Mathematical aspects of turbulence: where do we stand?
TUR
4 January 2022 to 24 June 2022
Programme theme
Anna Laura, Beverley, Leslie, Dan, Edriss, John, Rahul, Rich & Steven.
Despite the heavy deployment of effort and resources in the study of turbulent fluid flows for well over a century, fundamental questions remain stubbornly unanswered. The associated issues range so widely across the mathematical, physical and engineering sciences that no single research programme can hope to cover all aspects of the subject. This particular programme will concentrate upon the more mathematical concerns, addressing a significant range of topics including:
- Analysis of the incompressible Navier-Stokes and Euler equations;
- Modelling and analysis of turbulent transport, mixing and scaling processes;
- Inhomogeneous and anisotropic wall-bounded flows and transition to turbulence;
- Geophysical turbulence including atmospheric, oceanographic and planetary flows.
Recent years have witnessed many analytical and computational advances in our understanding of the structural and dynamical properties of solutions of the incompressible Navier-Stokes and Euler equations and associated models, but many mathematical issues require further investigation. And despite the pressing demand for practical answers, there is nevertheless a need for longer-term thinking about how the most recent developments in mathematical analysis can be leveraged into a wider understanding of physical processes. For example, the regularity and singularity results in the primitive equations of geophysical fluid dynamics can impact climate science models. The introduction of convex integration machinery that has been instrumental in completing the proof of the Onsager conjecture and establishing non-unique weak solutions for the Euler and the Navier-Stokes equations can bring insights into the dissipative anomaly conjecture, a.k.a. Kolmogorov's zero-th law of turbulence. Singularity results for the Euler equations and advances on the Prandtl equations and boundary layer theory relevant to wall-bounded turbulence can have significant engineering applications.
Through a range of events this programme will bring researchers from a broad range of disciplines together to consider these issues. It will provide the space for the type of collaborative interdisciplinary thinking necessary for the formulation of new ideas and research directions.
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TUR programme: interview with organisers John Gibbon, Jean-Luc Thiffeault and Rahul Pandit
Preprints
| Title | Year | Programme | |
|---|---|---|---|
Nonuniqueness of generalised weak solutions to the primitive and Prandtl equationsAuthors: Daniel Boutros, Simon Markfelder, Edriss Titi |
2021 | TUR | 25 May 2023 |
Rigorous justification of the hydrostatic approximation limit of viscous compressible owsAuthors: Xin Liu, Edriss Titi |
2021 | TUR | 16 May 2023 |
Derivation of a generalized quasi-geostrophic approximation for inviscid flows in a channel domain: The fast waves correctionAuthors: Claude Bardos, Xin Liu, Edriss Titi |
2021 | TUR | 19 April 2023 |
Hölder regularity of the pressure for weak solutions of the 3D Euler equations in bounded domainsAuthors: Daniel Boutros, Claude Bardos, Edriss Titi |
2021 | TUR | 11 April 2023 |
SUPER-EXPONENTIAL CONVERGENCE RATE OF A NONLINEAR CONTINUOUS DATA ASSIMILATION ALGORITHM: THE 2D NAVIER-STOKES EQUATIONS PARADIGMAuthors: Elizabeth Carlson, Adam Larios, Edriss Titi |
2021 | TUR | 4 April 2023 |
Phase transitions in the fractional three-dimensional Navier-Stokes equationsAuthors: John Gibbon, Daniel Boutros |
2021 | TUR | 15 March 2023 |
On the effect of fast rotation and vertical viscosity on the lifespan of the $3D$ primitive equationsAuthors: Quyuan Lin, Xin Liu, Edriss S. Titi |
2021 | TUR | 20 October 2022 |
On Energy Conservation for the Hydrostatic Euler Equations: An Onsager ConjectureAuthors: Daniel Boutros, Simon Markfelder, Edriss Titi |
2021 | TUR | 18 August 2022 |
Onsager's Conjecture for Subgrid Scale α-Models of TurbulenceAuthors: Edriss S. Titi, Daniel Boutros |
2021 | TUR | 20 July 2022 |
Global well-posedness for the thermodynamically refinded passively transported non linear moisture dynamics with phase changesAuthors: Rupert Klein, Edriss Titi, Sabine Hittmeir, Jinkai Li |
2021 | TUR | 4 July 2022 |
Global well-posedness of a three-dimensional Brinkman-Forchheimer-B´enard convection model in porous mediaAuthors: Edriss Titi, Saber Trabelsi |
2021 | TUR | 23 May 2022 |
Workshops
Turbulence: where do we stand and where are we heading?
