Time-Evolving Measures and Macroscopic Modeling of Pedestrian Flow

This paper introduces a new model of pedestrian flow, formulated within a measure-theoretic framework. It consists of a macroscopic representation of the system via a family of measures which, pushed forward by some flow maps, provide an estimate of the space occupancy by pedestrians at successive times. From the modeling point of view, this setting is particularly suitable for treating nonlocal interactions among pedestrians, obstacles, and wall boundary conditions. In addition, the analysis and numerical approximation of the resulting mathematical structures, which are the principal objectives of this work, follow more easily than for models based on standard hyperbolic conservation laws.     

Numerical simulation of pedestrian flow past a circular obstruction

In this paper, a revisiting Hughes' dynamic continuum model is used to investigate and predict the essential macroscopic characteristics of pedestrian flow, such as flow, density and average speed, in a two dimensional continuous walking facility scattered with a circular obstruction. It is assumed that pedestrians prefer to walk a path with the lowest instantaneous travel cost from origin to destination, under the consideration of the current traffic conditions and the tendency to avoid a high-density region and an obstruction. An algorithm for the pedestrian flow model is based on a cellcentered finite volume method for a scalar conservation law equation, a fast sweeping method for an Eikonal-type equation and a second-order TVD Runge-Kutta method for the time integration on unstructured meshes. Numerical results demonstrate the effectiveness of the algorithm. It is verified that density distribution of pedestrian flow is influenced by the position of the obstruction and the path-choice behavior of pedestrians.     

On a model for the pedestrians-induced lateral vibrations of footbridges

We study the synchronization of the pedestrians motion with the lateral motion of slender footbridges, which attracted the attention of researchers mainly after the Millennium Bridge well known event. We consider a bridge-pedestrians model developed by Strogatz et al. To better understand some aspects of the underlying mechanical phenomena and to increase the agreement of the model results to the effective behaviour of the walkers (as observed during the Millennium Bridge’s opening day and during Arup’s tests on site) we have introduced some modifications to the model and we have performed extensive parametric investigations, supported by many numerical simulations. Our approach is therefore computational, by means of a self-made code. This permits to highlight the parameters which mainly affect the trigger and the development of the phenomenon of synchronous lateral excitation, thus allowing a good understanding of the physical event and an evaluation of the engineering reliability of the Strogatz et al. model.     

基于连续模型的人员疏散仿真分析

行人流连续模型直观地反映人群疏散过程中的疏散特征,本文基于行人流连续模型。研究行人在典型疏散场景下的疏散特征．在COMSOL中建立行人流连续模型及其方程,通过编写MATLAB代码,实现了连续模型及其循环求解框架．利用快速扫描法求解Eikonal方程得到背景场值,在每一步迭代循环中将背景场值作为模型的初始变量导入,调用COMSOL计算模块求解模型的瞬态控制方程．通过两个标准算例,重现了典型的行人流自组织现象,验证了连续模型的合理性．结果表明,本文的疏散仿真分析模型和计算程序是可靠的,疏散仿真分析可以为实际工程中的人员疏散方案的制定以及平面设计与安全布置等方面提供技术支撑．     

A new lattice hydrodynamic model for bidirectional pedestrian flow considering the visual field effect

In this paper, a new lattice hydrodynamic model for bidirectional pedestrian flow is proposed by considering the pedestrian’s visual field effect. The stability condition of this model is obtained by the linear stability analysis. The mKdV equation near the critical point is derived to describe the density wave of pedestrian jam by applying the reductive perturbation method. The phase diagram indicates that the phase transition occurs among the freely moving phase, the coexisting phase, and the uniformly congested phase below the critical point \(a_c\) . Furthermore, the analytical results show that the visual field effect plays an important role in jamming transition. To take into account the visual information about the motion of more pedestrian in front can improve efficiently the stability of pedestrian system. In addition, the numerical simulations are in accordance with the theoretical analysis.     

An immersed‐boundary finite‐volume method for direct simulation of flows with suspended paramagnetic particles

In the present study, we have proposed an immersed‐boundary finite‐volume method for the direct numerical simulation of flows with inertialess paramagnetic particles suspended in a nonmagnetic fluid under an external magnetic field without the need for any model such as the dipole–dipole interaction. In the proposed method, the magnetic field (or force) is described by the numerical solution of the Maxwell equation without current, where the smoothed representation technique is employed to tackle the discontinuity of magnetic permeability across the particle–fluid interface. The flow field, on the other hand, is described by the solution of the continuity and momentum equations, where the discrete‐forcing‐based immersed‐boundary method is employed to satisfy the no‐slip condition at the interface. To validate the method, we performed numerical simulations on the two‐dimensional motion of two and three paramagnetic particles in a nonmagnetic fluid subjected to an external uniform magnetic field and then compared the results with the existing finite‐element and semi‐analytical solutions. Comparison shows that the proposed method is robust in the direct simulation of such magnetic particulate flows. This method can be extended to more general flows without difficulty: three‐dimensional particulate flows, flows with a great number of particles, or flows under an arbitrary external magnetic field. Copyright © 2010 John Wiley & Sons, Ltd.     

