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.     

Predicted binding rate of new cephalosporin antibiotics by a 3D-QSAR method: a new approach

Abstract  

Antibiotics are chemotherapeutic agents with activity against microorganisms, for example bacteria, fungi, or protozoa, used for the treatment of many types of diseases. Binding of antibiotics to serum proteins in human plasma is a major determinant of their pharmacodynamic and pharmacokinetic behavior and, consequently, can affect their systemic distribution in the body. Here, the predicted binding rates of ceftazidime and 13 other pharmacological agents classified as antibiotics to plasma proteins (percentage fraction bound; PFB) were evaluated by use of 3D-QSAR models. We attempted to establish the contribution of hydrogen bond donor/acceptor and hydrophobic properties supplied by electrostatic fields to the PFB. Significant cross-validated correlation q ² (0.5–0.7) and the fitted correlation r ² (0.7–0.97) coefficients revealed that these models have reasonable power to predict the design 19 new antibiotics using ceftazidime as template, these compounds being our suggestion for further studies.     

External Homogenization for Hopf Algebras: Applications to Maschke's Theorem

We apply to Hopf algebras a construction from graded rings, called the group ring of a graded ring. By using this construction we study the transfer of properties between certain categories of relative Hopf modules. As another application, we obtain a Maschke-type theorem for a Galois extension over a semisimple Hopf algebra.     

A priori error estimates for a mixed finite element discretization of the Richards’ equation

Summary. A mixed finite element discretization is applied to Richards equation, a nonlinear, possibly degenerate parabolic partial differential equation modeling water flow through porous medium. The equation is considered in its pressure formulation and includes both variably and fully saturated flow regime. Characteristic for such problems is the lack in regularity of the solution. To handle this we use a time-integrated scheme. We analyze the scheme and present error estimates showing its convergence.Mathematics Subject Classification (2000): 65M12, 65M60, 76S05, 35K65Acknowledgments. We would like to thank Markus Bause for very useful discussions and suggestions.     

Three-dimensional tracking of fluorescent nanoparticles with subnanometer precision by use of off-focus imaging

We show that the position of a fluorescent nanoparticle can be measured in three dimensions with subnanometer precision and 100-ms temporal resolution by use of standard epifluorescence video imaging in off-focus mode. The particle can be tracked without feedback in a volume of at least 40 microm x 60 microm x 3 microm. With the technique presented, the structure-mobility relationship of 216-nm latex particle in a porous polymer network was studied in three dimensions.     

The Statistics of the Trajectory of a Certain Billiard in a Flat Two-Torus

We consider a billiard in the punctured torus obtained by removing a small disk of radius >0 from the flat torus ², with trajectory starting from the center of the puncture. In this case the phase space is given by the range of the velocity only. Let (), and respectively R(), denote the first exit time (length of the trajectory), and respectively the number of collisions with the side cushions when ² is being identified with [0,1)². We prove that the probability measures on [0, ) associated with the random variables and R are weakly convergent as 0⁺ and explicitly compute the densities of the limits. Research partially supported by ANSTI grant C6189/2000.     

Shaping of intense ion beams into hollow cylindrical form

A specifically tailored plasma lens could shape a high-energy, heavy-ion beam into the form of a hollow cylinder without loss of beam intensity. It has been experimentally confirmed that both a positive as well as a negative radial gradient of the current density in the active plasma lens can be the underlying principle. Calculations were performed that yield the ideal current density distribution for both cases. A numerical simulation of an experiment with an intense ion beam highlights that the shaping of the beam increases the achievable compression in a lead sample.     

A hybrid optimization technique coupling an evolutionary and a local search algorithm

Evolutionary algorithms are robust and powerful global optimization techniques for solving large-scale problems that have many local optima. However, they require high CPU times, and they are very poor in terms of convergence performance. On the other hand, local search algorithms can converge in a few iterations but lack a global perspective. The combination of global and local search procedures should offer the advantages of both optimization methods while offsetting their disadvantages. This paper proposes a new hybrid optimization technique that merges a genetic algorithm with a local search strategy based on the interior point method. The efficiency of this hybrid approach is demonstrated by solving a constrained multi-objective mathematical test-case.     

Decomposition of Methylene Blue in Water by Corona Discharges

The decomposition of methylene blue (MB) in aqueous solution was investigated using a pulsed corona discharge. The discharge was ignited in the gas bubbled in the solution through several needle electrodes. The influence of treatment time, volume of the treated solution and initial concentration of the dye in solution on MB degradation was studied. The effect of the nature of the gas introduced was also investigated. For the same energy input, MB conversion increased in the order air < argon < oxygen. When using oxygen, the decomposition of MB exceeded 95% after ~20 min plasma treatment. Higher efficiency was obtained for higher treated volume and higher initial concentration. At 90% conversion the yield obtained with oxygen was ~5 g/kWh for an initial concentration of 150 mg/l and a treated volume of solution of 100 ml.