On the stability of two-dimensional digital filters

In the first part of this paper opportunity has been taken to make some adjustments in certain general formulae of previous papers, the necessity for which appeared in discussions with other workers on this subject. The general results thus amended are then applied to a general discussion of the stability problem including the effect of the trailing wake which was deliberately excluded in the previous paper. The general conclusion is that to a first approximation the wake, as usually assumed, has little or no effect on the reality of the roots of the period equation, but that it may introduce instability of the oscillations, if the centre of gravity of the element is not sufficiently far forward. During the discussion contact is made with certain partial results recently obtained by von Karman and Sears, which are shown to be particular cases of the general formulae. An Appendix is also added containing certain results on the motion of a vortex behind a moving cylinder, which were obtained to justify certain of the assumptions underlying the trail theory.

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Distributed learning and mutual adaptation

Pragmatics & Cognition ◽

10.1075/pc.14.2.11sch ◽

2006 ◽

Vol 14 (2) ◽

pp. 313-332 ◽

Cited By ~ 13

Author(s):

Daniel L. Schwartz ◽

Taylor Martin

Keyword(s):

Distributed Cognition ◽

Dimensional Space ◽

Distributed Learning ◽

Early Learning ◽

Learning Technologies ◽

Two Dimensional ◽

Present Evidence ◽

Mutual Adaptation ◽

Initial Learning ◽

The Stability

If distributed cognition is to become a general analytic frame, it needs to handle more aspects of cognition than just highly efficient problem solving. It should also handle learning. We identify four classes of distributed learning: induction, repurposing, symbiotic tuning, and mutual adaptation. The four classes of distributed learning fit into a two-dimensional space defined by the stability and adaptability of individuals and their environments. In all four classes of learning, people and their environments are highly interdependent during initial learning. At the same time, we present evidence indicating that certain types of interdependence in early learning, most notably mutual adaptation, can help prepare people to be less dependent on their immediate environment and more adaptive when they confront new environments. We also describe and test examples of learning technologies that implement mutual adaptation.

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Interactions between steady and oscillatory convection in mushy layers

Journal of Fluid Mechanics ◽

10.1017/s0022112009992709 ◽

2010 ◽

Vol 645 ◽

pp. 411-434 ◽

Cited By ~ 13

Author(s):

PETER GUBA ◽

M. GRAE WORSTER

Keyword(s):

Standing Waves ◽

Mushy Layer ◽

Two Dimensional ◽

Oscillatory Convection ◽

Mushy Layers ◽

Theoretical Predictions ◽

Convection Patterns ◽

The Stability ◽

Nonlinear Solutions ◽

Steady Convection

We study nonlinear, two-dimensional convection in a mushy layer during solidification of a binary mixture. We consider a particular limit in which the onset of oscillatory convection just precedes the onset of steady overturning convection, at a prescribed aspect ratio of convection patterns. This asymptotic limit allows us to determine nonlinear solutions analytically. The results provide a complete description of the stability of and transitions between steady and oscillatory convection as functions of the Rayleigh number and the compositional ratio. Of particular focus are the effects of the basic-state asymmetries and non-uniformity in the permeability of the mushy layer, which give rise to abrupt (hysteretic) transitions in the system. We find that the transition between travelling and standing waves, as well as that between standing waves and steady convection, can be hysteretic. The relevance of our theoretical predictions to recent experiments on directionally solidifying mushy layers is also discussed.

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