Models of fragmentation and partitioning phenomena based on the symmetric groupSnand combinational analysis

Abstract

Various models for fragmentation and partitioning phenomena are developed using methods from permutation groups and combinational analysis. The appearance and properties of power laws in these models are discussed. Several exactly soluble cases are studied. An application to nuclear fragmentation and clusterization is given. A connection with Ewenss approach [Theor. Popul. Biol. 3, 87 (1972); Mathematical Population Genetics (Springer, Berlin, 1979)] to genetic diversity is mentioned. Applications to the social behavior of a vervet monkey troop and to the group behavior of people are given.PACS number(s): 05.40. +j, 02.50.+s

The thermodynamic model for nuclear multifragmentation

“…That is, for any given permutation, the total A is equal to the sum of the cycle length times the number of cycles of that length in that specific permutation. The canonical partition function for non-interacting particles such as Fermi-Dirac or Bose-Einstein particles in a box or in a one body potential well such as a harmonic oscillator well has a form given by eq.2 in section 2 [85,86,87]. For identical particles in a box of volume V and a system at temperature T , the ω weight factor for a cycle of length k is that of eq.6 with the q k = 1 in that equation for Bose-Einstein particles and q k = (−1) (k+1) for Fermi-Dirac particles.…”

“…A reader interested in the application of the methods of sect.2 to multiparticle multiplicity distributions can find the details and several other individual cases in [89,90]. In a series of papers [85,86], Hegyi has considered many interesting aspects of multiparticle production and has also introduced a generalized distribution for its description.…”

Nuclear fragmentation and its parallels

“…A previous set of papers [1][2][3] proposed a statistical model for describing this behavior. Each possible fragmentation outcome is given a particular probability, and the resulting partition functions and ensemble averages are known to be exactly solvable.…”

Heated Nuclear Matter, Condensation Phenomena, and the Hadronic Equation of State

“…Most treatments of the equation of state have treated heated nuclear matter as a homogeneous system. Statistical [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and percolation [24][25][26] models have been used by many groups to study nuclear multifragmentation and the role of clusters on nuclear properties. This paper explores various thermodynamic properties using an exactly solvable canonical ensemble model that allows for clusterization and leads to simple analytic expressions for thermodynamic quantities such as the equation of state.…”

“…In earlier papers [20][21][22][23] the question of the thermodynamics of a fragmenting system was raised. There, it was assumed that the thermodynamic variables were contained in a single parameter x such that the weight of a particular cluster partition was proportional to x m , where m is the total number of clusters in that partition.…”