4 January 2022 to 7 January 2022
Rigorous analysis of incompressible fluid models and turbulence
14 February 2022 to 18 February 2022
Modelling and analysis of turbulent transport, mixing and scaling
7 March 2022 to 11 March 2022
Wall-bounded turbulence: beyond current boundaries
28 March 2022 to 1 April 2022
Advances in geophysical and astrophysical turbulence
16 May 2022 to 20 May 2022
Seminars
| Wednesday 26th January 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Bartosz Protas McMaster University |
Room 1 | |
| Thursday 27th January 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Bartosz Protas McMaster University |
Room 1 | |
| Tuesday 1st February 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Simon Markfelder University of Cambridge |
Room 1 | |
| Thursday 3rd February 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Simon Markfelder University of Cambridge |
Room 1 | |
| Monday 7th February 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Simon Markfelder University of Cambridge |
Room 1 | |
| Tuesday 8th February 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Sergei Chernyshenko Imperial College London |
Room 2 | |
| Thursday 10th February 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Giovanni Fantuzzi Imperial College London |
Room 2 | |
| Monday 21st February 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Dwight Barkley University of Warwick |
Room 2 | 
|
| Tuesday 22nd February 2022 | |||
|---|---|---|---|
| 12:00 to 13:00 |
Jacob Bedrossian University of Maryland, College Park |
Room 2 | |
| 16:00 to 17:00 |
Adam Larios None / Other |
Room 2 |
|
| Thursday 24th February 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Chuong Tran University of St Andrews |
Room 2 |
|
| Tuesday 1st March 2022 | |||
|---|---|---|---|
| 11:15 to 12:15 |
Elizabeth Carlson University of Victoria |
Room 2 |
|
| 16:00 to 17:00 |
Xin Liu Weierstraß-Institut für Angewandte Analysis und Stochastik |
Room 2 | |
| Wednesday 2nd March 2022 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Avi Mayorcas University of Cambridge |
Room 2 | |
| Thursday 3rd March 2022 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Paolo Luchini Università degli Studi di Salerno |
Room 2 |
|
| Wednesday 16th March 2022 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Jack Coughlin University of Washington |
Room 2 |
|
| 13:00 to 14:00 |
Elizabeth Carlson University of Victoria |
Room 2 |
|
| Monday 21st March 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Slim IBRAHIM University of Victoria |
Room 2 |
|
| Tuesday 22nd March 2022 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Milton da Costa Lopes Filho Universidade Federal do Rio de Janeiro (UFRJ) |
Room 2 |
|
| Wednesday 23rd March 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Martin Oberlack Technische Universität Darmstadt |
Room 2 |
|
| Thursday 24th March 2022 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Philip Hall Monash University |
Room 2 |
|
| Friday 25th March 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Tim Colonius CALTECH (California Institute of Technology) |
Room 2 |
|
| Monday 4th April 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Dwight Barkley University of Warwick |
Room 2 | |
| Tuesday 5th April 2022 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Paolo Luchini Università degli Studi di Salerno |
Room 2 |
|
| Wednesday 6th April 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Laurette Tuckerman PMMH-ESPCI; CNRS (Centre national de la recherche scientifique) |
Room 2 |
|
| Thursday 7th April 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Yongyun Hwang Imperial College London |
Room 2 | |
| Wednesday 13th April 2022 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Xiaochuan Yang Brunel University |
Room 2 |
|
| 13:00 to 14:00 |
Pavan Pranjivan Mehta Brown University |
Room 2 |
|
| Thursday 14th April 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Gregory Eyink Johns Hopkins University |
Room 2 |
|
| Wednesday 20th April 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Darryl Holm Imperial College London |
Room 2 |
|
| Thursday 21st April 2022 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Takeshi Matsumoto Kyoto University |
Room 2 |
|
| 16:00 to 17:00 |
Konstantin Khanin University of Toronto |
Room 2 |
|
