# INSTITUT DE MATHEMATIQUES DE BOURGOGNE

UMR 5584

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• ### [hal-01648248] Families of rational solutions of order $6$ to the KPI equation depending on 10 parameters.

27 novembre 2017, par Pierre Gaillard
Here we constuct rational solutions of order 6 to the Kadomtsev-Petviashvili equation (KPI) as a quotient of 2 polynomials of degree 84 in x, y and t depending on 10 parameters. We verify that the maximum of modulus of these solutions at order 6 is equal to 2(2N + 1) 2 = 338. We study the (...)
• ### [hal-01326790] Optimal strokes at low Reynolds number : a geometric and numerical study of Copepod and Purcell swimmers

23 novembre 2017, par Piernicola Bettiol, Bernard Bonnard, Jérémy Rouot
In this article, we provide a comparative geometric and numerical analysis of optimal strokes for two different rigid links swimmer models at low Reynolds number: the Copepod swimmer (a symmetric swimmer recently introduced by [31]) and the long-standing three-link Purcell swimmer [29]. The (...)
• ### [hal-01442880] Sub-Riemannian geometry and swimming at low Reynolds number : the Copepod case

23 novembre 2017, par Piernicola Bettiol, Bernard Bonnard, Alice Nolot, Jérémy Rouot
Based on copepod observations, Takagi proposed a model to interpret the swimming behavior of these microorganisms using sinusoidal paddling or sequential paddling followed by a recovery stroke in unison, and compares them invoking the concept of efficiency. Our aim is to provide an (...)
• ### [hal-01504996] On codimension two embeddings up to link-homotopy

31 octobre 2017, par Benjamin Audoux, Jean-Baptiste Meilhan, Emmanuel Wagner
We consider knotted annuli in 4–space, called 2–string-links, which are knotted surfaces in codi-mension two that are naturally related, via closure operations, to both 2–links and 2–torus links. We classify 2–string-links up to link-homotopy by means of a 4–dimensional version of Milnor invariants. (...)
• ### [hal-01622447] Deformations of $\mathbb{A}^1$-cylindrical varieties

27 octobre 2017, par Adrien Dubouloz, Takashi Kishimoto
An algebraic variety is called $\mathbbA^1$-cylindrical if it contains an $\mathbbA^1$-cylinder, i.e. a Zariski open subset of the form $Z\times\mathbbA^1$ for some algebraic variety $Z$. We show that the generic fiber of a family $f:X\rightarrow S$ of normal $\mathbbA^1$-cylindrical varieties (...)

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