Higher dimensional abelian Chern-Simons theories and their link invariants

The role played by Deligne-Beilinson cohomology in establishing the relation between Chern-Simons theory and link invariants in dimensions higher than three is investigated. Deligne-Beilinson cohomology classes provide a natural abelian Chern-Simons action, non trivial only in dimensions $4l+3$, whose parameter $k$ is quantized. The generalized Wilson $(2l+1)$-loops are observables of the theory and their charges are quantized. The Chern-Simons action is then used to compute invariants for links of $(2l+1)$-loops, first on closed $(4l+3)$-manifolds through a novel geometric computation, then on $\mathbb{R}^{4l+3}$ through an unconventional field theoretic computation.Comment: 40 page

Elastic medium confined in a column versus the Janssen experiment

We compute the stresses in an elastic medium confined in a vertical column, when the material is at the Coulomb threshold everywhere at the walls. Simulations are performed in 2 dimensions using a spring lattice, and in 3 dimensions, using Finite Element Method. The results are compared to the Janssen model and to experimental results for a granular material. The necessity to consider elastic anisotropy to render qualitatively the experimental findings is discussed

On Damage Spreading Transitions

We study the damage spreading transition in a generic one-dimensional stochastic cellular automata with two inputs (Domany-Kinzel model) Using an original formalism for the description of the microscopic dynamics of the model, we are able to show analitically that the evolution of the damage between two systems driven by the same noise has the same structure of a directed percolation problem. By means of a mean field approximation, we map the density phase transition into the damage phase transition, obtaining a reliable phase diagram. We extend this analysis to all symmetric cellular automata with two inputs, including the Ising model with heath-bath dynamics.Comment: 12 pages LaTeX, 2 PostScript figures, tar+gzip+u

A Class of Topological Actions

We review definitions of generalized parallel transports in terms of Cheeger-Simons differential characters. Integration formulae are given in terms of Deligne-Beilinson cohomology classes. These representations of parallel transport can be extended to situations involving distributions as is appropriate in the context of quantized fields.Comment: 41 pages, no figure

Linear and Nonlinear Rogue Wave Statistics in the Presence of Random Currents

We review recent progress in modeling the probability distribution of wave heights in the deep ocean as a function of a small number of parameters describing the local sea state. Both linear and nonlinear mechanisms of rogue wave formation are considered. First, we show that when the average wave steepness is small and nonlinear wave effects are subleading, the wave height distribution is well explained by a single "freak index" parameter, which describes the strength of (linear) wave scattering by random currents relative to the angular spread of the incoming random sea. When the average steepness is large, the wave height distribution takes a very similar functional form, but the key variables determining the probability distribution are the steepness, and the angular and frequency spread of the incoming waves. Finally, even greater probability of extreme wave formation is predicted when linear and nonlinear effects are acting together.Comment: 25 pages, 12 figure

PlatoSim: an end-to-end PLATO camera simulator for modelling high-precision space-based photometry

Context. PLAnetary Transits and Oscillations of stars (PLATO) is the ESA M3 space mission dedicated to detect and characterise transiting exoplanets including information from the asteroseismic properties of their stellar hosts. The uninterrupted and high-precision photometry provided by space-borne instruments such as PLATO require long preparatory phases. An exhaustive list of tests are paramount to design a mission that meets the performance requirements and, as such, simulations are an indispensable tool in the mission preparation. Aims. To accommodate PLATO’s need of versatile simulations prior to mission launch that at the same time describe innovative yet complex multi-telescope design accurately, in this work we present the end-to-end PLATO simulator specifically developed for that purpose, namely PlatoSim. We show, step-by-step, the algorithms embedded into the software architecture of PlatoSim that allow the user to simulate photometric time series of charge-coupled device (CCD) images and light curves in accordance to the expected observations of PLATO. Methods. In the context of the PLATO payload, a general formalism of modelling, end-to-end, incoming photons from the sky to the final measurement in digital units is discussed. According to the light path through the instrument, we present an overview of the stellar field and sky background, the short- and long-term barycentric pixel displacement of the stellar sources, the cameras and their optics, the modelling of the CCDs and their electronics, and all main random and systematic noise sources. Results. We show the strong predictive power of PlatoSim through its diverse applicability and contribution to numerous working groups within the PLATO mission consortium. This involves the ongoing mechanical integration and alignment, performance studies of the payload, the pipeline development, and assessments of the scientific goals. Conclusions. PlatoSim is a state-of-the-art simulator that is able to produce the expected photometric observations of PLATO to a high level of accuracy. We demonstrate that PlatoSim is a key software tool for the PLATO mission in the preparatory phases until mission launch and prospectively beyond

PlatoSim: an end-to-end PLATO camera simulator for modelling high-precision space-based photometry

Context. PLAnetary Transits and Oscillations of stars (PLATO) is the ESA M3 space mission dedicated to detect and characterise transiting exoplanets including information from the asteroseismic properties of their stellar hosts. The uninterrupted and high-precision photometry provided by space-borne instruments such as PLATO require long preparatory phases. An exhaustive list of tests are paramount to design a mission that meets the performance requirements and as such simulations are an indispensable tool in the mission preparation. Aims. To accommodate PLATOs need of versatile simulations prior to mission launch that at the same time describe innovative yet complex multi-telescope design accurately, in this work we present the end-to-end PLATO simulator specifically developed for that purpose, namely PlatoSim. We show, step-by-step, the algorithms embedded into the software architecture of PlatoSim that allow the user to simulate photometric time series of charge-coupled device (CCD) images and light curves in accordance to the expected observations of PLATO. Methods. In the context of the PLATO payload, a general formalism of modelling, end-to-end, incoming photons from the sky to the final measurement in digital units is discussed. According to the light path through the instrument, we present an overview of the stellar field and sky background, the short- and long-term barycentric pixel displacement of the stellar sources, the cameras and their optics, the modelling of the CCDs and their electronics, and all main random and systematic noise sources. Results. We show the strong predictive power of PlatoSim through its diverse applicability and contribution to numerous working groups within the PLATO mission consortium. This involves the ongoing mechanical integration and alignment, performance studies of the payload, the pipeline development, and assessments of the scientific goals. Conclusions. PlatoSim is a state-of-the-art simulator that is able to produce the expected photometric observations of PLATO to a high level of accuracy. We demonstrate that PlatoSim is a key software tool for the PLATO mission in the preparatory phases until mission launch and prospectively beyond