Related papers: Fractality of eroded coastlines of correlated land…
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…
The margins within the geographic range of species are often specific in terms of ecological and evolutionary processes, and can strongly influence the species' reaction to climate change. One of the frequently observed features at range…
The roughness properties of two-dimensional fracture surfaces as created by the slow failure of random fuse networks are considered and compared to yield surfaces of perfect plasticity with similar disorder. By studying systems up to a…
Discretized landscapes can be mapped onto ranked surfaces, where every element (site or bond) has a unique rank associated with its corresponding relative height. By sequentially allocating these elements according to their ranks and…
We approach the problem of heterogeneous dynamic fracture by considering spatiotemporal perturbations to planar crack fronts. Front propagation is governed by local energy balance between the elastic energy per unit area available to…
Spatial patterns and processes of cities can be described with various entropy functions. However, spatial entropy always depends on the scale of measurement, and it is difficult to find a characteristic value for it. In contrast, fractal…
We investigate the geometry of a critical system undergoing a second order thermal phase transition. Using a local description for the dynamics characterizing the system at the critical point T=Tc, we reveal the formation of clusters with…
Disorder and long-range interactions are two of the key components that make material failure an interesting playfield for the application of statistical mechanics. The cornerstone in this respect has been lattice models of the fracture in…
Fractals emerge everywhere in nature, exhibiting intricate geometric complexities through the self-organizing patterns that span across multiple scales. Here, we investigate beyond steady-states the interplay between this geometry and the…
Two surfaces are "sticky" if breaking their mutual contact requires a finite tensile force. At low fractal dimensions D, there is consensus stickiness does not depend on the upper truncation frequency of roughness spectrum (or…
Strong interaction of closely located, nearly parallel hydraulic fractures and its influence on their propagation are studied. Both computational and physical aspects of the problem are considered. It is shown that from the computational…
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…
As is well known, structure formation in the Universe at times after decoupling can be described by hydrodynamic equations. These are shown here to be equivalent to a generalization of the stochastic Kardar--Parisi--Zhang equation with…
Diffusion-limited erosion is a distinct universality class of fluctuating interfaces. Although its dynamical exponent $z=1$, none of the known variants of conformal invariance can act as its dynamical symmetry. In $d=1$ spatial dimensions,…
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…
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…
Fractal dimensions are tools for probing the structure of quantum states and identifying whether they are localized or delocalized in a given basis. These quantities are commonly extracted through finite-size scaling, which limits the…
We consider the time-dependent statistical distributions of diffusive processes in relaxation to a stationary state for simple, two dimensional chaotic models based upon random walks on a line. We show that the cumulative functions of the…
In this report we present a study on the strength of rocks which are partially fractured from before. We have considered a two dimensional case of a rock in the form of a lattice structure. The fiber bundle model is used for modelling the…
The scaling behavior of the mutifractality for the sea-bottom topography of the South Sea in Korea is numerically investigated. In particular, we focus on the behavior of the $q$th-moment depth-depth correlation function of the sea-bottom…