Related papers: On the fractal properties microaccelerations
We describe space--time fluctuations by means of small fluctuations of the metric on a given background metric. From a minimally coupled Klein--Gordon equation we obtain within a weak-field approximation up to second order and an averaging…
The internal structure of self-interacting quantum particle like electron is independent on space-time position. Then at least infinitesimal kinematic space-time shift, rotation or boost lead to the equivalent internal quantum state. This…
Assuming fractality of hadronic constituents, we argue that asymmetry of space-time can be induced in the ultra-relativistic interactions of hadrons and nuclei. The asymmetry is expressed in terms of the anomalous fractal dimensions of the…
Examples of self propulsion in strongly fluctuating environment is abound in nature, e.g., molecular motors and pumps operating in living cells. Starting from Langevin equation of motion, we develop a fluctuating thermodynamic description…
We consider quantum interferences of ballistic electrons propagating inside fractal structures with nanometric size of their arms. We use a scaling argument to calculate the density of states of free electrons confined in a simple model…
Fractal structures emerge from statistical and hierarchical processes in urban development or network evolution. In a class of efficient and robust geographical networks, we derive the size distribution of layered areas, and estimate the…
When the vacuum state of a scalar or electromagnetic field is modified by the presence of a reflecting boundary, an interacting test particle undergoes velocity fluctuations. Such effect is regarded as a sort of quantum analog of the…
Multifractal dimensions allow for characterizing the localization properties of states in complex quantum systems. For ergodic states the finite-size versions of fractal dimensions converge to unity in the limit of large system size.…
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…
We introduce a duality for Affine Iterated Function Systems (AIFS) which is naturally motivated by group duality in the context of traditional harmonic analysis. Our affine systems yield fractals defined by iteration of contractive affine…
Predicting the mechanical response of the soft gel materials under external deformation is of paramount importance in many areas, such as foods, pharmaceuticals, solid-liquid separations, cosmetics, aerogels and drug delivery. Most of the…
We present some recent results on the motion of test bodies with internal structure in General Relativity. On the basis of a multipolar approximation scheme, we study the motion of extended test bodies endowed with an explicit model for the…
A number of experimental small-angle scattering (SAS) data are characterized by a succession of power-law decays with arbitrarily decreasing values of scattering exponents. To describe such data, here we develop a new theoretical model…
We study, both with numerical simulations and theoretical methods, a cellular automata model for continuum equations describing growth processes in the presence of an external flux of particles. As a result of local instabilities we find a…
The Sierpinski Triangle (ST) is a fractal mathematical structure that has been used to explore the emergence of flat bands in lattices of different geometries and dimensions in condensed matter. Here we look into fractal features in the…
Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of…
The distribution function of local amplitudes of eigenstates of a two-dimensional disordered metal is calculated. Although the distribution of comparatively small amplitudes is governed by laws similar to those known from the random matrix…
This paper proposes a novel quantum effect wherein particle spectra show extra broadening due to local short-time acceleration (as well as in a deSitter spacetime background). This effect provides a simple interpretation for the…
Electrons moving through a spatially periodic lattice potential develop a quantized energy spectrum consisting of discrete Bloch bands. In two dimensions, electrons moving through a magnetic field also develop a quantized energy spectrum,…
The fact that galaxy distribution exhibits fractal properties is well established since twenty years. Nowadays, the controversy concerns the range of the fractal regime, the value of the fractal dimension and the eventual presence of a…