Instabilities and Spatio-temporal Chaos of Long-wave Hexagon Patterns in Rotating Marangoni Convection

We consider surface-tension driven convection in a rotating fluid layer. For nearly insulating boundary conditions we derive a long-wave equation for the convection planform. Using a Galerkin method and direct numerical simulations we study the stability of the steady hexagonal patterns with respect to general side-band instabilities. In the presence of rotation steady and oscillatory instabilities are identified. One of them leads to stable, homogeneously oscillating hexagons. For sufficiently large rotation rates the stability balloon closes, rendering all steady hexagons unstable and leading to spatio-temporal chaos.Comment: 26 pages, 9 jpeg figures. Postscript file with all figures included available at http://www.esam.northwestern.edu/~riecke/lit/lit.html Movies available at http://www.esam.northwestern.edu/~riecke/research/Marangoni/marangoni.htm

Barriers to transport in aperiodically time-dependent two-dimensional velocity fields: Nekhoroshev's theorem and "Nearly Invariant" tori

In this paper we consider fluid transport in two-dimensional flows from the dynamical systems point of view, with the focus on elliptic behaviour and aperiodic and finite time dependence. We give an overview of previous work on general nonautonomous and finite time vector fields with the purpose of bringing to the attention of those working on fluid transport from the dynamical systems point of view a body of work that is extremely relevant, but appears not to be so well known. We then focus on the Kolmogorov–Arnold–Moser (KAM) theorem and the Nekhoroshev theorem. While there is no finite time or aperiodically time-dependent version of the KAM theorem, the Nekhoroshev theorem, by its very nature, is a finite time result, but for a "very long" (i.e. exponentially long with respect to the size of the perturbation) time interval and provides a rigorous quantification of "nearly invariant tori" over this very long timescale. We discuss an aperiodically time-dependent version of the Nekhoroshev theorem due to Giorgilli and Zehnder (1992) (recently refined by Bounemoura, 2013 and Fortunati and Wiggins, 2013) which is directly relevant to fluid transport problems. We give a detailed discussion of issues associated with the applicability of the KAM and Nekhoroshev theorems in specific flows. Finally, we consider a specific example of an aperiodically time-dependent flow where we show that the results of the Nekhoroshev theorem hold

Preface "Nonlinear processes in oceanic and atmospheric flows"

Nonlinear phenomena are essential ingredients in many oceanic and atmospheric processes, and successful understanding of them benefits from multidisciplinary collaboration between oceanographers, meteorologists, physicists and mathematicians. The present Special Issue on ``Nonlinear Processes in Oceanic and Atmospheric Flows'' contains selected contributions from attendants to the workshop which, in the above spirit, was held in Castro Urdiales, Spain, in July 2008. Here we summarize the Special Issue contributions, which include papers on the characterization of ocean transport in the Lagrangian and in the Eulerian frameworks, generation and variability of jets and waves, interactions of fluid flow with plankton dynamics or heavy drops, scaling in meteorological fields, and statistical properties of El Ni\~no Southern Oscillation.Comment: This is the introductory article to a Special Issue on "Nonlinear Processes in Oceanic and Atmospheric Flows'', published in the journal Nonlinear Processes in Geophysics, where the different contributions are summarized. The Special Issue itself is freely available from http://www.nonlin-processes-geophys.net/special_issue103.htm

Lagrangian descriptors and the assessment of the predictive capacity of oceanic data sets

We use a recently developed Lagrangian transport tool, <i>Lagrangian descriptors</i>, to compare the transport properties of data distributed by AVISO and numerical simulations obtained from the HYCOM model in the Yucatán–Florida current system. Our data correspond to the months from June through August 2010. Structures obtained from HYCOM are noisier than those from AVISO; however, both AVISO and HYCOM succeed in identifying Lagrangian structures that influence the paths of drifters, such as eddies, currents, lobes, etc. We find evidence in which AVISO gives the positions of important hyperbolic trajectories in a manner that is inconsistent with the trajectories of the drifters, while for the same examples HYCOM succeeds to this end

Natural Connection with Totally Skew-Symmetric Torsion on Riemannian Almost Product Manifolds

On a Riemannian almost product manifold $(M,P,g)$ we consider a linear connection preserving the almost product structure $P$ and the Riemannian metric $g$ and having a totally skew-symmetric torsion. We determine the class of the manifolds $(M,P,g)$ admitting such a connection and prove that this connection is unique in terms of the covariant derivative of $P$ with respect to the Levi-Civita connection. We find a necessary and sufficient condition the curvature tensor of the considered connection to have similar properties like the ones of the K\"ahler tensor in Hermitian geometry. We pay attention to the case when the torsion of the connection is parallel. We consider this connection on a Riemannian almost product manifold $(G,P,g)$ constructed by a Lie group $G$.Comment: 14 pages, a revised edition, an example is adde

Evolución clínica de la enteritis crónica linfoplasmocitaria canina : antes, durante y después del tratamiento

El objetivo de este trabajo consistió en la valoración de 16 perros con ECLP, antes durante y después del tratamiento. Para ello, se evaluaron periódicamente el peso, los signos clíncos y el índice de actividad de cada uno de los perros. El incremento de peso medio respecto al peso inicial observado durante el tratamiento fue de 4, 74 el día 30 tras el inicio del tratamiento del 9, 61 el día 60, del 11.69 el día 90 y del 11, 52 el día 120. El signos clínico más frecuente en los perros con ECLP de nuestro estudio fue la existencia de vómitos (87, 5%). Durante y tras el tratamiento, se observó una marcada reducción de todos los signos clínicos avaluados, antes de comenzar el protocolo terapéutico fue de 7, 31 (enfermedad clínicamente moderada). A lo largo de dicho protocolo, el índice de actividad medio fue disminuyendo progresivamente hasta alcanzar un valor medio fue disminuyendo progresivamente hasta alcanzar un valor medio de 0, 19 a los 120 días de iniciado el mismo (enfermedad clínicamente insignificante). Por tanto, la aplicación del tratamiento adecuado a los perros con ECLP, se acompaña de una importante mejoría clínica, con una disminución de los signos clínicos y un incremento de peso.

Valoración de parámetros endoscópicos en perros con enteritis crónica linfoplásmocitaria

El objetivo del presente trabajo, es la valoración de la frecuencia de presentación y gravedad de las lesiones endoscópicos de estómago y de duodeno de 45 perros con enteritis crónica linfoplasmocitaria (ECLP). En función de las mismas, se propone una clasificación de los animales en cuanto al grado de lesión endocópica hallado. Nuestros resultados muestran que el hallazgo durante una gastroduodenoscopia de una mucosa congestiva o engrosada en estómago y de una mucosa congestiva, engrosada, irregular o friable en duodeno, puede sugerir la existencia de una de una ECLP. La inespecificidad de estas lesiones, junto con la subjetividad en la valoración de las mismas, resalta la importancia de la toma de biopsias, en todos los perros con sospecha de ECLP, para su diagnóstico definitivo.

Distinguished trajectories in time dependent vector fields

We introduce a new definition of distinguished trajectory that generalises the concepts of fixed point and periodic orbit to aperiodic dynamical systems. This new definition is valid for identifying distinguished trajectories with hyperbolic and non-hyperbolic types of stability. The definition is implemented numerically and the procedure consist in determining a path of limit coordinates. It has been successfully applied to known examples of distinguished trajectories. In the context of highly aperiodic realistic flows our definition characterises distinguished trajectories in finite time intervals, and states that outside these intervals trajectories are no longer distinguished.Comment: Chaos 19 (2009), 013111-1-013111-1