4 papers · 1 filter
Localized Enhanced Dissipation: A Hypocoercivity Approach
Siming He
In this paper, we consider the passive scalar solutions in shear flows with critical points. With a detailed hypocoercivity functional, we develop streamline-wise enhanced dissipat…
Mixing, Enhanced Dissipation and Phase Transition in the Kinetic Vicsek Model
Mengyang Gu, Siming He
In this paper, we study the kinetic Vicsek model, which serves as a starting point for describing the polarization phenomena observed in the experiments of fibroblasts moving on li…
Time-dependent Flows and Their Applications in Parabolic-parabolic Patlak-Keller-Segel Systems Part II: Shear Flows
Siming He
In this study, we investigate the behavior of three-dimensional parabolic-parabolic Patlak-Keller-Segel (PKS) systems in the presence of ambient shear flows. Our findings demonstra…
Time-dependent Flows and Their Applications in Parabolic-parabolic Patlak-Keller-Segel Systems Part I: Alternating Flows
Siming He
We consider the three-dimensional parabolic-parabolic Patlak-Keller-Segel equations (PKS) subject to ambient flows. Without the ambient fluid flow, the equation is super-critical i…