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.

Self-assembly in chains, rings, and branches: a single component system with two critical points

Agências financiadoras: FCT - PEstOE/FIS/UI0618/2011; PTDC/FIS/098254/2008 ERC-PATCHYCOLLOIDS e MIUR-PRIN

James W. Carey as critical theorist of the information age

This paper suggests that the thought of the North-American critical theorist James W. Carey provides a relevant perspective on communication and technology. Having as background American social pragmatism and progressive thinkers of the beginning of the 20th century (as Dewey, Mead, Cooley, and Park), Carey built a perspective that brought together the political economy of Harold A. Innis, the social criticism of David Riesman and Charles W. Mills and incorporated Marxist topics such as commodification and sociocultural domination. The main goal of this paper is to explore the connection established by Carey between modern technological communication and what he called the “transmissive model”, a model which not only reduces the symbolic process of communication to instrumentalization and to information delivery, but also politically converges with capitalism as well as power, control and expansionist goals. Conceiving communication as a process that creates symbolic and cultural systems, in which and through which social life takes place, Carey gives equal emphasis to the incorporation processes of communication.If symbolic forms and culture are ways of conditioning action, they are also influenced by technological and economic materializations of symbolic systems, and by other conditioning structures. In Carey’s view, communication is never a disembodied force; rather, it is a set of practices in which co-exist conceptions, techniques and social relations. These practices configure reality or, alternatively, can refute, transform and celebrate it. Exhibiting sensitiveness favourable to the historical understanding of communication, media and information technologies, one of the issues Carey explored most was the history of the telegraph as an harbinger of the Internet, of its problems and contradictions. For Carey, Internet was seen as the contemporary heir of the communications revolution triggered by the prototype of transmission technologies, namely the telegraph in the 19th century. In the telegraph Carey saw the prototype of many subsequent commercial empires based on science and technology, a pioneer model for complex business management; an example of conflict of interest for the control over patents; an inducer of changes both in language and in structures of knowledge; and a promoter of a futurist and utopian thought of information technologies. After a brief approach to Carey’s communication theory, this paper focuses on his seminal essay "Technology and ideology. The case of the telegraph", bearing in mind the prospect of the communication revolution introduced by Internet. We maintain that this essay has seminal relevance for critically studying the information society. Our reading of it highlights the reach, as well as the problems, of an approach which conceives the innovation of the telegraph as a metaphor for all innovations, announcing the modern stage of history and determining to this day the major lines of development in modern communication systems.

Generalization of Wertheim's theory for the assembly of various types of rings

We generalize Wertheim's first order perturbation theory to account for the effect in the thermodynamics of the self-assembly of rings characterized by two energy scales. The theory is applied to a lattice model of patchy particles and tested against Monte Carlo simulations on a fcc lattice. These particles have 2 patches of type A and 10 patches of type B, which may form bonds AA or AB that decrease the energy by epsilon(AA) and by epsilon(AB) = r epsilon(AA), respectively. The angle theta between the 2 A-patches on each particle is fixed at 601, 90 degrees or 120 degrees. For values of r below 1/2 and above a threshold r(th)(theta) the models exhibit a phase diagram with two critical points. Both theory and simulation predict that rth increases when theta decreases. We show that the mechanism that prevents phase separation for models with decreasing values of theta is related to the formation of loops containing AB bonds. Moreover, we show that by including the free energy of B-rings ( loops containing one AB bond), the theory describes the trends observed in the simulation results, but that for the lowest values of theta, the theoretical description deteriorates due to the increasing number of loops containing more than one AB bond.