scholarly journals A kinetic theory approach for 2D crowd dynamics with emotional contagion

2021 ◽  
pp. 1-26
Author(s):  
Daewa Kim ◽  
Kaylie O’Connell ◽  
William Ott ◽  
Annalisa Quaini
Keyword(s):  
Experimental Study ◽  
Kinetic Theory ◽  
Computational Modeling ◽  
Walking Speed ◽  
Operator Splitting ◽  
Emotional Contagion ◽  
Theory Approach ◽  
Splitting Scheme ◽  
Active Particles ◽  
Fear Level

In this paper, we present a computational modeling approach for the dynamics of human crowds, where the spreading of an emotion (specifically fear) has an influence on the pedestrians’ behavior. Our approach is based on the methods of the kinetic theory of active particles. The model allows us to weight between two competing behaviors depending on fear level: the search for less congested areas and the tendency to follow the stream unconsciously (herding). The fear level of each pedestrian influences their walking speed and is influenced by the fear levels of their neighbors. Numerically, we solve our pedestrian model with emotional contagion using an operator splitting scheme. We simulate evacuation scenarios involving two groups of interacting pedestrians to assess how domain geometry and the details of fear propagation impact evacuation dynamics. Further, we reproduce the evacuation dynamics of an experimental study involving distressed ants.

Hilbert method toward a multiscale analysis from kinetic to macroscopic models for active particles

2017 ◽  
Vol 27 (07) ◽  
pp. 1327-1353 ◽  
Author(s):  
D. Burini ◽  
N. Chouhad
Keyword(s):  
Kinetic Theory ◽  
Multiscale Analysis ◽  
Second Step ◽  
Theory Approach ◽  
Type Method ◽  
Macroscopic Models ◽  
Active Particles ◽  
Time Space ◽  
Large Systems ◽  
Hilbert Type

This paper develops a Hilbert type method to derive models at the macroscopic scale for large systems of several interacting living entities whose statistical dynamics at the microscopic scale is delivered by kinetic theory methods. The presentation is in three steps, where the first one presents the structures of the kinetic theory approach used toward the aforementioned analysis; the second step presents the mathematical method; while the third step provides a number of specific applications. The approach is focused on a simple system and with a binary mixture, where different time-space scalings are used. Namely, parabolic, hyperbolic, and mixed in the case of a mixture.

Analysis of binary and ternary granular mixtures behavior using the kinetic theory approach

2005 ◽  
Vol 151 (1-3) ◽  
pp. 117-125 ◽  
Author(s):  
Hadjira Iddir ◽  
Hamid Arastoopour ◽  
Christine M. Hrenya
Keyword(s):  
Kinetic Theory ◽  
Theory Approach ◽  
Granular Mixtures

scholarly journals Operator splitting around Euler-Maruyama scheme and high order discretization of heat kernels

2020 ◽  
Author(s):  
Toshihiro Yamada ◽  
Yuga Iguchi
Keyword(s):  
Commutative Algebra ◽  
Computational Algorithm ◽  
Diffusion Processes ◽  
Operator Splitting ◽  
Heat Kernels ◽  
Heat Equations ◽  
Discretization Method ◽  
Splitting Scheme ◽  
Order Operator ◽  
Numerical Examples

This paper proposes a general higher order operator splitting scheme for diffusion semigroups using the Baker-Campbell-Hausdorff type commutator expansion of non-commutative algebra and the Malliavin calculus. An accurate discretization method for the fundamental solution of heat equations or the heat kernel is introduced with a new computational algorithm which will be useful for the inference for diffusion processes. The approximation is regarded as the splitting around the Euler-Maruyama scheme for the density. Numerical examples for diffusion processes are shown to validate the proposed scheme.

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