The fuzzy boundary: the spatial definition of urban areas

Cities seem to have some kind of area structure, usually distinguished in terms of land use types, socio-economic variables, physical appearance or historical and culturalcharacteristics. Is there any possibility that urban areas could in general be differentiated from the spatial perspective? What is the nature of boundaries between areas in terms of space? These questions could be approached by the analysis of internal or contextual spatial structure, or the relation between the two. Most studies on area structure however had focused in the main on the internal area with a secondaryrole for the context. Is there any way in which we could give more explicit attention to the context, following the clue that had come out of the earlier studies?This paper is to try to develop spatial techniques for identifying area boundaries, and looking at their performance in both the traditional areas, such as the Central London and the Inner City of Beijing, and the new development of the London Docklands. It focuses on explicitly exploring the properties of contextual structure in the formation ofarea boundaries rather than simply the properties of internal structure. After much experimentation, a new technique was arrived at for exploring properties of the context. Each axial line or segment in the whole map is taken as the root of a graph, and the numbers of axial lines, or segments, found with increasing radius from the root is calculated, and expressed as a rate of change. This rate of change value is thenassigned to the original axial line and expressed through bands of color. The results show strong areal effects, in that groups of neighbouring lines tend to have similar coloring, and in many cases, these suggest natural areas.Through the case studies, this paper suggests that historic areas typically have what we will call fuzzy boundaries. Fuzzy boundaries arise from the way space is structured internally and how this relates to the external structure of space. Such boundaries can be effective in supporting functional differentiation of areas or the growth of areal identities and characters, but do not depend on the area being either spatially self contained or geometrically differentiated, or having clear spatial limits. It is the relation of urban areas and their further surroundings that determine fuzzy boundaries of these urban areas

On the Importance of the Interclump Medium for Superionization: O VI Formation in the Wind of Zeta Pup

We have studied superionization and X-ray line formation in the spectra of Zeta Pup using our new stellar atmosphere code (XCMFGEN) that can be used to simultaneously analyze optical, UV, and X-ray observations. Here, we present results on the formation of the O VI ll1032, 1038 doublet. Our simulations, supported by simple theoretical calculations, show that clumped wind models that assume void in the interclump space cannot reproduce the observed O VI profiles. However, enough O VI can be produced if the voids are filled by a low density gas. The recombination of O VI is very efficient in the dense material but in the tenuous interclump region an observable amount of O VI can be maintained. We also find that different UV resonance lines are sensitive to different density regimes in Zeta Pup : C IV is almost exclusively formed within the densest regions, while the majority of O VI resides between clumps. N V is an intermediate case, with contributions from both the tenuous gas and clumps.Comment: Accepted for publication in ApJL, 4 pages with 3 figure

Metric and topo-geometric properties of urban street networks: some convergences, divergences, and new results

The theory of cities, which has grown out of the use of space syntax techniques in urban studies, proposes a curious mathematical duality: that urban space is locally metric but globally topo-geometric. Evidence for local metricity comes from such generic phenomena as grid intensification to reduce mean trip lengths in live centres, the fall of movement from attractors with metric distance, and the commonly observed decay of shopping with metric distance from an intersection. Evidence for global topo-geometry come from the fact that we need to utilise both the geometry and connectedness of the larger scale space network to arrive at configurational measures which optimally approximate movement patterns in the urban network. It might be conjectured that there is some threshold above which human being use some geometrical and topological representation of the urban grid rather than the sense of bodily distance to making movement decisions, but this is unknown. The discarding of metric properties in the large scale urban grid has, however, been controversial. Here we cast a new light on this duality. We show first some phenomena in which metric and topo-geometric measures of urban space converge and diverge, and in doing so clarify the relation between the metric and topo-geometric properties of urban spatial networks. We then show how metric measures can be used to create a new urban phenomenon: the partitioning of the background network of urban space into a network of semi-discrete patches by applying metric universal distance measures at different metric radii, suggesting a natural spatial area-isation of the city at all scales. On this basis we suggest a key clarification of the generic structure of cities: that metric universal distance captures exactly the formally and functionally local patchwork properties of the network, most notably the spatial differentiation of areas, while the top-geometric measures identifying the structure which overcomes locality and links the urban patchwork into a whole at different scales

Metric and topo-geometric properties of urban street networks: some convergences, divergences and new results

