相关论文: Zipf's Law and the Universality Class of the Fragm…
Some of the progress in determining the phase boundaries of the nuclear phase diagram, the location of the critical point of the nuclear fragmentation phase transition, and the values of the critical exponents of this transition is…
We discuss the meaning of Zipf's law in nuclear multifragmentation. We remark that Zipf's law is a consequence of a power law fragment size distribution with exponent $\tau \simeq 2$. We also recall why the presence of such distribution is…
Zipf's law in the field of linguistics is tested in the nuclear disassembly within the framework of isospin dependent lattice gas model. It is found that the average cluster charge (or mass) of rank $n$ in the charge (or mass) list shows…
We describe the link between the Zipf law and statistical distributions for the Fortuin-Kasteleyn clusters in Ising as well as Potts models. From these results it is seen that Zipf's law can be a criterion of a phase transition, but it does…
We investigate the average sizes of the $n$ largest fragments in nuclear multifragmentation events near the critical point of the nuclear matter phase diagram. We perform analytic calculations employing Poisson statistics as well as Monte…
Zipf's law is the most common statistical distribution displaying scaling behavior. Cities, populations or firms are just examples of this seemingly universal law. Although many different models have been proposed, no general theoretical…
Two fundamental issues surrounding research on Zipf's law regarding city sizes are whether and why this law holds. This paper does not deal with the latter issue with respect to why, and instead investigates whether Zipf's law holds in a…
Zipf's law describes the empirical size distribution of the components of many systems in natural and social sciences and humanities. We show, by solving a statistical model, that Zipf's law co-occurs with the maximization of the diversity…
Zipf's law states that the frequency of an observation with a given value is inversely proportional to the square of that value; Taylor's law, instead, describes the scaling between fluctuations in the size of a population and its mean.…
Universality, encompassing critical exponents, scaling functions, and dimensionless quantities, is fundamental to phase transition theory. In finite systems, universal behaviors are also expected to emerge at the pseudocritical point.…
Human development has far-reaching impacts on the surface of the globe. The transformation of natural land cover occurs in different forms and urban growth is one of the most eminent transformative processes. We analyze global land cover…
Quantitative linguistics has provided us with a number of empirical laws that characterise the evolution of languages and competition amongst them. In terms of language usage, one of the most influential results is Zipf's law of word…
The statistical characterization of the distribution of visible matter in the universe is a central problem in modern cosmology. In this respect, a crucial question still lacking a definitive answer concerns how large are the greatest…
The moment analysis method and nuclear Zipf's law of fragment size distributions are reviewed to study nuclear disassembly. In this report, we present a compilation of both theoretical and experimental studies on moment analysis and Zipf…
The finite-size scaling theory for continuous phase transition plays an important role in determining critical point and critical exponents from the size-dependent behaviors of quantities in the thermodynamic limit. For percolation phase…
With Zipf's law being originally and most famously observed for word frequency, it is surprisingly limited in its applicability to human language, holding over no more than three to four orders of magnitude before hitting a clear break in…
This paper provides a new geospatial perspective on whether or not Zipf's law holds for all cities or for the largest cities in the United States using a massive dataset and its computing. A major problem around this issue is how to define…
Zipf's law is shown to arise as the variational solution of a problem formulated in Fisher's terms. An appropriate minimization process involving Fisher information and scale-invariance yields this universal rank distribution. As an example…
We introduce and analyse a class of fragmentation-coalescence processes defined on finite systems of particles organised into clusters. Coalescent events merge multiple clusters simultaneously to form a single larger cluster, while…
We present a unifying, consistent, finite-size-scaling picture for percolation theory bringing it into the framework of a general, renormalization-group-based, scaling scheme for systems above their upper critical dimensions $d_c$.…