Helical buckling of Skyrme-Faddeev solitons

Solitons in the Skyrme-Faddeev model on R^2xS^1 are shown to undergo buckling transitions as the circumference of the S^1 is varied. These results support a recent conjecture that solitons in this field theory are well-described by a much simpler model of elastic rods.Comment: 24 pages, 9 figure

Dynamic modelling of a three-sector transitional economy

Rural industry provides inputs and markets for agriculture, which in turn provides inputs and markets for rural industry. As the mutually supportive linkages between rural industry and agriculture develop, the size of both sectors increases. Under certain conditions rural industry grows more rapidly than agriculture, resulting in the structural transformation of the rural sector. But the growth of rural industry may hurt the state-owned industrial sector if both sectors compete for similar resources and product markets. To protect their state enterprises, transitional economies have at times suppressed the growth of non-state rural industries. This can hurt the economy overall. We show how the growth rates of agriculture and rural industry may decline, and, surprisingly, how the growth of state industry might fall if rural industry is suppressed. This is especially so if agriculture supports state industry. By suppressing rural industry, agriculture is hurt. The decline in agriculture then hurts state industry, undermining the objective of protecting state industry. Depending on the magnitude of the relevant impacts, intervention to protect state industry may or may not be optimal, leaving governments with difficult policy decisions

Helical buckling of Skyrme-Faddeev solitons

Solitons in the Skyrme-Faddeev model on R^2xS^1 are shown to undergo buckling transitions as the circumference of the S^1 is varied. These results support a recent conjecture that solitons in this field theory are well-described by a much simpler model of elastic rods.Comment: 24 pages, 9 figure

Chains of solitons

We construct and analyse chains of solitons in various field theories. Particular emphasis is placed on the constituent structure, which appears to be be a generic feature of chains. In Yang-Mills theory, we construct axially symmetric chains of instantons (calorons) with instanton charge 2, making essential use of the Nahm transform. We show that there are two distinct families of caloron, which can be distinguished using representation theory. We also construct calorons on hyperbolic space with instanton charge 1 and monopole charge 0. This generalises earlier work of Garland and Murray, in the same way that non-integer-mass hyperbolic monopoles generalise the integer-mass hyperbolic monopoles of Atiyah. We study chains of skyrmions with charge 1 in both the Skyrme and planar Skyrme models, using various approximate analytic Ansätze. In the Skyrme model chains are argued to exist and to have an energy per baryon number lower than the charge 2 skyrmion. In the planar Skyrme model, we show that the stability of chains depends on the choice of potential function. We study chains and kinks in the CP(^n) sigma models analytically, in particular, we show that chains are kinks in a sigma model whose target is a homogeneous space for a loop group. This is the Sigma model analog of the statement that a caloron is a monopole whose gauge group is a loop group

Approximating the parallel transport of an induced connection

Efficient numerical methods to approximate the parallel transport operators of the induced connection on a sub-bundle of a vector bundle are presented. These methods are simpler than naive applications of a Runge--Kutta algorithm, and have accuracy up to order 4. They have the desirable property of being insensitive to choices of trivialisation of the sub-bundle. The methods were developed in order to solve a problem of computing skyrmions using the Atiyah--Manton--Sutcliffe and Atiyah--Drinfeld--Hitchin--Manin constructions, but are applicable to a broader range of problems in computational geometry.Comment: 17 page

Kinks, chains, and loop groups in the CP^n sigma models

We consider topological solitons in the CP^n sigma models in two space dimensions. In particular, we study "kinks", which are independent of one coordinate up to a rotation of the target space, and "chains", which are periodic in one coordinate up to a rotation of the target space. Kinks and chains both exhibit constituents, similar to monopoles and calorons in SU(n) Yang-Mills-Higgs and Yang-Mills theories. We examine the constituent structure using Lie algebras.Comment: 19 pages, 3 figures v2: Discussions improved, examples added, references added, typos correcte