Related papers: A physically based connection between fractional c…
We study the formation of fractal structure in one-dimensional many-body systems with attractive power-law potentials. Numerical analysis shows that the range of the index of the power for which fractal structure emerges is limited.…
A new phase of temporal evolution of the one-dimensional self-gravitating system is numerically discovered. Fractal structure is dynamically created from non-fractal initial conditions. Implication to astrophysics and mathematical physics…
Soft materials often exhibit a distinctive power-law viscoelastic response arising from broad distribution of time-scales present in their complex internal structure. A promising tool to accurately describe the rheological behaviour of soft…
Starting from the model of continuous time random walk, we focus our interest on random walks in which the probability distributions of the waiting times and jumps have fat tails characterized by power laws with exponent between 0 and 1 for…
The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and…
In the interstellar medium, as well as in the Universe, large density fluctuations are observed, that obey power-law density distributions and correlation functions. These structures are hierarchical, chaotic, turbulent, but are also…
The notion of fractality, in the context of positive-valued probability distributions, is conventionally associated with the class of Paretian probability laws. In this research we show that the Paretian class is merely one out of six…
In this study, we explore the field of physics through the lens of fractional dimensionality. We propose that space is not confined to integer dimensions alone, but can also be understood as a superposition of spaces that exist between…
We study the kinetics of random sequential adsorption of a mixture of particles with continuous distribution of sizes for different deposition rules. It appears in the long time limit the resulting system can be described using the fractal…
This paper presents a new perspective of looking at the relation between fractals and chaos by means of cities. Especially, a principle of space filling and spatial replacement is proposed to explain the fractal dimension of urban form. The…
It is argued that the evolution of complex phenomena ought to be described by fractional, differential, stochastic equations whose solutions have scaling properties and are therefore random, fractal functions. To support this argument we…
Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations…
Dynamical systems in nature exhibit selfsimilar fractal fluctuations and the corresponding power spectra follow inverse power law form signifying long-range space-time correlations identified as self-organized criticality. The physics of…
The paper deals with the fundamental problem of a modeling of the physical, in particular, thermal hydraulic processes, in various media of fractal structure of the natural, technological and technical systems and devices. The examples of a…
The presence of the power-law memory is a significant feature of many natural (biological, physical, etc.) and social systems. Continuous and discrete fractional calculus is the instrument to describe the behavior of systems with the…
A generalization of the economic model of natural growth, which takes into account the power-law memory effect, is suggested. The memory effect means the dependence of the process not only on the current state of the process, but also on…
In physics, phenomena of diffusion and wave propagation have great relevance; these physical processes are governed in the simplest cases by partial differential equations of order 1 and 2 in time, respectively. By replacing the time…
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
Fractional calculus is an effective tool in incorporating the effects of non-locality and memory into physical models. In this regard, successful applications exist rang- ing from signal processing to anomalous diffusion and quantum…
Breast cancer exhibits intricate morphological and dynamical heterogeneity across cellular, tissue, and tumor scales, posing challenges to conventional modeling approaches that fail to capture its nonlinear, self-similar, or self-affine,…