Some Empirical Criteria for Attributing Creativity to a Computer Program

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A Computational Procedure to Detect a New Type of High Dimensional Chaotic Saddle and its Application to the 3-D Hill's Problem

A computational procedure that allows the detection of a new type of high-dimensional chaotic saddle in Hamiltonian systems with three degrees of freedom is presented. The chaotic saddle is associated with a so-called normally hyperbolic invariant manifold (NHIM). The procedure allows to compute appropriate homoclinic orbits to the NHIM from which we can infer the existence a chaotic saddle. NHIMs control the phase space transport across an equilibrium point of saddle-centre-...-centre stability type, which is a fundamental mechanism for chemical reactions, capture and escape, scattering, and, more generally, ``transformation'' in many different areas of physics. Consequently, the presented methods and results are of broad interest. The procedure is illustrated for the spatial Hill's problem which is a well known model in celestial mechanics and which gained much interest e.g. in the study of the formation of binaries in the Kuiper belt.Comment: 12 pages, 6 figures, pdflatex, submitted to JPhys

Chirped pulse Raman amplification in plasma: high gain measurements

High power short pulse lasers are usually based on chirped pulse amplification (CPA), where a frequency chirped and temporarily stretched ``seed'' pulse is amplified by a broad-bandwidth solid state medium, which is usually pumped by a monochromatic ``pump'' laser. Here, we demonstrate the feasibility of using chirped pulse Raman amplification (CPRA) as a means of amplifying short pulses in plasma. In this scheme, a short seed pulse is amplified by a stretched and chirped pump pulse through Raman backscattering in a plasma channel. Unlike conventional CPA, each spectral component of the seed is amplified at different longitudinal positions determined by the resonance of the seed, pump and plasma wave, which excites a density echelon that acts as a "chirped'" mirror and simultaneously backscatters and compresses the pump. Experimental evidence shows that it has potential as an ultra-broad bandwidth linear amplifier which dispenses with the need for large compressor gratings

Normal Form and Nekhoroshev stability for nearly-integrable Hamiltonian systems with unconditionally slow aperiodic time dependence

The aim of this paper is to extend the results of Giorgilli and Zehnder for aperiodic time dependent systems to a case of general nearly-integrable convex analytic Hamiltonians. The existence of a normal form and then a stability result are shown in the case of a slow aperiodic time dependence that, under some smallness conditions, is independent on the size of the perturbation.Comment: Corrected typo in the title and statement of Lemma 3.

A case study on practical live event sound exposure monitoring

The recently launched WHO Global Standard for Safe Listening Venues and Events aims to make listening safer and more enjoyable for audiences around the world. Some key questions remain on how to practically monitor sound exposure as well as on how patrons’ hearing may be affected after significant exposure. This paper presents a case study where various sound exposure monitoring systems and methods were trialed in an indoor music venue. The aim of the work was to develop and validate a practical, accurate and repeatable technique to track sound exposure across music venues that can be presented in real-time. Results indicate that this can be achieved with no more than four, and as few as two, sound level monitoring locations alongside fixed calibration measurements and a small number of spot measurements at the mix position during a performance

Stability of Simple Periodic Orbits and Chaos in a Fermi -- Pasta -- Ulam Lattice

We investigate the connection between local and global dynamics in the Fermi -- Pasta -- Ulam (FPU) $\beta$ -- model from the point of view of stability of its simplest periodic orbits (SPOs). In particular, we show that there is a relatively high $q$ mode $(q=2(N+1)/{3})$ of the linear lattice, having one particle fixed every two oppositely moving ones (called SPO2 here), which can be exactly continued to the nonlinear case for $N=5+3m, m=0,1,2,...$ and whose first destabilization, $E_{2u}$, as the energy (or $\beta$) increases for {\it any} fixed $N$, practically {\it coincides} with the onset of a ``weak'' form of chaos preceding the break down of FPU recurrences, as predicted recently in a similar study of the continuation of a very low ($q=3$) mode of the corresponding linear chain. This energy threshold per particle behaves like $\frac{E_{2u}}{N}\propto N^{-2}$. We also follow exactly the properties of another SPO (with $q=(N+1)/{2}$) in which fixed and moving particles are interchanged (called SPO1 here) and which destabilizes at higher energies than SPO2, since $\frac{E_{1u}}{N}\propto N^{-1}$. We find that, immediately after their first destabilization, these SPOs have different (positive) Lyapunov spectra in their vicinity. However, as the energy increases further (at fixed $N$), these spectra converge to {\it the same} exponentially decreasing function, thus providing strong evidence that the chaotic regions around SPO1 and SPO2 have ``merged'' and large scale chaos has spread throughout the lattice.Comment: Physical Review E, 18 pages, 6 figure

A Kolmogorov theorem for nearly-integrable Poisson systems with asymptotically decaying time-dependent perturbation

The aim of this paper is to prove the Kolmogorov theorem of persistence of Diophantine flows for nearly-integrable Poisson systems associated to a real analytic Hamiltonian with aperiodic time dependence, provided that the perturbation is asymptotically vanishing. The paper is an extension of an analogous result by the same authors for canonical Hamiltonian systems; the flexibility of the Lie series method developed by A. Giorgilli et al., is profitably used in the present generalisation.Comment: 10 page