Extension of the characteristic equation to absorption chillers with adiabatic absorbers

Various researchers have developed models of conventional H2O–LiBr absorption machines with the aim of predicting their performance. In this paper, the methodology of characteristic equations developed by Hellmann et al. (1998) is applied. This model is able to represent the capacity of single effect absorption chillers and heat pumps by means of simple algebraic equations. An extended characteristic equation based on a characteristic temperature difference has been obtained, considering the facility features. As a result, it is concluded that for adiabatic absorbers a subcooling temperature must be specified. The effect of evaporator overflow has been characterized. Its influence on cooling capacity has been included in the extended characteristic equation. Taking into account the particular design and operation features, a good agreement between experimental performance data and those obtained through the extended characteristic equation has been achieved at off-design operation. This allows its use for simulation and control purposes.

On the dominance of roots of characteristic equations for neutral functional differential equations

We present a sufficient condition for a zero of a function that arises typically as the characteristic equation of a linear functional differential equations of neutral type, to be simple and dominant. This knowledge is useful in order to derive the asymptotic behaviour of solutions of such equations. A simple characteristic equation, arisen from the study of delay equations with small delay, is analyzed in greater detail. (C) 2009 Elsevier Inc. All rights reserved.

Necessary and Sufficient Condition for Oscillations of Neutral Differential Equation

2000 Mathematics Subject Classification: 34K15, 34C10.

Abordagem prática para execução de taludes em obras rodoviárias com recurso a pré‐corte

Este trabalho é realizado no domínio das obras de engenharia, área onde o desmonte de rocha com recurso a explosivos em obras rodoviárias é uma actividade específica e consistiu no acompanhamento e execução de três obras rodoviárias de média e grande dimensão. A necessidade de executar escavações, recorrendo a técnicas de desmonte cuidadoso de contorno, onde o plano de corte do talude final deve obedecer a requisitos de localização, alinhamento, inclinação, estabilidade e também estéticos, acrescendo a isto a necessidade de optimizar os meios envolvidos, obriga a que esta actividade seja encarada de uma forma sistematizada, visando o racional aproveitamento de recursos. A execução desta actividade requer conhecimentos no domínio das técnicas de desmonte de contorno, dos explosivos, do mecanismo de rotura de rochas, da operação de perfuração e da geomecânica dos maciços. A abordagem deste trabalho incide sobre a técnica denominada de pré‐corte e tem como objectivo encontrar uma equação característica que permita relacionar diferentes parâmetros envolvidos nesta actividade. Este objectivo é alcançado recorrendo à correlação entre equações relativas à pressão de detonação, à pressão no furo e ao espaçamento entre furos consecutivos, desenvolvidas por outros autores. Desta forma obteve‐se uma equação que relaciona parâmetros relativos ao maciço rochoso (resistência à tracção), ao explosivo (velocidade de detonação e densidade) e ao diagrama de fogo (concentração de carga – volume de explosivo e comprimento do furo – volume do furo). A comparação entre os valores destes parâmetros obtidos na produção e os obtidos com recurso à equação característica permite concluir que a sua aplicação para execução de futuras obras possibilita uma optimização dos meios envolvidos.

Root locus of fractional linear systems

In this paper an algorithm for the calculation of the root locus of fractional linear systems is presented. The proposed algorithm takes advantage of present day computational resources and processes directly the characteristic equation, avoiding the limitations revealed by standard methods. The results demonstrate the good performance for different types of expressions.

Semigroup analysis of structured populations with distributed states-at-birth arising in mathematical aquaculture

Motivated by the modelling of structured parasite populations in aquaculture we consider a class of physiologically structured population models, where individuals may be recruited into the population at different sizes in general. That is, we consider a size-structured population model with distributed states-at-birth. The mathematical model which describes the evolution of such a population is a first order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral theory of semigroups to establish conditions for the existence of a positive equilibrium solution of our model. Then we formulate conditions that guarantee that the linearised system is governed by a positive quasicontraction semigroup on the biologically relevant state space. We also show that the governing linear semigroup is eventually compact, hence growth properties of the semigroup are determined by the spectrum of its generator. In case of a separable fertility function we deduce a characteristic equation and investigate the stability of equilibrium solutions in the general case using positive perturbation arguments.

