Coupled lubrication and Stokes flow finite elements

A method is developed for performing a local reduction of the governing physics for fluid problems with domains that contain a combination of narrow and non‐narrow regions, and the computational accuracy and performance of the method are measured. In the narrow regions of the domain, where the fluid is assumed to have no inertia and the domain height and curvature are assumed small, lubrication, or Reynolds, theory is used locally to reduce the two‐dimensional Navier–Stokes equations to the one‐dimensional Reynolds equation while retaining a high degree of accuracy in the overall solution. The Reynolds equation is coupled to the governing momentum and mass equations of the non‐narrow region with boundary conditions on the mass and momentum flux. The localized reduction technique, termed ‘stitching,’ is demonstrated on Stokes flow for various geometries of the hydrodynamic journal bearing—a non‐trivial test problem for which a known analytical solution is available. The computational advantage of the coupled Stokes–Reynolds method is illustrated on an industrially applicable fully‐flooded deformable‐roll coating example. The examples in this paper are limited to two‐dimensional Stokes flow, but extension to three‐dimensional and Navier–Stokes flow is possible. Copyright © 2003 John Wiley & Sons, Ltd.     

Competitive influence of atactic polystyrene and supercritical carbon dioxide on the conformation of syndiotactic polystyrene

The crystallization behavior of miscible syndiotactic polystyrene (sPS) and atactic polystyrene (aPS) blends with different sPS/aPS weight ratios was investigated in supercritical CO₂ by using Fourier‐transform infrared spectroscopy, differential scanning calorimetry, and wide‐angle X‐ray diffraction. Supercritical CO₂ and aPS exhibited different effects on the conformational change of sPS and competed with each other. Increasing the content of amorphous aPS in the blends made its effect on the conformational change of sPS gradually surpass that of supercritical CO₂. Supercritical CO₂ favored the formation of the helical conformation of sPS in lower temperature range and the all trans planar conformation in higher temperature range, instead of forming the latter one only in higher temperature range in ambient atmosphere. However, increasing aPS content in the blends pushed the range for forming the helical conformation to lower temperature and made the all trans planar conformation dominant in aPS/sPS 25/75 blend after treating in supercritical CO₂ above 60 °C. The all trans planar zigzag conformation was more favorable than the helical conformation after mixing aPS in sPS in supercritical CO₂. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1755–1764, 2007     

Minkowski-type and Alexandrov-Type Theorems for Polyhedral Herissons

Classical H. Minkowski theorems on existence and uniqueness of convex polyhedra with prescribed directions and areas of faces as well as the well-known generalization of H. Minkowski uniqueness theorem due to A.D. Alexandrov are extended to a class of nonconvex polyhedra which are called polyhedral herissons and may be described as polyhedra with injective spherical image.     

Fundamental solutions of the acoustic and diffusion equations in nonhomogeneous medium

A fundamental solution of the acoustical equation with a variable refraction coefficient is constructed. The solution satisfies the limiting absorption and radiation conditions. The optimal high frequency estimate is proved for square means of the solution. The source function for the diffusion equation is a by-product of this construction. Partially supported by a stipend of the Mathematical Scientific Research Institute at Berkeley, 2001.     

SURFACE METALLIZATION OF CENOSPHERES AND PRECIPITATORS BY ELECTROLESS PLATING

This paper reports the use of a colloidal Pd^0 catalysis system to metallize the surface of precipitators separated from coal fly-ash, and metals such as Cu, Ni etc. are deposited on the precipitators surface. Alternatively, according to the characteristic surface of cenospheres, an Ag coating catalysis system is adopted to first deposit Ag on the cenospheres surface, followed, if necessary, by the deposition of other metals such as Cu, Ni, etc. on the Ag coating to produce monolayer and multilayer metal-coated cenospheres. The surface characteristics and the morphologies of the metal coatings are examined in detail with scanning electron microscopy (SEM), energy dispersive spectroscopy (EDX) and X-ray photoelectron spectroscopy (XPS) techniques. It can be shown that the quality of metal coatings derived from the Aa coatina catalysis system, is better than that of the colloidal Pd^0 catalysis system.     

双障碍问题阻尼牛顿法的二阶收敛性

本文研究由双障碍问题导出的一类B可微函数的性质，并在一定条件下证明了求解相应的B可微方程阻尼牛顿法的全局收效性和二阶收效性．数值例子表明这一算法是有效的．     

Shape Hessian for generalized Oseen flow by differentiability of a minimax: A Lagrangian approach

The goal of this paper is to compute the shape Hessian for a generalized Oseen problem with nonhomogeneous Dirichlet boundary condition by the velocity method. The incompressibility will be treated by penalty approach. The structure of the shape gradient and shape Hessian with respect to the shape of the variable domain for a given cost functional are established by an application of the Lagrangian method with function space embedding technique. This work was supported by the National Natural Science Fund of China (No. 10371096) for ZM Gao and YC Ma.     

Angular momentum effect in prescission particle multiplicities for a light system by diffusion model

The effect of angular momentum on the competition between fission and particle emission during light system fission process was studied via fission diffusion model. The prescission particle multiplicities were found to increase with decreasing angular momentum. The experimental prescission proton and α particle multiplicities can be fitted for 10.6 MeV/nucleon ⁸⁴Kr(²⁷Al,binary fission) reaction with this model. Entrance channel effect found in [1] is proved to be angular momentum effect.     

A conjecture of M. J. Taylor concerning determinantal congruences

Let G be a finite group. The class group of the group ring of G is a quotient of the idèlic homomorphisms of R(G) by the global functions and the determinantal functions. Using Explicit Brauer Induction, we prove Adams operations, applied to determinantal functions, satisfy some congruences which were conjectured by M. J. Taylor. As an application, we construct some new maps defined on the class group.In memory of J. Frank Adams (1930–1989)Research partially supported by NSERC Grant # 0GP0042580.