Modeling cities

Cities are systems with a large number of constituents and agents interacting with each other and can be considered as emblematic of complex systems. Modeling these systems is a real challenge and triggered the interest of many disciplines such as quantitative geography, spatial economics, geomatics and urbanism, and more recently physics. (Statistical) Physics plays a major role by bringing tools and concepts able to bridge theory and empirical results, and we will illustrate this on some fundamental aspects of cities: the growth of their surface area and their population, their spatial organization, and the spatial distribution of activities. We will present state-of-the-art results and models but also open problems for which we still have a partial understanding and where physics approaches could be particularly helpful. We will end this short review with a discussion about the possibility of constructing a science of cities.     

Modeling the Internet

We model the Internet as a network of interconnected Autonomous Systems which self-organize under an absolute lack of centralized control. Our aim is to capture how the Internet evolves by reproducing the assembly that has led to its actual structure and, to this end, we propose a growing weighted network model driven by competition for resources and adaptation to maintain functionality in a demand and supply balance. On the demand side, we consider the environment, a pool of users which need to transfer information and ask for service. On the supply side, ASs compete to gain users, but to be able to provide service efficiently, they must adapt their bandwidth as a function of their size. Hence, the Internet is not modeled as an isolated system but the environment, in the form of a pool of users, is also a fundamental part which must be taken into account. ASs compete for users and big and small come up, so that not all ASs are identical. New connections between ASs are made or old ones are reinforced according to the adaptation needs. Thus, the evolution of the Internet can not be fully understood if just described as a technological isolated system. A socio-economic perspective must also be considered.     

Modeling plasma loudspeakers

This paper deals with the acoustic modeling and measurement of a needle-to-grid plasma loudspeaker using a negative Corona discharge. In the first part, we summarize the model described in previous papers, where the electrode gap is divided into a charged particle production region near the needle and a drift region which occupies most of the inter-electrode gap. In each region, interactions between charged and neutral particles in the ionized gas lead to a perturbation of the surrounding air, and thus generate an acoustic field. In each region, viewed as a separate acoustic source, an acoustical model requiring only a few parameters is proposed. In the second part of the paper, an experimental setup is presented for measuring acoustic pressures and directivities. This setup was developed and used to study the evolution of the parameters with physical properties, such as the geometrical and electrical configuration and the needle material. In the last part of this paper, a study on the electroacoustic efficiency of the plasma loudspeaker is described, and differences with respect to the design parameters are analyzed. Although this work is mainly aimed at understanding transduction phenomena, it may be found useful for the development of an audio loudspeaker.     

Modeling binaural loudness

A survey of data on the perception of binaurally presented sounds indicates that loudness summation across ears is less than perfect; a diotic sound is less than twice as loud as the same sound presented monaurally. The loudness model proposed by Moore et al. [J. Audio Eng. Soc. 45, 224-240 (1997)] determines the loudness of binaural stimuli by a simple summation of loudness across ears. It is described here how the model can be modified so as to give more accurate predictions of the loudness of binaurally presented sounds, including cases where the sounds at the two ears differ in level, frequency or both. The modification is based on the idea that there are inhibitory interactions between the internal representations of the signals at the two ears, such that a signal at the left ear inhibits (reduces) the loudness evoked by a signal at the right ear, and vice versa. The inhibition is assumed to spread across frequency channels. The modified model gives reasonably accurate predictions of a variety of data on the loudness of binaural stimuli, including data obtained using loudness scaling and loudness matching procedures.     

Modeling monofractal microscopy images

Methods for modeling monofractal microscopy images on the basis of space-frequency filtration are proposed. The spectral density and structural function of the monofractal images are assumed to be constant. Space-frequency filtration of the initial image is used for modeling; it transforms the amplitude distribution so that the integral frequency characteristic of the Fourier spectrum of individual segments is modified into a function that diminishes in accordance with a power law. The degree to which it diminishes for each segment is selected to ensure that estimates of the structural functions of the first and higher orders in a double logarithmic scale are approximated well by linear dependencies. The possibilities of our methods are demonstrated by modeling monofractal images of nanostructures for samples of amorphous alloys obtained via electrolytic deposition.     

Modeling worldwide highway networks

This Letter addresses the problem of modeling the highway systems of different countries by using complex networks formalism. More specifically, we compare two traditional geographical models with a modified geometrical network model where paths, rather than edges, are incorporated at each step between the origin and the destination vertices. Optimal configurations of parameters are obtained for each model and used for the comparison. The highway networks of Australia, Brazil, India, and Romania are considered and shown to be properly modeled by the modified geographical model.     

Modeling the oldest old

We use the Penna bit-string biological ageing model to simulate the particular feature of the oldest old of presenting a higher survival rate than the usual one. Three different strategies are proposed, all leading to the desired effect.     

Modeling spatio-temporal field evolution

Prediction of spatio-temporal field evolution is based on the extraction of a physical law from joint experimental data. This extraction is usually described by a set of differential equations. If the only source of information is a field record, a method of field generators based on nonparametric modeling by conditional average can successfully replace differential equations. In this article we apply the method of field generators to a two-dimensional chaotic field record that describes the asynchronous motion of high-amplitude striations. We show how to choose the model structure in order to optimize the quality of the prediction process.     

