This fascinating book, penned by Luc Tartar of America’s Carnegie Mellon University, starts from the premise that equations of state are not always effective in continuum mechanics. Tartar relies on H-measures, a tool created for homogenization, to explain some of the weaknesses in the theory. These include looking at the subject from the point of view of quantum mechanics. Here, there are no "particles", so the Boltzmann equation and the second principle, can’t apply.
Homogenization is not about periodicity, or Gamma-convergence, but about understanding which effective equations to use at macroscopic level, knowing which partial differential equations govern mesoscopic levels, without using probabilities (which destroy physical reality); instead, one uses various topologies of weak type, the G-convergence of Sergio Spagnolo, the H-convergence of François Murat and the author, and some responsible for the appearance of nonlocal effects, which many theories in continuum mechanics or physics guessed wrongly. For a better understanding of 20th century science, new mathematical tools must be introduced, like the author’s H-measures, variants by Patrick Gérard, and others yet to be discovered.
After publishing an introduction to the Navier–Stokes equation and oceanography (Vol. 1 of this series), Luc Tartar follows with another set of lecture notes based on a graduate course in two parts, as indicated by the title. A draft has been available on the internet for a few years. The author has now revised and polished it into a text accessible to a larger audience.
This text corresponds to a graduate mathematics course taught at Carnegie Mellon University in the spring of 1999. Included are comments added to the lecture notes, a bibliography containing 23 items, and brief biographical information for all scientists mentioned in the text, thus showing that the creation of scientific knowledge is an international enterprise.
This book is the first volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume I is divided into 23 chapters plus two appendices on Banach and Hilbert spaces and on differential calculus. This volume focuses on the fundamental ideas regarding the construction of finite elements and their approximation properties. It addresses the all-purpose Lagrange finite elements, but also vector-valued finite elements that are crucial to approximate the divergence and the curl operators. In addition, it also presents and analyzes quasi-interpolation operators and local commuting projections. The volume starts with four chapters on functional analysis, which are packed with examples and counterexamples to familiarize the reader with the basic facts on Lebesgue integration and weak derivatives. Volume I also reviews important implementation aspects when either developing or using a finite element toolbox, including the orientation of meshes and the enumeration of the degrees of freedom.
This text presenting the mathematical theory of finite elements is organized into three main sections. The first part develops the theoretical basis for the finite element methods, emphasizing inf-sup conditions over the more conventional Lax-Milgrim paradigm. The second and third parts address various applications and practical implementations of the method, respectively. It contains numerous examples and exercises.
This book is the second volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume II is divided into 32 chapters plus one appendix. The first part of the volume focuses on the approximation of elliptic and mixed PDEs, beginning with fundamental results on well-posed weak formulations and their approximation by the Galerkin method. The material covered includes key results such as the BNB theorem based on inf-sup conditions, Céa's and Strang's lemmas, and the duality argument by Aubin and Nitsche. Important implementation aspects regarding quadratures, linear algebra, and assembling are also covered. The remainder of Volume II focuses on PDEs where a coercivity property is available. It investigates conforming and nonconforming approximation techniques (Galerkin, boundary penalty, Crouzeix—Raviart, discontinuous Galerkin, hybrid high-order methods). These techniques are applied to elliptic PDEs (diffusion, elasticity, the Helmholtz problem, Maxwell's equations), eigenvalue problems for elliptic PDEs, and PDEs in mixed form (Darcy and Stokes flows). Finally, the appendix addresses fundamental results on the surjectivity, bijectivity, and coercivity of linear operators in Banach spaces.
This book is the second volume of a compilation of lecture notes on various topics in nonlinear physics delivered by specialists during the summer schools organized by the Institut Non Linaeaire de Nice ... in Peyresq ... since 1998. The first volume, edited by R. Kaiser and J. Montaldi, contains courses from the years 1998 and 1999. This volume collects notes of the lectures given from the summers of 2000, 2001 and 2002"--Preface, v. 2.
