Simplified models of diffusion in radially-symmetric geometries

Radially Symmetric Patterns of Reaction-Diffusion Systems

In this paper, bifurcations of stationary and time-periodic solutions to reactiondiffusion systems are studied. We develop a center-manifold and normal form theory for radial dynamics which allows for a complete description of radially symmetric patterns. In particular, we show the existence of localized pulses near saddle-nodes, critical Gibbs kernels in the cusp, focus patterns in Turing inst...

Left-Right Symmetric Models in Noncommutative Geometries?

In the Standard Model of electro-weak and strong forces, parity is broken explicitly by the choice of inequivalent representations for leftand right-handed fermions. Within the frame work of Yang-Mills-Higgs models this is certainly an aesthetic draw back that physicists have tried to correct by the introduction of left-right symmetric models. These are Yang-Mills-Higgs models where parity is b...

Radially symmetric nonlinear photonic crystals

Different types of quadratic, radially symmetric, nonlinear photonic crystals are presented. The modulation of the nonlinear coefficient may be a periodic or an aperiodic function of the radial coordinate, whereas the azimuthal symmetry of the crystal may be either continuous or discrete. Nonlinear interactions within these structures are studied in two orientations, transverse and longitudinal...

On Symmetric Moore Geometries

Diffusion in confined geometries.

Diffusive transport of particles or, more generally, small objects, is a ubiquitous feature of physical and chemical reaction systems. In configurations containing confining walls or constrictions, transport is controlled both by the fluctuation statistics of the jittering objects and the phase space available to their dynamics. Consequently, the study of transport at the macro- and nanoscales ...