Rational maps, monopoles and skyrmions

We discuss the similarities between BPS monopoles and skyrmions, and point to an underlying connection in terms of rational maps between Riemann spheres. This involves the introduction of a new ansatz for Skyrme fields. We use this to construct good approximations to several known skyrmions, including all the minimal energy configurations up to baryon number nine, and some new solutions such as a baryon number seventeen Skyrme field with the truncated icosahedron structure of a buckyball.

The new approach is also used to understand the low-lying vibrational modes of skyrmions, which are required for quantization. Along the way we discover an interesting Morse function on the space of rational maps which may be of use in understanding the Sen forms on the monopole moduli spaces.     

Control of a coupled map lattice model for vortex shedding in the wake of a cylinder

The flow behind a vibrating flexible cable at low Reynolds numbers can exhibit complex wake structures such as lace-like patterns, vortex dislocations and frequency cells. These structures have been observed in experiments and numerical simulations, and are predicted by a previously developed low-order coupled map lattice (CML). The discrete (in time and space) CML models consist of a series of diffusively coupled circle map oscillators along the cable span. Motivated by a desire to modify the complex wake patterns behind flexible vibrating cables we have studied the addition of control terms into the highly efficient CML models and explored the resulting dynamics. Proportional, adaptive proportional and discontinuous non-linear (DNL) control methods were used to derive the control laws. The first method employed occasional proportional feedback. The adaptive method used spatio-temporal feedback control. The DNL method used a discontinuous feedback linearization procedure, and the controller was designed for the resulting linearized system using eigenvalue assignment. These techniques were applied to a modeled vortex dislocation structure in the wake of a vibrating cable in uniform freestream flow. Parallel shedding patterns were achieved for a range of forcing frequency-forcing amplitude combinations studied to validate the control theory. The adaptive proportional and DNL methods were found to be more effective than the proportional control method due to the incorporation of a spatially varying feedback gain across the cylinder span. The DNL method was found to be the most efficient controller of the low-order CML model. The required control level across the cable span was correlated to the 1/1 lock-on behavior of the temporal circle map.     

The development of information storage materials — How microscopy can help?

The response of giant magnetoresistance (GMR) devices depends critically on the film microstructure, with parameters such as layer thickness and interfacial abruptness being crucial. This paper presents results obtained using high resolution electron microscopy (HREM), chemical mapping and atom probe microanalysis. Local variations in the magnetic properties are induced by the microstructure and also when the films are patterned to form small elements. These lead to changes in the magnetization reversal mechanism. Some results of the studies of the magnetization reversal carried out using in situ in Lorentz transmission electron microscopy (LTEM) magnetizing experiments are also included.     

Fermions and parity violation in dimensional reduction schemes

Dimensional reduction, previously applied to Yang-Mills theories, is extended to gauge theories with spinor fields. It is shown that a fairly realistic model in Minkowski space can be obtained from the simplest initial lagrangian, defined in a space-time with extra, compact dimensions. Left-right asymmetry in the fermion sector in four dimensions is possible, and its occurrence is related to a non-vanishing Atiyah-Singer index.     

Vortex motion on surfaces of small curvature

We consider a single Abelian Higgs vortex on a surface Σ$\Sigma$ whose Gaussian curvature K$K$ is small relative to the size of the vortex, and analyse vortex motion by using geodesics on the moduli space of static solutions. The moduli space is Σ$\Sigma$ with a modified metric, and we propose that this metric has a universal expansion, in terms of K$K$ and its derivatives, around the initial metric on Σ$\Sigma$. Using an integral expression for the Kähler potential on the moduli space, we calculate the leading coefficients of this expansion numerically, and find some evidence for their universality. The expansion agrees to first order with the metric resulting from the Ricci flow starting from the initial metric on Σ$\Sigma$, but differs at higher order. We compare the vortex motion with the motion of a point particle along geodesics of Σ$\Sigma$. Relative to a particle geodesic, the vortex experiences an additional force, which to leading order is proportional to the gradient of K$K$. This force is analogous to the self-force on bodies of finite size that occurs in gravitational motion.