Nonlinear theory of solitary waves associated with longitudinal particle motion in lattices - Application to longitudinal grain oscillations in a dust crystal

The nonlinear aspects of longitudinal motion of interacting point masses in a lattice are revisited, with emphasis on the paradigm of charged dust grains in a dusty plasma (DP) crystal. Different types of localized excitations, predicted by nonlinear wave theories, are reviewed and conditions for their occurrence (and characteristics) in DP crystals are discussed. Making use of a general formulation, allowing for an arbitrary (e.g. the Debye electrostatic or else) analytic potential form phi(r) and arbitrarily long site-to-site range of interactions, it is shown that dust-crystals support nonlinear kink-shaped localized excitations propagating at velocities above the characteristic DP lattice sound speed v(0). Both compressive and rarefactive kink-type excitations are predicted, depending on the physical parameter values, which represent pulse- (shock-)like coherent structures for the dust grain relative displacement. Furthermore, the existence of breather-type localized oscillations, envelope-modulated wavepackets and shocks is established. The relation to previous results on atomic chains as well as to experimental results on strongly-coupled dust layers in gas discharge plasmas is discussed.

Nonlinear Lagrangian theory of envelope electrostatic plasma waves in a two-electron-temperature plasma

An analytical model based on Lagrangian variables is presented for the description of ion-acoustic waves propagating in an unmagnetized, collisionless, three-component plasma composed of inertial positive ions and two thermalized electron populations, characterized by different temperatures. The wave's amplitude is shown to be modulationally unstable. Different types of localized envelope electrostatic excitations are shown to exist, and their forms are analytically and numerically investigated in terms of the plasma dispersion and nonlinearity laws. These results are in qualitative agreement with satellite observations in the magnetosphere. (C) 2004 American Institute of Physics.

Complete nonlinear theory of longitudinal-to-transverse dust lattice mode coupling in a single-layer dusty plasma crystal

A comprehensive nonlinear model is put forward for coupled longitudinal to transverse displacements in a horizontal dust mono-layer, levitated under the combined influence of gravity and an electric and/or magnetic sheath field. A set of coupled nonlinear evolution equations are obtained in a discrete description, and a pair of coupled (Boussinesq-like) PDEs are obtained in the continuum approximation. Finally, the amplitude modulation of the coupled modes is discussed, pointing out the importance of the coupling. All these results are generic, i.e. valid for any assumed form of the inter-grain interaction potential U and the sheath potential Phi.

A note on the graded K-theory of certain graded rings

Following ideas of Quillen we prove that the graded K-theory of a Z-multi-graded ring with support contained in a pointed cone is entirely determined by the K-theory of the sub-ring of elements of degree 0.

A splitting result for the algebraic K-theory of projective toric schemes

Suppose X is a projective toric scheme defined over a ring R and equipped with an ample line bundle L . We prove that its K-theory has a direct summand of the form K(R)(k+1) where k = 0 is minimal such that L?(-k-1) is not acyclic. Using a combinatorial description of quasi-coherent sheaves we interpret and prove this result for a ring R which is either commutative, or else left noetherian.

Beyond the Sign. Henri Meschonnic's Poetics of Rhythm and Continuum. Towards an Anthropological Theory of Language

Basing the conception of language on the sign represents also an obstacle to the awareness of certain elements of human life, especially to a full understanding of what language or art do, Henri Meschonnic’s poetics of the continuum and of rhythm criticizes the sign based on Benveniste’s terms of rhythm and discourse, developing an anthropology of language. Rhythm, for Meschonnic, is no formal metrical but a semantic principle, each time unique and unforeseeable. As for Humboldt, his starting point is not the word but the ensemble of speech; language is not ergon but energeia. The poem then is not a literary form but a process of transformation that Meschonnic defines as the invention of a form of life by a form of language and vice versa. Thus a poem is a way of thinking and rhythm is form in movement. The particular subject of art and literature is consequently not the author but a process of subjectivation – this is the contrary of the conception of the sign. By demonstrating the limits of the sign, Meschonnic’s poetics attempts to thematize the intelligibility of presence. Art and literature raise our awareness of this element of human life we cannot grasp conceptually. This poetical thinking is a necessary counterforce against all institutionalization.

Bridging Jeffrey's Rule, AGM Revision and Dempster Conditioning in the Theory of Evidence

Belief revision characterizes the process of revising an agent’s beliefs when receiving new evidence. In the field of artificial intelligence, revision strategies have been extensively studied in the context of logic-based formalisms and probability kinematics. However, so far there is not much literature on this topic in evidence theory. In contrast, combination rules proposed so far in the theory of evidence, especially Dempster rule, are symmetric. They rely on a basic assumption, that is, pieces of evidence being combined are considered to be on a par, i.e. play the same role. When one source of evidence is less reliable than another, it is possible to discount it and then a symmetric combination operation
is still used. In the case of revision, the idea is to let prior knowledge of an agent be altered by some input information. The change problem is thus intrinsically asymmetric. Assuming the input information is reliable, it should be retained whilst the prior information should be changed minimally to that effect. To deal with this issue, this paper defines the notion of revision for the theory of evidence in such a way as to bring together probabilistic and logical views. Several revision rules previously proposed are reviewed and we advocate one of them as better corresponding to the idea of revision. It is extended to cope with inconsistency between prior and input information. It reduces to Dempster
rule of combination, just like revision in the sense of Alchourron, Gardenfors, and Makinson (AGM) reduces to expansion, when the input is strongly consistent with the prior belief function. Properties of this revision rule are also investigated and it is shown to generalize Jeffrey’s rule of updating, Dempster rule of conditioning and a form of AGM revision.