BIOLUMINESCENCE TOMOGRAPHY： BIOMEDICAL BACKGROUND,MATHEMATICAL THEORY,AND NUMERICAL APPROXIMATION

Over the last couple of years molecular imaging has been rapidly developed to study physiological and pathological processes in vivo at the cellular and molecular levels. Among molecular imaging modalities, optical imaging stands out for its unique advantages, especially performance and cost-effectiveness. Bioluminescence tomography （BLT） is an emerging optical imaging mode with promising biomedical advantages. In this survey paper, we explain the biomedical significance of BLT, summarize theoretical results on the analysis and numerical solution of a diffusion based BLT model, and comment on a few extensions for the study of BLT.     

RELIABILITY ASSESSMENT OF STRUCTURAL SYSTEMS BASED ON DIRECTIONAL VECTOR SIMULATION TECHNIQUE

The new improved directional vector simulation method for analyzing the reliability of structural systems failure probability is researched. This paper also points out the defects of general directional vector simulation, and gives rise to a new higher accuracy approximate integral formula of structural systems failure probability. A new geometric meaning of characteristic function is obtained. A new simple method of generating uniformly distributed random vector samples inn-dimensional unit hyper-spherical surface is put forward and strictly proved. This method is easy to put into practice. Numerical examples are given to show the applicability and effectiveness of the suggested approach to structural systems reliability problems. Supported by Chinese Postdoctor Fund([1998]6, 23).     

First-principles molecular dynamics simulations of the structure of germanium dioxide under pressures

We have carried out first-principles molecular dynamics simulations of glass and liquid germanium dioxide (GeO₂) over a wide range of pressure. Our results show that in the glass GeO₂ system nearly all Ge–O coordination environments are fourfold at low compression, whereas at high compression five- and sixfold coordination types coexist. In the liquid GeO₂ system although most Ge–O coordination environments are fourfold, some threefold coordination types exist at low compression. Pentahedral units also exist in the liquid state while less than that in the glass state. At high compression, pentahedral units disappear and GeO₆ octahedron is dominant in the liquid state going with some sevenfold coordination.     

SPH分析中的齿轮建模方法研究

对利用光滑粒子动力学(SPH-Smoothed Particle Hydrodynanlics)方法进行轮齿动态力学数值分析中的齿轮建模方法进行了研究.确定了齿轮齿根过渡曲线以及其他部分的参数方程,并根据所确定的参数方程建立了三维齿轮离散粒子模型的数学模型.编制了划分齿轮整体及局部离散粒子的SPH前处理程序.并对划分后齿轮离散粒子与齿轮理论轮廓之间进行了误差分析.分析结果表明,利用此办法可正确划分齿轮的SPH离散化粒子,是一种较好的前处理方法.     

Numerical semigroups with many gaps of the same parity

Let g _e (S) (respectively, g _o (S)) be the number of even (respectively, odd) gaps of a numerical semigroup S. In this work we study and characterize the numerical semigroups S that verify 2|g _e (S)−g _o (S)|+1∈S. As a consequence we will see that every numerical semigroup can be represented by means of a numerical semigroup with maximal embedding dimension with all its minimal generators odd. The first author is supported by the project MTM2007-62346 and FEDER funds. The authors want to thank P.A. García-Sánchez and the referee for their comments and suggestions.     

Synthesis of self‐healing supramolecular rubbers from fatty acid derivatives,diethylene triamine,and urea

We describe the synthesis of supramolecular self‐healing elastomers from vegetable oil fatty acid derivatives, diethylene triamine, and urea. Our strategy to obtain materials that are self‐healing but do not flow relies on the use of a wide molecular distribution of randomly branched oligomers equipped with self‐complementary and complementary hydrogen bonding groups. We prepared such oligomers with a two steps procedure. In the first step, diethylene triamine was condensed with dimer acids. In the second step, the oligomers obtained were allowed to react with urea. The molecules were characterized by NMR and IR spectroscopies and Monte‐Carlo simulations were used to analyze the molecular size distribution. The sensitivity to small variations of the experimental conditions has been examined and the robustness of the synthetic procedure optimized. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 7925–7936, 2008     

Unusual conformation of molecular cylindrical brushes strongly adsorbed on a flat solid surface

Conformational properties of comb-like polymers strongly adsorbed on a flat solid surface were investigated using computer simulation and scanning force microscopy. The computer simulation showed that the macromolecules with asymmetric distribution of the side chains relatively to the backbone are effectively in a collapsed state even under conditions of a good solvent. They formed peculiar helical superstructures which could be observed by scanning force microscopy of cylindrical brushes of polymethylmethacrylate on mica. Received 13 September 1999     

Progress and challenges in computational rheology

Our research work over the last few years serves to illustrate the basic issues associated with the numerical prediction of rheologically-complex flows, with particular emphasis on viscoelastic fluids. Numerical challenges in this field are shown to be tightly coupled to the mathematical nature of the governing equations, as well as to fundamental physical issues such as flow behavior close to walls and singularities.Delivered as a Keynote Lecture at the Golden Jubilee Conference of the British Society of Rheology and Third European Rheology Conference, Edinburgh, 3–7 September, 1990.     

Time-dependent natural convection in a square cavity: Application of a new finite volume method

A new finite volume (FV) approach with adaptive upwind convection is used to predict the two-dimensional unsteady flow in a square cavity. The fluid is air and natural convection is induced by differentially heated vertical walls. The formulation is made in terms of the vorticity and the integral velocity (induction) law. Biquadratic interpolation formulae are used to approximate the temperature and vorticity fields over the finite volumes, to which the conservation laws are applied in integral form. Image vorticity is used to enforce the zero-penetration condition at the cavity walls. Unsteady predictions are carried sufficiently forward in time to reach a steady state. Results are presented for a Prandtl number (Pr) of 0-71 and Rayleigh numbers equal to 10³, 10⁴ and 10⁵. Both 11 × 11 and 21 × 21 meshes are used. The steady state predictions are compared with published results obtained using a finite difference (FD) scheme for the same values of Pr and Ra and the same meshes, as well as a numerical bench-mark solution. For the most part the FV predictions are closer to the bench-mark solution than are the FD predictions.     

Identifying the radiating core of Lighthill’s source term

A decomposition of the Lighthill source term is effected which yields ten sub-terms comprising velocity, vorticity, dilatation and density fields. An analysis methodology is then developed, aimed at understanding the respective roles played by these sub-terms in the production of sound. By Direct Numerical Simulation of a temporal mixing-layer—chosen both for its simplicity and its amenability to analysis in wavenumber space—the radiating components of the different sub-terms are isolated and studied. Interesting identities are observed between specific events in the evolution of the flow and the various sub-terms of the source, and the essence of the sound production mechanism is found to comprise subtle imbalances which disrupt inherent space–time symmetries which exist between the various sub-terms.