Solving Sequences of Refined Multistage Stochastic Linear Programs

Multistage stochastic programs with continuous underlying distributions involve the obstacle of high-dimensional integrals where the integrands' values again are given by solutions of stochastic programs. A common solution technique consists of discretizing the support of the original distributions leading to scenario trees and corresponding LPs which are – up to a certain size – easy to solve. In order to improve the accuracy of approximation, successive refinements of the support result in rapidly expanding scenario trees and associated LPs. Hence, the solvability of the multistage stochastic program is limited by the numerical solvability of sequences of such expanding LPs. This work describes an algorithmic technique for solving the large-scale LP of refinement ν based on the solutions at the previous ν?1 refinements. Numerical results are presented for practical problem statements within financial applications demonstrating significant speedup (depending on the size of the LP instances).     

Azimuthal orientational correlations due to excluded volume epitaxy in growing anisotropic grains

The microstructure of anisotropically shaped grains can strongly influence a range of material properties, including transport, mechanical and electro-optical. A grain-structure-related phenomenon, known as excluded volume epitaxy (EVE), is reported in this study. EVE is a local, inter-grain orientational correlations effect, which results from a combination of continuous nucleation of anisotropic grains and impingement of growing grains. Due to EVE, anisotropically shaped grains have a tendency to be similarly aligned in a local neighbourhood, despite the absence of any forced global orientation in the sample. The effect has been repeatedly observed by the authors in block copolymers, as illustrated by a representative TEM image. Optical microscopy of anisotropically shaped non-polymeric crystals revealed the generality of this effect. The simulation study revealed a tendency for azimuthal, inter-grain orientational correlation and re-confirmed the experimental observation of EVE.     

Stigmergy in comparative settlement choice and palaeoenvironment simulation

Decisions on settlement location in the face of climate change and coastal inundation may have resulted in success, survival or even catastrophic failure for early settlers in many parts of the world. In this study, we investigate various questions related to how individuals respond to a palaeoenvironmental simulation, on an interactive tabletop device where participants have the opportunity to build a settlement on a coastal landscape, balancing safety, and access to resources, including sea and terrestrial foodstuffs, while taking into consideration the threat of rising sea levels. The results of the study were analyzed to consider whether decisions on settlement were predicated to be near to locations where previous structures were located, stigmergically, and whether later settler choice would fare better, and score higher, as time progressed. The proximity of settlements was investigated and the reasons for clustering were considered. The interactive simulation was exhibited to thousands of visitors at the 2012 Royal Society Summer Science Exhibition at the “Europe's Lost World” exhibit. 347 participants contributed to the simulation, providing a sufficiently large sample of data for analysis. © 2014 Wiley Periodicals, Inc. Complexity 21: 59–73, 2016     

Chain homogeneous Souslin algebras

Assuming Jensen's principle ?⁺ we construct Souslin algebras all of whose maximal chains are pairwise isomorphic as total orders, thereby answering questions of Koppelberg and Todor?evi?.     

Interfacial Microcompartmentalization by Kinetic Control of Selective Interfacial Accumulation

Reported here is a 2D, interfacial microcompartmentalization strategy governed by 3D phase separation. In aqueous polyethylene glycol (PEG) solutions doped with biotinylated polymers, the polymers spontaneously accumulate in the interfacial layer between the oil-surfactant-water interface and the adjacent polymer phase. In aqueous two-phase systems, these polymers first accumulated in the interfacial layer separating two polymer solutions and then selectively migrated to the oil-PEG interfacial layer. By using polymers with varying photopolymerizable groups and crosslinking rates, kinetic control and capture of spatial organisation in a variety of compartmentalized macroscopic structures, without the need of creating barrier layers, was achieved. This selective interfacial accumulation provides an extension of 3D phase separation towards synthetic compartmentalization, and is also relevant for understanding intracellular organisation.     

Nanostructured block-random copolymers with tunable magnetic properties

It was recently shown that block copolymers (BCPs) produced room-temperature ferromagnetic materials (RTFMs) due to their nanoscopic ordering and the cylindrical phase yielded the highest coercivity. Here, a series of metal-containing block-random copolymers composed of an alkyl-functionalized homo block (C(16)) and a random block of cobalt complex- (Co) and ferrocene-functionalized (Fe) units was synthesized via ring-opening metathesis polymerization. Taking advantage of the block-random architecture, the influence of dipolar interactions on the magnetic properties of these nanostructured BCP materials was studied by varying the molar ratio of the Co units to the Fe units, while maintaining the cylindrical phase-separated morphology. DC magnetic measurements, including magnetization versus field, zero-field-cooled, and field-cooled, as well as AC susceptibility measurements showed that the magnetic properties of the nanostructured BCP materials could be easily tuned by diluting the cobalt density with Fe units in the cylindrical domains. Decreasing the cobalt density weakened the dipolar interactions of the cobalt nanoparticles, leading to the transition from a room temperature ferromagnetic (RTF) to a superparamagnetic material. These results confirmed that dipolar interactions of the cobalt nanoparticles within the phase-separated domains were responsible for the RTF properties of the nanostructured BCP materials.     

Nanoparticle-driven assembly of block copolymers: a simple route to ordered hybrid materials

The addition of nanoparticles that selectively hydrogen bond with one of the segments of a block copolymer is shown to induce order in otherwise disordered systems. This enables the fabrication of well-ordered hybrid materials with spherical, cylindrical, or lamellar domains at particle loadings of more than 40%, as evidenced by TEM and SAXS. The approach described is simple and applicable to a wide range of nanoparticles and block copolymers, and it lays the groundwork for the design of cooperatively assembled functional devices.