Analysis of the self-similar spreading of power law fluids

Capillarity driven spreading of circular drops of shear-thinning fluid

We investigate the spreading of thin, circular liquid drops of power-law rheology. We derive the equation of motion using the thin film approximation, construct source-type similarity solutions and compute the spreading rate, aparent contact angles and height profiles. In contrast with the spreading of newtonian liquids, the contact line paradox does not arise for shear thinning fluids.

Scaling Estimates for Solutions and Dynamical Lower Bounds on Wavepacket Spreading

We establish quantum dynamical lower bounds for discrete one-dimensional Schrödinger operators in situations where, in addition to power-law upper bounds on solutions corresponding to energies in the spectrum, one also has lower bounds following a scaling law. As a consequence, we obtain improved dynamical results for the Fibonacci Hamiltonian and related models.

Spreading Estimates for Quantum Walks on the Integer Lattice via Power-Law Bounds on Transfer Matrices

We discuss spreading estimates for dynamical systems given by the iteration of an extended CMV matrix. Using a connection due to Cantero--Grünbaum--Moral--Velázquez, this enables us to study spreading rates for quantum walks in one spatial dimension. We prove several general results which establish quantitative upper and lower bounds on the spreading of a quantum walk in terms of estimates on a pair of associated matrix cocycles. To demonstrate the power and utility of these methods, we apply them to several concrete cases of interest. In the case where the coins are distributed according to a…

幂律势下的动力学扩散与记忆保留

Dynamical Spreading and Memory Retention Under Power Law Potential

该研究探究了排斥幂律势下粒子悬浮液的过阻尼动力学扩散，通过实验与模拟发现临界幂次下粒子会在边缘积累并保留初始图案的长期记忆，为动态系统结构演化提供了新认识。

Liouville-type theorems for steady flows of degenerate power law fluids in the plane

We extend the Liouville-type theorems of Gilbarg and Weinberger and of Koch, Nadirashvili, Seregin and Sverák valid for the stationary variant of the classical Navier-Stokes equations in 2D to the degenerate power law fluid model.

A comparison of slip, disjoining pressure, and interface formation models for contact line motion through asymptotic analysis of thin two-dimensional droplet spreading

The motion of a contact line is examined, and comparisons drawn, for a variety of models proposed in the literature. Pressure and stress behaviours at the contact line are examined in the prototype system of quasistatic spreading of a thin two-dimensional droplet on a planar substrate. The models analysed include three disjoining pressure models based on van der Waals interactions, a model introduced for polar fluids, and a liquid-gas diffuse-interface model; Navier-slip and two non-linear slip models are investigated, with three microscopic contact angle boundary conditions imposed (two of th…