On the numerical integration of rigid body nonlinear dynamics in presence of parameters singularities

One of the main complexities in the simulation of the nonlinear dynamics of rigid bodies consists in describing properly the finite rotations that they may undergo. It is well known that, to avoid singularities in the representation of the SO(3) rotation group, at least four parameters must be used. However, it is computationally expensive to use a four-parameters representation since, as only three of the parameters are independent, one needs to introduce constraint equations in the model, leading to differential-algebraic equations instead of ordinary differential ones. Three-parameter representations are numerically more efficient. Therefore, the objective of this paper is to evaluate numerically the influence of the parametrization and its singularities on the simulation of the dynamics of a rigid body. This is done through the analysis of a heavy top with a fixed point, using two three-parameter systems, Euler's angles and rotation vector. Theoretical results were used to guide the numerical simulation and to assure that all possible cases were analyzed. The two parametrizations were compared using several integrators. The results show that Euler's angles lead to faster integration compared to the rotation vector. An Euler's angles singular case, where representation approaches a theoretical singular point, was analyzed in detail. It is shown that on the contrary of what may be expected, 1) the numerical integration is very efficient, even more than for any other case, and 2) in spite of the uncertainty on the Euler's angles themselves, the body motion is well represented.

Analysis of Regular and Irregular Dynamics of a Non Ideal Gear Rattling Problem

This paper presents a study on the dynamics of the rattling problem in gearboxes under non-ideal excitation. The subject has being analyzed by a number of authors such as Karagiannis and Pfeiffer (1991), for the ideal excitation case. An interesting model of the same problem by Moon (1992) has been recently used by Souza and Caldas (1999) to detect chaotic behavior. We consider two spur gears with different diameters and gaps between the teeth. Suppose the motion of one gear to be given while the motion of the other is governed by its dynamics. In the ideal case, the driving wheel is supposed to undergo a sinusoidal motion with given constant amplitude and frequency. In this paper, we consider the motion to be a function of the system response and a limited energy source is adopted. Thus an extra degree of freedom is introduced in the problem. The equations of motion are obtained via a Lagrangian approach with some assumed characteristic torque curves. Next, extensive numerical integration is used to detect some interesting geometrical aspects of regular and irregular motions of the system response.

On non-ideal and non-linear portal frame dynamics analysis using bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.

WHEAT HERBAGE AMENDMENTS ALTER EMERGENCE DYNAMICS, SEEDLING GROWTH OF LAMBSQUARTER AND SOIL PROPERTIES

ABSTRACT Crop allelopathy is a potential tool for weed management but allelopathic potential often varies among cultivars and developmental stages of crop. Bioassays were conducted to appraise the allelopathic potential of herbage (incorporated at 8 g kg-1 soil) of different hexaploid wheat (Triticum aestivum) cultivars (Millat-2011, AARI-2011, Lasani-2008 and Faisalabad-2008) collected at different crop growth stages [tillering (Z-30), anthesis (Z-60) and maturity (Z-90)] against lambsquarter (Chenopodium album). Mean emergence time taken by lambsquarter was prolonged over control by anthesis and maturity stage herbage of all wheat cultivars. Final emergence percentage was dropped by 3-17% in response to different growth stages of herbage collection. Maximum suppression in shoot (45 and 78%) and root (60 and 90%) length, and seedling dry biomass (65 and 96%) of lambsquarter over control was recorded under the amendment of anthesis and maturity stages herbage of wheat cultivars. Total chlorophyll contents declined in response to herbage collected at anthesis and maturity stage of all wheat cultivars over control. Phenolic contents on the other hand were increased. Activities of enzymatic antioxidants also varied among all wheat cultivars, and declined by the incorporation of tillering, anthesis and maturity stage herbage. Wheat herbage induced lipid peroxidation in lambsquarter seedling and higher malondialdehyde content (0.56 and 0.77 nmol g-1 FW) was observed by the incorporation of wheat cultivars herbage collected at anthesis and maturity stage, respectively. Anthesis and maturity stage herbage of wheat cultivars Millat-2011, AARI-2011 and Lasani-2008 was more phytotoxic than Faisalabad-2008. Moreover, tillering stage herbage of all wheat cultivars had less inhibitory potential against emergence, seedling growth and biochemical attributes of lambsquarter. Wheat herbage amendment increased the soil pH, phenolic, organic carbon and nitrogen contents as compared to control.

