Ring solitons on vortices

Electromagnetic Waves in Annular Regions

In suitable bounded regions immersed in vacuum, time periodic wave solutions solving a full set of electrodynamics equations can be explicitly computed. Analytical expressions are available in special cases, whereas numerical simulations are necessary in more complex situations. The attention here is given to selected three-dimensional geometries, which are topologically equivalent to a toroid, where the behavior of the waves is similar to that of fluid-dynamics vortex rings. The results show that the shape of the sections of these rings depends on the behavior of the eigenvalues of a certain elliptic differential operator. Time-periodic solutions are obtained when at least two of such eigenvalues attain the same value. The solutions obtained are discussed in view of possible applications in electromagnetic whispering galleries or plasma physics.

From form to function: the ways to know a neuron

The shape of a neuron, its morphological signature, dictates the neuron's function by establishing its synaptic partnerships. Here, we review various anatomical methods used to reveal neuron shape and the contributions these have made to our current understanding of neural function in the Drosophila brain, especially the optic lobe. These methods, including Golgi impregnation, genetic reporters, and electron microscopy (EM), necessarily incorporate biases of various sorts that are easy to overlook, but that filter the morphological signatures we see. Nonetheless, the application of these methods to the optic lobe has led to reassuringly congruent findings on the number and shapes of neurons and their connection patterns, indicating that morphological classes are actually genetic classes. Genetic methods using, especially, GAL4 drivers and associated reporters have largely superceded classical Golgi methods for cellular analyses and, moreover, allow the manipulation of neuronal activity, thus enabling us to establish a bridge between morphological studies and functional ones. While serial-EM reconstruction remains the only reliable, albeit labor-intensive, method to determine actual synaptic connections, genetic approaches in combination with EM or high-resolution light microscopic techniques are promising methods for the rapid determination of synaptic circuit function.