Dr Cesare Tronci
I obtained a Laurea in Nuclear Engineering in May 2004 at the Politecnico di Torino (Italy). Then, after spending two years (06/2003 - 05/2005) at CERN (Switzerland) working on microwave electronics under the direction of Ugo Amaldi (also at TU München and TERA Foundation), I moved to the Theoretical Division (in the former Plasma Theory Group) of the Los Alamos National Lab (LANL, USA), where I visited Giovanni Lapenta (now at KU Leuven, Belgium) for several months. In 10/2005, I entered a PhD program in Applied Mathematics at Imperial College, under the direction of Darryl Holm. Between 2006 and 2007, I also spent two summers at LANL, working with Bruce Carlsten in the former International, Space & Response Division (High Power Electrodynamics Group). In 09/2008, I joined the Mathematics Section of EPF Lausanne (Switzerland) as a research assistant in Tudor Ratiu's group (Geometric Analysis). In 01/2012, I was appointed as a Lecturer (Assistant Professor) at Surrey, where I became Reader (Associate Professor) in 08/2018.
Over the years, I have worked with engineers, physicists and mathematicians and shared with them the excitement of doing research in each of the corresponding fields. I have developed an understanding of the needs and the challenges in these disciplines and this experience is for me a continuous source of inspiration. This diversified path has led me to the discovery of mathematical research and its interconnections with other pure and applied sciences. Then, applied mathematics emerges not only as a discipline that applies mathematical concepts to other fields, but also as an area in which other fields of science serve as a continuous inspiration to develop new exciting directions in mathematical research - this two-way vision is precisely where my research stands. Over the last ten years, I have been working on geometric approaches to the formulation of nonlinear multi-physics models systems with multiple scales. Applications include complex fluids, plasma physics and quantum molecular dynamics.
Specific interests include:Momentum maps and reduction by symmetry; applications of symplectic and Poisson geometry; Hamiltonian and Lagrangian techniques in nonlinear dynamics; multi-physics modelling of nonlinear multiscale dynamics; nonlinear modelling of magnetized plasmas; liquid crystals and fluids with internal structure; nonlocal dynamics of aggregation and self-assembly; phase-space methods in classical and quantum mechanics; mixed classical-quantum dynamics and applications in chemistry.
International collaboration network:Within a 4-year Leverhulme Research Project, I am leading an international collaboration composed of Emanuele Tassi at the Centre of Theoretical Physics in Marseille (France), Giovanni Lapenta at the Centre for Plasma Astrophysics of KU Leuven (Belgium), and Philip J. Morrison at the Institute of Fusion Studies at UT Austin (USA). Within the same project, I also collaborate with Alain J. Brizard (St. Michael College of Vermont, USA), Enrico Camporeale (CWI Amsterdam, The Netherlands), and Maria Elena Innocenti (KU Leuven, Belgium).
National collaboration network:Within a London Mathematical Society Scheme 3 award, I am the coordinator of a national Network in Applied Geometric Mechanics involving three groups working on core topics in geometric mechanics: geometric quantum dynamics (Brunel University), geometric imaging science (Imperial College), and geometric fluid dynamics (University of Surrey).
Other collaborations:Over the last 10 years, I have worked with several (mainly international) collaborators on different mathematical problems, with special emphasis on applications. Recent collaborators include: Joshua W. Burby (Courant Institute - NYU, USA), Bin Cheng (U. Surrey, UK), François Gay-Balmaz (ENS-CNRS Paris, France), Darryl D. Holm (Imperial College, UK), Tomoki Ohsawa (UT Dallas, USA), Tudor S. Ratiu (EPF Lausanne, Switzerland), Vakhtang Putkaradze (U. Alberta, Canada), Endre Süli (Oxford, UK), Cornelia Vizman (U. West Timisoara, Romania).
Leverhulme Research Project Grant:in 2014, I was awarded the Leverhulme Research Grant RPG2014-112 “From geometry to kinetic-fluid systems (and back)”. Total budget: £252K. Duration: 4 years (started 7/1/15). This grant involves two 2-years research assistants and three international collaborations in Europe and USA.
Small awards:over the last five years, I have been awarded a series of small grants (<£3K) by the London Mathematical Society, the Institute of Mathematics and Applications and the internal Faculty Research Support Fund at the University of Surrey.
