Global optimization of robust chance constrained problems

We propose a stochastic algorithm for the global optimization of chance constrained problems. We assume that the probability measure with which the constraints are evaluated is known only through its moments. The algorithm proceeds in two phases. In the first phase the probability distribution is (coarsely) discretized and solved to global optimality using a stochastic algorithm. We only assume that the stochastic algorithm exhibits a weak* convergence to a probability measure assigning all its mass to the discretized problem. A diffusion process is derived that has this convergence property. In the second phase, the discretization is improved by solving another nonlinear programming problem. It is shown that the algorithm converges to the solution of the original problem. We discuss the numerical performance of the algorithm and its application to process design.     

Asymptotic approximation of eigenelements of the Dirichlet problem for the Laplacian in a domain with shoots

We study the asymptotic behavior of the eigenelements of the Dirichlet problem for the Laplacian in a two‐dimensional bounded domain with thin shoots, depending on a small parameter ε. Under the assumption that the width of the shoots goes to zero, as ε tends to zero, we construct the limit (homogenized) problem and prove the convergence of the eigenvalues and eigenfunctions to the eigenvalues and eigenfunctions of the limit problem, respectively. Under the additional assumption that the shoots, in a fixed vicinity of the basis, are straight and periodic, and their width and the distance between the neighboring shoots are of order ε, we construct the two‐term asymptotics of the eigenvalues of the problem, as ε→0. Copyright © 2009 John Wiley & Sons, Ltd.     

An Interior-Point Algorithm for Nonlinear Minimax Problems

We present a primal-dual interior-point method for constrained nonlinear, discrete minimax problems where the objective functions and constraints are not necessarily convex. The algorithm uses two merit functions to ensure progress toward the points satisfying the first-order optimality conditions of the original problem. Convergence properties are described and numerical results provided.     

Dynamical aspects of the adsorption hysteresis phenomenon

Equilibrium and nonequilibrium transport properties of adsorbates in mesoporous Vycor porous glass have been experimentally studied using nuclear magnetic resonance techniques. With the known geometrical characteristics of porous glass and with measured self-diffusivities, transient sorption curves have been quantitatively compared to those predicted within a Fick's law model. This model correctly describes data outside a hysteresis region. In contrast, in the hysteresis region, a two-step mechanism of density relaxation is required to explain the behavior. These two mechanisms are identified as diffusion at early stages and activated density redistribution at later stages of adsorption. The latter mechanism, being intrinsically slow in nature, is anticipated to prevent the system from reaching equilibrium.     

Revealing the Transient Concentration of CO2 in a Mixed‐Matrix Membrane by IR Microimaging and Molecular Modeling

Through IR microimaging the spatially and temporally resolved development of the CO₂ concentration in a ZIF‐8@6FDA‐DAM mixed matrix membrane (MMM) was visualized during transient adsorption. By recording the evolution of the CO₂ concentration, it is observed that the CO₂ molecules propagate from the ZIF‐8 filler, which acts as a transport “highway”, towards the surrounding polymer. A high‐CO₂‐concentration layer is formed at the MOF/polymer interface, which becomes more pronounced at higher CO₂ gas pressures. A microscopic explanation of the origins of this phenomenon is suggested by means of molecular modeling. By applying a computational methodology combining quantum and force‐field based calculations, the formation of microvoids at the MOF/polymer interface is predicted. Grand canonical Monte Carlo simulations further demonstrate that CO₂ tends to preferentially reside in these microvoids, which is expected to facilitate CO₂ accumulation at the interface.     

Millisecond kinetics on a microfluidic chip using nanoliters of reagents

This paper describes a microfluidic chip for performing kinetic measurements with better than millisecond resolution. Rapid kinetic measurements in microfluidic systems are complicated by two problems: mixing is slow and dispersion is large. These problems also complicate biochemical assays performed in microfluidic chips. We have recently shown (Song, H.; Tice, J. D.; Ismagilov, R. F. Angew. Chem., Int. Ed. 2003, 42, 768-772) how multiphase fluid flow in microchannels can be used to address both problems by transporting the reagents inside aqueous droplets (plugs) surrounded by an immiscible fluid. Here, this droplet-based microfluidic system was used to extract kinetic parameters of an enzymatic reaction. Rapid single-turnover kinetics of ribonuclease A (RNase A) was measured with better than millisecond resolution using sub-microliter volumes of solutions. To obtain the single-turnover rate constant (k = 1100 +/- 250 s(-1)), four new features for this microfluidics platform were demonstrated: (i) rapid on-chip dilution, (ii) multiple time range access, (iii) biocompatibility with RNase A, and (iv) explicit treatment of mixing for improving time resolution of the system. These features are discussed using kinetics of RNase A. From fluorescent images integrated for 2-4 s, each kinetic profile can be obtained using less than 150 nL of solutions of reagents because this system relies on chaotic advection inside moving droplets rather than on turbulence to achieve rapid mixing. Fabrication of these devices in PDMS is straightforward and no specialized equipment, except for a standard microscope with a CCD camera, is needed to run the experiments. This microfluidic platform could serve as an inexpensive and economical complement to stopped-flow methods for a broad range of time-resolved experiments and assays in chemistry and biochemistry.     

Diffusion in complementary pore spaces

The rate of mass transfer is among the key numbers determining the efficiency of nanoporous materials in their use for matter upgrading by heterogeneous catalysis or mass separation. Transport enhancement by pore space optimization is, correspondingly, among the main strategies of efficiency promotion. Any such activity involves probing and testing of the appropriate routes of material synthesis and post-synthesis modification just as the exploration of the transport characteristics of the generated material. Modelling and molecular simulation is known to serve as a most helpful tool for correlating these two types of activities and their results. The present paper reports about a concerted research activity comprising these three types of activities. Recent progress in producing pore space replicas enabled focusing, in these studies, on “complementary” pore spaces, i.e. on pairs of material, where the pore space of one sample did just coincide with the solid space of the other. We report about the correlations in mass transfer as observable, in this type of material, by pulsed field gradient NMR diffusion studies, with reference to the prediction as resulting from a quite general, theoretical treatment of mass transfer in complementary pore spaces.