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Stability and Transitions in Physical Processes

Total Cost €


EC-Contrib. €






Project "TraX" data sheet

The following table provides information about the project.


Organization address
address: ASHBY ROAD
postcode: LE11 3TU

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country United Kingdom [UK]
 Project website
 Total cost 711˙000 €
 EC max contribution 526˙500 € (74%)
 Programme 1. H2020-EU.1.3.3. (Stimulating innovation by means of cross-fertilisation of knowledge)
 Code Call H2020-MSCA-RISE-2016
 Funding Scheme MSCA-RISE
 Starting year 2017
 Duration (year-month-day) from 2017-03-01   to  2021-02-28


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
2    UNIVERSITAT DE BARCELONA ES (BARCELONA) participant 144˙000.00
4    UNIVERSITAET STUTTGART DE (STUTTGART) participant 72˙000.00
7    UNIVERSITE D'AIX MARSEILLE FR (Marseille) participant 40˙500.00


 Project objective

Many dynamical processes in natural sciences are organized by invariant objects that behave in rather simple ways under time evolution, such as equilibria, periodic orbits, or higher-dimensional invariant surfaces. These objects and the invariant manifolds attached to them act as landmarks that organize the behavior of other trajectories and yield a qualitative description of the dynamics. By computing strategically chosen landmarks, one can obtain considerable information of the possible behaviors of the system. This strategy is particularly fruitful in Hamiltonian systems, in which a large number of invariant manifolds coexist. For example, it has been realized in recent years that Transition State theory, a framework first developed in chemistry and then applied to other fields of science, relies on the existence of invariant manifolds in phase space. These manifolds encode the essential dynamics of various reorganization processes. The objective of this RISE proposal is to build a multidisciplinary exchange programme around the determination of invariant dynamical objects which encompass applied mathematics, atomic and molecular physics, chemistry and celestial mechanics. The project aims at linking mathematicians, physicists and chemists to identify the universal mechanisms behind dynamical transition processes. The proposed collaborative project will be coordinated by the School of Mathematics of Loughborough University, and will involve the Department of Mathematics of the University of Barcelona, the Center for Theoretical Physics (CNRS / Aix Marseille University), the Physics Department of the Polytechnic University of Madrid, the Chemistry Department at the Universidad Autónoma of Madrid and the Physics Department at the University of Stuttgart. The third country partners are Georgia Institute of Technology, represented by the School of Mathematics and the School of Physics and Johns Hopkins University, represented by the School of Chemistry.


