Ronchi test applied to measurement of surface roughness

Ronchi test is applied to measure microscopic variations in surface roughness or flatness of metallized test specimens. Light is projected through a diffraction grating onto the test specimen, and the light reflected from the specimen is viewed or photographed through the grating

Three-dimensional stability of Burgers vortices

Burgers vortices are explicit stationary solutions of the Navier-Stokes equations which are often used to describe the vortex tubes observed in numerical simulations of three-dimensional turbulence. In this model, the velocity field is a two-dimensional perturbation of a linear straining flow with axial symmetry. The only free parameter is the Reynolds number $Re = \Gamma/\nu$, where $\Gamma$ is the total circulation of the vortex and $\nu$ is the kinematic viscosity. The purpose of this paper is to show that Burgers vortex is asymptotically stable with respect to general three-dimensional perturbations, for all values of the Reynolds number. This definitive result subsumes earlier studies by various authors, which were either restricted to small Reynolds numbers or to two-dimensional perturbations. Our proof relies on the crucial observation that the linearized operator at Burgers vortex has a simple and very specific dependence upon the axial variable. This allows to reduce the full linearized equations to a vectorial two-dimensional problem, which can be treated using an extension of the techniques developped in earlier works. Although Burgers vortices are found to be stable for all Reynolds numbers, the proof indicates that perturbations may undergo an important transient amplification if $Re$ is large, a phenomenon that was indeed observed in numerical simulations.Comment: 31 pages, no figur

The Insula of Reil Revisited: Multiarchitectonic Organization in Macaque Monkeys

The insula of Reil represents a large cortical territory buried in the depth of the lateral sulcus and subdivided into 3 major cytoarchitectonic domains: agranular, dysgranular, and granular. The present study aimed at reinvestigating the architectonic organization of the monkey's insula using multiple immunohistochemical stainings (parvalbumin, PV; nonphosphorylated neurofilament protein, with SMI-32; acetylcholinesterase, AChE) in addition to Nissl and myelin. According to changes in density and laminar distributions of the neurochemical markers, several zones were defined and related to 8 cytoarchitectonic subdivisions (Ia1-Ia2/Id1-Id3/Ig1-Ig2/G). Comparison of the different patterns of staining on unfolded maps of the insula revealed: 1) parallel ventral to dorsal gradients of increasing myelin, PV- and AChE-containing fibers in middle layers, and of SMI-32 pyramidal neurons in supragranular layers, with merging of dorsal and ventral high-density bands in posterior insula, 2) definition of an insula "proper” restricted to two-thirds of the "morphological” insula (as bounded by the limiting sulcus) and characterized most notably by lower PV, and 3) the insula proper is bordered along its dorsal, posterodorsal, and posteroventral margin by a strip of cortex extending beyond the limits of the morphological insula and continuous architectonically with frontoparietal and temporal opercular areas related to gustatory, somatosensory, and auditory modalitie

Global exponential convergence to variational traveling waves in cylinders

We prove, under generic assumptions, that the special variational traveling wave that minimizes the exponentially weighted Ginzburg-Landau functional associated with scalar reaction-diffusion equations in infinite cylinders is the long-time attractor for the solutions of the initial value problems with front-like initial data. The convergence to this traveling wave is exponentially fast. The obtained result is mainly a consequence of the gradient flow structure of the considered equation in the exponentially weighted spaces and does not depend on the precise details of the problem. It strengthens our earlier generic propagation and selection result for "pushed" fronts.Comment: 23 page

Analysis of enhanced diffusion in Taylor dispersion via a model problem

We consider a simple model of the evolution of the concentration of a tracer, subject to a background shear flow by a fluid with viscosity $\nu \ll 1$ in an infinite channel. Taylor observed in the 1950's that, in such a setting, the tracer diffuses at a rate proportional to $1/\nu$, rather than the expected rate proportional to $\nu$. We provide a mathematical explanation for this enhanced diffusion using a combination of Fourier analysis and center manifold theory. More precisely, we show that, while the high modes of the concentration decay exponentially, the low modes decay algebraically, but at an enhanced rate. Moreover, the behavior of the low modes is governed by finite-dimensional dynamics on an appropriate center manifold, which corresponds exactly to diffusion by a fluid with viscosity proportional to $1/\nu$

