arXiv subjects

Pierre Guillot

Publications and source records attributed to Pierre Guillot.

26 records · Page 2Linked to original sources

arXiv2009

Extracting the hydrodynamic resistance of droplets from their behavior in microchannel networks

The overall traffic of droplets in a network of microfluidic channels is strongly influenced by the liquid properties of the moving droplets. In particular, the effective hydrodynamic resistance of individual droplets plays a key role in their global behavior. We here propose two simple and low-cost experimental methods for measuring this parameter by analyzing the dynamics of a regular sequence of droplets injected into an "asymmetric loop" network. The choice of a droplet taking either route through the loop is influenced by the presence of previous droplets which modulate the hydrodynamic resistance of the branches they are sitting in. We propose to extract the effective resistance of a droplet from easily observable time series, namely from the choices the droplets make at junctions and from the inter-droplet distances. This becomes possible when utilizing a recently proposed theoretical model, based on a number of simplifying assumptions. We here present several sets of measurements of the hydrodynamic resistance of droplets, expressed in terms of a "resistance length". The aim is twofold, (1) to reveal its dependence on a number of parameters, such as the viscosity, the volume of droplets, their velocity as well as the spacing between them. At the same time (2), by using a standard measurement technique, we compare the limitations of the proposed methods. As an important result of this comparison we obtain the range of validity of the simplifying assumptions made in the theoretical model.

physics.flu-dyn↗

arXiv2008

Spatiotemporal instability of a confined capillary jet

Recent experimental studies on the instability appearance of capillary jets have revealed the capabilities of linear spatiotemporal instability analysis to predict the parametrical map where steady jetting or dripping takes place. In this work, we present an extensive analytical, numerical and experimental analysis of confined capillary jets extending previous studies. We propose an extended, accurate analytic model in the limit of low Reynolds flows, and introduce a numerical scheme to predict the system response when the liquid inertia is not negligible. Theoretical predictions show a remarkable accuracy with results from the extensive experimental exploration provided.

physics.flu-dyn↗

arXiv2008

The Chow rings of $G_2$ and $Spin_7$

We compute $CH^*BG_2$ and $CH^*BSpin_7$, using in particular the stratification method introduced by Vezzosi. We also give some information on the Chow rings of the finite groups $G_2(q)$. This new version includes an appendix, which will be published on its own as an addendum. It explains how one can use our results to produce a counter-example to the conjecture, due to Totaro, which predicted that the Chow ring of a finite group was generated by transfers of Chern classes.

math.AG↗

arXiv2007

Geometric methods for cohomological invariants

We explain how to exploit Rost's theory of Chow groups with coefficients to carry some computations of cohomological invariants (i.e. characteristic classes for G-torsors in Galois cohomology, for an algebraic group G). In particular, we use the idea of the ``stratification method'' introduced by Vezzosi. We recover a number of known results, with very different proofs. We obtain some new information on spin groups..

math.AG↗

arXiv2006

Adams operations in cohomotopy

We study a collection of operations on the cohomotopy of any space, with which it becomes a "beta-ring", an algebraic structure analogous to a lambda-ring. In particular, this ring possesses Adams operations, represented by maps on the infinite loop space of the sphere spectrum. We compute their effect in homotopy on the image of J, and in mod 2 cohomology. The motivation comes from the interpretation of the symmetric group as the general linear group of the "field with one element", which leads to an analogy between cohomotopy and algebraic K-theory. A good deal of this article may be considered as a survey of the theory of beta-rings.

math.AT↗

arXiv2005

The representation ring of a simply-connected Lie group as a lambda-ring

Adams and Conway have stated without proof a result which says, roughly speaking, that the representation ring $R(G)$ of a compact, connected Lie group $G$ is generated as a $λ$-ring by elements in 1-to-1 correspondance with the branches of the Dynkin diagram. In this note we present an elementary proof of this.

math.RT↗

arXiv2004

Steenrod operations on the Chow ring of a classifying space

We use the Steenrod algebra to study $CH^*BG$, the mod $p$ Chow ring of the classifying space of $G$. We describe a localization property which relates a given $G$ to its elementary abelian subgroups, and we study a number of particular cases, namely symmetric groups and Chevalley groups. It turns out that the Chow rings of these groups are completely determined by the abelian subgroups and their fusion.

math.AG↗

arXiv2004

Chow rings and cobordism of some Chevalley groups

We compute the cobordism ring $MU^*(BG)\otimes \mathbb{F}_p$ when $G$ is a Chevalley group. In the particular case of the general linear group, we prove that it agrees with the Chow ring (as defined by Totaro).

math.AT↗