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.

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.

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.

On the analytical solutions of the Hindmarsh-Rose neuronal model

In this article we analytically solve the Hindmarsh-Rose model (Proc R Soc Lond B221:87-102, 1984) by means of a technique developed for strongly nonlinear problems-the step homotopy analysis method. This analytical algorithm, based on a modification of the standard homotopy analysis method, allows us to obtain a one-parameter family of explicit series solutions for the studied neuronal model. The Hindmarsh-Rose system represents a paradigmatic example of models developed to qualitatively reproduce the electrical activity of cell membranes. By using the homotopy solutions, we investigate the dynamical effect of two chosen biologically meaningful bifurcation parameters: the injected current I and the parameter r, representing the ratio of time scales between spiking (fast dynamics) and resting (slow dynamics). The auxiliary parameter involved in the analytical method provides us with an elegant way to ensure convergent series solutions of the neuronal model. Our analytical results are found to be in excellent agreement with the numerical simulations.

Travelling wave profiles in some models with nonlinear diffusion

We study some properties of the monotone solutions of the boundary value problem (p(u'))' - cu' + f(u) = 0, u(-infinity) = 0, u(+infinity) = 1, where f is a continuous function, positive in (0, 1) and taking the value zero at 0 and 1, and P may be an increasing homeomorphism of (0, 1) or (0, +infinity) onto [0, +infinity). This problem arises when we look for travelling waves for the reaction diffusion equation partial derivative u/partial derivative t = partial derivative/partial derivative x [p(partial derivative u/partial derivative x)] + f(u) with the parameter c representing the wave speed. A possible model for the nonlinear diffusion is the relativistic curvature operator p(nu)= nu/root 1-nu(2). The same ideas apply when P is given by the one- dimensional p- Laplacian P(v) = |v|(p-2)v. In this case, an advection term is also considered. We show that, as for the classical Fisher- Kolmogorov- Petrovski- Piskounov equations, there is an interval of admissible speeds c and we give characterisations of the critical speed c. We also present some examples of exact solutions. (C) 2014 Elsevier Inc. All rights reserved.

Pensar uma saúde integral a partir de uma prática teatral em comunidades: o teatro como território da experiência

Esta investigação debruça-se sobre dois universos: o do Teatro e Comunidade e o da Saúde a fim de refletir sobre uma interação entre essas duas áreas de conhecimento. O trabalho dedica-se à reflexão do conceito de comunidade a partir da análise de três “S” propostos pelo filósofo Agostinho da Silva: Sustento, Saber e Saúde. Para tanto, o estudo faz um contraponto entre o Saber e a Ciência sob a ótica do conhecimento cartesiano e o Saber adquirido a partir da experiência, das narrativas. Defende o Saber libertador enquanto possibilidade de autonomia dos sujeitos. O indivíduo, então protagonista de sua própria vida, passa a ter um melhor conhecimento sobre saúde, na visão integral da mesma, promovendo-a, consequentemente. Para fundamentar tal argumento, esse trabalho analisa os conceitos da promoção da saúde e da saúde integral, abordando aspectos históricos da medicina preventiva, sanitarista e analisando práticas da educação em saúde. Como possibilidade para se chegar a esse Saber e à Saúde Integral, o estudo propõe a linguagem teatral como uma alternativa. O binômio saúde e arte, portanto, encontra na conceituação de Teatro e Comunidade o campo de conhecimento que mais fundamenta essa interação. O estudo se propõe a contextualizar o surgimento e as práticas desse teatro e a analisar quatro grupos que têm esse binômio como premissa comum. Por fim, o trabalho levanta as características fundamentais de uma prática teatral nessa linha, a fim de promover o teatro como uma alternativa para se pensar a arte como saúde.

Risk Aversion in a Mixed-Integer Nonlinear Approach to Support Decision-Making for a Hydro Power Producer

In this paper, a mixed-integer nonlinear approach is proposed to support decision-making for a hydro power producer, considering a head-dependent hydro chain. The aim is to maximize the profit of the hydro power producer from selling energy into the electric market. As a new contribution to earlier studies, a risk aversion criterion is taken into account, as well as head-dependency. The volatility of the expected profit is limited through the conditional value-at-risk (CVaR). The proposed approach has been applied successfully to solve a case study based on one of the main Portuguese cascaded hydro systems.

Mixed-integer nonlinear approach for the optimal scheduling of a head-dependent hydro chain

This paper is on the problem of short-term hydro scheduling (STHS), particularly concerning a head-dependent hydro chain We propose a novel mixed-integer nonlinear programming (MINLP) approach, considering hydroelectric power generation as a nonlinear function of water discharge and of the head. As a new contribution to eat her studies, we model the on-off behavior of the hydro plants using integer variables, in order to avoid water discharges at forbidden areas Thus, an enhanced STHS is provided due to the more realistic modeling presented in this paper Our approach has been applied successfully to solve a test case based on one of the Portuguese cascaded hydro systems with a negligible computational time requirement.

