Bogomol'nyi Bounds for Gravitational Cosmic Strings

We present a new method for finding lower bounds on the energy of topological cosmic string solutions in gravitational field theories. This new method produces bounds that are valid over the entire space of solutions, unlike the traditional approach, where the bounds obtained are only valid for cylindrically symmetric solutions. This method is shown to be a generalisation of the well-known Bogomol'nyi procedure for non-gravitational theories and as such, it can be used to find gravitational Bogomol'nyi bounds for models wherever the traditional Bogomol'nyi procedure can be applied in the non-gravitational limit. Furthermore, this method yields Bogomol'nyi equations that do not rule out the existence of asymmetric bound-saturating solutions.Comment: 17 pages - final version (accepted for publication in JHEP

Cusps on cosmic superstrings with junctions

The existence of cusps on non-periodic strings ending on D-branes is demonstrated and the conditions, for which such cusps are generic, are derived. The dynamics of F-, D-string and FD-string junctions are investigated. It is shown that pairs of FD-string junctions, such as would form after intercommutations of F- and D-strings, generically contain cusps. This new feature of cosmic superstrings opens up the possibility of extra channels of energy loss from a string network. The phenomenology of cusps on such cosmic superstring networks is compared to that of cusps formed on networks of their field theory analogues, the standard cosmic strings.Comment: 22 pages, 5 figure

Active estimation for switching linear dynamic systems

models for systems that exhibit both continuous dynamics and discrete mode changes. Estimating the hybrid discretecontinuous state of these systems is important for control and fault detection. Existing solutions for hybrid estimation approximate the belief state by maintaining a subset of the possible discrete mode sequences. This approximation can cause the estimator to lose track of the true mode sequence when the effects of discrete mode changes are subtle. In this paper we present a method for active hybrid estimation, where control inputs can be designed to discriminate between possible mode sequences. By probing the system for the purposes of estimation, such a sequence of control inputs can greatly reduce the probability of losing the true mode sequence compared to a nominal control sequence. Furthermore, by using a constrained finite horizon optimization formulation, we are able to guarantee that a given control task is achieved, while optimally detecting the hybrid state. I