We develop a continuum hydrodynamic model for two-phase immiscible flows that involve electroosmotic effect in an electrolyte and moving contact line at solid surfaces. The model is derived through a variational approach based on the On- sager principle of minimum energy dissipation. This approach was first presented in the derivation of a continuum hydrodynamic model for moving contact line in neu- tral two-phase immiscible flows (Qian, Wang, and Sheng, J. Fluid Mech. 564, 333–360 (2006)). Physically, the electroosmotic effect can be formulated by the Onsager prin- ciple as well in the linear response regime. Therefore, the same variational approach is applied here to the derivation of the continuum hydrodynamic model for charged two-phase immiscible flows where one fluid component is an electrolyte exhibiting electroosmotic effect on a charged surface. A phase field is employed to model the diffuse interface between two immiscible fluid components, one being the electrolyte and the other a nonconductive fluid, both allowed to slip at solid surfaces. Our model consists of the incompressible Navier-Stokes equation for momentum transport, the Nernst-Planck equation for ion transport, the Cahn-Hilliard phase-field equation for interface motion, and the Poisson equation for electric potential, along with all the necessary boundary conditions. In particular, all the dynamic boundary conditions at solid surfaces, including the generalized Navier boundary condition for slip, are de- rived together with the equations of motion in the bulk region. Numerical examples in two-dimensional space, which involve overlapped electric double layer fields, have been presented to demonstrate the validity and applicability of the model, and a few salient features of the two-phase immiscible electroosmotic flows at solid surface. The wall slip in the vicinity of moving contact line and the Smoluchowski slip in the electric double layer are both investigated.
Jurisprudential regime theory is a legal explanation of decision-making on the U.S. Supreme Court that asserts that a key precedent in an area of law fundamentally restructures the relationship between case characteristics and the outcomes of future cases. In this article, we offer a multivariate multiple change-point probit model that can be used to endogenously test for the existence of jurisprudential regimes. Unlike the previously employed methods, our model does so by estimating the locations of many possible changepoints along with structural parameters. We estimate the model using Markov chain Monte Carlo methods, and use Bayesian model comparison to determine the number of change-points. Our findings are consistent with jurisprudential regimes in the Establishment Clause and administrative law contexts. We find little support for hypothesized regimes in the areas of free speech and search-and-seizure. The Bayesian multivariate change-point model we propose has broad potential applications to studying structural breaks in either regular or irregular time-series data about political institutions or processes.
Within the framework of the cluster-tunneling model, a folded ¶¡ -core potential that is based on the Woods®CSaxon potential is proposed to investigate ¶¡ -decays in the superheavy mass region. The calculated ¶¡ -decay half-lives of even®Ceven superheavy nuclei from Z = 100 to Z = 116 are in reasonable agreement with the experimental data.