On the steady solution of linear advection problems in steady recirculating flows

Numerical modelling of non-Newtonian flows typically involves the coupling between equations of motion characterized by an elliptic behaviour, and the fluid constitutive equation, which is an advection equation linked to the fluid history. In this paper we prove that linear steady advection problems in steady recirculating flows have only one solution when the kinematics differs from a rigid motion. We also give a numerical procedure to determine this steady solution. We will describe this numerical procedure for two linear models the first will be the SFRT flow model and the second will be a simplified linear formulation of the Pom–Pom viscoelastic model.     

The synchronous lateral excitation phenomenon: modelling framework and an application

A mathematical model conceived to simulate the mechanics of synchronous lateral excitation induced by pedestrians on footbridges is presented in this Note. The model is based on the mathematical and numerical decomposition of the coupled multiphysical non-linear system into two interacting subsystems: the Structure system, whose dynamics is described by the non-linear equation of motion, and the Crowd system, which is described by a first-order hydrodynamic model governed by the mass conservation equation. The model was applied to the simulation of a crowd event recorded on the T-bridge in Japan and results are commented on. To cite this article: F. Venuti, L. Bruno, C. R. Mecanique 335 (2007).     

Some problems in metallurgical fluid mechanics

Application of computational fluid mechanics in two areas of metallurgy is considered: solidification of liquid alloys and MHD turbulence. In the first class of problems, where the technical issue is to obtain a reasonably homogeneous composition of the cast, one has to consider not only the completely molten and solidified regions but also the “mushy zone” that is made up of small-scale dendrites, which appear between the first two regions. In the completely molten region, the composition is practically constant and the fluid is set into motion due to the inhomogeneous temperature field. In the mushy zone, on the other hand, solutal convection often dominates strongly over thermal convection. It is shown that laminar convection is of prime importance for the composition of the solidified alloy. In the second class of problems, two cases of turbulent MHD flows in cylindrical containers are considered: an electromagnetic furnace and an electromagnetic stirrer. In the electromagnetic furnace, the mean flow consists of two toroidal vortices. The mean motion in the electromagnetic stirrer is a swirling motion that is accompanied by a weak meridional circulation, which is reminiscent of that occuring in spin down phenomena. The MHD flows are computed by using large eddy simulation methodology with a new subgrid model of the Smagorinsky type that accounts for a variable mesh. Predictions from the all model computations are compared with experimental observations. In general, the agreement between theory and experiments is satisfactory.     

基于MTMD的大跨度人行悬索桥人致振动控制

大跨度人行悬索桥柔度大且阻尼小,易在人群荷载激励下产生过大振动,导致舒适度不满足规范要求.对于此类结构,需要采取有效减振措施控制其动力响应.本文介绍了多重调谐质量阻尼器(MTMD)对主跨600 m人行悬索桥的人致振动控制性能.利用有限元软件建立了某大跨度人行悬索桥模型,以德国EN03规范为计算依据,计算了悬索桥的人致振...     

On variational principles for coherent vortex structures

Different approaches are discussed of variational principles characterizing coherent vortex structures in two-dimensional flows. Turbulent flows seem to form ordered structures in the large scales of the motion and the self-organization principle predicts asymptotic states realizing an extremal value of the energy or a minimum of enstrophy. On the other hand the small scales take care of the increase of entropy, and asymptotic results can be obtained by applying the theory of equilibrium statistical mechanics.     

Measuring the asymmetric contributions of individual subsystems

Information on the structure of a complex system can be obtained by measuring at what rate the individual subsystems exchange information among each other and to what extent they contribute to the information production. In this paper, we use relative transfer entropy to analyze the contributions of asymmetric information flow from one subsystem to another. We also propose information-theoretic tools to estimate the contributions of individual subsystems to the information production of system over time. On one hand, we analyze the artificial processes, including unidirectionally coupled linear processes, unidirectionally coupled Rössler systems, and bidirectionally coupled Hénon maps that reveal the information flows between variables and the contributions to the information production of each variable. On the other hand, we apply these measures to real-world systems, the stock markets that uncover the interactions between high-frequency stock price and trading volume.     

