相关论文: Why is topography fractal?

In this paper, we study the topology associated to the fractal manifold model. It turns out that this topology is actually a family of topologies that gives to the fractal manifold a structure of variable topological space. Additionally, we…

Through this research, embedded synthetic fracture networks in rock masses are studied. To analysis the fluid flow complexity in fracture networks with respect to the variation of connectivity patterns, two different approaches are…

We detail the energy balance of a propagating hydraulic fracture. Using the linear hydraulic fracture model which combines lubrication flow and linear elastic fracture mechanics, we demonstrate how different propagation regimes are related…

We propose a new method for quantitative characterization of spatial network-like patterns with loops, such as surface fracture patterns, leaf vein networks and patterns of urban streets. Such patterns are not well characterized by purely…

A comparison of the displacements of the earth's surface after an earthquake was made, calculating with the analytical expressions coming from an infinite flat slab approximation and compared with these numerically considering the…

Coastal erosion is a major and growing environmental problem describing the movement of sand caused by tides, waves or currents. Several phenomena contribute to the significant advance of the sea. These include climate change, with rising…

Topological properties of "scale-free" networks are investigated by determining their spectral dimensions $d_S$, which reflect a diffusion process in the corresponding graphs. Data bases for citation networks and metabolic networks together…

Although geographic features, such as mountains and coastlines, are fractal, some studies have claimed that the fractal property is not universal. This claim, which is false, is mainly attributed to the strict definition of fractal…

We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…

We calculate the spectral dimension of a wide class of tree-like fractals by solving the random walk problem through a new analytical technique, based on invariance under generalized cutting-decimation transformations. These fractals are…

Surfacic networks are structures built upon a two-dimensional manifold. Many systems, including transportation networks and various urban networks, fall into this category. The fluctuations of node elevations imply significant deviations…

River networks serve as a paradigmatic example of all branching networks. Essential to understanding the overall structure of river networks is a knowledge of their detailed architecture. Here we show that sub-branches are distributed…

The topological structure of the power grid plays a key role in the reliable delivery of electricity and price settlement in the electricity market. Incorporation of new energy sources and loads into the grid over time has led to its…

From social interactions to the human brain, higher-order networks are key to describe the underlying network geometry and topology of many complex systems. While it is well known that network structure strongly affects its function, the…

Seismic and geodynamic studies indicate that the boundary between the Earth's liquid outer core and solid mantle is not spherical, but is likely characterized by topography in the form of inverted mountains and valleys that have typical…

Climate change exacerbates riverine floods, which occur with higher frequency and intensity than ever. The much-needed forecasting systems typically rely on accurate river discharge predictions. To this end, the SOTA data-driven approaches…

Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with…

In this paper we study self-similar and fractal networks from the combinatorial perspective. We establish analogues of topological (Lebesgue) and fractal (Hausdorff) dimensions for graphs and demonstrate that they are naturally related to…

Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber reinforced materials are also common in technology. An important characteristic of such materials is their…

Scale is a fundamental concept that has attracted persistent attention in geography literature over the past several decades. However, it creates enormous confusion and frustration, particularly in the context of geographic information…