Session B10: Undergraduate Research I

Damping of a Simple Pendulum Due to Drag on Its String

A basic classical example of simple harmonic motion is the simple pendulum, consisting of a small bob and a massless string. In a vacuum with zero air resistance, such a pendulum will continue to oscillate indefinitely with a constant amplitude. However, the amplitude of a simple pendulum oscillating in air continuously decreases as its mechanical energy is gradually lost due to air resistance. To this end, it is generally perceived that the main role in the dissipation of mechanical energy is played by the bob of the pendulum, and that the string's contribution is negligible. The purpose of this research is to experimentally investigate the merit of this assumption. Thus, we experimentally investigate the damping of a simple pendulum as a function of its string diameter and compare that to the contribution from its bob. We find out that although in some cases the effect of the string might be small or even negligible, in general the string can play a significant role, and in some cases even a greater role on the damping of the pendulum than its bob.   

Homoclinic orbits in Pipe flow

We study pipe flow numerically in the transitional regime at which spatially localized turbulent dynamics coexists with the laminar flow. Under certain symmetry restrictions, Avila et. al. (Phys. Rev. Lett., vol. 110, 2013, 224502) showed that the laminar-turbulent boundary in this system is set by the stable manifold of a relative periodic orbit (RPO). We investigate the unstable manifold of this RPO in order to demonstrate that it contains so-called ``homoclinic orbits" that are the trajectories which lie at the intersections of the stable and unstable manifolds. To this end, we employed a simple bisection algorithm that locates orbits that come back to the vicinity of the RPO after exploring the chaotic regions of the state space. We then visualized these trajectories on Poincar\'e section projections for verification. Presence of these orbits implies the existence of ``homoclinic structure", which in turn explains the transient chaotic dynamics exhibited by the system.   

Observation of an Optical Spring with a Beamsplitter

The current generation of gravitational wave detectors such as LIGO and VIRGO utilize high power lasers to reduce the shot noise within an interferometer. This high power creates a significant radiation pressure that couples the laser fields and the mechanical motion of the test masses opto-mechanically. This opto-mechanical coupling gives rise to an optical spring that changes the resonance of the interferometer, and thus should be studied. We present the observation of a stable optical spring without the use of an optical cavity. We used a Michelson-Sagnac interferometer with a GaAs microresonator as a common/end mirror. Our measurements were done using input powers up to 363mW and show that the shift of the optical spring frequency as a function of input power is in excellent agreement with theoretical predictions. We also show that the optical spring can keep the interferometer stable and locked without the use of external feedback.   

Numerical Simulations of Non-Spherical Compact Stars

Recent theoretical work of highly magnetized neutron stars, such as Magnetars, indicate that these objects undergo radial deformations resulting in prolate or oblate spheroids. Due to these deformations, traditional models using spherical symmetry can not be applied. In this work, we cover how deformed compact stars can be modelled to take this deformity into consideration in the framework of general relativity. In addition, a visual simulation tool has been created to make showcasing these types of models and simulations easier. Visual simulations serve as a quick way to verify data integrity, while simultaneously providing a clear way to explain and present concepts.   

Scalar Dark Earth-Shine

Dark matter may interact with itself and with ordinary matter through new forces with new mediator particles. We extend the work of a recent study of the dark photon mediator to a spin-0 scalar mediator, the dark Higgs. In this scenario, dark matter collects in the center of the earth and annihilates into these mediators which could decay into detectible particles near the surface of the Earth. In the annihilation rate, we include Sommerfeld enhancements, which play a critical role in decreasing the timescale for the capture-annihilation process to equilibrate. We also highlight the importance of the s-wave 2-to-4 annihilation in the dark Higgs model, as opposed to the s-wave 2-to-2 annihilation in the dark photon model. This search may compliment the dark photon search by allowing for a broader distribution of signal events which point back towards the center of the earth.