Examples of signature (2,2) manifolds with commuting curvature operators

We exhibit Walker manifolds of signature (2,2) with various commutativity properties for the Ricci operator, the skew-symmetric curvature operator, and the Jacobi operator. If the Walker metric is a Riemannian extension of an underlying affine structure A, these properties are related to the Ricci tensor of A

Solid flow drives surface nanopatterning by ion-beam irradiation

Ion Beam Sputtering (IBS) is known to produce surface nanopatterns over macroscopic areas on a wide range of materials. However, in spite of the technological potential of this route to nanostructuring, the physical process by which these surfaces self-organize remains poorly under- stood. We have performed detailed experiments of IBS on Si substrates that validate dynamical and morphological predictions from a hydrodynamic description of the phenomenon. Our results elucidate flow of a nanoscopically thin and highly viscous surface layer, driven by the stress created by the ion-beam, as a description of the system. This type of slow relaxation is akin to flow of macroscopic solids like glaciers or lead pipes, that is driven by defect dynamics.Comment: 12 pages, 4 figure

Variations on Kaluza-Klein Cosmology

We investigate the cosmological consequences of having quantum fields living in a space with compactified dimensions. We will show that the equation of state is not modified by topological effects and so the dynamics of the universe remains as it is in the infinite volume limit. On the contrary the thermal history of the universe depends on terms that are associated with having non-trivial topology. In the conclusions we discuss some issues about the relationship between the $c=1$ non-critical string-inspired cosmology and the result obtained with matter given by a hot massless field in S^{1}\times \mbox{\bf R}.Comment: 22 pages, 7 figures in a uuencoded file (using uufiles), LaTeX, FTUAM-93/13 (LaTeX errors corrected

Optical sensing in microchip capillary electrophoresis by femtosecond laser written waveguides

Capillary electrophoresis separation in an on-chip integrated microfluidic channel is typically monitored with bulky, bench-top optical excitation/detection instrumentation. Optical waveguides allow confinement and transport of light in the chip directing it to a small volume of the microfluidic channel and collecting the emitted/transmitted radiation. However, the fabrication of optical waveguides or more complex photonic components integrated with the microfluidic channels is not a straightforward process, since it requires a localized increase of the refractive index of the substrate.\ud Recently, a novel technique has emerged for the direct writing of waveguides and photonic circuits in transparent glass substrates by focused femtosecond laser pulses.\ud In this work we demonstrate the integration of femtosecond laser written optical waveguides into a commercial microfluidic chip. We fabricate high quality waveguides intersecting the microchannels at arbitrary positions and use them to optically address with high spatial selectivity their content. In particular, we apply our technique to integrate optical detection in microchip capillary electrophoresis. Waveguides are inscribed at the end of the separation channel in order to optically excite the different plugs reaching that point; fluorescence from the labelled biomolecules crossing the waveguide output is efficiently collected at a 90° angle by a high numerical aperture optical fiber. The sensitivity of the integrated optical detection system was first evaluated filling the chip with a dye solution, obtaining a minimum detectable concentration of 40 pM. \ud After dynamic coating of the microchannels with an EPDMA polymer we demonstrate electrophoresis of an oligonucleotide plug with concentration down to 1 nM and wavelength-selective monitoring of on-chip separation of three fluorescent dyes. Work is in progress on separation and detection of fluorescent-labeled DNA fragments, targeting specific, diagnostically relevant regions of a template DNA, for application to the detection of chromosome aberrations

Entropy Rate of Diffusion Processes on Complex Networks

The concept of entropy rate for a dynamical process on a graph is introduced. We study diffusion processes where the node degrees are used as a local information by the random walkers. We describe analitically and numerically how the degree heterogeneity and correlations affect the diffusion entropy rate. In addition, the entropy rate is used to characterize complex networks from the real world. Our results point out how to design optimal diffusion processes that maximize the entropy for a given network structure, providing a new theoretical tool with applications to social, technological and communication networks.Comment: 4 pages (APS format), 3 figures, 1 tabl