The renowned philosopher contemplates the medium of drawing in “a book full of dazzling insights, imaginative curves and provocative renewals” (Sarah Clift, University of King’s College). In 2007, philosopher Jean-Luc Nancy curated an exhibition at the Museum of Fine Arts in Lyon. This book, originally written for that exhibition, explores the interplay between drawing and form—viewing the act of drawing as a formative force. Recalling that the terms ‘drawing’ and ‘design’ were once used interchangeably, Nancy notes that drawing designates a design that remains without project, plan, or intention. His argument offers a way of rethinking a number of historical terms (sketch, draft, outline, plan, mark, notation), which includes rethinking drawing in its graphic, filmic, choreographic, poetic, melodic, and rhythmic senses. For Nancy, drawing resists any kind of closure, and therefore never resolves a tension specific to itself. Drawing allows the gesture of a desire that remains in excess of all knowledge to come to appearance. Situating drawing in these terms, Nancy engages a number of texts in which Freud addresses the force of desire in the rapport between aesthetic and sexual pleasure, texts that also turn around questions concerning form in its formation. Between sections of his text, Nancy includes a series of “sketchbooks” on drawing, composed of quotations on art from different writers, artists, or philosophers.
Faith and reason, especially in Roman Catholic thought, are less contradictory today than ever. But does the supposed opposition even make sense to begin with? One can lose faith, but surely not because one gains in reason. Some, in fact, lose faith when reason is not able to make sense of the experiences of our lives. We very quickly realize that reason does not understand everything. Immense areas remain incomprehensible and irrational, which we abandon to belief and opinion. Soon we definitively renounce thinking what that has been excluded from the realm of the thinkable. Ideological nightmares arise from this slumber of reason. Thus, the separation between faith and reason, too quickly taken as self-evident and even natural, is born from a lack of rationality, an easy capitulatin of reason before what is supposedly unthinkable. Rather than lose faith through excessive rationality, we often lose rationality because faith is too quickly excluded from the realm that it claims to open, that of revelation. We lose reason by losing faith. Examining such topics as the role of the intellectual in the church, the rationality of faith, the infinite worth and incomprehensibility of the human, the phenomenality of the sacraments, and the phenomenological nature of miracles and of revelation more broadly, this book spans the range of Marion’s thought on Christianity. Throughout he stresses that faith has its own rationality, structured according to the logic of the gift that calls forth a response of love and devotion through kenotic abandon.
Philosophers have largely ignored sleep, treating it as a useless negativity, mere repose for the body or at best a source for the production of unconscious signs out of the night of the soul. In an extraordinary theoretical investigation written with lyric intensity, The Fall of Sleep puts an end to this neglect by providing a deft yet rigorous philosophy of sleep. What does it mean to "fall" asleep? Might there exist something like a "reason" of sleep, a reason at work in its own form or modality, a modality of being in oneself, of return to oneself, without the waking "self" that distinguishes "I" from "you" and from the world? What reason might exist in that absence of ego, appearance, and intention, in an abandon thanks to which one is emptied out into a non-place shared by everyone? Sleep attests to something like an equality of all that exists in the rhythm of the world. With sleep, victory is constantly renewed over the fear of night, an a confidence that we will wake with the return of day, in a return to self, to us--though to a self, an us, that is each day different, unforeseen, without any warning given in advance. To seek anew the meaning stirring in the supposed loss of meaning, of consciousness, and of control that occurs in sleep is not to reclaim some meaning already familiar in philosophy, religion, progressivism, or any other -ism. It is instead to open anew a source that is not the source of a meaning but that makes up the nature proper to meaning, its truth: opening, gushing forth, infinity. This beautiful, profound meditation on sleep is a unique work in the history of phenomenology--a lyrical phenomenology of what can have no phenomenology, since sleep shows itself to the waking observer, the subject of phenomenology, only as disappearance and concealment.
