相关论文: Describing urban evolution with the fractal parame…

There are three important types of structural properties that remain unchanged under the structural transformation of condensed matter physics and chemistry. They are the properties that remain unchanged under the structural periodic…

The rank-size distribution of cities follows Zipf's law, and the Zipf scaling exponent often tends to a constant 1. This seems to be a general rule. However, a recent numerical experiment shows that there exists a contradiction between the…

Cities are centers for the integration of capital and incubators of invention, and attracting venture capital (VC) is of great importance for cities to advance in innovative technology and business models towards a sustainable and…

Urban analytics increasingly relies on AI-driven trajectory analysis, yet current approaches suffer from methodological fragmentation: trajectory learning captures movement patterns but ignores spatial context, while spatial embedding…

Commuting is a key mechanism that governs the dynamics of cities. Despite its importance, very little is known of the properties and mechanisms underlying this crucial urban process. Here, we capitalize on $\sim$ 50 million individuals'…

Large-scale models are generally associated with big modelling units in space, like counties or super grids (several to dozens km2). Few applied urban models can pursue large-scale extent with fine-level units simultaneously due to data…

In this work, we present a mathematical model to describe the adsorption-diffusion process on fractal porous materials. This model is based on the fractal continuum approach and considers the scale-invariant properties of the surface and…

The scaling relations between city attributes and population are emergent and ubiquitous aspects of urban growth. Quantifying these relations and understanding their theoretical foundation, however, is difficult due to the challenge of…

Local fractional calculus deals with everywhere continuous but nowhere differentiable functions in fractal space. The Yang-Fourier transform based on the local fractional calculus is a generalization of Fourier transform in fractal space.…

The fractal dimension is a central quantity in nonlinear dynamics and can be estimated via several different numerical techniques. In this review paper we present a self-contained and comprehensive introduction to the fractal dimension. We…

Cities are often compared through scaling laws, usually expressed as power-law relations between population size and aggregate urban quantities related to infrastructure, socioeconomic activity, or environmental impacts. These laws are…

In previous papers by A. Kameyama and by J. Kigami distances on fractals have been discussed having two different but similar properties. One property is that the maps defining the fractal are Lipschitz of prescribed constants less than 1,…

The main goal of this paper has a double purpose. On the one hand, we propose a new definition in order to compute the fractal dimension of a subset respect to any fractal structure, which completes the theory of classical box-counting…

We show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose…

If our aesthetic preferences are affected by fractal geometry of nature, scaling regularities would be expected to appear in all art forms, including music. While a variety of statistical tools have been proposed to analyze time series in…

Cities can be characterised and modelled through different urban measures. Consistency within these observables is crucial in order to advance towards a science of cities. Bettencourt et al have proposed that many of these urban measures…

Fractals and quasiperiodic structures share self-similarity as a structural property. Motivated by the link between Fibonacci fractals and quasicrystals which are scaled by the golden mean ratio $\frac{1+\sqrt{5}}{2}$, we introduce and…

The estimation of commuting flows at different spatial scales is a fundamental problem for different areas of study. Many current methods rely on parameters requiring calibration from empirical trip volumes. Their values are often not…

The dynamics of urban systems can be understood from an evolutionary perspective, in some sense extending biological and cultural evolution. Models for systems of cities implementing elementary evolutionary processes remain however to be…

A second derivative-based moment method is proposed for describing the thickness and shape of the region where viscous forces are dominant in turbulent boundary layer flows. Rather than the fixed location sublayer model presently employed,…