Etaoin Shrdlu Non-Crashing Sets

The designers of the Linotype machine arranged its keyboard for optimum speed, assuming that the most common letters of English were e,t,a,o,i,n,s,h,r,d,l,u in that order. The Oxford English Dictionary (Second Edition) has some amusing citations

Comparative Analysis of Numerically Computed Chaos Diagrams in Duffing Oscillator

Abstract This study utilised optimum fractal disk dimension algorithms to characterize the evolved strange attractor (Poincare section) when adaptive time steps Runge-Kutta fourth and fifth order algorithms are employed to compute simultaneously multiple trajectories of a harmonically excited Duffing oscillator from very close initial conditions. The challenges of insufficient literature that explore chaos diagrams as visual aids in dynamics characterization strongly motivate this study. The object of this study is to enable visual comparison of the chaos diagrams in the excitation amplitude versus frequency plane. The chaos diagrams obtained at two different damp coefficient levels conforms generally in trend to literature results[1] and qualitatively the same for all algorithms. The chances of chaotic behaviour are higher for combined higher excitation frequencies and amplitudes in addition to smaller damp coefficient. Fourth and fifth order Runge-Kutta algorithms indicates respectively 62.3% and 53.3% probability of chaotic behaviour at 0.168 damp coefficient and respectively 77.9% and 78.9% at 0.0168 damp coefficient. The chaos diagrams obtained by fourth order algorithms is accepted to be more reliable than its fifth order counterpart, its utility as tool for searching possible regions of parameter space where chaotic behaviour/motion exist may require additional dynamic behaviour tests

Characterization of unwanted noise in realistic cavities

The problem of the description of absorption and scattering losses in high-Q cavities is studied. The considerations are based on quantum noise theories, hence the unwanted noise associated with scattering and absorption is taken into account by introduction of additional damping and noise terms in the quantum Langevin equations and input--output relations. Completeness conditions for the description of the cavity models obtained in this way are studied and corresponding replacement schemes are discussed.Comment: Contribution to XI International Conference on Quantum Optics, Minsk, Belarus, 26-31 May, 200

A comparison of the eigenvalues of the Dirac and Laplace operator on the two-dimensional torus

We compare the eigenvalues of the Dirac and Laplace operator on a two-dimensional torus with respect to the trivial spin structure. In particular, we compute their variation up to order 4 upon deformation of the flat metric, study the corresponding Hamiltonian and discuss several families of examples.Comment: Latex2.09, 28 pages, with figure