This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including the stabilization property of the damped wave equation and the null-controllability of the heat equation. All analysis is performed in the case of open sets in the Euclidean space; a second volume will extend this treatment to Riemannian manifolds. The first three chapters illustrate the derivation of Carleman estimates using pseudo-differential calculus with a large parameter. Continuation issues are then addressed, followed by a proof of the logarithmic stabilization of the damped wave equation by means of two alternative proofs of the resolvent estimate for the generator of a damped wave semigroup. The authors then discuss null-controllability of the heat equation, its equivalence with observability, and how the spectral inequality allows one to either construct a control function or prove the observability inequality. The final part of the book is devoted to the exposition of some necessary background material: the theory of distributions, invariance under change of variables, elliptic operators with Dirichlet data and associated semigroup, and some elements from functional analysis and semigroup theory.
First published in 1979 but never available in English until now, Ego Sum challenges, through a careful and unprecedented reading of Descartes’s writings, the picture of Descartes as the father of modern philosophy: the thinker who founded the edifice of knowledge on the absolute self-certainty of a Subject fully transparent to itself. While other theoretical discourses, such as psychoanalysis, have also attempted to subvert this Subject, Nancy shows how they always inadvertently reconstituted the Subject they were trying to leave behind. Nancy’s wager is that, at the moment of modern subjectivity’s founding, a foundation that always already included all the possibilities of its own exhaustion, another thought of “the subject” is possible. By paying attention to the mode of presentation of Descartes’s subject, to the masks, portraits, feints, and fables that populate his writings, Jean-Luc Nancy shows how Descartes’s ego is not the Subject of metaphysics but a mouth that spaces itself out and distinguishes itself.
The epoch of representation is as old as the West. Indeed, representation is the West, understood as what at once designates and expands its own limits. But what comes after the West? What comes after representation's disclosure of its own limit? The central problem posed in these essays, collected from over a decade of work, is how in the wake of Western ontologies to conceive the coming, the birth that characterizes being. We are now at the limit of representation, where objects as we experience them have been show to be merely objects of representation--or rather, of presentation, since there is nothing to (re)present. The first part of this book, "Existence," asks how, today, one can give sense of meaning to existence as such, arguing that existence itself, as it comes nude into the world, must now be our "sense." In examining what this birth to presence might be, we should not ask what presence "is"; rather we should conceive presence as presence to someone, including to presence itself. This birth is not the constitution of an identity, but the endless departure of an identity from, and from within, its other, or others. Its coming is not desire but jouissance, the joy of averring oneself to be continually in the state of being born--a rejoicing of birth, a birth of rejoicing. The second section, "Poetry," asks: What art exposes this? In writing, in the voice, in painting? And what if art is exposed to it? How does it inscribe (or rather, "exscribe," in a term the book develops) the coming existence as such? The author's trajectory in this book crosses those of Hegel, Schlegel, Baudelaire, Nietzsche, Freud, and Heidegger, in their comments on art and politics, existence and corporeality, everyday life and its modes of existence and ecstasy. An analysis that dares this crossing involves all the varied accounts of existence, political as well as philosophical, and all the realms of poverty.
Exploring the ever-changing philosophy of city life with Jean-Luc Nancy In The City in the Distance, Jean-Luc Nancy embarks on nothing less than a philosophy of the city. Drawing on his widely discussed accounts of sense and of the fraught question of community, Nancy views the city as the site of a disposition that is constantly undergoing metamorphoses. Far from an abstract account, Nancy attends in the most concrete way possible to the workings of a city not typically taken as paradigmatic, Los Angeles. As Jean-Christophe Bailly suggests in his foreword, Nancy joins Walter Benjamin in thinking the city not from an external vantage point, but on its own terms.
This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including quantified unique continuation, logarithmic stabilization of the wave equation, and null-controllability of the heat equation. Where the first volume derived these estimates in regular open sets in Euclidean space and Dirichlet boundary conditions, here they are extended to Riemannian manifolds and more general boundary conditions. The book begins with the study of Lopatinskii-Sapiro boundary conditions for the Laplace-Beltrami operator, followed by derivation of Carleman estimates for this operator on Riemannian manifolds. Applications of Carleman estimates are explored next: quantified unique continuation issues, a proof of the logarithmic stabilization of the boundary-damped wave equation, and a spectral inequality with general boundary conditions to derive the null-controllability result for the heat equation. Two additional chapters consider some more advanced results on Carleman estimates. The final part of the book is devoted to exposition of some necessary background material: elements of differential and Riemannian geometry, and Sobolev spaces and Laplace problems on Riemannian manifolds.
