Optimal streaks in a Falkner-Skan boundary layer

This paper deals with the optimal streaky perturbations (which maximize the perturbed energy growth) in a wedge flow boundary layer. These three dimensional perturbations are governed by a system of linearized boundary layer equations around the Falkner-Skan base flow. Based on an asymptotic analysis of this system near the free stream and the leading edge singularity, we show that for acute wedge semi-angle, all solutions converge after a streamwise transient to a single streamwise-growing solution of the linearized equations, whose initial condition near the leading edge is given by an eigenvalue problem first formulated in this context by Tumin (2001). Such a solution may be regarded as a streamwise evolving most unstable streaky mode, in analogy with the usual eigenmodes in strictly parallel flows, and shows an approximate self-similarity, which was partially known and is completed in this paper. An important consequence of this result is that the optimization procedure based on the adjoint equations heretofore used to define optimal streaks is not necessary. Instead, a simple low-dimensional optimization process is proposed and used to obtain optimal streaks. Comparison with previous results by Tumin and Ashpis (2003) shows an excellent agreement. The unstable streaky mode exhibits transient growth if the wedge semi-angle is smaller than a critical value that is slightly larger than $\pi/6$, and decays otherwise. Thus the cases of right and obtuse wedge semi-angles exhibit less practical interest, but they show a qualitatively different behavior, which is briefly described to complete the analysis

Invariant Regions and Global Asymptotic Stability in an Isothermal Catalyst

A well-known model for the evolution of the (space-dependent) concentration and (lumped) temperature in a porous catalyst is considered. A sequence of invariant regions of the phase space is given, which converges to a globally asymptotically stable region $B$. Quantitative sufficient conditions are obtained for (the region $B$ to consist of only one point and) the problem to have a (unique) globally asymptotically stable steady state

Out of necessity comes unbridled imagination for survival: contributive justice in Spanish libraries during economic crisis

The call for this journal issue notes that “social justice in LIS/services involves achieving action-oriented socially relevant outcomes via information-related work.” There is not a more fitting time and place for such action than in Spain, where the current economic crisis left more than 6 million (27 percent of the population) unemployed as of 2013. It is not just communities that are grappling with the pain of the economic downturn; libraries are also suffering from the crisis as a result of budget cuts due to reduced public funding. This article presents the case of Spanish academic and public libraries that have found solutions to keep themselves open, providing services vital to the economic and sociocultural needs of their communities. This case is an example of contributive justice, as evidenced in the actions taken by Spanish libraries and their communities as well as in the manner in which the research data were collected. Eight library-related actions were found: professional, community, social, political, digital, cultural/heritage, economic, and ontological. Despite economic hardships all around, these Spanish examples reveal the impact of libraries as social justice institutions, the role of librarians as agents of change, and the value of contributive and grassroots efforts when governments fail to provide. Moreover, these contributions to social justice illustrate actions appropriate to a contributive justice framework for libraries, as proposed in this article.published or submitted for publicatio

Drift instability of standing Faraday waves

We consider the weakly nonlinear evolution of the Faraday waves produced in a vertically vibrated two-dimensional liquid layer, at small viscosity. It is seen that the surface wave evolves to a drifting standing wave, namely a wave that is standing in a moving reference frame. This wave is determined up to a spatial phase, whose calculation requires consideration of the associated mean flow. This is just the streaming flow generated in the boundary layer attached to the lower plate supporting the liquid. A system of equations is derived for the coupled slow evolution of the spatial phase and the streaming flow. These equations are numerically integrated to show that the simplest reflection symmetric steady state (the usual array of counter-rotating eddies below the surface wave) becomes unstable for realistic values of the parameters. The new states include limit cycles (the array of eddies oscillating laterally), drifted standing waves (patterns that are standing in a uniformly propagating reference frame) and some more complex attractors

A Model of Porous Catalyst Accounting for Incipiently Non-isothermal Effects*

An approximate model accounting for incipiently non-isothermal effects is derived from a well-known model of porous catalyst for appropriate, realistic limiting values of the parameters. In this limit, the original model is a singularly perturbed, m-D reaction–diffusion system, and the approximate model is given by the m-D heat equation with nonlinear boundary condition, coupled with infinitely many (ifm2) 1-D semilinear parabolic equations, one for each point of the boundary of the spatial domain. Some limiting cases are still considered in the approximate model that lead to further simplifications

