BENZAQUEN Michael

Recent empirical analyses have revealed the existence of the Zumbach effect. This discovery led to the development of the quadratic Hawkes process, adapted to reproduce this effect. Since this model does not relate to the price formation process, we extended it to the order book with a generalized quadratic Hawkes process (GQ-Hawkes). Using market data, we show that there is a Zumbach-like effect that decreases future liquidity. Microfounding the Zumbach effect, it is responsible for a potential destabilization of financial markets. Moreover, the exact calibration of a QM-Hawkes process tells us that markets are at the edge of criticality. This empirical evidence has therefore prompted us to analyze an order book model constructed with a Zumbach-type coupling. We therefore introduced the Santa Fe quadratic model and proved numerically that there is a phase transition between a stable market and an unstable market subject to liquidity crises. Thanks to a finite size analysis we were able to determine the critical exponents of this transition, belonging to a new universality class. Not being analytically solvable, this led us to introduce simpler models to describe liquidity crises. Putting aside the microstructure of the order book, we obtain a class of spread models where we have computed the critical parameters of their transitions. Even if these exponents are not those of the Santa Fe quadratic transition, these models open new horizons to explore the spread dynamics. One of them has a nonlinear coupling that reveals a metastable state. This elegant alternative scenario does not need critical parameters to obtain an unstable market, even if the empirical evidence is not in its favor. Finally, we looked at order book dynamics from another angle: reaction-diffusion. We modeled a liquidity that reveals itself in the order book with a certain frequency. Solving this model in equilibrium reveals that there is a stability condition on the parameters beyond which the order book empties completely, corresponding to a liquidity crisis. By calibrating it on market data, we were able to qualitatively analyze the distance to this unstable region.

Once immersed in a liquid saturated with surfactants, a microdrop composed of water or oil can self-propel at a speed of a few rays per second. Although the exact physico-chemical origin of this phenomenon is still debated, recent work has shown that it is linked to the solubilization of these drops in their medium. An active drop appears to emit a set of chemical species, called solute, which increases the surface tension. Consequently, an inhomogeneous distribution of solute at the interface of the drop generates a so-called Marangoni flow that propels the drop. The self-propulsion is then explained by an instability resulting from the coupling between the transport dynamics of the solute and the resulting Marangoni flow.This thesis aims to study the interactions between several of these drops or in the presence of confinement. The first chapter introduces general notions of low Reynolds fluid mechanics as well as a description of experimentally studied active droplet systems. The second chapter presents the mathematical framework modeling the self-propulsion of a single drop, and then provides a discussion dealing with the hydro-chemical interactions expected in the presence of several drops or a wall. The third chapter presents an exact derivation of the hydro-chemical interactions between an active drop and a wall in the axisymmetric case. This approach allowed to quantify the influence of the solute advection on the collision dynamics and to raise delay effects occurring at high Peclet number. In the fourth chapter, we study the consequences on the collision dynamics of a size difference between two active drops. It is then shown that even a small difference in radius can lead to very different regimes called rebound, pursuit and pause. The fifth chapter introduces a simplified model of the dynamics of an active drop, used in the study of oblique collisions. If a symmetrical collision tends to align the drops, asymmetrical initial conditions can conversely disperse them. Finally, the sixth chapter brings the conclusion of this manuscript and suggests various perspectives for the further study of active drop interactions.

We derive analytical formulas for the wake and wave drag of a disturbance moving arbitrarily at the air-water interface. We show that, provided a constant velocity is reached in finite time, the unsteady surface displacement converges to its well-known steady counterpart as given by Havelock's famous formula. Finally we assess, in a specific situation, to which extent one can rightfully use Havelock's steady wave drag formula for non-uniform motion (quasi-static). Such an approach can be used to legitimize or discredit a number of studies which used steady wave drag formulas in unsteady situations.

