Related papers: The Lagrangian coordinate system and what it means…
We present results from several projects aimed at enabling the real-time understanding of crowds and their behaviour in the built environment. We make use of CCTV video cameras that are ubiquitous throughout the developed and developing…
As the population of world is increasing, and even more concentrated in urban areas, ensuring public safety is becoming a taunting job for security personnel and crowd managers. Mass events like sports, festivals, concerts, political…
The non-linear evolution of a stratified perturbation in a three dimensional expanding Universe is considered. A general Lagrangian scheme (Q model) is introduced and numerical investigations are performed. The asymptotic contraction of the…
We formulate Lagrangian descriptors (LDs) in the path integral framework. Averaging the classical LD over fluctuations about extremal trajectories defines a quantum LD that incorporates quantum effects. Invariant manifolds, which sharply…
The statistical properties of velocity and acceleration fields along the trajectories of fluid particles transported by a fully developed turbulent flow are investigated by means of high resolution direct numerical simulations. We present…
This paper presents a new approach to behavioral-social dynamics of human crowds. First order models are derived based on mass conservation at the macroscopic scale, while methods of the kinetic theory are used to model the decisional…
The routing results are playing an increasingly important role in transportation efficiency, but they could generate traffic congestion unintentionally. This is because the traffic condition and routing system are disconnected components in…
Using certain solutions of the curve shortening flow, including self-shrinking and self-expanding curves or spirals, we construct and characterize many new examples of translating solitons for mean curvature flow in complex Euclidean plane.…
Evidences are presented concerning tantalizing regularities in cities' population-flows in what regards to space and time correlations. The former exhibit a distance-behavior (for large distances) compatible with the inverse square law,…
We report on simulations of two-dimensional turbulence in the inverse energy cascade regime. Focusing on the statistics of Lagrangian tracer particles, scaling behavior of the probability density functions of velocity fluctuations is…
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…
Predicting particle transport in complex flows is traditionally achieved by solving the Navier-Stokes equations. While various numerical and experimental methods exist, they typically require deep physical insights and incur high…
A two-dimensional cellular automaton model of traffic flow with open boundaries are investigated by computer simulations. The outflow of cars from the system and the average velocity are investigated. The time sequences of the outflow and…
In this paper we propose a new modeling technique for vehicular traffic flow, designed for capturing at a macroscopic level some effects, due to the microscopic granularity of the flow of cars, which would be lost with a purely continuous…
We show that the properties of Lagrangian mean curvature flow are a special case of a more general phenomenon, concerning couplings between geometric flows of the ambient space and of totally real submanifolds. Both flows are driven by…
The dynamical formulation of the optimal transport can be extended through various choices of the underlying geometry (kinetic energy), and the regularization of density paths (potential energy). These combinations yield different…
The main goal of this paper is to present results of comparison study for the level set and direct Lagrangian methods for computing evolution of the Willmore flow of embedded planar curves. To perform such a study we construct new numerical…
We consider mixed model of traffic flow distribution in large networks (BMW model, 1954 & Stable Dynamic model, 1999). We build dual problem and consider primal-dual mirror descent method for the dual problem. There are two ways to recover…
We consider a hybrid compressible/incompressible system with memory effects introduced by Lefebvre Lepot and Maury (2011) for the description of one-dimensional granular flows. We prove a first global existence result for this system…
Recently, Lobb and Nijhoff initiated the study of variational (Lagrangian) structure of discrete integrable systems from the perspective of multi-dimensional consistency. In the present work, we follow this line of research and develop a…