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

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.

Quasi-static cracks and minimal energy surfaces

We compare the roughness of minimal energy(ME) surfaces and scalar ``quasi-static'' fracture surfaces(SQF). Two dimensional ME and SQF surfaces have the same roughness scaling, w sim L^zeta (L is system size) with zeta = 2/3. The 3-d ME and SQF results at strong disorder are consistent with the random-bond Ising exponent zeta (d >= 3) approx 0.21(5-d) (d is bulk dimension). However 3-d SQF surfaces are rougher than ME ones due to a larger prefactor. ME surfaces undergo a ``weakly rough'' to ``algebraically rough'' transition in 3-d, suggesting a similar behavior in fracture.Comment: 7 pages, aps.sty-latex, 7 figure

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

Dynamic decision making for situational awareness using drones: Requirements, identification and comparison of decision support methods

Decision makers increasingly operate in real-time information-rich environments, where limited time is available for interpreting data to inform decisions. These environments are driven by static or mobile sensing devices that can provide numerous dynamic data points. A prominent approach in this space is to utilise drones, which can be deployed to gather targeted information. However, deciding how best to deploy available drones is nontrivial, and stands to benefit from decision support aids that plan routes. Such a system must operate under time constraints created by the changing attributes of routes as the situation unfolds. This study describes a dynamic decision support system (DSS) for situational awareness with drones. The system applies Multi-Criteria Decision Making (MCDM) methods within a dynamic genetic algorithm to provide a continuously revised ranking of routes. Five desiderata for dynamic decision support are presented. It is shown how a dynamic DSS can be equipped with declarative specification of preferences (Desiderata 1), dynamic revision of recommendations (Desiderata 2), and high diversity of options (Desiderata 3). The study then compares four MCDM methods, namely the Weighted Product Model (WPM), the Analytic Hierarchy Process (AHP), the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), and the Preference Ranking Organization METHod for Enrichment Evaluation (PROMETHEE), with regards to how consistently they trade-off between criteria (Desiderata 4) and the stability of results under small changes to criteria values (Desiderata 5). To evaluate the trade-offs between criteria we analyse the smoothness of change in criteria outcomes as criteria weightings increase for each algorithm. The outcomes are calculated by automating the selection of routes in a case study that applies drones to the task of harbour management. The stability of results for the different MCDM methods are compared. Perturbations were applied to sets of routes ranked by each algorithm then each algorithm was reapplied and the magnitude of the changes in ranking was assessed. Overall, TOPSIS was found to be the algorithm which made the most consistent trade-offs between criteria, only under-performing another algorithm with respect to a single criterion. AHP and WPM were the next most consistent algorithms and PROMETHEE was the least consistent algorithm. TOPSIS was also found to be the most stable method under small changes to criteria values. AHP was the second most stable, followed by PROMETHEE and WPM respectively. The results show that TOPSIS achieves the best result for both Desiderata 4 and 5 and consequently the study finds TOPSIS to be an appropriate MCDM method for dynamic decision support.<br/

Extremal statistics in the energetics of domain walls

We study at T=0 the minimum energy of a domain wall and its gap to the first excited state concentrating on two-dimensional random-bond Ising magnets. The average gap scales as $\Delta E_1 \sim L^\theta f(N_z)$, where $f(y) \sim [\ln y]^{-1/2}$, $\theta$ is the energy fluctuation exponent, $L$ length scale, and $N_z$ the number of energy valleys. The logarithmic scaling is due to extremal statistics, which is illustrated by mapping the problem into the Kardar-Parisi-Zhang roughening process. It follows that the susceptibility of domain walls has also a logarithmic dependence on system size.Comment: Accepted for publication in Phys. Rev.

Scaling of interfaces in brittle fracture and perfect plasticity

The roughness properties of two-dimensional fracture surfaces as created by the slow failure of random fuse networks are considered and compared to yield surfaces of perfect plasticity with similar disorder. By studying systems up to a linear size L=350 it is found that in the cases studied the fracture surfaces exhibit self-affine scaling with a roughness exponent close to 2/3, which is asymptotically exactly true for plasticity though finite-size effects are evident for both. The overlap of yield or minimum energy and fracture surfaces with exactly the same disorder configuration is shown to be a decreasing function of the system size and to be of a rather large magnitude for all cases studied. The typical ``overlap cluster'' length between pairs of such interfaces converges to a constant with $L$ increasing.Comment: Accepted for publication in Phys. Rev.

Minimum spanning trees on random networks

We show that the geometry of minimum spanning trees (MST) on random graphs is universal. Due to this geometric universality, we are able to characterise the energy of MST using a scaling distribution ($P(\epsilon)$) found using uniform disorder. We show that the MST energy for other disorder distributions is simply related to $P(\epsilon)$. We discuss the relationship to invasion percolation (IP), to the directed polymer in a random media (DPRM) and the implications for the broader issue of universality in disordered systems.Comment: 4 pages, 3 figure

Random-field Ising model on complete graphs and trees

We present exact results for the critical behavior of the RFIM on complete graphs and trees, both at equilibrium and away from equilibrium, i.e., models for hysteresis and Barkhausen noise. We show that for stretched exponential and power law distributions of random fields the behavior on complete graphs is non-universal, while the behavior on Cayley trees is universal even in the limit of large co-ordination.Comment: 4 pages, 4 figure

Temporally disordered Ising models

We present a study of the influence of different types of disorder on systems in the Ising universality class by employing both a dynamical field theory approach and extensive Monte Carlo simulations. We reproduce some well known results for the case of quenched disorder (random temperature and random field), and analyze the effect of four different types of time-dependent disorder scarcely studied so far in the literature. Some of them are of obvious experimental and theoretical relevance (as for example, globally fluctuating temperatures or random fields). All the predictions coming from our field theoretical analysis are fully confirmed by extensive simulations in two and three dimensions, and novel qualitatively different, non-Ising transitions are reported. Possible experimental setups designed to explore the described phenomenologies are also briefly discussed.Comment: Submitted to Phys. Rev. E. Rapid Comm. 4 page