Society of Physics Students

hbar@phys.columbia.edu

Columbia University in the City of New York

Summer 2004

 June 15, 2004

Speaker: Arthur Lipstein

Talk Title: Deriving the Magnus Effect

Abstract:

In this talk, we will derive the Magnus effect for a ball exhibiting translational and rotational motion through an ideal fluid (AKA "topspin"), using only rudimentary fluid mechanics and complex analysis. Don't worry if you're unfamiliar with either of these; the basics of fluid mechanics (Bernoulli's effect, the continuity equation, etc.) and complex analysis (analytic functions, the Cauchy-Reimann equations, etc.) will be reviewed.

June 24, 2004

Speaker: Dhruv Bansal

Talk Title: The Twin Paradox with One Compact Spatial Dimension

Abstract:

We consider the twin paradox of special relativity in a universe with a compact spatial dimesion. Such a topology eschews the traditional solution to the twin paradox but at the same time endows the manifold with a preferred coordinate system which allows for a distinction to be made between the twin observers and a resolution of the paradox via a global experiment. We explore the local electrodynamic consequences of the global topology and exhibit a local experiment that also resolves the paradox.

July 6, 2004

Speaker: Eitan Chatav

Talk Title: Lie Groups and Rigid Body Mechanics

Abstract:

The mathematical concept of Lie groups gets used all the time in physics. A Lie group is just a differentiable manifold with a group structure on it. As such, they are the perfect tool for describing continuous symmetries. I'll discuss in particular how to understand rigid body mechanics using the Lie group SO(3), the group of all rotations in space. A nodding familiarity with differential geometry will be useful but is not necessary.

July 20, 2004

Speaker: Elizabeth Peele Hicks

Talk Title: Universe Models and the Accelerating Universe

Abstract:

In the past few years, exciting observations have indicated that the Universe is accelerating, instead of decelerating as had previously been thought. This talk will put these observations in the context of the general theory of models of the Universe. Topics will include the Friedman Equation, the Fluid Equation and the Acceleration Equation- the three equations necessary to determine the evolution of the Universe. I will discuss the evolution of different parameters such as the energy density and the scale factor as well. This will lead to a discussion of single-component Universe models and then to multiple-component Universe models. Finally I will present a probable model for our own Universe and briefly describe the observational evidence in its favor.