A variational problem determined by probability measures

ABSTRACT

An optimization problem of maximizing an integral of a function over a family of probability measures is considered. The problem is a generalization of a well-studied variational problem in mathematical economics, concerning optimal allocations. The specific generalization that we examine arises also in the limit of singularly perturbed optimal control problems. We examine the mathematical problem and allude to the singular perturbation motivation.     

Estimation of viscosities of 1-alkyl-3-methylimidazolium ionic liquids over a range of temperatures using a simple correlation

In this study, a new correlation is proposed for estimating 1-alkyl-3-methylimidazolium ionic liquid (IL) viscosities at different temperatures and atmospheric pressure. Since ILs are rather novel, many of their physical properties are still unavailable. Because of this limitation, the aim of this work was to propose a correlation with a new insight and approach, which requires a minimum number of physical properties as input parameters. In addition to minimal dependency on physical properties, further goals in the development of the model were generality, ease-of-use, simplicity and high accuracy. A total of 2073 literature viscosity datapoints at different temperatures for 38 different ILs were used and a correlation was developed which satisfied the above-mentioned goals. The IL viscosity models of Lazzús and Pulgar-Villarroel, and Gardas and Coutinho were compared to the proposed correlation. More reliable results were obtained by the proposed relation in comparison to literature models.     

碘小姐的旅行

将碘元素拟人化,让其以卤素家族"四小姐"的身份,在这美丽的世界上走一走,并拟人化讨论了碘小姐的元素分布、物理性质以及生理活性,让读者在获得知识之余还能有美的享受。     

Overwriting information: Correlations,physical costs,and environment models

In this sequel to our previous study of the entropic and energetic costs of information erasure [N.G. Anderson, Phys. Lett. A 372 (2008) 5552], we consider direct overwriting of classical information encoded in a quantum-mechanical memory system interacting with a heat bath. Lower bounds on physical costs of overwriting – in both “single-shot” and “sequential” overwriting scenarios – are obtained from globally unitary quantum dynamics and entropic inequalities alone, all within a referential approach that grounds information content in correlations between physical system states. A heterogeneous environment model, required for consistent treatment of sequential overwriting, is introduced and used to establish and relate bounds for various cases.     

The role of microstructure on the mechanical properties of polyurethane foams containing thermoregulating microcapsules

Rigid polyurethane foams with up to 50 wt% of microcapsules from LDPE-EVA containing Rubitherm^®RT27 were synthesized. The influence of microcapsules on the foams density, microstructure and mechanical resistance was studied. Cell size and strut and wall thicknesses were analyzed by SEM. The relationships between densities and foam microstructures with their Young's moduli and collapse stress were found by the Gibson and Ashby formulations and the Kerner equation for mechanical properties of composites. It was found a cell structure change from polyhedral closed-cells to spherical or amorphous open-cells. A good agreement between the experimental and theoretical data was observed but requiring a cell form factor. Thus, Fitting parameters confirmed the high trend of these microcapsules to be incorporated into the foam cell walls and the form factors depicted the abrupt change of cell morphology. Thus, these equations are suitable for predicting the mechanical properties of foams containing fillers of low mechanical resistance.