On the modeling of pedestrian motion

A model for the simulation of pedestrian flows and crowd dynamics has been developed. The model is based on a series of forces, such as: will forces (the desire to reach a place at a certain time), pedestrian collision avoidance forces, obstacle/wall avoidance forces; pedestrian contact forces, and obstacle/wall contact forces. Except for the will force, it is assumed that for any given pedestrian these forces are the result of only local (nearest neighbour) situations. The near-neighbour search problem is solved by an efficient incremental Delaunay triangulation that is updated at every timestep. In order to allow for general geometries a so-called background triangulation is used to carry all geographic information. At any given time the location of any given pedestrian is updated on this mesh. The results obtained to date show that the model performs well for standard benchmarks, and allows for typical crowd dynamics, such as lane forming, overtaking, avoidance of obstacles and panic behaviour.     

Estimating contact forces and pressure in a dense crowd: Microscopic and macroscopic models

This paper deals with the estimation of pressure at collisions times during the movement of a dense crowd. Through the non-smooth contact dynamics approach for rigid and deformable solids, proposed by Frémond and his collaborators, the value of pressure and contact forces at collisions points, generated through congestion or panic situation are estimated. Firstly, we propose a second-order microscopic model, in which the crowd is treated as a system of rigid solids. Contact forces are rigorously defined by taking into account multiple simultaneous contacts and the non-overlapping condition between pedestrians. We show that for a dense crowd, percussions can be seen as contact forces. Secondly, in order to overcome the restrictive hypothesis related to the geometric form adapted to model the pedestrian, a continuous equivalent approach is proposed where the crowd is modeled as a deformable solid, the pressure is then defined by the divergence of the stress tensor and calculated according to volume and surface constraints. This approach makes it possible to retain an admissible right-velocity, including both the non-local interactions between non-neighbor pedestrians and the choice of displacement strategy of each pedestrian. Finally, the comparison between the two proposed approaches and some other existing approaches are presented on several illustrative examples to estimate the contact forces between pedestrians.     

On the application of substochastic semigroup theory to fragmentation models with mass loss

A linear integro-differential equation modelling multiple fragmentation with inherent mass loss is investigated by means of substochastic semigroup theory. The existence of a semigroup is established and, under natural conditions on certain coefficients, the generator of this semigroup is identified. This yields, in particular, a validation of the formal mass-loss rate equation for the model.     

突发公共卫生事件情境下基于群体恐慌情绪的应急防护物资管理演化分析

针对突发公共卫生事件下民众对应急防护物资疯狂抢购的问题,以及衍生的供求失衡、价格暴涨、质量良莠不齐等问题,基于演化博弈理论构建政府、企业和民众三方参与的博弈模型。考虑到恐慌情绪对抢购行为的影响,首先刻画了民众在恐慌情绪下的防护物资购买价值;然后结合模型特征,运用非线性系统理论探讨了不同参与主体间的演化机制,得出不同情境下的博弈均衡点和稳定性;最后通过仿真模拟进一步分析不同恐慌强度对参与主体行为演化的影响。研究结果对识别突发公共卫生事件下应急防护物资管理的演化机理具有一定理论价值。     

Non-local first-order modelling of crowd dynamics: A multidimensional framework with applications

In this work a physical modelling framework is presented, describing the intelligent, non-local, and anisotropic behaviour of pedestrians. Its phenomenological basics and constitutive elements are detailed, and a qualitative analysis is provided. Within this common framework, two first-order mathematical models, along with related numerical solution techniques, are derived. The models are oriented to specific real world applications: a one-dimensional model of crowd–structure interaction in footbridges and a two-dimensional model of pedestrian flow in an underground station with several obstacles and exits. The noticeable heterogeneity of the applications demonstrates the significance of the physical framework and its versatility in addressing different engineering problems. The results of the simulations point out the key role played by the physiological and psychological features of human perception on the overall crowd dynamics.     

Lattice hydrodynamic model of pedestrian flow considering the asymmetric effect

The original lattice hydrodynamic model of traffic flow is extended to single-file pedestrian movement at middle and high density by considering asymmetric interaction (i.e., attractive force and repulsive force). A new optimal velocity function is introduced to depict the complex behaviors of pedestrian movement. The stability condition of this model is obtained by using the linear stability theory. It is shown that the modified optimal velocity function has a remarkable influence on the neutral stability curve and the pedestrian phase transitions. The modified Korteweg-de Vries (mKdV) equation near the critical point is derived by applying the reductive perturbation method, and its kink-antikink soliton solution can better describe the stop-and-go phenomenon of pedestrian flow. From the density profiles, it can be found that the asymmetric interaction is more efficient than the symmetric interaction in suppressing the pedestrian jam. The numerical results are consistent with the theoretical analysis.     

