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 parity between protein-based electrophoretic methods for the characterization of oral Candida species

Electrophoretic studies of multilocus-enzymes (MLEE) and whole-cell protein (SDS-PAGE) were carried out in order to evaluate the parity between different methods for the characterization of five Candida species commonly isolated from oral cavity of humans by numerical taxonomy methods. The obtained data revealed that sodium dodecyl sulfate polyacrylamide gel electrophoresis is more efficient in grouping strains in their respective species while MLEE has much limited resolution in organizing all strains in their respective species-specific clusters. MLEE technique must be regarded for surveys in which just one species of Candida is involved.

Desenvolvimento e aplicação de células eletroquímicas em camada delgada

Theoretical and practical aspects concerning construction and use of a thin layer electrochemical cell are presented. Construction was realized by a simple technic and geometry was optimized in order to minimize the problems of electrical resistance. A well known redox system was studied ((Fe(III)(CN)6(3-)/Fe(II)(CN) 6(4-)) using two experimental methods, cyclic voltammetry and pulse chronopotentiometry. A numerical integration based-program was developed to calculate the voltammetric current in case of nernstian and non-nernstian behaviours and a diffusional model was used to treat the chronopotentiometric data. Thermodynamic (potential, concentration) and kinetic parameters (diffusion coefficient) were successfully determined for the redox system studied in this work.

Cinética não-isotérmica na análise térmica de sólidos

In this work, a computer program called Thermal Kinetics was implemented to simulate thermal analysis experiments by numerical integration of the kinetics equations. The computer program was tested in two different examples: non-isothermal transformation of a Cu-Al alloy and non-isothermal decomposition of calcium oxalate monohydrated. In spite of the rather crude approximations of the model, the simulated profiles are very similar to the experimental curves. Both, the dalpha /dt and the dalpha /dT profiles reproduce the experimental transition temperatures with an error smaller than 25%.

Integração numérica de leis de velocidade diferenciais com o uso do SCILAB

In this work, we applied the free open source SCILAB software for the numerical integration of differential rate law equations to obtain the concentration profiles of chemical species involved in the kinetics of some complex reactions. An automated method was applied to construct the system of ordinary differential equations (ODE) from the postulated chemical models. The solutions of the ODEs were obtained numerically by standard SCILAB functions. We successfully simulated even complex chemical systems such as pH oscillators. This communication opens up the possibility of using SCILAB in simulations and modeling by our chemistry undergraduate students.

Estimating Attractor Dimension on the Nonlinear Pendulum Time Series

Chaotic dynamical systems exhibit trajectories in their phase space that converges to a strange attractor. The strangeness of the chaotic attractor is associated with its dimension in which instance it is described by a noninteger dimension. This contribution presents an overview of the main definitions of dimension discussing their evaluation from time series employing the correlation and the generalized dimension. The investigation is applied to the nonlinear pendulum where signals are generated by numerical integration of the mathematical model, selecting a single variable of the system as a time series. In order to simulate experimental data sets, a random noise is introduced in the time series. State space reconstruction and the determination of attractor dimensions are carried out regarding periodic and chaotic signals. Results obtained from time series analyses are compared with a reference value obtained from the analysis of mathematical model, estimating noise sensitivity. This procedure allows one to identify the best techniques to be applied in the analysis of experimental data.

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.

Assessment of integration of the leprosy program into primary health care in Aracaju, state of Sergipe, Brazil

INTRODUCTION: The aim of this study was to assess the epidemiological and operational characteristics of the Leprosy Program before and after its integration into the Primary healthcare Services of the municipality of Aracaju-Sergipe, Brazil. METHODS: Data were drawn from the national database. The study periods were divided into preintegration (1996-2000) and postintegration (2001-2007). Annual rates of epidemiological detection were calculated. Frequency data on clinico-epidemiological variables of cases detected and treated for the two periods were compared using the Chi-squared (χ2) test adopting a 5% level of significance. RESULTS: Rates of detection overall, and in subjects younger than 15 years, were greater for the postintegration period and were higher than rates recorded for Brazil as a whole during the same periods. A total of 780 and 1,469 cases were registered during the preintegration and postintegration periods, respectively. Observations for the postintegration period were as follows: I) a higher proportion of cases with disability grade assessed at diagnosis, with increase of 60.9% to 78.8% (p < 0.001), and at end of treatment, from 41.4% to 44.4% (p < 0.023); II) an increase in proportion of cases detected by contact examination, from 2.1% to 4.1% (p < 0.001); and III) a lower level of treatment default with a decrease from 5.64 to 3.35 (p < 0.008). Only 34% of cases registered from 2001 to 2007 were examined. CONCLUSIONS: The shift observed in rates of detection overall, and in subjects younger than 15 years, during the postintegration period indicate an increased level of health care access. The fall in number of patients abandoning treatment indicates greater adherence to treatment. However, previous shortcomings in key actions, pivotal to attaining the outcomes and impact envisaged for the program, persisted in the postintegration period.

Analysis of the detection coefficient for the association between leprosy and pregnancy in the integration region of Carajas, State of Para, Brazil

Introduction The association between leprosy and pregnancy is currently poorly understood and has been linked to serious clinical consequences. Methods A retrospective study between 2007 and 2009 was performed in the integration region of Carajás, Brazil on a population of pregnant lepers, with non-lepers of ages 12-49 years serving as the reference population. Results Twenty-nine pregnant lepers were studied during the study period. The detection rates (DRs) for the studied association were 4.7 in 2007, 9.4 in 2008, and 4.3 in 2009. Conclusions The Carajás region presented a medium pattern of endemicity during most of the study period, with a high DR found in 2008.

