Filtered Noise Can Mimic Low-Dimensional Chaotic Attractors

This contribution presents four results. First, calculations indicate that when examined by the Grassberger-Procaccia algorithm alone, filtered noise can mimic low-dimensional chaotic attractors. Given the ubiquity Of signal filtering in experimental investigations, this is potentially important. Second, a criterion is derived which provides an estimate of the minimum data accuracy needed to resolve the dimension of an attractor. Third, it is shown that a criterion derived by Eckmann and Ruelle [Physica D 56, 185 (1992)] to estimate the minimum number of data points required in a Grassberger-Procaccia calculation can be used to provide a further check on these dimension estimates. Fourth, it is shown that surrogate data techniques recently published by Theiler and his colleagues [in Nonlinear Modeling and Forecasting, edited by M. Casdagli and S. Eubanks (Addison Wesley, Reading, MA, 1992)] can successfully distinguish between linearly correlated noise and nonlinear structure. These results, and most particularly the first, indicate that Grassberger-Procaccia results must be interpreted with far greater circumspection than has previously been the case, and that the algorithm should be used in combination with additional procedures such as calculations with surrogate data. When filtered signals are examined by this algorithm alone, a finite noninteger value of D2 is consistent with low-dimensional chaotic behavior, but it is certainly not a definitive diagnostic of chaos

Filtered Noise Can Mimic Low-Dimensional Chaotic Attractors

This contribution presents four results. First, calculations indicate that when examined by the Grassberger-Procaccia algorithm alone, filtered noise can mimic low-dimensional chaotic attractors. Given the ubiquity Of signal filtering in experimental investigations, this is potentially important. Second, a criterion is derived which provides an estimate of the minimum data accuracy needed to resolve the dimension of an attractor. Third, it is shown that a criterion derived by Eckmann and Ruelle [Physica D 56, 185 (1992)] to estimate the minimum number of data points required in a Grassberger-Procaccia calculation can be used to provide a further check on these dimension estimates. Fourth, it is shown that surrogate data techniques recently published by Theiler and his colleagues [in Nonlinear Modeling and Forecasting, edited by M. Casdagli and S. Eubanks (Addison Wesley, Reading, MA, 1992)] can successfully distinguish between linearly correlated noise and nonlinear structure. These results, and most particularly the first, indicate that Grassberger-Procaccia results must be interpreted with far greater circumspection than has previously been the case, and that the algorithm should be used in combination with additional procedures such as calculations with surrogate data. When filtered signals are examined by this algorithm alone, a finite noninteger value of D2 is consistent with low-dimensional chaotic behavior, but it is certainly not a definitive diagnostic of chaos

Filtered Noise Can Mimic Low-Dimensional Chaotic Attractors

This contribution presents four results. First, calculations indicate that when examined by the Grassberger-Procaccia algorithm alone, filtered noise can mimic low-dimensional chaotic attractors. Given the ubiquity Of signal filtering in experimental investigations, this is potentially important. Second, a criterion is derived which provides an estimate of the minimum data accuracy needed to resolve the dimension of an attractor. Third, it is shown that a criterion derived by Eckmann and Ruelle [Physica D 56, 185 (1992)] to estimate the minimum number of data points required in a Grassberger-Procaccia calculation can be used to provide a further check on these dimension estimates. Fourth, it is shown that surrogate data techniques recently published by Theiler and his colleagues [in Nonlinear Modeling and Forecasting, edited by M. Casdagli and S. Eubanks (Addison Wesley, Reading, MA, 1992)] can successfully distinguish between linearly correlated noise and nonlinear structure. These results, and most particularly the first, indicate that Grassberger-Procaccia results must be interpreted with far greater circumspection than has previously been the case, and that the algorithm should be used in combination with additional procedures such as calculations with surrogate data. When filtered signals are examined by this algorithm alone, a finite noninteger value of D2 is consistent with low-dimensional chaotic behavior, but it is certainly not a definitive diagnostic of chaos

