Self-interacting scalar field cosmologies: unified exact solutions and symmetries

We investigate a mechanism that generates exact solutions of scalar field cosmologies in a unified way. The procedure investigated here permits to recover almost all known solutions, and allows one to derive new solutions as well. In particular, we derive and discuss one novel solution defined in terms of the Lambert function. The solutions are organised in a classification which depends on the choice of a generating function which we have denoted by x(phi) that reflects the underlying thermodynamics of the model. We also analyse and discuss the existence of form-invariance dualities between solutions. A general way of defining the latter in an appropriate fashion for scalar fields is put forward.

Benchmark exact solutions for the static analysis of multi-layered piezoelectric composite using PVDF

The three-dimensional (3D) exact solutions developed in the early 1970s by Pagano for simply supported multilayered orthotropic composite plates and later in the 1990s extended to piezoelectric plates by Heyliger have been extremely useful in the assessment and development of advanced laminated plate theories and related finite element models. In fact, the well-known test cases provided by Pagano and by Heyliger in those earlier works are still used today as benchmark solutions. However, the limited number of test cases whose 3D exact solutions have been published has somewhat restricted the assessment of recent advanced models to the same few test cases. This work aims to provide additional test cases to serve as benchmark exact solutions for the static analysis of multilayered piezoelectric composite plates. The method introduced by Heyliger to derive the 3D exact solutions has been successfully implemented using symbolic computing and a number of new test cases are here presented thoroughly. Specifically, two multilayered plates using PVDF piezoelectric material are selected as test cases under two different loading conditions and considering three plate aspect ratios for thick, moderately thick and thin plate, in a total of 12 distinct test cases. (C) 2013 Elsevier Ltd. All rights reserved.

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.

Modelling a Rotating Shaft as an Elastically Restrained Bernoulli-Euler Beam

Industrial rotating machines may be exposed to severe dynamic excitations due to resonant working regimes. Dealing with the bending vibration, problem of a machine rotor, the shaft - and attached discs - can be simply modelled using the Bernoulli-Euler beam theory, as a continuous beam subjected to a specific set of boundary conditions. In this study, the authors recall Rayleigh's method to propose an iterative strategy, which allows for the determination of natural frequencies and mode shapes of continuous beams taking into account the effect of attached concentrated masses and rotational inertias, including different stiffness coefficients at the right and the left end sides. The algorithm starts with the exact solutions from Bernoulli-Euler's beam theory, which are then updated through Rayleigh's quotient parameters. Several loading cases are examined in comparison with the experimental data and examples are presented to illustrate the validity of the model and the accuracy of the obtained values.

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.

Layerwise mixed models for analysis of multilayered piezoelectric composite plates using least-squares formulation

This work provides an assessment of layerwise mixed models using least-squares formulation for the coupled electromechanical static analysis of multilayered plates. In agreement with three-dimensional (3D) exact solutions, due to compatibility and equilibrium conditions at the layers interfaces, certain mechanical and electrical variables must fulfill interlaminar C-0 continuity, namely: displacements, in-plane strains, transverse stresses, electric potential, in-plane electric field components and transverse electric displacement (if no potential is imposed between layers). Hence, two layerwise mixed least-squares models are here investigated, with two different sets of chosen independent variables: Model A, developed earlier, fulfills a priori the interiaminar C-0 continuity of all those aforementioned variables, taken as independent variables; Model B, here newly developed, rather reduces the number of independent variables, but also fulfills a priori the interlaminar C-0 continuity of displacements, transverse stresses, electric potential and transverse electric displacement, taken as independent variables. The predictive capabilities of both models are assessed by comparison with 3D exact solutions, considering multilayered piezoelectric composite plates of different aspect ratios, under an applied transverse load or surface potential. It is shown that both models are able to predict an accurate quasi-3D description of the static electromechanical analysis of multilayered plates for all aspect ratios.

Positive solutions of fourth order problems with clamped beam boundary conditions

n this paper we make an exhaustive study of the fourth order linear operator u((4)) + M u coupled with the clamped beam conditions u(0) = u(1) = u'(0) = u'(1) = 0. We obtain the exact values on the real parameter M for which this operator satisfies an anti-maximum principle. Such a property is equivalent to the fact that the related Green's function is nonnegative in [0, 1] x [0, 1]. When M < 0 we obtain the best estimate by means of the spectral theory and for M > 0 we attain the optimal value by studying the oscillation properties of the solutions of the homogeneous equation u((4)) + M u = 0. By using the method of lower and upper solutions we deduce the existence of solutions for nonlinear problems coupled with this boundary conditions. (C) 2011 Elsevier Ltd. All rights reserved.

Reversible Photorheology in Solutions of Cetyltrimethylammonium Bromide, Salicylic Acid, and trans-2,4,4 '-Trihydroxychalcone

We show photorheology in aqueous solutions of weakly entangled wormlike micelles prepared with cetyltrimethylammonium bromide (CTAB), salicylic acid (HSal), and dilute amounts of the photochromic multistate compound trans-2,4,4'-trihydroxychalcone (Ct). Different chemical species of Ct are associated with different colorations and propensities to reside within or outside CTAB micelles. A light-induced transfer between the intra- and intermicellar space is used to alter the mean length of wormlike micelles and hence the rheological properties of the fluid, studied in steady-state shear Bow and in dynamic rheological measurements. Light-induced changes of fluid rheology are reversible by a the relaxation process. at relaxation rates which depend on pH and which are consistent with photochromic reversion rates measured by UV-vis absorption spectroscopy. Parameterizing viscoelostic rheological states by their effective relaxation time tau(c) and corresponding response modulus G(c), we find the light and dark states of the system to fall onto a characteristic state curve defined by comparable experiments conducted without photosensitive components. These reference experiments were prepared with the same concentration of CTAB, but different concentrations of HSal or sodium salicylote (NaSal), and tested at different temperatures.

