We describe a study on the conceptual difficulties faced by college students in understanding hydrodynamics of ideal fluids. This study was based on responses obtained in hundreds of written exams and oral interviews, which were held with first-year Engineering and Science university students. Their responses allowed us to identify a series of misconceptions unreported in the literature so far. The study findings demonstrate that the most important difficulties arise from the students' inability to establish a link between the kinematics and dynamics of moving fluids, and from a lack of understanding regarding how different regions of a system interact.

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In this paper we study the possible relationship between the Birth of the Double Scroll [L. O. Chua et al., IEEE-CAS 33 (11) (1986) 1073] and the homoclinic bifurcations in the traditional Chua's equations. Using a one-dimensional Poincarà e map we determine the existence of secondary symmetric homoclinic orbits of Shil'nikov type, born with the Chua's attractor, connecting unstable and stable manifolds of the trivial equilibrium point. In addition, taking into account the presence of other homoclinic orbits for the asymmetric attractor and heteroclinic orbits for the symmetric attractor (connecting unstable and stable manifold of the non-trivial equilibrium points), we suggest a hypothesis about the Birth of Double Scroll structure on the ( ; ÿ) plane.

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We investigate analytically and numerically a nonfeedback control technique for spatially extended systems. The method is suited for systems where some parameters can be modified. We apply the control scheme to a model used to describe vectorial transverse pattern formation in nonlinear optical systems, the Vector Complex Ginzburg–Landau Equation (VCGLE). Our scheme stabilizes a periodic regime where otherwise a chaotic regime is observed. We confirm by analytical calculation and direct simulation how this scheme, based in the use of a nonlinear diffraction term, stabilizes unstable polarized standing waves and linearly polarized traveling waves in a chaotic scenery.