On the convergence of difference schemes for one nonlocal boundary-value problem

We consider a nonlocal boundary-value problem for the Poisson equation in a rectangular domain. Dirichlet conditions are posed on a pair of adjacent sides of a rectangle, and integral constraints are given instead of standard boundary conditions on the other pair. The corresponding difference scheme is constructed and investigated; an a priori estimate of the solution is obtained with the help of energy inequality method. Discretization error estimate that is compatible with the smoothness of the solution sought is obtained.     

The Effect of Number of Arms on the Aggregation Behavior of Thermoresponsive Poly(N-isopropylacrylamide) Star Polymers

The thermoresponsive nature of aqueous solutions of poly(N-isopropylacrylamide) (PNIPAAM) star polymers containing 2, 3, 4, and 6 arms has been investigated by turbidity, dynamic light scattering, rheology, and rheo-SALS. Simulations of the thermosensitive nature of the single star polymers have also been conducted. Some of the samples form aggregates even at temperatures significantly below the lower critical solution temperature (LCST) of PNIPAAM. Increasing concentration and number of arms promotes associations at low temperatures. When the temperature is raised, there is a competition between size increase due to enhanced aggregation and a size reduction caused by contraction. Monte Carlo simulations show that the single stars contract with increasing temperature, and that this contraction is more pronounced when the number of arms is increased. Some samples exhibit a minimum in the turbidity data after the initial increase at the cloud point. The combined rheology and rheo-SALS data suggest that this is due to a fragmentation of the aggregates followed by re-aggregation at even higher temperatures. Although the 6-arm star polymer aggregates more than the other stars at low temperatures, the more compact structure renders it less prone to aggregation at temperatures above the cloud point.     

Effects of addition of anionic and cationic surfactants to poly(N-isopropylacrylamide) microgels with and without acrylic acid groups

The interaction of the anionic surfactant sodium dodecyl sulfate (SDS) and the cationic surfactant hexadecyl trimethyl ammonium bromide with poly(N-isopropylacrylamide) (PNIPAAM) microgels with and without poly(acrylic acid) (PAA) was investigated by means of dynamic light scattering (DLS), zeta potential, and turbidimetry measurements. The DLS results show that the PNIPAAM microgels with PAA will contract when an anionic or cationic surfactant is added to the suspension, while the PNIPAAM microgels without PAA expand in the presence of an ionic surfactant. A collapse of the PNIPAAM microgels is observed when the temperature is increased. From the zeta potential measurements, it is observed that the charge density of PNIPAAM microgels in the presence of an ionic surfactant is significantly affected by temperature and the attachment of the negatively charged PAA groups. The turbidity measurements clearly indicate that the interaction between PNIPAAM and SDS is more pronounced than that of the cationic surfactant.     

Effects of Hofmeister anions on the flocculation behavior of temperature-responsive poly(N-isopropylacrylamide) microgels

Effects of some sodium salts (NaCl, NaClO₃, and NaSCN) in the Hofmeister series on deswelling and temperature-induced aggregation behavior of microgels of poly(N-isopropylacrylamide) (PNIPAAM) and PNIPAAM-co-PAA with attached poly(acrylic acid) moieties were investigated with the aid of turbidimetry and dynamic light scattering. Addition of salt in the concentration range 0.1–0.5?M generated aggregation of the PNIPAAM microgel particles at elevated temperatures, but it was no distinct difference between chaotropic and kosmotropic anions. In contrast, the flocculation behavior at high temperatures for PNIPAAM-co-PAA revealed a prominent influence of salinity and type of anion on the formation of aggregates. The aggregation transition was shifted to the highest temperature for the most chaotropic anion (SCN^?), and the aggregation transition at the same salt concentration is consistent with the typical Hofmeister series. The turbidity results from the PNIPAAM-co-PAA microgels disclosed a two-step transition for the considered anions, and both a low and high temperature change in the turbidity data was observed. The high-temperature transition followed the Hofmeister series.     

A cross entropy based algorithm for reliability problems

The Cross Entropy method has recently been applied to combinatorial optimization problems with promising results. This paper proposes a Cross Entropy based algorithm for reliability optimization of complex systems, where one wants to maximize the reliability of a system through optimal allocation of redundant components while respecting a set of budget constraints. We illustrate the effectiveness of the proposed algorithm on two classes of problems, software system reliability optimization and complex network reliability optimization, by testing it on instances from the literature as well as on randomly generated large scale instances. Furthermore, we show how a Cross Entropy-based algorithm can be fine-tuned by using a training scheme based upon the Response Surface Methodology. Computational results show the effectiveness as well as the robustness of the algorithm on different classes of problems.     

On a numerical solution of one nonlocal boundary-value problem with mixed Dirichlet–Neumann conditions

We consider a nonlocal boundary-value problem for the Poisson equation in a rectangular domain. Dirichlet and Neumann conditions are posed on a pair of adjacent sides of a rectangle, and integral constraints are given instead of boundary conditions on the other pair. The corresponding difference scheme is constructed and investigated; an a priori estimate of the solution is obtained with the help of energy inequality method. Discretization error estimate that is compatible with the smoothness of the solution sought is obtained.