CROISSANCE · Analytic approaches to planar growth processes
FP7 — People (Marie Curie Actions)
- Duration
- 2010-11-08 → 2013-08-07
- EU contribution
- €222,547
- Participants
- 1
- Scheme
- MC-IEF
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Results in brief
Analytic approaches to planar growth processes
Several serious advances has been done on the scientific subjects indicated in the work plan during reporting period. Majority of the project objectives have been achieved. In particular advances have been made in: • Study of competitive models of Laplacian growth, which resulted in publication in Journal of Statistical Physics: November 2011, Volume 145, Issue 4, pp 919-931 • Work on new applications of algebraically integrable systems in fluid dynamics, which resulted in publication in Analysis and Mathematical Physics: September 2013, Volume 3, Issue 3, pp 277-294 • Work on Schramm-Loewner and Levy-Loewner evolution: Two articles have been published in 1) Journal of Physics A: Mathematical and Theoretical Volume 45 Number 27, 275001, 2)Journal of Statistical Mechanics: Theory and Experiment, Volume 2013, April 2013, P04007 • The habilitation thesis entitled ”Integrable systems in theory of moving fronts”, which completely corresponds to the project objectives , has been successfully defended during the first year at the Fellow host institution (http://people.math.jussieu.fr/ aboutet/hdr/). There has been no deviation from the project work plan. The list of results, publications, including habilitation thesis, and the dissemination activities is provided in the attachement.
Data: CORDIS, © European Union
Project objective
Many important phenomena reveal stochastic geometrical objects and shapes. Among them are fluctuating domain boundaries in statistical mechanics, growing patterns in non-equilibrium processes, and fluctuating surfaces studied in random matrix theory. These geometrical objects naturally arise in the theory of 2D growth processes, disordered systems and random media. In many interesting cases they are fractal in nature. The project focuses on a wide class of processes involving stochastic geometry in two dimensions and the related deterministic objects arising in free-boundary problems, such as Laplacian and elliptic growth. In spite of discovery of many deep connections between the theory of moving interfaces in two dimensions to a number of modern branches of mathematics such as advanced complex analysis, deformations of Riemann surfaces, integrable systems and theory of random matrices, there are many important questions to be addressed. For instance, complete analytic description, classification and universality of random growth processes and their deterministic counterparts on the plane as well as theory of singularity formation and regularisation are far from being complete. The project goal is to apply novel analytical and numeric techniques and combine ideas from different disciplines, in order to attack the above problems. Remarkable developments in Laplacian and elliptic growth due to recent achievements in theory of integrable systems and random matrices as well as revitalization of the study of 2D critical phenomena as a stochastic evolution of geometry due to recent discovery of the Stochastic Loewner Evolution make feasible further significant advances in the field. Multi-disciplinarity of the present project is addressed to combine the most recent advances in the named adjacent topics to shed light on the nature of fascinating interaction amongst phenomena both of pure physical and mathematical origin.
Original text from CORDIS.
Participants
- CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS · ParisCoordinatorFrance
Links
Data: CORDIS, © European Union