Using the Cayley-Hamilton theorem with N-partitioned matrices

A definition is given for the characteristic equation of anN-partitioned matrix. It is then proved that this matrix satisfies its own characteristic equation. This can then be regarded as a version of the Cayley-Hamilton theorem, of use withN-dimensional systems.

Permanence of stability for a class of system of differential equations with two delays

The paper studies a class of a system of linear retarded differential difference equations with several parameters. It presents some sufficient conditions under which no stability changes for an equilibrium point occurs. Application of these results is given. (c) 2007 Elsevier Ltd. All rights reserved.

On the dynamic behaviour of a mass supported by a parallel combination of a spring and an elastically connected damper

This paper presents a consistent and concise analysis of the free and forced vibration of a mass supported by a parallel combination of a spring and an elastically supported damper (a Zener model). The results are presented in a compact form and the physical behaviour of the system is emphasised. This system is very similar to the conventional single-degree-of freedom system (sdof)-(Voigt model), but the dynamics can be quite different depending on the system parameters. The usefulness of the additional spring in series with the damper is investigated, and optimum damping values for the system subject to different types of excitation are determined and compared.There are three roots to the characteristic equation for the Zener model; two are complex conjugates and the third is purely real. It is shown that it is not possible to achieve critical damping of the complex roots unless the additional stiffness is at least eight times that of the main spring. For a harmonically excited system, there are some possible advantages in using the additional spring when the transmitted force to the base is of interest, but when the displacement response of the system is of interest then the benefits are marginal. It is shown that the additional spring affords no advantages when the system is excited by white noise. (c) 2007 Elsevier Ltd. All rights reserved.

Método experimental para determinação das capacitancias parasitas do motor de indução trifásico acionado por inversor MLP

A proposta deste trabalho é apresentar uma nova metodologia para determinação experimental das capacitancias parasitas do motor de indução trifásico de rotor em gaiola. As capacitancias parasitas fazem parte do circuito equivalente do motor para estudos de interferência eletromagnética causada no motor de indução em modo comum quando ele for acionado por inversor controlado por modulação por largura de pulsos (MLP). Os procedimentos propostos para o desenvolvimento deste novo método consistem em: a) determinação dos parâmetros do circuito equivalente do motor de indução trifásico, em regime permanente, através de ensaio em laboratório; b) estabelecer configurações de ligações entre o inversor MLP e o motor para medições das grandezas de interesse que são as seguintes: tensões de modo comum e de eixo, correntes de fuga e de eixo, através de circuito de medição desenvolvido para este fim; c) calcular os valores das capacitancias parasitas entre estator e carcaça do motor; estator e rotor; rotor e carcaça e de rolamento utilizando a expressão matemática da definição de capacitancia; d) utilizar o software Pspice para simular o sistema motor de indução trifásico, alimentado por inversor MLP, com os circuitos equivalentes em baixas e altas frequências; e) obter as formas de onda características do fenômeno de modo comum.

Efeito da espessura da parede no desempenho hidráulico de mangueiras gotejadoras

Pós-graduação em Agronomia (Irrigação e Drenagem) - FCA

Análise da estabilidade do movimento rotacional de satélites artificiais com quatérnions e sob a influência de torques externos

