Tilt, Warp, and Simultaneous Precessions in Disks

Warps are suspected in disks around massive compact objects. However, the proposed warping source -- non-axisymmetric radiation pressure -- does not apply to white dwarfs. In this letter we report the first Smoothed Particle Hydrodynamic simulations of accretion disks in SU UMa-type systems that naturally tilt, warp, and simultaneously precess in the prograde and retrograde directions using white dwarf V344 Lyrae in the Kepler field as our model. After ~79 days in V344 Lyrae, the disk angular momentum L_d becomes misaligned to the orbital angular momentum L_o. As the gas stream remains normal to L_o, hydrodynamics (e.g., the lift force) is a likely source to disk tilt. In addition to tilt, the outer disk annuli cyclically change shape from circular to highly eccentric due to tidal torques by the secondary star. The effect of simultaneous prograde and retrograde precession is a warp of the colder, denser midplane as seen along the disk rim. The simulated rate of apsidal advance to nodal regression per orbit nearly matches the observed ratio in V344 Lyrae.Comment: 3 figures, Lette

A Generalized Montgomery Phase Formula for Rotating Self Deforming Bodies

We study the motion of self deforming bodies with non zero angular momentum when the changing shape is known as a function of time. The conserved angular momentum with respect to the center of mass, when seen from a rotating frame, describes a curve on a sphere as it happens for the rigid body motion, though obeying a more complicated non-autonomous equation. We observe that if, after time $\Delta T$, this curve is simple and closed, the deforming body \'{}s orientation in space is fully characterized by an angle or phase $\theta_{M}$. We also give a reconstruction formula for this angle which generalizes R. Montgomery\'{}s well known formula for the rigid body phase. Finally, we apply these techniques to obtain analytical results on the motion of deforming bodies in some concrete examples.Comment: 20 page

Review of Mobilizing Mercy: A History of the Canadian Red Cross by Sarah Glassford

Review of Mobilizing Mercy: A History of the Canadian Red Cross by Sarah Glassford

Chapel Springs Church: Christian Service

Student perspectives on worship services from Instructor Jennifer Garvin-Sanchez\u27s Religious Studies 108 Human Spirituality course at Virginia Commonwealth University

Who's Afraid of the Hill Boundary?

The Jacobi-Maupertuis metric allows one to reformulate Newton's equations as geodesic equations for a Riemannian metric which degenerates at the Hill boundary. We prove that a JM geodesic which comes sufficiently close to a regular point of the boundary contains pairs of conjugate points close to the boundary. We prove the conjugate locus of any point near enough to the boundary is a hypersurface tangent to the boundary. Our method of proof is to reduce analysis of geodesics near the boundary to that of solutions to Newton's equations in the simplest model case: a constant force. This model case is equivalent to the beginning physics problem of throwing balls upward from a fixed point at fixed speeds and describing the resulting arcs, see Fig. 2

Teensites.com: A Field Guide to the New Digital Landscape

A 2001 report from the Center for Media Education, provided here as background to work produced by Kathryn Montgomery after coming to American University and CSM (see http://www.centerforsocialmedia.org/resources/publications/ecitizens/index2.htm -- Youth as E-Citizens'), surveys the burgeoning digital media culture directed at -- and in some cases created by -- teens.This report surveys the burgeoning new media culture directed at -- and in some cases created by -- teens. TeenSites.com -- A Field Guide to the New Digital Landscape examines the uniquely interactive nature of the new media, and explores the ways in which teens are at once shaping and being shaped by the electronic culture that surrounds them

Logarithmically-small Minors and Topological Minors

Mader proved that for every integer $t$ there is a smallest real number $c(t)$ such that any graph with average degree at least $c(t)$ must contain a $K_t$-minor. Fiorini, Joret, Theis and Wood conjectured that any graph with $n$ vertices and average degree at least $c(t)+\epsilon$ must contain a $K_t$-minor consisting of at most $C(\epsilon,t)\log n$ vertices. Shapira and Sudakov subsequently proved that such a graph contains a $K_t$-minor consisting of at most $C(\epsilon,t)\log n \log\log n$ vertices. Here we build on their method using graph expansion to remove the $\log\log n$ factor and prove the conjecture. Mader also proved that for every integer $t$ there is a smallest real number $s(t)$ such that any graph with average degree larger than $s(t)$ must contain a $K_t$-topological minor. We prove that, for sufficiently large $t$, graphs with average degree at least $(1+\epsilon)s(t)$ contain a $K_t$-topological minor consisting of at most $C(\epsilon,t)\log n$ vertices. Finally, we show that, for sufficiently large $t$, graphs with average degree at least $(1+\epsilon)c(t)$ contain either a $K_t$-minor consisting of at most $C(\epsilon,t)$ vertices or a $K_t$-topological minor consisting of at most $C(\epsilon,t)\log n$ vertices.Comment: 19 page