相关论文: Limits of fractality: Zeno boxes and relativistic …

Fractal structures appear in a vast range of physical systems. A literature survey including all experimental papers on fractals which appeared in the six Physical Review journals (A-E and Letters) during the 1990's shows that experimental…

We demonstrate fractal noise in the quantum evolution of wave packets moving either ballistically or diffusively in periodic and quasiperiodic tight-binding lattices, respectively. For the ballistic case with various initial superpositions…

For semiclassical problems we establish upper bounds on the number of resonances in boxes of size $h$ along the real axis, in terms of the dimension of the set of trapped trajectories. The proof uses second microlocalization.

We show that when the standard techniques for calculating fractal dimensions in empirical data (such as the box counting) are applied on uniformly random structures, apparent fractal behavior is observed in a range between physically…

We examine the fractal structure of the physical universe from the large scale to the smallest scale, including the phenomenon of fractal scaling. This is explained in terms of a stochastic underpinning for the laws of physics. A picture in…

We discuss the definition and measurability questions of random fractals and find under certain conditions a formula for upper and lower Minkowski dimensions. For the case of a random self-similar set we obtain the packing dimension.

Cohesive particles form agglomerates that are usually very porous. Their geometry, particularly their fractal dimension, depends on the agglomeration process (diffusion-limited or ballistic growth by adding single particles or…

The formation length of particles produced in the relativistic collisions of hadrons and nuclei has relevance to fundamental principles of physics at small interaction distances. The relation is expressed by z scaling observed in the…

We consider a fractal with a variable fractal dimension, which is a generalization of the well known triadic Cantor set. In contrast with the usual Cantor set, the fractal dimension is controlled using a scaling factor, and can vary from…

We study algorithmic problems on subsets of Euclidean space of low fractal dimension. These spaces are the subject of intensive study in various branches of mathematics, including geometry, topology, and measure theory. There are several…

For asymptotically hyperbolic manifolds with hyperbolic trapped sets we prove a fractal upper bound on the number of resonances near the essential spectrum, with power determined by the dimension of the trapped set. This covers the case of…

We study the dynamics of a particle in a horizontally and periodically shaken box as a function of the box parameters and the coefficient of restitution. For certain parameter values, the particle becomes regularly chattered at one of the…

The fractal nature of complex networks has received a great deal of research interest in the last two decades. Similarly to geometric fractals, the fractality of networks can also be defined with the so-called box-covering method. A network…

We discuss a number of techniques for determining the Minkowski dimension of bounded subsets of some Euclidean space of any dimension, including: the box-counting dimension and equivalent definitions based on various box-counting functions;…

We study the porosity properties of fractal percolation sets $E\subset\mathbb{R}^d$. Among other things, for all $0<\varepsilon<\tfrac12$, we obtain dimension bounds for the set of exceptional points where the upper porosity of $E$ is less…

The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using…

The notion of the abundance of fractals is critically re-examined in light of surprising data regarding the scaling range in empirical reports on fractality.

In this work, we first recall the definition of the relative distance zeta function in [42, 43, 44, 46, 47] and slightly generalize this notion from sets to probability measures, and then move on to propose a novel definition a relative…

In this article we investigate the energy spectrum statistics of fractals at the quantum level. We show that the energy-level distribution of a fractal follows a power-law behaviour, if its energy spectrum is a limit set of piece-wise…

Under general assumptions, the numbers of semiclassical resonances is known to be bounded from above by a negative power of $h$ which is given by the fractal dimension of the trapped set. In this paper we provide examples of operators with…