Symbolic dynamics generated by a hybrid chaotic systems

We consider piecewise defined differential dynamical systems which can be analysed through symbolic dynamics and transition matrices. We have a continuous regime, where the time flow is characterized by an ordinary differential equation (ODE) which has explicit solutions, and the singular regime, where the time flow is characterized by an appropriate transformation. The symbolic codification is given through the association of a symbol for each distinct regular system and singular system. The transition matrices are then determined as linear approximations to the symbolic dynamics. We analyse the dependence on initial conditions, parameter variation and the occurrence of global strange attractors.

Unbounded solutions for functional problems on the half-line

This paper presents an existence and localization result of unbounded solutions for a second-order differential equation on the half-line with functional boundary conditions. By applying unbounded upper and lower solutions, Green's functions and Schauder fixed point theorem, the existence of at least one solution is shown for the above problem. One example and one application to an Emden-Fowler equation are shown to illustrate our results.

Solvabilty of generalized Hammerstein integral equations on unbounded domains, with sign-changing kernels

In this work we study an Hammerstein generalized integral equation u(t)=∫_{-∞}^{+∞}k(t,s) f(s,u(s),u′(s),...,u^{(m)}(s))ds, where k:ℝ²→ℝ is a W^{m,∞}(ℝ²), m∈ℕ, kernel function and f:ℝ^{m+2}→ℝ is a L¹-Carathéodory function. To the best of our knowledge, this paper is the first one to consider discontinuous nonlinearities with derivatives dependence, without monotone or asymptotic assumptions, on the whole real line. Our method is applied to a fourth order nonlinear boundary value problem, which models moderately large deflections of infinite nonlinear beams resting on elastic foundations under localized external loads.

Unbounded solutions for functional problems on the half-line

This paper presents an existence and localization result of unbounded solutions for a second-order differential equation on the half-line with functional boundary conditions. By applying unbounded upper and lower solutions, Green's functions and Schauder fixed point theorem, the existence of at least one solution is shown for the above problem. One example and one application to an Emden-Fowler equation are shown to illustrate our results.

A staggered approach for the coupling of Cahn–Hilliard type diffusion and finite strain elasticity

We develop an algorithm and computational implementation for simulation of problems that combine Cahn–Hilliard type diffusion with finite strain elasticity. We have in mind applications such as the electro-chemo- mechanics of lithium ion (Li-ion) batteries. We concentrate on basic computational aspects. A staggered algorithm is pro- posed for the coupled multi-field model. For the diffusion problem, the fourth order differential equation is replaced by a system of second order equations to deal with the issue of the regularity required for the approximation spaces. Low order finite elements are used for discretization in space of the involved fields (displacement, concentration, nonlocal concentration). Three (both 2D and 3D) extensively worked numerical examples show the capabilities of our approach for the representation of (i) phase separation, (ii) the effect of concentration in deformation and stress, (iii) the effect of Electronic supplementary material The online version of this article (doi:10.1007/s00466-015-1235-1) contains supplementary material, which is available to authorized users. B P. Areias pmaa@uevora.pt 1 Department of Physics, University of Évora, Colégio Luís António Verney, Rua Romão Ramalho, 59, 7002-554 Évora, Portugal 2 ICIST, Lisbon, Portugal 3 School of Engineering, Universidad de Cuenca, Av. 12 de Abril s/n. 01-01-168, Cuenca, Ecuador 4 Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstraße 15, 99423 Weimar, Germany strain in concentration, and (iv) lithiation. We analyze con- vergence with respect to spatial and time discretization and found that very good results are achievable using both a stag- gered scheme and approximated strain interpolation.

As imagens de vestir da Procissão dos Terceiros: história, conceitos, e tradições. Um legado patrimonial franciscano na ilha de S. Miguel, Açores, nos séculos XVII a XIX

A temática proposta como objeto de estudo na presente tese, é o resultado de uma investigação dedicada ao fenómeno de utilização da imaginária processional nos cortejos de penitência de pendor franciscano, nos séculos XVII a XX na ilha de S. Miguel, Açores. Este tipo de manifestações religiosas, particularmente característico no espaço Iberoamericano, evidencia-se pela originalidade cenográfica, na qual são utilizados vestuário e adereços cénicos como complementos dos respetivos conjuntos escultóricos, as denominadas imagens de vestir. No arquipélago dos Açores, a Venerável Ordem Terceira da Penitência teve um papel de grande importância na organização destes eventos processionais, sendo que as ilhas de S. Miguel e da Terceira representam atualmente um dos últimos redutos na organização de procissões penitenciais, com recurso à utilização de imagens de vestir. No caso especifíco de S. Miguel, este tipo de imaginária pode ser ainda observada nos acervos de algumas das antigas igrejas conventuais da Ordem dos Frades Menores existentes nesta ilha, bem como na única procissão oriunda do espírito penitencial da Ordem Terceira, que se realiza anualmente na cidade da Ribeira Grande. O estudo agora apresentado pretende compreender as diversas componentes da utilização deste tipo de imaginária, bem como o registo do legado patrimonial que os seculares franciscanos perpetuaram até à atualidade, materializado num processo de patrimonialização das suas imagens de vestir, expresso na dicotomia entre os objetos, enquanto matéria, e as suas realidades biográficas, ligadas às comunidades de Terceiros que estiveram por detrás do uso destas imagens processionais; ABSTRACT: Religious sculptures for dressing of the Third Procession: history, concepts, typologies and traditions - A Franciscan heritage legacy in the island of S. Miguel, Azores, between the 17th and 19th centuries. The theme proposed as object of study in this thesis is the result of a research dedicated to the custom of adorning religious sculptures and displaying them in Franciscan penitential processions between the seventeenth and twentieth centuries, in the island of S. Miguel, Azores. This type of religious expression, particularly characteristic in the Ibero-American space, featuring up by scenic originality, in which clothing and scenic props are used to complement the respective sculptural groups, called religious sculptures for dressing. In the Azores, the Venerable Third Order of Penance had a major role in organizing these processional events, and the islands of S. Miguel and Terceira currently represents one of the last holdouts in organizing penitential processions, with the use of religious sculptures for dressing. In the case of S. Miguel, this type of imaginary can still be seen in the collections of some of the ancient Order of the convent churches of the Friars Minor existing on this island, and the only procession coming from the penitential spirit of the Third Order, which is held annually in the city of Ribeira Grande. The study now being presented aims to understand the various components of the use of such imaginary, and the recording of heritage legacy that the Franciscan secular perpetuated to the present day, materialized in a patrimonialization process of their dress images, expressed in the dichotomy between objects, as matter, and their biographical realities, linked to third-party communities that were behind the use of these processional images.

Existence of Homoclinic Solutions for Nonlinear Second-Order Problems

In this work, we consider the second-order discontinuous equation in the real line, u′′(t)−ku(t)=f(t,u(t),u′(t)),a.e.t∈R, with k>0 and f:R3→R an L1 -Carathéodory function. The existence of homoclinic solutions in presence of not necessarily ordered lower and upper solutions is proved, without periodicity assumptions or asymptotic conditions. Some applications to Duffing-like equations are presented in last section.