| Monday 25th April 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Helena Judith Nussenzveig Lopes Universidade Federal do Rio de Janeiro (UFRJ) |
Room 2 |
|
| Wednesday 27th April 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Helena Judith Nussenzveig Lopes Universidade Federal do Rio de Janeiro (UFRJ) |
Room 2 |
|
| Thursday 28th April 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Helena Judith Nussenzveig Lopes Universidade Federal do Rio de Janeiro (UFRJ) |
Room 2 |
|
| Tuesday 3rd May 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Yanqiu Guo |
Room 2 |
|
| Wednesday 4th May 2022 | |||
|---|---|---|---|
| 11:00 to 12:00 |
William Golding University of Texas at Austin |
Room 2 |
|
| 13:00 to 14:00 |
Antoine Remond-Tiedrez University of Cambridge |
Room 2 |
|
| Thursday 5th May 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Rama Govindarajan International Centre for Theoretical Sciences, TIFR, Bangalore |
Room 1 |
|
| Wednesday 11th May 2022 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Xin Liu Weierstraß-Institut für Angewandte Analysis und Stochastik |
Room 2 | |
| 13:00 to 14:00 |
Noemi David Sorbonne Université; Università di Bologna |
Room 2 | |
| 16:00 to 17:00 |
Miles Couchman University of Cambridge |
Room 1 | |
| Friday 13th May 2022 | |||
|---|---|---|---|
| 13:30 to 14:30 |
Samriddhi Sankar Ray International Centre for Theoretical Sciences, TIFR, Bangalore; Tata Institute of Fundamental Research |
Room 2 | |
| Friday 27th May 2022 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Dario Vincenzi CNRS (Centre national de la recherche scientifique) |
Room 2 | |
| Monday 30th May 2022 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Yukio Kaneda Nagoya University |
Room 2 | |
| Tuesday 31st May 2022 | |||
|---|---|---|---|
| 11:00 to 13:00 |
Robert Kerr University of Warwick |
Room 1 | |
| 16:00 to 17:00 |
Alain Pumir ENS - Lyon; Max Planck Institute for Dynamics and Self Organisation |
Room 1 | |
| Wednesday 1st June 2022 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Daniel Han University of Manchester; University of Cambridge |
Room 2 |
|
| 13:00 to 14:00 |
Vanja Wagner University of Zagreb |
Room 2 |
|
| 16:00 to 17:00 |
Rupert Klein Freie Universität Berlin |
Room 1 | |
| Monday 6th June 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Michael Graham University of Wisconsin-Madison |
Room 2 |
|
| Tuesday 7th June 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Aseel Farhat Florida State University |
Room 2 |
|
| Wednesday 8th June 2022 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Jo Evans University of Warwick |
Room 2 |
|
| 13:00 to 14:00 |
Akhilesh Kumar Verma University of Warwick |
Room 2 | |
| Friday 10th June 2022 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Tarek Elgindi Duke University |
No Room Required | |
| Monday 13th June 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Koji Ohkitani Research Institute for Mathematical Sciences , Kyoto University |
Room 2 |
|
| Wednesday 15th June 2022 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Daniel Boutros University of Cambridge |
Room 2 | |
| 13:00 to 14:00 |
Arran Fernandez Eastern Mediterranean University |
Room 2 |
|
| Thursday 16th June 2022 | |||
|---|---|---|---|
| 14:00 to 15:30 |
Anupam Gupta Indian Institute of Technology |
Room 2 |
|
| Friday 17th June 2022 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Milton da Costa Lopes Filho Universidade Federal do Rio de Janeiro (UFRJ) |
Room 2 | |
| Wednesday 22nd June 2022 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Santiago Benavides University of Warwick; Massachusetts Institute of Technology |
Room 2 |
|
| 13:00 to 14:00 |
Oscar de Wit University of Cambridge |
Room 2 | |
Organisers
- Charles R. Doering University of Michigan
- John Gibbon Imperial College London
- Dan Henningson KTH - Royal Institute of Technology
- Rich Kerswell University of Cambridge
- Anna Laura Mazzucato Pennsylvania State University
- Beverley McKeon CALTECH (California Institute of Technology)
- Rahul Pandit Indian Institute of Science
- Leslie Smith University of Wisconsin-Madison
- Jean-Luc Thiffeault University of Wisconsin-Madison
- Edriss Titi University of Cambridge; Texas A&M University
- Steven Tobias University of Leeds
Speakers
- Dwight Barkley University of Warwick
- Jacob Bedrossian University of Maryland, College Park
