Strange Term Research Articles

Homogenization of Dirichlet optimal control problems with exact partial controllability constraints

We consider an elliptic distributed quadratic optimal control problem with exact controllability constraints on a part of the domain which, in turn, is parametrized by a small parameter e. The quadratic tracking type functional is defined on the remaining part of the domain. We thus consider a family of optimal control problems with state equality constraints. The purpose of this paper is to study the asymptotic limit of the optimal control problems as the parameter e tends to zero. The analysis presented is in the spirit of the direct approach of the calculus of variations. This is achieved in the framework of relaxed problems. We finally apply the procedure to an optimal control problem on a perforated domain with holes of critical size. It is shown that a strange term in the terminology of Cioranescu and Murat (Prog. Nonlinear Diff. Eq. Appl., Vol. 31, Birkhauser-Verlag, Boston, 1997, pp. 49-93) appears in the limiting homogenized problem.

Bloch wave homogenization of a non-homogeneous Neumann problem

In this paper, we use the Bloch wave method to study the asymptotic behavior of the solution of the Laplace equation in a periodically perforated domain, under a non-homogeneous Neumann condition on the boundary of the holes, as the size of the holes goes to zero more rapidly than the domain period. This method allows to prove that, when the hole size exceeds a given threshold, the non-homogeneous boundary condition generates an additional term in the homogenized problem, commonly referred to as “the strange term” in the literature.

Bloch wave homogenization in a medium perforated by critical holes

In this Note, we use the Bloch wave method to study the asymptotic behavior of the solution of the Laplace equation in a periodically perforated domain, under a non-homogeneous Neumann condition on the boundary of the holes, as the hole size goes to zero more rapidly than the domain period. We prove that for a critical size, the non-homogeneous boundary condition generates an additional term in the homogenized problem, commonly referred to as ‘the strange term’ in the literature. To cite this article: J. Ortega et al., C. R. Mecanique 335 (2007).

Metaphor and ideological critique: the case of Aristotle

Aristotle’s Poetics (1457b 6-9) defines the trope of resemblance in the following terms:“Metaphor is the application of a strange term either transferred from the genus and applied to the species or from the species and applied to the genus, or from one species to another or else by analogy”It is both a definition and a classification which offers three types of binary combinations. It would be easy to indicate that this typology rests not only in depicting resemblance of two things, but also in the relation of exclusion and inclusion, as is the case with synecdoche (inclusion) and metonymy (exclusion). But the ideological analysis that the present paper undertakes may be all the more readily accommodated by the Aristotelian conception of the work his works and their commentators. The analysis begins with examining a few explicit metaphors, some unprecedented metaphors. Later, the attitude of some linguists regarding metaphor is presented, their trials, or actually the lack of thereof, to metamorphose the Greek philosopher as a lifeguard of a contemporary thought locked in a series of ideological impasses.

Modelling of a fluid: homogenization and mixed scales

The limit behavior of a mixture made of drops of some fluid immersed in another fluid is analysed in the framework of periodic homogenization when the size of the drops is critical compared with the period of the underlying network. More precisely, a strange term is obtained in the limit thus leading to a Brinkmann law. To cite this article: I. Gruais, C. R. Acad. Sci. Paris, Ser. I 337 (2003).

A Generalized Strange Term in Signorini's Type Problems

The limit behavior of the solutions of Signorini's type-like problems in periodically perfo- rated domains with period is studied. The main feature of this limit behaviour is the existence of a critical size of the perforations that separates dierent emerging phenomena as ! 0. In the critical case, it is shown that Signorini's problem converges to a problem associated to a new operator which is the sum of a standard homogenized operator and an extra zero order term (\strange term) coming from the geometry; its appearance is due to the special size of the holes. The limit problem captures the two sources of oscillations involved in this kind of free boundary-value problems, namely, those arising from the size of the holes and those due to the periodic inhomogeneity of the medium. The main ingredient of the method used in the proof is an explicit construction of suitable test functions which provide a good understanding of the interactions between the above mentioned sources of oscillations.

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Origen, Plato, and Conscience (<i>Synderesis</i>) in Jerome's Ezekiel Commentary

Due especially to the pioneering work of Lottin, philosophers and theologians interested in the medieval discussion of the human conscience are today well aware that the Scholastic debate was framed principally in relation to two words, conscientia and synderesis. In the now classic formulation of the distinction between those two terms by Thomas Aquinas, synderesis is understood as the special habitus of the practical intellect whereby human beings know the basic principles of morality, whereas conscientia is the act whereby the practical reasoning powers of a human being apply the fundamental principles to the particular matter at hand. It is also generally acknowledged by scholars today that the argument about the relationship between conscientia and synderesis began many years prior to Thomas's work, that the medieval debate was originally spurred by the introduction of the strange term synderesis into the conversation, and that the term entered the discussion by means of an enigmatic passage in Jerome's Commentary on Ezekiel. Finally, most scholars acknowledge that the appearance of synderesis in the medieval manuscripts of Jerome's commentary is in all likelihood a corruption of the Greek word syneidēsis, which is the standard correlate in Greek Patristic literature for the Latin conscientia.

