Pedestrian demand modelling of large cities: an applied example from London

This paper introduces a methodology for the development of city wide pedestrian demand models and shows its application to London. The approach used for modelling is Multiple Regression Analysis of independent variables against the dependent variable of observed pedestrian flows. The test samples were from manual observation studies of average total pedestrian flow per hour on 237 sample sites. The model will provide predicted flow values for all 7,526 street segments in the 25 square kilometres of Central London. It has been independently validated by Transport for London and is being tested against further observation data. The longer term aim is to extend the model to the entire greater London area and to incorporate additional policy levers for use as a transport planning and evaluation tool

A periodic elastic medium in which periodicity is relevant

We analyze, in both (1+1)- and (2+1)- dimensions, a periodic elastic medium in which the periodicity is such that at long distances the behavior is always in the random-substrate universality class. This contrasts with the models with an additive periodic potential in which, according to the field theoretic analysis of Bouchaud and Georges and more recently of Emig and Nattermann, the random manifold class dominates at long distances in (1+1)- and (2+1)-dimensions. The models we use are random-bond Ising interfaces in hypercubic lattices. The exchange constants are random in a slab of size $L^{d-1} \times \lambda$ and these coupling constants are periodically repeated along either {10} or {11} (in (1+1)-dimensions) and {100} or {111} (in (2+1)-dimensions). Exact ground-state calculations confirm scaling arguments which predict that the surface roughness $w$ behaves as: $w \sim L^{2/3}, L \ll L_c$ and $w \sim L^{1/2}, L \gg L_c$, with $L_c \sim \lambda^{3/2}$ in $(1+1)$-dimensions and; $w \sim L^{0.42}, L \ll L_c$ and $w \sim \ln(L), L \gg L_c$, with $L_c \sim \lambda^{2.38}$ in $(2+1)$-dimensions.Comment: Submitted to Phys. Rev.

The origin of the grooves on Phobos

Various theories for the long, linear depressions on the surface of Phobos are reviewed. Imagery from Viking Orbiters is used to map the surface distribution of the grooves, study their morphology, and date them by means of the density of superimposed impact craters. Data is presented which tends to support the hypothesis that the deep-seated fracturing was caused by a large, nearly catastrophic cratering event. It is suggested that the grooves were produced during the creation of the Stickney crater, rather than as the result of tidal stresses induced by Mars or by drag forces during the hypothetical capture of the satellite by Mars

Intermittence and roughening of periodic elastic media

We analyze intermittence and roughening of an elastic interface or domain wall pinned in a periodic potential, in the presence of random-bond disorder in (1+1) and (2+1) dimensions. Though the ensemble average behavior is smooth, the typical behavior of a large sample is intermittent, and does not self-average to a smooth behavior. Instead, large fluctuations occur in the mean location of the interface and the onset of interface roughening is via an extensive fluctuation which leads to a jump in the roughness of order $\lambda$, the period of the potential. Analytical arguments based on extreme statistics are given for the number of the minima of the periodicity visited by the interface and for the roughening cross-over, which is confirmed by extensive exact ground state calculations.Comment: Accepted for publication in Phys. Rev.

Phobos: Photometry and origin of dark markings on crater floors

High resolution photographs of Phobos taken during close flybys of Viking Orbiter 1 reveal many dark patches on the floors of several craters. The apparently dark material is only prominent at large phase angles. Analysis of the photometric properties indicates that the dark patches represent areas of unusually rough textures whose reflectance near zero phase is similar to that of the mean surface (approximately 6 percent in the visible), but whose phase curve is much steeper. The contrast of such areas is less than 10 percent zero phase but approaches 100 percent near phase angles of 90 degrees. It is proposed that these intricately textured deposits represent patches of vesticular impact melt

Structural compliance, misfit strain and stripe nanostructures in cuprate superconductors

Structural compliance is the ability of a crystal structure to accommodate variations in local atomic bond-lengths without incurring large strain energies. We show that the structural compliance of cuprates is relatively small, so that short, highly doped, Cu-O-Cu bonds in stripes are subject to a tensile misfit strain. We develop a model to describe the effect of misfit strain on charge ordering in the copper oxygen planes of oxide materials and illustrate some of the low energy stripe nanostructures that can result.Comment: 4 pages 5 figure

Disorder-induced roughening in the three-dimensional Ising model

Using an exact method, we numerically study the zero-temperature roughness of interfaces in the random bond, cubic lattice, Ising model (of size L3, with L<~80). Interfaces oriented along the {100} direction undergo a roughening transition from a weak disorder phase, which is almost flat, to a strong disorder phase with interface width w∼cL0.42 (c is a function of the disorder). For random dilution we find the roughening threshold p∗=0.89±0.01 and c∼p∗−p for p<~p∗ (p is the volume fraction of present bonds). In contrast {111} interfaces are algebraically rough for all disorder.Peer reviewe

Self-Attracting Walk on Lattices

We have studied a model of self-attracting walk proposed by Sapozhnikov using Monte Carlo method. The mean square displacement $\sim t^{2\nu}$ and the mean number of visited sites $\sim t^{k}$ are calculated for one-, two- and three-dimensional lattice. In one dimension, the walk shows diffusive behaviour with $\nu=k=1/2$. However, in two and three dimension, we observed a non-universal behaviour, i.e., the exponent $\nu$ varies continuously with the strength of the attracting interaction.Comment: 6 pages, latex, 6 postscript figures, Submitted J.Phys.

Strength Reduction in Electrical and Elastic Networks

Particular aspects of problems ranging from dielectric breakdown to metal insu- lator transition can be studied using electrical o elastic networks. We present an expression for the mean breakdown strength of such networks.First, we intro- duce a method to evaluate the redistribution of current due to the removal of a finite number of elements from a hyper-cubic network of conducatances.It is used to determine the reduction of breakdown strength due to a fracture of size $\kappa$.Numerical analysis is used to show that the analogous reduction due to random removal of elements from electrical and elastic networks follow a similar form.One possible application, namely the use of bone density as a diagnostic tools for osteorosporosis,is discussed.Comment: one compressed file includes: 9 PostScrpt figures and a text fil