On a free boundary problem for the Reynolds equation derived from the Stokes system with Tresca boundary conditions

The asymptotic behaviour of a Stokes flow with Tresca free boundary friction conditions when one dimension of the fluid domain tends to zero is studied. A specific Reynolds equation associated with variational inequalities is obtained and uniqueness is proved.     

Rhythmic growth of ring‐banded spherulites in blends of liquid crystalline methoxy‐poly(aryl ether ketone) and poly(aryl ether ether ketone)

Rhythmic growth of ring‐banded spherulites in blends of liquid crystalline methoxy‐poly(aryl ether ketone) (M‐PAEK) and poly(aryl ether ether ketone) (PEEK) has been investigated by means of differential scanning calorimetry (DSC), polarized light microscopy (PLM), and scanning electron microscopy (SEM) techniques. The measurements reveal that the formation of the rhythmically grown ring‐banded spherulites in the M‐PAEK/PEEK blends is strongly dependent on the blend composition. In the M‐PAEK‐rich blends, upon cooling, an unusual ring‐banded spherulite is formed, which is ascribed to structural discontinuity caused by a rhythmic radial growth. For the 50:50 M‐PAEK/PEEK blend, ring‐banded spherulites and individual PEEK spherulites coexist in the system. In the blends with PEEK as the predominant component, M‐PAEK is rejected into the boundary of PEEK spherulites. The cooling rate and crystallization temperature have great effect on the phase behavior, especially the ring‐banded spherulite formation in the blends. In addition, the effects of M‐PAEK phase transition rate and phase separation rate on banded spherulite formation is discussed. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3011–3024, 2007     

广义多目标minmax问题的最优性条件和极大熵方法

本文讨论了广义多目标minmax问题的最优性条件。利用极大熵逼近函数，研究了广义多目标minmax；问题的逼近问题，在较弱的条件下，证明了由极大熵逼近函数导出的多目标逼近问题的临界点的任一极限点均为原广义多目标minmax问题的临界点。     

A non‐linear and non‐local boundary condition for a diffusion equation in petroleum engineering

This article deals with a boundary value problem for Laplace equation with a non‐linear and non‐local boundary condition. This problem comes from petroleum engineering and is used to obtain an estimation of well productivity. The non‐linear and non‐local boundary condition is written on the well boundary. On the outer reservoir boundaries, we have both Dirichlet and Neumann conditions. In this paper, we prove the existence and uniqueness of a solution to this problem. The existence is proved by Schauder theorem and the uniqueness is obtained under more restricted conditions, when the involved operator is a contraction. Copyright © 2005 John Wiley & Sons, Ltd.     

Detecting instabilities in flows of viscoelastic fluids

There is a growing interest in developing numerical tools to investigate the onset of physical instabilities observed in experiments involving viscoelastic flows, which is a difficult and challenging task as the simulations are very sensitive to numerical instabilities. Following a recent linear stability analysis carried out in order to better understand qualitatively the origin of numerical instabilities occurring in the simulation of flows viscoelastic fluids, the present paper considers a possible extension for more complex flows. This promising method could be applied to track instabilities in complex (i.e. essentially non‐parallel) flows. In addition, results related to transient growth mechanism indicate that it might be responsible for the development of numerical instabilities in the simulation of viscoelastic fluids. Copyright © 2003 John Wiley & Sons, Ltd.     

Minimum Distance Between the Faces of Two Convex Polyhedra: A Sufficient Condition

The problem of finding the Euclidean distance between two convex polyhedra can be reduced to the combinatorial optimization problem of finding the minimum distance between their faces. This paper presents a global optimality criterion for this problem. An algorithm (QLDPA) for the fast computation of the distance between convex and bounded polyhedra is proposed as an application of it. Computer experiments show its fast performance, especially when the total number of vertices is large.     

