Coarsening in the two-dimensional incompressible Toner-Tu equation: Signatures of turbulence

Phase ordering, topological defects, and turbulence in the 3D incompressible Toner-Tu equation

We investigate phase ordering dynamics of the incompressible Toner-Tu equation in three dimensions. We show that the phase ordering proceeds via defect merger events and the dynamics is controlled by the Reynolds number Re. At low Re, the dynamics is similar to that of the Ginzburg-Landau equation. At high Re, turbulence controls phase ordering. In particular, we observe a forward energy cascade from the coarsening length scale to the dissipation scale.

An analytical and computational study of the incompressible Toner-Tu Equations

The incompressible Toner-Tu (ITT) partial differential equations (PDEs) are an important example of a set of active-fluid PDEs. While they share certain properties with the Navier-Stokes equations (NSEs), such as the same scaling invariance, there are also important differences. The NSEs are usually considered in either the decaying or the additively forced cases, whereas the ITT equations have no additive forcing. Instead, they include a linear, activity term $α\bu$ ($\bu$ is the velocity field) which pumps energy into the system, but also a negative $\bu|\bu|^{2}$-term which provides a platf…

主动湍流的Toner-Tu-Swift-Hohenberg方程的全局吸引子及其性质

The global attractor of the Toner-Tu-Swift-Hohenberg equations of active turbulence and its properties

本文研究了TTSH方程的全局吸引子及其性质，证明其具有有限维紧致吸引子并给出了李雅普诺夫维度的估计，同时通过数值模拟验证了理论结果与实验观测的一致性。

Finite-size scaling and double-crossover critical behavior in two-dimensional incompressible polar active fluids

We study the order-disorder transition in two-dimensional incompressible systems of motile particles with alignment interactions through extensive numerical simulations of the incompressible Toner-Tu (ITT) field theory and a detailed finite-size scaling (FSS) analysis. The transition looks continuous in the explored parameter space, but the effective susceptibility exponent $γ/ν$ and the dynamic exponent $z$ exhibit a strong, non-monotonic variation on the system size in the form of double crossovers. At small sizes, mean-field exponents are observed for the homogeneous $k=0$ mode whereas spat…

An adaptive variational procedure for the conservative and positivity preserving Allen-Cahn phase-field model

We present an adaptive variational procedure for unstructured meshes to capture fluid-fluid interfaces in two-phase flows. The two phases are modeled by the phase-field finite element formulation, which involves the conservative Allen-Cahn equation coupled with the incompressible Navier-Stokes equations. The positivity preserving variational formulation is designed to maintain the bounded and stable solution of the Allen-Cahn equation. For the adaptivity procedure, we consider the residual-based error estimates for the underlying differential equations of the two-phase system. In particular, t…