Le prix de l'individualité. Maine de Brian, Samuel Taylor Coleridge et la volonté: Deux postétités distinctes

This thesis is concerned with Maine de Biran’s and Samuel Taylor Coleridge’s conceptions of will, and the way in which both thinkers’ posterities have been affected by the central role of these very conceptions in their respective bodies of thought. The research question that animates this work can therefore be divided into two main parts, one of which deals with will, while the other deals with its effects on posterity. In the first pages of the Introduction, I make the case for a comparison between two philosophers, and show how this comparison can bring one closer to truth, understood not in objective, but in subjective terms. I then justify my choice by underlining that, in spite of their many differences, Maine de Biran and Samuel Taylor Coleridge followed comparable paths, intellectually and spiritually, and came to similar conclusions concerning the essential activity of the human mind. Finally, I ask whether it is possible that this very focus on the human will may have contributed to the state of both thinkers’ works and of the reception of those works. This prologue is followed by five parts. In the first part, the similarities and differences between the two thinkers are explored further. In the second part, the connections between philosophy and singularity are examined, in order to show the ambivalence of the will as a foundation for truth. The third part is dedicated to the traditional division between subject and object in psychology, and its relevance in history and in moral philosophy. The fourth part tackles the complexity of the question of influence, with respect to both Maine de Biran’s and Coleridge’s cases, both thinkers being indebted to many philosophers of all times and places, and having to rely heavily on others for the publication, or the interpretation of their own works. The fifth part is concerned with the different aspects of the faculty of will, and primarily its relationship with interiority, as incommensurability, and actual, conditioned existence in a certain historical and spatial context. It ends with a return to the question of will and posterity and an announcement of what will be covered in the main body of the thesis. The main body is divided into three parts:‘L’émancipation’, ‘L’affirmation, and ‘La projection’. The first part is devoted to the way Maine de Biran and Samuel Taylor Coleridge extricated themselves from one epistemological paradigm to contribute to the foundation of another. It is divided in four chapters. The first chapter deals with the aforementioned change of paradigm, as corresponding to the emergence of two separate but associated movements, Romanticism and what the French philosopher refers to as ‘The Age of History’. The second chapter concerns the movement that preceded them, i.e. the Enlightenment, its main features according to both of our thinkers, and the two epistemological models that prevailed under it and influenced them heavily in their early years: Sensationism (Maine de Biran) and Associationism (Coleridge). The third chapter is about the probable influence of Immanuel Kant and his followers on Maine de Biran and Coleridge, and the various facts that allow us to claim originality for both thinkers’ works. In the fourth chapter, I contrast Maine de Biran and Coleridge with other movements and thinkers of their time, showing that, contrary to their respective thoughts, Maine de Biran and Coleridge could not but break free from the then prevailing systematic approach to truth. The second part of the thesis is concerned with the first part of its research question, namely, Maine de Biran’s and Coleridge’s conceptions of the will. It is divided into four chapters. The first chapter is a reflection on the will as a paradox: on the one hand, the will cannot be caused by any other phenomenon, or it is no longer a will; but it cannot be left purely undetermined, as if it is, it is then not different from chance. It thus needs, in order to be, to be contradictorily already moral. The second chapter is a comparison between Maine de Biran’s and Coleridge’s accounts of the origin of the will, where it is found that the French philosopher only observes that he has a will, whereas the English philosopher postulates the existence of this will. The comparison between Maine de Biran’s and Coleridge’s conceptions of the will is pursued in the third chapter, which tackles the question of the coincidence between the will and the self, in both thinkers’ works. It ends with the fourth chapter, which deals with the question of the relationship between the will and what is other to it, i.e. bodily sensations, passions and desires. The third part of the thesis focuses on the second part of its research question, namely the posterity of Maine de Biran’s and Coleridge’s works. It is divided into four chapters. The first chapter constitutes a continuation of the last chapter of the preceding part, in that that it deals with Maine de Biran’s and Coleridge’s relations to the ‘other’, and particularly their potential and actual audience, and with the way these relations may have affected their writing and publishing practices. The second chapter is a survey of both thinkers’ general reception, where it is found that, while Maine de Biran has been claimed by two important movements of thoughts as their initiator, Coleridge has been neglected by the only real movement he could have, or may indeed have pioneered. The third chapter is more directly concerned with the posterities of Maine de Biran’s and Coleridge’s conceptions of will, and attempts to show that the approach to, and the meaning of the will have evolved throughout the nineteenth century, and in the French Spiritualist and the British Idealist movements, from an essentially personal one to a more impersonal one. The fourth chapter is a partial conclusion, whose aim is to give a precise idea of where Maine de Biran and Coleridge stand, in relation to their century and to the philosophical movements and matters we are concerned with. The conclusion is a recapitulation of what has been found, with a particular emphasis on the dialogue initiated between Maine de Biran and Coleridge on the will, and the relation between will and posterity. It suggests that both thinkers have to pay the price of a problematic reception for the individuality that pervades their respective works, and goes further in suggesting that s/he who chooses to found his individuality on the will is bound to feel this incompleteness in his/her own personal life more acutely than s/he who does not. It ends with a reflection on fixedness and movement, as the two antagonistic states that the theoretician of the will paradoxically aspires to.

