Exact solution of the zero-range process: fundamental diagram of the corresponding exclusion process

In this paper, we propose a general way of computing expectation values in the zero-range process, using an exact form of the partition function. As an example, we provide the fundamental diagram (the flux-density plot) of the asymmetric exclusion process corresponding to the zero-range process.We express the partition function for the steady state by the Lauricella hypergeometric function, and thereby have two exact fundamental diagrams each for the parallel and random sequential update rules. Meanwhile, from the viewpoint of equilibrium statistical mechanics, we work within the canonical ensemble but the result obtained is certainly in agreement with previous works done in the grand canonical ensemble.Comment: 12 pages, 2 figure

Cities on and off the map: A bibliometric assessment of urban globalisation research

Growing out of writings on Global (North) cities, urban globalisation research (UGR) has expanded its canon to engage with an increasing diversity of cities and locations. Yet, this broadening has been uneven and controversial in its theoretical horizons and empirical universe. Focusing on the latter, this paper combines bibliometric, demographic, economic and georeferenced data to assess how UGR maps onto internationally documented cities ( n : 1692). Our study analyses city-themed publications by city location, demographic size and home-country income (2000–2014). Drawing on social science publications indexed in English (Scopus database), our results provide grounds for cautious optimism: recent publications offer broader, though still uneven coverage. The moving spatial average of publication counts also implies that the topical centre of published research gravity is shifting away from Euro-America. Yet, UGR lags in its coverage of the urban geographical universe, failing to keep pace with the economic/demographic trends that are resulting in southward/eastward shifts in worldwide urbanisation. Furthermore, while smaller cities and those in lower-income countries are still sidelined, cities in upper-middle income countries exhibit the largest gaps between observed and expected publication values. In our conclusion, we contend that urban bibliometrics could be further mobilised to identify publication foci and lacunae. Applied to cities on and off the map and a broader universe of urban knowledges, bibliometrics could help move contentious debates forward, identifying newer paradigms that may be engaging the world of cities beyond the globalisation umbrella and charting out multiple and complex topical relations across variegated worlds of urbanism

Calibration of the Particle Density in Cellular-Automaton Models for Traffic Flow

We introduce density dependence of the cell size in cellular-automaton models for traffic flow, which allows a more precise correspondence between real-world phenomena and what observed in simulation. Also, we give an explicit calibration of the particle density particularly for the asymmetric simple exclusion process with some update rules. We thus find that the present method is valid in that it reproduces a realistic flow-density diagram.Comment: 2 pages, 2 figure

Ultra-discrete Optimal Velocity Model: a Cellular-Automaton Model for Traffic Flow and Linear Instability of High-Flux Traffic

In this paper, we propose the ultra-discrete optimal velocity model, a cellular-automaton model for traffic flow, by applying the ultra-discrete method for the optimal velocity model. The optimal velocity model, defined by a differential equation, is one of the most important models; in particular, it successfully reproduces the instability of high-flux traffic. It is often pointed out that there is a close relation between the optimal velocity model and the mKdV equation, a soliton equation. Meanwhile, the ultra-discrete method enables one to reduce soliton equations to cellular automata which inherit the solitonic nature, such as an infinite number of conservation laws, and soliton solutions. We find that the theory of soliton equations is available for generic differential equations, and the simulation results reveal that the model obtained reproduces both absolutely unstable and convectively unstable flows as well as the optimal velocity model.Comment: 9 pages, 6 figure

Exact solution and asymptotic behaviour of the asymmetric simple exclusion process on a ring

In this paper, we study an exact solution of the asymmetric simple exclusion process on a periodic lattice of finite sites with two typical updates, i.e., random and parallel. Then, we find that the explicit formulas for the partition function and the average velocity are expressed by the Gauss hypergeometric function. In order to obtain these results, we effectively exploit the recursion formula for the partition function for the zero-range process. The zero-range process corresponds to the asymmetric simple exclusion process if one chooses the relevant hop rates of particles, and the recursion gives the partition function, in principle, for any finite system size. Moreover, we reveal the asymptotic behaviour of the average velocity in the thermodynamic limit, expanding the formula as a series in system size.Comment: 10 page

Reading the Number of Extra Dimensions in the Spectrum of Hawking Radiation

After a brief review of the production and decay of Schwarzschild-like (4+n)-dimensional black holes in the framework of theories with Large Extra Dimensions, we proceed to derive the greybody factors and emission rates for scalars, fermions and gauge bosons on the brane. We present and discuss analytic and numerical methods for obtaining the above results, and demonstrate that both the amount and type of Hawking radiation emitted by the black hole can help us to determine the number of spacelike dimensions that exist in nature.Comment: 8 pages, Latex file, 1 figure, to appear in the proceedings of the String Phenomenology 2003 Conference, Durham, UK, 29th July-4th August, 200

Entanglement of orbital angular momentum states between an ensemble of cold atoms and a photon

Recently, atomic ensemble and single photons were successfully entangled by using collective enhancement [D. N. Matsukevich, \textit{et al.}, Phys. Rev. Lett. \textbf{95}, 040405(2005).], where atomic internal states and photonic polarization states were correlated in nonlocal manner. Here we experimentally clarified that in an ensemble of atoms and a photon system, there also exists an entanglement concerned with spatial degrees of freedom. Generation of higher-dimensional entanglement between remote atomic ensemble and an application to condensed matter physics are also discussed.Comment: 5 pages, 3 figure