Orbital stability of periodic waves for the nonlinear Schroedinger equation

The nonlinear Schroedinger equation has several families of quasi-periodic travelling waves, each of which can be parametrized up to symmetries by two real numbers: the period of the modulus of the wave profile, and the variation of its phase over a period (Floquet exponent). In the defocusing case, we show that these travelling waves are orbitally stable within the class of solutions having the same period and the same Floquet exponent. This generalizes a previous work where only small amplitude solutions were considered. A similar result is obtained in the focusing case, under a non-degeneracy condition which can be checked numerically. The proof relies on the general approach to orbital stability as developed by Grillakis, Shatah, and Strauss, and requires a detailed analysis of the Hamiltonian system satisfied by the wave profile.Comment: 34 pages, 7 figure

Carbon based double layer capacitors with aprotic electrolyte solutions: the possible role of intercalation/insertion processes

The extraordinary stability and cycle life performance of today's electrochemical double-layer capacitors (EDLCs) are generally ascribed to the fact that charge storage in activated carbon (AC) is based on pure double-layer charging. In contrast, Faradaic charge-transfer reactions like those occurring in batteries are often connected with dimensional changes, which can affect the cycle life of these storage devices. Here we report the charge-induced height change of an AC electrode in an aprotic electrolyte solution, 1mol/l (C2H5)4NBF4 (TEABF4) in acetonitrile. The results are compared with those obtained for a graphite electrode in the same electrolyte. For both electrodes, we observe an expansion/contraction of several percent for a potential window of ±2V vs. the immersion potential (ip). For the EDLC electrode, significant expansion starts at about 1V remote from the ip and hence is well within the normal EDLC operation range. For the graphite electrode, the height changes are unambiguously caused by intercalation/deintercalation of both anions and cations. The close analogies between the graphite and the EDLC electrode suggest that ion intercalation or insertion processes might play a major role for charge storage, self discharge, cyclability, and the voltage limitation of EDLC

Phase Slips and the Eckhaus Instability

We consider the Ginzburg-Landau equation, $\partial_t u= \partial_x^2 u + u - u|u|^2$, with complex amplitude $u(x,t)$. We first analyze the phenomenon of phase slips as a consequence of the {\it local} shape of $u$. We next prove a {\it global} theorem about evolution from an Eckhaus unstable state, all the way to the limiting stable finite state, for periodic perturbations of Eckhaus unstable periodic initial data. Equipped with these results, we proceed to prove the corresponding phenomena for the fourth order Swift-Hohenberg equation, of which the Ginzburg-Landau equation is the amplitude approximation. This sheds light on how one should deal with local and global aspects of phase slips for this and many other similar systems.Comment: 22 pages, Postscript, A

Review of the twelfth West Coast retrovirus meeting

Every year the Cancer Research Institute from University of California at Irvine organizes the West Coast Retrovirus Meeting where participants have a chance to discuss the latest progress in understanding the pathology of retroviruses. The 12(th )meeting was held at the Hyatt Regency Suites in Palm Springs, California from October 6(th )to October 9(th )2005, with the major focus on human immunodeficiency virus (HIV) pathogenesis. Philippe Gallay from The Scripps Research Institute and Thomas J. Hope from Northwestern University organized the meeting, which covered all the steps involved in the lifecycle of retroviruses with an emphasis on virus:host interactions. The trend in research appeared to be on the restriction of viral infection, both by the endogenous, cellular restriction factors, as well as by the potential antimicrobial compounds of known or unknown mechanisms. Additionally, new stories on the inevitable feedback from the host immune system were presented as well. HIV still represents a challenge that an army of motivated people has been working on for over 20 years. And yet, the field has not reached the plateau in knowledge nor enthusiasm, which was proven again in October 2005 in Palm Springs

Interaction of vortices in viscous planar flows

We consider the inviscid limit for the two-dimensional incompressible Navier-Stokes equation in the particular case where the initial flow is a finite collection of point vortices. We suppose that the initial positions and the circulations of the vortices do not depend on the viscosity parameter \nu, and we choose a time T > 0 such that the Helmholtz-Kirchhoff point vortex system is well-posed on the interval [0,T]. Under these assumptions, we prove that the solution of the Navier-Stokes equation converges, as \nu -> 0, to a superposition of Lamb-Oseen vortices whose centers evolve according to a viscous regularization of the point vortex system. Convergence holds uniformly in time, in a strong topology which allows to give an accurate description of the asymptotic profile of each individual vortex. In particular, we compute to leading order the deformations of the vortices due to mutual interactions. This allows to estimate the self-interactions, which play an important role in the convergence proof.Comment: 39 pages, 1 figur