Optimizing system resilience: A facility protection model with recovery time

Optimizing system resilience is concerned with the development of strategies to restore a system to normal operations as quickly and efficiently as possible following potential disruption. To this end, we present in this article a bilevel mixed integer linear program for protecting an uncapacitated median type facility network against worst-case losses, taking into account the role of facility recovery time on system performance and the possibility of multiple disruptions over time. The model differs from previous types of facility protection models in that protection is not necessarily assumed to prevent facility failure altogether, but more precisely to speed up recovery time following a potential disruption. Three different decomposition approaches are devised to optimally solve medium to large problem instances. Computational results provide a cross comparison of the efficiency of each algorithm. Additionally, we present an analysis to estimate cost-efficient levels of investments in protection resources.     

Effect of agitation on removal of acetic acid from pretreated hydrolysate by activated carbon

The effect of agitation on the adsorption of acetic acid by activated carbon was tested utilizing an external mass transfer-diffusion model. Simulated pretreated biomass was contacted with activated carbon under prescribed conditions of temperature and agitation. Adsorption isotherm studies are presented as well as batch kinetic rate studies. Use of these data enabled the determination of isotherm constants, an external mass transfer coefficient, and an effective diffusivity for each agitation rate studied. The external film coefficient results ranged from 33.62 μm/s to a complete absence of external mass transfer resistance, and the diffusivity results ranged from 0.8625 to 10.70 μm²/s. The optimum combination of no external film resistance, and highest diffusivity, 10.70 μm²/s, occurred at 250 rpm and 25°C. The results of these models and the experimental parameters suggested an efficacious method and conditions for the removal of this undesirable chemical.     

Farrell sets for harmonic functions

Let denote a relatively closed subset of the unit ball of . The purpose of this paper is to characterize those sets which have the following property: any harmonic function on which satisfies on (where 0$">) can be locally uniformly approximated on by a sequence of harmonic polynomials which satisfy the same inequality on . This answers a question posed by Stray, who had earlier solved the corresponding problem for holomorphic functions on the unit disc.