Related papers: Fractals, Multifractals and the Science of Complex…
The concept of multifractality offers a powerful formal tool to filter out multitude of the most relevant characteristics of complex time series. The related studies thus far presented in the scientific literature typically limit themselves…
The paper deals with the mathematical - numerical analysis of the Mandelbrot equation extended by the dynamic continuous term. The possibilities of generation of fractal patterns with the mathematical form, defined in such a manner, were…
This paper discusses some topics of enquiry concerning fractals, functions on them, and so on.
Recent advances in classical density functional theory are combined with stochastic process theory and rare event techniques to formulate a theoretical description of nucleation, including crystallization, that can predict nonclassical…
Fractals are geometric shapes that can display complex and self-similar patterns found in nature (e.g., clouds and plants). Recent works in visual recognition have leveraged this property to create random fractal images for model…
The kinetic theory is used to study the evolution of the self-gravitating disk of planetesimals. The effects of frequent collisions between planetesimals are taken into account by using a Krook integral in the Boltzmann kinetic equation. It…
This paper introduced a way of fractal to solve the problem of taking count of the integer partitions, furthermore, using the method in this paper some recurrence equations concerning the integer partitions can be deduced, including the…
In this study the general formula for differential and integral operations of fractional calculus via fractal operators by the method of cumulative diminution and cumulative growth is obtained. The under lying mechanism in the success of…
An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
In this paper we examine a number of models that generate random fractals. The models are studied using the tools of computational complexity theory from the perspective of parallel computation. Diffusion limited aggregation and several…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
Recently, attempts have been made to take into account the fractal properties of seismicity when mapping the long-term rate of earthquakes. The paper touches upon the theoretical aspects of fractality and provides a critical analysis of its…
A stochastic model relating the parameters of astrophysical structures to the parameters of their granular components is applied to the formation of hierarchical, large-scale structures from galaxies assumed as point-like objects. If the…
The electrostatics properties of composite materials with fractal geometry are studied in the framework of fractional calculus. An electric field in a composite dielectric with a fractal charge distribution is obtained in the spherical…
The fragmentation of diatomic molecules under a stochastic force is investigated both classically and quantum mechanically, focussing on their dissociation probabilities. It is found that the quantum system is more robust than the classical…
Fractals and multifractals and their associated scaling laws provide a quantification of the complexity of a variety of scale invariant complex systems. Here, we focus on lattice multifractals which exhibit complex exponents associated with…
We present an overview of concepts and results obtained with statistical models in study of nuclear multifragmentation. Conceptual differences between statistical and dynamical approaches, and selection of experimental observables for…
We develop a new definition of fractals which can be considered as an abstraction of the fractals determined through self-similarity. The definition is formulated through imposing conditions which are governed the relation between the…
Complex-dynamical fractal is a hierarchy of permanently, chaotically changing versions of system structure, obtained as the unreduced, causally probabilistic general solution of arbitrary interaction problem (physics/0305119,…