Objective
"This project aims at understanding the generation of abstract concepts and theories in mathematical physics and their relation with theoretical practices. To achieve this, it focuses upon the emergence of the modern concepts of order and chaos in celestial and statistical mechanics. The research is articulated into three phases. The first phase discusses the problem of stability in a three-body system from the origin of celestial mechanics to Henri Poincaré’s discovery of homoclinic trajectories. Initially, the problem of stability was attacked by using analytical and algebraic techniques whose main goal was to show that approximate solutions of the equations of motion do not contain secular terms. Drawing on this vast culture of mathematical techniques and generalizing them further, Poincaré introduced a new qualitative approach, which led him to extend periodicity from periodic motion to complicate recurrence up to chaotic trajectories. The second phase focuses upon the intersections between mechanical and statistical arguments in the work of Ludwig Boltzmann. Facing the problem of dealing with mechanical systems with many degrees of freedom, Boltzmann combined the analysis of the equations of motion with statistical techniques which allowed him to describe the macroscopic behavior of the system. Thus, macroscopic order was understood as a probabilistic, long-term phenomenon deriving from a complex, microscopic disorder. Notions such as the ergodic hypothesis and molecular chaos were introduced by Boltzmann to conceptualize this disorder. The third phase concerns George D. Birkhoff’s path from the theory of dynamical systems to the ergodic theorem. Taking up Poincaré’s legacy in celestial mechanics in 1912, Birkhoff honed the analytical and topological techniques of the European mathematical culture and, in 1931, he rigorously formulated the conditions for a mechanical systems to be ergodic so unifying the two previous lines of investigation on order/chaos."
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: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
- natural sciences mathematics applied mathematics mathematical physics
- natural sciences mathematics applied mathematics dynamical systems
- natural sciences physical sciences classical mechanics statistical mechanics
- natural sciences physical sciences astronomy planetary sciences celestial mechanics
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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-2013-IOF
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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
08193 Cerdanyola Del Valles
Spain
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.