Development and experimental validation of a control-oriented Diesel engine model for fuel consumption and brake torque predictions

This article describes the development and experimental validation of a control-oriented, real-time capable, Diesel engine instantaneous fuel consumption and brake torque model under warmed-up conditions with only two inputs: torque request and the engine speed and no other measurements. Such a model, with the capability of reliably and computationally efficiently estimating the aforementioned variables at both steady-state and transient engine-operating conditions, can be utilized in the context of real-time control and optimization of hybrid power train systems. Although Diesel engine dynamics are highly non-linear and very complex, by considering the Diesel engine and its control system, that is, engine control unit together as an entity, it becomes possible to predict the engine instantaneous fuel consumption and torque based on only those two inputs. A synergy between different modelling methodologies including physically based grey-box and data-driven black-box approaches were integrated in the Diesel engine model. The fuelling and torque predictions have been validated by means of experimental data from a medium-duty Diesel engine at both steady-state and transient operations, including engine start-ups and shutdowns.     

Dynamic navigation field in the social force model for pedestrian evacuation

This paper presents a generalized walking cost distribution to determine a dynamic navigation field in the social force model for pedestrian evacuation. The local walking cost per unit distance of movement includes the cost associated with travel time and other additional costs incurred by pedestrians to avoid colliding with obstacles in a dynamic environment. In the dynamic navigation field, pedestrians expect to choose an optimal path with the lowest walking cost to reach their target destination reactively based on available instantaneous information. The social force model with the dynamic navigation field is validated by comparing the simulation results with empirical observations. The fundamental diagrams for observations and simulation data agree well, which indicates the effectiveness of the model. Numerical results show that the model with the dynamic navigation field can reproduce typical stages of the dynamics of pedestrian evacuation, such as self-organized arching and queuing phenomena, and can capture the route choice and exit choice behaviors of pedestrians during the evacuation process. Compared to the model with the static navigation field, the model with the dynamic navigation field can reduce the total evacuation time of the room and save the required CPU time for a large group of pedestrians. Furthermore, the strong tendency to avoid local high-density regions (i.e., minimizing collisions) can also reduce the total evacuation time under the same conditions.     

Turing pattern formation in a predator–prey system with cross diffusion

The paper explores the impacts of cross-diffusion on the formation of spatial patterns in a ratio-dependent predator–prey system with zero-flux boundary conditions. Our results show that under certain conditions, cross-diffusion can trigger the emergence of spatial patterns which is however impossible under the same conditions when cross-diffusion is absent. We give a rigorous proof that the model has at least one spatially heterogenous steady state by means of the Leray–Schauder degree theory. In addition, numerical simulations are performed to visualize the complex spatial patterns.     

A stochastic model for internal HIV dynamics

In this paper we analyse a stochastic model representing HIV internal virus dynamics. The stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modelling. We show that the model established in this paper possesses non-negative solutions as this is essential in any population dynamics model. We also carry out analysis on the asymptotic behaviour of the model. We approximate one of the variables by a mean reverting process and find out the mean and variance of this process. Numerical simulations conclude the paper.     

Global dynamics of reaction–diffusion systems with delays

Taking the effect of spatial diffusion into account, we introduce an exponential ordering and give sufficient conditions under which reaction–diffusion systems with delays generate monotone semi-flows on a suitable phase space even if they are not quasi-monotone. The powerful theory of monotone semi-flows is applied to describe the threshold dynamics for a nonlocal delayed reaction–diffusion system modelling the spread of bacterial infections.     

Hybrid systems: Modelling and analysis using emergent dynamics

In this paper, we discuss modelling and analysis of hybrid systems with physical interaction dynamics. Such systems are typically considered complex and they are modelled using abstractions. Abstractions may, however, unintentionally exclude critical details, leading to partial or false results. Therefore, we study here use of a particle system in modelling and analysis. The novelty of the particle system is that it is designed to reveal interaction dynamics as emergent dynamics; thus, supporting analysis of complex and intricate interaction dynamics with acceptable modelling effort. As the main contribution, we formalize the particle system, and use it to model and analyze hybrid systems, both mechanical and biological, with nontrivial interaction dynamics.     

Generalized M/G/C/C state dependent queueing models and pedestrian traffic flows

The generality and usefulness ofM/G/C/C state dependent queueing models for modelling pedestrian traffic flows is explored in this paper. We demonstrate that the departure process and the reversed process of these generalizedM/G/C/C queues is a Poisson process and that the limiting distribution of the number of customers in the queue depends onG only through its mean. Consequently, the models developed in this paper are useful not only for the analysis of pedestrian traffic flows, but also for the design of the physical systems accommodating these flows. We demonstrate how theM/G/C/C state dependent model is incorporated into the modelling of large scale facilities where the blocking probabilities in the links of the network can be controlled. Finally, extensions of this work to queueing network applications where blocking cannot be controlled are also presented, and we examine an approximation technique based on the expansion method for incorporating theseM/G/C/C queues in series, merge, and splitting topologies of these networks.     

