2019-01576 - Post-Doctoral Research Visit F/M Stochastic approach and numerical methods for rupture phenomena. Applications to avalanches [S]
Le descriptif de l’offre ci-dessous est en Anglais

Type de contrat : CDD de la fonction publique

Niveau de diplôme exigé : Thèse ou équivalent

Fonction : Post-Doctorant

Contexte et atouts du poste

Scientific context
The rupture phenomena arise in many applicative fields as : in snow or rock avalanche, in geophysics,
in crystallography, etc. The mathematical description is still not very well developed and many important
questions need to be answered. Recently Madalina Deaconu and her co-authors Lucian Beznea
and Oana Lupascu obtained significative results in this direction by giving a probabilistic interpretation
to the fragmentation model for the avalanche. They considered the interpretation of the rupture
in terms of fragmentation models. In a first work [1] they connect the probabilistic interpretation of
the fragmentation equation by a stochastic differential equation with jumps to a branching process.
Afterwards, by considering a particular fragmentation kernel [2], [3], which illustrates a physical characteristic
of the snow avalanche, they construct a stochastic interpretation for the avalanche and also
a new numerical techniques to approximate it.
In this first approach the model gives the evolution of a particle system which are characterized only
by their masses. The aim is here to extend these approaches to the fragmentation process where the
particles are both characterized by their mass and their position. Another step will be the introduction
of the evolution of the avalanche before the rupture phase [4], [5] and [6], which can be interpreted
as a a coagulation model, the detection of the rupture time and also the description of the rupture
as a fragmentation process (the study done before). The implementation of the numerical stochastic
methods will be crucial for the understanding of the phenomenon. This approach is new and proposes
an alternative approach to avalanche modeling by stochastic processes. The success of this study will
allow to give some insight on important problems concerning avalanches and the connected risk.

Mission confiée

Missions
This project aims to develop the existing interest of Tosca Nancy in the probabilistic interpretation of
rupture phenomena like avalanches in terms of fragmentation models.
More precisely we will construct a stochastic approach for the avalanche model by using some particular
properties of an avalanche. This approach is an important issue in controlling the risk. The
originality is here to include also the position of the particle (snow) one of the important parameters
of the physical model. The numerical part of this work will be done in collaboration with researcher
from Irstea, Grenoble.
Our aim is twofold. First, we intend to investigate the evolution equation of the fragmentation including
both position and mass of the particle. This microscopic vision should conduce to a better
understanding of this complex process. The second direction is to improve the model by considering
coagulation/fragmentation models based on the physical properties of the avalanches in order to
characterize the different stages of the physical phenomenon.
An important part of this project wil be dedicated to the construction and the analysis of numerical
probabilistic methods.
Bibliography
[1] L. Beznea, M. Deaconu and O. Lupascu, Branching processes for the fragmentaion equation,
Stochastic Processes and Their Applications, 125 (2015), no. 5, 1861–1885.
[2] L. Beznea, M. Deaconu and O. Lupascu, Stochastic equation of fragmentation and branching
processes related to avalanches, Journal of Statistical Physics, 162 (2016), 824-841.
[3] L. Beznea, M. Deaconu and O. Lupascu, Numerical approach for stochastic differential equations
of fragmentation, application to avalanches. Submitted, 2017.
[4] M. Deaconu, N. Fournier, and E. Tanre, A pure jump Markov process associated with Smoluchowski’s
coagulation equation. Ann. Probab., 30 (2002), 1763-1796.
[5] M. Deaconu, N. Fournier, and E. Tanre, Rate of convergence of a stochastic particle system for
the Smoluchowski coagulation equation, Methodol. Comput. Appl. Probab., 5 (2003), 131-158.
[6] M. Deaconu and N. Fournier, Probabilistic approach of some discrete and continuous

Principales activités

 
- develop the mathematical modelling of the fragmentation  for the avalanches context, by including the spatial variable and the physical properties of the kernel
- construct and implement a probabilistic numerical method for this problem
- write reports and research articles on this subject,
- collaborate with researcher from Irstea Grenoble

Compétences

Required qualification : PhD in applied mathematics and basis in numerical probabilistic methods

Avantages

  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
  • Possibility of teleworking (after 6 months of employment) and flexible organization of working hours
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural and sports events and activities
  • Access to vocational training
  • Social security coverage

Rémunération

Salary: 2653€ gross/month