Temporal dynamics of two species of Chaetophoraceae (Chlorophyta) in tropical streams of São Paulo State, Southeastern Brazil

Temporal dynamics of the chaetophoracean green algae Chaetophora elegans (Roth) C.A. Agardh and Stigeoclonium amoenum Kützing populations was investigated biweekly during late autumn trhough early spring (April to October) in two tropical streams from northwestern São Paulo State, southeastern Brazil. Abundances of one population of each species was evaluated by the quadrat technique in terms of percent cover and frequency. The fluctuations were related to the following stream variables: temperature, turbidity, specific conductance, pH, oxygen saturation, depth, substratum type, current velocity, irradiance and nutrients. Percent cover and frequency of C. elegans had lower values throughout the study period and was positively correlated to rainfall. Other correlations (i.e. positive of percent cover with depth and current velocity and negative with irradiance) were consistently found, reinforcing the strong influence of rainfall. On the other hand, percent cover and frequency of S. amoenum had higher values, with maximum growth from June to September. Percent cover was negatively correlated to rainfall. Results suggest the precipitation regime as the most important driving force to temporal changes in both populations, but playing different roles in each one. The gelatinous thallus of C. elegans seem to be favored by the increment of current velocity, since higher flows can improve the nutrient uptake by means of reduction in diffusion shell without promoting excessive drag force. In contrast, tufts of S. amoenum are, presumably, more exposed to drag force, and, consequently, more susceptible to mechanical damage effects due to higher current velocities.

The succession dynamics of a macroalgal community after a flood disturbance in a tropical stream from São Paulo State, southeastern Brazil

The succession dynamics of a macroalgal community in a tropical stream (20º58' S and 49º25' W) was investigated after disturbance by a sequence of intensive rains. High precipitation levels caused almost complete loss of the macroalgal community attached to the substratum and provided a strong pressure against its immediate re-establishment. After this disturbance, a weekly sampling program from May 1999 to January 2000 was established to investigate macroalgal recolonization. The community changed greatly throughout the succession process. The number of species varied from one to seven per sampling. Global abundance of macroalgal community did not reveal a consistent temporal pattern of variation. In early succession stages, the morphological form of tufts dominated, followed by unbranched filaments. Latter succession stages showed the almost exclusive occurrence of gelatinous forms, including filaments and colonies. The succession trajectory was mediated by phosphorus availability in which community composition followed a scheme of changes in growth forms. However, we believe that deterministic and stochastic processes occur in lotic ecosystems, but they are dependent on the length of time considered in the succession analyses.

Tree population and community dynamics in a Brazilian tropical semideciduous forest

The dynamics of the tree community and 30 tree populations were examined in an area of tropical semideciduous forest located on the margin of the Rio Grande, SE Brazil, based on surveys done in 1990 and 1997 in three 0.18 ha plots. The main purpose was to assess whether variations in dynamics were related to topography and the effects of a catastrophic flood in 1992. Rates of mortality and recruitment of trees and gain and loss of basal area in two topographic sites, lower (flooded) and upper (non-flooded), were obtained. Projected trajectories of mean and accelerated growth in diameter were obtained for each species. In both topographic sites, mortality rates surpassed recruitment rates, gain rates of basal area surpassed loss rates, and size distributions changed, with declining proportions of smaller trees. These overall changes were possibly related to increased underground water supply after the 1992 flood as well as to a c. 250-year-old process of primary succession on abandoned gold mines. Possible effects of the 1992 flood showed up in the higher proportions of dead trees in the flooded sites and faster growth rates in the flood-free sites. Species of different regeneration guilds showed particular trends with respect to their demographic changes and diameter growth patterns. Nevertheless, patterns of population dynamics differed between topographic sites for only two species.