This second volume in Nancy's The Deconstruction of Christianity explores the stance or bearing that would be appropriate for us now, in the wake of the dis-enclosure of religion and the retreat of God: that of adoration. Adoration is stretched out toward things, but without phenomenological intention. In our present historical time, we have come to see relation itself as the divine. The address and exclamation--the salut!--that constitutes adoration celebrates this relation: both the relation among all beings that the world is and what is beyond relation, the outside of the world that opens us in the midst of the world. A major contribution to the contemporary philosophy of religion, Adoration clarifies and builds upon not only Dis-Enclosure, the first volume in this project, but also Nancy's other previous writings on sense, the world, and the singular plurality of being.
This book is a profound and eagerly anticipated investigation into what is left of a monotheistic religious spirit—notably, a minimalist faith that is neither confessional nor credulous. Articulating this faith as works and as an objectless hope, Nancy deconstructs Christianity in search of the historical and reflective conditions that provided its initial energy. Working through Blanchot and Nietzsche, re-reading Heidegger and Derrida, Nancy turns to the Epistle of Saint James rather than those of Saint Paul, discerning in it the primitive essence of Christianity as hope. The “religion that provided the exit from religion,” as he terms Christianity, consists in the announcement of an end. It is the announcement that counts, however, rather than any finality. In this announcement there is a proximity to others and to what was once called parousia. But parousia is no longer presence; it is no longer the return of the Messiah. Rather, it is what is near us and does not cease to open and to close, a presence deferred yet imminent. In a demystified age where we are left with a vision of a self-enclosed world—in which humans are no longer mortals facing an immortal being, but entities whose lives are accompanied by the time of their own decline—parousia stands as a question. Can we venture the risk of a decentered perspective, such that the meaning of the world can be found both inside and outside, within and without our so-immanent world? The deconstruction of Christianity that Nancy proposes is neither a game nor a strategy. It is an invitation to imagine a strange faith that enacts the inadequation of life to itself. Our lives overflow the self-contained boundaries of their biological and sociological interpretations. Out of this excess, wells up a fragile, overlooked meaning that is beyond both confessionalism and humanism.
Ranging across artists from Raphael to Rothko, Caravaggio to Pollock, The Crossing of the Visible offers both a critique of contemporary accounts of the visual and a constructive alternative. According to Marion, the proper response to the 'nihilism' of postmodernity is not iconoclasm, but rather a radically iconic account of the visual and the arts which opens them to the invisible.
Our contemporary challenge, according to Jean-Luc Nancy and Aurelien Barrau, is that a new world has stolen up on us. We no longer live in a world, but in worlds. We do not live in a universe anymore, but rather in a multiverse. We no longer create; we appropriate and montage. And we no longer build sovereign, hierarchical political institutions; we form local assemblies and networks of cross-national assemblages— and we do this at the same time as we form multinational corporations that no longer pay taxes to the state. In such a time, one of the world’s most eminent philosophers and an emerging astrophysicist return to the ancient art of cosmology. Nancy and Barrau’s work is a study of life, plural worlds, and what the authors call the struction or rebuilding of these worlds. Nancy and Barrau invite us on an uncharted walk into barely known worlds when an everyday French idiom, “What’s this world coming to?,” is used to question our conventional thinking about the world. We soon find ourselves living among heaps of odd bits and pieces that are amassing without any unifying force or center, living not only in a time of ruin and fragmentation but in one of rebuilding. Astrophysicist Aurelien Barrau articulates a major shift in the paradigm of contemporary physics from a universe to a multiverse. Meanwhile, Jean-Luc Nancy’s essay “Of Struction” is a contemporary comment on the project of deconstruction and French poststructuralist thought. Together Barrau and Nancy argue that contemporary thought has shifted from deconstruction to what they carefully call the struction of dis-order.