Anticipating client needs is crucial for any company - this is especially true for investment banks such as BNP Paribas Corporate and Institutional Banking given their role in the financial markets. This thesis focuses on the problem of predicting future customer interests in the financial markets, with a particular emphasis on the development of ad hoc algorithms designed to solve specific problems in the financial world.This manuscript consists of five chapters, divided as follows:- Chapter 1 presents the problem of predicting future customer interests in the financial markets. The purpose of this chapter is to provide the reader with all the keys necessary for a good understanding of the rest of this thesis. These keys are divided into three parts: a highlighting of the datasets available to us for solving the future interest prediction problem and their characteristics, a non-exhaustive overview of the algorithms that can be used to solve this problem, and the development of metrics to evaluate the performance of these algorithms on our datasets. This chapter closes with the challenges that can be encountered when designing algorithms to solve the problem of predicting future interests in finance, challenges that will be, in part, solved in the following chapters: - Chapter 2 compares some of the algorithms introduced in Chapter 1 on a dataset from BNP Paribas CIB, and highlights the difficulties encountered when comparing algorithms of different nature on the same dataset, as well as some ways to overcome these difficulties. This comparison puts into practice classical recommendation algorithms only considered from a theoretical point of view in the previous chapter, and allows us to acquire a more detailed understanding of the different metrics introduced in chapter 1 through the analysis of the results of these algorithms. Chapter 3 introduces a new algorithm, Experts Network, i.e., a network of experts, designed to solve the problem of heterogeneous behavior of investors in a given market through an original neural network architecture, inspired by research on expert mixtures. In this chapter, this new methodology is used on three distinct datasets: a synthetic dataset, an open access dataset, and a dataset from BNP Paribas CIB. Chapter 4 also introduces a new algorithm, called History-augmented collaborative filtering, which proposes to augment the classical matrix factorization approaches with the help of the interaction histories of the considered customers and products. This chapter continues the study of the dataset studied in Chapter 2 and extends the introduced algorithm with many ideas. Specifically, this chapter adapts the algorithm to address the cold start problem, i.e., the inability of a recommender system to provide predictions for new users, as well as a new application case on which this adaptation is tried.- Chapter 5 highlights a collection of ideas and algorithms, both successful and unsuccessful, that have been tried in the course of this thesis. This chapter closes with a new algorithm combining the ideas of the algorithms introduced in chapters 3 and 4.

Several optimization problems - in water or at the interface with air - are addressed, ranging from the optimization of the shape of boat hulls to that of propulsion in rowing and fin swimming. Theoretical, experimental and numerical approaches are combined. We first develop a minimal theoretical approach to determine, for a given immersed volume and power, the optimal aspect ratios of boat hulls, which are discussed and compared to the aspect ratios of real boats. The effect of fore-and-aft hull asymmetry is then discussed. In a second part, we study propulsion in rowing and finning. In the case of rowing, we revisit the issue of the synchronization of the rowers on the boat using a model of a robotic boat and investigate which synchronization allows the crew to go the fastest. Finally, we analyze the effect of fin geometry to find the optimal swimming strategies.

Hydrodynamic slip, the motion of a liquid along a solid surface, represents a fundamental phenomenon in fluid dynamics that governs liquid transport at small scales. For polymeric liquids, de Gennes predicted that the Navier boundary condition together with polymer reptation implies extraordinarily large interfacial slip for entangled polymer melts on ideal surfaces. this Navier-de Gennes model was confirmed using dewetting experiments on ultrasmooth, low-energy substrates. Here, we use capillary leveling—surface tension driven flow of films with initially non-uniform thickness—of polymeric films on these same substrates. Measurement of the slip length from a robust one parameter fit to a lubrication model is achieved. We show that at the low shear rates involved in leveling experiments as compared to dewetting ones, the employed substrates can no longer be considered ideal. The data is instead consistent with a model that includes physical adsorption of polymer chains at the solid/liquid interface.

We perform an experimental and theoretical study of the wave pattern generated by the leg strokes of water striders during a propulsion cycle. Using the synthetic schlieren method, we are able to measure the dynamic response of the free surface accurately. In order to match experimental conditions, we extend Bühler's theory of impulsive forcing (J. Fluid Mech., vol. 573, 2007, pp. 211-236) to finite depth. We demonstrate the improved ability of this approach to reproduce the experimental findings, once the observed continuous forcing and hence non-zero temporal and spatial extent of the leg strokes is also taken into account.

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We report on how the relaxation of patterns prepared on a thin film can be controlled by manipu- lating the symmetry of the initial shape. The validity of a lubrication theory for the capillary-driven relaxation of surface profiles is verified by atomic force microscopy measurements, performed on films that were patterned using focused laser spike annealing. In particular, we observe that the shape of the surface profile at late times is entirely determined by the initial symmetry of the perturba- tion, in agreement with the theory. Moreover, in this regime the perturbation amplitude relaxes as a power-law in time, with an exponent that is also related to the initial symmetry. The results have relevance in the dynamical control of topographic perturbations for nanolithography and high density memory storage.