An SPH model for free surface flows with moving rigid objects

This paper presents a computational model for free surface flows interacting with moving rigid bodies. The model is based on the SPH method, which is a popular meshfree, Lagrangian particle method and can naturally treat large flow deformation and moving features without any interface/surface capture or tracking algorithm. Fluid particles are used to model the free surface flows which are governed by Navier–Stokes equations, and solid particles are used to model the dynamic movement (translation and rotation) of moving rigid objects. The interaction of the neighboring fluid and solid particles renders the fluid–solid interaction and the non‐slip solid boundary conditions. The SPH method is improved with corrections on the SPH kernel and kernel gradients, enhancement of solid boundary condition, and implementation of Reynolds‐averaged Navier–Stokes turbulence model. Three numerical examples including the water exit of a cylinder, the sinking of a submerged cylinder and the complicated motion of an elliptical cylinder near free surface are provided. The obtained numerical results show good agreement with results from other sources and clearly demonstrate the effectiveness of the presented meshfree particle model in modeling free surface flows with moving objects. Copyright © 2013 John Wiley & Sons, Ltd.     

Quadratic and rate-independent limits for a large-deviations functional

We construct a stochastic model showing the relationship between noise, gradient flows and rate-independent systems. The model consists of a one-dimensional birth–death process on a lattice, with rates derived from Kramers’ law as an approximation of a Brownian motion on a wiggly energy landscape. Taking various limits, we show how to obtain a whole family of generalized gradient flows, ranging from quadratic to rate-independent ones, connected via ‘L log L’ gradient flows. This is achieved via Mosco-convergence of the renormalized large-deviations rate functional of the stochastic process.     

基于MEMS惯性测量单元的多源信息自适应步数检测方法

针对基于MEMS惯性测量单元的行人航迹推算中步数检测方法仅利用单一的加速度信号检测精度较低的问题,提出一种多源信息自适应步数检测方法。该方法通过综合考虑人体运动过程中的加速度信号和角速度信号,根据不同的步态特征通过设定不同的自适应阈值条件实现步数的检测。虽然常规的峰值检测算法和固定阈值检测算法在单一步态下步数检测精度相对较高,但是对复杂运动状态下的步数检测精度很差,无法适用于真实的行人运动过程中步数的检测。然而多源信息自适应步数检测方法却能够在行人不同运动状态下精确检测步数,该方法明显优于常规的峰值检测方法和阈值检测方法。试验结果表明,本文提出的多源信息自适应阈值检测方法在行人不同运动状态下的步数检测精度可达98%以上。     

A study of simple shearing flows in polar fluids

Summary In the present paper we have made a study of simple shearing flows in three polar fluids — (i) the model ofCondiff andDahler, (ii) the model ofEringen, and (iii) the model ofStokes. We have investigated in detail the components of stress, equations governing the motion and boundary conditions in the above fluids in flows induced by motion of boundaries or a pressure gradient. By means of tables, we have studied the common features of these fluids and related the fluid parameters involved in each case.     

The emergence of dynamic form through phase relations in dynamical systems

Theories of visual form have been plagued with the problem of the correspondence between aspects of the form across time and across spatial location. Following Bateson's idea that knowledge emerges from the relations among multiple flows of difference, our computational model illustrates how visual form can emerge from the phase relations between two such flows in a way that eliminates the correspondence problem. Computationally, the first flow of process in a Boolean network falls into one among many different attractor cycles each of which cycles at a given fundamental frequency. A second cyclic systemic flow, with its own frequency, is computationally necessary before a person can experience the patterns (transients, attractors) of the first flow on a computer monitor; and the frequency of this second flow is a control variable. Dynamic visual form, in this computational logic, emerges from the phase relations between the frequencies of the two flows. These dynamic forms exhibit, simultaneously, many kinds of apparent motion suggesting that the processes generating apparent motion are not merely illusions but are in the service of dynamic form perception. This model of perceptual organization and moving form is discussed in relation to other approaches.     

On the motion of flexible threads in a stokes shear field

We consider the motion of a flexible threadlike filament suspended in an unbounded Stokes shear flow. As the extension of a well-established slender-body theory, we treat the case of a highly anisotropic drag relation, as reflected by a small ratio ? of transverse to longitudinal filament mobility. This provides one potentially useful model of hindered filament motion in highly concetrated filamentary suspensions. In the limit ? → 0, which corresponds to the kinematics associated with a recent model (of Doi and Edwards) for polymer chains, the filament motion is governed by a non-linear kinematic-wave equation. We show that this equation can be solved in closed form, for inextensible filaments and general time-dependent shear flows. We investigate the permanence and stability of threads having uniform axial mobility, showing that only piecewise straight threads have permanent shape. Also, we investigate the stability of fully-extended treads by means of both finite and infinitesimal stability analyses, and we provide equations for the growth rate of arbitrary intial disturbances. These are applied to simple shear and simple-extensional flows. Finally, we discuss the failure of our model for small but non-zero ?, near points of extreme curvature of “entaglement”, and the possible relevance to the rheology of fibrous composites and suspensions.