Molecular hydrodynamics of the moving contact line in two-phase immiscible flows

The ``no-slip'' boundary condition, i.e., zero fluid velocity relative to the solid at the fluid-solid interface, has been very successful in describing many macroscopic flows. A problem of principle arises when the no-slip boundary condition is used to model the hydrodynamics of immiscible-fluid displacement in the vicinity of the moving contact line, where the interface separating two immiscible fluids intersects the solid wall. Decades ago it was already known that the moving contact line is incompatible with the no-slip boundary condition, since the latter would imply infinite dissipation due to a non-integrable singularity in the stress near the contact line. In this paper we first present an introductory review of the problem. We then present a detailed review of our recent results on the contact-line motion in immiscible two-phase flow, from MD simulations to continuum hydrodynamics calculations. Through extensive MD studies and detailed analysis, we have uncovered the slip boundary condition governing the moving contact line, denoted the generalized Navier boundary condition. We have used this discovery to formulate a continuum hydrodynamic model whose predictions are in remarkable quantitative agreement with the MD simulation results at the molecular level. These results serve to affirm the validity of the generalized Navier boundary condition, as well as to open up the possibility of continuum hydrodynamic calculations of immiscible flows that are physically meaningful at the molecular level.Comment: 36 pages with 33 figure

Gevrey estimates of the resolvent and sub-exponential time-decay of solutions

In this article, we study a class of non-selfadjoint Schr{\"o}dinger operators H which are perturbation of some model operator H 0 satisfying a weighted coercive assumption. For the model operator H 0 , we prove that the derivatives of the resolvent satisfy some Gevrey estimates at threshold zero. As application, we establish large time expansions of semigroups e --tH and e --itH for t > 0 with subexponential time-decay estimates on the remainder, including possible presence of zero eigenvalue and real resonances

Large-time asymptotics of solutions to the Kramers-Fokker-Planck equation with a short-range potential

In this work, we use scattering method to study the Kramers-Fokker-Planck equation with a potential whose gradient tends to zero at the infinity. For short-range potentials in dimension three, we show that complex eigenvalues do not accumulate at low-energies and establish the low-energy resolvent asymptotics. This combined with high energy pseudospectral estimates valid in more general situations gives the large-time asymptotics of the solution in weighted $L^2$ spaces

Stability of vortex in a two-component superconductor

Thermodynamic stability of composite vortex in a two-component superconductor is investigated by the Ginzburg-Landau theory. The predicted nature of these vortices has recently attracted much attention. Here we consider axially symmetric quantized vortex and show that the stability of vortex depends on three independent dimensionless parameters: $\kappa _{1}$, $\kappa _{2}$, $\kappa _{\xi}$, where $\kappa _{i}(i=1,2)$ is the Ginzburg-Landau parameter of individual component, $\kappa _{\xi }=\xi _{1}/\xi _{2}$ is the ratio of two coherence lengths. We also show that there exists thermodynamic stable vortex in type-1+type-2 or type-2+type-2 materials over a range of these three parameters.Comment: 7 pages, 2 figure

Lenard scheme for two dimensional periodic Volterra chain

We prove that for compatible weakly nonlocal Hamiltonian and symplectic operators, hierarchies of infinitely many commuting local symmetries and conservation laws can be generated under some easily verified conditions no matter whether the generating Nijenhuis operators are weakly nonlocal or not. We construct a recursion operator of the two dimensional periodic Volterra chain from its Lax representation and prove that it is a Nijenhuis operator. Furthermore we show this system is a (generalised) bi-Hamiltonian system. Rather surprisingly, the product of its weakly nonlocal Hamiltonian and symplectic operators gives rise to the square of the recursion operator.Comment: Submit to Journal of Mathematical Physic

The integration of the credit default swap markets during the US subprime crisis: Dynamic correlation analysis

This is the post-print version of the final paper published in Journal of International Financial Markets, Institutions and Money. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2011 Elsevier B.V.This paper investigates the integration of the credit default swap (CDS) markets of 38 developed and emerging countries with the US market during the subprime crisis period by utilising dynamic conditional correlation from the multivariate GARCH model. Evidence reveals that the Lehman shock seems to have strengthened the integration, in particular, for developed markets. For both developed and emerging markets, declining US interest rates are found to be the main driving factor behind the higher level of correlation, suggesting that the CDS markets were heavily driven by the world largest economy when the crisis reached its peak