K+ and K- production in heavy-ion collisions at SIS-energies

The production and the propagation of K+ and of K- mesons in heavy-ion collisions at beam energies of 1 to 2 AGeV have systematically been investigated with the Kaon Spectrometer KaoS at the SIS at the GSI. The ratio of the K+ production excitation function for Au+Au and for C+C reactions increases with decreasing beam energy, which is expected for a soft nuclear equation-of-state. At 1.5 AGeV a comprehensive study of the K+ and of the K- emission as a function of the size of the collision system, of the collision centrality, of the kaon energy, and of the polar emission angle has been performed. The K-/K+ ratio is found to be nearly constant as a function of the collision centrality. The spectral slopes and the polar emission patterns are different for K- and for K+. These observations indicate that K+ mesons decouple earlier from the reaction zone than K- mesons.Comment: invited talk given at the SQM2003 conference in Atlantic Beach, USA (March 2003), to be published in Journal of Physics G, 10pages, 7 figure

Development of a GEM-TPC prototype

The use of GEM foils for the amplification stage of a TPC instead of a con- ventional MWPC allows one to bypass the necessity of gating, as the backdrift is suppressed thanks to the asymmetric field configuration. This way, a novel continuously running TPC, which represents one option for the PANDA central tracker, can be realized. A medium sized prototype with a diameter of 300 mm and a length of 600 mm will be tested inside the FOPI spectrometer at GSI using a carbon or lithium beam at intermediate energies (E = 1-3AGeV). This detector test under realistic experimental conditions should allow us to verify the spatial resolution for single tracks and the reconstruction capability for displaced vertexes. A series of physics measurement implying pion beams is scheduled with the FOPI spectrometer together with the GEM-TPC as well.Comment: 5 pages, 4 figures, Proceedings for 11th ICATTP conference in como (italy

Phase space structures governing reaction dynamics in rotating molecules

Recently the phase space structures governing reaction dynamics in Hamiltonian systems have been identified and algorithms for their explicit construction have been developed. These phase space structures are induced by saddle type equilibrium points which are characteristic for reaction type dynamics. Their construction is based on a Poincar{\'e}-Birkhoff normal form. Using tools from the geometric theory of Hamiltonian systems and their reduction we show in this paper how the construction of these phase space structures can be generalized to the case of the relative equilibria of a rotational symmetry reduced $N$-body system. As rotations almost always play an important role in the reaction dynamics of molecules the approach presented in this paper is of great relevance for applications.Comment: 28 pages, 7 figures, pdflate

Inclusive dielectron production in proton-proton collisions at 2.2 GeV beam energy

Data on inclusive dielectron production are presented for the reaction p+p at 2.2 GeV measured with the High Acceptance DiElectron Spectrometer (HADES). Our results supplement data obtained earlier in this bombarding energy regime by DLS and HADES. The comparison with the 2.09 GeV DLS data is discussed. The reconstructed e+e- distributions are confronted with simulated pair cocktails, revealing an excess yield at invariant masses around 0.5 GeV/c2. Inclusive cross sections of neutral pion and eta production are obtained

Searching a Dark Photon with HADES

We present a search for the e+e- decay of a hypothetical dark photon, also names U vector boson, in inclusive dielectron spectra measured by HADES in the p (3.5 GeV) + p, Nb reactions, as well as the Ar (1.756 GeV/u) + KCl reaction. An upper limit on the kinetic mixing parameter squared epsilon^{2} at 90% CL has been obtained for the mass range M(U) = 0.02 - 0.55 GeV/c2 and is compared with the present world data set. For masses 0.03 - 0.1 GeV/c^2, the limit has been lowered with respect to previous results, allowing now to exclude a large part of the parameter region favoured by the muon g-2 anomaly. Furthermore, an improved upper limit on the branching ratio of 2.3 * 10^{-6} has been set on the helicity-suppressed direct decay of the eta meson, eta-> e+e-, at 90% CL