Selected invited talks
Symmetry methods for quantum variational principles and expectation value dynamics, PACM Colloquium, Princeton University, November 6 2017, Princeton NJ, USA
Variational formulations of low frequency kinetic-MHD in the current-coupling scheme, Mini-conference on "New Developments in Algorithms and Verification of Gyro Kinetic Simulations", 58th Annual Meeting of the APS Division of Plasma Physics, October 31 - November 4, 2016, San Jose CA, USA. (Solicited talk)
Modeling efforts in hybrid kinetic-MHD and fully kinetic theories, Princeton Plasma Physics Laboratory, October 27 2016, Princeton NJ, USA
Multiphysics models for hybrid kinetic-fluid systems, Courant Institute of Mathematical Sciences, New York University, April 7 2016, New York NY, USA
Classical-quantum variational principles, Classic and Stochastic Geometric Mechanics Workshop, June 8-11, 2015, École Polytechnique Fédérale de Lausanne, Switzerland
Relabeling symmetry in fluid dynamics, Geometry and Fluids, April 7-11 2014, Clay Mathematics Institute, Oxford, UK
Hydrodynamic vorticity and helicity of conservative liquid crystal flows, Isaac Newton Institute for Mathematical Sciences, June 11 2103, Cambridge, UK
Geometry and symmetry in multi-physics models for magnetized plasmas, Fields Institute for Research in Mathematical Sciences, July 9 2012, Toronto, Canada
Summary: Since I joined the University of Surrey, I introduced a new 4th year module (thought 6 times) in Geometric Mechanics. The module introduces symmetry methods in mechanical problems for different applications, from rigid body dynamics to quantum mechanics. I introduced a new partial assessment method that requires students to give presentations to the rest of the class. Also, I have thought (5 times) an online mini-course (10 hours) in Geometric Mechanics (with more advanced content) to PhD students across the UK, within the Mathematics Access Grid group of universities. Since 2016, I have also been teaching a first-year module in Linear Algebra & Vector Calculus (including a small part on MATLAB).
The Hamiltonian setting of Koopman-von Neumann theory and the dynamics of hybrid classical-quantum systems, F. Gay-Balmaz; C. Tronci, (to be submitted)
Momentum maps for mixed states in quantum and classical mechanics, C. Tronci, J. Geom. Mech. (submitted)
A variational principle for fluid sloshing with vorticity, dynamically coupled to vessel motion, H. Alemi Ardakani, T.J. Bridges, F. Gay-Balmaz, Y. Huang, C. Tronci, Proc. R. Soc. Lond. Ser. A (submitted)
Geometry of nonadiabatic quantum hydrodynamics, M.S. Foskett, D.D. Holm, C. Tronci, Acta Appl. Math. (submitted)
A low-frequency variational model for energetic particle effects in the pressure-coupling scheme, A.R.D. Close, J.W. Burby, C. Tronci, J. Plasma Phys. 84 (2018), no. 4, 905840401
Geometry and dynamics of Gaussian wave packets and their Wigner transforms, T. Ohsawa, C. Tronci, J. Math. Phys., 58 (2017), no. 1, 092105
Existence of global weak solutions to a hybrid Vlasov-MHD model for magnetized plasmas, B. Cheng, E. Süli, C. Tronci, Proc. London Math. Soc., 115 (2017), no. 4, 1-43
Electron inertia and quasi-neutrality in the Weibel instability, E. Camporeale, C. Tronci, J. Plasma Phys., 83 (2017), no. 3, 705830301
Variational approach to low-frequency kinetic-MHD in the current-coupling scheme, J.W. Burby, C. Tronci, Plasma Phys. Control. Fusion, 59 (2017), no. 4, 045013
From liquid crystal models to the guiding-center theory of magnetized plasmas, C. Tronci, Ann. Phys., 371 (2016), 323-337
Variational formulations of guiding-center Vlasov-Maxwell theory, A.J. Brizard, C. Tronci, Phys. Plasmas, 23 (2016), no. 6, 062107
Hamiltonian approach to Ehrenfest expectation values and Gaussian quantum states, E. Bonet Luz, C. Tronci, Proc. R. Soc. Lond. Ser. A, 472 (2016), no. 2189, 20150777
Grid coupling mechanism in the semi-implicit adaptive Multi-Level Multi-Domain method, M.E. Innocenti, C. Tronci, S. Markidis, G. Lapenta, J. Phys.: Conf. Ser., 719 (2016), no. 1, 012019
Equivalent variational approaches to biaxial liquid crystal dynamics, A.R.D. Close, C. Tronci, Proc. R. Soc. Lond. Ser. A, 471 (2015), no. 2183, 20150308
Geometry and symmetry of quantum and classical-quantum variational principles, E. Bonet Luz, C. Tronci, J. Math. Phys., 56 (2015), no. 8, 082104
Neutral Vlasov kinetic theory of magnetized plasmas, C. Tronci, E. Camporeale, Phys. Plasmas, 22 (2015), no. 2, 020704
Energy-Casimir stability of hybrid Vlasov-MHD models, C. Tronci, E. Tassi, P.J. Morrison, J. Phys. A, 48 (2015), no. 18, 185501 (selected for interview as “Publisher's pick”; also appeared in “J. Phys. A Highlights 2015”)
Hybrid Vlasov-MHD models: Hamiltonian vs. non-Hamiltonian, C. Tronci, E. Tassi, E. Camporeale, P.J. Morrison, Plasma Phys. Control. Fusion, 56 (2014), no. 9, 095008
Equivalent theories of liquid crystal dynamics, F. Gay-Balmaz, T.S. Ratiu, C. Tronci, Arch. Ration. Mech. Anal., 210 (2013), no. 3, 773-811
Energy stability analysis for a hybrid fluid-kinetic plasma model, P.J. Morrison, E. Tassi, C. Tronci, in Nonlinear Physical Systems (eds O.N. Kirillov and D.E. Pelinovsky), John Wiley & Sons, Inc., Hoboken, USA, 2013.
