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Moments Analysis and Zipf law

Determine the shape of fragment size distributions (s.f.d) and compare experimental and theoretical distributions. Extract "signals" and compare conditional moments. Study percolation and equiprobable partitions. Compare models with data. Extract "signals" from f.s.d. and analyze fluctuations using factorial moments. Caution with "signals" of critical behavior in f.s.d. Finite size scaling is the most robust signal of critical behavior.

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Moments Analysis and Zipf law

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  1. Moments Analysis and Zipf law

  2. MOMENTS of the f.s.d. • -Determination of the shape of fragment size distributions (s.f.d). • -Comparison of experimental and theoretical f.s.d. • -Extraction of « signals ».

  3. Conditional Moments Comparison of models Percolation Mekjian rec. Equiprobablepartitions Cascade

  4. Comparison of model with data

  5. Au + Au 35 A MeV M. D’Agostino et al. Nucl. Phys. A650 (1999) 329.

  6. Extracting « signals » fromf.s.d.

  7. If this scaling is present, in an infinite system, momentsof order k > tau-1, divergeBy analogy with thermal phase transitions, one says that thesemoments exhibit a critical behaviour

  8. In Fischer model, the (thermal) critical point is also a critical point for moments of the f.s.d. However, this is NOT always true. Ex: Lattice-gas model with Coniglio-Klein clusters or Lennard-Jones fluid with Hill, Dorso-Randrup,… clusters. (N. Sator, Phys. Rep. (2001)).

  9. Lennard-Jones fluid N=125 particles Iso-contour lines of the variance of the f.s.d.

  10. Caution with « signals » of critical behaviour in the f.s.d. !

  11. Finite size scaling (scaling with the size of the system) is the most robust signal of critical behaviour in the f.s.d.

  12. Analysis of fluctuations of thef.s.d.

  13. Factorial moments -The signal vanishes for large systems -A signal of « intermittency » appears for randomly generated partitions when the mean f.s.d is a power law.

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