Modeling U-turn traffic flow

Median U-turns are sometimes installed to improve the traffic flow at busy intersections by eliminating left turns. Using a microscopic traffic model, we confirmed the presence of transitions from free flow to congested flow with increasing car inflow density. In addition, our proposed rules inside a U-turn curve, which accounted for safety issues and an asymmetric lane changing behavior (outer-to-inner vs. inner-to-outer lane transitions), predicted the speed distribution of cars after the U-turn curve. We found that U-turn curves installed for improving traffic flow at busy intersections produced their desired effects only when there is minimal interaction between cars.     

Modeling of HMX combustion

A mechanism of HMX combustion was proposed and the corresponding model was developed under the assumption that the combustion wave consists of two zones, with consideration given to the reaction of decomposition and vaporization of the initial energetic material in the condensed phase and the subsequent decomposition of its vapor in the gas phase. An analysis of the results showed that, at low pressures, the burning rate is largely determined by the exothermic decomposition of the material in the condensed phase, but at pressure above ∼20 atm, the processes in the gas phase begin to play an increasingly important role, where the limiting process is the bimolecular activation reaction with the subsequent dissociation of HMX accompanied by the secondary reactions between the products. A comparison of the calculation results with experimental data showed that the model adequately describes a number of characteristics of the combustion wave and ballistic properties, such as the burning rate and its sensitivity to pressure and initial temperature.     

Numerical Modeling of PMD

A procedure for evaluating system performance considering all orders of polarization mode dispersion (PMD) is presented. The method provides engineering rules for computing system penalty introduced by PMD. Computer simulation of PMD induced penalty indicates that for generating a realistic system budget, effect of higher order PMD in presence of chromatic dispersion is essential. Considering all of these penalties, in order to obtain a system-reach of 3200 km at 40 Gb/s, a fiber PMD of less than 0.04 ps/km^1/2 is required when at the signal wavelength chromatic dispersion is 0. In presence of 18 ps/nm chromatic dispersion for the same system reach this PMD value reduces to about 0.02 ps/km^1/2.     

Modeling media and structures

The minimum number of equivalent electrical circuit elements corresponding to models of finite volumes of physical media and structures with constant and variable parameters is obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 89–91, July, 1991.     

Modeling exchange bias microscopically

Exchange bias is a horizontal shift of the hysteresis loop observed for a ferromagnetic layer in contact with an antiferromagnetic layer. Since exchange bias is related to the spin structure of the antiferromagnet, for its fundamental understanding a detailed knowledge of the physics of the antiferromagnetic layer is inevitable. A model is investigated where domains are formed in the volume of the AFM stabilized by dilution. These domains become frozen during the initial cooling procedure carrying a remanent net magnetization which causes and controls exchange bias. Varying the anisotropy of the antiferromagnet, we find a non-trivial dependence of the exchange bias on the anisotropy of the antiferromagnet.     

Modeling of concentrated suspensions

The constitutive equation of a concentrated suspension of spherical particles in a Newtonian medium is derived. To this end the method of local volume averaging is employed. To calculate the contribution of the particles to the stress tensor it is assumed that the stress generated in the interstitial holes between the particles is negligible compared to the stress generated in !he narrow gaps separating the particles. The use of the resulting expression is demonstrated with two examples on a cubical arrangement of particles: pure shear and simple shear. Furthermore, the validity of the lubrication approximation employed in this work is checked against the results derived by Nunan and Keller for periodic suspensions.     

Modeling of breaststroke swimming

A mechanical system that models swimming using a pair of two-chain extremities is considered. The motion of the system under study is similar to swimming of a frog and some other animals, in which lower extremities play the main role. This type of motion is characteristic of competitive breaststroke swimming.     

Modeling Transverse Relative Locality

We investigate some aspects of relativistic classical theories with “relative locality”, in which pairs of events established to be coincident by nearby observers may be described as non-coincident by distant observers. While previous studies focused mainly on the case of longitudinal relative locality, where the effect occurs along the direction connecting the distant observer to the events, we here focus on transverse relative locality, in which instead the effect is found in a direction orthogonal to the one connecting the distant observer to the events. Our findings suggest that, at least for theories of free particles, transverse relative locality is as significant as longitudinal relative locality both conceptually and quantitatively. And we observe that “dual gravity lensing” can be viewed as one of two components of transverse relative locality. We also speculate about a type of spacetime noncommutativity for which transverse relative locality could be particularly significant.     

Modeling urban street patterns

Urban street patterns form planar networks whose empirical properties cannot be accounted for by simple models such as regular grids or Voronoi tesselations. Striking statistical regularities across different cities have been recently empirically found, suggesting that a general and detail-independent mechanism may be in action. We propose a simple model based on a local optimization process combined with ideas previously proposed in studies of leaf pattern formation. The statistical properties of this model are in good agreement with the observed empirical patterns. Our results thus suggest that in the absence of a global design strategy, the evolution of many different transportation networks indeed follows a simple universal mechanism.