Generic bifurcation of Hamiltonian vector fields with symmetry

One of the goals of this paper is to describe explicitly the generic movement of eigenvalues through a one-to-one resonance in a linear Hamiltonian system which is equivariant with respect to a symplectic representation of a compact Lie group. We classify this movement, and hence answer the question of when the collisions are 'dangerous' in the sense of Krein by using a combination of group theory and definiteness properties of the associated quadratic Hamiltonian. For example, for systems with no symmetry or O(2) symmetry generically the eigenvalues split, whereas for systems with S1 symmetry, generically the eigenvalues may split or pass. It is in this last case that one has to use both group theory and energetics to determine the generic eigenvalue movement. The way energetics and group theory are combined is summarized in table 1. The result is to be contrasted with the bifurcation of steady states (zero eigenvalue) where one can use either group theory alone (Golubitsky and Stewart) or definiteness properties of the Hamiltonian (Cartan-Oh) to determine whether the eigenvalues split or pass on the imaginary axis

Interplanetary Trajectory Optimization with Powerlimited Propulsion Systems

A trajectory-optimization process is described in which the optimum thrust equations are derived using the calculus of variations. The magnitude of the thrust is constrained within an upper and a lower bound, but the thrust direction is arbitrary. This formulation allows both the constant-thrust program and the variable-thrust program to be considered. For the constant-thrust program, certain propulsion-system parameters are optimized for maximum final vehicle mass. This theory has been used to study interplanetary missions to Venus and Mars using a power-limited propulsion system. Both one-way and round trip rendezvous trajectories are considered. The analysis employs a two-body inverse-square force-field model of three dimensions. An iterative routine used to solve the two-point boundary-value problem is described in the Appendix

Spatially Resolved Stellar Populations of Eight GOODS-South AGN at z~1

We present a pilot study of the stellar populations of 8 AGN hosts at z~1 and compare to (1) lower redshift samples and (2) a sample of nonactive galaxies of similar redshift. We utilize K' images in the GOODS South field obtained with the laser guide star adaptive optics (LGSAO) system at Keck Observatory. We combine this K' data with B, V, i, and z imaging from the ACS on HST to give multi-color photometry at a matched spatial resolution better than 100 mas in all bands. The hosts harbor AGN as inferred from their high X-ray luminosities (L_X > 10^42 ergs/s) or mid-IR colors. We find a correlation between the presence of younger stellar populations and the strength of the AGN, as measured with [OIII] line luminosity or X-ray (2-10 keV) luminosity. This finding is consistent with similar studies at lower redshift. Of the three Type II galaxies, two are disk galaxies and one is of irregular type, while in the Type I sample there only one disk-like source and four sources with smooth, elliptical/spheroidal morphologies. In addition, the mid-IR SEDs of the strong Type II AGN indicate that they are excited to LIRG (Luminous InfraRed Galaxy) status via galactic starbursting, while the strong Type I AGN are excited to LIRG status via hot dust surrounding the central AGN. This supports the notion that the obscured nature of Type II AGN at z~1 is connected with global starbursting and that they may be extincted by kpc-scale dusty features that are byproducts of this starbursting.Comment: 56 pages, 39 figures, accepted to A

Optical Morphology Evolution of Infrared Luminous Galaxies in GOODS-N

We combine optical morphologies and photometry from HST, redshifts from Keck, and mid-infrared luminosities from Spitzer for an optically selected sample of~800 galaxies in GOODS-N to track morphology evolution of infrared luminous galaxies (LIRGs) since redshift z=1. We find a 50% decline in the number of LIRGs from z~1 to lower redshift, in agreement with previous studies. In addition, there is evidence for a morphological evolution of the populations of LIRGs. Above z=0.5, roughly half of all LIRGs are spiral, the peculiar/irregular to spiral ratio is ~0.7, and both classes span a similar range of L_{IR} and M_B. At low-z, spirals account for one-third of LIRGs, the peculiar to spiral fraction rises to 1.3, and for a given M_B spirals tend to have lower IR luminosity than peculiars. Only a few percent of LIRGs at any redshift are red early-type galaxies. For blue galaxies (U-B < 0.2), M_B is well correlated with log(L_{IR}) with an RMS scatter (about a bivariate linear fit) of ~0.25 dex in IR luminosity. Among blue galaxies that are brighter than M_B = -21, 75% are LIRGs, regardless of redshift. These results can be explained by a scenario in which at high-z, most large spirals experience an elevated star formation rate as LIRGs. Gas consumption results in a decline of LIRGs, especially in spirals, to lower redshifts.Comment: 6 pages, 2 figures, accepted ApJ

Spatially Resolved Stellar Populations of Eight GOODS-South Active Galactic Nuclei at z ~ 1

