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?.     

Self-injection length in La0.7Ca0.3MnO3-YBa2Cu3O7-δ ferromagnet-superconductor multilayer thin films

We have carried out extensive studies on the self-injection problem in barrierless heterojunctions between La_0.7Ca_0.3MnO₃ (LCMO) and YBa₂Cu₃O_7-δ (YBCO) thin films. The heterojunctions were formed in situ by sequentially growing LCMO and YBCO films on 〈100〉 LaAlO₃ (LAO) substrate using a pulsed laser deposition (PLD) system. YBCO micro-bridges with 64 μm width were patterned both on the LAO (control) and LCMO side of the substrate. Critical current, I _c, was measured at 77 K on both the control side as well as the LCMO side for different YBCO film thickness. It was observed that while the control side showed a J _c of ∼ 2 × 10⁶ A/cm², the LCMO side showed about half the value for the same thickness (1800 ?). The difference in J _c indicates that a certain thickness of YBCO has become ‘effectively’ normal due to self-injection. From the measurement of J _c at two different thicknesses (1800 ? and 1500 ?) of YBCO films both on the LAO as well as the LCMO side, the value of self-injection length (at 77 K) was estimated to be ∼ 900 ?. To the authors’ best knowledge, this is the first time that self-injection length has been quantified. A control experiment carried out with LaNiO₃ deposited by PLD on YBCO did not show any evidence of self-injection.     

Study of magnetoresistance and conductance of bicrystal grain boundary in La0.67Ba0.33MnO3 thin film

La_0.67Ba_0.33MnO₃ (LBMO) thin film is deposited on a 36.7°C SrTiO₃ bicrystal substrate using laser ablation technique. A microbridge is created across bicrystal grain boundary and its characteristics are compared with a microbridge on the LBMO film having no grain boundary. Presence of grain boundary exhibits substantial magnetoresistance ratio (MRR) in the low field and low temperature region. Bicrystal grain boundary contribution in MRR disappears at temperature T>175 K. At low temperature, I-V characteristic of the microbridge across bicrystal grain boundary is nonlinear. Analysis of temperature dependence of dynamic conductance-voltage characteristics of the bicrystal grain boundary indicates that at low temperatures (T<175 K) carrier transport across the grain boundary in LBMO film is dominated by inelastic tunneling via pairs of manganese atoms and tunneling through disordered oxides. At higher temperatures (T>175 K), magnetic scattering process is dominating. Decrease of bicrystal grain boundary contribution in magnetoresistance with the increase in temperature is due to enhanced spin-flip scattering process.     

Molar extinction coefficients of some carbohydrates in aqueous solutions

Molar extinction coefficients of some carbohydrates viz. l-arabinose (C₅H₁₀O₅), d-glucose (C₆H₁₂O₆), d-mannose (C₆H₁₂O₆), d-galactose (C₆H₁₂O₆), d(-) fructose (C₆H₁₂O₆) and maltose (C₁₂H₂₄O₁₂) in aqueous solutions have been determined at 81, 356, 511, 662, 1173 and 1332 keV by gamma ray transmission method in a narrow beam good geometry set-up. These coefficients have been found to depend upon the photon energy following a 4-parameter polynomial. These extinction coefficients for different sugars having the same molecular formula have same values varying within experimental uncertainty. Within concentration ranges studied, Beer-Lambert law is obeyed very well.     

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.