Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations

An improved class of nonlinear bidirectional Boussinesq equations of sixth order using a wave surface elevation formulation is derived. Exact travelling wave solutions for the proposed class of nonlinear evolution equations are deduced. A new exact travelling wave solution is found which is the uniform limit of a geometric series. The ratio of this series is proportional to a classical soliton-type solution of the form of the square of a hyperbolic secant function. This happens for some values of the wave propagation velocity. However, there are other values of this velocity which display this new type of soliton, but the classical soliton structure vanishes in some regions of the domain. Exact solutions of the form of the square of the classical soliton are also deduced. In some cases, we find that the ratio between the amplitude of this wave and the amplitude of the classical soliton is equal to 35/36. It is shown that different families of travelling wave solutions are associated with different values of the parameters introduced in the improved equations.

Measuring and Controlling the Chaotic Motion of Profits

The study of economic systems has generated deep interest in exploring the complexity of chaotic motions in economy. Due to important developments in nonlinear dynamics, the last two decades have witnessed strong revival of interest in nonlinear endogenous business chaotic models. The inability to predict the behavior of dynamical systems in the presence of chaos suggests the application of chaos control methods, when we are more interested in obtaining regular behavior. In the present article, we study a specific economic model from the literature. More precisely, a system of three ordinary differential equations gather the variables of profits, reinvestments and financial flow of borrowings in the structure of a firm. Firstly, using results of symbolic dynamics, we characterize the topological entropy and the parameter space ordering of kneading sequences, associated with one-dimensional maps that reproduce significant aspects of the model dynamics. The analysis of the variation of this numerical invariant, in some realistic system parameter region, allows us to quantify and to distinguish different chaotic regimes. Finally, we show that complicated behavior arising from the chaotic firm model can be controlled without changing its original properties and the dynamics can be turned into the desired attracting time periodic motion (a stable steady state or into a regular cycle). The orbit stabilization is illustrated by the application of a feedback control technique initially developed by Romeiras et al. [1992]. This work provides another illustration of how our understanding of economic models can be enhanced by the theoretical and numerical investigation of nonlinear dynamical systems modeled by ordinary differential equations.

Surge damping analysis in pipe systems: modelling and experiments

The current study focuses on the analysis of pressure surge damping in single pipeline systems generated by a fast change of flow, conditions. A dimensionless form of pressurised transient flow equations was developed. presenting the main advantage of being independent of the system characteristics. In lack of flow velocity profiles. the unsteady friction in turbulent regimes is analysed based on two new empirical corrective-coefficients associated with local and convective acceleration terms. A new, surge damping approach is also presented taking into account the pressure peak time variation. The observed attenuation effect in the pressure wave for high deformable pipe materials can be described by a combination of the non-elastic behaviour of the pipe-wall with steady and unsteady friction effects. Several simulations and experimental tests have been carried out. in order to analyse the dynamic response of single pipelines with different characteristics, such as pipe materials. diameters. thickness. lengths and transient conditions.

Optical confinement and colour separation in a double colour laser scanned photodiode (D/CLSP)

Large area n-i-p-n-i-p a-SiC:H heterostructures are used as sensing element in a double colour laser scanned photodiode image sensor (D/CLSP). This work aims to clarify possible improvements, physical limits and performance of CLSP image sensor when used as non-pixel image reader. Here, the image capture device and the scanning reader are optimized and the effects of the sensor structure on the output characteristics discussed. The role of the design of the sensing element, the doped layer composition and thickness, the read-out parameters (applied voltage and scanner frequency) on the image acquisition and the colour detection process are analysed. A physical model is presented and supported by a numerical simulation of the output characteristics of the sensor.

Optical confinement and colour separation in a double colour laser scanned photodiode (D/CLSP)

Large area n-i-p-n-i-p a-SiC:H heterostructures are used as sensing element in a Double Color Laser Scanned Photodiode image sensor (D/CLSP). This work aims to clarify possible improvements, physical limits and performance of CLSP image sensor when used as non-pixel image reader. Here, the image capture device and the scanning reader are optimized and the effects of the sensor structure on the output characteristics discussed. The role of the design of the sensing element, the doped layer composition and thickness, the read-out parameters (applied voltage and scanner frequency) on the image acquisition and the color detection process are analyzed. A physical model is presented and supported by a numerical simulation of the output characteristics of the sensor.

