Menu
MapConnectionsTopicsBulgariaThe Night (K-TRIO)Marie Skłodowska-CurieFor studentsFor teachersMethodologySurprise me
H2020Staff exchange2017–2022

TraX · Stability and Transitions in Physical Processes

Horizon 2020 — Marie Skłodowska-Curie Actions

Duration
2017-03-01 → 2022-10-31
EU contribution
€526,500
Participants
9
Scheme
MSCA-RISE

Lines connect the coordinator with its partners.

Results in brief

Stability and Transitions in Physical Processes

In many dynamical processes in natural sciences, understanding qualitative changes of a system, i.e., how, where and when reorganization of the dynamics takes place, provides the key to the understanding of the mechanisms at play and to the global understanding of the dynamics. This applies to processes as diverse as chemical reactions, the rearrangement of clusters, the ionization of atoms, the capture of asteroids by large celestial bodies, phase transitions in cosmology, and other systems. The most important problems in the study of reorganization processes are to predict and, where possible, to control whether the reorganization will happen. Many reorganization processes share a common formal structure that can be exploited in their study: The qualitative structure of the dynamics is determined by invariant geometric objects in phase space, called invariant manifolds. These manifolds act as barriers that channel the dynamics of typical trajectories. Once the invariant manifolds are known, it can be predicted which initial conditions/states of the system will or will not lead to a qualitative reorganization. This structural description also yields quantitative information like, for example, chemical reaction rates, ionization yields and other transport properties. Unfortunately, in a realistic situation the invariant manifolds are often quite difficult to compute, in particular in a high-dimensional system. It is also not always as easy to see how to use the manifolds once they are known. In TraX, we tackle both these problems: We develop computational methods of wide applicability along with the mathematical theory that underlies them, and to demonstrate the applicability of these methods in various fields of science. The research results of the network include applications to celestial mechanics, chemistry and atomic physics.

Data: CORDIS, © European Union

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.

Original text from CORDIS.

Participants

  • LOUGHBOROUGH UNIVERSITY · LoughboroughCoordinatorUnited Kingdom
  • CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS · ParisFrance
  • GEORGIA TECH RESEARCH CORPORATION · Atlanta GaUnited States
  • JOHNS HOPKINS UNIVERSITY · BaltimoreUnited States
  • UNIVERSIDAD AUTONOMA DE MADRID · MadridSpain
  • UNIVERSIDAD POLITECNICA DE MADRID · MadridSpain
  • UNIVERSITAT DE BARCELONA · BarcelonaSpain
  • UNIVERSITE D'AIX MARSEILLE · MarseilleFrance
  • UNIVERSITY OF STUTTGART · StuttgartGermany

Links

Data: CORDIS, © European Union