The Korteweg-de Vries hierarchy and long water-waves

By using the multiple scale method with the simultaneous introduction of multiple times, we study the propagation of long surface-waves in a shallow inviscid fluid. As a consequence of the requirements of scale invariance and absence of secular terms in each order of the perturbative expansion, we show that the Korteweg-de Vries hierarchy equations do play a role in the description of such waves. Finally, we show that this procedure of eliminating secularities is closely related to the renormalization technique introduced by Kodama and Taniuti. © 1995 American Institute of Physics.

The Role of the Korteweg-de Vries Hierarchy in the N-Soliton Dynamics of the Shallow Water Wave Equation

We apply a multiple-time version of the reductive perturbation method to study long waves as governed by the shallow water wave model equation. As a consequence of the requirement of a secularity-free perturbation theory, we show that the well known N-soliton dynamics of the shallow water wave equation, in the particular case of α = 2β, can be reduced to the N-soliton solution that satisfies simultaneously all equations of the Korteweg-de Vries hierarchy.

Dominance hierarchy in different stages of development in colonies of the primitively eusocial wasp Mischocyttarus cerberus styx (Hymenoptera, Vespidae)

In primitively eusocial insect societies, reproductive division of labor is established by dominance-submission interactions which determine a linear dominance hierarchy. As previously observed for other species, in Mischocyttarus cerberus styx (Hymenoptera, Vespidae), the dominant female is the main egg layer. Most of her attacks were to the females directly beneath in the rank establishing a hierarchy. During the pre-emergence stage, the hierarchy was already defined and in the post-emergence stage, pre-male substage, the frequency of dominance interactions were strong but the hierarchy was still maintained by the first-ranked female. In the decline stage there were many neutral individuals which could be the reproductives of a new colony.

Dominance hierarchy in different stages of development in colonies of the primitively eusocial wasp Mischocyttarus cassununga (Hymenoptera, Vespidae)

Seven colonies of Mischocyttarus cassununga were studied under field conditions at Universidade Federal de Juiz de Fora, MG, in southeastern Brazil: in pre-emergence, post-emergence and decline stages, during 145.8 hours. Dominance interactions among the females were quantified to verify the dynamics of succession in the social hierarchy of the colonies. Early pre-emergence colonies present more intense aggressive interactions than late pre-emergence ones, because the females are engaged in securing the role of main egg layer in the nest. In post-emergence (pre-male) colonies the dominance hierarchy is more defined and the frequency of dominance and subordination behaviors were lower than in pre-emergence stages: most of the agonistic behaviors are restricted to the first ranked females (potentially queens) and the subordinate individuals play the role of workers in the nests. In the post-emergence, post-male, and decline stages the hierarchy is still maintained by the aggressive behaviors of the 1st-ranked female but because the presence of males and future nest foundresses these interactions are not well defined in a linear way.

Nutritional and social hierarchy establishment of the primitively eusocial wasp Mischocyttarus cassununga (Hymenoptera, Vespidae, Mischocyttarini) and related aspects

The results on the nutritional influence in the social hierarchy establishment among females from six colonies of Mischocyttarus cassununga show that: - there was no caste determination in the pre-imaginal period concerning ingested food quantities, however, in relation to qualification (proteins and carbohydrate) the Mann-Whitney test applied showed variation among colonies: in two colonics (colony 3, p=0.0209; colony 4, p=0.0090) the larvae which ingested a higher quantity of solid food became adults of hierarchically higher position, however in two other colonies, colony 1 (p=0.6744) and colony 2 (p=0.3367) this difference was not statistically significant; in two experimentally manipulated colonies the caste determination was observed in the imaginal phase (it was verified that the larger the food quantity consumed, the higher the assumed hierarchical position by the individuals); - adult individuals of hierarchically higher position in two colonies ingested a greater amount of solid than liquid food (Mann-Whitney; p ≤ 0.05), however in the other three colonies there was no difference. It can be seen that for all colonies (2, 3, 4, 5 and 6) the high tendency to solid food ingestion occurs. In colony 1, this data was not collected because the observation purpose was different); - inside the colony hierarchy, the older individuals were the ones that occupied higher hierarchical positions; - more than one inseminated female per colony was found in the two experimentally manipulated colonies ; - ovarian development is greater in inseminated females; - the average height of the 3rd tergite was greater for inseminated females, indicating an adaptation to accommodate larger ovary development (t-Student test; p ≤ 0.05).

On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation?