year authors and title journal last update
List of publications.
2020 Martin Tschöpe, Matthias Feldmaier, Jörg Main, Rigoberto Hernandez
Neural network approach for the dynamics on the normally hyperbolic invariant manifold of periodically driven systems
published pages: , ISSN: 2470-0045, DOI: 10.1103/physreve.101.022219
Physical Review E 101/2 2020-03-05
2019 Matthias Feldmaier, Robin Bardakcioglu, Johannes Reiff, Jörg Main, Rigoberto Hernandez
Phase-space resolved rates in driven multidimensional chemical reactions
published pages: 244108, ISSN: 0021-9606, DOI: 10.1063/1.5127539
The Journal of Chemical Physics 151/24 2020-02-06
2019 J. Dubois, S. A. Berman, C. Chandre, T. Uzer
Inclusion of Coulomb effects in laser-atom interactions
published pages: 53405, ISSN: 2469-9926, DOI: 10.1103/PhysRevA.99.053405
Physical Review A 99/5 2020-02-06
2019 S A Berman, C Chandre, J Dubois, M Perin, T Uzer
Classical versus quantum views of intense laser pulse propagation in gases
published pages: 125601, ISSN: 0953-4075, DOI: 10.1088/1361-6455/ab1c12
Journal of Physics B: Atomic, Molecular and Optical Physics 52/12 2020-02-06
2018 S.A. Berman, C. Chandre, J. Dubois, F. Mauger, M. Perin, T. Uzer
Variational formulation of classical and quantum models for intense laser pulse propagation
published pages: 66-84, ISSN: 0003-4916, DOI: 10.1016/j.aop.2018.10.002
Annals of Physics 399 2019-10-09
2018 Lei Zhang, Rafael de la Llave
Transition state theory with quasi-periodic forcing
published pages: 229-243, ISSN: 1007-5704, DOI: 10.1016/j.cnsns.2018.02.014
Communications in Nonlinear Science and Numerical Simulation 62 2019-07-18
2018 S. A. Berman, J. Dubois, C. Chandre, M. Perin, T. Uzer
Coherent buildup of high-order harmonic radiation: The classical perspective
published pages: 061402(R), ISSN: 2469-9926, DOI: 10.1103/PhysRevA.97.061402
Physical Review A 97/6 2019-07-18
2017 Matthias Feldmaier, Andrej Junginger, Jörg Main, Günter Wunner, Rigoberto Hernandez
Obtaining time-dependent multi-dimensional dividing surfaces using Lagrangian descriptors
published pages: 194-199, ISSN: 0009-2614, DOI: 10.1016/j.cplett.2017.09.008
Chemical Physics Letters 687 2019-07-18
2017 Andrej Junginger, Lennart Duvenbeck, Matthias Feldmaier, Jörg Main, Günter Wunner, Rigoberto Hernandez
Chemical dynamics between wells across a time-dependent barrier: Self-similarity in the Lagrangian descriptor and reactive basins
published pages: 64101, ISSN: 0021-9606, DOI: 10.1063/1.4997379
The Journal of Chemical Physics 147/6 2019-07-18
2018 F. Revuelta, Thomas Bartsch, R. M. Benito, and F. Borondo
The geometry of transition states: How invariant manifolds determine reaction rates
published pages: 305-318, ISSN: 2241-0503, DOI:
Chaotic Modeling and Simulation 3 2019-07-18
2017 Andrej Junginger, Jörg Main, Günter Wunner, Rigoberto Hernandez
Variational principle for the determination of unstable periodic orbits and instanton trajectories at saddle points
published pages: , ISSN: 2469-9926, DOI: 10.1103/PhysRevA.95.032130
Physical Review A 95/3 2019-07-18
2019 Matthias Feldmaier, Philippe Schraft, Robin Bardakcioglu, Johannes Reiff, Melissa Lober, Martin Tschöpe, Andrej Junginger, Jörg Main, Thomas Bartsch, Rigoberto Hernandez
Invariant Manifolds and Rate Constants in Driven Chemical Reactions
published pages: 2070-2086, ISSN: 1520-6106, DOI: 10.1021/acs.jpcb.8b10541
The Journal of Physical Chemistry B 123/9 2019-07-18
2017 F. Revuelta, Galen T. Craven, Thomas Bartsch, F. Borondo, R. M. Benito, Rigoberto Hernandez
Transition state theory for activated systems with driven anharmonic barriers
published pages: 74104, ISSN: 0021-9606, DOI: 10.1063/1.4997571
The Journal of Chemical Physics 147/7 2019-07-18
2018 Robin Bardakcioglu, Andrej Junginger, Matthias Feldmaier, Jörg Main, Rigoberto Hernandez
Binary contraction method for the construction of time-dependent dividing surfaces in driven chemical reactions
published pages: 32204, ISSN: 2470-0045, DOI: 10.1103/physreve.98.032204
Physical Review E 98/3 2019-07-18
2018 Philippe Schraft, Andrej Junginger, Matthias Feldmaier, Robin Bardakcioglu, Jörg Main, Günter Wunner, Rigoberto Hernandez
Neural network approach to time-dependent dividing surfaces in classical reaction dynamics
published pages: , ISSN: 2470-0045, DOI: 10.1103/PhysRevE.97.042309
Physical Review E 97/4 2019-07-18
2018 Marc Jorba-Cuscó, Ariadna Farrés, Àngel Jorba
Solar Sail resonant periodic orbits in the augmented Earth-Moon Quasi-Bicircular Problem
published pages: , ISSN: , DOI:
Proceedings of the 69th International Astronautical Congress 2019-07-18
2018 Marc Jorba-Cuscó, Ariadna Farrés, Àngel Jorba
Two Periodic Models for the Earth-Moon System
published pages: 32, ISSN: 2297-4687, DOI: 10.3389/fams.2018.00032
Frontiers in Applied Mathematics and Statistics 4 2019-07-18
2018 Joan Gimeno, Àngel Jorba, Josep Sardanyés
On the effect of time lags on a saddle-node remnant in hyperbolic replicators
published pages: 385601, ISSN: 1751-8113, DOI: 10.1088/1751-8121/aad02f
Journal of Physics A: Mathematical and Theoretical 51/38 2019-07-18
2019 Alex Haro, Alejandro Luque
A-posteriori KAM theory with optimal estimates for partially integrable systems
published pages: 1605-1674, ISSN: 0022-0396, DOI: 10.1016/j.jde.2018.08.003
Journal of Differential Equations 266/2-3 2019-07-18
2018 J. Dubois, S. A. Berman, C. Chandre, T. Uzer
Capturing Photoelectron Motion with Guiding Centers
published pages: 113202, ISSN: 0031-9007, DOI: 10.1103/PhysRevLett.121.113202
Physical Review Letters 121/11 2019-07-18

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