arXiv subjects
Publications and source records attributed to Michael Smith.
Assuming a lower bound on the Ricci curvature of a complete Riemannian manifold, for $p< 1/2$ we show the existence of bounds on the local $L^p$ norm of the Ricci curvature that depend only on the dimension and which improve with volume collapse.
The Planet Formation Imager (PFI) project aims to provide a strong scientific vision for ground-based optical astronomy beyond the upcoming generation of Extremely Large Telescopes. We make the case that a breakthrough in angular resolution imaging capabilities is required in order to unravel the processes involved in planet formation. PFI will be optimised to provide a complete census of the protoplanet population at all stellocentric radii and over the age range from 0.1 to about 100 Myr. Within this age period, planetary systems undergo dramatic changes and the final architecture of planetary systems is determined. Our goal is to study the planetary birth on the natural spatial scale where the material is assembled, which is the "Hill Sphere" of the forming planet, and to characterise the protoplanetary cores by measuring their masses and physical properties. Our science working group has investigated the observational characteristics of these young protoplanets as well as the migration mechanisms that might alter the system architecture. We simulated the imprints that the planets leave in the disk and study how PFI could revolutionise areas ranging from exoplanet to extragalactic science. In this contribution we outline the key science drivers of PFI and discuss the requirements that will guide the technology choices, the site selection, and potential science/technology tradeoffs.
This is an overview of the adaptive optics used in Advanced LIGO (aLIGO), known as the thermal compensation system (TCS). The thermal compensation system was designed to minimize thermally-induced spatial distortions in the interferometer optical modes and to provide some correction for static curvature errors in the core optics of aLIGO. The TCS is comprised of ring heater actuators, spatially tunable CO$_{2}$ laser projectors and Hartmann wavefront sensors. The system meets the requirements of correcting for nominal distortion in Advanced LIGO to a maximum residual error of 5.4nm, weighted across the laser beam, for up to 125W of laser input power into the interferometer.
In order to understand the formation of the multipolar structures of the pre-planetary nebula (PPN) CRL 618, we perform 3D simulations using a multi-directional bullet model. The optical lobes of CRL 618 and fast molecular outflows at the tips of the lobes have been found to have similar expansion ages of ~ 100 yr. Additional fast molecular outflows were found near the source along the outflow axes with ages of ~ 45 yr, suggesting a second episode of bullet ejections. Thus, in our simulations, two episodes of bullet ejections are assumed. The shaping process is simulated using the ZEUS-3D hydrodynamics code that includes molecular and atomic cooling. In addition, molecular chemistry is also included to calculate the CO intensity maps. Our results show the following: (1) Multi-epoch bullets interacting with the toroidal dense core can produce the collimated multiple lobes as seen in CRL 618. The total mass of the bullets is ~ 0.034 solar mass, consistent with the observed high-velocity CO emission in fast molecular outflows. (2) The simulated CO J=3-2 intensity maps show that the low-velocity cavity wall and the high-velocity outflows along the lobes are reasonably consistent with the observations. The position-velocity diagram of the outflows along the outflow axes shows a linear increase of velocity with distance, similar to the observations. The ejections of these bullets could be due to magneto-rotational explosions or nova-like explosions around a binary companion.
The VISTA Variables in the Vía Láctea (VVV) survey is one of six public ESO surveys, and is now in its 4th year of observing. Although far from being complete, the VVV survey has already delivered many results, some directly connected to the intended science goals (detection of variables stars, microlensing events, new star clusters), others concerning more exotic objects, e.g. novae. Now, at the end of the fourth observing period, and comprising roughly 50% of the proposed observations, the actual status of the survey, as well some of the results based on the VVV data, are presented.
The sets of closed and closed-normal subgroups of a profinite group carry a natural profinite topology. Through a combination of algebraic and topological methods the size of these subgroup spaces is calculated, and the spaces partially classified up to homeomorphism.
The set of all closed subgroups of a profinite carries a natural profinite topology. This space of subgroups can be classified up to homeomorphism in many cases, and tight bounds placed on its complexity as expressed by its scattered height.
We report on the optical response of a suspended-mass detuned resonant sideband extraction (RSE) interferometer with power recycling. The purpose of the detuned RSE configuration is to manipulate and optimize the optical response of the interferometer to differential displacements (induced by gravitational waves) as a function of frequency, independently of other parameters of the interferometer. The design of our interferometer results in an optical gain with two peaks: an RSE optical resonance at around 4 kHz and a radiation pressure induced optical spring at around 41 Hz. We have developed a reliable procedure for acquiring lock and establishing the desired optical configuration. In this configuration, we have measured the optical response to differential displacement and found good agreement with predictions at both resonances and all other relevant frequencies. These results build confidence in both the theory and practical implementation of the more complex optical configuration being planned for Advanced LIGO.
Peer to peer networks will become an increasingly important distribution channel for consumer information goods and may play a role in the distribution of information within corporations. Our research analyzes optimal membership rules for these networks in light of positive and negative externalities additional users impose on the network. Using a dataset gathered from the six largest OpenNap-based networks, we find that users impose a positive network externality based on the desirability of the content they provide and a negative network externality based on demands they place on the network. Further we find that the marginal value of additional users is declining and the marginal cost is increasing in the number of current users. This suggests that multiple small networks may serve user communities more efficiently than single monolithic networks and that network operators may wish to specialize in their content and restrict membership based on capacity constraints and user content desirability.
Low search costs in Internet markets can be used by consumers to find low prices, but can also be used by retailers to monitor competitors' prices. This price monitoring can lead to price matching, resulting in dampened price competition and higher prices in some cases. This paper analyzes price data for 316 bestselling, computer, and random book titles gathered from 32 retailers between August 1999 and January 2000. In contrast to previous studies we find no evidence of leader-follow behavior for the vast majority of retailers we study. Further, the few cases of leader-follow behavior we observe seem to be associated with managerial convenience as opposed to anti-competitive behavior. We offer a methodology that can be used by future academic researchers or government regulators to check for anti-competitive price matching behavior in future time periods or in additional product categories.