Bioconversion of D-glucose into D-glucosone by Glucose 2-oxidase from Coriolus versicolor at Moderate Pressures

Glucose 2-oxidase (pyranose oxidase, pyranose: oxygen-2-oxidoreductase, EC 1.1.3.10) from Coriolus versicolor catalyses the oxidation of D-glucose at carbon 2 in the presence of molecular O(2) producing D-glucosone (2-keto-glucose and D-arabino-2-hexosulose) and H(2)O(2). It was used to convert D-glucose into D-glucosone at moderate pressures (i.e. up to 150 bar) with compressed air in a modified commercial batch reactor. Several parameters affecting biocatalysis at moderate pressures were investigated as follows: pressure, [enzyme], [glucose], pH, temperature, nature of fluid and the presence of catalase. Glucose 2-oxidase was purified by immobilized metal affinity chromatography on epoxy-activated Sepharose 6B-IDA-Cu(II) column at pH 6.0. The rate of bioconversion of D-glucose increased with the pressure since an increase in the pressure with compressed air resulted in higher rates of conversion. On the other hand, the presence of catalase increased the rate of reaction which strongly suggests that H(2)O(2) acted as inhibitor for this reaction. The rate of bioconversion of D-glucose by glucose 2-oxidase in the presence of either nitrogen or supercritical CO(2) at 110 bar was very low compared with the use of compressed air at the same pressure. The optimum temperature (55 degrees C) and pH (5.0) of D-glucose bioconversion as well as kinetic parameters for this enzyme were determined under moderate pressure. The activation energy (E(a)) was 32.08 kJmol(-1) and kinetic parameters (V(max), K(m), K(cat) and K(cat)/K(m)) for this bioconversion were 8.8 Umg(-1) protein, 2.95 mM, 30.81 s(-1) and 10,444.06 s(-1)M(-1), respectively. The biomass of C. versicolor as well as the cell-free extract containing glucose 2-oxidase activity were also useful for bioconversion of D-glucose at moderate pressures. The enzyme was apparently stable at moderate pressures since such pressures did not affect significantly the enzyme activity.

Bioconversion of D-glucose into D-glucosone by immobilized glucose 2-oxidase from Coriolus versicolorat moderate pressures

The immobilized glucose 2-oxidase (pyranose oxidase, pyranose:oxygen-2-oxidoreductase, EC 1.1.3.10) from Coriolus versicolor was used to convert D-glucose into D-glucosone at moderate pressures, up to 150 bar, with compressed air in a modified commercial batch reactor. Several parameters affecting biocatalysis at moderate pressures were investigated as follows: pressure, different forms of immobilized biocatalysts, glucose concentration, pH, temperature and the presence of catalase. Glucose 2-oxidase (GOX2) was purified by immobilized metal affinity chromatography on epoxy-activated Sepharose 6B-IDA-Cu(II) column at pH 6.0. Purified enzyme and catalase were immobilized into a polyethersulfone (PES) membrane in the presence of glutaraldehyde and gelatin. Enhancement of the bioconversion of D-glucose was done by the pressure since an increase in the pressure with compressed air increases the conversion rates. The optimum temperature and pH for bioconversion of D-glucose were found to be 62 degrees C and pH 6.0, respectively and the activation energy (E(a)) was 28.01 kJ mol(-1). The apparent kinetic constants (V(max)' K(m)', K(cat)' and K(cat)/K(m)') for this bioconversion were 2.27 U mg(-1) protein, 11.15 mM, 8.33 s(-1) and 747.38 s(-1) M(-1), respectively. The immobilized biomass of C. versicolor as well as crude extract containing GOX2 activity were also useful for bioconversion of D-glucose at 65 bar with a yield of 69.9 +/- 3.8% and 91.3 +/- 1.2%, respectively. The immobilized enzyme was apparently stable for several months without any significant loss of enzyme activity. On the other hand, this immobilized enzyme was also stable at moderate pressures, since such pressures did not affect significantly the enzyme activity. (C) 2010 Elsevier Ltd. All rights reserved.

Considerações finais : das voltas que o projeto dá...

A metodologia de projeto constitui a temática central de seis dos textos incluídos neste número do CIED. Tratando-se de contributos diversos, é possível encontrar algumas linhas de organização a partir da sua abordagem:

Validação de um método de cromatografia líquida de alta resolução (HPLC) para doseamento da vitamina D em géneros alimentícios: aplicação do método em diferentes matrizes alimentares

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia Química e Biológica

Simulation and theory of hybrid aligned liquid crystal films

We present a study of the effects of nanoconfinement on a system of hard Gaussian overlap particles interacting with planar substrates through the hard-needle-wall potential, extending earlier work by two of us [D. J. Cleaver and P. I. C. Teixeira, Chem. Phys. Lett. 338, 1 (2001)]. Here, we consider the case of hybrid films, where one of the substrates induces strongly homeotropic anchoring, while the other favors either weakly homeotropic or planar anchoring. These systems are investigated using both Monte Carlo simulation and density-functional theory, the latter implemented at the level of Onsager's second-virial approximation with Parsons-Lee rescaling. The orientational structure is found to change either continuously or discontinuously depending on substrate separation, in agreement with earlier predictions by others. The theory is seen to perform well in spite of its simplicity, predicting the positional and orientational structure seen in simulations even for small particle elongations.