Origen, Plato, and Conscience (Synderesis) in Jerome's Ezekiel Commentary

Due especially to the pioneering work of Lottin, philosophers and theologians interested in the medieval discussion of the human conscience are today well aware that the Scholastic debate was framed principally in relation to two words, conscientia and synderesis. In the now classic formulation of the distinction between those two terms by Thomas Aquinas, synderesis is understood as the special habitus of the practical intellect whereby human beings know the basic principles of morality, whereas conscientia is the act whereby the practical reasoning powers of a human being apply the fundamental principles to the particular matter at hand. It is also generally acknowledged by scholars today that the argument about the relationship between conscientia and synderesis began many years prior to Thomas's work, that the medieval debate was originally spurred by the introduction of the strange term synderesis into the conversation, and that the term entered the discussion by means of an enigmatic passage in Jerome's Commentary on Ezekiel. Finally, most scholars acknowledge that the appearance of synderesis in the medieval manuscripts of Jerome's commentary is in all likelihood a corruption of the Greek word syneidēsis, which is the standard correlate in Greek Patristic literature for the Latin conscientia.

Superfluid properties of3He-A

The unique superfluid properties which distinguish the A phase of 3He from other superfluids (He II, the B phase of 3He, and electrons in superconductors) are described. These properties result from the specific breaking of the invariance of the state under gauge transformations and rotations in orbital space, so that all the superfluid properties are related in a fundamental way to the dynamics of textures of the liquid-crystal-anisotropy vector. The flow of the superfluid component of the liquid, for example, is not a potential flow; its vortical part is related to textures. The relationship between the structure of the superfluid velocity and the nature of the symmetry breaking is analyzed in detail. Simple phenomenological considerations are used to derive an expression for the current and to explain the strange term in the current which is not present in the model of a Bose gas of molecules having a Cooper-pair structure in the A phase. The existence of a normal density at T=0 and the nonlocal properties of the density of the intrinsic orbital angular momentum of the liquid are discussed. The coexistence of superfluid properties with a nonpotential superfluid flow and also with the vanishing of the critical Landau velocity for the creation of excitations is discussed. Conditions for the global and local stability of the superfluid flow are described. The changes in stability upon changes caused in the topological structure of the order parameter by external conditions are discussed. The relaxation dynamics of a superfluid flow is analyzed. An instanton mechanism for phase slippage is analyzed; this mechanism leads to observable oscillations analogous to the ac Josephson effect in superconductors. Principles for constructing a generalized two-fluid Landau hydrodynamics taking an orbital variable into account are outlined. Continuous and singular vortex structures which arise upon rotation are discussed, as are their topology, phase transitions between them, and some other topologically nontrivial structures: a vortex with a free end, a boojum, and an instanton. The basic experiments in which the unique superfluid properties are observed are discussed. Some other existing or possible systems in which a nonstandard breaking of gauge invariance leads to unusual properties are cited; examples are a neutron star and a superconductor with the A-phase structure. In the latter medium there is a structure similar to a Dirac magnetic monopole. This structure is discussed.

Irving in Shakespeare: Interpretation or Creation?

HE publication in i95i of pardonably adulatory biography of Henry Irving by grandson Laurence suggests that recon-g Go sideration and brisk summary, of the great actor's handling of Shakespearian roles may be of general interest. It is surprising how large Henry Irving's name bulks in the discussion of the playing of Shakespeare and how large in treatments of him bulks the discussion of Shakespearian roles. During career he played six hundred and seventy-one parts; of these only forty-one were Shakespearian roles, twenty-eight being minor parts played during provincial days. Altogether he played in but fourteen of the plays, and in London he played only thirteen roles. According to Bernard Shaw, he was never interpretative actor: his creations were all own; and they were all Irvings. Certainly Hamlet was strange creature, whose lack of physical beauty and gesticulatory and elocutionary grace was greeted by admirers as proof of new psychological interpretation, strange term to be loosely used of all later Shakespearian appearances. Admitting that In moments of high excitement Irving rapidly plods across and across the stage with gait peculiar to him-a walk somewhat resembling that of fretful man trying to get quickly over ploughed field, and that In certain passages voice has querulous piping impatience which cannot be reconciled with stage elegance, Edward R. Russell argued, there is no reason why Hamlet should not have had these peculiarities, and he claimed that Irving's mannerisms had enabled him to make playgoers know Hamlet as a new and distinct and actual person, like an interesting acquaintance . . . made at dinner-table or in travelling. Is man no more than this? . . . no more but such poor, bare, forked animal as this? Surely the Prince of Denmark is something much more. But Irving was not even attempting to interpret Shakespeare's Hamlet; he was simply and definitely making audiences accept Hamlet as Henry Irving. Late in life he told young stage aspirant: my boy, there are only two ways of portraying character on the stage. Either you try to turn yourself into that person-which is impossible-or, and this is the way to act, you can take that person and turn him into yourself. That is how I do it! Russell felt that Irving managed to turn Hamlet into himself by a bold combination of tragedy and character acting. The new character acting made much of detailed and intimate business and gesture. Such by-play Irving believed