arXiv subjects
Publications and source records attributed to Roisin Braddell.
In this article, motivated by the study of symplectic structures on manifolds with boundary and the systematic study of $b$-symplectic manifolds started in [12], we prove a slice theorem for Lie group actions on $b$-symplectic manifolds.
Motivated by the group of Galilean transformations and the subgroup of Galilean transformations which fix time zero, we introduce the notion of a $b$-Lie group as a pair $(G,H)$ where $G$ is a Lie group and $H$ is a codimension-one Lie subgroup. Such a notion allows us to give a theoretical framework for transformations of space-time where the initial time can be seen as a boundary. In this theoretical framework, we develop the basics of the theory and study the associated canonical $b$-symplectic structure on the $b$-cotangent bundle $^b {T}^\ast G$ together with its reduction theory. Namely, we extend the minimal coupling procedure to $^bT^*G/H$ and prove that the Poisson reduction under the cotangent lifted action of $H$ by left translations can be described in terms of the Lie Poisson structure on $\mathfrak{h}^\ast$ (where $\mathfrak{h}$ is the Lie algebra of $H$) and the canonical $b$-symplectic structure on $^b {T}^\ast(G/H)$, where $G/H$ is viewed as a one-dimensional $b$-manifold having as critical hypersurface (in the sense of $b$-manifolds) the identity element.
We study global transverse Poincaré sections and give topological conditions for their existence, showing they never exist in many important cases. We prove that an energy hypersurface possessing global transverse Poincaré section is equivalent to the hypersuface having a cosymplectic structure. We give a family of Hamiltonian systems with global Poincaré sections of all possible topologies. Finally, we address the question of when a compact hypersurface of a symplectic manifold possesses an induced cosymplectic structure.
In this paper we analyze in detail a collection of motivating examples to consider $b^m$-symplectic forms and folded-type symplectic structures. In particular, we provide models in Celestial Mechanics for every $b^m$-symplectic structure. At the end of the paper, we introduce the odd-dimensional analogue to $b$-symplectic manifolds: $b$-contact manifolds.
We perform density functional calculations to investigate the structure of the inter-metallic alloy FeRh under epitaxial strain. Bulk FeRh exhibits a metamagnetic transition from a low-temperature antiferromagnetic (AFM) phase to a ferromagnetic (FM) phase at 350K, and its strain dependence is of interest for tuning the transition temperature to the room-temperature operating conditions of typical memory devices. We find an unusually strong dependence of the structural energetics on the choice of exchange-correlation functional, with the usual local density approximation (LDA) yielding the wrong ground-state structure, and generalized gradient (GGA) extensions being in better agreement with the bulk experimental structure. Using the GGA we show the existence of a metastable face-centered-cubic (fcc)-like AFM structure that is reached from the ground state body-centered-cubic (bcc) AFM structure by following the epitaxial Bain path. We predict that this metastable fcc-like structure has a significantly higher conductivity than the bcc AFM phase. We show that the behavior is well described using non-linear elasticity theory, which captures the softening and eventual sign change of the orthorhombic shear modulus under compressive strain, consistent with this structural instability. Finally, we predict the existence of an additional unit-cell-doubling lattice instability, which should be observable at low temperature.