Evanescent field of vectorial highly non-paraxial beams

In terms of the Fourier spectrum, a simple but general analytical expression is given for the evanescent field associated to a certain kind of non-paraxial exact solutions of the Maxwell equations. This expression enables one to compare the relative weight of the evanescent wave with regard to the propagating field. In addition, in those cases in which the evanescent term is significant, the magnitude of the field components across the transverse profile (including the evanescent features) can be determined. These results are applied to some illustrative examples.

Full instability behavior of N-dimensional dynamical systems with a one-directional nonlinear vector field

We show how certain N-dimensional dynamical systems are able to exploit the full instability capabilities of their fixed points to do Hopf bifurcations and how such a behavior produces complex time evolutions based on the nonlinear combination of the oscillation modes that emerged from these bifurcations. For really different oscillation frequencies, the evolutions describe robust wave form structures, usually periodic, in which selfsimilarity with respect to both the time scale and system dimension is clearly appreciated. For closer frequencies, the evolution signals usually appear irregular but are still based on the repetition of complex wave form structures. The study is developed by considering vector fields with a scalar-valued nonlinear function of a single variable that is a linear combination of the N dynamical variables. In this case, the linear stability analysis can be used to design N-dimensional systems in which the fixed points of a saddle-node pair experience up to N21 Hopf bifurcations with preselected oscillation frequencies. The secondary processes occurring in the phase region where the variety of limit cycles appear may be rather complex and difficult to characterize, but they produce the nonlinear mixing of oscillation modes with relatively generic features

The use of mixed methods research in the behavioral sciences field

Mixed methods research involves the combined use of quantitative and qualitative methods in the same research study, and it is becoming increasingly important in several scientific areas. The aim of this paper is to review and compare through a mixed methods multiple-case study the application of this methodology in three reputable behavioural science journals: the Journal of Organizational Behavior, Addictive Behaviors and Psicothema. A quantitative analysis was carried out to review all the papers published in these journals during the period 2003-2008 and classify them into two blocks: theoretical and empirical, with the latter being further subdivided into three subtypes (quantitative, qualitative and mixed). A qualitative analysis determined the main characteristics of the mixed methods studies identified, in order to describe in more detail the ways in which the two methods are combined based on their purpose, priority, implementation and research design. From the journals selected, a total of 1.958 articles were analysed, the majority of which corresponded to empirical studies, with only a small number referring to research that used mixed methods. Nonetheless, mixed methods research does appear in all the behavioural science journals studied within the period selected, showing a range of designs, where the sequential equal weight mixed methods research design seems to stand out.