The theory of cities, which has grown out of the use of space syntax techniques in urban studies, proposes a curious mathematical duality: that urban space is locally metric but globally topo-geometric. Evidence for local metricity comes from such generic phenomena as grid intensification to reduce mean trip lengths in live centres, the fall of movement from attractors with metric distance, and the commonly observed decay of shopping with metric distance from an intersection. Evidence for global topo-geometry come from the fact that we need to utilise both the geometry and connectedness of the larger scale space network to arrive at configurational measures which optimally approximate movement patterns in the urban network. It might be conjectured that there is some threshold above which human being use some geometrical and topological representation of the urban grid rather than the sense of bodily distance to making movement decisions, but this is unknown. The discarding of metric properties in the large scale urban grid has, however, been controversial. Here we cast a new light on this duality. We show first some phenomena in which metric and topo-geometric measures of urban space converge and diverge, and in doing so clarify the relation between the metric and topo-geometric properties of urban spatial networks. We then show how metric measures can be used to create a new urban phenomenon: the partitioning of the background network of urban space into a network of semi-discrete patches by applying metric universal distance measures at different metric radii, suggesting a natural spatial area-isation of the city at all scales. On this basis we suggest a key clarification of the generic structure of cities: that metric universal distance captures exactly the formally and functionally local patchwork properties of the network, most notably the spatial differentiation of areas, while the top-geometric measures identifying the structure which overcomes locality and links the urban patchwork into a whole at different scales

The Impact of Spatial Parameters on Spatial Structuring

How is the spatial structure of a city organised at different scales, varying from connecting one street with its neighbouring streets to aggregating all the streets into a well‐structured city as a whole? In order to approach this question, this paper seeks to investigate the sequence of the streets encountered at a series of consecutive radii, from the point of view of any an individual street as a root space, termed as the embeddedness trajectory in this paper. If we clarify such embeddedness trajectory on which each individual street is progressively interconnected with all other streets with regards to its distance to them, this will enable us to better understand the spatial structuring of the whole city, because a collection of the embeddedness trajectories of all the streets of the city can illustrate the entire configuration of the city. Based on the axial and segment representations of the empirical cases, it examines the mathematical relation between node count at the radius of k (NC_Rk), measuring the accumulated number of the new streets encountered up to the radius of k, and radius (Rk). The two‐parameter Weibull relation seems to approximate the variation of node count with an increase of radius, which is expressed by the formula of NC_Rk ~ f(Rk; a, b), where ‘a’ is the scale parameter and ‘b’ is the shape parameter. Then, a strong linear correlation is found between the parameter of ‘a’ and mean topological depth (or mean metric depth) at the infinite radius, which suggests that as for each street, the number of the encountered streets up to a constricted radius is influenced by the mean topological/metric depth from that street to all other streets in the system. And meanwhile, the parameter of ‘b’ is correlated with the average embeddedness pace, meaning the average change rate of node count across all the radii. Thus, as for each street, its embeddedness trajectory is in general impacted on by the parameters of mean depth Rn and the embeddedness pace. From the above analyses, it suggests two things: first, the spatial structuring of a city is influenced by two spatial parameters: the average distance from all streets to all other streets and the average change rate of node count from the local to the global; second, the spatial structuring of all the parts of a city at the local and medium scales are constricted by the emergence of the whole structure – arising from the local structuring ‐ of the city at the global scale (measured by the infinite radius), which supports Hillier’s theory of the emergence of urban structure (Hillier, 1996, 2001)

Probing the superconducting ground state of the rare-earth ternary boride superconductors RRRuB2_2 (RR = Lu,Y) using muon-spin rotation and relaxation