Along with Husserl's Ideas and Heidegger's Being and Time, Being Given is one of the classic works of phenomenology in the twentieth century. Through readings of Kant, Husserl, Heidegger, Derrida, and twentieth-century French phenomenology (e.g., Merleau-Ponty, Levinas, and Henry), it ventures a bold and decisive reappraisal of phenomenology and its possibilities. Its author's most original work to date, the book pushes phenomenology to its limits in an attempt to redefine and recover the phenomenological ideal, which the author argues has never been realized in any of the historical phenomenologies. Against Husserl's reduction to consciousness and Heidegger's reduction to Dasein, the author proposes a third reduction to givenness, wherein phenomena appear unconditionally and show themselves from themselves at their own initiative. Being Given is the clearest, most systematic response to questions that have occupied its author for the better part of two decades. The book articulates a powerful set of concepts that should provoke new research in philosophy, religion, and art, as well as at the intersection of these disciplines. Some of the significant issues it treats include the phenomenological definition of the phenomenon, the redefinition of the gift in terms not of economy but of givenness, the nature of saturated phenomena, and the question "Who comes after the subject?" Throughout his consideration of these issues, the author carefully notes their significance for the increasingly popular fields of religious studies and philosophy of religion. Being Given is therefore indispensable reading for anyone interested in the question of the relation between the phenomenological and the theological in Marion and emergent French phenomenology.
This book seeks to deepen readers’ understanding of world history by investigating urbanization and the evolution of urban systems, as well as the urban world, from the perspective of historical analysis. The theoretical framework of the approach stems directly from space-economy, and, more generally, from location theory and the theory of urban systems. The author explores a certain logic to be found in world history, and argues that this logic is spatial (in terms of spatial inertia, spatial trends, attractive and repulsive forces, vector fields, etc.) rather than geographical (in terms of climate, precipitation, hydrography). Accordingly, the book puts forward a truly original vision of urban world history, one that will benefit economists, historians, regional scientists, and anyone with a healthy curiosity.
This collection of writings by the renowned French critic and poet Jean-Luc Nancy delves into the history of philosophy in order to locate a fundamentally poetic modus operandi, representing a mix of philosophical essays, writings about artworks and the author's own artistic creations.
Nancy's The Speculative Remark played a significant role in transforming the practice of philosophy away from system building to analysis of specific linguistic detail.
This text corresponds to a graduate mathematics course taught at Carnegie Mellon University in the spring of 1999. Included are comments added to the lecture notes, a bibliography containing 23 items, and brief biographical information for all scientists mentioned in the text, thus showing that the creation of scientific knowledge is an international enterprise.
After publishing an introduction to the Navier–Stokes equation and oceanography (Vol. 1 of this series), Luc Tartar follows with another set of lecture notes based on a graduate course in two parts, as indicated by the title. A draft has been available on the internet for a few years. The author has now revised and polished it into a text accessible to a larger audience.
This fascinating book, penned by Luc Tartar of America’s Carnegie Mellon University, starts from the premise that equations of state are not always effective in continuum mechanics. Tartar relies on H-measures, a tool created for homogenization, to explain some of the weaknesses in the theory. These include looking at the subject from the point of view of quantum mechanics. Here, there are no "particles", so the Boltzmann equation and the second principle, can’t apply.
Homogenization is not about periodicity, or Gamma-convergence, but about understanding which effective equations to use at macroscopic level, knowing which partial differential equations govern mesoscopic levels, without using probabilities (which destroy physical reality); instead, one uses various topologies of weak type, the G-convergence of Sergio Spagnolo, the H-convergence of François Murat and the author, and some responsible for the appearance of nonlocal effects, which many theories in continuum mechanics or physics guessed wrongly. For a better understanding of 20th century science, new mathematical tools must be introduced, like the author’s H-measures, variants by Patrick Gérard, and others yet to be discovered.
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