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The effects of the social hierarchy destabilization on the foraging activity of eusocial wasp Mischocyttarus cerberus styx Richards, 1940 (Hymenoptera: Vespidae: Polistinae)

The genus Mischocyttarus comprises 245 species of neotropical basal eusocial wasps. They form small colonies (rarely more than few tens of individuals); castes are morphologically undifferentiated and determined behaviorally by agonistic interactions. The aim of this study was to verify the effects of the experimental disruption of social hierarchy on foraging activity of Mischocyttarus cerberus styx. We observed six colonies in postemergence phase and recorded data on the foraging activity under two experimental conditions: (1) removal of lower-ranked females and (2) removal of higher ranked females, except the queen. Our results showed that the removal of higher-ranked females had higher effect on the number of foraging trips of M. cerberus styx than the removal of lower-ranked females (the number of foraging trips/hour decreased by 66.4 and 32.7, resp.). Such results are likely due to the social organization of this species and the presence of a distinct class of females, which in this study were regarded as intermediates. Our data also showed that, irrespective of the hierarchical status of the females, the removal of two or three individuals affected significantly the number of foraging trips in this species. Copyright 2011 Vanderlei Conceio Costa Filho et al.

Division of labor in stable social hierarchy of the independent-founding wasp Mischocyttarus (Monocyttarus) cassununga, von Ihering (Hymenoptera, Vespidae)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the mKdV-Liouville hierarchy and its self-similarity reduction

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Asymmetrical Bloch branes and the hierarchy problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Backlund transformation for integrable hierarchies: example - mKdV hierarchy

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On two-current realization of KP hierarchy

A simple description of the KP hierarchy and its multi-hamiltonian structure is given in terms of two Bose currents. A deformation scheme connecting various W-infinity algebras and the relation between two fundamental nonlinear structures are discussed. Properties of Faá di Bruno polynomials are extensively explored in this construction. Applications of our method are given for the Conformal Affine Toda model, WZNW models and discrete KP approach to Toda lattice chain.

The effect of increased light intensity on the aggressive behavior of the Nile tilapia, Oreochromis niloticus (Teleostei: Cichlidae)

Animals show behavioral and physiological changes that emerge in response to environmental perturbations (i.e., emergency life-history stages). In this study, we investigate the effects of light intensity on aggressive encounters and social stability in groups of adult male Nile tilapia, Oreochromis niloticus (Linnaeus, 1758). The study compared the behavior observed under low (280.75 ± 50.60 lx) and high (1394.14 ± 520.32 lx) light intensities, with 12 replicates for each treatment. Adult fish were isolated in 36-L aquaria for 96 hours, and three males were grouped for 11 days in 140-L aquaria. Agonistic behavior was video-recorded (10 min/day) on the 3rd, 5th, 7th, and 9th day to quantify aggressive interactions and social stability. There was an effect of light intensity and day of observation on the total number of agonistic behaviors performed by the fish group. Besides, increased frequency of aggressive interactions (the sum of the four sessions) by the alpha, beta and gamma fish occurred at the higher light intensity. The dominance ranks of the fish remained unchanged across the observation sessions under both the low and high light intensities. We concluded that enhanced light intensity has a cumulative effect that increases the aggressiveness of the Nile tilapia but that this effect is not sufficiently strong to destabilize the social hierarchy.

Comparison of different nonlinear functions to describe Nelore cattle growth

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Soil erosion fragility assessment using an impact model and geographic information system

A study was taken in a 1566 ha watershed situated in the Capivara River basin, municipality of Botucatu, São Paulo State, Brazil. This environment is fragile and can be subjected to different forms of negative impacts, among them soil erosion by water. The main objective of the research was to develop a methodology for the assessment of soil erosion fragility at the various different watershed positions, using the geographic information system ILWIS version 3.3 for Windows. An impact model was created to generate the soil's erosion fragility plan, based on four indicators of fragility to water erosion: land use and cover, slope, percentage of soil fine sand and accumulated water flow. Thematic plans were generated in a geographic information system (GIS) environment. First, all the variables, except land use and cover, were described by continuous numerical plans in a raster structure. The land use and cover plan was also represented by numerical values associated with the weights attributed to each class, starting from a pairwise comparison matrix and using the analytical hierarchy process. A final field check was done to record evidence of erosive processes in the areas indicated as presenting the highest levels of fragility, i.e., sites with steep slopes, high percentage of soil fine sand, tendency to accumulate surface water flow, and sites of pastureland. The methodology used in the environmental problems diagnosis of the study area can be employed at places with similar relief, soil and climatic conditions.