Hairpin vortex solution in planar Couette flow: a tapestry of knotted vortices

A numerical continuation method has been carried out seeking solutions for two distinct flow configurations, planar Couette flow (PCF) and laterally heated flow in a vertical slot (LHF). We found that the spanwise vortex solution in LHF identifies a new solution in PCF. The vortical structure of our new solution has the shape of a hairpin observed ubiquitously in high-Reynolds-number turbulent flow, and we believe this discovery may provide the paradigm for a hierarchical organization of coherent structures in turbulent shear layers.

Characterization of the hairpin vortex solution in plane Couette flow

Quantitative evidence that establishes the existence of the hairpin vortex state (HVS) in plane Couette flow (PCF) is provided in this work. The evidence presented in this paper shows that the HVS can be obtained via homotopy from a flow with a simple geometrical configuration, namely, the laterally heated flow (LHF). Although the early stages of bifurcations of LHF have been previously investigated, our linear stability analysis reveals that the root in the LHF yields multiple branches via symmetry breaking. These branches connect to the PCF manifold as steady nonlinear amplitude solutions. Moreover, we show that the HVS has a direct bifurcation route to the Rayleigh-Bénard convection. © 2010 The American Physical Society.

Modelling vortex formation in an unbaffled stirred tank reactors

Agitating liquids in unbaffled stirred tank leads to the formation of a vortex in the region of the impeller shaft when operating in the turbulent flow regime. A numerical model is presented here that captures such a vortex. The volume of fluid model, a multiphase flow model was employed in conjunction with a multiple reference frame model and the shear stress turbulence model. The dimensions of the tank considered here, were 0.585 m for the liquid depth and tank diameter with a 0.2925 m diameter impeller at a height of 0.2925 m. The impeller considered was an eight-bladed paddle type agitator that was rotating with an angular velocity of 7.54 rad s (72 rpm) giving a Reynolds number of 10 and Froude number of 0.043. Preliminary results of a second investigation into the effect of liquid phase properties on the vortex formed are also presented. © 2006 Elsevier B.V. All rights reserved.

Vortex shedding from a row of square bars

Interactions of wakes in a flow past a row of square bars, which is placed across a uniform flow, are investigated by numerical simulations and experiments on the tassumption that the flow is two-dimensional and incompressible. At small Reynolds numbers the flow is steady and symmetric with respect not only to streamwise lines through the center of each square bar but also to streamwise centerlines between adjacent square bars. However, the steady symmetric flow becomes unstable at larger Reynolds numbers and make a transition to a steady asymmetric flow with respect to the centerlines between adjacent square bars in some cases or to an oscillatory flow in other cases. It is found that vortices are shed synchronously from adjacent square bars in the same phase or in anti-phase depending upon the distance between the bars when the flow is oscillatory. The origin of the transition to the steady asymmetric flow is identified as a pitchfork bifurcation, while the oscillatory flows with synchronous shedding of vortices are clarified to originate from a Hopf bifurcation. The critical Reynolds numbers of the transitions are evaluated numerically and the bifurcation diagram of the flow is obtained.

A note on the propagation of quantized vortex rings through a quantum turbulence tangle:energy transport or energy dissipation?

We investigate quantum vortex ring dynamics at scales smaller than the inter-vortex spacing in quantum turbulence. Through geometrical arguments and high-resolution numerical simulations, we examine the validity of simple estimates for the mean free path and the structure of vortex rings post-reconnection. We find that a large proportion of vortex rings remain coherent objects where approximately 75% of their energy is preserved. This leads us to consider the effectiveness of energy transport in turbulent tangles. Moreover, we show that in low density tangles, appropriate for the ultra-quantum regime, ring emission cannot be ruled out as an important mechanism for energy dissipation. However at higher vortex line densities, typically associated with the quasi-classical regime, loop emission is expected to make a negligible contribution to energy dissipation, even allowing for the fact that our work shows rings can survive multiple reconnection events. Hence the Kelvin wave cascade seems the most plausible mechanism leading to energy dissipation

Universal profile of the vortex condensate in two-dimensional turbulence

An inverse turbulent cascade in a restricted two-dimensional periodic domain creates a condensate—a pair of coherent system-size vortices. We perform extensive numerical simulations of this system and carry out theoretical analysis based on momentum and energy exchanges between the turbulence and the vortices. We show that the vortices have a universal internal structure independent of the type of small-scale dissipation, small-scale forcing, and boundary conditions. The theory predicts not only the vortex inner region profile, but also the amplitude, which both perfectly agree with the numerical data.

Vortex-density fluctuations, energy spectra, and vortical regions in superfluid turbulence

Measurements of the energy spectrum and of the vortex-density fluctuation spectrum in superfluid turbulence seem to contradict each other. Using a numerical model, we show that at each instance of time the total vortex line density can be decomposed into two parts: one formed by metastable bundles of coherent vortices, and one in which the vortices are randomly oriented. We show that the former is responsible for the observed Kolmogorov energy spectrum, and the latter for the spectrum of the vortex line density fluctuations.

Kelvin-wave cascade in the vortex filament model

The small-scale energy-transfer mechanism in zero-temperature superfluid turbulence of helium-4 is still a widely debated topic. Currently, the main hypothesis is that weakly nonlinear interacting Kelvin waves (KWs) transfer energy to sufficiently small scales such that energy is dissipated as heat via phonon excitations. Theoretically, there are at least two proposed theories for Kelvin-wave interactions. We perform the most comprehensive numerical simulation of weakly nonlinear interacting KWs to date and show, using a specially designed numerical algorithm incorporating the full Biot-Savart equation, that our results are consistent with the nonlocal six-wave KW interactions as proposed by L'vov and Nazarenko.