The Symplectic Penrose Kite

The purpose of this article is to view the Penrose kite from the perspective of symplectic geometry.Comment: 24 pages, 7 figures, minor changes in last version, to appear in Comm. Math. Phys

Smooth stable and unstable manifolds for stochastic partial differential equations

Invariant manifolds are fundamental tools for describing and understanding nonlinear dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite dimensional random dynamical systems generated by a class of stochastic partial differential equations. We first show the existence of Lipschitz continuous stable and unstable manifolds by the Lyapunov-Perron's method. Then, we prove the smoothness of these invariant manifolds

The Smallest Mass Ratio Young Star Spectroscopic Binaries

Using high resolution near-infrared spectroscopy with the Keck telescope, we have detected the radial velocity signatures of the cool secondary components in four optically identified pre-main-sequence, single-lined spectroscopic binaries. All are weak-lined T Tauri stars with well-defined center of mass velocities. The mass ratio for one young binary, NTTS 160905-1859, is M2/M1 = 0.18+/-0.01, the smallest yet measured dynamically for a pre-main-sequence spectroscopic binary. These new results demonstrate the power of infrared spectroscopy for the dynamical identification of cool secondaries. Visible light spectroscopy, to date, has not revealed any pre-main-sequence secondary stars with masses <0.5 M_sun, while two of the young systems reported here are in that range. We compare our targets with a compilation of the published young double-lined spectroscopic binaries and discuss our unique contribution to this sample.Comment: Accepted for publication in the April, 2002, ApJ; 6 figure

Functionalized Carbon Nanotubes in the Brain: Cellular Internalization and Neuroinflammatory Responses

The potential use of functionalized carbon nanotubes (f-CNTs) for drug and gene delivery to the central nervous system (CNS) and as neural substrates makes the understanding of their in vivo interactions with the neural tissue essential. The aim of this study was to investigate the interactions between chemically functionalized multi-walled carbon nanotubes (f-MWNTs) and the neural tissue following cortical stereotactic administration. Two different f-MWNT constructs were used in these studies: shortened (by oxidation) amino-functionalized MWNT (oxMWNT-NH3+) and amino-functionalized MWNT (MWNT-NH3+). Parenchymal distribution of the stereotactically injected f-MWNTs was assessed by histological examination. Both f-MWNT were uptaken by different types of neural tissue cells (microglia, astrocytes and neurons), however different patterns of cellular internalization were observed between the nanotubes. Furthermore, immunohistochemical staining for specific markers of glial cell activation (GFAP and CD11b) was performed and secretion of inflammatory cytokines was investigated using real-time PCR (qRT-PCR). Injections of both f-MWNT constructs led to a local and transient induction of inflammatory cytokines at early time points. Oxidation of nanotubes seemed to induce significant levels of GFAP and CD11b over-expression in areas peripheral to the f-MWNT injection site. These results highlight the importance of nanotube functionalization on their interaction with brain tissue that is deemed critical for the development nanotube-based vector systems for CNS application

Numerical modelling of concrete curing, regarding hydration and temperature phenomena

A numerical model that accounts for the hydration and aging phenomena during the early ages of concrete curing is presented in a format suitable for a finite element implementation. Assuming the percolation of water through the hydrates already formed as the&nbsp;dominant mechanism&nbsp;of cement hydration, the model adopts an internal variable called hydration degree, whose evolution law&nbsp;is easily calibrated and allows an accurate prediction of the hydration heat production.&nbsp;Compressive strength&nbsp;evolution is related to the aging degree, a concept that accounts for the influences of the hydration and&nbsp;curing temperature&nbsp;on the final mechanical&nbsp;properties of concrete. The model capabilities are illustrated by means of a wide set of experimental tests involving ordinary and&nbsp;high performance concretes, and through the simulation of the concrete curing on a viaduct deck of the &Ouml;resund Link

Star Spot Induced Radial Velocity Variability in LkCa 19

We describe a new radial velocity survey of T Tauri stars and present the first results. Our search is motivated by an interest in detecting massive young planets, as well as investigating the origin of the brown dwarf desert. As part of this survey, we discovered large-amplitude, periodic, radial velocity variations in the spectrum of the weak line T Tauri star LkCa 19. Using line bisector analysis and a new simulation of the effect of star spots on the photometric and radial velocity variability of T Tauri stars, we show that our measured radial velocities for LkCa19 are fully consistent with variations caused by the presence of large star spots on this rapidly rotating young star. These results illustrate the level of activity-induced radial velocity noise associated with at least some very young stars. This activity-induced noise will set lower limits on the mass of a companion detectable around LkCa 19, and similarly active young stars.Comment: ApJ accepted, 27 pages, 12 figures, aaste

On the Navier-Stokes equations with rotating effect and prescribed outflow velocity

We consider the equations of Navier-Stokes modeling viscous fluid flow past a moving or rotating obstacle in $\mathbb{R}^d$ subject to a prescribed velocity condition at infinity. In contrast to previously known results, where the prescribed velocity vector is assumed to be parallel to the axis of rotation, in this paper we are interested in a general outflow velocity. In order to use $L^p$-techniques we introduce a new coordinate system, in which we obtain a non-autonomous partial differential equation with an unbounded drift term. We prove that the linearized problem in $\mathbb{R}^d$ is solved by an evolution system on $L^p_{\sigma}(\mathbb{R}^d)$ for $1<p<\infty$. For this we use results about time-dependent Ornstein-Uhlenbeck operators. Finally, we prove, for $p\geq d$ and initial data $u_0\in L^p_{\sigma}(\mathbb{R}^d)$, the existence of a unique mild solution to the full Navier-Stokes system.Comment: 18 pages, to appear in J. Math. Fluid Mech. (published online first