Related papers: Zipf's law in Multifragmentation
We found that in transition arrays of complex atomic spectra, the strengths of electric-dipolar lines obey Benford's law, which means that their significant digits follow a logarithmic distribution favoring the smallest values. This…
A curious observation was made that the rank statistics of scientific citation numbers follows Zipf-Mandelbrot's law. The same pow-like behavior is exhibited by some simple random citation models. The observed regularity indicates not so…
Progress on nuclear liquid gas phase transition (LGPT) or critical behavior has been simply reviewed and some signals of LGPT in heavy ion collisions, especially in NIMROD data, are focused. These signals include the power-law charge…
This work proves that ranks and shares are statistically dependent on one another, based on simple combinatorics. It presents a formula for rank-share distribution and illustrates that Zipfs law, is descended from expected values of various…
We propose a model that provides a unified description of nuclear equation of state and fragmentations. The equation of state is evaluated in Bragg-Williams as well as in Bethe-Peierls approximations and compared with that in the mean field…
This comment on Moretto et al.PRL 76:372,1996 argues that the IMF-charge distribution may not be useful as signal for phase-transitions in nuclear multifragmentation. Fluctuations of different origin may corrupt this signal. Energy…
Zipf's power law is a general empirical regularity found in many natural and social systems. A recently developed theory predicts that Zipf's law corresponds to systems that are growing according to a maximally sustainable path in the…
Recent analyses of multifragmentation in terms of Fisher's model and the related construction of a phase diagram brings forth the problem of the true existence of the vapor phase and the meaning of its associated pressure. Our analysis…
The Zipf distribution also known as scale-free distribution or discrete Pareto distribution, is the particular case of Power Law distribution with support the strictly positive integers. It is a one-parameter distribution with a linear…
A statistical model for the fragmentation of a conserved quantity is analyzed, using the principle of maximum entropy and the theory of partitions. Upper and lower bounds for the restricted partitioning problem are derived and applied to…
Collisions resulting in fragmentation are important in shaping the mass spectrum of minor bodies in the asteroid belt, the Kuiper belt, and debris disks. Models of fragmentation cascades typically find that in steady-state, the solution for…
It is shown phenomenologically that the fractional derivative $\xi=D^\alpha u$ of order $\alpha$ of a multifractal function has a power-law tail $\propto |\xi| ^{-p_\star}$ in its cumulative probability, for a suitable range of $\alpha$'s.…
Multifragmentation is the dominant decay mode of heavy nuclear systems with excitation energies near their binding energies and is characterized by a multiple production of nuclear fragments with intermediate mass. At relativistic…
Power law distributions characterise several natural and social phenomena. The Zipf law for cities is one of those. The study views the question of whether that global regularity is independent of different spatial distributions of cities.…
Two roads are presently being followed in order to establish the existence of a liquid-gas phase transition in finite nuclear systems from nuclear reactions at high energy. The clean experiment of observing the thermodynamic properties of a…
Zipf's law, and power laws in general, have attracted and continue to attract considerable attention in a wide variety of disciplines - from astronomy to demographics to software structure to economics to linguistics to zoology, and even…
Zipf's law states that the probability of a variable being larger than $s$ is roughly inversely proportional to $s$. In this paper, we evaluate Zipf's law for the distribution of firm size by the number of employees in Brazil. We use…
Two models of binary fragmentation are introduced in which a time dependent transition size produces two regions of fragment sizes above and below the transition size. In the models we consider a fixed rate of fragmentation for the largest…
The present paper describes a stochastic model of fracture, whose fragment size distribution can be calculated analytically as a power-law-like distribution. The model is basically cascade fracture, but incorporates the effect that each…
This paper studies the limits of language models' statistical learning in the context of Zipf's law. First, we demonstrate that Zipf-law token distribution emerges irrespective of the chosen tokenization. Second, we show that Zipf…