Non-existence of Skyrmion-Skyrmion and Skyrmion-anti-Skyrmion static equilibria

We consider classical static Skyrmion-anti-Skyrmion and Skyrmion-Skyrmion configurations, symmetric with respect to a reflection plane, or symmetric up to a $G$-parity transformation respectively. We show that the stress tensor component completely normal to the reflection plane, and hence its integral over the plane, is negative definite or positive definite respectively. Classical Skyrmions always repel classical Skyrmions and classical Skyrmions always attract classical anti-Skyrmions and thus no static equilibrium, whether stable or unstable, is possible in either case. No other symmetry assumption is made and so our results also apply to multi-Skyrmion configurations. Our results are consistent with existing analyses of Skyrmion forces at large separation, and with numerical results on Skymion-anti-Skyrmion configurations in the literature which admit a different reflection symmetry. They also hold for the massive Skyrme model. We also point out that reflection symmetric self-gravitating Skyrmions or black holes with Skyrmion hair cannot rest in symmetric equilibrium with self-gravitating anti-Skyrmions.Comment: v2 Typos corrected, refs added. v3 Journal versio

HST Imaging of the Globular Clusters in the Fornax Cluster: NGC 1399 and NGC 1404

The Fornax cluster galaxies NGC 1399 and NGC 1404 are ideal for studying the effects of a cluster environment on globular cluster systems. Here we present new optical imaging of these two galaxies from both the Hubble Space Telescope's Wide Field and Planetary Camera 2 and the Cerro Tololo Inter-American Observatory's 1.5m telescope. The combination of both data sets provides unique insight on the spatial and colour distribution of globular clusters. From B-I colours, we find that both galaxies have a broad globular cluster metallicity distribution that is inconsistent with a single population. Two Gaussians provide a reasonable representation of the metallicity distribution in each galaxy. The metal-rich subpopulation is more centrally concentrated than the metal-poor one. We show that the radial metallicity gradient can be explained by the changing relative mix of the two globular cluster subpopulations. We derive globular cluster surface density profiles, and find that they are flatter (i.e. more extended) than the underlying starlight. The total number of globular clusters and specific frequency are calculated to be N = 5700 +/- 500, S_N = 11.5 +/- 1.0 for NGC 1399 and N = 725 +/- 145, S_N = 2.0 +/- 0.5 for NGC 1404. Our results are compared to the expectations of globular cluster formation scenarios.Comment: 21 pages, Latex, 13 figures, submitted to MNRA

Moyal star product approach to the Bohr-Sommerfeld approximation

The Bohr-Sommerfeld approximation to the eigenvalues of a one-dimensional quantum Hamiltonian is derived through order $\hbar^2$ (i.e., including the first correction term beyond the usual result) by means of the Moyal star product. The Hamiltonian need only have a Weyl transform (or symbol) that is a power series in $\hbar$, starting with $\hbar^0$, with a generic fixed point in phase space. The Hamiltonian is not restricted to the kinetic-plus-potential form. The method involves transforming the Hamiltonian to a normal form, in which it becomes a function of the harmonic oscillator Hamiltonian. Diagrammatic and other techniques with potential applications to other normal form problems are presented for manipulating higher order terms in the Moyal series.Comment: 27 pages, no figure

Zero Temperature Thermodynamics of Asymmetric Fermi Gases at Unitarity

The equation of state of a dilute two-component asymmetric Fermi gas at unitarity is subject to strong constraints, which affect the spatial density profiles in atomic traps. These constraints require the existence of at least one non-trivial partially polarized (asymmetric) phase. We determine the relation between the structure of the spatial density profiles and the T=0 equation of state, based on the most accurate theoretical predictions available. We also show how the equation of state can be determined from experimental observations.Comment: 10 pages and 7 figures. (Minor changes to correspond with published version.

The quantum metrology triangle and the re-definition of the SI ampere and kilogram; Analysis of a reduced set of observational equations

We have developed a set of seven observational equations that include all of the physics necessary to relate the most important of the fundamental constants to the definitions of the SI kilogram and ampere. We have used these to determine the influence of alternative definitions being considered for the SI kilogram and ampere on the uncertainty of three of the fundamental constants (h, e and mu). We have also reviewed the experimental evidence for the exactness of the quantum metrology triangle resulting from experiments combining the quantum Hall effect, the Josephson effects and single-electron tunnelling.Comment: 16 pages, 3 figures & 5 table

Exercise interventions for preventing dementia or delaying cognitive decline in people with mild cognitive impairment

This is the protocol for a review and there is no abstract. The objectives are as follows: To evaluate the effects of exercise interventions for preventing dementia in people with mild cognitive impairment. We refer to Forbes 2015b and Forbes 2015c for the review protocols on exercise interventions for maintaining cognitive function in cognitively healthy people in mid and late life

Dynamical evolution of globular cluster systems in clusters of galaxies I. The case of NGC 1404 in the Fornax cluster

We investigate, via numerical simulations, the tidal stripping and accretion of globular clusters (GCs). In particular, we focus on creating models that simulate the situation for the GC systems of NGC 1404 and NGC 1399 in the Fornax cluster, which have poor (specific frequency $S_{\rm N}$ $\sim$ 2) and rich ($S_{\rm N}$ $\sim$ 10) GC systems respectively. We initially assign NGC 1404 in our simulation a typical $S_{\rm N}$ ($\sim$ 5) for cluster ellipticals, and find that its GC system can only be reduced through stripping to the presently observed value, if its orbit is highly eccentric (with orbital eccentricity of $>$ 0.5) and if the initial scale length of the GCs system is about twice as large as the effective radius of NGC 1404 itself. These stripped GCs can be said to have formed a `tidal stream' of intracluster globular clusters (ICGCs) orbiting the centre of Fornax cluster (many of which would be assigned to NGC 1399 in an imaging study). The physical properties of these GCs (e.g., number, radial distribution) depend on the orbit and initial distribution of GCs in NGC 1404. Our simulations also predict a trend for $S_{\rm N}$ to rise with increasing clustercentric distance - a trend for which there is some observational support in the Fornax cluster.Comment: 12 pages 12 figures, MNRAS in pres