A Pitch Control Malfunction Analysis for Wind Turbines with Permanent Magnet Synchronous Generator and Full-power Converters: Proportional Integral Versus Fractional-order Controllers

A transient analysis for two full-power converter wind turbines equipped with a permanent magnet synchronous generator is studied in this article, taking into consideration, as a new contribution to earlier studies, a pitch control malfunction. The two full-power converters considered are, respectively, a two-level and a multi-level converter. Moreover, a novel control strategy based on fractional-order controllers for wind turbines is studied. Simulation results are presented; conclusions are in favor of the novel control strategy, improving the quality of the energy injected into the electric grid.

Active and passive behaviors of soft tissues: Pelvic floor muscles

: A new active-contraction visco-elastic numerical model of the pelvic floor (skeletal) muscle is presented. Our model includes all elements that represent the muscle constitutive behavior, contraction and relaxation. In contrast with the previous models, the activation function can be null. The complete equations are shown and exactly linearized. Small verification and validation tests are performed and the pelvis is modeled using the data from the intra-abdominal pressure tests

Comportamento dinâmico da rede eléctrica da ilha de São Vicente em Cabo Verde: estabilidade de tensão

Neste trabalho é efectuado, não só o diagnóstico em regime permanente, mas também o estudo, simulação e análise do comportamento dinâmico da rede eléctrica da ilha de São Vicente em Cabo Verde. Os estudos de estabilidade transitória desempenham um importante papel, tanto no planeamento como na operação dos sistemas de potência. Tais estudos são realizados, em grande parte, através de simulação digital no domínio do tempo, utilizando integração numérica para resolver as equações não-lineares que modelam a dinâmica do sistema e dependem da existência de registos reais de perturbação (ex: osciloperturbografia). O objectivo do trabalho será também verificar a aplicabilidade dos requisitos técnicos que as unidades geradoras devem ter, no que concerne ao controlo de tensão, estabelecidos na futura regulamentação europeia desenvolvida pela ENTSO-E (European Network Transmission System Operator for Electricity). De entre os requisitos analisou-se a capacidade das máquinas existentes suportarem cavas de tensão decorrentes de curto-circuitos trifásicos simétricos, Fault Ride Through, no ponto de ligação à rede. Identificaram-se para o efeito os factores que influenciam a estabilidade desta rede, em regime perturbado nomeadamente: (i) duração do defeito, (ii) caracterização da carga, com e sem a presença do sistema de controlo de tensão (AVR) em unidades de geração síncronas. Na ausência de registos reais sobre o comportamento do sistema, conclui-se que este é sensível à elasticidade das cargas em particular do tipo potência constante, existindo risco de perda de estabilidade, neste caso, para defeitos superiores a 5ms sem AVR. A existência de AVR nesta rede afigura-se como indispensável para garantir estabilidade de tensão sendo contudo necessário proceder a uma correcta parametrização.

Nonlinear optimization method for short-term hydro scheduling considering head-dependency

This paper is on the problem of short-term hydro scheduling, particularly concerning head-dependent reservoirs under competitive environment. We propose a new nonlinear optimization method to consider hydroelectric power generation as a function of water discharge and also of the head. Head-dependency is considered on short-term hydro scheduling in order to obtain more realistic and feasible results. The proposed method has been applied successfully to solve a case study based on one of the main Portuguese cascaded hydro systems, providing a higher profit at a negligible additional computation time in comparison with a linear optimization method that ignores head-dependency.

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.

Hydro energy systems management in Portugal: Profit-based evaluation of a mixed-integer nonlinear approach

In this paper, a novel mixed-integer nonlinear approach is proposed to solve the short-term hydro scheduling problem in the day-ahead electricity market, considering not only head-dependency, but also start/stop of units, discontinuous operating regions and discharge ramping constraints. Results from a case study based on one of the main Portuguese cascaded hydro energy systems are presented, showing that the proposedmixed-integer nonlinear approach is proficient. Conclusions are duly drawn. (C) 2010 Elsevier Ltd. All rights reserved.

3D-2D image registration by nonlinear regression

We propose a 3D-2D image registration method that relates image features of 2D projection images to the transformation parameters of the 3D image by nonlinear regression. The method is compared with a conventional registration method based on iterative optimization. For evaluation, simulated X-ray images (DRRs) were generated from coronary artery tree models derived from 3D CTA scans. Registration of nine vessel trees was performed, and the alignment quality was measured by the mean target registration error (mTRE). The regression approach was shown to be slightly less accurate, but much more robust than the method based on an iterative optimization approach.