Numerical procedure for estimating temperature in solarized soils

The objective of this work was to develop a simplified numerical procedure for the estimation of accumulated monthly hours of solarized soil temperatures. The proposed model requires monthly means of daily solar radiation and maximum air temperature as input data, and a daily pattern of temperature variation assumed to be sine-shaped. The procedure was verified using observations made during the years 1992 and 1993 in Jaguariúna, SP. The proposed procedure can predict monthly temperature hours at 10 cm depth in the solarized soil, with acceptable accuracy, in the region for which it was developed.

Method of numerical correction of errors occasioned by delay of records during the monitoring of environmental variables of interest for animal production

Thermal and air conditions inside animal facilities change during the day due to the influence of the external environment. For statistical and geostatistical analyses to be representative, a large number of points spatially distributed in the facility area must be monitored. This work suggests that the time variation of environmental variables of interest for animal production, monitored within animal facility, can be modeled accurately from discrete-time records. The aim of this study was to develop a numerical method to correct the temporal variations of these environmental variables, transforming the data so that such observations are independent of the time spent during the measurement. The proposed method approached values recorded with time delays to those expected at the exact moment of interest, if the data were measured simultaneously at the moment at all points distributed spatially. The correction model for numerical environmental variables was validated for environmental air temperature parameter, and the values corrected by the method did not differ by Tukey's test at 5% significance of real values recorded by data loggers.

Corn production for silage intercropped with forage in the farming-cattle breeding integration

Corn cropping for silage, due to the plant material exportation, intercropping with forage provides greater ground cover and straw formation for the Direct Planting System (DPS) continuity. The objective of this study was to evaluate corn production for silage in DPS intercropped with four forages (Urochloa brizantha cv. Marandu, U. ruziziensis cv. Ruziziensis, Panicum maximum cv. Tanzânia and P. maximum cv. Áries). We applied three sowing methods (in row together with corn fertilizer; by no-till sowing simultaneously to corn sowing and at V4 corn stage) and corn without intercropping. The experiment was conducted in autumn/ winter of 2010, in Selvíria - MS, in a randomized block design in factorial arrangement (4 x 3 + 1) and 4 replications. For corn, we evaluated plant height, basal stem diameter, initial and final stand and silage production and for forage dry matter production. Morphological characteristics and corn yield were not affected by intercropping when compared to sole corn crop. Forage dry matter production sown in corn row with fertilizer is a highlight, which in addition to providing greater productivity, harnesses the operation during sowing.

Dynamics of coherent vortices in mixing layers using direct numerical and large-eddy simulations

Coherent vortices in turbulent mixing layers are investigated by means of Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES). Subgrid-scale models defined in spectral and physical spaces are reviewed. The new "spectral-dynamic viscosity model", that allows to account for non-developed turbulence in the subgrid-scales, is discussed. Pseudo-spectral methods, combined with sixth-order compact finite differences schemes (when periodic boundary conditions cannot be established), are used to solve the Navier- Stokes equations. Simulations in temporal and spatial mixing layers show two types of pairing of primary Kelvin-Helmholtz (KH) vortices depending on initial conditions (or upstream conditions): quasi-2D and helical pairings. In both cases, secondary streamwise vortices are stretched in between the KH vortices at an angle of 45° with the horizontal plane. These streamwise vortices are not only identified in the early transitional stage of the mixing layer but also in self-similar turbulence conditions. The Re dependence of the "diameter" of these vortices is analyzed. Results obtained in spatial growing mixing layers show some evidences of pairing of secondary vortices; after a pairing of the primary Kelvin-Helmholtz (KH) vortices, the streamwise vortices are less numerous and their diameter has increased than before the pairing of KH vortices.

An experimental/numerical study of the turbulent boundary layer development along a surface with a sudden change in roughness

A theory for the description of turbulent boundary layer flows over surfaces with a sudden change in roughness is considered. The theory resorts to the concept of displacement in origin to specify a wall function boundary condition for a kappa-epsilon model. An approximate algebraic expression for the displacement in origin is obtained from the experimental data by using the chart method of Perry and Joubert(J.F.M., vol. 17, pp. 193-122, 1963). This expression is subsequently included in the near wall logarithmic velocity profile, which is then adopted as a boundary condition for a kappa-epsilon modelling of the external flow. The results are compared with the lower atmospheric observations made by Bradley(Q. J. Roy. Meteo. Soc., vol. 94, pp. 361-379, 1968) as well as with velocity profiles extracted from a set of wind tunnel experiments carried out by Avelino et al.( 7th ENCIT, 1998). The measurements are found to be in good agreement with the theoretical computations. The skin-friction coefficient was calculated according to the chart method of Perry and Joubert(J.F.M., vol. 17, pp. 193-122, 1963) and to a balance of the integral momentum equation. In particular, the growth of the internal boundary layer thickness obtained from the numerical simulation is compared with predictions of the experimental data calculated by two methods, the "knee" point method and the "merge" point method.

On the numerical simulation of machining processes

Numerical simulation of machining processes can be traced back to the early seventies when finite element models for continuous chip formation were proposed. The advent of fast computers and development of new techniques to model large plastic deformations have favoured machining simulation. Relevant aspects of finite element simulation of machining processes are discussed in this paper, such as solution methods, material models, thermo-mechanical coupling, friction models, chip separation and breakage strategies and meshing/re-meshing strategies.