The superconductivity in the rare-earth transition metal ternary borides $R$RuB$_2$ (where $R$ = Lu and Y) has been investigated using muon-spin rotation and relaxation. Measurements made in zero-field suggest that time-reversal symmetry is preserved upon entering the superconducting state in both materials; a small difference in depolarization is observed above and below the superconducting transition in both compounds, however this has been attributed to quasistatic magnetic fluctuations. Transverse-field measurements of the flux-line lattice indicate that the superconductivity in both materials is fully gapped, with a conventional s-wave pairing symmetry and BCS-like magnitudes for the zero-temperature gap energies. The electronic properties of the charge carriers in the superconducting state have been calculated, with effective masses $m^*/ m_\mathrm{e} =$ $9.8\pm0.1$ and $15.0\pm0.1$ in the Lu and Y compounds, respectively, with superconducting carrier densities $n_\mathrm{s} =$ ($2.73\pm0.04$) $\times 10^{28}$ m$^{-3}$ and ($2.17\pm0.02$) $\times 10^{28}$ m$^{-3}$. The materials have been classified according to the Uemura scheme for superconductivity, with values for $T_\mathrm{c}/T_\mathrm{F}$ of $1/(414\pm6)$ and $1/(304\pm3)$, implying that the superconductivity may not be entirely conventional in nature.Comment: 8 pages, 8 figure

Studies of the superconducting properties of Sn1-xInxTe (x=0.38 to 0.45) using muon-spin spectroscopy

The superconducting properties of Sn1-xInxTe (x = 0.38 to 0.45) have been studied using magnetization and muon-spin rotation or relaxation (muSR) measurements. These measurements show that the superconducting critical temperature Tc of Sn1-xInxTe increases with increasing x, reaching a maximum at around 4.8 K for x = 0.45. Zero-field muSR results indicate that time-reversal symmetry is preserved in this material. Transverse-field muon-spin rotation has been used to study the temperature dependence of the magnetic penetration depth lambda(T) in the mixed state. For all the compositions studied, lambda(T) can be well described using a single-gap s-wave BCS model. The magnetic penetration depth at zero temperature lambda(0) ranges from 500 to 580 nm. Both the superconducting gap Delta(0) at 0 K and the gap ratio Delta(0)/kBTc indicate that Sn1-xInxTe (x = 0.38 to 0.45) should be considered as a superconductor with intermediate to strong coupling.Comment: 7 pages, 6 figures, 3 table

On the sensitivity of HeI singlet lines to the FeIV model atom in O stars

Recent calculations and analyses of O star spectra have revealed discrepancies between theory and observations, and between different theoretical calculations, for the strength of optical HeI singlet transitions.We investigate the source of these discrepancies. Using a non-LTE radiative transfer code we have undertaken detailed test calculations for a range of O star properties. Our principal test model has parameters similar to those of the O9V star, 10 Lac. We show that the discrepancies arise from uncertainties in the radiation field in the HeI resonance transition near 584Angs. The radiation field at 584Angs. is influenced by model assumptions, such as the treatment of line-blanketing and the adopted turbulent velocity, and by the FeIV atomic data. It isshown that two FeIV transitions near 584Angs can have a substantial influence on the strength of the HeI singlet transitions. Because of the difficulty of modeling the HeI singlet lines, particularly in stars with solar metalicity, the HeI triplet lines should be preferred in spectral analyses. These lines are much less sensitive to model assumptions.Comment: 7 pages, 9 figures, accepted for publication in A&

On the changes in the physical properties of the ionized region around the Weigelt structures in Eta Carinae over the 5.54-yr spectroscopic cycle

We present HST/STIS observations and analysis of two prominent nebular structures around the central source of Eta Carinae, the knots C and D. The former is brighter than the latter for emission lines from intermediate or high ionization potential ions. The brightness of lines from intermediate and high ionization potential ions significantly decreases at phases around periastron. We do not see conspicuous changes in the brightness of lines from low ionization potential (<13.6 eV) that the total extinction towards the Weigelt structures is that the total extinction towards the Weigelt structures is AsubV =2/0. that the total extinction towards the Weigelt structures is AV = 2.0. Weigelt C and D are characterized by an electron density of that the total extinction towards the Weigelt structures is AV = 2.0. Weigelt C and D are characterized by an electron density of 10exp6.9 cm-3 that does not significantly change throughout the orbital cycle. The electron temperature varies from 5500 K (around periastron) to 7200 K (around apastron). The relative changes in the brightness of He I lines are well reproduced by the variations in the electron temperature alone. We found that, at phases around periastron, the electron temperature seems to be higher for Weigelt C than that of D. The Weigelt structures are located close to the Homunculus equatorial plane, at a distance of about 1240 AU from the central source. From the analysis of proper motion and age, the Weigelt complex can be associated with the equatorial structure called the Butterfly Nebula surrounding the central binary system.Comment: 19 pages, 18 figure