see Darren Crowdy's SIAM monograph "Solving problems in multiply connected domains".

 

Recent news and activities

The Applied and Computational Complex Analysis group of the Department of Mathematics at Imperial College London is part of a wider network of UK-based universities, the ACCA-UK network, bringing together expertise in applied and computational complex analysis challenges with a view to fostering synergetic interaction and collaboration. 

Darren Crowdy to deliver a Colloquium in the Math Dept at New Jersey Institute of Technology (NJIT) on Feb 11 2022 (11.30am EST) 

Congratulations to Vikas Krishnamurthy

Vikas Krishnamurthy began his role as Assistant Professor in the Department of Mathematics at IIT Hyderabad, India on Feb 1 2022. Congratulations on this new position!

Welcome!

Anna Curran is the newest member of the ACCA group, having joined as a PhD student in October 2021.

Hot-off-the-press papers from the ACCA group:

Exact solutions for the formation of stagnant caps of insoluble surfactant on a planar free surface by Darren Crowdy (J. Eng. Math., (2021)).

Viscous Marangoni flow driven by insoluble surfactant and the complex Burgers equation by Darren Crowdy (SIAM J. Appl. Math. (2021)).

Equilibrium tilt of slippery elliptical rods in creeping simple shear by Darren Crowdy (J. Fluid Mech., (2021)).

Darren Crowdy delivered an MIT Physical Mathematics Seminar on May 18 2021 (2.30 EST)

Darren gave an online seminar entitled "Surfactant dynamics and the complex Burgers equation" in the Department of Mathematics MIT. More information, including zoom access links, can be found here.

New papers in 2021

Check out some "hot off the press" papers by the ACCA group:

"Fay meets van der Pauw: the trisecant identity and the resistivity of holey samples" by H. Miyoshi. D. Crowdy & R. Nelson.

"H-states: exact solutions for a rotating hollow vortex" by D. Crowdy, R. Nelson &  V. Krishnamurthy.

"Liouville chains: new hybrid vortex equilibria of the two-dimensional Euler equation" by V. Krishnamurthy, M. Wheeler, D. Crowdy & A. Constantin.

Chosen as "Editor's Choice" in Physical Review Fluids:

"Collective viscous propulsion of a two-dimensional flotilla of Marangoni boats" by Darren Crowdy.

"Viscous propulsion of a two-dimensional Marangoni boat driven by reaction and diffusion of insoluble surfactant" by Darren Crowdy.

 Welcome!

Henry Rodriguez-Broadbent is the newest member of the ACCA group, having joined as a PhD student in October 2020.

ACCA Alumni news

It is always a pleasure to tell of the "new destinations" of ACCA group alumni. Since 2020 Dr. Elena Luca has been a Senior Research Fellow in the Dept. of Mathematics at University College London. Dr. Vikas Krishnamurthy is now at the Dept. of Mathematics at the University of Vienna where he is a postdoctoral fellow. Dr. Peter Baddoo has joined the faculty in the Mathematics Department at MIT where he is now an Instructor in Applied Mathematics. Dr Samuel Brzezicki remains at Imperial College but is now a Teaching Fellow in Mathematics. Dr. Jonathan Marshall is a Lecturer (Teaching) in Mathematics at University College London. Dr Christopher Green is now Assistant Professor of Mathematics at the University of Wichita. Congratulations all!

Congratulations to Dr. Peter Baddoo on the publication of his book

Analytic solutions for flows through cascadesPeter is currently a Research Associate and EPSRC Postdoctoral Prize holder in the ACCA group at Imperial College. The book, based on his PhD thesis work, has just been published in the Springer Theses Series. Some video abstracts describing some of the contents can be found below.

 

Cover of Proc. Roy. Soc. A (August 2020): 

 

 
The cover image of Proc. Roy. Soc. A (Aug 2020) shows a sequence of point vortex equilibria generated by a new "transformation" between rational functions representing such equililbria due to Darren Crowdy and his collaborators Vikas Krishnamurthy and Adrian Constantin (Vienna) and M. Wheeler (Bath).

Review of "Solving problems in multiply connected domains"

The Mathematical Association of America recently published a review of Darren Crowdy's SIAM monograph "Solving problems in multiply connected domains".

