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The question of decoupling and freeze-out is reinvestigated and analysed in terms of transparent semi-classical decoupling formulae, which provide a smooth decoupling in time both, for single and two particle inclusive spectra. They…
In this paper, we extend the principles of Nambu mechanics by incorporating fractal calculus. This extension introduces Hamiltonian and Lagrangian mechanics that incorporate fractal derivatives. By doing so, we broaden the scope of our…
We introduce a simple geometric model which describes the kinetics of fragmentation of d-dimensional objects. In one dimension our model coincides with the random scission model and show a simple scaling behavior in the long-time limit. For…
We study derivations and Fredholm modules on metric spaces with a local regular conservative Dirichlet form. In particular, on finitely ramified fractals, we show that there is a non-trivial Fredholm module if and only if the fractal is not…
Many 0/1 datasets have a very large number of variables; on the other hand, they are sparse and the dependency structure of the variables is simpler than the number of variables would suggest. Defining the effective dimensionality of such a…
The method of spectral decimation is applied to an infinite collection of self--similar fractals. The sets considered belong to the class of nested fractals, and are thus very symmetric. An explicit construction is given to obtain formulas…
The fractal structure of real world objects is often analyzed using digital images. In this context, the compression fractal dimension is put forward. It provides a simple method for the direct estimation of the dimension of fractals stored…
We propose and investigate a simple model which describes the kinetics of aggregation of Brownian particles with stochastic self-replication. An exact solution and the scaling theory are presented alongside numerical simulation which fully…
Fractal geometry provides a powerful tool for scale-free spatial analysis of cities, but the fractal dimension calculation results always depend on methods and scopes of study area. This phenomenon has been puzzling many researchers. This…
The multi-scale expansions and contractions of the Earth's magnetosphere explain fundamental issues of magnetic storm-substorm relationship. This magnetospheric behavior is in agreement with a model of 3D-spirally-faster-inward-oscillating…
When flat or on a firm mechanical substrate, the atomic composition and atomistic structure of two-dimensional crystals dictate their chemical, electronic, optical, and mechanical properties. These properties change when the two-dimensional…
In the recent development in a various disciplines of physics, it is noted the need for including the deformed versions of the exponential functions. In this paper, we consider the deformations which have two purposes: to have them like…
The variation of fractal dimension and entropy during a damage evolution process, especially approaching critical failure, has been recently investigated. A sudden drop of fractal dimension has been proposed as a quantitative indicator of…
We compare the properties of transmission across one-dimensional finite samples which are associated with two types of "quantum diffusion", one related to a classical chaotic dynamics, the other to a multifractal energy spectrum. We…
We compute the dynamical degrees of certain compositions of reflections in points on a smooth cubic fourfold. Our interest in these computations stems from the irrationality problem for cubic fourfolds. Namely, we hope that they will…
Precise analyses of the statistical and scaling properties of galaxy distribution are essential to elucidate the large-scale structure of the universe. Given the ongoing debate on its statistical features, the development of statistical…
We introduce appropriate definitions of dimensions in order to characterize the fractal properties of complex networks. We compute these dimensions in a hierarchically structured network of particular interest. In spite of the nontrivial…
Understanding irreversibility in macrophysics from reversible microphysics has been the holy grail in statistical physics ever since the mid-19th century. Here the central question concerns the arrow of time, which boils down to deriving…
We introduce a lattice model able to describe damage and yielding in heterogeneous materials ranging from brittle to ductile ones. Ductile fracture surfaces, obtained when the system breaks once the strain is completely localized, are shown…
Cracks, the major vehicle for material failure, tend to accelerate to high velocities in brittle materials. In three-dimensions, cracks generically undergo a micro-branching instability at about 40% of their sonic limiting velocity. Recent…