We consider a general class of non-local MCS models whose usual minimal coupling to a conserved current is supplemented with a (non-minimal) magnetic Pauli-type coupling. We find that the considered models exhibit a self-duality whenever the magnetic coupling constant reaches a special value: the partition function is invariant under a set of transformations among the parameter space (the duality transformations) while the original action and its dual counterpart have the same form. The duality transformations have a structure similar to the one underlying self-duality of the (2+1)-dimensional Zn-abelian Higgs model with Chern-Simons and bare mass term.

F. Chandelier Y. Georgelin T. Masson J. -C. Wallet

A recently proposed definition of a linear connection in non-commutative geometry, based on a generalized permutation, is used to construct linear connections on GL_q(n). Restrictions on the generalized permutation arising from the stability of linear connections under involution are discussed. Candidates for generalized permutation on GL_q(n) are found. It is shown that, for a given generalized permutation, there exists one and only one associated linear connection. Properties of the linear connection are discussed, in particular its bicovariance, torsion and commutative limit.

Y. Georgelin J. Madore T. Masson J. Mourad

We apply a recently proposed definition of a linear connection in non commutative geometry based on the natural bimodule structure of the algebra of differential forms to the case of the two-parameter quantum plane. We find that there exists a non trivial family of linear connections only when the two parameters obeys a specific relation.

Y. Georgelin T. Masson J. -C. Wallet

Digestion in the small intestine is the result of complex mechanical and biological phenomena which can be modelled at different scales. In a previous article, we introduced a system of ordinary differential equations for describing the transport and degradation-absorption processes during the digestion. The present article sustains this simplified model by showing that it can be seen as a macroscopic version of more realistic models including biological phenomena at lower scales. In other words, our simplified model can be considered as a limit of more realistic ones by averaging-homogenization methods on biological processes representation.

Masoomeh Taghipoor Guy Barles Christine Georgelin Jean-René Licois Philippe Lescoat

Thin elastic two-dimensionnal systems under compressive stresses may relieve part of their stretching energy by developing out of plane undulations. We investigate experimentally and theoretically the indentation of an elastic disk supported by a circular ring and show that compressive stresses are relieved via two different routes : either developing \textit{buckles} which are spread over the system or developing a \textit{d-cone} where deformation is concentrated in a subregion of the system. We characterize the indentation threshold for wrinkles or d-cone existence as a function of aspect ratio.

Tristan Suzanne Julien Deschamps Marc Georgelin Gwenn Boedec

Kinetic equations are derived from the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy for point vortex systems in an infinite plane. As the level of approximation for the Landau equation, the collision term of the kinetic equation derived coincides with that by Chavanis ({\it Phys. Rev. E} {\bf 64}, 026309 (2001)). Furthermore, we derive a kinetic equation corresponding to the Balescu-Lenard equation for plasmas, using the theory of the Fredholm integral equation. For large $N$, this kinetic equation is reduced to the Landau equation above.

Mitsusada M. Sano

We introduce a construction of pseudo-Anosov homeomorphisms on n-times punctured spheres and surfaces with higher genus using only sufficiently many positive half-twists. These constructions can produce explicit examples of pseudo-Anosov maps with various number-theoretic properties associated to the stretch factors, including examples where the trace field is not totally real and the Galois conjugates of the stretch factor are on the unit circle.

Yvon Verberne

Building on work of Farb and the second author, we prove that the group of automorphisms of the fine curve graph for a surface is isomorphic to the group of homeomorphisms of the surface. This theorem is analogous to the seminal result of Ivanov that the group of automorphisms of the (classical) curve graph is isomorphic to the extended mapping class group of the corresponding surface.

Adele Long Dan Margalit Anna Pham Yvon Verberne Claudia Yao

We adapt the properties of Kim-independence in NSOP1 theories with existence proven in [5],[4] and [2] by Ramsey, Kaplan, Chernikov, Dobrowolski and Kim to hyperimaginaries by adding the assumption of existence for hyperimaginaries. We show that Kim-independence over hyperimaginaries satisfies a version of Kim's lemma, symmetry, the independence theorem, transitivity and witnessing. As applications we adapt Kim's results around colinearity and weak canonical bases from [8] to hyperimaginaries and give some new results about Lascar strong types and Kim-forking using boundedly closed hyperimaginaries.

Yvon Bossut

We present here some known and some new examples of non-simple NSOP1 theories andsome behaviour that Kim-forking can exhibit in these theories, in particular that Kim-forking afterforcing base monotonicity can or can not satisfy extension (on arbitrary sets). This study is based onthe results of Chernikov, Ramsey, Dobrowolski and Granger.

Yvon Bossut