- Santiago Benavides University of Warwick; Massachusetts Institute of Technology
- Daniel Boutros University of Cambridge
- Elizabeth Carlson University of Victoria
- Sergei Chernyshenko Imperial College London
- Tim Colonius CALTECH (California Institute of Technology)
- Miles Couchman University of Cambridge
- Jack Coughlin University of Washington
- Milton da Costa Lopes Filho Universidade Federal do Rio de Janeiro (UFRJ)
- Noemi David Sorbonne Université; Università di Bologna
- Oscar de Wit University of Cambridge
- Tarek Elgindi Duke University
- Jo Evans University of Warwick
- Gregory Eyink Johns Hopkins University
- Giovanni Fantuzzi Imperial College London
- Aseel Farhat Florida State University
- Arran Fernandez Eastern Mediterranean University
- William Golding University of Texas at Austin
- Rama Govindarajan International Centre for Theoretical Sciences, TIFR, Bangalore
- Michael Graham University of Wisconsin-Madison
- Yanqiu Guo
- Anupam Gupta Indian Institute of Technology
- Philip Hall Monash University
- Daniel Han University of Manchester; University of Cambridge
- Darryl Holm Imperial College London
- Yongyun Hwang Imperial College London
- Slim IBRAHIM University of Victoria
- Yukio Kaneda Nagoya University
- Robert Kerr University of Warwick
- Konstantin Khanin University of Toronto
- Rupert Klein Freie Universität Berlin
- Adam Larios University of Nebraska
- Xin Liu Texas A&M University
- Paolo Luchini Università degli Studi di Salerno
- Simon Markfelder University of Cambridge
- Takeshi Matsumoto Kyoto University
- Avi Mayorcas University of Cambridge
- Helena Judith Nussenzveig Lopes Universidade Federal do Rio de Janeiro (UFRJ)
- Martin Oberlack Technische Universität Darmstadt
- Koji Ohkitani Research Institute for Mathematical Sciences , Kyoto University
- Pavan Pranjivan Mehta Brown University
- Bartosz Protas McMaster University
- Alain Pumir ENS - Lyon; Max Planck Institute for Dynamics and Self Organisation
- Antoine Remond-Tiedrez University of Cambridge
- Samriddhi Sankar Ray International Centre for Theoretical Sciences, TIFR, Bangalore; Tata Institute of Fundamental Research
- Chuong Tran University of St Andrews
- Laurette Tuckerman PMMH-ESPCI; CNRS (Centre national de la recherche scientifique)
- Akhilesh Kumar Verma University of Warwick
- Dario Vincenzi CNRS (Centre national de la recherche scientifique)
- Vanja Wagner University of Zagreb
- Xiaochuan Yang Brunel University
Participants
- Marc Avila University of Bremen
- Jane Bae CALTECH (California Institute of Technology)
- Claude Bardos Université Paris 7 - Denis-Diderot
- Tobias Barker University of Warwick
- Dwight Barkley University of Warwick
- Jeremie Bec CNRS (Centre national de la recherche scientifique); INRIA Sophia Antipolis
- Luca Biferale Università degli Studi di Roma Tor Vergata
- Hugh Blackburn Monash University
- Freddy Bouchet ENS - Lyon; CNRS (Centre national de la recherche scientifique)
- Daniel Boutros University of Cambridge
- Zdzislaw Brzezniak University of York
- Tristan Buckmaster Princeton University
- Angela Busse University of Glasgow
- Elizabeth Carlson University of Victoria
- Colm-cille Caulfield University of Cambridge
- Andre Cavalieri Instituto Tecnológico de Aeronáutica
- Paola Cessi University of California, San Diego
- Sergei Chernyshenko Imperial College London
- Alexey Cheskidov University of Illinois at Chicago
- Greg Chini University of New Hampshire
- Daniel Chung University of Melbourne
- Maria Colombo EPFL - Ecole Polytechnique Fédérale de Lausanne
- Tim Colonius CALTECH (California Institute of Technology)
- Peter Constantin Princeton University
- Michele Coti Zelati Imperial College London
- Stephen Cowley University of Cambridge
- Gianluca Crippa Universität Basel
- Mike Cullen Met Office (retired)
- Diego Córdoba ICMAT
- Milton da Costa Lopes Filho Universidade Federal do Rio de Janeiro (UFRJ)
- Mimi Dai University of Illinois at Chicago; Institute for Advanced Study, Princeton
- Anne-Laure Dalibard Sorbonne Université
- Sara Daneri Gran Sasso Science Institute, L'Aquila
- Emmanuel Dormy CNRS - Ecole Normale Superieure Paris
- David Dritschel University of St Andrews
- Theo Drivas Stony Brook University
- Berengere Dubrulle CEA/Saclay; Université Paris Saclay
- Yohann Duguet CNRS (Centre national de la recherche scientifique); Université Paris Saclay
- Tarek Elgindi Duke University