Neural-network approach to modeling liquid crystals in complex confinement

Finding the structure of a confined liquid crystal is a difficult task since both the density and order parameter profiles are nonuniform. Starting from a microscopic model and density-functional theory, one has to either (i) solve a nonlinear, integral Euler-Lagrange equation, or (ii) perform a direct multidimensional free energy minimization. The traditional implementations of both approaches are computationally expensive and plagued with convergence problems. Here, as an alternative, we introduce an unsupervised variant of the multilayer perceptron (MLP) artificial neural network for minimizing the free energy of a fluid of hard nonspherical particles confined between planar substrates of variable penetrability. We then test our algorithm by comparing its results for the structure (density-orientation profiles) and equilibrium free energy with those obtained by standard iterative solution of the Euler-Lagrange equations and with Monte Carlo simulation results. Very good agreement is found and the MLP method proves competitively fast, flexible, and refinable. Furthermore, it can be readily generalized to the richer experimental patterned-substrate geometries that are now experimentally realizable but very problematic to conventional theoretical treatments.

A class of singular first order differential equations with applications in reaction-diffusion

Agências Financiadoras: FCT e MIUR

The organ verses of Frei Jerónimo da Madre de Deus: Portuguese organ music in the time of D. João V

Contrastando com o importante legado dos mestres organistas portugueses dos séculos XVI e XVII, a música portuguesa para órgão pós-1700 parece quase inexistente (excluindo raros exemplos, como as quatro sonatas para órgão de Carlos Seixas). Seja devido à destruição causada pelo grande terramoto de Lisboa em 1755, ou a outras causas, a ausência de fontes é surpreendente, considerando os testemunhos de actividade musical durante aquele período. Este artigo lida com uma fonte até hoje relativamente ignorada: o manuscrito CLI/1-4 nº 7 da Biblioteca do Palácio Ducal de Vila Viçosa (Versos / Sobre o Canto Chão / Para Orgão / De Fr. Jeronimo da M.dre de DS.). Esta colecção de vinte versos para órgão de Jerónimo da Madre de Deus é, de longe, a maior obra portuguesa para órgão da primeira metade do século XVIII até hoje conhecida. Claramente pensadas para o órgão, estas curtas peças testemunham a transformação da escrita para tecla em Portugal durante o reinado de D. João V (nomeadamente através da absorção de influências italianas) e fornecem informações preciosas sobre o tipo de instrumento em que eram tocadas.

Neural-network approach to modeling liquid crystals in complex confinement

Finding the structure of a confined liquid crystal is a difficult task since both the density and order parameter profiles are nonuniform. Starting from a microscopic model and density-functional theory, one has to either (i) solve a nonlinear, integral Euler-Lagrange equation, or (ii) perform a direct multidimensional free energy minimization. The traditional implementations of both approaches are computationally expensive and plagued with convergence problems. Here, as an alternative, we introduce an unsupervised variant of the multilayer perceptron (MLP) artificial neural network for minimizing the free energy of a fluid of hard nonspherical particles confined between planar substrates of variable penetrability. We then test our algorithm by comparing its results for the structure (density-orientation profiles) and equilibrium free energy with those obtained by standard iterative solution of the Euler-Lagrange equations and with Monte Carlo simulation results. Very good agreement is found and the MLP method proves competitively fast, flexible, and refinable. Furthermore, it can be readily generalized to the richer experimental patterned-substrate geometries that are now experimentally realizable but very problematic to conventional theoretical treatments.

A numerical analysis of generalized Boussinesq-type equation using continuos/discontinuous FEM

An improved class of Boussinesq systems of an arbitrary order using a wave surface elevation and velocity potential formulation is derived. Dissipative effects and wave generation due to a time-dependent varying seabed are included. Thus, high-order source functions are considered. For the reduction of the system order and maintenance of some dispersive characteristics of the higher-order models, an extra O(mu 2n+2) term (n ??? N) is included in the velocity potential expansion. We introduce a nonlocal continuous/discontinuous Galerkin FEM with inner penalty terms to calculate the numerical solutions of the improved fourth-order models. The discretization of the spatial variables is made using continuous P2 Lagrange elements. A predictor-corrector scheme with an initialization given by an explicit RungeKutta method is also used for the time-variable integration. Moreover, a CFL-type condition is deduced for the linear problem with a constant bathymetry. To demonstrate the applicability of the model, we considered several test cases. Improved stability is achieved.