# Difference between revisions of "Applied/ACMS/absF15"

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=== Li Wang (UCLA) === | === Li Wang (UCLA) === | ||

− | ' | + | ''Singular shocks: From particle-laden flow to human crowd dynamics'' |

In this talk, we will present two examples in which singular shock arises. The first example, gravity-driven thin film flow with a suspension of particles down an incline, is described by a system of conservation laws equipped with an equilibrium theory for particle settling and resuspension. Singular shock appears in the high particle concentration case that relates to the particle-rich ridge observed in the experiments. We analyze the formation of the singular shock as well as its local structure, and extend to the finite volume case, which leads to a linear relationship between the shock front with time to the one-third power. The second example, a panicking crowd with a spread of fear, is modeled via ``emotional contagion”. Singular shock happens in an extreme case whose continuum limit is a pressure less Euler equation. Such system is then modified with a nonlocal alignment to regularize the singularity. We will discuss the hierarchy of models and their mathematical properties. Novel numerical methods will be presented for both examples. | In this talk, we will present two examples in which singular shock arises. The first example, gravity-driven thin film flow with a suspension of particles down an incline, is described by a system of conservation laws equipped with an equilibrium theory for particle settling and resuspension. Singular shock appears in the high particle concentration case that relates to the particle-rich ridge observed in the experiments. We analyze the formation of the singular shock as well as its local structure, and extend to the finite volume case, which leads to a linear relationship between the shock front with time to the one-third power. The second example, a panicking crowd with a spread of fear, is modeled via ``emotional contagion”. Singular shock happens in an extreme case whose continuum limit is a pressure less Euler equation. Such system is then modified with a nonlocal alignment to regularize the singularity. We will discuss the hierarchy of models and their mathematical properties. Novel numerical methods will be presented for both examples. |

## Revision as of 10:30, 19 July 2015

# ACMS Abstracts: Fall 2015

### Li Wang (UCLA)

*Singular shocks: From particle-laden flow to human crowd dynamics*

In this talk, we will present two examples in which singular shock arises. The first example, gravity-driven thin film flow with a suspension of particles down an incline, is described by a system of conservation laws equipped with an equilibrium theory for particle settling and resuspension. Singular shock appears in the high particle concentration case that relates to the particle-rich ridge observed in the experiments. We analyze the formation of the singular shock as well as its local structure, and extend to the finite volume case, which leads to a linear relationship between the shock front with time to the one-third power. The second example, a panicking crowd with a spread of fear, is modeled via ``emotional contagion”. Singular shock happens in an extreme case whose continuum limit is a pressure less Euler equation. Such system is then modified with a nonlocal alignment to regularize the singularity. We will discuss the hierarchy of models and their mathematical properties. Novel numerical methods will be presented for both examples.