Spatial Interval Adaptation

The single reference to Thompson s survey [73] must suffice to represent the numerical literature, and the references in the papers of Bieniasz [9, 54, 58, 59] provide further background. 

The procedure is then as follows. At a given time, a trial step is taken to the next time level. This produces a provisional new concentration profile. From this, the -function (7.27) is generated and from it, a new set of positions for the points. Now the concentrations are interpolated at these points, between the present concentration points, and the step to the next time level repeated on the new set of points. 

Some remarks are in order, starting with the purpose of the a term in (7.28). As mentioned, the numerical literature appears to prefer it to be close to unity. If one were to set it to zero, one would obtain an unacceptably wide spacing at parts of the profile where the second derivative is close to zero. In effect, a finite a value ensures a finite positive gradient of (X) at large X. If this is not 

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For the case of time-varying signals (as encountered in speech, music and video or in applications with time transients), it is possible to segment the time axis into disjoint intervals and construct wavelet bases on each interval -called spatial segmentation. This allows the WPT to adapt to each time interval. This is referred to as a multi-tree WPT or spatially adaptive WPT (see Fig. 3 for an example two-way segmentation of the time axis for the case of a dyadic WPT). 

All species of teleost fish examined to date have been found to use sex pheromones (Liley 1982 Liley Stacey 1983 Stacey, Kyle Liley 1986 Stacey, Cardwell, Liley, Scott Sorensen 1994). Further, where examined (about a dozen species Sorensen Stacey, this volume), these cues have been found to be derived from sex hormones. However, the temporal nature of pheromone release has yet to be characterized. Temporal characteristics of pheromone release (i.e. pulse frequency and duration and interpulse interval) might be important for two reasons (Dusenbery 1989). First, intermittent release of pheromone could produce temporal and spatial variations in pheromone concentration that might prevent or reduce sensory adaptation. Second, the temporal characteristics of pheromone release may provide information about the proximity and identity of the signal s sender. 

Bieniasz LK (2002) Use of dynamically adaptive grid techniques for the solution of electrochemical kinetic equations. Part 10. Extension of the patch-adaptive strategy to kinetic models involving spatially localised unknowns at the boundaries, multiple space intervals, and nonlocal boundary conditions, in one-dimensional space geometry. J Electroanal Chem 527 1—10. Corrigendum ibid. 565 137 (2004)... 

Figure 12.12 Left panel spiral patterns, a few micrometers in size, measured at different times, for oxidation of CO on Pt (110). Shown are the local variations in the work function, low at CO-covered surface, bright areas, and high for O atom coverage, dark areas. The time interval between the frames is 30 s and as can be seen different spirals rotate at different rates. Right panel the different spatial patterns that have been analyzed as a function of temperature and partial pressure of CO, for a low (4-10 mbar) O2 partial pressure. [Both adapted from Rotermund (1997)].

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