392 research outputs found
Embeddings of SL(2,Z) into the Cremona group
Geometric and dynamic properties of embeddings of SL(2,Z) into the Cremona
group are studied. Infinitely many non-conjugate embeddings which preserve the
type (i.e. which send elliptic, parabolic and hyperbolic elements onto elements
of the same type) are provided. The existence of infinitely many non-conjugate
elliptic, parabolic and hyperbolic embeddings is also shown.
In particular, a group G of automorphisms of a smooth surface S obtained by
blowing-up 10 points of the complex projective plane is given. The group G is
isomorphic to SL(2,Z), preserves an elliptic curve and all its elements of
infinite order are hyperbolic.Comment: to appear in Transformation Group
Symetries birationnelles des surfaces feuilletees
We provide a classification of complex projective surfaces with a holomorphic
foliation whose group of birational symetries is infinite.Comment: 42 pages, 2 figure
Normal subgroups in the Cremona group (long version)
Let k be an algebraically closed field. We show that the Cremona group of all
birational transformations of the projective plane P^2 over k is not a simple
group. The strategy makes use of hyperbolic geometry, geometric group theory,
and algebraic geometry to produce elements in the Cremona group that generate
non trivial normal subgroups.Comment: With an appendix by Yves de Cornulier. Numerous but minors
corrections were made, regarding proofs, references and terminology. This
long version contains detailled proofs of several technical lemmas about
hyperbolic space
Structure-dependent mobility of a dry aqueous foam flowing along two parallel channels
The velocity of a two-dimensional aqueous foam has been measured as it flows
through two parallel channels, at a constant overall volumetric flow rate. The
flux distribution between the two channels is studied as a function of the
ratio of their widths. A peculiar dependence of the velocity ratio on the width
ratio is observed when the foam structure in the narrower channel is either
single staircase or bamboo. In particular, discontinuities in the velocity
ratios are observed at the transitions between double and single staircase and
between single staircase and bamboo. A theoretical model accounting for the
viscous dissipation at the solid wall and the capillary pressure across a film
pinned at the channel outlet predicts the observed non-monotonic evolution of
the velocity ratio as a function of the width ratio. It also predicts
quantitatively the intermittent temporal evolution of the velocity in the
narrower channel when it is so narrow that film pinning at its outlet
repeatedly brings the flow to a near stop
Microwave probes Dipole Blockade and van der Waals Forces in a Cold Rydberg Gas
We show that microwave spectroscopy of a dense Rydberg gas trapped on a
superconducting atom chip in the dipole blockade regime reveals directly the
dipole-dipole many-body interaction energy spectrum. We use this method to
investigate the expansion of the Rydberg cloud under the effect of repulsive
van der Waals forces and the breakdown of the frozen gas approximation. This
study opens a promising route for quantum simulation of many-body systems and
quantum information transport in chains of strongly interacting Rydberg atoms.Comment: PACS: 03.67.-a, 32.80.Ee, 32.30.-
Mechanical probing of liquid foam aging
We present experimental results on the Stokes experiment performed in a 3D
dry liquid foam. The system is used as a rheometric tool : from the force
exerted on a 1cm glass bead, plunged at controlled velocity in the foam in a
quasi static regime, local foam properties are probed around the sphere. With
this original and simple technique, we show the possibility of measuring the
foam shear modulus, the gravity drainage rate and the evolution of the bubble
size during coarsening
Influence of shear flow on vesicles near a wall: a numerical study
We describe the dynamics of three-dimensional fluid vesicles in steady shear
flow in the vicinity of a wall. This is analyzed numerically at low Reynolds
numbers using a boundary element method. The area-incompressible vesicle
exhibits bending elasticity. Forces due to adhesion or gravity oppose the
hydrodynamic lift force driving the vesicle away from a wall. We investigate
three cases. First, a neutrally buoyant vesicle is placed in the vicinity of a
wall which acts only as a geometrical constraint. We find that the lift
velocity is linearly proportional to shear rate and decreases with increasing
distance between the vesicle and the wall. Second, with a vesicle filled with a
denser fluid, we find a stationary hovering state. We present an estimate of
the viscous lift force which seems to agree with recent experiments of Lorz et
al. [Europhys. Lett., vol. 51, 468 (2000)]. Third, if the wall exerts an
additional adhesive force, we investigate the dynamical unbinding transition
which occurs at an adhesion strength linearly proportional to the shear rate.Comment: 17 pages (incl. 10 figures), RevTeX (figures in PostScript
Post-critical set and non existence of preserved meromorphic two-forms
We present a family of birational transformations in depending on
two, or three, parameters which does not, generically, preserve meromorphic
two-forms. With the introduction of the orbit of the critical set (vanishing
condition of the Jacobian), also called ``post-critical set'', we get some new
structures, some "non-analytic" two-form which reduce to meromorphic two-forms
for particular subvarieties in the parameter space. On these subvarieties, the
iterates of the critical set have a polynomial growth in the \emph{degrees of
the parameters}, while one has an exponential growth out of these subspaces.
The analysis of our birational transformation in is first carried out
using Diller-Favre criterion in order to find the complexity reduction of the
mapping. The integrable cases are found. The identification between the
complexity growth and the topological entropy is, one more time, verified. We
perform plots of the post-critical set, as well as calculations of Lyapunov
exponents for many orbits, confirming that generically no meromorphic two-form
can be preserved for this mapping. These birational transformations in ,
which, generically, do not preserve any meromorphic two-form, are extremely
similar to other birational transformations we previously studied, which do
preserve meromorphic two-forms. We note that these two sets of birational
transformations exhibit totally similar results as far as topological
complexity is concerned, but drastically different results as far as a more
``probabilistic'' approach of dynamical systems is concerned (Lyapunov
exponents). With these examples we see that the existence of a preserved
meromorphic two-form explains most of the (numerical) discrepancy between the
topological and probabilistic approach of dynamical systems.Comment: 34 pages, 7 figure
A characterization of compact complex tori via automorphism groups
We show that a compact Kaehler manifold X is a complex torus if both the
continuous part and discrete part of some automorphism group G of X are
infinite groups, unless X is bimeromorphic to a non-trivial G-equivariant
fibration. Some applications to dynamics are given.Comment: title changed, to appear in Math. An
Morphology of axisymmetric vesicles with encapsulated filaments and impurities
The shape deformation of a three-dimensional axisymmetric vesicle with
encapsulated filaments or impurities is analyzed by integrating a dissipation
dynamics. This method can incorporate systematically the constraint of a fixed
surface area and/or a fixed volume. The filament encapsulated in a vesicle is
assumed to take a form of a rod or a ring so as to imitate cytoskeletons. In
both cases, results of the shape transition of the vesicle are summarized in
phase diagrams in the phase space of the vesicular volume and a rod length or a
ring radius.
We also study the dynamics of a vesicle with impurities coupled to the
membrane curvature. The phase separation and the associated shape deformation
in the early stage of the dynamical evolution can well be explained by the
linear stability analysis. Long runs of simulation demonstrate the nonlinear
coarsening of the wavy deformation of the vesicle in the late stage.Comment: 9 pages, 9 figure
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