On a kinetic theory approach to modelling degradation phenomena in conservation sciences

This paper deals with the modelling of degradation phenomena for works of art under the action applied by external agents. The analysis is based on a suitable development of the methods of the kinetic theory for active particles. The model consists in an evolution equation for the probability distribution of the degradation stage. The interpretation of empirical data provides the identification of the parameters of the model and a quantitative prediction of degradation events.     

Linear and nonlinear dynamics of a circular cylindrical shell connected to a rigid disk

The dynamics of a circular cylindrical shell carrying a rigid disk on the top and clamped at the base is investigated. The Sanders–Koiter theory is considered to develop a nonlinear analytical model for moderately large shell vibration. A reduced order dynamical system is obtained using Lagrange equations: radial and in-plane displacement fields are expanded by using trial functions that respect the geometric boundary conditions.The theoretical model is compared with experiments and with a finite element model developed with commercial software: comparisons are carried out on linear dynamics.The dynamic stability of the system is studied, when a periodic vertical motion of the base is imposed. Both a perturbation approach and a direct numerical technique are used. The perturbation method allows to obtain instability boundaries by means of elementary formulae; the numerical approach allows to perform a complete analysis of the linear and nonlinear response.     

Simulation with system dynamics and fuzzy reasoning of a tax policy to reduce CO2 emissions in the residential sector

This methodological paper presents a planning and control methodology illustrated by a simplified case study on the carbon-tax design in the residential sector. The first objective is to show how to simulate with system dynamics the consumers’ behaviour and the continuous tax-control mechanism depending on few important feedbacks, often ignored in static macroeconomic modelling. A second objective is to show how to aggregate external data driving this model and stemming from different sources with various credibility levels. This is realised by means of fuzzy-reasoning techniques incorporated into the system-dynamics model.     

具有年龄结构和约束的群落系统的最优收获

研究一类有年龄结构和相互作用的两种群构成的群落系统的最优收获问题,要求控制过程结束时的种群状态充分接近预先指定的年龄分布.证明了最优控制的存在性,运用Dubovitskii-Milyutin理论导出了最优性条件.这种处理方法为研究连续年龄分布下种群收获问题提供了统一框架.     

Challenges of operations research practice in agricultural value chains

Operations research (OR) methodologies in optimization have been extensivelyapplied to problems in different agricultural value chains in recent years. Wetake a critical stock take of such applications to date, and reflect on theircontribution to value chain sustainability and resilience. The stock take showsthat the rate of industry or policy adoption has been limited, partly due to thecomplex interactions across the segments of agricultural value chains, and themathematical representation being different to the way the decision makerunderstands the problem. OR practice in agriculture is also being asked to covergreater spatial scales and engage more stakeholders, and is required to embraceresilience and sustainability objectives. A single-minded focus on optimizingparts of these complex systems without considering the whole system is no longeradequate, and new methods and approaches are required. Complex systems sciencemethods are being applied to analyse the dynamics of complexsocial–ecological systems, and are starting to find a home in industrialsupply chain analysis. We demonstrate how three complex system methods,agent-based modelling, dynamical systems modelling and network analysis, can beapplied to agricultural value chains as a means of gaining insights into systemdynamics under different and dynamic conditions. The relevance and utility of ORin ensuring the success of agricultural value chains into the future willrequire practitioners to understand and model value chains as complex adaptivesystems.     

Investigating pedestrian navigation in indoor open space environments using big data

Reliable empirical data are required to understand and model realistic pedestrian navigation behaviours at public crowd-gathering places such as public transportation hubs and shopping malls. Naturalistic walking big data could provide reliable information for investigating realistic pedestrian behaviours and to overcome critical shortcomings of the data collected through controlled laboratory experiments. In this work, we investigate pedestrian navigation in indoor open spaces using naturalistic walking big data collected through video recordings. The extracted data include 299,082 trajectories of individual pedestrians who navigated through the atrium of the Informatics Forum building of the University of Edinburgh. We compare several pedestrian vector fields by calibrating several cellular automaton (CA) models and we finally identify a generalized vector field for pedestrians who are walking in indoor open space environments under normal walking conditions.The output of this study could be useful in enhancing CA-based pedestrian simulation models by representing pedestrian navigation as well as route-choice behaviours more realistically in those models. Simulation tools based on such enhanced models can facilitate practitioners, such as public building designers, to optimize designs considering naturalistic pedestrian behaviours in open spaces.