Characterization of sulfate-reducing bacteria in yeast industry waste by microcalorimetry and PCR amplification

Sulfate-reducing bacteria (SRB) were isolated from anaerobic sludge of yeast factory wastewater treatment plant by cultivation on Postgate C medium. Microcalorimetry was used to monitor the anaerobic digestion processes and to measure the growth rates of sulfate-reducing bacteria. The maximum growth rates determined by microcalorimetry and ATP analysis were different—μ_max(dQ/dt) = 0.165 ± 0.008 h⁻¹ and μ_max(N_ATP) = 0.207 ± 0.013 h⁻¹. Experiments on the cultivation of SRB from yeast industry wastewater treatment plant in batch culture showed that during the first 20 h the concentration of sulfate decreased from 78.3 mM down to 62.2 mM while the increase of sulfide production was negligible. Perceptible amount of sulfide (7.82 mM) appeared on the 33.5 h of fermentation together with a peak on the power–time curve and considerable increase in the cell count (1.26 × 10⁹). First steps of sulfate metabolism (activation of sulfate by ATP sulfurylase, production of H₂) are accompanied by endothermic heat effects, therefore the values of thermal power remain moderate until the evolution of sulfide starts. The influence of green microalgae Chlorococcum sp. (preparation Biotreat 100) on the growth characteristics of microorganisms was also studied. Identification of one SRB strain was started by sequencing of PCR-amplified 16S rRNA gene. Two sets of primers were used for PCR amplification, both specific for domain Bacteria but giving different gene fragments. PCR-products were purified with JETQUICK kit according to the manufacturer instructions.     

Methods for implementing the stream boundary condition in DSMC computations

In the direct simulation Monte‐Carlo (DSMC) method for simulating rarefied gas flows, the velocities of simulator particles that cross a simulation boundary and enter the simulation space are typically generated using the acceptance–rejection procedure that samples the velocities from a truncated theoretical velocity distribution that excludes low and high velocities. This paper analyses an alternative technique, where the velocities of entering particles are obtained by extending the simulation procedures to a region adjacent to the simulation space, and considering the movement of particles generated within that region during the simulation time step. The alternative method may be considered as a form of acceptance–rejection procedure, and permits the generation of all possible velocities, although the population of high velocities is depleted with respect to the theoretical distribution. Nevertheless, this is an improvement over the standard acceptance–rejection method. Previous implementations of the alternative method gave a number flux lower than the theoretical number required. Two methods for obtaining the correct number flux are presented. For upstream boundaries in high‐speed flows, the alternative method is more computationally efficient than the acceptance–rejection method. However, for downstream boundaries, the alternative method is extremely inefficient. The alternative method, with the correct theoretical number flux, should therefore be used in DSMC computations in favour of the acceptance–rejection method for upstream boundaries in high‐speed flows. Copyright © 2003 John Wiley & Sons, Ltd.     

On the application of slip boundary condition on curved boundaries

Hydrodynamic simulations of sloshing phenomena often involve the application of slip boundary condition at the wetted surfaces. If these surfaces are curved, the ambiguous nature of the normal vector in the discretized problem can interfere with the application of such a boundary condition. Even the use of consistent normal vectors, preferred from the point of view of conservation, does not assure good approximation of the continuum slip condition in the discrete problem, and non‐physical recirculating flow fields may be observed. As a remedy, we consider the Navier slip condition, and more successfully, the so‐called BC‐free boundary condition. Copyright © 2004 John Wiley & Sons, Ltd.     

LINEAR ACTIVE STRUCTURES AND MODES (Ⅱ)--DISCRETE SYSTEMS AND BEAMS

The basic concepts about the active structures and some attributes of the modes were presented in paper "Liner Active Structures and Modes ( Ⅰ ) ". The characteristics of the active discrete systems and active beams were discussed, especially, the stability of the active structures and the orthogonality of the eigenvectors. The notes about modes were portrayed by a model of a seven-storeyed building with sensors and actuators. The concept of the adjoint active structure was extended from the discrete systems to the beams that were the representations of the continuous structures. Two types of beams with different placements of the measuring and actuating systems were discussed in detail. One is the beam with the discrete sensors and actuators, and the other is the beam with distributed sensor and actuator function. The orthogonality conditions were derived with the modal shapes of the active beam and its adjoint active beam. An example shows that the variation of eigenvalues with feedback amplitude for the homo-configuration and non-homo-configuration active structures.