On the tribological characteristics of dynamically loaded journal bearing with micropolar fluids

The addition of the additives to the lubricant oil to enhance the characteristics of the lubricant will influence the performance of the bearings. Based on the theory of micropolar fluids, the tribological characteristics of a dynamically-loaded journal bearing are numerically studied. Comparisons are made between the Newtonian fluids and the micropolar fluids. It is shown that for a dynamically-loaded journal bearing, the micropolar fluids yield an increase not only in the friction force, but also in the friction coefficient. In addition, the oil film pressure and the oil film thickness are obviously higher than that of Newtonian fluids.     

On the stationary Lp-approximation power to derivatives by radial basis function interpolation

In this paper, we consider approximation to derivatives of a function by using radial basis function interpolation. Most of well-known theories for this problem provide error analysis in terms of the so-called native space, say C_φ. However, if a basis function φ is smooth, the space C_φ is extremely small. Thus, the purpose of this study is to extend this result to functions in the homogenous Sobolev space.     

Zero-divisor graphs, von Neumann regular rings, and Boolean algebras

For a commutative ring R with set of zero-divisors Z(R), the zero-divisor graph of R is Γ(R)=Z(R)−{0}, with distinct vertices x and y adjacent if and only if xy=0. In this paper, we show that Γ(T(R)) and Γ(R) are isomorphic as graphs, where T(R) is the total quotient ring of R, and that Γ(R) is uniquely complemented if and only if either T(R) is von Neumann regular or Γ(R) is a star graph. We also investigate which cardinal numbers can arise as orders of equivalence classes (related to annihilator conditions) in a von Neumann regular ring.     

Note on André's reflection principle

This note generalizes André's reflection principle to give a new combinatorial proof of a formula for the number of lattice paths lying within certain trapezoids.     

A structured light-based system for human heads

The 3-D modeling of heads by using optical triangulation techniques is of great interest in the context of virtual reality, telecommunication and computer animation. This paper presents a structured light-based system mainly for human heads. It is named “3-D Laser Color Scanner” (3DLCS). A 3-D model is obtained with a cylindrical scan. The laser beam is switched on and off using a “light valve” and two successive CCD frames are captured, one with the laser line showing and one without. We can simplify the laser line extracting by subtracting these two images.In this system, two CCD cameras are used to avoid occlusion problems. Color information is read from the CCD when the laser light is absent. Since traditional laser scanner will miss the range data in the low-reflectance areas such as the hair area of human head, a shape from silhouette algorithm is presented to overcome this problem. Finally, we give some results using our system. The resulting model is suitable for many applications.     

The modified characteristic finite difference fractional steps method for the coupled system of fluid dynamics in porous media and its analysis

For the coupled system of multilayer fluid dynamics in porous media, the modified characteristic finite difference fractional steps method applicable to parallel arithmetic is put forward and two‐dimensional and three‐dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, energy method, piecewise biquadratic interpolation, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L² norm are derived to determine the error in the approximate solution. This method has already been applied to the numerical simulation of multilayer fluid dynamics in porous media. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 665–681, 2003.     

Approximation of a laminated microstructure for a rotationally invariant,double well energy density

Summary. We give error estimates for the approximation of a laminated microstructure which minimizes the energy for a rotationally invariant, double well energy density . We present error estimates for the convergence of the deformation in the convergence of directional derivatives of the deformation in the “twin planes,” the weak convergence of the deformation gradient, the convergence of the microstructure (or Young measure) of the deformation gradients, and the convergence of nonlinear integrals of the deformation gradient. Received July 25, 1995 / Revised version received November 20, 1995     

Discontinuous Galerkin method with a posterioriL_p(0,t_i) error estimate for second-kind Volterra problems

Summary. We consider a discontinuous Galerkin finite element method applied in time to a model Volterra equation of the second kind. A residual-based computable Galerkin-error estimate is derived for . This estimate does not explicitly contain the time step and therefore the time step control must be based on a heuristic criterion, the estimate can then be used to demonstrate the integrity, or otherwise, of the finite element solution. After performing some numerical experiments we conclude that this approach is at least competetive with classical discretizations since it is computationally simple to implement, but has the added advantage of reliable error feedback. Received June 25, 1995     

On the free boundary of surfaces with bounded mean curvature: the non-perpendicular case

H?lder continuity up to the free boundary is proved for minimizing solutions if they meet the supporting surface in an angle which is bounded away from zero. The problem is localized by proving the continuity of the distance function, a result which is also true for stationary points. Received: 14 April 1998