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

Hydrodynamic slip boundary condition at chemically patterned surfaces: A continuum deduction from molecular dynamics

We investigate the slip boundary condition for single-phase flow past a chemically patterned surface. Molecular dynamics (MD) simulations show that modulation of fluid-solid interaction along a chemically patterned surface induces a lateral structure in the fluid molecular organization near the surface. Consequently, various forces and stresses in the fluid vary along the patterned surface. Given the presence of these lateral variations, a general scheme is developed to extract hydrodynamic information from MD data. With the help of this scheme, the validity of the Navier slip boundary condition is verified for the chemically patterned surface, where a local slip length can be defined. Based on the MD results, a continuum hydrodynamic model is formulated using the Navier-Stokes equation and the Navier boundary condition, with a slip length varying along the patterned surface. Steady-state velocity fields from continuum calculations are in quantitative agreement with those from MD simulations. It is shown that, when the pattern period is sufficiently small, the solid surface appears to be homogeneous, with an effective slip length that can be controlled by surface patterning. Such a tunable slip length may have important applications in nanofluidics.Comment: 41 pages, 17 figure

Optimal Drug Policy in Low-Income Neighborhoods

Part of the debate over the control of drug activity in cities is concerned with the effectiveness of implementing demand- versus supply-side drug policies. This paper is motivated by the relative lack of research providing formal economic underpinning for the implementation of either policy. We construct a simple model of drug activity, in which the drug price and the distribution of population in a community are determined according to a career choice rule and a predetermined drug demand. Three potential government objectives are considered. We find that both demand- and supply-side policies have theoretical support under different community conditions. While the demand-side policy discourages active drug sellers, the supply-side policy has an additional drug-dealing replacement effect on inducing potential entry of drug dealers. In low-income neighborhoods, demand-side policy is more effective if the drug problem is more sever or if the government objective is to deter dealer entry or to promote community's aggregate income rather than minimizing active drug selling.

Experience of nursing care for diabetes patients undergoing cervical intervertebral disc arthroplasty

目的  探讨糖尿病患者行人工颈椎间盘置换术手术前后的护理方法。方法  对64例颈椎病合并糖尿病患者进行降糖治疗和护理，行择期手术，术后在创伤骨科疾病护理的基础上结合糖尿病患者的护理常规，对64例患者进行护理，包括观察伤口，预防并发症，监测血糖，降糖宣教，饮食护理和功能锻炼等措施。结果  64例行人工颈椎间盘置换术的糖尿病患者均顺利渡过围术期，切口甲级愈合，未发生并发症，临床症状缓解或消失。置换节段稳定并部分恢复了颈椎正常的活动范围。结论  做好手术全过程的护理，尤其是加强术后护理，积极控制血糖对减少并发症，巩固手术疗效和促进患者康复至关重要。Objective:To explore nursing methods for diabetes patients of cervical intervertebral disc arthroplasty before and after surgery. Methods: 64 patients having cervical spondylosis with diabetes mellitus were treated with hypoglycemic therapy, and underwent elective surgery. Basic nursing care for diabetes patients on the basis of nursing care for orthopaedic trauma is needed during postoperative period. Observing wound, preventing complications, monitoring the blood sugar, hypoglycemic mission, diet nursing and functional exercise.Results: 64 routine cervical intervertebral disc arthroplasty patients with diabetes are through perioperative period. Class A healing of incision was presented, no complications appeared, and clinical symptoms disappeared. Segmental stability and replacement parts returned to normal cervical range of motion.Conclusion: Nursing care for the whole process of operation, especially postoperative period, plays an important role in controlling blood sugar, reducing complication, consolidating surgical curative effect and promoting rehabilitation

Bosonic Haldane insulator in the presence of local disorder: A quantum Monte Carlo study

The Haldane phase (HP) is a paradigmatic example of symmetry protected topological phase. We explore how the bosonic HP behaves in the presence of local disorder, employing quantum Monte Carlo simulations of an extended Bose-Hubbard model subject to uncorrelated, quenched disorders. We find that the HP is robust against a weak disorder and the non-local string order of HP exhibits a reentrant behavior. Besides, a direct transition between the HP and superfluid phase is uncovered. A significant part of the ground-state phase diagram is established for the model, unveiling the location of HP surrounded by Bose glass, charge density wave and superfluid phases. We also mention a possible experimental scheme with optical lattice emulator to realize the present findings.Comment: 6 pages, 5 figure

The covering number for some Mercer kernel Hilbert spaces

AbstractIn the present paper, we investigate the estimates for the covering number of a ball in a Mercer kernel Hilbert space on [0,1]. Let Pl(x) be the Legendre orthogonal polynomial of order l, al>0 be real numbers satisfying ∑l=0+∞lal<+∞. Then, for the Mercer kernel functionK(x,t)=∑l=0+∞alPl(x)Pl(t),x,t∈[0,1],we provide the upper estimates of the covering number for the Mercer kernel Hilbert space reproducing from K(x,t). For some particular al we give the lower estimates. Meanwhile, a kind of l2-norm estimate for the inverse Mercer matrix associated with the Mercer kernel K(x,t) is given