Experimental test of scaling of mixing by chaotic advection in droplets moving through microfluidic channels

This letter describes an experimental test of a simple argument that predicts the scaling of chaotic mixing in a droplet moving through a winding microfluidic channel. Previously, scaling arguments for chaotic mixing have been described for a flow that reduces striation length by stretching, folding, and reorienting the fluid in a manner similar to that of the baker's transformation. The experimentally observed flow patterns within droplets (or plugs) resembled the baker's transformation. Therefore, the ideas described in the literature could be applied to mixing in droplets to obtain the scaling argument for the dependence of the mixing time, t~(aw/U)log(Pe), where w [m] is the cross-sectional dimension of the microchannel, a is the dimensionless length of the plug measured relative to w, U [m s(-1)] is the flow velocity, Pe is the Péclet number (Pe=wU/D), and D [m(2)s(-1)] is the diffusion coefficient of the reagent being mixed. Experiments were performed to confirm the scaling argument by varying the parameters w, U, and D. Under favorable conditions, submillisecond mixing has been demonstrated in this system.     

Minimax hedging strategy

We present several variants of a robust risk management strategy based on minimax for the writer of a European call option on a stock and show that it performs at least as well as the standard hedging strategy, delta hedging. When using the minimax strategy, the hedger specifies a worst case scenario in terms of the price of the underlying stock. The minimax strategy recommends the number of shares in the underlying stock the hedger should hold in order to minimize the hedging error against the worst case occurring. The minimax hedging error may correspond to an extreme point of the price range being considered or to a mid-range solution. Simulation and empirical results suggest that the minimax strategy is particularly powerful for hedging the risk of writing an option when the price of the underlying stock is both highly volatile and crosses over the exercise frequently.     

A Pricing Mechanism for Resource Management in Grid Computing

We consider the problem of efficient resource allocation in a grid computing environment. Grid computing is an emerging paradigm that allows the sharing of a large number of a heterogeneous set of resources. We propose an auction mechanism for decentralized resource allocation. The problem is modeled as a multistage stochastic programming problem. Convergence of the auction allocations to the social optimum is established. Numerical experiments illustrate the efficacy of the method.     

Gold Supported on Oxide Surfaces: Environmental Effects as Studied by STM

This paper begins by providing a short review of STM studies of gold particles supported on oxide surfaces. Following this, the morphology of Au particles deposited on thin FeO(111) films at elevated pressures of CO, O₂, CO+O₂, and H₂ has been examined using in situ STM at room temperature. The Au particles are found to be quite stable in oxygen and hydrogen environments at pressures up to 2 mbar. However, in CO and CO+O₂ atmospheres, the destabilization of Au particles located at the step edges occurs leading to the formation of mobile Au species, which migrate across the oxide surface. General problems encountered with high-pressure STM studies are discussed, and data clearly showing the effects of ambient gas impurities is provided. These effects may lead to erroneous conclusions, particularly about morphological changes of and CO dissociation on the gold surfaces at elevated pressures.     

Respecifying the weighting matrix of a quadratic objective function

A method based on a rank-one updating formula well known in function optimisation is described for respecifying the weighting matrix of the quadratic criterion function. The criterion function is thus altered systematically until an optimal solution acceptable to the policy-maker is generated. An iterative procedure is developed for this purpose.