A new view of nonlinear water waves: the Hilbert spectrum

We survey the newly developed Hilbert spectral analysis method and its applications to Stokes waves, nonlinear wave evolution processes, the spectral form of the random wave field, and turbulence. Our emphasis is on the inadequacy of presently available methods in nonlinear and nonstationary data analysis. Hilbert spectral analysis is here proposed as an alternative. This new method provides not only a more precise definition of particular events in time-frequency space than wavelet analysis, but also more physically meaningful interpretations of the underlying dynamic processes

Following the density perturbations through a bounce with AdS/CFT Correspondence

A bounce universe model, known as the coupled-scalar-tachyon bounce (CSTB) universe, has been shown to solve the Horizon, Flatness and Homogeneity problems as well as the Big Bang Singularity problem. Furthermore a scale invariant spectrum of primordial density perturbations generated from the phase of pre-bounce contraction is shown to be stable against time evolution. In this work we study the detailed dynamics of the bounce and its imprints on the scale invariance of the spectrum. The dynamics of the gravitational interactions near the bounce point may be strongly coupled as the spatial curvature becomes big. There is no a prior reason to expect the spectral index of the primordial perturbations of matter density can be preserved. By encoding the bounce dynamics holographically onto the dynamics of dual Yang-Mills system while the latter is weakly coupled, via the AdS/CFT correspondence, we can safely evolve the spectrum of the cosmic perturbations with full control. In this way we can compare the post-bounce spectrum with the pre-bounce one: in the CSTB model we explicitly show that the spectrum of primordial density perturbations generated in the contraction phase preserves its stability as well as scale invariance throughout the bounce process.Comment: 19 pages, 4 figure

Determination of electron-nucleus collision geometry with forward neutrons

There are a large number of physics programs one can explore in electron-nucleus collisions at a future electron-ion collider. Collision geometry is very important in these studies, while the measurement for an event-by-event geometric control is rarely discussed in the prior deep inelastic scattering experiments off a nucleus. This paper seeks to provide some detailed studies on the potential of tagging collision geometries through forward neutron multiplicity measurements with a zero degree calorimeter. This type of geometry handle, if achieved, can be extremely beneficial in constraining nuclear effects for the electron-nucleus program at an electron-ion collider