The local and global stability of confined planar wakes at intermediate Reynolds number

At high Reynolds numbers, wake flows become more globally unstable when they are confined within a duct or between two flat plates. At Reynolds numbers around 100, however, global analyses suggest that such flows become more stable when confined, while local analyses suggest that they become more unstable. The aim of this paper is to resolve this apparent contradiction by examining a set of obstacle-free wakes. In this theoretical and numerical study, we combine global and local stability analyses of planar wake flows at $\mathit{Re}= 100$ to determine the effect of confinement. We find that confinement acts in three ways: it modifies the length of the recirculation zone if one exists, it brings the boundary layers closer to the shear layers, and it can make the flow more locally absolutely unstable. Depending on the flow parameters, these effects work with or against each other to destabilize or stabilize the flow. In wake flows at $\mathit{Re}= 100$ with free-slip boundaries, flows are most globally unstable when the outer flows are 50 % wider than the half-width of the inner flow because the first and third effects work together. In wake flows at $\mathit{Re}= 100$ with no-slip boundaries, confinement has little overall effect when the flows are weakly confined because the first two effects work against the third. Confinement has a strong stabilizing effect, however, when the flows are strongly confined because all three effects work together. By combining local and global analyses, we have been able to isolate these three effects and resolve the apparent contradictions in previous work.

Global analysis of dynamical decision-making models through local computation around the hidden saddle

Bistable dynamical switches are frequently encountered in mathematical modeling of biological systems because binary decisions are at the core of many cellular processes. Bistable switches present two stable steady-states, each of them corresponding to a distinct decision. In response to a transient signal, the system can flip back and forth between these two stable steady-states, switching between both decisions. Understanding which parameters and states affect this switch between stable states may shed light on the mechanisms underlying the decision-making process. Yet, answering such a question involves analyzing the global dynamical (i.e., transient) behavior of a nonlinear, possibly high dimensional model. In this paper, we show how a local analysis at a particular equilibrium point of bistable systems is highly relevant to understand the global properties of the switching system. The local analysis is performed at the saddle point, an often disregarded equilibrium point of bistable models but which is shown to be a key ruler of the decision-making process. Results are illustrated on three previously published models of biological switches: two models of apoptosis, the programmed cell death and one model of long-term potentiation, a phenomenon underlying synaptic plasticity. © 2012 Trotta et al.

Motor learning of novel dynamics is not represented in a single global coordinate system: evaluation of mixed coordinate representations and local learning.

Successful motor performance requires the ability to adapt motor commands to task dynamics. A central question in movement neuroscience is how these dynamics are represented. Although it is widely assumed that dynamics (e.g., force fields) are represented in intrinsic, joint-based coordinates (Shadmehr R, Mussa-Ivaldi FA. J Neurosci 14: 3208-3224, 1994), recent evidence has questioned this proposal. Here we reexamine the representation of dynamics in two experiments. By testing generalization following changes in shoulder, elbow, or wrist configurations, the first experiment tested for extrinsic, intrinsic, or object-centered representations. No single coordinate frame accounted for the pattern of generalization. Rather, generalization patterns were better accounted for by a mixture of representations or by models that assumed local learning and graded, decaying generalization. A second experiment, in which we replicated the design of an influential study that had suggested encoding in intrinsic coordinates (Shadmehr and Mussa-Ivaldi 1994), yielded similar results. That is, we could not find evidence that dynamics are represented in a single coordinate system. Taken together, our experiments suggest that internal models do not employ a single coordinate system when generalizing and may well be represented as a mixture of coordinate systems, as a single system with local learning, or both.

The local and global dimensions of metalliferous pollution derived from a reconstruction of an eight thousand year record of copper smelting and mining at a desert-mountain frontier in southern Jordan

Grattan, J.P., Gilbertson, D.D., Hunt, C.O. (2007). The local and global dimensions of metaliferrous air pollution derived from a reconstruction of an 8 thousand year record of copper smelting and mining at a desert-mountain frontier in southern Jordan. Journal of Archaeological Science 34, 83-110

Performing the Local and the Global : The Theatre Festivals of Lake Constance

Wilkinson, Jane, Performing the Local and the Global: The Theatre Festivals of Lake Constance (Peter Lang, 2007), pp.286 RAE2008

Trash: a local solution to a global problem

Gemstone Team GREEN JUSTICE

Tránsito entre representaciones en matemáticas ¿pensamiento global o local?

Este trabajo pretende dar a conocer el avance, que hasta el momento se ha logrado, en la línea de investigación: “Visualización y pensamiento global en Matemáticas”, la cual persigue, a partir de la Teoría de Representaciones Semióticas de Duval, la caracterización del estilo de pensamiento global y local, de estudiantes de nivel medio superior y superior y de sus profesores. En particular reporto los resultados preliminares encontrados hasta el momento con estudiantes de primeros semestres de licenciatura al abordar un problema de precálculo, contrastado con desempeños en ajedrez para interpretar aspectos semejantes en cuanto a la forma local o global de pensar un problema viendo sus registros que lleven a resultados que pudieran servir en la mejora de la enseñanza de algunos temas de matemáticas.

Global and local contributions to the optical specification of time to contact: Observer sensitivity to composite tau

First-order time remaining until a moving observer will pass an environmental element is optically specified in two different ways. The specification provided by global tau (based on the pattern of change of angular bearing) requires that the element is stationary and that the direction of motion is accurately detected, whereas the specification provided by composite tau (based on the patterns of change of optical size and optical distance) does not require either of these. We obtained converging evidence,for our hypothesis. that observers are sensitive to composite tau in four experiments involving, relative judgments of, time to, passage with forced-choice methodology. Discrimination performance was enhanced in the presence of a local expansion component, while being unaffected when the detection of the direction of heading was impaired. Observers relied on the information carried in composite tau rather than on the information carried in its constituent components. Finally, performance was similar under conditions of observer motion and conditions of object motion. Because composite tau specifies first-order time remaining for a large number of situations, the different ways in which it may be detected are discussed.

Path-Dependency, Stocks, Switching Points, Flows: Reflections on Long-term Global Change and Local Opportunities

This paper examines the possibilities for peripheral localities to achieve upward mobility in the world-system by “hooking on” to larger processes of world-system accumulation. In particular, is it possible for economies that are dependent on foreign investment to receive a flow of investments that is high enough to overcome the negative impacts of a high stock of foreign investment, thus enabling them to cross a threshold and achieve upward mobility in the world-system? An analysis of therecent experience of the southern Irish “Celtic Tiger” economy during 1990-2000 indicates that such an upward movement is possible on the basis of massive foreign investment inflows. On closer examination, however, the Irish-type model appears to be highly deficient, because a high proportion of growth is illusionary and also on grounds of social desirability and lack of generalizability.