A convergence result in the study of bone remodeling contact problems

We consider the approximation of a bone remodeling model with the Signorini contact conditions by a contact problem with normal compliant obstacle, when the obstacle's deformability coefficient converges to zero (that is, the obstacle's stiffness tends to infinity). The variational problem is a coupled system composed of a nonlinear variational equation (in the case of normal compliance contact conditions) or a variational inequality (for the case of Signorini's contact conditions), for the mechanical displacement field, and a first-order ordinary differential equation for the bone remodeling function. A theoretical result, which states the convergence of the contact problem with normal compliance contact law to the Signorini problem, is then proved. Finally, some numerical simulations, involving examples in one and two dimensions, are reported to show this convergence behaviour.     

CSPD-1溶液物理显影研究

本文介绍了命名为CSPD-1溶液物理显影处理工艺,用于中国全息干板的实验研究结果;全面地总结了实验操作中的技术关键问题;对观察到的新工艺优越性产生的机制,作了初步的理论讨论。     

A SET OF SYMMETRIC QUADRATURE RULES ON TRIANGLES AND TETRAHEDRA

We present a program for computing symmetric quadrature rules on triangles and tetrahedra. A set of rules are obtained by using this program. Quadrature rules up to order 21 on triangles and up to order 14 on tetrahedra have been obtained which are useful for use in finite element computations. All rules presented here have positive weights with points lying within the integration domain.     

Low-temperature, solution processing of TiO2 thin films and fabrication of multilayer dielectric optical elements

High-quality TiO₂ thin films have been deposited from aqueous titanium-peroxo solutions via spin coating. The effects of precursor solution pH on the crystallization behavior, morphology, density, and refractive index of the films are reported. From X-ray diffraction measurements, the amorphous as-deposited films are found to crystallize in the anatase phase at 250 °C. Surface and cross-section SEM images reveal that films deposited from an acidic precursor are more uniform and denser than those deposited from a basic precursor. X-ray reflectivity measurements show that films with smooth surfaces and high densities (up to 87% of single-crystal anatase) can be produced at temperatures as low as 300 °C. Measured densities are consistent with high refractive indices at 633 nm of 2.24 and 2.11 for films derived from acidic and basic precursors, respectively. The uniformity and dense nature of the films have allowed fabrication of multilayer dielectric optical elements with thermal processing at only 300 °C. The distributed Bragg reflector with four bilayers exhibits a reflectance of 92% and a stop band width of 150 nm. The optical microcavity has a quality factor of 20. The optical properties of all elements agree well with theoretical models, indicating good optical quality. Use of the precursor chemistry for direct photopatterning of TiO₂ films without a polymer resist is also demonstrated.     

Mean-square stability of Milstein method for linear hybrid stochastic delay integro-differential equations

In this paper we study the mean-square (MS) stability of the Milstein method for linear stochastic delay integro-differential equations (SDIDE) with Markovian switching by extending the techniques of [Z. Wang, C. Zhang, An analysis of stability of Milstein method for stochastic differential equations with delay, Computers and Mathematics with Applications 51 (2006) 1445–1452; L. Ronghua, H. Yingmin, Convergence and stability of numerical solutions to SDDEs with Markovian switching, Applied Mathematics and Computation 175 (2006) 1080–1091]. It is established that the Milstein method is MS-stable for linear stochastic delay differential equations (Wang and Zhang (2006); in the above reference). Here we prove that it is MS-stable for linear SDIDE with Markovian switching also under suitable conditions on the integral term. A numerical example is provided to illustrate the theoretical results.     

Error analysis of the numerical solution of split differential equations

The operator splitting method is a widely used approach for solving partial differential equations describing physical processes. Its application usually requires the use of certain numerical methods in order to solve the different split sub-problems. The error analysis of such a numerical approach is a complex task. In the present paper we show that an interaction error appears in the numerical solution when an operator splitting procedure is applied together with a lower-order numerical method. The effect of the interaction error is investigated by an analytical study and by numerical experiments made for a test problem.     

A convex analysis approach for convex multiplicative programming

Global optimization problems involving the minimization of a product of convex functions on a convex set are addressed in this paper. Elements of convex analysis are used to obtain a suitable representation of the convex multiplicative problem in the outcome space, where its global solution is reduced to the solution of a sequence of quasiconcave minimizations on polytopes. Computational experiments illustrate the performance of the global optimization algorithm proposed.      

Numerical simulations on the formation of laser speckles with nanofluids

Our recent work revealed that speckles can be formed when nanofluids containing a proper volume fraction of nanoparticles are illuminated by a monochromatic laser beam [Qian M, Liu J, Yan M-S, Shen Z-H, Lu J, Ni XW, et al. Investigation on utilizing laser speckle velocimetry to measure the velocities of nanoparticles in nanofluids. Opt Express 2006; 14: 7559–66]. In this paper, two different physical models are established to figure out the speckle-formation mechanism. The photon–nanoparticle-collision model emphasizes the random collisions between photons and nanoparticles, and Monte Carlo method is used to simulate how the incident photons move in the vessel containing nanofluids. However, in the electric-dipole model, each illuminated nanoparticle becomes an electric dipole and sends out scattering lights, and the coherent addition of the scattering lights from nanoparticles is numerically calculated. Finally, from the numerical results, the speckle-formation mechanism is figured out.     

Numerical solutions of a model for the propagation of a surface-catalysed flame in a tube

Numerical simulations of a surface-catalysed flame in a tubeare performed, corresponding to an experiment where a premixedfuel is fed into a tube whose inner surface is coated with acatalyst. In these experiments, subsequent to ignition, a reactionwave can be seen as a red-hot region which propagates back alongthe tube towards the inlet, and is due to low temperature combustionoccurring only on the inner surface of the tube where the catalystis present. The solutions of a mathematical model for this behaviourshow that initial-value problems do indeed result in such steadilypropagating waves. The numerically obtained wave speeds andsteady solution are compared to a previous large Damköhlernumber (D_a) asymptotic analysis using a simple reaction ratemodel, and agreement is very good even for moderately largevalues of D_a. However, for such Damköhler numbers, thewave speeds are found to be much larger than observed experimentally.Indeed, the simulations show that O(1) values of D_a are requiredto obtain the lower experimental wave speeds. Nevertheless,the wave speeds as a function of flow rate through the tubedo not agree well with the preliminary experimental resultsfor any choice of the parameters. A more realistic, Arrheniusreaction rate model is then considered. The Arrhenius modelpredicts a rapid change in temperature at the wave front, inmuch better agreement with the experiments than for the simplerreaction model.     

On the sign-stability of numerical solutions of one-dimensional parabolic problems

The preservation of the qualitative properties of physical phenomena in numerical models of these phenomena is an important requirement in scientific computations. In this paper, the numerical solutions of a one-dimensional linear parabolic problem are analysed. The problem can be considered as a altitudinal part of a split air pollution transport model or a heat conduction equation with a linear source term. The paper is focussed on the so-called sign-stability property, which reflects the fact that the number of the spatial sign changes of the solution does not grow in time. We give sufficient conditions that guarantee the sign-stability both for the finite difference and the finite element methods.