Mathematics and Morphogenesis of the City: A Geometrical Approach

Cities are living organisms. They are out of equilibrium, open systems that never stop developing and sometimes die. The local geography can be compared to a shell constraining its development. In brief, a city's current layout is a step in a running morphogenesis process. Thus cities display a huge diversity of shapes and none of traditional models from random graphs, complex networks theory or stochastic geometry takes into account geometrical, functional and dynamical aspects of a city in the same framework. We present here a global mathematical model dedicated to cities that permits describing, manipulating and explaining cities' overall shape and layout of their street systems. This street-based framework conciliates the topological and geometrical sides of the problem. From the static analysis of several French towns (topology of first and second order, anisotropy, streets scaling) we make the hypothesis that the development of a city follows a logic of division / extension of space. We propose a dynamical model that mimics this logic and which from simple general rules and a few parameters succeeds in generating a large diversity of cities and in reproducing the general features the static analysis has pointed out.Comment: 13 pages, 13 figure

Possible Indication of Narrow Baryonic Resonances Produced in the 1720-1790 MeV Mass Region

Signals of two narrow structures at M=1747 MeV and 1772 MeV were observed in the invariant masses M_{pX} and M_{\pi^{+}X} of the pp->ppX and pp->p\pi^{+}X reactions respectively. Many tests were made to see if these structures could have been produced by experimental artefacts. Their small widths and the stability of the extracted masses lead us to conclude that these structures are genuine and may correspond to new exotic baryons. Several attempts to identify them, including the possible "missing baryons" approach, are discussed.Comment: 17 pages including 8 figures and 3 tables. ReVte

Subthreshold K+ production in deuteron and alpha induced nuclear reactions

Double differential cross sections have been measured for pi+ and K+ emitted around midraidity in d+A and He+A collisions at a beam kinetic energy of 1.15 GeV/nucleon. The total pi+ yield increases by a factor of about 2 when using an alpha projectile instead of a deuteron whereas the K+ yield increases by a factor of about 4. According to transport calculations, the K+ enhancement depends both on the number of hadron-hadron collisions and on the energy available in those collisions: their center-of-mass energy increases with increasing number of projectile nucleons

\pi N and \eta p deexcitation channels of the N^* and \Delta baryonic resonances between 1470 and 1680 MeV

Two reactions, pp->ppX and pp->p\pi^+X, are used to study the 1.47<M<1.68 GeV baryonic mass range. Three different final states are considered in the invariant masses: N^* or \Delta^+, p\pi^0, and p\eta. The last two channels are defined by software cuts applied to the missing mass of the first reaction. Several narrow structures are extracted with widths \sigma(\Gamma) varying between 3 and 9 MeV. Some structures are observed in one channel but not in others. Such nonobservation may be due either to the spectrometer momenta limits or to the physics (e.g. no such disintegration channel is allowed from the narrow state considered). We tentatively conclude that the broad Particle Data Group (PDG) baryonic resonances N(1520)D13, N(1535)S11, Delta(1600)P33, and N(1675)D15 are collective states built from several narrow and weakly excited resonances, each having a (much) smaller width than the one reported by PDG.Comment: 29 pages, plus 50 (.png) figures Will be published in a slightly reduced size in Phys. Rev.

Comparison of eta and eta' production in the pp -> pp eta(eta') reactions near threshold

The total cross section of the pp -> pp eta' reaction has been measured at two energies near threshold by detecting the final protons in a magnetic spectrometer. The values obtained are about a factor of 70 less than for the corresponding eta production, in good agreement with the predictions of a one-pion-exchange model.Comment: 10 pages, Latex with 3 eps figure

Elementary processes governing the evolution of road networks

Urbanisation is a fundamental phenomenon whose quantitative characterisation is still inadequate. We report here the empirical analysis of a unique data set regarding almost 200 years of evolution of the road network in a large area located north of Milan (Italy). We find that urbanisation is characterised by the homogenisation of cell shapes, and by the stability throughout time of high-centrality roads which constitute the backbone of the urban structure, confirming the importance of historical paths. We show quantitatively that the growth of the network is governed by two elementary processes: (i) `densification', corresponding to an increase in the local density of roads around existing urban centres and (ii) `exploration', whereby new roads trigger the spatial evolution of the urbanisation front. The empirical identification of such simple elementary mechanisms suggests the existence of general, simple properties of urbanisation and opens new directions for its modelling and quantitative description.Comment: 10 pages, 6 figure

Eta-Helium Quasi-Bound States

The cross section and tensor analysing power t_20 of the d\vec{d}->eta 4He reaction have been measured at six c.m. momenta, 10 < p(eta) < 90 MeV/c. The threshold value of t_20 is consistent with 1/\sqrt{2}, which follows from parity conservation and Bose symmetry. The much slower momentum variation observed for the reaction amplitude, as compared to that for the analogous pd->eta 3He case, suggests strongly the existence of a quasi-bound state in the eta-4He system and optical model fits indicate that this probably also the case for eta-3He.Comment: LaTeX, uses elsart.sty, 10 pages, 3 Postscript figures, Submitted to Physics Letters

SEARCH FOR NARROW ISOVECTOR DIBARYONS CLOSE TO LOW MASSES THRESHOLD

For masses larger than 2 MN + Mπ, narrow peaks in two proton invariant (missing) masses spectra : Mpp (Mx) are now well established. The existence of such narrow peaks is not so unquestionable below 2 MN + Mπ. Tensor analyzing power T20 of the invariant mass Mpp has been studied using the p ([MATH], pp) reaction. Depending on the assumption done for background substraction -a hole or an oscillation may appear at Mpp = 1941 MeV. Additional data are under analysis and will improve the statistics