Chance Constrained Mixed Integer Program: Bilinear and Linear Formulations, and Benders Decomposition

In this paper, we study chance constrained mixed integer program with consideration of recourse decisions and their incurred cost, developed on a finite discrete scenario set. Through studying a non-traditional bilinear mixed integer formulation, we derive its linear counterparts and show that they could be stronger than existing linear formulations. We also develop a variant of Jensen's inequality that extends the one for stochastic program. To solve this challenging problem, we present a variant of Benders decomposition method in bilinear form, which actually provides an easy-to-use algorithm framework for further improvements, along with a few enhancement strategies based on structural properties or Jensen's inequality. Computational study shows that the presented Benders decomposition method, jointly with appropriate enhancement techniques, outperforms a commercial solver by an order of magnitude on solving chance constrained program or detecting its infeasibility

Production of syndiotactic polystyrene powder for part manufacturing through SLS

Selective laser sintering (SLS) is a well-established additive manufacturing (AM) process. While AM originally found its use as rapid prototyping technique, it is nowadays more and more considered for the production of actual end-use parts. A widely acknowledged hindrance in the evolution of this technology is the limited range of materials available for processing with SLS, making the application window rather small. Introducing new materials with the correct morphology and thermal requirements for SLS could broaden this window and give rise to new products. This research aims at identifying such promising materials, considering the relevant requirements for selecting and processing a new material. Considered foremost within this manuscript is the processability of syndiotactic polystyrene from pellet form into spherical particles of 50-90 μm without significantly changing their properties. Regarding processing methods, the focus of this work is on solution based techniques (single phase precipitation, emulsion precipitation) instead of more conventional mechanical processing methods (ball milling) as these are believed to be more accessible and more suitable as a precursor step for a wide range of processing technique

Processing and characterization of syndiotactic polystyrene into a free flowing powder

C

Optimising bioreactor processes with in-situ product removal using mathematical programming: A case study for propionate production

Designing and operating bioreactors with in-situ product removal (ISPR) can be challenging, particularly in discontinuous systems, where the ISPR and substrate feeding need to be effectively scheduled. Mathematical models can help assess different scheduling regimes in the fermentation medium and provide a means to optimise the process. Focusing on a propionate production case study, a model of a co-culture batch fermentation with electrodialysis (the ISPR system), was developed. Using this model, the product yield and/or the productivity were maximised by 1) single objective optimisation maximising the product yield (0.49 gpropionate /gglucose) or productivity (0.75 gpropionate/L/h), 2) multi objective optimisation to pursue trade-off solutions between the yield and productivity and 3) a stochastic optimisation maximising the productivity robustly (0.64 gpropionate/L/h) to account for uncertainties associated to the model parameters. With this contribution it is demonstrated that, through mathematical models, ISPR can be implemented and adapted to the user's objectivesThis work was supported by project ALQUIMIA (PID2019-110993RJ-I00) funded by the Agencia Estatal de Investigación Alquimia: Proyecto de I- d-i Programa Retos de la sociedad modalidad Jovenes investigadores convocatoria. A. Regueira would like to acknowledge the support of the Xunta de Galicia through a postdoctoral fellowship (ED481B-2021-012)S

Ultrafast Hole Trapping and Relaxation Dynamics in p-Type CuS Nanodisks

CuS nanocrystals are potential materials for developing low-cost solar energy conversion devices. Understanding the underlying dynamics of photoinduced carriers in CuS nanocrystals is essential to improve their performance in these devices. In this work, we investigated the photoinduced hole dynamics in CuS nanodisks (NDs) using the combination of transient optical (OTA) and X-ray (XTA) absorption spectroscopy. OTA results show that the broad transient absorption in the visible region is attributed to the photoinduced hot and trapped holes. The hole trapping process occurs on a subpicosecond time scale, followed by carrier recombination (~100 ps). The nature of the hole trapping sites, revealed by XTA, is characteristic of S or organic ligands on the surface of CuS NDs. These results not only suggest the possibility to control the hole dynamics by tuning the surface chemistry of CuS but also represent the first time observation of hole dynamics in semiconductor nanocrystals using XTA

F-Theorem without Supersymmetry

The conjectured F-theorem for three-dimensional field theories states that the finite part of the free energy on S^3 decreases along RG trajectories and is stationary at the fixed points. In previous work various successful tests of this proposal were carried out for theories with {\cal N}=2 supersymmetry. In this paper we perform more general tests that do not rely on supersymmetry. We study perturbatively the RG flows produced by weakly relevant operators and show that the free energy decreases monotonically. We also consider large N field theories perturbed by relevant double trace operators, free massive field theories, and some Chern-Simons gauge theories. In all cases the free energy in the IR is smaller than in the UV, consistent with the F-theorem. We discuss other odd-dimensional Euclidean theories on S^d and provide evidence that (-1)^{(d-1)/2} \log |Z| decreases along RG flow; in the particular case d=1 this is the well-known g-theorem.Comment: 34 pages, 2 figures; v2 refs added, minor improvements; v3 refs added, improved section 4.3; v4 minor improvement