Steep Street

Undergraduate Graphic Desig

The classical mechanics of non-conservative systems

Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often goes unnoticed in physics: it is formulated as a boundary value problem in time but is used to derive equations of motion that are solved with initial data. This subtlety can have undesirable effects. I present a formulation of Hamilton's principle that is compatible with initial value problems. Remarkably, this leads to a natural formulation for the Lagrangian and Hamiltonian dynamics of generic non-conservative systems, thereby filling a long-standing gap in classical mechanics. Thus dissipative effects, for example, can be studied with new tools that may have application in a variety of disciplines. The new formalism is demonstrated by two examples of non-conservative systems: an object moving in a fluid with viscous drag forces and a harmonic oscillator coupled to a dissipative environment.Comment: 5 pages, 1 figure. Updated to incorporate referees' comments. Matches published versio

Caustic echoes from a Schwarzschild black hole

We present the first numerical construction of the scalar Schwarzschild Green function in the time-domain, which reveals several universal features of wave propagation in black hole spacetimes. We demonstrate the trapping of energy near the photon sphere and confirm its exponential decay. The trapped wavefront propagates through caustics resulting in echoes that propagate to infinity. The arrival times and the decay rate of these caustic echoes are consistent with propagation along null geodesics and the large l-limit of quasinormal modes. We show that the four-fold singularity structure of the retarded Green function is due to the well-known action of a Hilbert transform on the trapped wavefront at caustics. A two-fold cycle is obtained for degenerate source-observer configurations along the caustic line, where the energy amplification increases with an inverse power of the scale of the source. Finally, we discuss the tail piece of the solution due to propagation within the light cone, up to and including null infinity, and argue that, even with ideal instruments, only a finite number of echoes can be observed. Putting these pieces together, we provide a heuristic expression that approximates the Green function with a few free parameters. Accurate calculations and approximations of the Green function are the most general way of solving for wave propagation in curved spacetimes and should be useful in a variety of studies such as the computation of the self-force on a particle.Comment: 18 pages, 23 figure

Using Cloudworks to Support OER Activities

This report forms the third and final output of the Pearls in the Clouds project, funded by the Higher Education Academy. It focuses on evaluation of the use of a social networking site, Cloudworks, to support evidence-based practice. The aim of this project (Pearls in the Clouds) has been to evaluate the ways in which web 2.0 tools like Cloudworks can support evidence-informed practices in relation to learning and teaching. We have reviewed evidence from empirically grounded studies surrounding the uses of web2.0 in higher education and highlighted the gap between using web2.0 to support learning and teaching, and using it to support learning about learning and teaching (in an evidence-informed way) (Conole and Alevizou, 2010). We have reported on findings from a case study focusing on the use of Cloudworks by a community of practice - educational technologists - reflecting upon, and, negotiating their role in enhancing teaching and learning in higher education (Galley et al., 2010). The object of this study is to explore and evaluate the use of the site by individuals and communities involved in the production of, and research on, the development, delivery and use of Open Educational Resources (OER)

Deriving analytic solutions for compact binary inspirals without recourse to adiabatic approximations

We utilize the dynamical renormalization group formalism to calculate the real space trajectory of a compact binary inspiral for long times via a systematic resummation of secularly growing terms. This method generates closed form solutions without orbit averaging, and the accuracy can be systematically improved. The expansion parameter is $v^5 \nu \Omega(t-t_0)$ where $t_0$ is the initial time, $t$ is the time elapsed, and $\Omega$ and $v$ are the angular orbital frequency and initial speed, respectively, and $\nu$ is the binary's symmetric mass ratio. We demonstrate how to apply the renormalization group method to resum solutions beyond leading order in two ways. First, we calculate the second order corrections of the leading radiation reaction force, which involves highly non-trivial checks of the formalism (i.e. its renormalizability). Second, we show how to systematically include post-Newtonian corrections to the radiation reaction force. By avoiding orbit averaging we gain predictive power and eliminate ambiguities in the initial conditions. Finally, we discuss how this methodology can be used to find analytic solutions to the spin equations of motion that are valid over long times.Comment: 18 pages, 2 figure

Case Study: Using Cloudworks for an Open Literature Review

This case study is one of a series exploring the ongoing use and development of the Cloudworks site. This case study will focus on an expert elicitation Cloudscape established to support a literature review project led by the University of Exeter and funded by the Higher Education Academy (HEA): "The positioning of educational technologists in enhancing the student experience". We will look in detail at the way the site was utilised by the project teams and other participants in the review, and evaluate the site's effectiveness in supporting this piece of research. We will make recommendations for the development of support resources associated with the site and suggest factors that might impact on the success of similar activities