Objective
"The study of Arnold diffusion in Hamiltonian systems has received a lot of attention in the last years. This phenomenon arises when a small perturbation in a system causes big changes in it leading to global instabilities. In recent years there have been partial results characterizing this phenomenon and proving its existence in Hamiltonian systems but mostly for systems of low dimension. This project wants to be a step forward showing that such instabilities also arise in Dynamical Systems on lattices and in Hamiltonian Partial Differential Equations (HPDEs), which can be seen as Dynamical Systems of infinite dimension. We will focus our attention on two different problems: the Fermi-Pasta-Ulam model and the energy transfer phenomenon in Hamiltonian PDEs.
Regarding the first part, we will consider the Fermi-Pasta-Ulam model (FPU), which is a model of a discretized nonlinear string. One would expect that as time evolves, the system reaches equipartition of energy among the modes. Nevertheless, numerical experiments by Fermi, Pasta and Ulam (1955) showed that in some settings it is not reached in the time range for which the numerical experiments are reliable. This fact is called the FPU paradox. To understand how the equipartition of energy can be reached after longer times we plan to find instability mechanisms in the low energy regime.
In the second part we will prove the existence of solutions of some HPDEs in the d dimensional torus which undergo transfer of energy to higher modes as time tends to infinity. This transfer of energy can be measured by the growth of high Sobolev norms. First, we plan to prove the existence of orbits with arbitrarily large finite growth of Sobolev norms for different Hamiltonian PDEs. Finally we plan to prove Bourgain's conjecture, which asserts the existence of orbits of the cubic defocusing nonlinear Schrodinger equation in the two torus whose s-Sobolev norms tend to infinity as time tends to infinity."
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics applied mathematics dynamical systems
- natural sciences mathematics pure mathematics mathematical analysis differential equations partial differential equations
You need to log in or register to use this function
We are sorry... an unexpected error occurred during execution.
You need to be authenticated. Your session might have expired.
Thank you for your feedback. You will soon receive an email to confirm the submission. If you have selected to be notified about the reporting status, you will also be contacted when the reporting status will change.
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP7-PEOPLE-2012-IEF
See other projects for this call
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Coordinator
75794 PARIS
France
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.