Related papers: Fractal dimension analysis of spatio-temporal patt…
The Directed Landscape, a random directed metric on the plane (where the first and the second coordinates are termed spatial and temporal respectively), was constructed in the breakthrough work of Dauvergne, Ortmann, and Vir\'ag, and has…
This work proposes the development and study of a novel technique for the generation of fractal descriptors used in texture analysis. The novel descriptors are obtained from a multiscale transform applied to the Fourier technique of fractal…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the…
We investigate a quasisymmetrically invariant counterpart of the topological Hausdorff dimension of a metric space. This invariant, called the topological conformal dimension, gives a lower bound on the topological Hausdorff dimension of…
In this work, we investigate scale invariance in the temporal evolution and chaotic regime of discrete dynamical systems. By exploiting the close interrelation between scaling and inversion transformations, we formulate scale symmetry in…
Fractional nonlinear differential equations present an interplay between two common and important effective descriptions used to simplify high dimensional or more complicated theories: nonlinearity and fractional derivatives. These…
This paper delves into the world of fractal calculus, investigating its implications for fractal sets. It introduces the Fractal Schr\"{o}dinger Equation and provides insights into its consequences. The study presents a General Solution for…
Since the recent dissertation by Steffen Winter, for certain self-similar sets $F$ the growth behaviour of the Minkowski functionals of the parallel sets $F_\varepsilon := \{x\in \mathbb R^d : d(x,F)\leq \varepsilon\}$ as $\varepsilon…
Fractal plays an important role in nonlinear science. The most important parameter to model fractal is fractal dimension. Existing information dimension can calculate the dimension of probability distribution. However, given a mass function…
Static structure factors are computed for large-scale, mechanically stable, jammed packings of frictionless spheres (three dimensions) and disks (two dimensions) with broad, power-law size dispersity characterized by the exponent $-\beta$.…
Wireless mesh networks (WMNs) depend on the spatial distribution of nodes, which directly influences connectivity, routing efficiency, and overall network performance. Conventional models typically assume uniform or random node placement,…
The fractal dimension of domain walls produced by changing the boundary conditions from periodic to anti-periodic in one spatial direction is studied using both the strong-disorder renormalization group and the greedy algorithm for the…
Irregular boundary lines can be characterized by fractal dimension, which provides important information for spatial analysis of complex geographical phenomena such as cities. However, it is difficult to calculate fractal dimension of…
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…
The area-perimeter scaling can be employed to evaluate the fractal dimension of urban boundaries. However, the formula in common use seems to be not correct. By means of mathematical method, a new formula of calculating the boundary…
We use exponential sums to study the fractal dimension of the graphs of solutions to linear dispersive PDE. Our techniques apply to Schr\"odinger, Airy, Boussinesq, the fractional Schr\"odinger, and the gravity and gravity-capillary water…
We study the fractal structure of space-time of two-dimensional quantum gravity coupled to c=-2 conformal matter by means of computer simulations. We find that the intrinsic Hausdorff dimension d_H = 3.58 +/- 0.04. This result supports the…
We analyse the spatial inhomogeneities ('spatial clustering') in the distribution of particles accelerated by a force that changes randomly in space and time. To quantify spatial clustering, the phase-space dynamics of the particles must be…
The geometry of fracture patterns in a dilute elastic network is explored using molecular dynamics simulation. The network in two dimensions is subjected to a uniform strain which drives the fracture to develop by the growth and coalescence…