Mixing snapshots and fast time integration of PDEs

A local proper orthogonal decomposition (POD) plus Galerkin projection method was recently developed to accelerate time dependent numerical solvers of PDEs. This method is based on the combined use of a numerical code (NC) and a Galerkin system (GS) in a sequence of interspersed time intervals, INC and IGS, respectively. POD is performed on some sets of snapshots calculated by the numerical solver in the INC intervals. The governing equations are Galerkin projected onto the most energetic POD modes and the resulting GS is time integrated in the next IGS interval. The major computational effort is associated with the snapshots calculation in the first INC interval, where the POD manifold needs to be completely constructed (it is only updated in subsequent INC intervals, which can thus be quite small). As the POD manifold depends only weakly on the particular values of the parameters of the problem, a suitable library can be constructed adapting the snapshots calculated in other runs to drastically reduce the size of the first INC interval and thus the involved computational cost. The strategy is successfully tested in (i) the one-dimensional complex Ginzburg-Landau equation, including the case in which it exhibits transient chaos, and (ii) the two-dimensional unsteady lid-driven cavity problem

Utilidad de la Guía Didáctica de Teledetección y Medio Ambiente para la enseñanza activa de la Geografía

La guía está concebida como un atlas en el que se ha compilado una abundante colección de imágenes de la Tierra y de los océanos, adquiridas desde distintos satélites, plataformas espaciales tripuladas y desde la Estación Espacial Internacional. Ilustran distintos fenómenos y riesgos naturales y diferentes impactos provocados por el hombre sobre los recursos naturales. En resumen, se trata de un recurso didáctico para la enseñanza activa de la Geografía, y de otras ciencias afines, en Secundaria y Bachillerato. También se comentan las razones que dificultan el empleo de este tipo de recursos audiovisuales en las aulas.Peer reviewe

Circumnuclear Keplerian Disks in Galaxies

In this paper we demonstrate the possibility of inferring the presence of Keplerian gaseous disks using optical ground-based telescopes properly equipped. We have modeled the peculiar bidimensional shape of the emission lines in a sample of five S0-Sa galaxies as due to the motion of a gaseous disk rotating in the combined potential of a central point-like mass and of an extended stellar disk. The value of the central mass concentration estimated for four galaxies of the sample (NGC 2179, NGC 4343, NGC 4435 and NGC 4459) is ~10^9 Msolar. For the remaining galaxy NGC 5064 an upper limit of 5*10^7 Msolar is estimated.Comment: 11 pages, LaTeX, with 3 PostScript figures, Submitted to The Astrophysical Journal Letter

One-dimensional dynamics of nearly unstable axisymmetric liquid bridges

A general one-dimensional model is considered that describes the dynamics of slender, axisymmetric, noncylindrical liquid bridges between two equal disks. Such model depends on two adjustable parameters and includes as particular cases the standard Lee and Cosserat models. For slender liquid bridges, the model provides sufficiently accurate results and involves much easier and faster calculations than the full three-dimensional model. In particular, viscous effects are easily accounted for. The one-dimensional model is used to derive a simple weakly nonlinear description of the dynamics near the instability limit. Small perturbations of marginal instability conditions are also considered that account for volume perturbations, nonequality of the supporting disks, and axial gravity. The analysis shows that the dynamics breaks the reflection symmetry on the midplane between the supporting disks. The weakly nonlinear evolution of the amplitude of the perturbation is given by a Duffing equation, whose coefficients are calculated in terms of the slenderness as a part of the analysis and exhibit a weak dependence on the adjustable parameters of the one-dimensional model. The amplitude equation is used to make quantitative predictions of both the (first stage of) breakage for unstable configurations and the (slow) dynamics for stable configurations

Modulated surface waves in large-aspect-ratio horizontally vibrated containers

We consider the harmonic and subharmonic modulated surface waves that appear upon horizontal vibration along the surface of the liquid in a two-dimensional large-aspect-ratio (length large compared to depth) container, whose depth is large compared to the wavelength of the surface waves. The analysis requires us also to consider an oscillatory bulk flow and a viscous mean flow. A weakly nonlinear description of the harmonic waves is made which provides the threshold forcing amplitude to trigger harmonic instabilities, which are of various qualitatively different kinds. A linear analysis provides the threshold amplitude for the appearance of subharmonic waves through a subharmonic instability. The results obtained are used to make several specific qualitative and quantitative predictions