- Gregory Eyink Johns Hopkins University
- Giovanni Fantuzzi Imperial College London
- Yuanyuan Feng Pennsylvania State University
- Baylor Fox-Kemper Brown University
- Koji Fukagata Keio University
- Paolo Galdi University of Pittsburgh
- Isabelle Gallagher Université Paris 7 - Denis-Diderot; ENS - Paris
- Dennice Gayme Johns Hopkins University
- Fabiola Antonietta Gerosa Observatoire de la Côte d' Azur
- John Gibbon Imperial College London
- David Goluskin University of Victoria
- Rama Govindarajan International Centre for Theoretical Sciences, TIFR, Bangalore
- Michael Graham University of Wisconsin-Madison
- Emmanuel Grenier ENS - Lyon
- Anupam Gupta Indian Institute of Technology
- Philip Hall Monash University
- Dan Henningson KTH - Royal Institute of Technology
- Matthias Hieber Technische Universität Darmstadt
- Sabine Hittmeir Technische Universität Wien
- Darryl Holm Imperial College London
- Susanne Horn Coventry University
- Ibrahim Hoteit King Abdullah University of Science and Technology (KAUST)
- Yongyun Hwang Imperial College London
- Takashi Ishihara Okayama University
- Gautam Iyer Carnegie Mellon University
- Javier Jimenez Universidad Politécnica de Madrid
- Yukio Kaneda Nagoya University
- Genta Kawahara Osaka University
- Robert Kerr University of Warwick
- Rich Kerswell University of Cambridge
- Konstantin Khanin University of Toronto
- Boualem Khouider University of Victoria
- Alexander Kiselev Duke University
- Rupert Klein Freie Universität Berlin
- Peter Korn Max-Planck-Institut für Meteorology
- Igor Kukavica University of Southern California
- Adam Larios University of Nebraska
- Marie-Pascale Lelong NorthWest Research Associates, USA; University of Washington
- Jinkai Li South China Normal University
- Xin Liu Texas A&M University
- Adrian Lozano-Duran Massachusetts Institute of Technology
- Paolo Luchini Università degli Studi di Salerno
- Anagha Madhusudanan University of Cambridge
- Brad Marston Brown University
- Ivan Marusic University of Melbourne
- Takeshi Matsumoto Kyoto University
- Anna Laura Mazzucato Pennsylvania State University
- Beverley McKeon CALTECH (California Institute of Technology)
- Charles Meneveau Johns Hopkins University
- Monica Musso University of Bath
- Camilla Nobili University of Surrey
- Helena Judith Nussenzveig Lopes Universidade Federal do Rio de Janeiro (UFRJ)
- Koji Ohkitani Research Institute for Mathematical Sciences , Kyoto University
- Nairita Pal Los Alamos National Laboratory
- Tim Palmer University of Oxford
- Rahul Pandit Indian Institute of Science
- Daniel Peralta-Salas ICMAT
- Pavan Pranjivan Mehta Brown University
- Bartosz Protas McMaster University
- Alain Pumir ENS - Lyon; Max Planck Institute for Dynamics and Self Organisation
- Antoine Remond-Tiedrez University of Cambridge
- James Robinson University of Warwick
- José Rodrigo University of Warwick
- Samriddhi Sankar Ray International Centre for Theoretical Sciences, TIFR, Bangalore; Tata Institute of Fundamental Research
- Philipp Schlatter KTH - Royal Institute of Technology
- Peter Schmid King Abdullah University of Science and Technology (KAUST)
- Tobias Schneider EPFL - Ecole Polytechnique Fédérale de Lausanne
- Joerg Schumacher Technische Universität Ilmenau
- Christian Seis Westfalische Wilhelms-Universitat Munster
- Gregory Seregin University of Oxford
- Zhen-Su She Peking University
- Roman Shvydkoy University of Illinois at Chicago
- Leslie Smith University of Wisconsin-Madison
- Katepalli Sreenivasan Courant Institute of Mathematical Sciences; New York University
- Samuel Stechmann University of Wisconsin-Madison
- Kunihiko Taira University of California, Los Angeles
- Jean-Luc Thiffeault University of Wisconsin-Madison
- Edriss Titi University of Cambridge; Texas A&M University
- Steven Tobias University of Leeds
- Chuong Tran University of St Andrews
- Laurette Tuckerman PMMH-ESPCI; CNRS (Centre national de la recherche scientifique)
- Alexandra Tzella University of Birmingham
- Nicolas Valade INRIA Sophia Antipolis
- Jacques Vanneste University of Edinburgh
- Dario Vincenzi CNRS (Centre national de la recherche scientifique)
- Fabian Waleffe University of Wisconsin-Madison
- Emil Wiedemann Universität Ulm
- Beth Wingate University of Exeter
- Yao Yao National University of Singapore
- Tamer Zaki Johns Hopkins University
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