Motivated by a model for the perception of textures by the visual cortex in primates, we analyse the bifurcation of periodic patterns for nonlinear equations describing the state of a system defined on the space of structure tensors, when these equations are further invariant with respect to the isometries of this space. We show that the problem reduces to a bifurcation problem in the hyperboli...

We present a new technique, based on a clever numerical minimization of certain Sobolev norms, for the numerical solution of partial differential equations. The new method is very high order even for complex geometries and variable coefficient problems. One surprising feature of the method is that we prefer to pose the problem in first-order form. The system does not have to be square as long a...

A novel phased array antenna with wide bandwidth and wide scan angle is presented. The radiating aperture of the phased array consists of periodically and closely spaced octagonal ring elements. Tight capacitive coupling between adjacent elements is realized by interdigitating the end portions of the ring elements. To improve the impedance matching of the individual antenna elements over wide f...

Motivated by a model for the perception of textures by the visual cortex in primates, we analyse the bifurcation of periodic patterns for nonlinear equations describing the state of a system defined on the space of structure tensors, when these equations are further invariant with respect to the isometries of this space. We show that the problem reduces to a bifurcation problem in the hyperboli...

We consider a class of second order ordinary differential equations describing one-dimensional systems with a quasi-periodic analytic forcing term and in the presence of damping. As a physical application one can think of a resistorinductor-varactor circuit with a periodic (or quasi-periodic) forcing function, even if the range of applicability of the theory is much wider. In the limit of large...

The theory of magnetic symmetry in quasicrystals, described in a companion paper [Acta Crystallographica AXX (2003) xxx-xxx], is used to enumerate all 3-dimensional octagonal spin point groups and spin space-group types, and calculate the resulting selection rules for neutron diffraction experiments. 1. Introduction We enumerate here all three-dimensional octagonal spin groups and calculate the...