The aim of this work is to analyze the stability of the rotational motion’s artificial satellite using the Routh Hurwitz Algorithm (CRH) and the quaternions to describe the satellite’s attitude. This algorithm allows the investigation of the stability of the motion using the coefficients of the characteristic equation associated with the equation of the rotational motion in the linear form. The equations of the rotational motion are given by the four cinematic equations for the quaternion and the three equations of Euler for the spin velocity’s components. In the Euler equations are included the components of the gravity gradient torque (TGG) and the solar radiation torque (TRS). The TGG is generated by the difference of the Earth gravity force direction and intensity actuating on each satellite mass element and it depends on the mass distribution and the form of the satellite. The TRS is created by changing of the linear momentum, which happens due to the interactions of solar photons with the satellite surface. The equilibrium points are gotten by the equation of rotational motion and the CRH is applied in the linear form of these equations. Simulations are developed for small and medium satellites, but the gotten equilibrium points are not stable by CRH. However, when some of the eigenvalues of the characteristic equation are analyzed, it is found some equilibrium points which can be pointed out as stables for an interval of the time, due to small magnitude of the real part of these eigenvalue

Caracterização técnica e desempenho hidráulico de quatro gotejadores autocompensantes utilizados no Brasil

This study aimed to characterize and evaluate the performance of four models self-compensating drippers commonly used in drip irrigation systems in Brazil. To perform the study it was taking a sample of 25 emitters of each model. Evaluating their tubes (b) coefficient of manufacturing variation (c) wall thickness, (d) characteristic equation of the dripper, (e) internal diameter of the pipe, (f) spacing between emitters, (g) resistance water pressure at ambient temperature and to 40°C and (h) the tensile strength of the pipe with tension of 160 N and 180 N. The analysis showed variation coefficient of less than 0.045 for all manufacturing drippers (0.07 is maximum according to ABNT NBR ISO 9261). The exponents x of the equation pressure versus discharge ranged from 0.0082 to 0.0691 classifying them as self-compensating. From the results obtained it is clear that the tested products which are used in Brazil and used by irrigators had a satisfactory hydraulic performance in accordance with the standard.

Open-access operating algorithms for commercial videokeratographer and improvement of corneal sampling

We present an algorithm to process images of reflected Placido rings captured by a commercial videokeratoscope. Raw data are obtained with no Cartesian-to-polar-coordinate conversion, thus avoiding interpolation and associated numerical artifacts. The method provides a characteristic equation for the device and is able to process around 6 times more corneal data than the commercial software. Our proposal allows complete control over the whole process from the capture of corneal images until the computation of curvature radii.

Theoretical investigation of convective instability in inclined and fluid-saturated three-dimensional fault zones.

The convective instability of pore-fluid flow in inclined and fluid-saturated three-dimensional fault zones has been theoretically investigated in this paper. Due to the consideration of the inclined three-dimensional fault zone with any values of the inclined angle, it is impossible to use the conventional linear stability analysis method for deriving the critical condition (i.e., the critical Rayleigh number) which can be used to investigate the convective instability of the pore-fluid flow in an inclined three-dimensional fault zone system. To overcome this mathematical difficulty, a combination of the variable separation method and the integration elimination method has been used to derive the characteristic equation, which depends on the Rayleigh number and the inclined angle of the inclined three-dimensional fault zone. Using this characteristic equation, the critical Rayleigh number of the system can be numerically found as a function of the inclined angle of the three-dimensional fault zone. For a vertically oriented three-dimensional fault zone system, the critical Rayleigh number of the system can be explicitly derived from the characteristic equation. Comparison of the resulting critical Rayleigh number of the system with that previously derived in a vertically oriented three-dimensional fault zone has demonstrated that the characteristic equation of the Rayleigh number is correct and useful for investigating the convective instability of pore-fluid flow in the inclined three-dimensional fault zone system. The related numerical results from this investigation have indicated that: (1) the convective pore-fluid flow may take place in the inclined three-dimensional fault zone; (2) if the height of the fault zone is used as the characteristic length of the system, a decrease in the inclined angle of the inclined fault zone stabilizes the three-dimensional fundamental convective flow in the inclined three-dimensional fault zone system; (3) if the thickness of the stratum is used as the characteristic length of the system, a decrease in the inclined angle of the inclined fault zone destabilizes the three-dimensional fundamental convective flow in the inclined three-dimensional fault zone system; and that (4) the shape of the inclined three-dimensional fault zone may affect the convective instability of pore-fluid flow in the system. (C) 2004 Published by Elsevier B.V.