Finite element and sensitivity analysis of thermally induced flow instabilities

This paper presents a finite element algorithm for the simulation of thermo‐hydrodynamic instabilities causing manufacturing defects in injection molding of plastic and metal powder. Mold‐filling parameters determine the flow pattern during filling, which in turn influences the quality of the final part. Insufficiently, well‐controlled operating conditions may generate inhomogeneities, empty spaces or unusable parts. An understanding of the flow behavior will enable manufacturers to reduce or even eliminate defects and improve their competitiveness. This work presents a rigorous study using numerical simulation and sensitivity analysis. The problem is modeled by the Navier–Stokes equations, the energy equation and a generalized Newtonian viscosity model. The solution algorithm is applied to a simple flow in a symmetrical gate geometry. This problem exhibits both symmetrical and non‐symmetrical solutions depending on the values taken by flow parameters. Under particular combinations of operating conditions, the flow was stable and symmetric, while some other combinations leading to large thermally induced viscosity gradients produce unstable and asymmetric flow. Based on the numerical results, a stability chart of the flow was established, identifying the boundaries between regions of stable and unstable flow in terms of the Graetz number (ratio of thermal conduction time to the convection time scale) and B, a dimensionless ratio indicating the sensitivity of viscosity to temperature changes. Sensitivities with respect to flow parameters are then computed using the continuous sensitivity equations method. We demonstrate that sensitivities are able to detect the transition between the stable and unstable flow regimes and correctly indicate how parameters should change in order to increase the stability of the flow. Copyright © 2009 John Wiley & Sons, Ltd.     

Determining the effective density of airborne nanoparticles using multiple charging correction in a tandem DMA/ELPI setup

The cysteamine-modified hyaluronic acid (HA) polymer was employed to coat quantum dots (QDs) through a convenient one-step reverse micelle method, with the final QDs hydrodynamic size of around 22.6 nm. The HA coating renders the QDs with very good stability in PBS for more than 140 days and resistant to large pH range of 2–12. Besides, the HA-coated QDs also show excellent fluorescence stability in BSA-containing cell culture medium. In addition, the cell culture assay indicates no significant cytotoxicity for MD-MB-231 breast cancer cells, and its targeting ability to cancer receptor CD44 has been demonstrated on two breast cancer cell lines. The targeting mechanism was further proved by the HA competition experiment. This work has established a new approach to help solve the stability and toxicity problems of QDs, and moreover render the QDs cancer targeting property. The current results indicate that the HA polymer-coated QDs hold the potential application for both in vitro and in vivo cancer imaging researches.     

Synthesis of side‐chain‐substituted ifosfamide analogs

Three analogs of the cytostatic drug ifosfamide incorporating 1‐methyl‐2‐chloroethyl side chains were designed and prepared as an attempt to obtain drugs of lower toxicity.     

Evolutionary Pareto distributions

We consider here i.i.d. variables which are distributed according to a Pareto up to some point x₁ and a Pareto (with a different parameter) after this point. This model constitutes an approximation for estimating extreme tail probabilities, especially for financial or insurance data. We estimate the parameters by maximizing the likelihood of the sample, and investigate the rates of convergence and the asymptotic laws. We find here a problem which is very close to the change point question from the point of view of limits of experiments. Especially, the rates of convergence and the limiting law obtained here are the same as in a change point framework. Simulations are giving an illustration of the quality of the procedure.     

Graphs which are locally a cube

We prove that there are exactly two connected graphs which are locally a cube: a graph on 15 vertices which is the complement of the (3×5)-grid and a graph on 24 vertices which is the 1-skeleton of a certain 4-dimensional regular polytope called the 24-cell.     

A noncommutative version of the matrix inversion formula

The cofactor expression (? 1)^i+j$\text{det}\text{(I ? B)}{}_{\mathrm{<mtext>j</mtext><mtext>?</mtext><mtext>i</mtext><mtext>?</mtext>}}\text{det}\text{(I ? B)}$ for the (i, j)-entry in the inverse of a matrix (I ? B) is proved to be equal to the corresponding entry of the series Σ_m≥0B^m, by using purely combinatorial methods: circuit monoid techniques and monomial rearrangements. Moreover, the identity is shown to hold in a non-commutative formal power series algebra.