Geometric dynamics on the automorphism group of principal bundles, F. Gay-Balmaz, C. Tronci, C. Vizman, J. Geom. Mech., 5 (2013), no. 1, 39-84
A Lagrangian kinetic model for collisionless magnetic reconnection, C. Tronci, Plasma Phys. Control. Fusion, 55 (2013), no. 3, 035001
Collisionless kinetic theory of rolling molecules, D.D. Holm, V. Putkaradze, C. Tronci, Kinet. Relat. Models, 6 (2013), no. 2, 429-458
Vlasov moment flows and geodesics on the Jacobi group, F. Gay-Balmaz, C. Tronci, J. Math. Phys., 43 (2012), no. 12, 123502
Hybrid models for perfect complex fluids with multipolar interactions, C. Tronci, J. Geom. Mech., 4 (2012), no. 3, 333-363
Multiscale turbulence models based on convected fluid microstructure, D.D. Holm, C. Tronci, J. Math. Phys., 53 (2012), no. 11, 115614
Euler-Poincaré approaches to nematodynamics, F. Gay-Balmaz, T.S. Ratiu, C. Tronci, Acta Appl. Math. 120 (2012), no. 1, 127-151
Euler-Poincaré formulation of hybrid plasma models, D.D. Holm, C. Tronci, Comm. Math. Sci. 10 (2012), no.1, 191-222
The helicity and vorticity of liquid-crystal flows, F. Gay-Balmaz, C. Tronci, Proc. R. Soc. Lond. Ser. A 467 (2011), no. 2128, 1197-1213
Reduction theory for symmetry breaking with applications to nematic systems, F. Gay-Balmaz, C. Tronci, Phys. D 239 (2010), no. 20-22, 1929-1947
Hamiltonian approach to hybrid plasma models, C. Tronci, J. Phys. A 43 (2010), no. 37, 375501
Double bracket dissipation in kinetic theory for particles with anisotropic interactions, D.D. Holm, V. Putkaradze, C. Tronci, Proc. R. Soc. Lond. Ser. A 466 (2010), no. 2122, 2991-3012
Geodesic Vlasov equations and their integrable moment closures, D.D. Holm, C. Tronci, J. Geom. Mech. 1 (2009), no. 2, 181-208
Singular solutions of a modified two-component Camassa-Holm equation, D.D. Holm, L. Ó Náraigh, C. Tronci, Phys. Rev. E 79 (2009), no. 1, 016601
Geodesic flows on semidirect-product Lie groups: geometry of singular measure-valued solutions, D.D. Holm, C. Tronci, Proc. R. Soc. Lond. Ser. A 465 (2009), no. 2102, 457-476
Emergent singular solutions of nonlocal density-magnetization equations in one dimension, D.D. Holm, L. Ó Náraigh, C. Tronci, Phys. Rev. E 77 (2008), no. 3, 036211
Geometry of Vlasov kinetic moments: a bosonic Fock space for the Schouten concomitant, J. Gibbons, D.D. Holm, C. Tronci, Phys. Lett. A 40 8 (2008), no. 23, 4184-4196
Kinetic models of oriented self-assembly, D.D. Holm, V. Putkaradze, C. Tronci, J. Phys. A 41 (2008), no. 34, 344010
Geometric gradient-flow dynamics with singular solutions, D.D. Holm, V. Putkaradze, C. Tronci, Phys. D 237 (2008), no. 22, 2952-2965
Vlasov moments, integrable systems and singular solutions, J. Gibbons, D.D. Holm, C. Tronci, Phys. Lett. A 372 (2008), no. 7, 1024-1033
Singular solutions for geodesic flows of Vlasov moments, J. Gibbons, D.D. Holm, C. Tronci, Math. Sci. Res. Inst. Publ. 55 (2008) 199-220
Geometric dissipation in kinetic equations, D.D. Holm, V. Putkaradze, C. Tronci, C. R. Acad. Sci. Paris, Sér. I 345 (2007), no. 5, 297-302
Formulation of the relativistic moment implicit particle-in-cell method, K. Noguchi, C. Tronci, G. Zuccaro, G. Lapenta, Phys. Plasmas 14 (2007), no. 4, 042308
A high frequency H-mode coupled cavity linac for low and medium energies, U. Amaldi, A. Citterio, M. Crescenti, A. Giuliacci, C. Tronci, R. Zennaro, Nucl. Instr. Meth. A 579 (2007), no. 3, 924-936
Concept study and design of a low-medium β accelerating structure, U. Amaldi, A. Citterio, M. Crescenti, A. Giuliacci, C. Tronci, R. Zennaro, Nucl. Phys. B Proc. Supp. 172 (2007) 277-279