Video abstracts of recent work by the ACCA group

ACCA group member Dr Peter Baddoo has recorded video abstracts to accompany two recent research papers. The first video covers the paper "Periodic Schwarz–Christoffel mappings with multiple boundaries per period" by Baddoo & Crowdy in Proceedings of the Royal Society A, 2019. This paper extends the classical Schwarz–Christoffel formula to calculate conformal maps from circular domains to periodic polygonal domains.

Periodic Schwarz–Christoffel

 

 

  

 

 

 

 

 

 

 

 

The second video abstract covers the paper "Exact solutions for ground effect" by Baddoo et al. in JFM Rapids, 2020. This paper uncovers new solutions for the ground effect problem using conformal mappings.

 

Both papers use the Schottky–Klein prime function, which is the subject of Prof Darren Crowdy's recent book. These video abstracts were recorded in Prof Steve Brunton's lab at the University of Washington.

Distinguished lecture series

Dec 2-5 2019: three invited lectures by Professor Darren Crowdy @ Technion:

Distinguished Lecture Series

SIAM MONOGRAPH in press! To appear early in 2020

Professor Darren Crowdy has just completed an invited monograph entitled "Solving problems in multiply connected domains" that will appear early in 2020 as part of the NSF-CBMS Lecture Series. Watch out for more news!

Monograph cover

Upcoming Red Lotus Project Lecture series:

As part of the Red Lotus Project initiative, Profs Darren Crowdy and Marc Hodes (Tufts) are organising a week-long lecture series entitled "Transport phenomena on textured surfaces: Fundamentals and Applications". This lecture course will take place Oct 12--16 2020 at the International Centre for Mechanical Sciences, Udine, Italy. Click here to see the summer school flyer (PDF)

CISM Flyer

"Complex analysis: techniques, applications and computations" programme

The Newton Institute will host a 4-month programme on applied complex analysis entitled "Complex analysis: techniques, applications and computations", between Sep 2 - Dec 19. There are three one-week workshops scheduled throughout the programme for which anyone interested can apply. Find out more about the programme. The first workshop, on "The complex analysis toolbox", is Sep 9-13: click here to apply


Congratulations!

We would like to congratulate Dr. Jordan C. Hauge for recently completing his Ph.D. He will be commencing a postdoctorate project with the head of the ACCA-JP chapter Prof. Takashi Sakajo in Kyoto University, on topological flow data analysis. We wish him the very best of luck. 


IMA special issue

Prof. Darren Crowdy is a guest editor, with Profs. David Smith and Tim Pedley, of a special issue of the IMA J. Appl. Math commemorating the career of Prof. John Blake. Find out more about the special IMA issue here.

Best of luck and congratulations!

  • ACCA member Dr. Rhodri Nelson is now working in the Department of Earth Sciences and Engineering. We wish him the best of luck in his new position. 
  • We want to congratulate ACCA alumnus Dr. Elena Luca for being the recipient of the David Crighton Fellowship. She will be working with Prof. David Abrahams at the Department of Applied Mathematics and Theoretical Physics, University of Cambridge in the period May-July 2019. We wish her the very best of luck. 

Workshop on "Solving Problems in Multiply Connected Domains"

Prof. Darren Crowdy was invited to be the Principal Lecturer at the NSF-CBMS sponsored workshop on "Solving Problems in Multiply Connected Domains". He delivered a course of 10 lectures between June 18-22 2018, punctuated by invited lectures by a selection of other researchers. Find out more about the NSF-CBMS Conference on Solving Problems in Multiply-Connected Domains.


The 4th International ACCA-UK/JP workshop

The 4th International ACCA-UK/JP workshop took place at University of Kyoto, Japan in March 2018.


Professor Darren Crowdy: "Mathematical Aspects of Physical Oceanography"

Professor Darren Crowdy will deliver an invited lecture at the workshop on "Mathematical Aspects of Physical Oceanography" at the Erwin Schrodinger Institute, Vienna (March 12-16 2018).


ACCA alumnus news

ACCA alumnus Dr. Elena Luca was an invited speaker the the KTGU workshop at Kyoto University, Japan on Feb 17 2018.


Congratulations!

Congratulations to ACCA alumnus Dr. Vikas Krishnamurthy who will start a Fellowship at the Erwin Schrodinger Institute in Vienna, Austria on April 1 2018.

News and activities archive