3,608 research outputs found
Topological interactions in a Boltzmann-type framework
We consider a finite number of particles characterised by their positions and
velocities. At random times a randomly chosen particle, the follower, adopts
the velocity of another particle, the leader. The follower chooses its leader
according to the proximity rank of the latter with respect to the former. We
study the limit of a system size going to infinity and, under the assumption of
propagation of chaos, show that the limit equation is akin to the Boltzmann
equation. However, it exhibits a spatial non-locality instead of the classical
non-locality in velocity space. This result relies on the approximation
properties of Bernstein polynomials
Affine-ruled varieties without the Laurent cancellation property
We describe a method to construct hypersurfaces of the complex affine
-space with isomorphic -cylinders. Among these hypersurfaces,
we find new explicit counterexamples to the Laurent Cancellation Problem, i.e.
hypersurfaces that are non isomorphic, although their -cylinders
are isomorphic as abstract algebraic varieties. We also provide examples of non
isomorphic varieties and with isomorphic cartesian squares
and
New algorithms for decoding in the rank metric and an attack on the LRPC cryptosystem
We consider the decoding problem or the problem of finding low weight
codewords for rank metric codes. We show how additional information about the
codeword we want to find under the form of certain linear combinations of the
entries of the codeword leads to algorithms with a better complexity. This is
then used together with a folding technique for attacking a McEliece scheme
based on LRPC codes. It leads to a feasible attack on one of the parameters
suggested in \cite{GMRZ13}.Comment: A shortened version of this paper will be published in the
proceedings of the IEEE International Symposium on Information Theory 2015
(ISIT 2015
Convergence of a Vector Penalty Projection Scheme for the Navier-Stokes Equations with moving body
In this paper, we analyse a Vector Penalty Projection Scheme (see [1]) to
treat the displacement of a moving body in incompressible viscous flows in the
case where the interaction of the fluid on the body can be neglected. The
presence of the obstacle inside the computational domain is treated with a
penalization method introducing a parameter . We show the stability of
the scheme and that the pressure and velocity converge towards a limit when the
penalty parameter , which induces a small divergence and the time
step t tend to zero with a proportionality constraint =
t. Finally, when goes to 0, we show that the problem
admits a weak limit which is a weak solution of the Navier-Stokes equations
with no-sleep condition on the solid boundary. R{\'e}sum{\'e} Dans ce travail
nous analysons un sch{\'e}ma de projection vectorielle (voir [1]) pour traiter
le d{\'e}placement d'un corps solide dans un fluide visqueux incompressible
dans le cas o` u l'interaction du fluide sur le solide est n{\'e}gligeable. La
pr{\'e}sence de l'obstacle dans le domaine solide est mod{\'e}lis{\'e}e par une
m{\'e}thode de p{\'e}nalisation. Nous montrons la stabilit{\'e} du sch{\'e}ma
et la convergence des variables vitesse-pression vers une limite quand le param
etre qui assure une faible divergence et le pas de temps t
tendent vers 0 avec une contrainte de proportionalit{\'e} =
t. Finalement nous montrons que leprob{\`i} eme converge au
sens faible vers une solution des equations de Navier-Stokes avec une condition
aux limites de non glissement sur lafront{\`i} ere immerg{\'e}e quand le param
etre de p{\'e}nalisation tend vers 0
Inequivalent embeddings of the Koras-Russell cubic threefold
The Koras-Russell threefold is the hypersurface X of the complex affine
four-space defined by the equation x^2y+z^2+t^3+x=0. It is well-known that X is
smooth contractible and rational but that it is not algebraically isomorphic to
affine three-space. The main result of this article is to show that there
exists another hypersurface Y of the affine four-space, which is isomorphic to
X as an abstract variety, but such that there exists no algebraic automorphism
of the ambient space which restricts to an isomorphism between X and Y. In
other words, the two hypersurfaces are inequivalent. The proof of this result
is based on the description of the automorphism group of X. We show in
particular that all algebraic automorphisms of X extend to automorphisms of the
ambient space
- …