We present a pilot study of the stellar populations of eight active galactic nucleus (AGN) hosts at z ~ 1 and compare with (1) lower redshift samples and (2) a sample of nonactive galaxies of similar redshift. We utilize K' images in the Great Observatories Origins Deep Survey South field obtained with the laser guide star adaptive optics system at Keck Observatory. We combine these K' data with B, V, i, and z imaging from the Advanced Camera for Surveys on Hubble Space Telescope to give multicolor photometry at a matched spatial resolution better than 100 mas in all bands. The hosts harbor AGNs as inferred from their high X-ray luminosities (LX > 10^42 erg s^–1) or mid-IR colors. We find a correlation between the presence of younger stellar populations and the strength of the AGN, as measured with [O III] line luminosity or X-ray (2-10 keV) luminosity. This finding is consistent with similar studies at lower redshift. Of the three Type II galaxies, two are disk galaxies and one is of irregular type, while in the Type I sample there are only one disk-like source and four sources with smooth, elliptical/spheroidal morphologies. In addition, the mid-IR spectral energy distributions of the strong Type II AGNs indicate that they are excited to Luminous InfraRed Galaxy (LIRG) status via galactic starbursting, while the strong Type I AGNs are excited to LIRG status via hot dust surrounding the central AGN. This supports the notion that the obscured nature of Type II AGNs at z ~ 1 is connected with global starbursting and that they may be extincted by kpc-scale dusty features that are by-products of this starbursting

A test for a conjecture on the nature of attractors for smooth dynamical systems

Dynamics arising persistently in smooth dynamical systems ranges from regular dynamics (periodic, quasiperiodic) to strongly chaotic dynamics (Anosov, uniformly hyperbolic, nonuniformly hyperbolic modelled by Young towers). The latter include many classical examples such as Lorenz and H\'enon-like attractors and enjoy strong statistical properties. It is natural to conjecture (or at least hope) that most dynamical systems fall into these two extreme situations. We describe a numerical test for such a conjecture/hope and apply this to the logistic map where the conjecture holds by a theorem of Lyubich, and to the Lorenz-96 system in 40 dimensions where there is no rigorous theory. The numerical outcome is almost identical for both (except for the amount of data required) and provides evidence for the validity of the conjecture.Comment: Accepted version. Minor modifications from previous versio

Chaotic magnetic field reversals in turbulent dynamos

We present direct numerical simulations of reversals of the magnetic field generated by swirling flows in a spherical domain. In agreement with a recent model, we observe that coupling dipolar and quadrupolar magnetic modes by an asymmetric forcing of the flow generates field reversals. In addition, we show that this mechanism strongly depends on the value of the magnetic Prandtl number.Comment: 4 pages, 5 figure

A simple mechanism for the reversals of Earth's magnetic field

We show that a model, recently used to describe all the dynamical regimes of the magnetic field generated by the dynamo effect in the VKS experiment [1], also provides a simple explanation of the reversals of Earth's magnetic field, despite strong differences between both systems.Comment: update version, with new figure

Longitudinal measurement of the developing grey matter in preterm subjects using multi-modal MRI.

Preterm birth is a major public health concern, with the severity and occurrence of adverse outcome increasing with earlier delivery. Being born preterm disrupts a time of rapid brain development: in addition to volumetric growth, the cortex folds, myelination is occurring and there are changes on the cellular level. These neurological events have been imaged non-invasively using diffusion-weighted (DW) MRI. In this population, there has been a focus on examining diffusion in the white matter, but the grey matter is also critically important for neurological health. We acquired multi-shell high-resolution diffusion data on 12 infants born at ≤28weeks of gestational age at two time-points: once when stable after birth, and again at term-equivalent age. We used the Neurite Orientation Dispersion and Density Imaging model (NODDI) (Zhang et al., 2012) to analyse the changes in the cerebral cortex and the thalamus, both grey matter regions. We showed region-dependent changes in NODDI parameters over the preterm period, highlighting underlying changes specific to the microstructure. This work is the first time that NODDI parameters have been evaluated in both the cortical and the thalamic grey matter as a function of age in preterm infants, offering a unique insight into neuro-development in this at-risk population

Collective patterns arising out of spatio-temporal chaos

We present a simple mathematical model in which a time averaged pattern emerges out of spatio-temporal chaos as a result of the collective action of chaotic fluctuations. Our evolution equation possesses spatial translational symmetry under a periodic boundary condition. Thus the spatial inhomogeneity of the statistical state arises through a spontaneous symmetry breaking. The transition from a state of homogeneous spatio-temporal chaos to one exhibiting spatial order is explained by introducing a collective viscosity which relates the averaged pattern with a correlation of the fluctuations.Comment: 11 pages (Revtex) + 5 figures (postscript