Juvenile dynamics of the endemic and rare Enterolobium glaziovii Benth. (Mimosaceae) around reproductive trees in the Atlantic forest, Brazil

Studies on the regeneration and seedling mortality of rare tree species are important, but scarce. The aim of this study was to investigate the annual variation in recruitment, growth and mortality of juveniles of Enterolobium glaziovii Benth., a rare tree species from the Brazilian Atlantic Rain Forest. All seedlings and juveniles around four reproductive trees were labeled and their fate was followed from 1996 to 1999. There were no annual differences in juveniles' recruitment below and beyond the parental crown, but juveniles' survival and growth were lower below than beyond of the parental tree crowns. Small individuals (< 15 cm tall) showed the greatest mortality and the lowest growth, followed by medium (from 15 to 50 cm tall) and large ones (> 50 cm tall). Large juveniles were more widely dispersed from the conspecific parental tree than were medium and small ones. This suggests that distance dependent mortality of juveniles mediated by the parental tree is an important cause of spacing shifts associated with the growth of small individuals of E. glaziovii into large ones. Widely dispersed juveniles may escape the high mortality associated with pathogens, herbivores or seed predators concentrated around adult conspecifics. The negative influence of the parental tree on its juveniles may explain the sparse distribution of its adults in the forest.

Woody community dynamics in two fragments of "cerrado" stricto sensu over a seven-year period (1995-2002), MA, Brazil

This study was conducted in two fragments of "cerrado" stricto sensu in the Gerais de Balsas Colonization Project, located in southern Maranhão, Brazil. The objective was to evaluate the dynamics of the woody plant community, over seven years (1995-2002). Four transects of 160 × 20 m were monitored. All woody plants with a stem diameter > 3 cm, at 0.30 m above ground level, were recorded. In 1995, 983 and 1,177 stems were sampled in fragments 1 and 2, respectively; in 2002, 1057 and 1406 stems were sampled in the same fragments. In 1995, the Shannon diversity indices (H') were 3.07 and 3.33, in fragments 1 and 2, respectively, reaching their maximum value in 2002 of 3.11 and 3.35. The community of fragment 1 showed an increase of 7.5% in density and 4.4% in basal area between 1995 and 2002, while in fragment 2 there was an increment of 19.4% in density and 23.5% in basal area, over the same period. The annual increment in diameter was 0.13 cm year-1 and 0.17 cm year-1 in fragments 1 and 2, respectively. The mortality rate was 2.73% per year in fragment 1 and 4.88% per year in fragment 2, while the recruitment rate was 3.25% per year and 5.86% per year, respectively. The community presented high recruitment and mortality rates compared to the studies conducted in other sites, indicating a community that was highly dynamic in the period studied.

Structure and dynamics of a woody plant community of a tropical semi-deciduous seasonal forest in the "Estação Ecológica do Panga", municipality of Uberlândia, Minas Gerais, Brazil

Studies of plant community dynamics are essential in understanding the demographic patterns of species since changes in demographic rates can affect the floristic composition and future structure. The purpose of the present study was to analyze the changes in the community structure and floristic composition of woody plants in a tropical semi-deciduous forest in Uberlândia in central Brazil, during a 10-years period. The data were collected in 1989 and in 2000 in 50 quadrats (10 m x 10 m) where all trees with a minimum circumference at breast height of 10 cm were sampled. In 1989, 93 species and 1103 individuals were registered. Over a period of 10 years, seven new species were added to the community, although eight disappeared. The main change that occurred during this period in the floristic composition was the replacement of savannah species occurring in forest gaps by those from the forest understory.

