Symplectic Integration of Hamiltonian Systems using Polynomial Maps

In order to perform numerical studies of long-term stability in nonlinear Hamiltonian systems, one needs a numerical integration algorithm which is symplectic. Further, this algorithm should be fast and accurate. In this paper, we propose such a symplectic integration algorithm using polynomial map refactorization of the symplectic map representing the Hamiltonian system. This method should be particularly useful in long-term stability studies of particle storage rings in accelerators.Comment: 10 pages, 1 figur

Resolving the Inflationary Power Spectrum

Recently there have been differing viewpoints on how to evaluate the curvature power spectrum generated during inflation. In a series of papers by some authors it has been argued that the renormalization scheme adopted for the inflaton field phi(x) to make finite should also be applied to |phi_k|^2. But this then modifies the curvature power spectrum in a non-trivial way. On the other hand, others have criticized this approach and suggested alternatives, which have been further countered by the original authors. We discuss these differing viewpoints and indicate inconsistencies in both approaches. We then resolve the issue by showing why the standard expression, without any non-trivial regularization, is still valid.Comment: To appear in the proceedings of The 10th International Symposium on Cosmology and Particle Astrophysics (CosPA2013

Current Status of Warm Inflation

Warm inflation is an inflationary scenario in which a thermal bath coexists with the inflaton during inflation. This is unlike standard cold inflation in which the Universe is effectively devoid of particles during inflation. The thermal bath in warm inflation is maintained by the dissipation of the inflaton's energy through its couplings to other fields. Many models of warm inflation have been proposed and their predictions have been compared with cosmological data. Certain models of inflation that are disallowed in the context of cold inflation by the data are allowed in the warm inflationary scenario, and vice versa.Comment: 9 pages, 3 figures; Slightly longer version of a brief review talk at the 18th Lomonosov Conference on Elementary Particle Physics at Moscow State University, August 24-30, 201

Pleading Patents: Predicting the Outcome of Statutorily Heightening Pleading Standards

The tension between an extremely barebones Federal Rules of Civil Procedure Form 18 for patent infringement lawsuits and Supreme Court case law through Twombly and Iqbal has made it difficult for courts to dismiss frivolous patent litigation at the complaint stage. In this article, I look at the Federal Circuit’s treatment of Twombly and Iqbal, empirically evaluate 12(b)(6) motions from various district courts, and summarize local patent rules from the Eastern District of Texas. I conclude that the biggest likely impact of statutorily heightening and defining patent pleading standards through the proposed Innovation Act would be to provide much-needed uniformity in the endeavor of gatekeeping weak lawsuits, without serious adverse impact

Graphene etch mask for silicon

In this thesis, an alternative future use for graphene will be explored. Graphene, a popular two-dimensional material of remarkable electrical properties, has been thought to be a successor to current day microelectronic materials. With the many challenges posed by the manufacture of conventional devices from graphene, other adaptations for its properties are sought in the work that follows. Chiefly, its mechanical and chemical strength as an etch mask for silicon is tested.We attempt to present the progress toward a working model of a graphene etch mask. The influence of the mask geometry, etch method, etch conditions, substrate quality and other factors will be explored to present a clear understanding of methodology and requirements for carrying out the process. Along the way, other aspects of the project such as the growth and transfer of graphene, which are not the focus but extremely crucial to the results, will be elucidated as required. Possible future directions will also be presented to provide a notion of where the idea can head