On stability of differential equations with piecewise constant argument and the associated discrete equations using dichotomic map

Dichotomic maps are considered by means of the stability of the null solution of a class of differential equations with piecewise constant argument via associated discrete equations. Copyright © 2008 Watam Press.

Análise da execução de um algoritmo numérico cbs para simulação de escoamento utilizando elementos finitos

This work intends to analyze the application and execution time of a numerical algorithm that simulates incompressible and isothermal flows. It was used the explicit scheme of the Characteristic Based Split (CBS) algorithm and the Artificial Compressibility (AC) scheme for coupling pressure-velocity equations. The discretization was done with the finite element method using a bilinear elements grid. The free software GNU-Octave was used for implementation and execution of routines. The results were analyzed using the classic lid-driven cavity problem. This work shows results for tests with several Reynolds' number. The results for these tests show a good agreement when compared with previous ones obtained from bibliography. The code runtime's analysis shows yet that the matrix's assembly is the part of greater consumption time in the implementation.

Influence of environmental temperature, dietary energy level and sex on performance and carcass characteristics of pigs

Pigs are quite sensitive to high environmental temperatures and the thermoregulation mechanisms represent great expenses in energy for heating loss, reducing animal well-being and production performance, and altering carcass quality. The aim of this study was to assess the effects of sex and dietary energy level in growing-finishing pigs submitted to characteristic seasonal variation of temperature in subtropical humid climate, and to propose a mathematical model to predict growth performance and carcass characteristics. Twenty-eight crossbred growing-finishing pigs were randomly allotted to twelve treatments, in a 2x2x3 factorial trial (2 sex; 2 environmental conditions, and 3 energy levels). Heat stress condition (climatic chamber) showed temperatures of 31 oC at 7:00 and 22 oC at 17:00 (maximum of 33 °C) and thermal comfort condition (stall) showed temperatures of 18 °C at 7:00 and 24 °C (maximum of 27 °C). Pigs were fed ad libitum with diets containing 12.2 (low), 13.6 (medium) and 15.0 (high) MJ ME/ kg DM. Voluntary feed intake, daily weight gain, and final body weight were higher (P<0.01) at thermal comfort condition and were influenced by sex (P<0.01) in growing pigs. Feed to gain ratio decreased as the energy level increased (P<0.01), with values of 2.67, 2.59, and 2.32 (12.2, 13.6, and 15.0 MJ ME/kg DM, respectively). There was energy level and sex interaction only for daily weight gain. Regarding finishing pigs, environmental conditions also showed effects (P<0.01) on voluntary feed intake, daily weight gain, and final body weight. Performance of pigs was better at thermal comfort condition. Feed to gain ratio values were 3.55, 3.42, and 2.95 for low, medium, and high energy level, respectively. Interactions between energy level and sex were observed for voluntary feed intake, daily weight gain, and final body weight (P<0.05). Carcass yield and quality were affected by environmental condition and dietary energy level. Both hot and cold carcass weight increased as energy of ration increased. Cold carcass weight increased by 1.142 kg/MJ EM whereas backfat thickness was up to 252 mm/MJ EM. Longissimus thoracis muscle thickness was around 16 mm smaller in pigs under heat stress, but lean content was 2.68% higher in those animals. Regression equations were proposed to predict the performance values in the different situations studied.

On stability of differential equations with piecewise constant argument using dichotomic maps

This paper deals with the study of the basic theory of existence, uniqueness and continuation of solutions of di®erential equations with piecewise constant argument. Results about asymptotic stability of the equation x(t) =-bx(t) + f(x([t])) with argu- ment [t], where [t] designates the greatest integer function, are established by means of dichotomic maps. Other example is given to illustrate the application of the method. Copyright © 2011 Watam Press.

Charged Brownian particles: Kramers and Smoluchowski equations and the hydrothermodynamical picture

We consider a charged Brownian gas under the influence of external and non-uniform electric, magnetic and mechanical fields, immersed in a non-uniform bath temperature. With the collision time as an expansion parameter, we study the solution to the associated Kramers equation, including a linear reactive term. To the first order we obtain the asymptotic (overdamped) regime, governed by transport equations, namely: for the particle density, a Smoluchowski- reactive like equation; for the particle's momentum density, a generalized Ohm's-like equation; and for the particle's energy density, a MaxwellCattaneo-like equation. Defining a nonequilibrium temperature as the mean kinetic energy density, and introducing Boltzmann's entropy density via the one particle distribution function, we present a complete thermohydrodynamical picture for a charged Brownian gas. We probe the validity of the local equilibrium approximation, Onsager relations, variational principles associated to the entropy production, and apply our results to: carrier transport in semiconductors, hot carriers and Brownian motors. Finally, we outline a method to incorporate non-linear reactive kinetics and a mean field approach to interacting Brownian particles. © 2011 Elsevier B.V. All rights reserved.

A generalized Riemann- Stieltjes integral on time scales and discontinuous dynamical equations

This paper is concerned with a generalization of the Riemann- Stieltjes integral on time scales for deal with some aspects of discontinuous dynamic equations in which Riemann-Stieltjes integral does not works. © 2011 Academic Publications.

State Dependent Riccati Equation (SDRE) control method applied in cancellation of a parametric resonance in a magnetically levitated body

Here, a simplified dynamical model of a magnetically levitated body is considered. The origin of an inertial Cartesian reference frame is set at the pivot point of the pendulum on the levitated body in its static equilibrium state (ie, the gap between the magnet on the base and the magnet on the body, in this state). The governing equations of motion has been derived and the characteristic feature of the strategy is the exploitation of the nonlinear effect of the inertial force associated, with the motion of a pendulum-type vibration absorber driven, by an appropriate control torque [4]. In the present paper, we analyzed the nonlinear dynamics of problem, discussed the energy transfer between the main system and the pendulum in time, and developed State Dependent Riccati Equation (SDRE) control design to reducing the unstable oscillatory movement of the magnetically levitated body to a stable fixed point. The simulations results showed the effectiveness of the (SDRE) control design. Copyright © 2011 by ASME.

A set of linear equations to calculate the steady-state operation of an electrical distribution system

In this paper, the calculation of the steady-state operation of a radial/meshed electrical distribution system (EDS) through solving a system of linear equations (non-iterative load flow) is presented. The constant power type demand of the EDS is modeled through linear approximations in terms of real and imaginary parts of the voltage taking into account the typical operating conditions of the EDS's. To illustrate the use of the proposed set of linear equations, a linear model for the optimal power flow with distributed generator is presented. Results using some test and real systems show the excellent performance of the proposed methodology when is compared with conventional methods. © 2011 IEEE.

On the periodic solutions of a class of duffing differential equations

In this work we study the periodic solutions, their stability and bifurcation for the class of Duffing differential equation mathematical equation represented where C > 0, ε > 0 and Λ are real parameter, A(t), b(t) and h(t) are continuous T periodic functions and ε is sufficiently small. Our results are proved using the averaging method of first order.