Regular holonomic D[[h]]-modules

We describe the category of regular holonomic modules over the ring D[[h]] of linear differential operators with a formal parameter h. In particular, we establish the Riemann-Hilbert correspondence and discuss the additional t-structure related to h-torsion.Comment: 39 page

Changing time and emotions

In this paper, we consider that our experience of time (to come) depends on the emotions we feel when we imagine future pleasant or unpleasant events. A positive emotion such as relief or joy associated with a pleasant event that will happen in the future induces impatience. Impatience, in our context, implies that the experience of time up to the forthcoming event expands. A negative emotion such as grief or frustration associatedwith an unpleasant event thatwill happen in the future triggers anxiety. This will give the experience of time contraction. Time, therefore, is not exogeneously given to the individual and emotions, which link together events or situations, are a constitutive ingredient of time experience. Our theory can explain experimental evidence which shows that people tend to prefer to perform painful actions earlier than pleasurable ones, contrary to the predictions yielded by the standard exponential discounting framework.experience of time ; emotions ; impatience ; anxiety ; discount factor ; time preference

Structure, stability and evolution of 3D Rossby vortices in protoplanetary disks

Large-scale persistent vortices are known to form easily in 2D disks via the Rossby wave or the baroclinic instability. In 3D, however, their formation and stability is a complex issue and still a matter of debate. We study the formation of vortices by the Rossby wave instability in a stratified inviscid disk and describe their three dimensional structure, stability and long term evolution. Numerical simulations are performed using a fully compressible hydrodynamical code based on a second order finite volume method. We assume a perfect gas law and a non-homentropic adiabatic flow.The Rossby wave instability is found to proceed in 3D in a similar way as in 2D. Vortices produced by the instability look like columns of vorticity in the whole disk thickness; the small vertical motions are related to a weak inclination of the vortex axis appearing during the development of the RWI. Vortices with aspect ratios larger than 6 are unaffected by the elliptical instability. They relax to a quasi-steady columnar structure which survives hundred of rotations while slowly migrating inward toward the star at a rate that reduces with the vortex aspect ratio. Vortices with a smaller aspect ratio are by contrast affected by the elliptic instability. Short aspect ratio vortices are completely destroyed in a few orbital periods. Vortices with an intermediate aspect ratio are partially destroyed by the elliptical instability in a region away from the mid-plane where the disk stratification is sufficiently large. Elongated Rossby vortices can survive a large number of orbital periods in protoplanetary disks in the form of vorticity columns. They could play a significant role in the evolution of the gas and the gathering of the solid particles to form planetesimals or planetary cores, a possibility that receives a renewed interest with the recent discovery of a particle trap in the disk of Oph IRS48.Comment: 12 pages, 15 figures, Accepted for publication in A&

Duality and separation theorems in idempotent semimodules

We consider subsemimodules and convex subsets of semimodules over semirings with an idempotent addition. We introduce a nonlinear projection on subsemimodules: the projection of a point is the maximal approximation from below of the point in the subsemimodule. We use this projection to separate a point from a convex set. We also show that the projection minimizes the analogue of Hilbert's projective metric. We develop more generally a theory of dual pairs for idempotent semimodules. We obtain as a corollary duality results between the row and column spaces of matrices with entries in idempotent semirings. We illustrate the results by showing polyhedra and half-spaces over the max-plus semiring.Comment: 24 pages, 5 Postscript figures, revised (v2

Neutron scattering studies on URu2Si2

This paper is aiming to review some of the neutron scattering studies performed on URu2Si2 in Grenoble. This compound has been studied for a quarter of century because of a so-called hidden order ground state visible by most of the bulk experiments but almost invisible by microscopic probes like neutrons, muons NMR or x-ray. We stress on some aspects that were not addressed previously. Firstly, the comparison of the cell parameters in the 1-2-2 systems seems to point that the magnetic properties of URu2Si2 are leading by an U4+ electronic state. Secondly, a compilation of the different studies of the tiny antiferromagnetic moment indicates that the tiny antiferromagnetic moment has a constant value which may indicate that it is not necessary extrinsic. We also present the last development on the magnetic form factor measurement in which the magnetic density rotates when entering in the hidden order state. To end, the thermal dependence of the two most intense magnetic excitation at Q0=(1,0,0) and Q1=(0.6,0,0) seems to indicate two different origins or processes for these excitations.Comment: 18 pages, 18 figures, published in Philosophical Magazine, 201

Statistical extraction of process zones and representative subspaces in fracture of random composite

We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process cannot be correctly approximated in a low-dimensional deterministic space. Such a low-dimensional space is obtained by a spectral analysis performed on pre-computed solution samples. A greedy algorithm is proposed to identify both process zone and low-dimensional representative subspace for the solution in the complementary region. In addition to the novelty of the tools proposed in this paper for the analysis of localised phenomena, we show that the reduced space generated by the method is a valid basis for the construction of a reduced order model.Comment: Submitted for publication in International Journal for Multiscale Computational Engineerin

Noncommutative Locally Anti-de Sitter Black Holes

We give a review of our joint work on strict deformation of BHTZ 2+1 black holes \cite{BRS02,BDHRS03}. However some results presented here are not published elsewhere, and an effort is made for enlightening the instrinsical aspect of the constructions. This shows in particular that the three dimensional case treated here could be generalized to an anti-de Sitter space of arbitrary dimension provided one disposes of a universal deformation formula for the actions of a parabolic subgroup of its isometry group.Comment: 10 pages, based on a talk given by P.B., to appear in the proceedings of the workshop `Noncommutative Geometry and Physics 2004' (Feb. 2004, Keio University, Japan) (World Scientific