The calcium-modulated proteins, S100A1 and S100B, as potential regulators of the dynamics of type III intermediate filaments

The Ca2+-modulated, dimeric proteins of the EF-hand (helix-loop-helix) type, S100A1 and S100B, that have been shown to inhibit microtubule (MT) protein assembly and to promote MT disassembly, interact with the type III intermediate filament (IF) subunits, desmin and glial fibrillary acidic protein (GFAP), with a stoichiometry of 2 mol of IF subunit/mol of S100A1 or S100B dimer and an affinity of 0.5-1.0 µM in the presence of a few micromolar concentrations of Ca2+. Binding of S100A1 and S100B results in inhibition of desmin and GFAP assemblies into IFs and stimulation of the disassembly of preformed desmin and GFAP IFs. S100A1 and S100B interact with a stretch of residues in the N-terminal (head) domain of desmin and GFAP, thereby blocking the head-to-tail process of IF elongation. The C-terminal extension of S100A1 (and, likely, S100B) represents a critical part of the site that recognizes desmin and GFAP. S100B is localized to IFs within cells, suggesting that it might have a role in remodeling IFs upon elevation of cytosolic Ca2+ concentration by avoiding excess IF assembly and/or promoting IF disassembly in vivo. S100A1, that is not localized to IFs, might also play a role in the regulation of IF dynamics by binding to and sequestering unassembled IF subunits. Together, these observations suggest that S100A1 and S100B may be regarded as Ca2+-dependent regulators of the state of assembly of two important elements of the cytoskeleton, IFs and MTs, and, potentially, of MT- and IF-based activities.

The neuroimmune-endocrine axis: pathophysiological implications for the central nervous system cytokines and hypothalamus-pituitary-adrenal hormone dynamics

Cytokines are molecules that were initially discovered in the immune system as mediators of communication between various types of immune cells. However, it soon became evident that cytokines exert profound effects on key functions of the central nervous system, such as food intake, fever, neuroendocrine regulation, long-term potentiation, and behavior. In the 80's and 90's our group and others discovered that the genes encoding various cytokines and their receptors are expressed in vascular, glial, and neuronal structures of the adult brain. Most cytokines act through cell surface receptors that have one transmembrane domain and which transduce a signal through the JAK/STAT pathway. Of particular physiological and pathophysiological relevance is the fact that cytokines are potent regulators of hypothalamic neuropeptidergic systems that maintain neuroendocrine homeostasis and which regulate the body's response to stress. The mechanisms by which cytokine signaling affects the function of stress-related neuroendocrine systems are reviewed in this article.

The brain decade in debate: VI. Sensory and motor maps: dynamics and plasticity

This article is an edited transcription of a virtual symposium promoted by the Brazilian Society of Neuroscience and Behavior (SBNeC). Although the dynamics of sensory and motor representations have been one of the most studied features of the central nervous system, the actual mechanisms of brain plasticity that underlie the dynamic nature of sensory and motor maps are not entirely unraveled. Our discussion began with the notion that the processing of sensory information depends on many different cortical areas. Some of them are arranged topographically and others have non-topographic (analytical) properties. Besides a sensory component, every cortical area has an efferent output that can be mapped and can influence motor behavior. Although new behaviors might be related to modifications of the sensory or motor representations in a given cortical area, they can also be the result of the acquired ability to make new associations between specific sensory cues and certain movements, a type of learning known as conditioning motor learning. Many types of learning are directly related to the emotional or cognitive context in which a new behavior is acquired. This has been demonstrated by paradigms in which the receptive field properties of cortical neurons are modified when an animal is engaged in a given discrimination task or when a triggering feature is paired with an aversive stimulus. The role of the cholinergic input from the nucleus basalis to the neocortex was also highlighted as one important component of the circuits responsible for the context-dependent changes that can be induced in cortical maps.