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We present results on the dynamics of liquid interfaces at different scales. In the first part, we study confined liquid systems in the framework of the lubrication approximation. We obtain interesting analytical and numerical results on the thin film equation that governs the dynamics of such systems. The theoretical results are successfully confronted with atomic force microscopy experiments on polymer thin films in different geometries. We explore the physics resulting from the inherent effects of the nature of polymeric materials such as viscoelasticity, wall sliding and dynamics near the glass transition temperature. In the second part, we focus on the wake generated by the motion of a perturbation at the liquid-air interface. Motivated by experimental results that seem to challenge Kelvin's theory of the wake, we show that two angles can be distinguished in the wake. The angle formed by the edges of the domain is indeed constant, in accordance with Kelvin's theory, while the angle described by the waves of higher amplitude decreases with the Froude number. We also look at gravitocapillary waves and are particularly interested in the effects of finite size on the wave resistance. The two parts can be approached independently.

The capillary levelling of cylindrical holes in viscous polystyrene films was studied using atomic force microscopy as well as quantitative analytical scaling arguments based on thin film theory and self-similarity. The relaxation of the holes was shown to consist of two different time regimes: an early regime where opposing sides of the hole do not interact, and a late regime where the hole is filling up. For the latter, the self-similar asymptotic profile was derived analytically and shown to be in excellent agreement with experimental data. Finally, a binary system of two holes in close proximity was investigated where the individual holes fill up at early times and coalesce at longer times.

We present a theoretical study of gravity waves generated by an anisotropic moving disturbance. We model the moving object by an elliptical pressure field of given aspect ratio $\mathcal W$. We study the wake pattern as a function of $\mathcal W$ and the longitudinal hull Froude number $Fr = V/\sqrt{gL}$, where $V$ is the velocity, $g$ the acceleration of gravity and $L$ the size of the disturbance in the direction of motion. For large hull Froude numbers, we analytically show that the rescaled surface profiles for which $\sqrt{\mathcal W}/Fr$ is kept constant coincide. In particular, the angle outside which the surface is essentially flat remains constant and equal to the Kelvin angle, and the angle corresponding to the maximum amplitude of the waves scales as $\sqrt{\mathcal W}/Fr$, thus showing that previous work on the wake's angle for isotropic objects can be extended to anisotropic objects of given aspect ratio. We then focus on the wave resistance and discuss its properties in the case of an elliptical Gaussian pressure field. We derive an analytical expression for the wave resistance in the limit of very elongated objects, and show that the position of the speed corresponding to the maximum wave resistance scales as $\sqrt{gL}/\sqrt{\mathcal W}$.

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Gravity waves generated by an object moving at constant speed at the water surface form a specific pattern commonly known as the Kelvin wake. It was proved by Lord Kelvin that such a wake is delimited by a constant angle $\simeq 19.47^\circ$. However a recent study by Rabaud and Moisy based on the observation of airborne images showed that the wake angle seems to decrease as the Froude number $Fr$ increases, scaling as $Fr^{-1}$ for large Froude numbers. To explain such observations the authors make the strong hypothesis that an object of size $b$ cannot generate wavelengths larger than $b$. With no need of such an assumption and modelling the moving object by an axisymmetric pressure field, we analytically show that the angle corresponding to the maximum amplitude of the waves scales as $Fr^{-1}$ for large Froude numbers, whereas the angle delimiting the wake region outside which the surface is essentially flat remains constant and equal to the Kelvin angle for all $Fr$.

Using a thermodynamical approach, we calculate the deformation of a spherical elastic particle placed on a rigid substrate, under zero external load, and including an ingredient of importance in soft matter: the interfacial tension of the cap. In a first part, we limit the study to small deformation. In contrast with previous studies, we obtain an expression for the energy that precisely contains the JKR and Young–Dupre asymptotic regimes, and which establishes a continuous bridge between them. In the second part, we consider the large deformation case, which is relevant for future comparison with numerical simulations and experiments on very soft materials. Using a fruitful analogy with fracture mechanics, we derive the exact energy of the problem and thus obtain the equilibrium state for any given choice of physical parameters.

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We present an analytical and numerical study of the two-dimensional capillary-driven thin-film equation. In particular, we focus on the intermediate asymptotics of its solutions. Linearising the equation enables us to derive the associated Green's function and therefore obtain a complete set of solutions. Moreover, we show that the rescaled solution for any summable initial profile uniformly converges in time towards a universal self-similar attractor that is precisely the rescaled Green's function. Finally, a numerical study on compact-support initial profiles enables us to conjecture the extension of our results to the nonlinear equation.