For organisms that fly or swim, movement results from the combined effects of the moving medium - air or water - and the organism's own locomotion. For larger organisms, propulsion contributes significantly to progress but the flow usually still provides significant opposition or assistance, or produces lateral displacement ('drift'). Animals show a range of responses to flows, depending on the direction of the flow relative to their preferred direction, the speed of the flow relative to their own self-propelled speed, the incidence of flows in different directions and the proportion of the journey remaining. We here present a classification of responses based on the direction of the resulting movement relative to flow and preferred direction, which is applicable to a range of taxa and environments. The responses adopted in particular circumstances are related to the organisms' locomotory and sensory capacities and the environmental cues available. Advances in biologging technologies and particle tracking models are now providing a wealth of data, which often demonstrate a striking level of convergence in the strategies that very different animals living in very different environments employ when moving in a flow.

Automated tracking of bumblebees and computer simulations reveal how bees locate a series of flowers and optimize their routes to visit them all.

Honey bees (Apis mellifera) are regularly faced with the task of navigating back to their hives from remote food sources. They have evolved several methods to do this, including compass-directed "vector" flights and the use of landmarks. If these hive-centered mechanisms are disrupted, bees revert to searching for the hive, but the nature and efficiency of their searching strategy have hitherto been unknown. We used harmonic radar to record the flight paths of honey bees that were searching for their hives. Our subsequent analysis of these paths revealed that they can be represented by a series of straight line segments that have a scale-free, Lévy distribution with an inverse-square-law tail. We show that these results, combined with the "no preferred direction" characteristic of the segments, demonstrate that the bees were flying an optimal search pattern. Lévy movements have already been identified in a number of other animals. Our results are the best reported example where the movements are mostly attributable to the adoption of an optimal, scale-free searching strategy.

Over recent years there has been an accumulation of evidence from a variety of experimental, theoretical, and field studies that many organisms use a movement strategy approximated by Lévy flights when they are searching for resources. Lévy flights are random movements that can maximize the efficiency of resource searches in uncertain environments. This is a highly significant finding because it suggests that Lévy flights provide a rigorous mathematical basis for separating out evolved, innate behaviors from environmental influences. We discuss recent developments in random-search theory, as well as the many different experimental and data collection initiatives that have investigated search strategies. Methods for trajectory construction and robust data analysis procedures are presented. The key to prediction and understanding does, however, lie in the elucidation of mechanisms underlying the observed patterns. We discuss candidate neurological, olfactory, and learning mechanisms for the emergence of Lévy flight patterns in some organisms, and note that convergence of behaviors along such different evolutionary pathways is not surprising given the energetic efficiencies that Lévy flight movement patterns confer.

A series of Cu(I) and Cu(II) complexes of a variety of beta-diketiminate ligands (L(-)) with a range of substitution patterns were prepared and characterized by spectroscopic, electrochemical, and, in several cases, X-ray crystallographic methods. Specifically, complexes of the general formula [LCuCl](2) were structurally characterized and their magnetic properties assessed through EPR spectroscopy of solutions and, in one instance, by variable-temperature SQUID magnetization measurements on a powder sample. UV-vis spectra indicated reversible dissociation to 3-coordinate monomers LCuCl in solution at temperatures above -55 degrees C. The Cu(I) complexes LCu(MeCN) exhibited reversible Cu(I)/Cu(II) redox couples with E(1/2) values between +300 and +520 mV versus NHE (cyclic voltammetry, MeCN solutions). These complexes were highly reactive with O(2), yielding intermediates that were identified as rare examples of neutral bis(mu-oxo)dicopper complexes on the basis of their EPR silence, diagnostic UV-vis absorption data, and O-isotope-sensitive resonance Raman spectroscopic features. The structural features of the compounds [LCuCl](2) and LCu(MeCN) as well as the proclivity to form bis(mu-oxo)dicopper products upon oxygenation of the Cu(I) complexes are compared to data previously reported for complexes of more sterically hindered beta-diketiminate ligands (Aboelella, N. W.; Lewis, E. A.; Reynolds, A. M.; Brennessel, W. W.; Cramer, C. J.; Tolman, W. B. J. Am. Chem. Soc. 2002, 124, 10600. Spencer, D. J. E.; Aboelella, N. W.; Reynolds, A. M.; Holland, P. L.; Tolman, W. B. J. Am. Chem. Soc. 2002, 124, 2108. Holland, P. L.; Tolman, W. B. J. Am. Chem. Soc. 1999, 121, 7270). The observed structural and reactivity differences are rationalized by considering the steric influences of both the substituents on the flanking aromatic rings and those present on the beta-diketiminate backbone.

The X-ray structure of a 1:1 Cu/O(2) adduct revealed side-on (eta(2)) O(2) coordination. Density functional calculations corroborated the structure, indicated a significant contribution of a Cu(III)-(O(2)(2-)) resonance form, and provided insights into the key bonding interactions. Reaction of a 1:1 adduct supported by a slightly different beta-diketiminate ligand with Cu(I) reagents resulted in the formation of novel asymmetric bis(mu-oxo) complexes that were identified by EPR, UV-vis, and Raman spectroscopy, as well as by an X-ray structure in one instance.

. Consequently, Lévy-flights are said to be 'scale-free' because their statistical properties do not depend upon the observational scale. This absence of a characteristic scale makes Lévy-flights scaleThe foraging strategies used by animals are key to their success in spatially and temporally heterogeneous environments. We hypothesise that when a food source at a known location ceases to be available, flying insects will exhibit search patterns that optimise the rediscovery of such resources. In order to study these searching patterns, foraging honeybees were trained to an artificial feeder that was then removed, and the subsequent flight patterns of the bees were recorded using harmonic radar. We show that the flight patterns have a scale-free (Lévy-flight) characteristic that constitutes an optimal searching strategy for the location of the feeder. It is shown that this searching strategy would remain optimal even if the implementation of the Lévy-flights was imprecise due, for example, to errors in the bees' path integration system or difficulties in responding to variable wind conditions. The implications of these findings for animal foraging in general are discussed.

Copper(I) and -(II) complexes of beta-diketiminate ligands with identical flanking 2,6-diisopropylphenyl groups but divergent backbone substitution patterns were prepared and structurally characterized, and reactions of the Cu(I) species with O(2) at low temperature were explored. Despite being far removed from the coordinated metal ion, the different backbone patterns significantly influence the steric encumbrance exerted by the ligands, as revealed by differences in (a) the structural features of the Cu(I) and Cu(II) complexes and (b) the course of the oxygenation reactions of the Cu(I) compounds. With the less hindered ligand, a rare example of a neutral bis(mu-oxo)dicopper complex was identified on the basis of its diagnostic spectral features (UV-vis, resonance Raman, EPR) and the stoichiometry of O(2) uptake (Cu:O(2) = 2:1). In contrast, oxygenation of the Cu(I) complexes supported by the more hindered ligands yielded novel (superoxo)copper complexes, identified by a Cu:O(2) ratio of 1:1, a lack of an EPR signal, and O-isotope sensitive resonance Raman spectral features (nu(O)(-)(O) = 968 cm(-1), Delta(18)O(2) = 51 cm(-1)). Symmetric coordination of the superoxo ligand is proposed on the basis of Raman data acquired using (16)O(18)O (single peak at 943 cm(-1)).