Related papers: Dynamics of Cities
We investigate finite size scaling aspects of disorder reaction-diffusion processes in one dimension utilizing both numerical and analytical approaches. The former averages the spectrum gap of the associated evolution operators by doubling…
This paper proposes a new method to analyze the spatial structure of urban systems using ideas from fractals. Regarding a system of cities as a set of "particles" distributed randomly on a triangular lattice, we construct a spatial…
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…
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…
Urban form and growth can be described with fractal dimension, which is a measurement of space filling of urban evolution. Based on empirical analyses, a discovery is made that the time series of fractal dimension of urban form can be…
The growth curves of fractal dimension of urban form take on squashing effect and can be described by sigmoid functions. The fractal dimension growth of urban form in western countries can be modeled by Boltzmann's equation and logistic…
The time series of fractal dimension values of urban form always take on sigmoid curves. The basic model of these curves is logistic function. From the logistic model of fractal dimension curves, we can derive the growth rate formula and…
Fractal dimension curves of urban growth can be modeled with sigmoid functions, including logistic function and quadratic logistic function. Different types of logistic functions indicate different spatial dynamics. The fractal dimension…
The relationships between urban area and population size have been empirically demonstrated to follow the scaling law of allometric growth. This allometric scaling is based on exponential growth of city size and can be termed "exponential…
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…
This is a study of the information evolution of complex systems by geometrical consideration. We look at chaotic systems evolving in fractal phase space. The entropy change in time due to the fractal geometry is assimilated to the…
We study spreading dynamics of nematic liquid crystal droplets within the framework of the long-wave approximation. A fourth order nonlinear parabolic partial differential equation governing the free surface evolution is derived. The…
The morphology of urban agglomeration is studied here in the context of information exchange between different spatio-temporal scales. Cities are multidimensional non-linear phenomena, so understanding the relationships and connectivity…
The gravity model is one of important models of social physics and human geography, but several basic theoretical and methodological problems remain to be solved. In particular, it is hard to explain and evaluate the distance exponent using…
We study spatial clustering in a discrete, one-dimensional, stochastic, toy model of heavy particles in turbulence and calculate the spectrum of multifractal dimensions $D_q$ as functions of a dimensionless parameter, $\alpha$, that plays…
City is proved to be a scale-free phenomenon, and spatial autocorrelation is often employed to analyze spatial redundancy of cities. Unfortunately, spatial analysis results deviated practical requirement in many cases due to fractal nature…
Atmospheric flows, an example of turbulent fluid flows, exhibit fractal fluctuations of all space-time scales ranging from turbulence scale of mm -sec to climate scales of thousands of kilometers - years and may be visualized as a nested…
Quantum dynamics on quasiperiodic geometries has recently gathered significant attention in ultra-cold atom experiments where non trivial localised phases have been observed. One such quasiperiodic model is the so called Fibonacci model. In…
The fractal dimension curves of urban form and growth fall into two categories: One can be described by common logistic function, and the other can be described with quadratic logistic function. The approach to estimating the parameter of…
Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and…