An algorithmic definition of the axial map

The fewest-line axial map, often simply referred to as the 'axial map, is one of the primary tools of space syntax. Its natural language definition has allowed researchers to draw consistent maps that present a concise description of architectural space; it has been established that graph measures obtained from the map are useful for the analysis of pedestrian movement patterns and activities related to such movement: for example, the location of services or of crime. However, the definition has proved difficult to translate into formal language by mathematicians and algorithmic implementers alike. This has meant that space syntax has been criticised for a lack of rigour in the definition of one of its fundamental representations. Here we clarify the original definition of the fewest-line axial map and show that it can be implemented algorithmically. We show that the original definition leads to maps similar to those currently drawn by hand, and we demonstrate that the differences between the two may be accounted for in terms of the detail of the algorithm used. We propose that the analytical power of the axial map in empirical studies derives from the efficient representation of key properties of the spatial configuration that it captures

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

Type-I superconductivity in noncentrosymmetric superconductor AuBe

The noncentrosymmetric superconductor AuBe have been investigated using the magnetization, resistivity, specific heat, and muon-spin relaxation/rotation measurements. AuBe crystallizes in the cubic FeSi-type B20 structure with superconducting transition temperature observed at $T_{c}$ = 3.2 $\pm$ 0.1 K. The low-temperature specific heat data, $C_{el}$(T), indicate a weakly-coupled fully gapped BCS superconductivity with an isotropic energy gap 2$\Delta(0)/k_{B}T_{c}$ = 3.76, which is close to the BCS value of 3.52. Interestingly, type-I superconductivity is inferred from the $\mu$SR measurements, which is in contrast with the earlier reports of type-II superconductivity in AuBe. The Ginzburg-Landau parameter is $\kappa_{GL}$ = 0.4 $<$ 1/$\sqrt{2}$. The transverse-field $\mu$SR data transformed in the maximum entropy spectra depicting the internal magnetic field probability distribution, P(H), also confirms the absence of the mixed state in AuBe. The thermodynamic critical field, $H_{c}$, calculated to be around 259 Oe. The zero-field $\mu$SR results indicate that time-reversal symmetry is preserved and supports a spin-singlet pairing in the superconducting ground state.Comment: 9 pages, 9 figure

Further Criteria for the Existence of Steady Line-Driven Winds

In Paper I, we showed that steady line-driven disk wind solutions can exist by using "simple" models that mimic the disk environment. Here I extend the concepts introduced in Paper I and discuss many details of the analysis of the steady/unsteady nature of 1D line-driven winds. This work confirms the results and conclusions of Paper I, and is thus consistent with the steady nature of the 1D streamline line-driven disk wind models of Murray and collaborators and the 2.5D line-driven disk wind models of Pereyra and collaborators. When including gas pressures effects, as is routinely done in time-dependent numerical models, I find that the spatial dependence of the nozzle function continues to play a key role in determining the steady/unsteady nature of supersonic line-driven wind solutions. I show here that the existence/nonexistence of local wind solutions can be proved through the nozzle function without integrating the equation of motion. This work sets a detailed framework with which we will analyze, in a following paper, more realistic models than the "simple" models of Paper I.Comment: 30 pages, 5 figures, accepted for publication by The Astrophysical Journa

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