Related papers: Etude des jets de Demailly-Semple en dimension 3
Current design constraints have encouraged the studies of aeroacoustic fields around compressible jet flows. The present work addresses the numerical study of unsteady turbulent jet flows as a preparation for future aeroacoustic analyses of…
The Leibniz rule for derivations is invariant under cyclic permutations of co-multiples within the arguments of derivations. We explore the implications of this principle: in effect, we construct a class of noncommutative bundles in which…
We have performed high-resolution 3D simulations of relativistic jets with beam flow Lorentz factors up to 7, a spatial resolution of 8 cells per beam radius, and for up to 75 normalized time units to study the morphology and dynamics of 3D…
A non--relativistic and relativistic model in which astrophysical jets are deflected on passing through an isothermal high density region is analysed. The criteria for the stability of jets due to the formation of internal shocks are…
Given a scheme X over a field k, a generalized jet scheme parametrizes maps from Spec(A) to X, where A is a finite-dimensional, local algebra over k. We give an overview of known results concerning the dimensions of these schemes when A has…
We study invariant jet differentials in the framework of complex hyperbolicity, focusing on the algebra of invariants for the non--reductive reparametrization group $G_k = \mathbb{C}^{\ast} \ltimes U_k$. The paper develops a uniform,…
Of the two techniques introduced by Bloch, Green-Griffiths and developed by Siu, Demailly to establish Kobayashi hyperbolicity of generic high degree complex algebraic hypersurfaces X in P^(n+1), the second one, initiated by Clemens, Ein,…
The stable propagation of jets in FRII sources is remarkable if one takes into account that large-scale jets are subjected to potentially highly disruptive three-dimensional (3D) Kelvin-Helmholtz instabilities. Numerical simulations can…
The effect of optically thin radiative cooling on the Kelvin-Helmholtz instability of three dimensional jets is investigated via linear stability theory and nonlinear hydrodynamical simulation. Two different cooling functions are…
In our [Higher-order preconnections in synthetic differential geometry of jet bundles, Beitr\"{a}ge zur Algebra und Geometrie, 45 (2004), 677-696] we have established the affine bundle theorem in the synthetic approach to jet bundles in…
Following a suggestion made by J.-P. Demailly, for each $k\ge 1$, we endow, by an induction process, the $k$-th (anti)tautological line bundle $\mathcal O_{X_k}(1)$ of an arbitrary complex directed manifold $(X,V)$ with a natural smooth…
Experiments and numerical simulations were conducted to investigate the dispersion of turbulent jets issuing from realistic pipe geometries. The effect of jet densities and Reynolds numbers on vertical buoyant jets were investigated, as…
This article studies the scheme structure of the jet schemes of determinantal varieties. We show that in general, these jet schemes are not irreducible. In the case of the determinantal variety $X$ of $r \times s$ matrices of rank at most…
We study the stability of a non-rotating single-component jet using two-dimensional special relativistic hydrodynamic simulations. By assuming translational invariance along the jet axis, we exclude the destabilization effect by…
We study geometric aspects of horizontal 2-plane distributions on the complement of the zero section in the 5-dimensional total space of a rank-3 vector bundle equipped with connection over a surface. We show that any surface in…
This paper is devoted to the construction of differential geometric invariants for the classification of "Quaternionic" vector bundles. Provided that the base space is a smooth manifold of dimension two or three endowed with an involution…
For $m \in \mathbb{N}$, we determine the irreducible components of the $m$-th Jet Scheme of a complex branch $C$ and give formulas for their number $N(m)$ and for their codimensions, in terms of $m$ and the generators of the semigroup of…
This paper establishes new degree bounds for Kobayashi hyperbolicity in dimension two. Our main results are: -- A very generic surface in $\mathbb{P}^3$ of degree at least $17$ is Kobayashi hyperbolic. -- The complement of a {\em generic}…
In this article, we study some properties of deformation invariance of the Gamma-dimension (defined for X a compact k\"ahler manifold). This birational invariant is defined as the codimension of the maximal compact subvarieties in the…
A family of holomorphic vector bundles is constructed on a complex manifold $X$. The space of the holomorphic sections of these bundles are calculated in certain cases. As an application, if $X$ is an $N$-dimensional compact K\"ahler…