22 research outputs found
Towards Real-Time Crowd Simulation Under Uncertainty Using an Agent-Based Model and an Unscented Kalman Filter
Agent-based modelling (ABM) is ideally suited to simulating crowds of people as it captures the complex behaviours and interactions between individuals that lead to the emergence of crowding. Currently, it is not possible to use ABM for real-time simulation due to the absence of established mechanisms for dynamically incorporating real-time data. This means that, although models are able to perform useful offline crowd simulations, they are unable to simulate the behaviours of crowds in real time. This paper begins to address this drawback by demonstrating how a data assimilation algorithm, the Unscented Kalman Filter (UKF), can be used to incorporate pseudo-real data into an agent-based model at run time. Experiments are conducted to test how well the algorithm works when a proportion of agents are tracked directly under varying levels of uncertainty. Notably, the experiments show that the behaviour of unobserved agents can be inferred from the behaviours of those that are observed. This has implications for modelling real crowds where full knowledge of all individuals will never be known. In presenting a new approach for creating real-time simulations of crowds, this paper has important implications for the management of various environments in global cities, from single buildings to larger structures such as transportation hubs, sports stadiums, through to entire city regions
Continuation for thin film hydrodynamics and related scalar problems
This chapter illustrates how to apply continuation techniques in the analysis
of a particular class of nonlinear kinetic equations that describe the time
evolution through transport equations for a single scalar field like a
densities or interface profiles of various types. We first systematically
introduce these equations as gradient dynamics combining mass-conserving and
nonmass-conserving fluxes followed by a discussion of nonvariational amendmends
and a brief introduction to their analysis by numerical continuation. The
approach is first applied to a number of common examples of variational
equations, namely, Allen-Cahn- and Cahn-Hilliard-type equations including
certain thin-film equations for partially wetting liquids on homogeneous and
heterogeneous substrates as well as Swift-Hohenberg and Phase-Field-Crystal
equations. Second we consider nonvariational examples as the
Kuramoto-Sivashinsky equation, convective Allen-Cahn and Cahn-Hilliard
equations and thin-film equations describing stationary sliding drops and a
transversal front instability in a dip-coating. Through the different examples
we illustrate how to employ the numerical tools provided by the packages
auto07p and pde2path to determine steady, stationary and time-periodic
solutions in one and two dimensions and the resulting bifurcation diagrams. The
incorporation of boundary conditions and integral side conditions is also
discussed as well as problem-specific implementation issues
Homoclinic snaking near the surface instability of a polarisable fluid
The following Matlab 2014a codes have been stored for the manuscript of the same name: - Computation of the Maxwell curve in Figure 7 - Computation of the bifurcation curves for domain covering hexagons, planar fronts, hexagon patches and rhomboid patches. - Plots converting numerical data in non-dimensional units back to dimensional units
Efficient numerical continuation and stability analysis of spatiotemporal quadratic optical solitons
Efficient numerical continuation and stability analysis of spatiotemporal quadratic optical solitons
A numerical method is set out which efficiently computes stationary (z-independent) two- and three-dimensional spatiotemporal solitons in second-harmonic-generating media. The method relies on a Chebyshev decomposition with an infinite mapping, bunching the collocation points near the soliton core. Known results for the type-I interaction are extended and a stability boundary is found by two- parameter continuation as defined by the Vakhitov-Kolokolov criteria. The validity of this criterion is demonstrated in (2+1) dimensions by simulation and direct calculation of the linear spectrum. The method has wider applicability for general soliton-bearing equations in (2+1) and (3+1) dimensions.</p
Data for Exploring data assimilation and forecasting issues for an urban crime model
Matlab codes for carrying out the data assimilation described in the corresponding pape
Exploring data assimilation and forecasting issues for an urban crime model
Data assimilation code
On the interaction of uni-directional and bi-directional buckling of a plate supported by an elastic foundation
This is the author accepted manuscript. The final version is available from the Royal Society via the DOI in this record.A thin flat rectangular plate supported on its edges and subjected to in-plane loading exhibits stable post-buckling behaviour. However, the introduction of a nonlinear (softening) elastic foundation may cause the response to become unstable. Here the post-buckling of such a structure is investigated and several important phenomena are identified, including the transition of patterns from stripes to spots and back again. The interaction between these forms is of importance for understanding the possible post-buckling behaviours of this structural system. In addition, both periodic and some localized responses are found to exist as the dimensions of the plate are increased and this becomes relevant when the characteristic wavelengths of the buckle pattern are small compared to the size of the plate. Potential application of the model range from macroscopic industrial manufacturing of structural elements to the understanding of micro- and nano-scale deformations in materials
Linear and sigmoidal fuzzy cognitive maps: An analysis of fixed points
Fuzzy cognitive mapping is commonly used as a participatory modelling technique whereby stakeholders create a semi-quantitative model of a system of interest. This model is often turned into an iterative map, which should (ideally) have a unique stable fixed point. Several methods of doing this have been used in the literature but little attention has been paid to differences in output such different approaches produce, or whether there is indeed a unique stable fixed point. In this paper, we seek to highlight and address some of these issues. In particular we state conditions under which the ordering of the variables at stable fixed points of the linear fuzzy cognitive map (iterated to) is unique. Also, we state a condition (and an explicit bound on a parameter) under which a sigmoidal fuzzy cognitive map is guaranteed to have a unique fixed point, which is stable. These generic results suggest ways to refine the methodology of fuzzy cognitive mapping. We highlight how they were used in an ongoing case study of the shift towards a bio-based economy in the Humber region of the UK. © 2013 Elsevier B.V. All rights reserved
Linear and sigmoidal fuzzy cognitive maps: An analysis of fixed points
Fuzzy cognitive mapping is commonly used as a participatory modelling technique whereby stakeholders create a semi-quantitative model of a system of interest. This model is often turned into an iterative map, which should (ideally) have a unique stable fixed point. Several methods of doing this have been used in the literature but little attention has been paid to differences in output such different approaches produce, or whether there is indeed a unique stable fixed point. In this paper, we seek to highlight and address some of these issues. In particular we state conditions under which the ordering of the variables at stable fixed points of the linear fuzzy cognitive map (iterated to) is unique. Also, we state a condition (and an explicit bound on a parameter) under which a sigmoidal fuzzy cognitive map is guaranteed to have a unique fixed point, which is stable. These generic results suggest ways to refine the methodology of fuzzy cognitive mapping. We highlight how they were used in an ongoing case study of the shift towards a bio-based economy in the Humber region of the UK. © 2013 Elsevier B.V. All rights reserved