Eikonal algebra on a graph of simple structure

An eikonal algebra ${\mathfrak E}(\Omega)$ is a C*-algebra related to a metric graph $\Omega$. It is determined by trajectories and reachable sets of a dynamical system associated with the graph. The system describes the waves, which are initiated by boundary sources (controls) and propagate into the graph with finite velocity. Motivation and interest to eikonal algebras comes from the inverse problem of reconstruction of the graph via its dynamical and/or spectral boundary data. Algebra ${\mathfrak E}(\Omega)$ is determined by these data. In the mean time, its structure and algebraic invariants (irreducible representations) are connected with topology of $\Omega$. We demonstrate such connections and study ${\mathfrak E}(\Omega)$ by the example of $\Omega$ of a simple structure. Hopefully, in future, these connections will provide an approach to reconstruction.Comment: 38 pages, 11 figure

Canonical form of C∗C^*-algebra of eikonals related to the metric graph

The eikonal algebra $\mathfrak E$ of the metric graph $\Omega$ is an operator $C^*$--algebra defined by the dynamical system which describes the propagation of waves generated by sources supported in the boundary vertices of $\Omega$. This paper describes the canonical block form of the algebra $\mathfrak E$ of an arbitrary compact connected metric graph. Passing to this form is equivalent to constructing a functional model which realizes $\mathfrak E$ as an algebra of continuous matrix-valued functions on its spectrum $\widehat{\mathfrak{E}}$. The results are intended to be used in the inverse problem of reconstruction of the graph by spectral and dynamical boundary data. Bibliography: 28 items

Equation level matching: An extension of the method of matched asymptotic expansion for problems of wave propagation

We introduce an alternative to the method of matched asymptotic expansions. In the "traditional" implementation, approximate solutions, valid in different (but overlapping) regions are matched by using "intermediate" variables. Here we propose to match at the level of the equations involved, via a "uniform expansion" whose equations enfold those of the approximations to be matched. This has the advantage that one does not need to explicitly solve the asymptotic equations to do the matching, which can be quite impossible for some problems. In addition, it allows matching to proceed in certain wave situations where the traditional approach fails because the time behaviors differ (e.g., one of the expansions does not include dissipation). On the other hand, this approach does not provide the fairly explicit approximations resulting from standard matching. In fact, this is not even its aim, which to produce the "simplest" set of equations that capture the behavior

Direct visualization of lipid aggregates in native human bile by light- and cryo-transmission electron-microscopy

AbstractThe evolution of microstructures present in human gallbladder and hepatic bile was observed simultaneously by video-enhanced light microscopy (VELM) and transmission electron microscopy of vitrified specimens (cryo-TEM), as a function of time after withdrawal from patients. Fresh centrifuged gallbladder bile samples contained small (6 nm) spherical micelles in coexistence with vesicles (40 nm). Out of the seven bile samples investigated four contained, in addition, two types of elongated aggregates that have not been previously described. Uncentrifuged gallbladder bile also contained a mixture of ribbon- and plate-like crystals seen by VELM, but not by cryo-TEM. In aged (3–6-week-old) gallbladder bile samples VELM also revealed spiral and helical crystal structures. No such crystals were present in hepatic bile samples, although microcrystals, not observable by VELM were seen by cryo-TEM in addition to micelles and vesicles. The similarity of these observations to those observed in bile models lends strong support for the validity of the model systems. Furthermore, the presence of microcrystals in hepatic bile samples, apparently devoid of crystals by light microscopy, indicates that under certain conditions the common criterion of ‘nueleation time’ (NT), based on light microscopy, does not represent the real time of nucleation. In the human bile samples investigated in this study the dissociation between NT and the time of observation of microcrystals was seen in hepatic but not in gallbladder bile samples. Hence, crystal growth may be rate limiting only in dilute biles

Simple Viscous Flows: from Boundary Layers to the Renormalization Group

The seemingly simple problem of determining the drag on a body moving through a very viscous fluid has, for over 150 years, been a source of theoretical confusion, mathematical paradoxes, and experimental artifacts, primarily arising from the complex boundary layer structure of the flow near the body and at infinity. We review the extensive experimental and theoretical literature on this problem, with special emphasis on the logical relationship between different approaches. The survey begins with the developments of matched asymptotic expansions, and concludes with a discussion of perturbative renormalization group techniques, adapted from quantum field theory to differential equations. The renormalization group calculations lead to a new prediction for the drag coefficient, one which can both reproduce and surpass the results of matched asymptotics

The Introduction of DTT in Latin America: Politics and Policies

The switch to digital terrestrial television is now a global trend. In Latin America, where the terrestrial platform has a dominant role, the introduction of DTT raises important questions for economic and industrial development, as well as pluralism. This article focuses on the earliest experiences (Brazil, México and Argentina) and those of the newcomers (Chile, Colombia and Uruguay). The aim is to outline the differences between the various political decision processes and the way with which they have been turned into communication policies, so as to draw some conclusions that contribute to visualizing the future of television in the region.Publicad