Solutions of second-order and fourth-order ODEs on the half-line

We start by studying the existence of positive solutions for the differential equation u '' = a(x)u - g(u), with u ''(0) = u(+infinity) = 0, where a is a positive function, and g is a power or a bounded function. In other words, we are concerned with even positive homoclinics of the differential equation. The main motivation is to check that some well-known results concerning the existence of homoclinics for the autonomous case (where a is constant) are also true for the non-autonomous equation. This also motivates us to study the analogous fourth-order boundary value problem {u((4)) - cu '' + a(x)u = vertical bar u vertical bar(p-1)u u'(0) = u'''(0) = 0, u(+infinity) = u'(+infinity) = 0 for which we also find nontrivial (and, in some instances, positive) solutions.

Positive Solutions of the Dirichlet Problem for the One-dimensional Minkowski-Curvature Equation

We discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential equation-(u' / root 1 - u'(2))' = f(t, u). Depending on the behaviour of f = f(t, s) near s = 0, we prove the existence of either one, or two, or three, or infinitely many positive solutions. In general, the positivity of f is not required. All results are obtained by reduction to an equivalent non-singular problem to which variational or topological methods apply in a classical fashion.

Comparative study of amine solutions used in CO2 absorption/desorption cycles

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

Avaliação da eficácia de produtos inovadores de proteção da madeira para exteriores

Nesta dissertação procurou-se comparar os desempenhos de três produtos de proteção da madeira quando expostos a várias condições de degradação. Tendo em consideração a grande quantidade de variáveis quando se faz este tipo de estudos, tentou-se controlar o maior número possível destas, de modo a permitir a comparação com outros estudos que venham a ser feitos futuramente. O objetivo a longo prazo é a contribuição desta dissertação para um conjunto de resultados cada vez mais abrangente, facilitando a escolha do utilizador, quando pretender proteger a madeira das agressões exteriores com este tipo de produtos. A principal conclusão nesta dissertação é que a agressividade do meio tem um papel determinante para os resultados obtidos, bem como as condições de inclinação e orientação da madeira. Situações de má selagem de topos ou não consideração da presença agentes biológicos são outros dois fatores que influenciam a durabilidade da construção. Finalmente, concluiu-se que não existem soluções únicas, tendo que se estudar caso a caso, quais as condições exatas de exposição, de forma a escolher o produto, ou produtos, mais adequados.

Detection and diagnosis solutions for fault-tolerant VSI

This paper presents solutions for fault detection and diagnosis of two-level, three phase voltage-source inverter (VSI) topologies with IGBT devices. The proposed solutions combine redundant standby VSI structures and contactors (or relays) to improve the fault-tolerant capabilities of power electronics in applications with safety requirements. The suitable combination of these elements gives the inverter the ability to maintain energy processing in the occurrence of several failure modes, including short-circuit in IGBT devices, thus extending its reliability and availability. A survey of previously developed fault-tolerant VSI structures and several aspects of failure modes, detection and isolation mechanisms within VSI is first discussed. Hardware solutions for the protection of power semiconductors with fault detection and diagnosis mechanisms are then proposed to provide conditions to isolate and replace damaged power devices (or branches) in real time. Experimental results from a prototype are included to validate the proposed solutions.

From cellulosic based liquid crystalline sheared solutions to 1D and 2D soft materials

Liquid crystalline cellulosic-based solutions described by distinctive properties are at the origin of different kinds of multifunctional materials with unique characteristics. These solutions can form chiral nematic phases at rest, with tuneable photonic behavior, and exhibit a complex behavior associated with the onset of a network of director field defects under shear. Techniques, such as Nuclear Magnetic Resonance (NMR), Rheology coupled with NMR (Rheo-NMR), rheology, optical methods, Magnetic Resonance Imaging (MRI), Wide Angle X-rays Scattering (WAXS), were extensively used to enlighten the liquid crystalline characteristics of these cellulosic solutions. Cellulosic films produced by shear casting and fibers by electrospinning, from these liquid crystalline solutions, have regained wider attention due to recognition of their innovative properties associated to their biocompatibility. Electrospun membranes composed by helical and spiral shape fibers allow the achievement of large surface areas, leading to the improvement of the performance of this kind of systems. The moisture response, light modulated, wettability and the capability of orienting protein and cellulose crystals, opened a wide range of new applications to the shear casted films. Characterization by NMR, X-rays, tensile tests, AFM, and optical methods allowed detailed characterization of those soft cellulosic materials. In this work, special attention will be given to recent developments, including, among others, a moisture driven cellulosic motor and electro-optical devices.

Positive radial solutions of the Dirichlet problem for the Minkowski-Curvature equation in a ball

We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation { -div(del upsilon/root 1-vertical bar del upsilon vertical bar(2)) in B-R, upsilon=0 on partial derivative B-R,B- where B-R is a ball in R-N (N >= 2). According to the behaviour off = f (r, s) near s = 0, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.