We discuss the construction of Maxwellian electrodynamics in 2+1 dimensions and some of its applications. Special emphasis is given to the problem of the retarded potentials and radiation, where substantial differences with respect to the usual three-dimensional case arise. These stem from the general form of the solutions of the wave equation in two dimensions, which we discuss using the Green’s function method. We believe the topics presented here could be stimulating additions to an advanced electrodynamics course at the undergraduate level.

This contribution focuses on the transport of passengers on international routes and the legal regime set down by the Warsaw Convention of 1929 and reinforced by the Montréal Convention of 1999. These Conventions regulate commercial aviation by detailing a set of minimum standardised procedures for flight safety, such as standards for air navigation systems, amongst others, to ensure safe and efficient air travel. The legal regime also regulates the possible claims that may be made against airlines for the death of or harm to passengers, as well as relating to damage to and loss of baggage. The regime not only limits claims temporally and by location, but it also excludes the application of national legal regimes. With regard to claims of harm to dignity the regime disallows such claims to be brought within the restrictions placed by the legal regimes or on any other basis. The contribution does not address the full coverage of these Conventions, only the exclusion of mental / emotional injuries. The Convention excludes emotional harm from the definition of death and physical harm. However claimants have brought claims to undermine the main exclusion of claims with regard to compensation for emotional harm. This contribution explores the exclusion of claims in the Warsaw and Montréal Conventions and thereafter analyses two court decisions in common law countries where this exclusion of claims was challenged and the challenge failed.

This article studies the heat transport in a flow through a saturated rigid porous medium. The mechanical model is based on the Continuum Theory of Mixtures which considers the fluid and the porous matrix as overlapping continuous constituents of a binary mixture. A Petrov-Galerkin formulation is employed to approximate the resulting system of partial differential equations, overcoming the classical Galerkin method limitation in dealing with advective-dominated flows. The employed method is built in order to remain stable and accurate even for very high advective-dominated flows. Taking advantage of an appropriated upwind strategy, the applied finite element method proved to generate accurate approximations even for very high Péclet regime. Some two-dimensional simulations of the advective-diffusive heat transfer in a flow through a porous flat channel employing lagrangean bilinear and serendipity biquadratic elements have been performed attesting the reliability of the employed Petrov-Galerkin formulation as well as the poor performance of Galerkin one even when mesh refining is considered.

Extracellular matrix proteins and cell adhesion receptors (integrins) play essential roles in the regulation of cell adhesion and migration. Interactions of integrins with the extracellular matrix proteins lead to phosphorylation of several intracellular proteins such as focal adhesion kinase, activating different signaling pathways responsible for the regulation of a variety of cell functions, including cytoskeleton mobilization. Once leukocytes are guided to sites of infection, inflammation, or antigen presentation, integrins can participate in the initiation, maintenance, or termination of the immune and inflammatory responses. The modulation of neutrophil activation through integrin-mediated pathways is important in the homeostatic control of the resolution of inflammatory states. In addition, during recirculation, T lymphocyte movement through distinct microenvironments is mediated by integrins, which are critical for cell cycle, differentiation and gene expression. Disintegrins are a family of low-molecular weight, cysteine-rich peptides first identified in snake venom, usually containing an RGD (Arg-Gly-Asp) motif, which confers the ability to selectively bind to integrins, inhibiting integrin-related functions in different cell systems. In this review we show that, depending on the cell type and the microenvironment, disintegrins are able to antagonize the effects of integrins or to act agonistically by activating integrin-mediated signaling. Disintegrins have proven useful as tools to improve the understanding of the molecular events regulated by integrin signaling in leukocytes and prototypes in order to design therapies able to interfere with integrin-mediated effects.

In this work it is presented a systematic procedure for constructing the solution of a large class of nonlinear conduction heat transfer problems through the minimization of quadratic functionals like the ones usually employed for linear descriptions. The proposed procedure gives rise to an efficient and easy way for carrying out numerical simulations of nonlinear heat transfer problems by means of finite elements. To illustrate the procedure a particular problem is simulated by means of a finite element approximation.